Finite Group Databasebeta

← C107×#34506 #41060470

Subgroups — C107×#34506 #41060470

Order 27392.

2132 conjugacy classes of subgroups.

The subgroup lattice has 1480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#553×C107C211yesmaximal, characteristic
2C107×#2382C211yesmaximal, characteristic, complemented
3C107×#2377C211yesmaximal, characteristic, complemented
4C107×#2377C211yesmaximal, characteristic, complemented
5C107×#2376C211yesmaximal, characteristic, complemented
6C107×#2373C211yesmaximal, characteristic, complemented
7C107×#2373C211yesmaximal, characteristic, complemented
8C107×#2364C211yesmaximal, characteristic, complemented
9C107×#2363C211yesmaximal, characteristic, complemented
10C107×#2359C211yesmaximal, characteristic, complemented
11C107×#2357C211yesmaximal, characteristic, complemented
12C107×#2353C211yesmaximal, characteristic, complemented
13C107×#2352C211yesmaximal, characteristic, complemented
14C107×#2352C211yesmaximal, characteristic, complemented
15C107×#2344C211yesmaximal, characteristic, complemented
16C107×#2343C211yesmaximal, characteristic, complemented
17C107×#2336C211yesmaximal, characteristic, complemented
18C107×#2335C211yesmaximal, characteristic, complemented
19C107×#2334C211yesmaximal, characteristic, complemented
20C107×#2333C211yesmaximal, characteristic, complemented
21C107×#2333C211yesmaximal, characteristic, complemented
22C107×#2333C211yesmaximal, characteristic, complemented
23C107×#2324C211yesmaximal, characteristic, complemented
24C107×#2322C211yesmaximal, characteristic, complemented
25C107×#2319C211yesmaximal, characteristic, complemented
26C107×#2318C211yesmaximal, characteristic, complemented
27C107×#2318C211yesmaximal, characteristic, complemented
28C107×#2313C211yesmaximal, characteristic, complemented
29C4×#126×C107C211yesmaximal, characteristic, complemented
30C107×#2298C211yesmaximal, characteristic, complemented
31C107×#2293C211yesmaximal, characteristic, complemented
32#553×C107C4116yescomplemented
33C2×#126×C107C2211yescharacteristic
34C2×#126×C107C2211yescharacteristic
35C2×#125×C107C2211yescharacteristic
36C2×#123×C107C2211yescharacteristic
37C2×#123×C107C2211yescharacteristic
38C2×#121×C107C2211yescharacteristic
39C2×#121×C107C2211yescharacteristic
40C2×#121×C107C2211yescharacteristic
41C2×#121×C107C2211yescharacteristic
42C2×C4×D4×C107C2211yescharacteristic
43C2×C4×D4×C107C2211yescharacteristic
44C2×C4×D4×C107C2211yescharacteristic
45C2×C4×D4×C107C2211yescharacteristic
46C2×C4×D4×C107C2211yescharacteristic
47C2×C4×D4×C107C2211yescharacteristic
48C2×#117×C107C2211yescharacteristic
49C2×#117×C107C2211yescharacteristic
50C2×#117×C107C2211yescharacteristic
51C2×#117×C107C2211yescharacteristic
52C22×C4⋊C4×C107C2211yescharacteristic
53C22×C4⋊C4×C107C2211yescharacteristic
54#390×C107C2211yescharacteristic
55#390×C107C2211yescharacteristic
56#390×C107C2211yescharacteristic
57#390×C107C2211yescharacteristic
58#390×C107C2211yescharacteristic
59#390×C107C2211yescharacteristic
60#390×C107C2211yescharacteristic
61#390×C107C2211yescharacteristic
62#389×C107C2211yescharacteristic
63#389×C107C2211yescharacteristic
64#389×C107C2211yescharacteristic
65#389×C107C2211yescharacteristic
66#389×C107C2211yescharacteristic
67#389×C107C2211yescharacteristic
68#389×C107C2211yescharacteristic
69#389×C107C2211yescharacteristic
70#388×C107C2211yescharacteristic
71#388×C107C2211yescharacteristic
72#388×C107C2211yescharacteristic
73#388×C107C2211yescharacteristic
74#388×C107C2211yescharacteristic
75#388×C107C2211yescharacteristic
76#388×C107C2211yescharacteristic
77#388×C107C2211yescharacteristic
78#388×C107C2211yescharacteristic
79#388×C107C2211yescharacteristic
80#388×C107C2211yescharacteristic
81#388×C107C2211yescharacteristic
82#388×C107C2211yescharacteristic
83#388×C107C2211yescharacteristic
84#388×C107C2211yescharacteristic
85#388×C107C2211yescharacteristic
86#388×C107C2211yescharacteristic
87#388×C107C2211yescharacteristic
88#388×C107C2211yescharacteristic
89#388×C107C2211yescharacteristic
90#388×C107C2211yescharacteristic
91#388×C107C2211yescharacteristic
92#387×C107C2211yescharacteristic
93#387×C107C2211yescharacteristic
94#387×C107C2211yescharacteristic
95#387×C107C2211yescharacteristic
96#387×C107C2211yescharacteristic
97#387×C107C2211yescharacteristic
98#387×C107C2211yescharacteristic
99#387×C107C2211yescharacteristic
100#387×C107C2211yescharacteristic
101#387×C107C2211yescharacteristic
102#387×C107C2211yescharacteristic
103#387×C107C2211yescharacteristic
104#387×C107C2211yescharacteristic
105#387×C107C2211yescharacteristic
106#387×C107C2211yescharacteristic
107#387×C107C2211yescharacteristic
108#387×C107C2211yescharacteristic
109#387×C107C2211yescharacteristic
110#387×C107C2211yescharacteristic
111#387×C107C2211yescharacteristic
112#387×C107C2211yescharacteristic
113#387×C107C2211yescharacteristic
114#387×C107C2211yescharacteristic
115#387×C107C2211yescharacteristic
116#387×C107C2211yescharacteristic
117#387×C107C2211yescharacteristic
118#386×C107C2211yescharacteristic
119#386×C107C2211yescharacteristic
120#386×C107C2211yescharacteristic
121#386×C107C2211yescharacteristic
122#386×C107C2211yescharacteristic
123#386×C107C2211yescharacteristic
124#386×C107C2211yescharacteristic
125#386×C107C2211yescharacteristic
126#386×C107C2211yescharacteristic
127#386×C107C2211yescharacteristic
128#386×C107C2211yescharacteristic
129#386×C107C2211yescharacteristic
130#386×C107C2211yescharacteristic
131#386×C107C2211yescharacteristic
132#385×C107C2211yescharacteristic
133#385×C107C2211yescharacteristic
134#385×C107C2211yescharacteristic
135#385×C107C2211yescharacteristic
136#385×C107C2211yescharacteristic
137#385×C107C2211yescharacteristic
138#385×C107C2211yescharacteristic
