Finite Group Databasebeta

← C107×#22142 #41048106

Subgroups — C107×#22142 #41048106

Order 27392.

882 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#435×C107C211yesmaximal, characteristic, complemented
2C2×#433×C107C211yesmaximal, characteristic, complemented
3C107×#2392C211yesmaximal, characteristic
4C107×#1955C211yesmaximal, characteristic, complemented
5C107×#1954C211yesmaximal, characteristic, complemented
6C107×#1954C211yesmaximal, characteristic, complemented
7C107×#1939C211yesmaximal, characteristic, complemented
8C107×#1924C211yesmaximal, characteristic, complemented
9C107×#1923C211yesmaximal, characteristic, complemented
10C107×#1870C211yesmaximal, characteristic, complemented
11C107×#1869C211yesmaximal, characteristic, complemented
12C107×#1851C211yesmaximal, characteristic, complemented
13C107×#1850C211yesmaximal, characteristic, complemented
14C107×#1798C211yesmaximal, characteristic, complemented
15C107×#1771C211yesmaximal, characteristic, complemented
16C22×M16×C107C2211yescharacteristic
17C23×C8×C107C2211yescharacteristic
18C2×C4×D4×C107C2211yescharacteristic
19C2×C4×D4×C107C2211yescharacteristic
20C2×C4×D4×C107C2211yescharacteristic
21C2×#117×C107C2211yescharacteristic
22#435×C107—24no—
23#433×C107—24no—
24C2×C4⋊C8×C107C2211yescharacteristic
25C2×C4⋊C8×C107C2211yescharacteristic
26C2×C4⋊C8×C107C2211yescharacteristic
27C2×C4⋊C8×C107C2211yescharacteristic
28C2×C4⋊C8×C107C2211yescharacteristic
29C2×C4⋊C8×C107C2211yescharacteristic
30C2×C22⋊C8×C107C2211yescharacteristic
31C2×C22⋊C8×C107C2211yescharacteristic
32C2×C22⋊C8×C107C2211yescharacteristic
33C2×C22⋊C8×C107C2211yescharacteristic
34C2×C22⋊C8×C107C2211yescharacteristic
35C2×C22⋊C8×C107C2211yescharacteristic
36C2×C22⋊C8×C107C2211yescharacteristic
37C2×C22⋊C8×C107C2211yescharacteristic
38C2×C22⋊C8×C107C2211yescharacteristic
39C2×C22⋊C8×C107C2211yescharacteristic
40C2×#97×C107C2211yescharacteristic
41C2×#97×C107C2211yescharacteristic
42C2×C4×C8×C107C2211yescharacteristic
43C2×C4×C8×C107C2211yescharacteristic
44#398×C107C411yescharacteristic
45#397×C107C411yescharacteristic
46#396×C107C411yescharacteristic
47#396×C107C411yescharacteristic
48#394×C107C411yescharacteristic
49#394×C107C411yescharacteristic
50#394×C107C411yescharacteristic
51#392×C107C411yescharacteristic
52C4×C4⋊C4×C107C2211yescharacteristic
53C4×C22⋊C4×C107C2211yescharacteristic
54C4×C22⋊C4×C107C2211yescharacteristic
55#336×C107C2211yescharacteristic
56#336×C107C2211yescharacteristic
57#336×C107C2211yescharacteristic
58#336×C107C2211yescharacteristic
59#336×C107C2211yescharacteristic
60#336×C107C2211yescharacteristic
61C22×D4×C107C2×C411yescharacteristic
62C22×D4×C107C2×C411yescharacteristic
