Finite Group Databasebeta

← C107×#34486 #41060450

Subgroups — C107×#34486 #41060450

Order 27392.

2068 conjugacy classes of subgroups.

The subgroup lattice has 1388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#554×C107C211yesmaximal, characteristic
2C107×#2382C211yesmaximal, characteristic, complemented
3C107×#2381C211yesmaximal, characteristic, complemented
4C107×#2378C211yesmaximal, characteristic, complemented
5C107×#2378C211yesmaximal, characteristic, complemented
6C107×#2371C211yesmaximal, characteristic, complemented
7C107×#2368C211yesmaximal, characteristic, complemented
8C107×#2368C211yesmaximal, characteristic, complemented
9C107×#2362C211yesmaximal, characteristic, complemented
10C107×#2360C211yesmaximal, characteristic, complemented
11C107×#2356C211yesmaximal, characteristic, complemented
12C107×#2353C211yesmaximal, characteristic
13C107×#2353C211yesmaximal, characteristic
14C107×#2352C211yesmaximal, characteristic
15C107×#2345C211yesmaximal, characteristic, complemented
16C107×#2344C211yesmaximal, characteristic, complemented
17C107×#2336C211yesmaximal, characteristic, complemented
18C107×#2336C211yesmaximal, characteristic, complemented
19C107×#2332C211yesmaximal, characteristic, complemented
20C107×#2332C211yesmaximal, characteristic, complemented
21C107×#2329C211yesmaximal, characteristic, complemented
22C107×#2329C211yesmaximal, characteristic, complemented
23C107×#2327C211yesmaximal, characteristic, complemented
24C107×#2323C211yesmaximal, characteristic, complemented
25C107×#2320C211yesmaximal, characteristic, complemented
26C107×#2318C211yesmaximal, characteristic
27C107×#2318C211yesmaximal, characteristic
28C107×#2313C211yesmaximal, characteristic, complemented
29C4×C22⋊Q8×C107C211yesmaximal, characteristic, complemented
30C107×#2290C211yesmaximal, characteristic
31C2×#387×C107C211yesmaximal, characteristic, complemented
32#554×C107C4116yescomplemented
33C2×C4⋊Q8×C107C2211yescharacteristic
34C2×#125×C107C2211yescharacteristic
35C2×#125×C107C2211yescharacteristic
36C2×C22⋊Q8×C107C2211yescharacteristic
37C2×C22⋊Q8×C107C2211yescharacteristic
38C2×C22⋊Q8×C107C2211yescharacteristic
39C2×C22⋊Q8×C107C2211yescharacteristic
40C2×C22⋊Q8×C107C2211yescharacteristic
41C2×C22⋊Q8×C107C2211yescharacteristic
42C2×C4×Q8×C107C2211yescharacteristic
43C2×C4×Q8×C107C2211yescharacteristic
44C2×C4×Q8×C107C2211yescharacteristic
45C2×C4×D4×C107C2211yescharacteristic
46C2×C4×D4×C107C2211yescharacteristic
47C2×C4×D4×C107C2211yescharacteristic
48C2×#117×C107C2211yescharacteristic
49C2×#117×C107C2211yescharacteristic
50C22×C4⋊C4×C107C2211yescharacteristic
51C22×C4⋊C4×C107C2211yescharacteristic
52C22×C4⋊C4×C107C2211yescharacteristic
53C22×C42×C107C2211yescharacteristic
54#391×C107C2211yescharacteristic
55#391×C107C2211yescharacteristic
56#391×C107C2211yescharacteristic
57#391×C107C2211yescharacteristic
58#391×C107C2211yescharacteristic
59#391×C107C2211yescharacteristic
60#391×C107C2211yescharacteristic
61#391×C107C2211yescharacteristic
62#391×C107C2211yescharacteristic
63#391×C107C2211yescharacteristic
64#389×C107C2211yescharacteristic
65#389×C107C2211yescharacteristic
66#389×C107C2211yescharacteristic
67#389×C107C2211yescharacteristic
68#389×C107C2211yescharacteristic
69#389×C107C2211yescharacteristic
70#389×C107C2211yescharacteristic
71#389×C107C2211yescharacteristic
72#389×C107C2211yescharacteristic
73#389×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#387×C107C2211yescharacteristic
87#387×C107C2211yescharacteristic
88#387×C107C2211yescharacteristic
89#387×C107C2211yescharacteristic
90#387×C107C2211yescharacteristic
91#387×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#387×C107C2211yescharacteristic
119#387×C107C2211yescharacteristic
120#387×C107C2211yescharacteristic
121#387×C107C2211yescharacteristic
122#387×C107C2211yescharacteristic
123#387×C107C2211yescharacteristic
124#387×C107C2211yescharacteristic
125#387×C107C2211yescharacteristic
126#387×C107C2211yescharacteristic
127#387×C107C2211yescharacteristic
128#387×C107C2211yescharacteristic
129#387×C107C2211yescharacteristic
130#386×C107C2211yescharacteristic
131#386×C107C2211yescharacteristic
132#386×C107C2211yescharacteristic
133#386×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#383×C107C2211yescharacteristic
143#383×C107C2211yescharacteristic