139#385×C107C2211yescharacteristic
140#383×C107C2211yescharacteristic
141#383×C107C2211yescharacteristic
142#382×C107C2211yescharacteristic
143#382×C107C2211yescharacteristic
144#382×C107C2211yescharacteristic
145#381×C107C2211yescharacteristic
146#381×C107C2211yescharacteristic
147#381×C107C2211yescharacteristic
148#381×C107C2211yescharacteristic
149#381×C107C2211yescharacteristic
150#381×C107C2211yescharacteristic
151#380×C107C2211yescharacteristic
152#380×C107C2211yescharacteristic
153#380×C107C2211yescharacteristic
154#380×C107C2211yescharacteristic
155#380×C107C2211yescharacteristic
156#380×C107C2211yescharacteristic
157C4×C4⋊C4×C107C2211yescharacteristic
158C4×C4⋊C4×C107C2211yescharacteristic
159C4×C4⋊C4×C107C2211yescharacteristic
160C4×C4⋊C4×C107C2211yescharacteristic
161C4×C4⋊C4×C107C2211yescharacteristic
162C4×C4⋊C4×C107C2211yescharacteristic
163C4×C4⋊C4×C107C2211yescharacteristic
164C4×C4⋊C4×C107C2211yescharacteristic
165C4×C4⋊C4×C107C2211yescharacteristic
166C4×C4⋊C4×C107C2211yescharacteristic
167C4×C22⋊C4×C107C2211yescharacteristic
168C4×C22⋊C4×C107C2211yescharacteristic
169C4×C22⋊C4×C107C2211yescharacteristic
170C4×C22⋊C4×C107C2211yescharacteristic
171C4×C22⋊C4×C107C2211yescharacteristic
172C4×C22⋊C4×C107C2211yescharacteristic
173C4×C22⋊C4×C107C2211yescharacteristic
174C4×C22⋊C4×C107C2211yescharacteristic
175C4×C22⋊C4×C107C2211yescharacteristic
176C4×C22⋊C4×C107C2211yescharacteristic
177C4×C22⋊C4×C107C2211yescharacteristic
178C4×C22⋊C4×C107C2211yescharacteristic
179C4×C22⋊C4×C107C2211yescharacteristic
180C4×C22⋊C4×C107C2211yescharacteristic
181C4×C22⋊C4×C107C2211yescharacteristic
182C4×C22⋊C4×C107C2211yescharacteristic
183#376×C107C2211yescharacteristic
184#376×C107C2211yescharacteristic
185C2×#95×C107C2211yescharacteristic
186C2×#95×C107C2211yescharacteristic
187C43×C107C2211yescharacteristic
188C22×D4×C107C2311yescharacteristic
189C22×D4×C107C2311yescharacteristic
190C22×D4×C107C2311yescharacteristic
191C22×D4×C107C2311yescharacteristic
192C22×D4×C107C2311yescharacteristic
193C22×D4×C107C2311yescharacteristic
194C23×C4×C107C2311yescharacteristic
195C23×C4×C107C2311yescharacteristic
196C23×C4×C107C2311yescharacteristic
197C23×C4×C107C2311yescharacteristic
198C23×C4×C107C2311yescharacteristic
199C23×C4×C107C2311yescharacteristic
200C23×C4×C107C2311yescharacteristic
201C23×C4×C107C2311yescharacteristic
202C23×C4×C107C2311yescharacteristic
203C23×C4×C107C2311yescharacteristic
204C23×C4×C107C2311yescharacteristic
205C23×C4×C107C2311yescharacteristic
206#126×C107C2×C418yescomplemented
207#126×C107C2×C418yescomplemented
208#125×C107C2×C418yescomplemented
209#123×C107C2×C418yescomplemented
210#123×C107C2×C418yescomplemented
211#121×C107C2×C418yes—
212#121×C107C2×C418yescomplemented
213#121×C107C2×C418yescomplemented
214#121×C107C2×C418yescomplemented
215C4×D4×C107—42no—
216C4×D4×C107—42no—
217C4×D4×C107C2×C418yescomplemented
218C4×D4×C107C2×C418yescomplemented
219C4×D4×C107C2×C418yescomplemented
220C4×D4×C107C2×C418yescomplemented
221#117×C107—42no—
222#117×C107—42no—
223#117×C107—42no—
224#117×C107C2×C418yescomplemented
225C2×C4⋊C4×C107—42no—
226C2×C4⋊C4×C107C2×C418yescomplemented
227C2×C4⋊C4×C107C2311yescharacteristic
228C2×C4⋊C4×C107C2311yescharacteristic
229C2×C4⋊C4×C107C2311yescharacteristic
230C2×C4⋊C4×C107C2311yescharacteristic
231C2×C4⋊C4×C107C2311yescharacteristic
232C2×C4⋊C4×C107C2311yescharacteristic
233C2×C4⋊C4×C107C2311yescharacteristic
234C2×C4⋊C4×C107C2311yescharacteristic
235C2×C4⋊C4×C107C2311yescharacteristic
236C2×C4⋊C4×C107C2311yescharacteristic
237C2×C4⋊C4×C107C2311yescharacteristic
238C2×C4⋊C4×C107C2311yescharacteristic
239C2×C4⋊C4×C107C2311yescharacteristic
240C2×C4⋊C4×C107C2311yescharacteristic
241C2×C4⋊C4×C107C2311yescharacteristic
242C2×C4⋊C4×C107C2311yescharacteristic
243C2×C4⋊C4×C107C2311yescharacteristic
244C2×C4⋊C4×C107C2311yescharacteristic
245C2×C4⋊C4×C107C2311yescharacteristic
246C2×C4⋊C4×C107C2311yescharacteristic
247C2×C4⋊C4×C107C2311yescharacteristic
248C2×C4⋊C4×C107C2311yescharacteristic
249C2×C4⋊C4×C107C2311yescharacteristic
250C2×C4⋊C4×C107C2311yescharacteristic
251C2×C4⋊C4×C107C2311yescharacteristic
252C2×C4⋊C4×C107C2311yescharacteristic
253C2×C4⋊C4×C107C2311yescharacteristic
254C2×C4⋊C4×C107C2311yescharacteristic
255C2×C4⋊C4×C107C2311yescharacteristic
256C2×C4⋊C4×C107C2311yescharacteristic
257C2×C22⋊C4×C107C2311yescharacteristic
258C2×C22⋊C4×C107C2311yescharacteristic
259C2×C22⋊C4×C107C2311yescharacteristic
260C2×C22⋊C4×C107C2311yescharacteristic
261C2×C22⋊C4×C107C2311yescharacteristic
262C2×C22⋊C4×C107C2311yescharacteristic
263C2×C22⋊C4×C107C2311yescharacteristic
264C2×C22⋊C4×C107C2311yescharacteristic
265C2×C22⋊C4×C107C2311yescharacteristic
266C2×C22⋊C4×C107C2311yescharacteristic
267C2×C22⋊C4×C107C2311yescharacteristic
268C2×C22⋊C4×C107C2311yescharacteristic
269C2×C22⋊C4×C107C2311yescharacteristic
270C2×C22⋊C4×C107C2311yescharacteristic
271C2×C22⋊C4×C107C2311yescharacteristic
272C2×C22⋊C4×C107C2311yescharacteristic
273C2×C22⋊C4×C107C2311yescharacteristic
274C2×C22⋊C4×C107C2311yescharacteristic
275C2×C22⋊C4×C107C2311yescharacteristic
276C2×C22⋊C4×C107C2311yescharacteristic
277C2×C22⋊C4×C107C2311yescharacteristic
278C2×C22⋊C4×C107C2311yescharacteristic
279C2×C22⋊C4×C107C2311yescharacteristic
280C2×C22⋊C4×C107C2311yescharacteristic
281C2×C22⋊C4×C107C2311yescharacteristic
282C2×C22⋊C4×C107C2311yescharacteristic
283C2×C22⋊C4×C107C2311yescharacteristic
284C2×C22⋊C4×C107C2311yescharacteristic
285C2×C22⋊C4×C107C2311yescharacteristic
286C2×C22⋊C4×C107C2311yescharacteristic
287C2×C22⋊C4×C107C2311yescharacteristic
288C2×C22⋊C4×C107C2311yescharacteristic
289C2×C22⋊C4×C107C2311yescharacteristic
290C2×C22⋊C4×C107C2311yescharacteristic
291C2×C22⋊C4×C107C2311yescharacteristic