63C22×D4×C107C2×C411yescharacteristic
64C23×C4×C107C2311yescharacteristic
65C23×C4×C107C2311yescharacteristic
66C23×C4×C107C2311yescharacteristic
67C2×M16×C107—22no—
68C2×M16×C107—41no—
69C2×M16×C107—41no—
70C22×C8×C107—22no—
71C22×C8×C107—41no—
72C22×C8×C107—41no—
73C22×C8×C107C2311yescharacteristic
74C22×C8×C107C2311yescharacteristic
75C22×C8×C107C2311yescharacteristic
76C22×C8×C107C2311yescharacteristic
77C22×C8×C107C2311yescharacteristic
78C22×C8×C107C2311yescharacteristic
79C22×C8×C107C2311yescharacteristic
80C22×C8×C107C2311yescharacteristic
81C4×D4×C107—22no—
82C4×D4×C107—22no—
83C4×D4×C107—41no—
84C4×D4×C107—41no—
85C4×D4×C107—41no—
86C4×D4×C107—41no—
87#117×C107—22no—
88#117×C107—22no—
89C2×C4⋊C4×C107C2×C411yescharacteristic
90C2×C4⋊C4×C107C2×C411yescharacteristic
91C2×C4⋊C4×C107C2×C411yescharacteristic
92C2×C4⋊C4×C107C2×C411yescharacteristic
93C2×C4⋊C4×C107C2×C411yescharacteristic
94C2×C4⋊C4×C107C2×C411yescharacteristic
95C2×C4⋊C4×C107C2×C411yescharacteristic
96C2×C22⋊C4×C107C2×C411yescharacteristic
97C2×C22⋊C4×C107C2×C411yescharacteristic
98C2×C22⋊C4×C107C2×C411yescharacteristic
99C2×C22⋊C4×C107C2×C411yescharacteristic
100C2×C22⋊C4×C107C2×C411yescharacteristic
101C2×C22⋊C4×C107C2×C411yescharacteristic
102C2×C22⋊C4×C107C2×C411yescharacteristic
103C2×C22⋊C4×C107C2×C411yescharacteristic
104C2×C22⋊C4×C107C2×C411yescharacteristic
105C2×C22⋊C4×C107C2×C411yescharacteristic
106C2×C22⋊C4×C107C2×C411yescharacteristic
107C2×C22⋊C4×C107C2×C411yescharacteristic
108C2×C42×C107C2311yescharacteristic
109C2×C42×C107C2311yescharacteristic
110C2×C42×C107C2311yescharacteristic
111C2×C42×C107C2311yescharacteristic
112C4⋊C8×C107—22no—
113C4⋊C8×C107—22no—
114C4⋊C8×C107—22no—
115C4⋊C8×C107—22no—
116C4⋊C8×C107—41no—
117C4⋊C8×C107—41no—
118C22⋊C8×C107—22no—
119C22⋊C8×C107—22no—
120C22⋊C8×C107—22no—
121C22⋊C8×C107—22no—
122C22⋊C8×C107—41no—
123C22⋊C8×C107—41no—
124C22⋊C8×C107—41no—
125C22⋊C8×C107—41no—
126C22⋊C8×C107—41no—
127C22⋊C8×C107—41no—
128#97×C107—41no—
129#97×C107D414yescomplemented
130C4×C8×C107—22no—
131C4×C8×C107—41no—
132#95×C107C2×C411yescharacteristic
133#95×C107C2×C411yescharacteristic
134#95×C107C2×C411yescharacteristic
135#95×C107C2×C411yescharacteristic
136#95×C107C2×C411yescharacteristic
137#95×C107C2×C411yescharacteristic
138C24×C107C22×C411yescharacteristic
139C24×C107C22×C411yescharacteristic
140C24×C107C22×C411yescharacteristic
141C2×D4×C107—22no—
142C2×D4×C107—22no—
143C2×D4×C107—22no—
144C2×D4×C107—22no—
145C2×D4×C107—41no—
146C2×D4×C107—41no—
147C2×D4×C107—41no—
148C2×D4×C107—41no—
149C2×D4×C107—41no—
150C22×C4×C107—21no—
151C22×C4×C107—21no—
152C22×C4×C107—21no—
153C22×C4×C107—21no—
154C22×C4×C107—21no—
155C22×C4×C107—21no—
156C22×C4×C107—21no—