144#382×C107C2211yescharacteristic
145#382×C107C2211yescharacteristic
146#382×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×C4⋊C4×C107C2211yescharacteristic
168C4×C4⋊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
181#376×C107C2211yescharacteristic
182#376×C107C2211yescharacteristic
183#376×C107C2211yescharacteristic
184C2×#95×C107C2211yescharacteristic
185C2×#95×C107C2211yescharacteristic
186C2×#95×C107C2211yescharacteristic
187C2×#95×C107C2211yescharacteristic
188C22×Q8×C107C2311yescharacteristic
189C22×Q8×C107C2311yescharacteristic
190C22×Q8×C107C2311yescharacteristic
191C22×D4×C107C2311yescharacteristic
192C23×C4×C107C2311yescharacteristic
193C23×C4×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
202C4⋊Q8×C107C2×C418yescomplemented
203#125×C107C2×C418yescomplemented
204#125×C107C2×C418yescomplemented
205C22⋊Q8×C107C2×C418yes—
206C22⋊Q8×C107C2×C418yes—
207C22⋊Q8×C107C2×C418yes—
208C22⋊Q8×C107C2×C418yescomplemented
209C22⋊Q8×C107C2×C418yescomplemented
210C22⋊Q8×C107C2×C418yescomplemented
211C4×Q8×C107—42no—
212C4×Q8×C107—42no—
213C4×Q8×C107C2×C418yescomplemented
214C4×D4×C107C2×C418yes—
215C4×D4×C107C2×C418yes—
216C4×D4×C107C2×C418yes—
217#117×C107—42no—
218#117×C107—42no—
219C2×C4⋊C4×C107—42no—
220C2×C4⋊C4×C107C2×C418yes—
221C2×C4⋊C4×C107C2×C418yescomplemented
222C2×C4⋊C4×C107C2311yescharacteristic
223C2×C4⋊C4×C107C2311yescharacteristic
224C2×C4⋊C4×C107C2311yescharacteristic
225C2×C4⋊C4×C107C2311yescharacteristic
226C2×C4⋊C4×C107C2311yescharacteristic
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×C4⋊C4×C107C2311yescharacteristic
258C2×C4⋊C4×C107C2311yescharacteristic
259C2×C4⋊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×C42×C107—42no—
279C2×C42×C107C2311yescharacteristic
280C2×C42×C107C2311yescharacteristic
281C2×C42×C107C2311yescharacteristic
282C2×C42×C107C2311yescharacteristic
283C2×C42×C107C2311yescharacteristic
284C2×C42×C107C2311yescharacteristic
285C2×C42×C107C2311yescharacteristic
286C2×C42×C107C2311yescharacteristic
287C2×C42×C107C2311yescharacteristic
288C2×C42×C107C2311yescharacteristic
289C2×C42×C107C2311yescharacteristic
290C2×C42×C107C2311yescharacteristic
291C2×C42×C107C2311yescharacteristic
292C2×C42×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
304#95×C107C2311yescharacteristic
305#95×C107C2311yescharacteristic
306#95×C107C2311yescharacteristic
307#95×C107C2311yescharacteristic
308#95×C107C2311yescharacteristic
309#95×C107C2311yescharacteristic
310#95×C107C2311yescharacteristic
311#95×C107C2311yescharacteristic
312#95×C107C2311yescharacteristic
313#95×C107C2311yescharacteristic
314#95×C107C2311yescharacteristic
315#95×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
366C2×Q8×C107—41no—
367C2×Q8×C107—41no—
368C2×Q8×C107—41no—
369C2×Q8×C107—41no—
370C2×Q8×C107—41no—
371C2×Q8×C107—41no—
372C2×Q8×C107C22×C414yes—
373C2×Q8×C107C22×C414yes—
374C2×Q8×C107C22×C414yes—
375C2×D4×C107—22no—
376C2×D4×C107—22no—
377C2×D4×C107C22×C414yes—
378C22×C4×C107—22no—
379C22×C4×C107—22no—
380C22×C4×C107—22no—
381C22×C4×C107—22no—
382C22×C4×C107—22no—
383C22×C4×C107—41no—
384C22×C4×C107—41no—
385C22×C4×C107—41no—
386C22×C4×C107—41no—
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×C107C22×C414yes—
403C22×C4×C107C22×C414yes—
404C22×C4×C107C22×C414yes—
405C22×C4×C107C22×C414yes—
406C22×C4×C107C22×C414yes—
407C22×C4×C107C22×C414yes—
408C22×C4×C107C2411yescharacteristic
409C22×C4×C107C2411yescharacteristic
410C22×C4×C107C2411yescharacteristic
411C22×C4×C107C2411yescharacteristic
412C22×C4×C107C2411yescharacteristic
413C22×C4×C107C2411yescharacteristic
414C22×C4×C107C2411yescharacteristic
415C22×C4×C107C2411yescharacteristic
416C22×C4×C107C2411yescharacteristic
417C22×C4×C107C2411yescharacteristic
418C22×C4×C107C2411yescharacteristic
419C22×C4×C107C2411yescharacteristic
420C22×C4×C107C2411yescharacteristic
421C22×C4×C107C2411yescharacteristic
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
437C4⋊C4×C107—22no—
438C4⋊C4×C107—22no—
439C4⋊C4×C107—22no—
440C4⋊C4×C107—41no—
441C4⋊C4×C107—41no—
442C4⋊C4×C107—41no—
443C4⋊C4×C107—41no—
444C4⋊C4×C107—41no—
445C4⋊C4×C107—41no—
446C4⋊C4×C107—41no—
447C4⋊C4×C107—41no—
448C4⋊C4×C107—41no—
449C4⋊C4×C107—41no—
450C4⋊C4×C107—41no—
451C4⋊C4×C107—41no—
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×C107C22×C414yes—
460C4⋊C4×C107C22×C414yes—