292C2×C22⋊C4×C107C2311yescharacteristic
293C2×C42×C107C2311yescharacteristic
294C2×C42×C107C2311yescharacteristic
295C2×C42×C107C2311yescharacteristic
296C2×C42×C107C2311yescharacteristic
297C2×C42×C107C2311yescharacteristic
298C2×C42×C107C2311yescharacteristic
299C2×C42×C107C2311yescharacteristic
300C2×C42×C107C2311yescharacteristic
301C2×C42×C107C2311yescharacteristic
302C2×C42×C107C2311yescharacteristic
303C2×C42×C107C2311yescharacteristic
304C2×C42×C107C2311yescharacteristic
305C2×C42×C107C2311yescharacteristic
306C2×C42×C107C2311yescharacteristic
307C2×C42×C107C2311yescharacteristic
308C2×C42×C107C2311yescharacteristic
309C2×C42×C107C2311yescharacteristic
310C2×C42×C107C2311yescharacteristic
311C2×C42×C107C2311yescharacteristic
312C2×C42×C107C2311yescharacteristic
313C2×C42×C107C2311yescharacteristic
314C2×C42×C107C2311yescharacteristic
315C2×C42×C107C2311yescharacteristic
316#95×C107C2311yescharacteristic
317#95×C107C2311yescharacteristic
318#95×C107C2311yescharacteristic
319#95×C107C2311yescharacteristic
320#95×C107C2311yescharacteristic
321#95×C107C2311yescharacteristic
322#95×C107C2311yescharacteristic
323#95×C107C2311yescharacteristic
324#95×C107C2311yescharacteristic
325#95×C107C2311yescharacteristic
326#95×C107C2311yescharacteristic
327#95×C107C2311yescharacteristic
328#95×C107C2311yescharacteristic
329#95×C107C2311yescharacteristic
330#95×C107C2311yescharacteristic
331#95×C107C2311yescharacteristic
332#95×C107C2311yescharacteristic
333#95×C107C2311yescharacteristic
334#95×C107C2311yescharacteristic
335#95×C107C2311yescharacteristic
336#95×C107C2311yescharacteristic
337#95×C107C2311yescharacteristic
338#95×C107C2311yescharacteristic
339#95×C107C2311yescharacteristic
340#95×C107C2311yescharacteristic
341#95×C107C2311yescharacteristic
342#95×C107C2311yescharacteristic
343#95×C107C2311yescharacteristic
344#95×C107C2311yescharacteristic
345#95×C107C2311yescharacteristic
346#95×C107C2311yescharacteristic
347#95×C107C2311yescharacteristic
348#95×C107C2311yescharacteristic
349#95×C107C2311yescharacteristic
350#95×C107C2311yescharacteristic
351#95×C107C2311yescharacteristic
352#95×C107C2311yescharacteristic
353#95×C107C2311yescharacteristic
354#95×C107C2311yescharacteristic
355#95×C107C2311yescharacteristic
356#95×C107C2311yescharacteristic
357#95×C107C2311yescharacteristic
358#95×C107C2311yescharacteristic
359#95×C107C2311yescharacteristic
360#95×C107C2311yescharacteristic
361#95×C107C2311yescharacteristic
362#95×C107C2311yescharacteristic
363#95×C107C2311yescharacteristic
364C24×C107C2411yescharacteristic
365C24×C107C2411yescharacteristic
366C24×C107C2411yescharacteristic
367C24×C107C2411yescharacteristic
368C2×D4×C107—41no—
369C2×D4×C107—41no—
370C2×D4×C107—41no—
371C2×D4×C107—41no—
372C2×D4×C107—41no—
373C2×D4×C107—41no—
374C2×D4×C107—41no—
375C2×D4×C107—41no—
376C2×D4×C107—41no—
377C2×D4×C107—41no—
378C2×D4×C107—41no—
379C2×D4×C107—41no—
380C2×D4×C107C22×C414yes—
381C2×D4×C107C22×C414yes—
382C2×D4×C107C22×C414yes—
383C2×D4×C107C22×C414yes—
384C2×D4×C107C22×C414yes—
385C2×D4×C107C22×C414yes—
386C22×C4×C107—22no—
387C22×C4×C107—41no—
388C22×C4×C107—41no—
389C22×C4×C107—41no—
390C22×C4×C107—41no—
391C22×C4×C107—41no—
392C22×C4×C107—41no—
393C22×C4×C107—41no—
394C22×C4×C107—41no—
395C22×C4×C107—41no—
396C22×C4×C107—41no—
397C22×C4×C107—41no—
398C22×C4×C107—41no—
399C22×C4×C107—41no—
400C22×C4×C107—41no—
401C22×C4×C107—41no—
402C22×C4×C107—41no—
403C22×C4×C107—41no—
404C22×C4×C107—41no—
405C22×C4×C107—41no—
406C22×C4×C107—41no—
407C22×C4×C107—41no—
408C22×C4×C107—41no—
409C22×C4×C107—41no—
410C22×C4×C107—41no—
411C22×C4×C107—41no—
412C22×C4×C107—41no—
413C22×C4×C107—41no—
414C22×C4×C107—41no—
415C22×C4×C107—41no—
416C22×C4×C107C22×C414yes—
417C22×C4×C107C22×C414yes—
418C22×C4×C107C22×C414yes—
419C22×C4×C107C22×C414yes—
420C22×C4×C107C22×C414yes—
421C22×C4×C107C22×C414yes—
422C22×C4×C107C2411yescharacteristic
423C22×C4×C107C2411yescharacteristic
424C22×C4×C107C2411yescharacteristic
425C22×C4×C107C2411yescharacteristic
426C22×C4×C107C2411yescharacteristic
427C22×C4×C107C2411yescharacteristic
428C22×C4×C107C2411yescharacteristic
429C22×C4×C107C2411yescharacteristic
430C22×C4×C107C2411yescharacteristic
431C22×C4×C107C2411yescharacteristic
432C22×C4×C107C2411yescharacteristic
433C22×C4×C107C2411yescharacteristic
434C22×C4×C107C2411yescharacteristic
435C22×C4×C107C2411yescharacteristic
436C22×C4×C107C2411yescharacteristic
437C22×C4×C107C2411yescharacteristic
438C22×C4×C107C2411yescharacteristic
439C22×C4×C107C2411yescharacteristic
440C22×C4×C107C2411yescharacteristic
441C22×C4×C107C2411yescharacteristic
442C22×C4×C107C2411yescharacteristic
443C22×C4×C107C2411yescharacteristic
444C22×C4×C107C2411yescharacteristic
445C22×C4×C107C2411yescharacteristic
446C22×C4×C107C2411yescharacteristic
447C22×C4×C107C2411yescharacteristic
448C22×C4×C107C2411yescharacteristic
449C4⋊C4×C107—22no—
450C4⋊C4×C107—22no—
451C4⋊C4×C107—22no—
452C4⋊C4×C107—41no—
453C4⋊C4×C107—41no—
454C4⋊C4×C107—41no—
455C4⋊C4×C107—41no—
456C4⋊C4×C107—41no—
457C4⋊C4×C107—41no—
458C4⋊C4×C107—41no—
459C4⋊C4×C107—41no—
460C4⋊C4×C107—41no—
461C4⋊C4×C107—41no—
462C4⋊C4×C107—41no—
463C4⋊C4×C107—41no—
464C4⋊C4×C107—41no—
465C4⋊C4×C107—41no—
466C4⋊C4×C107—41no—
467C4⋊C4×C107—41no—
468C4⋊C4×C107—41no—
469C4⋊C4×C107C22×C414yes—
470C4⋊C4×C107C22×C414yes—
471C4⋊C4×C107C22×C414yes—
472C4⋊C4×C107C22×C414yes—
473C4⋊C4×C107C22×C414yes—
474C4⋊C4×C107C22×C414yes—
475C4⋊C4×C107C22×C414yes—
476C4⋊C4×C107C22×C414yes—
477C4⋊C4×C107C22×C414yes—
478C4⋊C4×C107C22×C414yes—
479C22⋊C4×C107—22no—
480C22⋊C4×C107—22no—
481C22⋊C4×C107—22no—
482C22⋊C4×C107—41no—
483C22⋊C4×C107—41no—
484C22⋊C4×C107—41no—
485C22⋊C4×C107—41no—
486C22⋊C4×C107—41no—
487C22⋊C4×C107—41no—
488C22⋊C4×C107—41no—
489C22⋊C4×C107—41no—