157C22×C4×C107—21no—
158C22×C4×C107—21no—
159C22×C4×C107—21no—
160C22×C4×C107—21no—
161C22×C4×C107—21no—
162C22×C4×C107—21no—
163C22×C4×C107—21no—
164C22×C4×C107—21no—
165C22×C4×C107—21no—
166C22×C4×C107—21no—
167C22×C4×C107—21no—
168C22×C4×C107C22×C411yescharacteristic
169C22×C4×C107C22×C411yescharacteristic
170C22×C4×C107C22×C411yescharacteristic
171C22×C4×C107C22×C411yescharacteristic
172C22×C4×C107C22×C411yescharacteristic
173C22×C4×C107C22×C411yescharacteristic
174C22×C4×C107C22×C411yescharacteristic
175C22×C4×C107C22×C411yescharacteristic
176C22×C4×C107C22×C411yescharacteristic
177C22×C4×C107C22×C411yescharacteristic
178C22×C4×C107C22×C411yescharacteristic
179C22×C4×C107C2411yescharacteristic
180M16×C107—44no—
181C2×C8×C107—21no—
182C2×C8×C107—21no—
183C2×C8×C107—21no—
184C2×C8×C107—21no—
185C2×C8×C107—21no—
186C2×C8×C107—21no—
187C2×C8×C107—21no—
188C2×C8×C107—21no—
189C2×C8×C107—21no—
190C2×C8×C107—21no—
191C2×C8×C107—21no—
192C2×C8×C107—21no—
193C2×C8×C107—21no—
194C2×C8×C107—21no—
195C2×C8×C107—21no—
196C2×C8×C107—21no—
197C2×C8×C107—21no—
198C2×C8×C107—21no—
199C2×C8×C107—21no—
200C2×C8×C107—21no—
201C2×C8×C107—21no—
202C2×C8×C107—21no—
203C2×C8×C107—44no—
204C2×C8×C107C2×D412yes—
205C2×C8×C107C2×D412yes—
206C4⋊C4×C107—22no—
207C4⋊C4×C107—22no—
208C4⋊C4×C107—22no—
209C4⋊C4×C107—22no—
210C4⋊C4×C107—41no—
211C4⋊C4×C107—41no—
212C4⋊C4×C107—41no—
213C22⋊C4×C107—22no—
214C22⋊C4×C107—22no—
215C22⋊C4×C107—22no—
216C22⋊C4×C107—22no—
217C22⋊C4×C107—22no—
218C22⋊C4×C107—22no—
219C22⋊C4×C107—41no—
220C22⋊C4×C107—41no—
221C22⋊C4×C107—41no—
222C22⋊C4×C107—41no—
223C22⋊C4×C107—41no—
224C22⋊C4×C107—41no—
225C42×C107—21no—
226C42×C107—21no—
227C42×C107—21no—
228C42×C107—21no—
229C42×C107—21no—
230C42×C107—21no—
231C42×C107C2×D412yes—
232C42×C107#4112yes—
233C23×C107—21no—
234C23×C107—21no—
235C23×C107—21no—
236C23×C107—21no—
237C23×C107—21no—
238C23×C107—21no—
239C23×C107—21no—
240C23×C107—21no—
241C23×C107—21no—
242C23×C107—21no—
243C23×C107—21no—
244C23×C107—21no—
245C23×C107—21no—
246C23×C107—21no—
247C23×C107—21no—
248C23×C107—21no—
249C23×C107—21no—
250C23×C107—21no—
251C23×C107—21no—
252C23×C107—21no—
253C23×C107#13112yes—
254C23×C107C23×C411yescharacteristic
255D4×C107—44no—
256D4×C107—44no—
257D4×C107—44no—
258C2×C4×C107—21no—
259C2×C4×C107—21no—
260C2×C4×C107—21no—
261C2×C4×C107—21no—
262C2×C4×C107—21no—
263C2×C4×C107—21no—
264C2×C4×C107—21no—
265C2×C4×C107—21no—
266C2×C4×C107—21no—
267C2×C4×C107—21no—
268C2×C4×C107—21no—
269C2×C4×C107—21no—
270C2×C4×C107—21no—
271C2×C4×C107—21no—
272C2×C4×C107—21no—
273C2×C4×C107—21no—
274C2×C4×C107—21no—
275C2×C4×C107—21no—
276C2×C4×C107—21no—
277C2×C4×C107—21no—
278C2×C4×C107—21no—
279C2×C4×C107—21no—
280C2×C4×C107—21no—