461C4⋊C4×C107C22×C414yes—
462C4⋊C4×C107C22×C414yes—
463C4⋊C4×C107C22×C414yes—
464C4⋊C4×C107C22×C414yes—
465C4⋊C4×C107C22×C414yes—
466C4⋊C4×C107C22×C414yes—
467C4⋊C4×C107C22×C414yes—
468C4⋊C4×C107C22×C414yes—
469C4⋊C4×C107C22×C414yes—
470C4⋊C4×C107C22×C414yes—
471C4⋊C4×C107C22×C414yes—
472C4⋊C4×C107C22×C414yes—
473C4⋊C4×C107C22×C414yes—
474C4⋊C4×C107C22×C414yes—
475C22⋊C4×C107—22no—
476C22⋊C4×C107—22no—
477C22⋊C4×C107—22no—
478C22⋊C4×C107—22no—
479C22⋊C4×C107—22no—
480C22⋊C4×C107—41no—
481C22⋊C4×C107—41no—
482C22⋊C4×C107—41no—
483C22⋊C4×C107—41no—
484C22⋊C4×C107—41no—
485C22⋊C4×C107—41no—
486C22⋊C4×C107—41no—
487C22⋊C4×C107C22×C414yes—
488C22⋊C4×C107C22×C414yes—
489C22⋊C4×C107C22×C414yes—
490C22⋊C4×C107C22×C414yes—
491C22⋊C4×C107C22×C414yes—
492C22⋊C4×C107C22×C414yes—
493C42×C107—22no—
494C42×C107—22no—
495C42×C107—22no—
496C42×C107—22no—
497C42×C107—41no—
498C42×C107—41no—
499C42×C107—41no—
500C42×C107—41no—
501C42×C107—41no—
502C42×C107—41no—
503C42×C107—41no—
504C42×C107—41no—
505C42×C107—41no—
506C42×C107—41no—
507C42×C107—41no—
508C42×C107—41no—
509C42×C107—41no—
510C42×C107—41no—
511C42×C107—41no—
512C42×C107—41no—
513C42×C107—41no—
514C42×C107—41no—
515C42×C107C22×C414yes—
516C42×C107C22×C414yes—
517C42×C107C22×C414yes—
518C23×C107—21no—
519C23×C107—21no—
520C23×C107—21no—
521C23×C107—21no—
522C23×C107—21no—
523C23×C107—21no—
524C23×C107—21no—
525C23×C107—21no—
526C23×C107—21no—
527C23×C107—21no—
528C23×C107C23×C412yes—
529C23×C107C23×C412yes—
530C23×C1072−1+412yes—
531C23×C1072−1+412yes—
532C23×C107C2511yescharacteristic
533Q8×C107—44no—
534Q8×C107—44no—
535Q8×C107—44no—
536D4×C107—28no—
537C2×C4×C107—21no—
538C2×C4×C107—21no—
539C2×C4×C107—21no—
540C2×C4×C107—21no—
541C2×C4×C107—21no—
542C2×C4×C107—21no—
543C2×C4×C107—21no—
544C2×C4×C107—21no—
545C2×C4×C107—21no—
546C2×C4×C107—21no—
547C2×C4×C107—21no—
548C2×C4×C107—21no—
549C2×C4×C107—21no—
550C2×C4×C107—21no—
551C2×C4×C107—21no—
552C2×C4×C107—21no—
553C2×C4×C107—21no—
554C2×C4×C107—21no—
555C2×C4×C107—21no—
556C2×C4×C107—21no—
557C2×C4×C107—21no—
558C2×C4×C107—21no—
559C2×C4×C107—21no—
560C2×C4×C107—21no—
561C2×C4×C107—21no—
562C2×C4×C107—21no—
563C2×C4×C107—21no—
564C2×C4×C107—21no—
565C2×C4×C107—21no—
566C2×C4×C107—21no—
567C2×C4×C107—21no—
568C2×C4×C107—21no—
569C2×C4×C107—21no—
570C2×C4×C107—21no—
571C2×C4×C107—21no—
572C2×C4×C107—21no—
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—44no—
611C2×C4×C107—44no—
612C2×C4×C107—44no—
613C2×C4×C107—44no—
614C2×C4×C107—44no—
615C2×C4×C107—44no—
616C2×C4×C107—44no—
617C2×C4×C107—44no—
618C2×C4×C107—82no—
619C2×C4×C107—82no—
620C2×C4×C107C23×C412yes—
621C2×C4×C107C23×C412yes—
622C2×C4×C107C23×C412yes—
623C2×C4×C107C23×C412yes—
624C2×C4×C107C23×C412yes—
625C2×C4×C107C23×C412yes—
626C2×C4×C107C23×C412yes—
627C2×C4×C107C23×C412yes—
628C2×C4×C107C23×C412yes—
629C2×C4×C107C23×C412yes—
630C2×C4×C107C23×C412yes—
631C2×C4×C107C23×C412yes—
632C2×C4×C107C23×C412yes—
633C2×C4×C107H(5,𝔽2)12yes—
634C22×C107—22no—
635C22×C107—22no—
636C22×C107—22no—
637C22×C107—22no—
638C22×C107—22no—
639C22×C107—22no—
640C22×C107—22no—
641C22×C107—22no—
642C22×C107—22no—
643C22×C107—41no—
644C22×C107—41no—
645C22×C107—41no—
646C22×C107—41no—
647C22×C107#51914yes—
648C22×C107C24×C411yescharacteristic
649C22×C107C2×H(5,𝔽2)11yescharacteristic
650C22×C107C2×2−1+411yescharacteristic
651C22×C107C2×2−1+411yescharacteristic
652C22×C107#58511yescharacteristic
653C22×C107#58511yescharacteristic
654C22×C107#58511yescharacteristic
655C4×C107—22no—
656C4×C107—22no—
657C4×C107—22no—
658C4×C107—22no—
659C4×C107—22no—
660C4×C107—22no—
661C4×C107—22no—
662C4×C107—22no—
663C4×C107—22no—
664C4×C107—22no—
665C4×C107—22no—
666C4×C107—22no—
667C4×C107—22no—
668C4×C107—22no—
669C4×C107—41no—
670C4×C107—41no—
671C4×C107—41no—
672C4×C107—41no—
673C4×C107—41no—
674C4×C107—41no—
675C4×C107—41no—
676C4×C107—41no—
677C4×C107—41no—
678C4×C107—41no—
679C4×C107—41no—
680C4×C107—41no—
681C4×C107—41no—
682C4×C107—41no—
683C4×C107—41no—
684#34486C10711yesmaximal, characteristic, direct product factor, Sylow
685C2×C107—24no—
686C2×C107—42no—
687C2×C107C2×#51911yescharacteristic
688C2×C107#342811yescharacteristic
689C2×C107C4×H(5,𝔽2)11yescharacteristic
690C2×C107#353511yescharacteristic
691C2×C107#354111yescharacteristic
692C2×C107#355311yescharacteristic
693C2×C107#356411yescharacteristic