490C22⋊C4×C107—41no—
491C22⋊C4×C107—41no—
492C22⋊C4×C107—41no—
493C22⋊C4×C107—41no—
494C22⋊C4×C107—41no—
495C22⋊C4×C107—41no—
496C22⋊C4×C107—41no—
497C22⋊C4×C107—41no—
498C22⋊C4×C107—41no—
499C22⋊C4×C107—41no—
500C22⋊C4×C107—41no—
501C22⋊C4×C107—41no—
502C22⋊C4×C107—41no—
503C22⋊C4×C107—41no—
504C22⋊C4×C107—41no—
505C22⋊C4×C107C22×C414yes—
506C22⋊C4×C107C22×C414yes—
507C22⋊C4×C107C22×C414yes—
508C22⋊C4×C107C22×C414yes—
509C22⋊C4×C107C22×C414yes—
510C22⋊C4×C107C22×C414yes—
511C22⋊C4×C107C22×C414yes—
512C22⋊C4×C107C22×C414yes—
513C22⋊C4×C107C22×C414yes—
514C22⋊C4×C107C22×C414yes—
515C42×C107—22no—
516C42×C107—22no—
517C42×C107—41no—
518C42×C107—41no—
519C42×C107—41no—
520C42×C107—41no—
521C42×C107—41no—
522C42×C107—41no—
523C42×C107—41no—
524C42×C107—41no—
525C42×C107—41no—
526C42×C107—41no—
527C42×C107—41no—
528C42×C107—41no—
529C42×C107—41no—
530C42×C107—41no—
531C42×C107—41no—
532C42×C107—41no—
533C42×C107—41no—
534C42×C107—41no—
535C42×C107C22×C414yes—
536C42×C107C22×C414yes—
537C42×C107C22×C414yes—
538C23×C107—21no—
539C23×C107—21no—
540C23×C107—21no—
541C23×C107—21no—
542C23×C107—21no—
543C23×C107—21no—
544C23×C107—21no—
545C23×C107—21no—
546C23×C107—21no—
547C23×C107—21no—
548C23×C107—21no—
549C23×C107—21no—
550C23×C107—21no—
551C23×C107—21no—
552C23×C107—21no—
553C23×C107—21no—
554C23×C107—21no—
555C23×C107—21no—
556C23×C107—21no—
557C23×C107—21no—
558C23×C107—21no—
559C23×C107—21no—
560C23×C107—21no—
561C23×C107—21no—
562C23×C107C23×C412yes—
563C23×C107C23×C412yes—
564C23×C107C23×C412yes—
565C23×C107C23×C412yes—
566C23×C107C2511yescharacteristic
567D4×C107—44no—
568D4×C107—44no—
569D4×C107—44no—
570D4×C107—44no—
571D4×C107—44no—
572D4×C107—44no—
573C2×C4×C107—21no—
574C2×C4×C107—21no—
575C2×C4×C107—21no—
576C2×C4×C107—21no—
577C2×C4×C107—21no—
578C2×C4×C107—21no—
579C2×C4×C107—21no—
580C2×C4×C107—21no—
581C2×C4×C107—21no—
582C2×C4×C107—21no—
583C2×C4×C107—21no—
584C2×C4×C107—21no—
585C2×C4×C107—21no—
586C2×C4×C107—21no—
587C2×C4×C107—21no—
588C2×C4×C107—21no—
589C2×C4×C107—21no—
590C2×C4×C107—21no—
591C2×C4×C107—21no—
592C2×C4×C107—21no—
593C2×C4×C107—21no—
594C2×C4×C107—21no—
595C2×C4×C107—21no—
596C2×C4×C107—21no—
597C2×C4×C107—21no—
598C2×C4×C107—21no—
599C2×C4×C107—21no—
600C2×C4×C107—21no—
601C2×C4×C107—21no—
602C2×C4×C107—21no—
603C2×C4×C107—21no—
604C2×C4×C107—21no—
605C2×C4×C107—21no—
606C2×C4×C107—21no—
607C2×C4×C107—21no—
608C2×C4×C107—21no—
609C2×C4×C107—21no—
610C2×C4×C107—21no—
611C2×C4×C107—21no—
612C2×C4×C107—21no—
613C2×C4×C107—21no—
614C2×C4×C107—21no—
615C2×C4×C107—21no—
616C2×C4×C107—21no—
617C2×C4×C107—21no—
618C2×C4×C107—21no—
619C2×C4×C107—21no—
620C2×C4×C107—21no—
621C2×C4×C107—21no—
622C2×C4×C107—21no—
623C2×C4×C107—21no—
624C2×C4×C107—21no—
625C2×C4×C107—21no—
626C2×C4×C107—21no—
627C2×C4×C107—21no—
628C2×C4×C107—21no—
629C2×C4×C107—21no—
630C2×C4×C107—21no—
631C2×C4×C107—21no—
632C2×C4×C107—21no—
633C2×C4×C107—21no—
634C2×C4×C107—21no—
635C2×C4×C107—21no—
636C2×C4×C107—21no—
637C2×C4×C107—21no—
638C2×C4×C107—21no—
639C2×C4×C107—21no—
640C2×C4×C107—21no—
641C2×C4×C107—21no—
642C2×C4×C107—44no—
643C2×C4×C107—44no—
644C2×C4×C107—44no—
645C2×C4×C107—44no—
646C2×C4×C107—44no—
647C2×C4×C107—44no—
648C2×C4×C107—82no—
649C2×C4×C107—82no—
650C2×C4×C107—82no—
651C2×C4×C107—82no—
652C2×C4×C107—82no—
653C2×C4×C107—82no—
654C2×C4×C107C23×C412yes—
655C2×C4×C107C23×C412yes—
656C2×C4×C107C23×C412yes—
657C2×C4×C107C23×C412yes—
658C2×C4×C107C23×C412yes—
659C2×C4×C107C23×C412yes—
660C2×C4×C107C23×C412yes—
661C2×C4×C107C23×C412yes—
662C2×C4×C107C23×C412yes—
663C2×C4×C107C23×C412yes—
664C2×C4×C107C23×C412yes—
665C2×C4×C107H(5,𝔽2)12yes—
666C22×C107—22no—
667C22×C107—22no—
668C22×C107—22no—
669C22×C107—22no—
670C22×C107—22no—
671C22×C107—22no—
672C22×C107—22no—
673C22×C107—22no—
674C22×C107—22no—
675C22×C107—22no—
676C22×C107—22no—
677C22×C107—22no—
678C22×C107—41no—
679C22×C107—41no—
680C22×C107—41no—
681C22×C107—41no—
682C22×C107—41no—
683C22×C107—41no—
684C22×C107—41no—
685C22×C107—41no—
686C22×C107—41no—
687C22×C107—41no—
688C22×C107—41no—
689C22×C107—41no—
690C22×C107—41no—
691C22×C107—41no—
692C22×C107—41no—
693C22×C107—41no—
694C22×C107C24×C411yescharacteristic
695C22×C107C2×H(5,𝔽2)11yescharacteristic
696C22×C107#58511yescharacteristic
697C22×C107#58511yescharacteristic
698C22×C107#58511yescharacteristic
699C22×C107#58511yescharacteristic
700C22×C107#58511yescharacteristic
701C4×C107—22no—
702C4×C107—22no—
703C4×C107—22no—
704C4×C107—22no—
705C4×C107—22no—
706C4×C107—22no—
707C4×C107—22no—
708C4×C107—22no—
709C4×C107—22no—
710C4×C107—22no—
711C4×C107—22no—
712C4×C107—22no—
713C4×C107—41no—
714C4×C107—41no—
715C4×C107—41no—
716C4×C107—41no—
717C4×C107—41no—
718C4×C107—41no—
719C4×C107—41no—
720C4×C107—41no—
721C4×C107—41no—
722C4×C107—41no—
723C4×C107—41no—
724C4×C107—41no—
725C4×C107—41no—
726C4×C107—41no—
727C4×C107—41no—
728#34506C10711yesmaximal, characteristic, direct product factor, Sylow
729C2×C107—42no—
730C2×C107—42no—
731C2×C107—42no—
732C2×C107—42no—
733C2×C107#342811yescharacteristic
734C2×C107#342811yescharacteristic
735C2×C107C4×H(5,𝔽2)11yescharacteristic
736C2×C107#356011yescharacteristic
737C2×C107#356211yescharacteristic
738C2×C107#356611yescharacteristic
739C2×C107#356711yescharacteristic
740C2×#553C2×C10711yescharacteristic
741#2382C2×C10711yescharacteristic, complemented
742#2377C2×C10711yescharacteristic, complemented
743#2377C2×C10711yescharacteristic, complemented
744#2376C2×C10711yescharacteristic, complemented
745#2373C2×C10711yescharacteristic, complemented
746#2373C2×C10711yescharacteristic, complemented
747#2364C2×C10711yescharacteristic, complemented
748#2363C2×C10711yescharacteristic, complemented
749#2359C2×C10711yescharacteristic, complemented
750#2357C2×C10711yescharacteristic, complemented
751#2353C2×C10711yescharacteristic, complemented
752#2352C2×C10711yescharacteristic, complemented
753#2352C2×C10711yescharacteristic, complemented
754#2344C2×C10711yescharacteristic, complemented
755#2343C2×C10711yescharacteristic, complemented
756#2336C2×C10711yescharacteristic, complemented
757#2335C2×C10711yescharacteristic, complemented
758#2334C2×C10711yescharacteristic, complemented
759#2333C2×C10711yescharacteristic, complemented
760#2333C2×C10711yescharacteristic, complemented
761#2333C2×C10711yescharacteristic, complemented
762#2324C2×C10711yescharacteristic, complemented
763#2322C2×C10711yescharacteristic, complemented
764#2319C2×C10711yescharacteristic, complemented
765#2318C2×C10711yescharacteristic, complemented
766#2318C2×C10711yescharacteristic, complemented
767#2313C2×C10711yescharacteristic, complemented
768C4×#126C2×C10711yescharacteristic, complemented
769#2298C2×C10711yescharacteristic, complemented
770#2293C2×C10711yescharacteristic, complemented
771C107#3450611yescharacteristic, direct product factor, Sylow
772#553C4×C107116yescomplemented
773C2×#126C22×C10711yescharacteristic
774C2×#126C22×C10711yescharacteristic
775C2×#125C22×C10711yescharacteristic
776C2×#123C22×C10711yescharacteristic
777C2×#123C22×C10711yescharacteristic
778C2×#121C22×C10711yescharacteristic
779C2×#121C22×C10711yescharacteristic
780C2×#121C22×C10711yescharacteristic
781C2×#121C22×C10711yescharacteristic
782C2×C4×D4C22×C10711yescharacteristic
783C2×C4×D4C22×C10711yescharacteristic
784C2×C4×D4C22×C10711yescharacteristic
785C2×C4×D4C22×C10711yescharacteristic
786C2×C4×D4C22×C10711yescharacteristic
787C2×C4×D4C22×C10711yescharacteristic
788C2×#117C22×C10711yescharacteristic
789C2×#117C22×C10711yescharacteristic
790C2×#117C22×C10711yescharacteristic
791C2×#117C22×C10711yescharacteristic
792C22×C4⋊C4C22×C10711yescharacteristic
793C22×C4⋊C4C22×C10711yescharacteristic
794#390C22×C10711yescharacteristic
795#390C22×C10711yescharacteristic
796#390C22×C10711yescharacteristic
797#390C22×C10711yescharacteristic
798#390C22×C10711yescharacteristic
799#390C22×C10711yescharacteristic
800#390C22×C10711yescharacteristic
801#390C22×C10711yescharacteristic
802#389C22×C10711yescharacteristic
803#389C22×C10711yescharacteristic
804#389C22×C10711yescharacteristic
805#389C22×C10711yescharacteristic
806#389C22×C10711yescharacteristic
807#389C22×C10711yescharacteristic
808#389C22×C10711yescharacteristic
809#389C22×C10711yescharacteristic
810#388C22×C10711yescharacteristic
811#388C22×C10711yescharacteristic
812#388C22×C10711yescharacteristic
813#388C22×C10711yescharacteristic
814#388C22×C10711yescharacteristic
815#388C22×C10711yescharacteristic
816#388C22×C10711yescharacteristic
817#388C22×C10711yescharacteristic
818#388C22×C10711yescharacteristic
819#388C22×C10711yescharacteristic
820#388C22×C10711yescharacteristic
821#388C22×C10711yescharacteristic
822#388C22×C10711yescharacteristic
823#388C22×C10711yescharacteristic
824#388C22×C10711yescharacteristic
825#388C22×C10711yescharacteristic
826#388C22×C10711yescharacteristic
827#388C22×C10711yescharacteristic
828#388C22×C10711yescharacteristic
829#388C22×C10711yescharacteristic
830#388C22×C10711yescharacteristic
831#388C22×C10711yescharacteristic
832#387C22×C10711yescharacteristic
833#387C22×C10711yescharacteristic
834#387C22×C10711yescharacteristic
835#387C22×C10711yescharacteristic
836#387C22×C10711yescharacteristic
837#387C22×C10711yescharacteristic
838#387C22×C10711yescharacteristic
839#387C22×C10711yescharacteristic
840#387C22×C10711yescharacteristic
841#387C22×C10711yescharacteristic
842#387C22×C10711yescharacteristic
843#387C22×C10711yescharacteristic
844#387C22×C10711yescharacteristic
845#387C22×C10711yescharacteristic
846#387C22×C10711yescharacteristic
847#387C22×C10711yescharacteristic
848#387C22×C10711yescharacteristic
849#387C22×C10711yescharacteristic
850#387C22×C10711yescharacteristic
851#387C22×C10711yescharacteristic
852#387C22×C10711yescharacteristic
853#387C22×C10711yescharacteristic
854#387C22×C10711yescharacteristic
855#387C22×C10711yescharacteristic
856#387C22×C10711yescharacteristic
857#387C22×C10711yescharacteristic
858#386C22×C10711yescharacteristic
859#386C22×C10711yescharacteristic
860#386C22×C10711yescharacteristic
861#386C22×C10711yescharacteristic
862#386C22×C10711yescharacteristic
863#386C22×C10711yescharacteristic
864#386C22×C10711yescharacteristic
865#386C22×C10711yescharacteristic
866#386C22×C10711yescharacteristic
867#386C22×C10711yescharacteristic
868#386C22×C10711yescharacteristic
869#386C22×C10711yescharacteristic
870#386C22×C10711yescharacteristic
871#386C22×C10711yescharacteristic
872#385C22×C10711yescharacteristic
873#385C22×C10711yescharacteristic
874#385C22×C10711yescharacteristic
875#385C22×C10711yescharacteristic
876#385C22×C10711yescharacteristic
877#385C22×C10711yescharacteristic
878#385C22×C10711yescharacteristic
879#385C22×C10711yescharacteristic
880#383C22×C10711yescharacteristic
881#383C22×C10711yescharacteristic
882#382C22×C10711yescharacteristic
883#382C22×C10711yescharacteristic
884#382C22×C10711yescharacteristic
885#381C22×C10711yescharacteristic
886#381C22×C10711yescharacteristic
887#381C22×C10711yescharacteristic
888#381C22×C10711yescharacteristic
889#381C22×C10711yescharacteristic
890#381C22×C10711yescharacteristic
891#380C22×C10711yescharacteristic
892#380C22×C10711yescharacteristic
893#380C22×C10711yescharacteristic
894#380C22×C10711yescharacteristic
895#380C22×C10711yescharacteristic
896#380C22×C10711yescharacteristic
897C4×C4⋊C4C22×C10711yescharacteristic
898C4×C4⋊C4C22×C10711yescharacteristic
899C4×C4⋊C4C22×C10711yescharacteristic
900C4×C4⋊C4C22×C10711yescharacteristic
901C4×C4⋊C4C22×C10711yescharacteristic