694C2×#554C2×C10711yescharacteristic
695#2382C2×C10711yescharacteristic, complemented
696#2381C2×C10711yescharacteristic, complemented
697#2378C2×C10711yescharacteristic, complemented
698#2378C2×C10711yescharacteristic, complemented
699#2371C2×C10711yescharacteristic, complemented
700#2368C2×C10711yescharacteristic, complemented
701#2368C2×C10711yescharacteristic, complemented
702#2362C2×C10711yescharacteristic, complemented
703#2360C2×C10711yescharacteristic, complemented
704#2356C2×C10711yescharacteristic, complemented
705#2353C2×C10711yescharacteristic
706#2353C2×C10711yescharacteristic
707#2352C2×C10711yescharacteristic
708#2345C2×C10711yescharacteristic, complemented
709#2344C2×C10711yescharacteristic, complemented
710#2336C2×C10711yescharacteristic, complemented
711#2336C2×C10711yescharacteristic, complemented
712#2332C2×C10711yescharacteristic, complemented
713#2332C2×C10711yescharacteristic, complemented
714#2329C2×C10711yescharacteristic, complemented
715#2329C2×C10711yescharacteristic, complemented
716#2327C2×C10711yescharacteristic, complemented
717#2323C2×C10711yescharacteristic, complemented
718#2320C2×C10711yescharacteristic, complemented
719#2318C2×C10711yescharacteristic
720#2318C2×C10711yescharacteristic
721#2313C2×C10711yescharacteristic, complemented
722C4×C22⋊Q8C2×C10711yescharacteristic, complemented
723#2290C2×C10711yescharacteristic
724C2×#387C2×C10711yescharacteristic, complemented
725C107#3448611yescharacteristic, direct product factor, Sylow
726#554C4×C107116yescomplemented
727C2×C4⋊Q8C22×C10711yescharacteristic
728C2×#125C22×C10711yescharacteristic
729C2×#125C22×C10711yescharacteristic
730C2×C22⋊Q8C22×C10711yescharacteristic
731C2×C22⋊Q8C22×C10711yescharacteristic
732C2×C22⋊Q8C22×C10711yescharacteristic
733C2×C22⋊Q8C22×C10711yescharacteristic
734C2×C22⋊Q8C22×C10711yescharacteristic
735C2×C22⋊Q8C22×C10711yescharacteristic
736C2×C4×Q8C22×C10711yescharacteristic
737C2×C4×Q8C22×C10711yescharacteristic
738C2×C4×Q8C22×C10711yescharacteristic
739C2×C4×D4C22×C10711yescharacteristic
740C2×C4×D4C22×C10711yescharacteristic
741C2×C4×D4C22×C10711yescharacteristic
742C2×#117C22×C10711yescharacteristic
743C2×#117C22×C10711yescharacteristic
744C22×C4⋊C4C22×C10711yescharacteristic
745C22×C4⋊C4C22×C10711yescharacteristic
746C22×C4⋊C4C22×C10711yescharacteristic
747C22×C42C22×C10711yescharacteristic
748#391C22×C10711yescharacteristic
749#391C22×C10711yescharacteristic
750#391C22×C10711yescharacteristic
751#391C22×C10711yescharacteristic
752#391C22×C10711yescharacteristic
753#391C22×C10711yescharacteristic
754#391C22×C10711yescharacteristic
755#391C22×C10711yescharacteristic
756#391C22×C10711yescharacteristic
757#391C22×C10711yescharacteristic
758#389C22×C10711yescharacteristic
759#389C22×C10711yescharacteristic
760#389C22×C10711yescharacteristic
761#389C22×C10711yescharacteristic
762#389C22×C10711yescharacteristic
763#389C22×C10711yescharacteristic
764#389C22×C10711yescharacteristic
765#389C22×C10711yescharacteristic
766#389C22×C10711yescharacteristic
767#389C22×C10711yescharacteristic
768#388C22×C10711yescharacteristic
769#388C22×C10711yescharacteristic
770#388C22×C10711yescharacteristic
771#388C22×C10711yescharacteristic
772#388C22×C10711yescharacteristic
773#388C22×C10711yescharacteristic
774#388C22×C10711yescharacteristic
775#388C22×C10711yescharacteristic
776#388C22×C10711yescharacteristic
777#388C22×C10711yescharacteristic
778#388C22×C10711yescharacteristic
779#388C22×C10711yescharacteristic
780#387C22×C10711yescharacteristic
781#387C22×C10711yescharacteristic
782#387C22×C10711yescharacteristic
783#387C22×C10711yescharacteristic
784#387C22×C10711yescharacteristic
785#387C22×C10711yescharacteristic
786#387C22×C10711yescharacteristic
787#387C22×C10711yescharacteristic
788#387C22×C10711yescharacteristic
789#387C22×C10711yescharacteristic
790#387C22×C10711yescharacteristic
791#387C22×C10711yescharacteristic
792#387C22×C10711yescharacteristic
793#387C22×C10711yescharacteristic
794#387C22×C10711yescharacteristic
795#387C22×C10711yescharacteristic
796#387C22×C10711yescharacteristic
797#387C22×C10711yescharacteristic
798#387C22×C10711yescharacteristic
799#387C22×C10711yescharacteristic
800#387C22×C10711yescharacteristic
801#387C22×C10711yescharacteristic
802#387C22×C10711yescharacteristic
803#387C22×C10711yescharacteristic
804#387C22×C10711yescharacteristic
805#387C22×C10711yescharacteristic
806#387C22×C10711yescharacteristic
807#387C22×C10711yescharacteristic
808#387C22×C10711yescharacteristic
809#387C22×C10711yescharacteristic
810#387C22×C10711yescharacteristic
811#387C22×C10711yescharacteristic
812#387C22×C10711yescharacteristic
813#387C22×C10711yescharacteristic
814#387C22×C10711yescharacteristic
815#387C22×C10711yescharacteristic
816#387C22×C10711yescharacteristic
817#387C22×C10711yescharacteristic
818#387C22×C10711yescharacteristic
819#387C22×C10711yescharacteristic
820#387C22×C10711yescharacteristic
821#387C22×C10711yescharacteristic
822#387C22×C10711yescharacteristic
823#387C22×C10711yescharacteristic
824#386C22×C10711yescharacteristic
825#386C22×C10711yescharacteristic
826#386C22×C10711yescharacteristic
827#386C22×C10711yescharacteristic
828#385C22×C10711yescharacteristic
829#385C22×C10711yescharacteristic
830#385C22×C10711yescharacteristic
831#385C22×C10711yescharacteristic
832#385C22×C10711yescharacteristic
833#385C22×C10711yescharacteristic
834#383C22×C10711yescharacteristic
835#383C22×C10711yescharacteristic
836#383C22×C10711yescharacteristic
837#383C22×C10711yescharacteristic
838#382C22×C10711yescharacteristic
839#382C22×C10711yescharacteristic
840#382C22×C10711yescharacteristic
841#381C22×C10711yescharacteristic
842#381C22×C10711yescharacteristic
843#381C22×C10711yescharacteristic
844#381C22×C10711yescharacteristic
845#380C22×C10711yescharacteristic
846#380C22×C10711yescharacteristic
847#380C22×C10711yescharacteristic
848#380C22×C10711yescharacteristic
849#380C22×C10711yescharacteristic
850#380C22×C10711yescharacteristic
851C4×C4⋊C4C22×C10711yescharacteristic
852C4×C4⋊C4C22×C10711yescharacteristic
853C4×C4⋊C4C22×C10711yescharacteristic
854C4×C4⋊C4C22×C10711yescharacteristic
855C4×C4⋊C4C22×C10711yescharacteristic
856C4×C4⋊C4C22×C10711yescharacteristic
857C4×C4⋊C4C22×C10711yescharacteristic
858C4×C4⋊C4C22×C10711yescharacteristic
859C4×C4⋊C4C22×C10711yescharacteristic
860C4×C4⋊C4C22×C10711yescharacteristic
861C4×C4⋊C4C22×C10711yescharacteristic
862C4×C4⋊C4C22×C10711yescharacteristic
863C4×C22⋊C4C22×C10711yescharacteristic
864C4×C22⋊C4C22×C10711yescharacteristic
865C4×C22⋊C4C22×C10711yescharacteristic
866C4×C22⋊C4C22×C10711yescharacteristic
867C4×C22⋊C4C22×C10711yescharacteristic
868C4×C22⋊C4C22×C10711yescharacteristic
869C4×C22⋊C4C22×C10711yescharacteristic
870C4×C22⋊C4C22×C10711yescharacteristic
871C4×C22⋊C4C22×C10711yescharacteristic
872C4×C22⋊C4C22×C10711yescharacteristic
873C4×C22⋊C4C22×C10711yescharacteristic
874C4×C22⋊C4C22×C10711yescharacteristic
875#376C22×C10711yescharacteristic
876#376C22×C10711yescharacteristic
877#376C22×C10711yescharacteristic
878C2×#95C22×C10711yescharacteristic
879C2×#95C22×C10711yescharacteristic
880C2×#95C22×C10711yescharacteristic
881C2×#95C22×C10711yescharacteristic
882C22×Q8C23×C10711yescharacteristic
883C22×Q8C23×C10711yescharacteristic
884C22×Q8C23×C10711yescharacteristic
885C22×D4C23×C10711yescharacteristic
886C23×C4C23×C10711yescharacteristic
887C23×C4C23×C10711yescharacteristic
888C23×C4C23×C10711yescharacteristic
889C23×C4C23×C10711yescharacteristic
890C23×C4C23×C10711yescharacteristic
891C23×C4C23×C10711yescharacteristic
892C23×C4C23×C10711yescharacteristic
893C23×C4C23×C10711yescharacteristic
894C23×C4C23×C10711yescharacteristic
895C23×C4C23×C10711yescharacteristic
896C4⋊Q8C2×C4×C10718yescomplemented
897#125C2×C4×C10718yescomplemented
898#125C2×C4×C10718yescomplemented
899C22⋊Q8C2×C4×C10718yes—
900C22⋊Q8C2×C4×C10718yes—
901C22⋊Q8C2×C4×C10718yes—
902C22⋊Q8C2×C4×C10718yescomplemented
903C22⋊Q8C2×C4×C10718yescomplemented
904C22⋊Q8C2×C4×C10718yescomplemented
905C4×Q8—42no—
906C4×Q8—42no—
907C4×Q8C2×C4×C10718yescomplemented
908C4×D4C2×C4×C10718yes—
909C4×D4C2×C4×C10718yes—
910C4×D4C2×C4×C10718yes—
911#117—42no—
912#117—42no—
913C2×C4⋊C4—42no—
914C2×C4⋊C4C2×C4×C10718yes—
915C2×C4⋊C4C2×C4×C10718yescomplemented
916C2×C4⋊C4C23×C10711yescharacteristic
917C2×C4⋊C4C23×C10711yescharacteristic
918C2×C4⋊C4C23×C10711yescharacteristic
919C2×C4⋊C4C23×C10711yescharacteristic
920C2×C4⋊C4C23×C10711yescharacteristic
921C2×C4⋊C4C23×C10711yescharacteristic
922C2×C4⋊C4C23×C10711yescharacteristic
923C2×C4⋊C4C23×C10711yescharacteristic
924C2×C4⋊C4C23×C10711yescharacteristic
925C2×C4⋊C4C23×C10711yescharacteristic