902C4×C4⋊C4C22×C10711yescharacteristic
903C4×C4⋊C4C22×C10711yescharacteristic
904C4×C4⋊C4C22×C10711yescharacteristic
905C4×C4⋊C4C22×C10711yescharacteristic
906C4×C4⋊C4C22×C10711yescharacteristic
907C4×C22⋊C4C22×C10711yescharacteristic
908C4×C22⋊C4C22×C10711yescharacteristic
909C4×C22⋊C4C22×C10711yescharacteristic
910C4×C22⋊C4C22×C10711yescharacteristic
911C4×C22⋊C4C22×C10711yescharacteristic
912C4×C22⋊C4C22×C10711yescharacteristic
913C4×C22⋊C4C22×C10711yescharacteristic
914C4×C22⋊C4C22×C10711yescharacteristic
915C4×C22⋊C4C22×C10711yescharacteristic
916C4×C22⋊C4C22×C10711yescharacteristic
917C4×C22⋊C4C22×C10711yescharacteristic
918C4×C22⋊C4C22×C10711yescharacteristic
919C4×C22⋊C4C22×C10711yescharacteristic
920C4×C22⋊C4C22×C10711yescharacteristic
921C4×C22⋊C4C22×C10711yescharacteristic
922C4×C22⋊C4C22×C10711yescharacteristic
923#376C22×C10711yescharacteristic
924#376C22×C10711yescharacteristic
925C2×#95C22×C10711yescharacteristic
926C2×#95C22×C10711yescharacteristic
927C43C22×C10711yescharacteristic
928C22×D4C23×C10711yescharacteristic
929C22×D4C23×C10711yescharacteristic
930C22×D4C23×C10711yescharacteristic
931C22×D4C23×C10711yescharacteristic
932C22×D4C23×C10711yescharacteristic
933C22×D4C23×C10711yescharacteristic
934C23×C4C23×C10711yescharacteristic
935C23×C4C23×C10711yescharacteristic
936C23×C4C23×C10711yescharacteristic
937C23×C4C23×C10711yescharacteristic
938C23×C4C23×C10711yescharacteristic
939C23×C4C23×C10711yescharacteristic
940C23×C4C23×C10711yescharacteristic
941C23×C4C23×C10711yescharacteristic
942C23×C4C23×C10711yescharacteristic
943C23×C4C23×C10711yescharacteristic
944C23×C4C23×C10711yescharacteristic
945C23×C4C23×C10711yescharacteristic
946#126C2×C4×C10718yescomplemented
947#126C2×C4×C10718yescomplemented
948#125C2×C4×C10718yescomplemented
949#123C2×C4×C10718yescomplemented
950#123C2×C4×C10718yescomplemented
951#121C2×C4×C10718yes—
952#121C2×C4×C10718yescomplemented
953#121C2×C4×C10718yescomplemented
954#121C2×C4×C10718yescomplemented
955C4×D4—42no—
956C4×D4—42no—
957C4×D4C2×C4×C10718yescomplemented
958C4×D4C2×C4×C10718yescomplemented
959C4×D4C2×C4×C10718yescomplemented
960C4×D4C2×C4×C10718yescomplemented
961#117—42no—
962#117—42no—
963#117—42no—
964#117C2×C4×C10718yescomplemented
965C2×C4⋊C4—42no—
966C2×C4⋊C4C2×C4×C10718yescomplemented
967C2×C4⋊C4C23×C10711yescharacteristic
968C2×C4⋊C4C23×C10711yescharacteristic
969C2×C4⋊C4C23×C10711yescharacteristic
970C2×C4⋊C4C23×C10711yescharacteristic
971C2×C4⋊C4C23×C10711yescharacteristic
972C2×C4⋊C4C23×C10711yescharacteristic
973C2×C4⋊C4C23×C10711yescharacteristic
974C2×C4⋊C4C23×C10711yescharacteristic
975C2×C4⋊C4C23×C10711yescharacteristic
976C2×C4⋊C4C23×C10711yescharacteristic
977C2×C4⋊C4C23×C10711yescharacteristic
978C2×C4⋊C4C23×C10711yescharacteristic
979C2×C4⋊C4C23×C10711yescharacteristic
980C2×C4⋊C4C23×C10711yescharacteristic
981C2×C4⋊C4C23×C10711yescharacteristic
982C2×C4⋊C4C23×C10711yescharacteristic
983C2×C4⋊C4C23×C10711yescharacteristic
984C2×C4⋊C4C23×C10711yescharacteristic
985C2×C4⋊C4C23×C10711yescharacteristic
986C2×C4⋊C4C23×C10711yescharacteristic
987C2×C4⋊C4C23×C10711yescharacteristic
988C2×C4⋊C4C23×C10711yescharacteristic
989C2×C4⋊C4C23×C10711yescharacteristic
990C2×C4⋊C4C23×C10711yescharacteristic
991C2×C4⋊C4C23×C10711yescharacteristic
992C2×C4⋊C4C23×C10711yescharacteristic
993C2×C4⋊C4C23×C10711yescharacteristic
994C2×C4⋊C4C23×C10711yescharacteristic
995C2×C4⋊C4C23×C10711yescharacteristic
996C2×C4⋊C4C23×C10711yescharacteristic
997C2×C22⋊C4C23×C10711yescharacteristic
998C2×C22⋊C4C23×C10711yescharacteristic
999C2×C22⋊C4C23×C10711yescharacteristic
1000C2×C22⋊C4C23×C10711yescharacteristic
1001C2×C22⋊C4C23×C10711yescharacteristic
1002C2×C22⋊C4C23×C10711yescharacteristic
1003C2×C22⋊C4C23×C10711yescharacteristic
1004C2×C22⋊C4C23×C10711yescharacteristic
1005C2×C22⋊C4C23×C10711yescharacteristic
1006C2×C22⋊C4C23×C10711yescharacteristic
1007C2×C22⋊C4C23×C10711yescharacteristic
1008C2×C22⋊C4C23×C10711yescharacteristic
1009C2×C22⋊C4C23×C10711yescharacteristic
1010C2×C22⋊C4C23×C10711yescharacteristic
1011C2×C22⋊C4C23×C10711yescharacteristic
1012C2×C22⋊C4C23×C10711yescharacteristic
1013C2×C22⋊C4C23×C10711yescharacteristic
1014C2×C22⋊C4C23×C10711yescharacteristic
1015C2×C22⋊C4C23×C10711yescharacteristic
1016C2×C22⋊C4C23×C10711yescharacteristic
1017C2×C22⋊C4C23×C10711yescharacteristic
1018C2×C22⋊C4C23×C10711yescharacteristic
1019C2×C22⋊C4C23×C10711yescharacteristic
1020C2×C22⋊C4C23×C10711yescharacteristic
1021C2×C22⋊C4C23×C10711yescharacteristic
1022C2×C22⋊C4C23×C10711yescharacteristic
1023C2×C22⋊C4C23×C10711yescharacteristic
1024C2×C22⋊C4C23×C10711yescharacteristic
1025C2×C22⋊C4C23×C10711yescharacteristic
1026C2×C22⋊C4C23×C10711yescharacteristic
1027C2×C22⋊C4C23×C10711yescharacteristic
1028C2×C22⋊C4C23×C10711yescharacteristic
1029C2×C22⋊C4C23×C10711yescharacteristic
1030C2×C22⋊C4C23×C10711yescharacteristic
1031C2×C22⋊C4C23×C10711yescharacteristic
1032C2×C22⋊C4C23×C10711yescharacteristic
1033C2×C42C23×C10711yescharacteristic
1034C2×C42C23×C10711yescharacteristic
1035C2×C42C23×C10711yescharacteristic
1036C2×C42C23×C10711yescharacteristic
1037C2×C42C23×C10711yescharacteristic
1038C2×C42C23×C10711yescharacteristic
1039C2×C42C23×C10711yescharacteristic
1040C2×C42C23×C10711yescharacteristic
1041C2×C42C23×C10711yescharacteristic
1042C2×C42C23×C10711yescharacteristic
1043C2×C42C23×C10711yescharacteristic
1044C2×C42C23×C10711yescharacteristic
1045C2×C42C23×C10711yescharacteristic
1046C2×C42C23×C10711yescharacteristic
1047C2×C42C23×C10711yescharacteristic
1048C2×C42C23×C10711yescharacteristic
1049C2×C42C23×C10711yescharacteristic
1050C2×C42C23×C10711yescharacteristic
1051C2×C42C23×C10711yescharacteristic
1052C2×C42C23×C10711yescharacteristic
1053C2×C42C23×C10711yescharacteristic