926C2×C4⋊C4C23×C10711yescharacteristic
927C2×C4⋊C4C23×C10711yescharacteristic
928C2×C4⋊C4C23×C10711yescharacteristic
929C2×C4⋊C4C23×C10711yescharacteristic
930C2×C4⋊C4C23×C10711yescharacteristic
931C2×C4⋊C4C23×C10711yescharacteristic
932C2×C4⋊C4C23×C10711yescharacteristic
933C2×C4⋊C4C23×C10711yescharacteristic
934C2×C4⋊C4C23×C10711yescharacteristic
935C2×C4⋊C4C23×C10711yescharacteristic
936C2×C4⋊C4C23×C10711yescharacteristic
937C2×C4⋊C4C23×C10711yescharacteristic
938C2×C4⋊C4C23×C10711yescharacteristic
939C2×C4⋊C4C23×C10711yescharacteristic
940C2×C4⋊C4C23×C10711yescharacteristic
941C2×C4⋊C4C23×C10711yescharacteristic
942C2×C4⋊C4C23×C10711yescharacteristic
943C2×C4⋊C4C23×C10711yescharacteristic
944C2×C4⋊C4C23×C10711yescharacteristic
945C2×C4⋊C4C23×C10711yescharacteristic
946C2×C4⋊C4C23×C10711yescharacteristic
947C2×C4⋊C4C23×C10711yescharacteristic
948C2×C4⋊C4C23×C10711yescharacteristic
949C2×C4⋊C4C23×C10711yescharacteristic
950C2×C4⋊C4C23×C10711yescharacteristic
951C2×C4⋊C4C23×C10711yescharacteristic
952C2×C4⋊C4C23×C10711yescharacteristic
953C2×C4⋊C4C23×C10711yescharacteristic
954C2×C22⋊C4C23×C10711yescharacteristic
955C2×C22⋊C4C23×C10711yescharacteristic
956C2×C22⋊C4C23×C10711yescharacteristic
957C2×C22⋊C4C23×C10711yescharacteristic
958C2×C22⋊C4C23×C10711yescharacteristic
959C2×C22⋊C4C23×C10711yescharacteristic
960C2×C22⋊C4C23×C10711yescharacteristic
961C2×C22⋊C4C23×C10711yescharacteristic
962C2×C22⋊C4C23×C10711yescharacteristic
963C2×C22⋊C4C23×C10711yescharacteristic
964C2×C22⋊C4C23×C10711yescharacteristic
965C2×C22⋊C4C23×C10711yescharacteristic
966C2×C22⋊C4C23×C10711yescharacteristic
967C2×C22⋊C4C23×C10711yescharacteristic
968C2×C22⋊C4C23×C10711yescharacteristic
969C2×C22⋊C4C23×C10711yescharacteristic
970C2×C22⋊C4C23×C10711yescharacteristic
971C2×C22⋊C4C23×C10711yescharacteristic
972C2×C42—42no—
973C2×C42C23×C10711yescharacteristic
974C2×C42C23×C10711yescharacteristic
975C2×C42C23×C10711yescharacteristic
976C2×C42C23×C10711yescharacteristic
977C2×C42C23×C10711yescharacteristic
978C2×C42C23×C10711yescharacteristic
979C2×C42C23×C10711yescharacteristic
980C2×C42C23×C10711yescharacteristic
981C2×C42C23×C10711yescharacteristic
982C2×C42C23×C10711yescharacteristic
983C2×C42C23×C10711yescharacteristic
984C2×C42C23×C10711yescharacteristic
985C2×C42C23×C10711yescharacteristic
986C2×C42C23×C10711yescharacteristic
987C2×C42C23×C10711yescharacteristic
988C2×C42C23×C10711yescharacteristic
989C2×C42C23×C10711yescharacteristic
990C2×C42C23×C10711yescharacteristic
991C2×C42C23×C10711yescharacteristic
992C2×C42C23×C10711yescharacteristic
993C2×C42C23×C10711yescharacteristic
994C2×C42C23×C10711yescharacteristic
995C2×C42C23×C10711yescharacteristic
996C2×C42C23×C10711yescharacteristic
997C2×C42C23×C10711yescharacteristic
998#95C23×C10711yescharacteristic
999#95C23×C10711yescharacteristic
1000#95C23×C10711yescharacteristic
1001#95C23×C10711yescharacteristic
1002#95C23×C10711yescharacteristic
1003#95C23×C10711yescharacteristic
1004#95C23×C10711yescharacteristic
1005#95C23×C10711yescharacteristic
1006#95C23×C10711yescharacteristic
1007#95C23×C10711yescharacteristic
1008#95C23×C10711yescharacteristic
1009#95C23×C10711yescharacteristic
1010#95C23×C10711yescharacteristic
1011#95C23×C10711yescharacteristic
1012#95C23×C10711yescharacteristic
1013#95C23×C10711yescharacteristic
1014#95C23×C10711yescharacteristic
1015#95C23×C10711yescharacteristic
1016#95C23×C10711yescharacteristic
1017#95C23×C10711yescharacteristic
1018#95C23×C10711yescharacteristic
1019#95C23×C10711yescharacteristic
1020#95C23×C10711yescharacteristic
1021#95C23×C10711yescharacteristic
1022#95C23×C10711yescharacteristic
1023#95C23×C10711yescharacteristic
1024#95C23×C10711yescharacteristic
1025#95C23×C10711yescharacteristic
1026#95C23×C10711yescharacteristic
1027#95C23×C10711yescharacteristic
1028#95C23×C10711yescharacteristic
1029#95C23×C10711yescharacteristic
1030#95C23×C10711yescharacteristic
1031#95C23×C10711yescharacteristic
1032#95C23×C10711yescharacteristic
1033#95C23×C10711yescharacteristic
1034#95C23×C10711yescharacteristic
1035#95C23×C10711yescharacteristic
1036#95C23×C10711yescharacteristic
1037#95C23×C10711yescharacteristic
1038#95C23×C10711yescharacteristic
1039#95C23×C10711yescharacteristic
1040#95C23×C10711yescharacteristic
1041#95C23×C10711yescharacteristic