1054C2×C42C23×C10711yescharacteristic
1055C2×C42C23×C10711yescharacteristic
1056#95C23×C10711yescharacteristic
1057#95C23×C10711yescharacteristic
1058#95C23×C10711yescharacteristic
1059#95C23×C10711yescharacteristic
1060#95C23×C10711yescharacteristic
1061#95C23×C10711yescharacteristic
1062#95C23×C10711yescharacteristic
1063#95C23×C10711yescharacteristic
1064#95C23×C10711yescharacteristic
1065#95C23×C10711yescharacteristic
1066#95C23×C10711yescharacteristic
1067#95C23×C10711yescharacteristic
1068#95C23×C10711yescharacteristic
1069#95C23×C10711yescharacteristic
1070#95C23×C10711yescharacteristic
1071#95C23×C10711yescharacteristic
1072#95C23×C10711yescharacteristic
1073#95C23×C10711yescharacteristic
1074#95C23×C10711yescharacteristic
1075#95C23×C10711yescharacteristic
1076#95C23×C10711yescharacteristic
1077#95C23×C10711yescharacteristic
1078#95C23×C10711yescharacteristic
1079#95C23×C10711yescharacteristic
1080#95C23×C10711yescharacteristic
1081#95C23×C10711yescharacteristic
1082#95C23×C10711yescharacteristic
1083#95C23×C10711yescharacteristic
1084#95C23×C10711yescharacteristic
1085#95C23×C10711yescharacteristic
1086#95C23×C10711yescharacteristic
1087#95C23×C10711yescharacteristic
1088#95C23×C10711yescharacteristic
1089#95C23×C10711yescharacteristic
1090#95C23×C10711yescharacteristic
1091#95C23×C10711yescharacteristic
1092#95C23×C10711yescharacteristic
1093#95C23×C10711yescharacteristic
1094#95C23×C10711yescharacteristic
1095#95C23×C10711yescharacteristic
1096#95C23×C10711yescharacteristic
1097#95C23×C10711yescharacteristic
1098#95C23×C10711yescharacteristic
1099#95C23×C10711yescharacteristic
1100#95C23×C10711yescharacteristic
1101#95C23×C10711yescharacteristic
1102#95C23×C10711yescharacteristic
1103#95C23×C10711yescharacteristic
1104C24C24×C10711yescharacteristic
1105C24C24×C10711yescharacteristic
1106C24C24×C10711yescharacteristic
1107C24C24×C10711yescharacteristic
1108C2×D4—41no—
1109C2×D4—41no—
1110C2×D4—41no—
1111C2×D4—41no—
1112C2×D4—41no—
1113C2×D4—41no—
1114C2×D4—41no—
1115C2×D4—41no—
1116C2×D4—41no—
1117C2×D4—41no—
1118C2×D4—41no—
1119C2×D4—41no—
1120C2×D4C22×C4×C10714yes—
1121C2×D4C22×C4×C10714yes—
1122C2×D4C22×C4×C10714yes—
1123C2×D4C22×C4×C10714yes—
1124C2×D4C22×C4×C10714yes—
1125C2×D4C22×C4×C10714yes—
1126C22×C4—22no—
1127C22×C4—41no—
1128C22×C4—41no—
1129C22×C4—41no—
1130C22×C4—41no—
1131C22×C4—41no—
1132C22×C4—41no—
1133C22×C4—41no—
1134C22×C4—41no—
1135C22×C4—41no—
1136C22×C4—41no—
1137C22×C4—41no—
1138C22×C4—41no—
1139C22×C4—41no—
1140C22×C4—41no—
1141C22×C4—41no—
1142C22×C4—41no—
1143C22×C4—41no—
1144C22×C4—41no—
1145C22×C4—41no—
1146C22×C4—41no—
1147C22×C4—41no—
1148C22×C4—41no—
1149C22×C4—41no—
1150C22×C4—41no—
1151C22×C4—41no—
1152C22×C4—41no—
1153C22×C4—41no—
1154C22×C4—41no—
1155C22×C4—41no—
1156C22×C4C22×C4×C10714yes—
1157C22×C4C22×C4×C10714yes—
1158C22×C4C22×C4×C10714yes—
1159C22×C4C22×C4×C10714yes—
1160C22×C4C22×C4×C10714yes—
1161C22×C4C22×C4×C10714yes—
1162C22×C4C24×C10711yescharacteristic
1163C22×C4C24×C10711yescharacteristic
1164C22×C4C24×C10711yescharacteristic
1165C22×C4C24×C10711yescharacteristic
1166C22×C4C24×C10711yescharacteristic
1167C22×C4C24×C10711yescharacteristic
1168C22×C4C24×C10711yescharacteristic
1169C22×C4C24×C10711yescharacteristic
1170C22×C4C24×C10711yescharacteristic
1171C22×C4C24×C10711yescharacteristic
1172C22×C4C24×C10711yescharacteristic
1173C22×C4C24×C10711yescharacteristic
1174C22×C4C24×C10711yescharacteristic
1175C22×C4C24×C10711yescharacteristic
1176C22×C4C24×C10711yescharacteristic
1177C22×C4C24×C10711yescharacteristic
1178C22×C4C24×C10711yescharacteristic
1179C22×C4C24×C10711yescharacteristic
1180C22×C4C24×C10711yescharacteristic
1181C22×C4C24×C10711yescharacteristic
1182C22×C4C24×C10711yescharacteristic
1183C22×C4C24×C10711yescharacteristic
1184C22×C4C24×C10711yescharacteristic
1185C22×C4C24×C10711yescharacteristic
1186C22×C4C24×C10711yescharacteristic
1187C22×C4C24×C10711yescharacteristic
1188C22×C4C24×C10711yescharacteristic
1189C4⋊C4—22no—
1190C4⋊C4—22no—
1191C4⋊C4—22no—
1192C4⋊C4—41no—
1193C4⋊C4—41no—
1194C4⋊C4—41no—
1195C4⋊C4—41no—
1196C4⋊C4—41no—
1197C4⋊C4—41no—
1198C4⋊C4—41no—
1199C4⋊C4—41no—
1200C4⋊C4—41no—
1201C4⋊C4—41no—
1202C4⋊C4—41no—
1203C4⋊C4—41no—
1204C4⋊C4—41no—
1205C4⋊C4—41no—
1206C4⋊C4—41no—
1207C4⋊C4—41no—
1208C4⋊C4—41no—
1209C4⋊C4C22×C4×C10714yes—
1210C4⋊C4C22×C4×C10714yes—
1211C4⋊C4C22×C4×C10714yes—
1212C4⋊C4C22×C4×C10714yes—
1213C4⋊C4C22×C4×C10714yes—
1214C4⋊C4C22×C4×C10714yes—
1215C4⋊C4C22×C4×C10714yes—
1216C4⋊C4C22×C4×C10714yes—
1217C4⋊C4C22×C4×C10714yes—
1218C4⋊C4C22×C4×C10714yes—
1219C22⋊C4—22no—
1220C22⋊C4—22no—
1221C22⋊C4—22no—
1222C22⋊C4—41no—
1223C22⋊C4—41no—
1224C22⋊C4—41no—
1225C22⋊C4—41no—
1226C22⋊C4—41no—
1227C22⋊C4—41no—
1228C22⋊C4—41no—
1229C22⋊C4—41no—
1230C22⋊C4—41no—
1231C22⋊C4—41no—
1232C22⋊C4—41no—
1233C22⋊C4—41no—
1234C22⋊C4—41no—
1235C22⋊C4—41no—
1236C22⋊C4—41no—
1237C22⋊C4—41no—
1238C22⋊C4—41no—
1239C22⋊C4—41no—
1240C22⋊C4—41no—
1241C22⋊C4—41no—
1242C22⋊C4—41no—
1243C22⋊C4—41no—
1244C22⋊C4—41no—
1245C22⋊C4C22×C4×C10714yes—
1246C22⋊C4C22×C4×C10714yes—
1247C22⋊C4C22×C4×C10714yes—
1248C22⋊C4C22×C4×C10714yes—
1249C22⋊C4C22×C4×C10714yes—
1250C22⋊C4C22×C4×C10714yes—
1251C22⋊C4C22×C4×C10714yes—
1252C22⋊C4C22×C4×C10714yes—
1253C22⋊C4C22×C4×C10714yes—
1254C22⋊C4C22×C4×C10714yes—
1255C42—22no—
1256C42—22no—
1257C42—41no—
1258C42—41no—
1259C42—41no—
1260C42—41no—
1261C42—41no—
1262C42—41no—
1263C42—41no—
1264C42—41no—
1265C42—41no—
1266C42—41no—
1267C42—41no—
1268C42—41no—
1269C42—41no—
1270C42—41no—
1271C42—41no—
1272C42—41no—
1273C42—41no—
1274C42—41no—
1275C42C22×C4×C10714yes—
1276C42C22×C4×C10714yes—
1277C42C22×C4×C10714yes—
1278C23—21no—
1279C23—21no—
1280C23—21no—
1281C23—21no—
1282C23—21no—
1283C23—21no—
1284C23—21no—
1285C23—21no—
1286C23—21no—
1287C23—21no—
1288C23—21no—
1289C23—21no—
1290C23—21no—
1291C23—21no—
1292C23—21no—
1293C23—21no—
1294C23—21no—
1295C23—21no—
1296C23—21no—
1297C23—21no—
1298C23—21no—
1299C23—21no—
1300C23—21no—
1301C23—21no—
1302C23C23×C4×C10712yes—
1303C23C23×C4×C10712yes—
1304C23C23×C4×C10712yes—
1305C23C23×C4×C10712yes—
1306C23C25×C10711yescharacteristic
1307D4—44no—
1308D4—44no—
1309D4—44no—
1310D4—44no—
1311D4—44no—
1312D4—44no—
1313C2×C4—21no—
1314C2×C4—21no—
1315C2×C4—21no—
1316C2×C4—21no—
1317C2×C4—21no—
1318C2×C4—21no—
1319C2×C4—21no—
1320C2×C4—21no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—21no—
1331C2×C4—21no—
1332C2×C4—21no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—44no—
1383C2×C4—44no—
1384C2×C4—44no—
1385C2×C4—44no—
1386C2×C4—44no—
1387C2×C4—44no—
1388C2×C4—82no—
1389C2×C4—82no—
1390C2×C4—82no—
1391C2×C4—82no—
1392C2×C4—82no—
1393C2×C4—82no—
1394C2×C4C23×C4×C10712yes—
1395C2×C4C23×C4×C10712yes—
1396C2×C4C23×C4×C10712yes—
1397C2×C4C23×C4×C10712yes—
1398C2×C4C23×C4×C10712yes—
1399C2×C4C23×C4×C10712yes—
1400C2×C4C23×C4×C10712yes—
1401C2×C4C23×C4×C10712yes—
1402C2×C4C23×C4×C10712yes—
1403C2×C4C23×C4×C10712yes—
1404C2×C4C23×C4×C10712yes—
1405C2×C4H(5,𝔽2)×C10712yes—
1406C22—22no—
1407C22—22no—
1408C22—22no—
1409C22—22no—
1410C22—22no—
1411C22—22no—
1412C22—22no—
1413C22—22no—
1414C22—22no—
1415C22—22no—
1416C22—22no—
1417C22—22no—
1418C22—41no—
1419C22—41no—
1420C22—41no—
1421C22—41no—
1422C22—41no—
1423C22—41no—
1424C22—41no—
1425C22—41no—
1426C22—41no—
1427C22—41no—
1428C22—41no—
1429C22—41no—
1430C22—41no—
1431C22—41no—
1432C22—41no—
1433C22—41no—
1434C22C24×C4×C10711yescharacteristic
1435C22C2×H(5,𝔽2)×C10711yescharacteristic
1436C22#585×C10711yescharacteristic
1437C22#585×C10711yescharacteristic
1438C22#585×C10711yescharacteristic
1439C22#585×C10711yescharacteristic
1440C22#585×C10711yescharacteristic
1441C4—22no—
1442C4—22no—
1443C4—22no—
1444C4—22no—
1445C4—22no—
1446C4—22no—
1447C4—22no—
1448C4—22no—
1449C4—22no—
1450C4—22no—
1451C4—22no—
1452C4—22no—
1453C4—41no—
1454C4—41no—
1455C4—41no—
1456C4—41no—
1457C4—41no—
1458C4—41no—
1459C4—41no—
1460C4—41no—
1461C4—41no—
1462C4—41no—
1463C4—41no—
1464C4—41no—
1465C4—41no—
1466C4—41no—
1467C4—41no—
1468C2—42no—
1469C2—42no—
1470C2—42no—
1471C2—42no—
1472C2C107×#342811yescharacteristic
1473C2C107×#342811yescharacteristic
1474C2C4×H(5,𝔽2)×C10711yescharacteristic
1475C2C107×#356011yescharacteristic
1476C2C107×#356211yescharacteristic
1477C2C107×#356611yescharacteristic
1478C2C107×#356711yescharacteristic
subgroupG/H
center, socleC23×C107C25
commutatorC22C24×C4×C107
Frattini, cosocleC23C25×C107
prime radicalC2×#553×C107C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C107 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C107×#2382C2semidirect
3. C107×#2377C2semidirect
4. C107×#2377C2semidirect
5. C107×#2376C2semidirect
6. C107×#2373C2semidirect
7. C107×#2373C2semidirect
8. C107×#2364C2semidirect
9. C107×#2363C2semidirect
10. C107×#2359C2semidirect
11. C107×#2357C2semidirect
12. C107×#2353C2semidirect
13. C107×#2352C2semidirect
14. C107×#2352C2semidirect
15. C107×#2344C2semidirect
16. C107×#2343C2semidirect
17. C107×#2336C2semidirect
18. C107×#2335C2semidirect
19. C107×#2334C2semidirect
20. C107×#2333C2semidirect
21. C107×#2333C2semidirect
22. C107×#2333C2semidirect
23. C107×#2324C2semidirect
24. C107×#2322C2semidirect
25. C107×#2319C2semidirect
26. C107×#2318C2semidirect
27. C107×#2318C2semidirect
28. C107×#2313C2semidirect
29. C4×#126×C107C2semidirect
30. C107×#2298C2semidirect
31. C107×#2293C2semidirect
32. #553×C107C4semidirect
206. #126×C107C2×C4semidirect
207. #126×C107C2×C4semidirect
208. #125×C107C2×C4semidirect
209. #123×C107C2×C4semidirect
210. #123×C107C2×C4semidirect
212. #121×C107C2×C4semidirect
213. #121×C107C2×C4semidirect
214. #121×C107C2×C4semidirect
217. C4×D4×C107C2×C4semidirect
218. C4×D4×C107C2×C4semidirect
219. C4×D4×C107C2×C4semidirect
220. C4×D4×C107C2×C4semidirect
224. #117×C107C2×C4semidirect
226. C2×C4⋊C4×C107C2×C4semidirect
728. #34506C107direct (N × H)
741. #2382C2×C107semidirect
742. #2377C2×C107semidirect
743. #2377C2×C107semidirect
744. #2376C2×C107semidirect
745. #2373C2×C107semidirect
746. #2373C2×C107semidirect
747. #2364C2×C107semidirect
748. #2363C2×C107semidirect
749. #2359C2×C107semidirect
750. #2357C2×C107semidirect
751. #2353C2×C107semidirect
752. #2352C2×C107semidirect
753. #2352C2×C107semidirect
754. #2344C2×C107semidirect
755. #2343C2×C107semidirect
756. #2336C2×C107semidirect
757. #2335C2×C107semidirect
758. #2334C2×C107semidirect
759. #2333C2×C107semidirect
760. #2333C2×C107semidirect
761. #2333C2×C107semidirect
762. #2324C2×C107semidirect
763. #2322C2×C107semidirect
764. #2319C2×C107semidirect
765. #2318C2×C107semidirect
766. #2318C2×C107semidirect
767. #2313C2×C107semidirect
768. C4×#126C2×C107semidirect
769. #2298C2×C107semidirect
770. #2293C2×C107semidirect
771. C107#34506direct (N × H)
772. #553C4×C107semidirect
946. #126C2×C4×C107semidirect
947. #126C2×C4×C107semidirect
948. #125C2×C4×C107semidirect
949. #123C2×C4×C107semidirect
950. #123C2×C4×C107semidirect
952. #121C2×C4×C107semidirect
953. #121C2×C4×C107semidirect
954. #121C2×C4×C107semidirect
957. C4×D4C2×C4×C107semidirect
958. C4×D4C2×C4×C107semidirect
959. C4×D4C2×C4×C107semidirect
960. C4×D4C2×C4×C107semidirect
964. #117C2×C4×C107semidirect
966. C2×C4⋊C4C2×C4×C107semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#553×C1072
C107×#23822
C107×#23772
C107×#23762
C107×#23732
C107×#23642
C107×#23632
C107×#23592
C107×#23572
C107×#23532
C107×#23522
C107×#23442
C107×#23432
C107×#23362
C107×#23352
C107×#23342
C107×#23332
C107×#23242
C107×#23222
C107×#23192
C107×#23182
C107×#23132
C4×#126×C1072
C107×#22982
C107×#22932
#34506107