1042#95C23×C10711yescharacteristic
1043#95C23×C10711yescharacteristic
1044#95C23×C10711yescharacteristic
1045#95C23×C10711yescharacteristic
1046#95C23×C10711yescharacteristic
1047#95C23×C10711yescharacteristic
1048#95C23×C10711yescharacteristic
1049#95C23×C10711yescharacteristic
1050#95C23×C10711yescharacteristic
1051#95C23×C10711yescharacteristic
1052#95C23×C10711yescharacteristic
1053#95C23×C10711yescharacteristic
1054#95C23×C10711yescharacteristic
1055#95C23×C10711yescharacteristic
1056#95C23×C10711yescharacteristic
1057#95C23×C10711yescharacteristic
1058C24C24×C10711yescharacteristic
1059C24C24×C10711yescharacteristic
1060C2×Q8—41no—
1061C2×Q8—41no—
1062C2×Q8—41no—
1063C2×Q8—41no—
1064C2×Q8—41no—
1065C2×Q8—41no—
1066C2×Q8C22×C4×C10714yes—
1067C2×Q8C22×C4×C10714yes—
1068C2×Q8C22×C4×C10714yes—
1069C2×D4—22no—
1070C2×D4—22no—
1071C2×D4C22×C4×C10714yes—
1072C22×C4—22no—
1073C22×C4—22no—
1074C22×C4—22no—
1075C22×C4—22no—
1076C22×C4—22no—
1077C22×C4—41no—
1078C22×C4—41no—
1079C22×C4—41no—
1080C22×C4—41no—
1081C22×C4—41no—
1082C22×C4—41no—
1083C22×C4—41no—
1084C22×C4—41no—
1085C22×C4—41no—
1086C22×C4—41no—
1087C22×C4—41no—
1088C22×C4—41no—
1089C22×C4—41no—
1090C22×C4—41no—
1091C22×C4—41no—
1092C22×C4—41no—
1093C22×C4—41no—
1094C22×C4—41no—
1095C22×C4—41no—
1096C22×C4C22×C4×C10714yes—
1097C22×C4C22×C4×C10714yes—
1098C22×C4C22×C4×C10714yes—
1099C22×C4C22×C4×C10714yes—
1100C22×C4C22×C4×C10714yes—
1101C22×C4C22×C4×C10714yes—
1102C22×C4C24×C10711yescharacteristic
1103C22×C4C24×C10711yescharacteristic
1104C22×C4C24×C10711yescharacteristic
1105C22×C4C24×C10711yescharacteristic
1106C22×C4C24×C10711yescharacteristic
1107C22×C4C24×C10711yescharacteristic
1108C22×C4C24×C10711yescharacteristic
1109C22×C4C24×C10711yescharacteristic
1110C22×C4C24×C10711yescharacteristic
1111C22×C4C24×C10711yescharacteristic
1112C22×C4C24×C10711yescharacteristic
1113C22×C4C24×C10711yescharacteristic
1114C22×C4C24×C10711yescharacteristic
1115C22×C4C24×C10711yescharacteristic
1116C22×C4C24×C10711yescharacteristic
1117C22×C4C24×C10711yescharacteristic
1118C22×C4C24×C10711yescharacteristic
1119C22×C4C24×C10711yescharacteristic
1120C22×C4C24×C10711yescharacteristic
1121C22×C4C24×C10711yescharacteristic
1122C22×C4C24×C10711yescharacteristic
1123C22×C4C24×C10711yescharacteristic
1124C22×C4C24×C10711yescharacteristic
1125C22×C4C24×C10711yescharacteristic
1126C22×C4C24×C10711yescharacteristic
1127C22×C4C24×C10711yescharacteristic
1128C22×C4C24×C10711yescharacteristic
1129C22×C4C24×C10711yescharacteristic
1130C22×C4C24×C10711yescharacteristic
1131C4⋊C4—22no—
1132C4⋊C4—22no—
1133C4⋊C4—22no—
1134C4⋊C4—41no—
1135C4⋊C4—41no—
1136C4⋊C4—41no—
1137C4⋊C4—41no—
1138C4⋊C4—41no—
1139C4⋊C4—41no—
1140C4⋊C4—41no—
1141C4⋊C4—41no—
1142C4⋊C4—41no—
1143C4⋊C4—41no—
1144C4⋊C4—41no—
1145C4⋊C4—41no—
1146C4⋊C4—41no—
1147C4⋊C4—41no—
1148C4⋊C4—41no—
1149C4⋊C4—41no—
1150C4⋊C4—41no—
1151C4⋊C4—41no—
1152C4⋊C4—41no—
1153C4⋊C4C22×C4×C10714yes—
1154C4⋊C4C22×C4×C10714yes—
1155C4⋊C4C22×C4×C10714yes—
1156C4⋊C4C22×C4×C10714yes—
1157C4⋊C4C22×C4×C10714yes—
1158C4⋊C4C22×C4×C10714yes—
1159C4⋊C4C22×C4×C10714yes—
1160C4⋊C4C22×C4×C10714yes—
1161C4⋊C4C22×C4×C10714yes—
1162C4⋊C4C22×C4×C10714yes—
1163C4⋊C4C22×C4×C10714yes—
1164C4⋊C4C22×C4×C10714yes—
1165C4⋊C4C22×C4×C10714yes—
1166C4⋊C4C22×C4×C10714yes—
1167C4⋊C4C22×C4×C10714yes—
1168C4⋊C4C22×C4×C10714yes—
1169C22⋊C4—22no—
1170C22⋊C4—22no—
1171C22⋊C4—22no—
1172C22⋊C4—22no—
1173C22⋊C4—22no—
1174C22⋊C4—41no—
1175C22⋊C4—41no—
1176C22⋊C4—41no—
1177C22⋊C4—41no—
1178C22⋊C4—41no—
1179C22⋊C4—41no—
1180C22⋊C4—41no—
1181C22⋊C4C22×C4×C10714yes—
1182C22⋊C4C22×C4×C10714yes—
1183C22⋊C4C22×C4×C10714yes—
1184C22⋊C4C22×C4×C10714yes—
1185C22⋊C4C22×C4×C10714yes—
1186C22⋊C4C22×C4×C10714yes—
1187C42—22no—
1188C42—22no—
1189C42—22no—
1190C42—22no—
1191C42—41no—
1192C42—41no—
1193C42—41no—
1194C42—41no—
1195C42—41no—
1196C42—41no—
1197C42—41no—
1198C42—41no—
1199C42—41no—
1200C42—41no—
1201C42—41no—
1202C42—41no—
1203C42—41no—
1204C42—41no—
1205C42—41no—
1206C42—41no—
1207C42—41no—
1208C42—41no—
1209C42C22×C4×C10714yes—
1210C42C22×C4×C10714yes—
1211C42C22×C4×C10714yes—
1212C23—21no—
1213C23—21no—
1214C23—21no—
1215C23—21no—
1216C23—21no—
1217C23—21no—
1218C23—21no—
1219C23—21no—
1220C23—21no—
1221C23—21no—
1222C23C23×C4×C10712yes—
1223C23C23×C4×C10712yes—
1224C232−1+4×C10712yes—
1225C232−1+4×C10712yes—
1226C23C25×C10711yescharacteristic
1227Q8—44no—
1228Q8—44no—
1229Q8—44no—
1230D4—28no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—21no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—21no—
1304C2×C4—44no—
1305C2×C4—44no—
1306C2×C4—44no—
1307C2×C4—44no—
1308C2×C4—44no—
1309C2×C4—44no—
1310C2×C4—44no—
1311C2×C4—44no—
1312C2×C4—82no—
1313C2×C4—82no—
1314C2×C4C23×C4×C10712yes—
1315C2×C4C23×C4×C10712yes—
1316C2×C4C23×C4×C10712yes—
1317C2×C4C23×C4×C10712yes—
1318C2×C4C23×C4×C10712yes—
1319C2×C4C23×C4×C10712yes—
1320C2×C4C23×C4×C10712yes—
1321C2×C4C23×C4×C10712yes—
1322C2×C4C23×C4×C10712yes—
1323C2×C4C23×C4×C10712yes—
1324C2×C4C23×C4×C10712yes—
1325C2×C4C23×C4×C10712yes—
1326C2×C4C23×C4×C10712yes—
1327C2×C4H(5,𝔽2)×C10712yes—
1328C22—22no—
1329C22—22no—
1330C22—22no—
1331C22—22no—
1332C22—22no—
1333C22—22no—
1334C22—22no—
1335C22—22no—
1336C22—22no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—41no—
1341C22#519×C10714yes—
1342C22C24×C4×C10711yescharacteristic
1343C22C2×H(5,𝔽2)×C10711yescharacteristic
1344C22C2×2−1+4×C10711yescharacteristic
1345C22C2×2−1+4×C10711yescharacteristic
1346C22#585×C10711yescharacteristic
1347C22#585×C10711yescharacteristic
1348C22#585×C10711yescharacteristic
1349C4—22no—
1350C4—22no—
1351C4—22no—
1352C4—22no—
1353C4—22no—
1354C4—22no—
1355C4—22no—
1356C4—22no—
1357C4—22no—
1358C4—22no—
1359C4—22no—
1360C4—22no—
1361C4—22no—
1362C4—22no—
1363C4—41no—
1364C4—41no—
1365C4—41no—
1366C4—41no—
1367C4—41no—
1368C4—41no—
1369C4—41no—
1370C4—41no—
1371C4—41no—
1372C4—41no—
1373C4—41no—
1374C4—41no—
1375C4—41no—
1376C4—41no—
1377C4—41no—
1378C2—24no—
1379C2—42no—
1380C2C2×#519×C10711yescharacteristic
1381C2C107×#342811yescharacteristic
1382C2C4×H(5,𝔽2)×C10711yescharacteristic
1383C2C107×#353511yescharacteristic
1384C2C107×#354111yescharacteristic
1385C2C107×#355311yescharacteristic
1386C2C107×#356411yescharacteristic
subgroupG/H
center, socleC23×C107C25
commutatorC22C24×C4×C107
Frattini, cosocleC23C25×C107
prime radicalC22×D4×C107C23
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×#2381C2semidirect
4. C107×#2378C2semidirect
5. C107×#2378C2semidirect
6. C107×#2371C2semidirect
7. C107×#2368C2semidirect
8. C107×#2368C2semidirect
9. C107×#2362C2semidirect
10. C107×#2360C2semidirect
11. C107×#2356C2semidirect
15. C107×#2345C2semidirect
16. C107×#2344C2semidirect
17. C107×#2336C2semidirect
18. C107×#2336C2semidirect
19. C107×#2332C2semidirect
20. C107×#2332C2semidirect
21. C107×#2329C2semidirect
22. C107×#2329C2semidirect
23. C107×#2327C2semidirect
24. C107×#2323C2semidirect
25. C107×#2320C2semidirect
28. C107×#2313C2semidirect
29. C4×C22⋊Q8×C107C2semidirect
31. C2×#387×C107C2semidirect
32. #554×C107C4semidirect
202. C4⋊Q8×C107C2×C4semidirect
203. #125×C107C2×C4semidirect
204. #125×C107C2×C4semidirect
208. C22⋊Q8×C107C2×C4semidirect
209. C22⋊Q8×C107C2×C4semidirect
210. C22⋊Q8×C107C2×C4semidirect
213. C4×Q8×C107C2×C4semidirect
221. C2×C4⋊C4×C107C2×C4semidirect
684. #34486C107direct (N × H)
695. #2382C2×C107semidirect
696. #2381C2×C107semidirect
697. #2378C2×C107semidirect
698. #2378C2×C107semidirect
699. #2371C2×C107semidirect
700. #2368C2×C107semidirect
701. #2368C2×C107semidirect
702. #2362C2×C107semidirect
703. #2360C2×C107semidirect
704. #2356C2×C107semidirect
708. #2345C2×C107semidirect
709. #2344C2×C107semidirect
710. #2336C2×C107semidirect
711. #2336C2×C107semidirect
712. #2332C2×C107semidirect
713. #2332C2×C107semidirect
714. #2329C2×C107semidirect
715. #2329C2×C107semidirect
716. #2327C2×C107semidirect
717. #2323C2×C107semidirect
718. #2320C2×C107semidirect
721. #2313C2×C107semidirect
722. C4×C22⋊Q8C2×C107semidirect
724. C2×#387C2×C107semidirect
725. C107#34486direct (N × H)
726. #554C4×C107semidirect
896. C4⋊Q8C2×C4×C107semidirect
897. #125C2×C4×C107semidirect
898. #125C2×C4×C107semidirect
902. C22⋊Q8C2×C4×C107semidirect
903. C22⋊Q8C2×C4×C107semidirect
904. C22⋊Q8C2×C4×C107semidirect
907. C4×Q8C2×C4×C107semidirect
915. 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×#554×C1072
C107×#23822
C107×#23812
C107×#23782
C107×#23712
C107×#23682
C107×#23622
C107×#23602
C107×#23562
C107×#23532
C107×#23522
C107×#23452
C107×#23442
C107×#23362
C107×#23322
C107×#23292
C107×#23272
C107×#23232
C107×#23202
C107×#23182
C107×#23132
C4×C22⋊Q8×C1072
C107×#22902
C2×#387×C1072
#34486107