281C2×C4×C107—21no—
282C2×C4×C107—21no—
283C2×C4×C107—21no—
284C2×C4×C107—21no—
285C2×C4×C107—21no—
286C2×C4×C107—21no—
287C2×C4×C107—21no—
288C2×C4×C107—41no—
289C2×C4×C107—41no—
290C2×C4×C107—41no—
291C2×C4×C107—41no—
292C2×C4×C107—41no—
293C2×C4×C107—41no—
294C2×C4×C107—41no—
295C2×C4×C107—41no—
296C2×C4×C107—41no—
297C2×C4×C107—41no—
298C2×C4×C107—41no—
299C2×C4×C107—41no—
300C2×C4×C107C4×D412yes—
301C2×C4×C107C4×D412yes—
302C2×C4×C107#13112yes—
303C2×C4×C107C22×D411yescharacteristic
304C2×C4×C107C2×#4111yescharacteristic
305C2×C4×C107H(5,𝔽2)11yescharacteristic
306C2×C4×C107H(5,𝔽2)11yescharacteristic
307C2×C4×C107H(5,𝔽2)11yescharacteristic
308C2×C4×C1072−1+411yescharacteristic
309C8×C107—22no—
310C8×C107—22no—
311C8×C107—41no—
312C8×C107—41no—
313C8×C107—41no—
314C8×C107—41no—
315C8×C107—41no—
316C8×C107—41no—
317C22×C107—22no—
318C22×C107—22no—
319C22×C107—22no—
320C22×C107—41no—
321C22×C107—41no—
322C22×C107—41no—
323C22×C107—41no—
324C22×C107—41no—
325C22×C107—41no—
326C22×C107—41no—
327C22×C107—41no—
328C22×C107—41no—
329C22×C107—41no—
330C22×C107—41no—
331C22×C107—41no—
332C22×C107—41no—
333C22×C107—41no—
334C22×C107—41no—
335C22×C107—41no—
336C22×C107—41no—
337C22×C107—41no—
338C22×C107C2×C4×D411yescharacteristic
339C22×C107#51811yescharacteristic
340C22×C107#52011yescharacteristic
341C22×C107C2×#13111yescharacteristic
342C22×C107C2×#13111yescharacteristic
343C22×C107#56811yescharacteristic
344C22×C107#56811yescharacteristic
345C4×C107—22no—
346C4×C107—22no—
347C4×C107—22no—
348C4×C107—41no—
349C4×C107—41no—
350C4×C107—41no—
351C4×C107—41no—
352C4×C107—41no—
353C4×C107—41no—
354C4×C107—41no—
355C4×C107—41no—
356C4×C107#53511yescharacteristic
357C4×C107#53711yescharacteristic
358C4×C107#54011yescharacteristic
359C4×C107#54211yescharacteristic
360#22142C10711yesmaximal, characteristic, direct product factor, Sylow
361C2×C107—42no—
362C2×C107—81no—
363C2×C107—81no—
364C2×C107#232411yescharacteristic
365C2×C107#293311yescharacteristic
366C2×C107#293511yescharacteristic
367C2×C107#297611yescharacteristic
368C2×C107#297611yescharacteristic
369C2×C107#299411yescharacteristic
370C2×C107#299511yescharacteristic
371C2×#435C2×C10711yescharacteristic, complemented
372C2×#433C2×C10711yescharacteristic, complemented
373#2392C2×C10711yescharacteristic
374#1955C2×C10711yescharacteristic, complemented
375#1954C2×C10711yescharacteristic, complemented
376#1954C2×C10711yescharacteristic, complemented
377#1939C2×C10711yescharacteristic, complemented
378#1924C2×C10711yescharacteristic, complemented
379#1923C2×C10711yescharacteristic, complemented
380#1870C2×C10711yescharacteristic, complemented
381#1869C2×C10711yescharacteristic, complemented
382#1851C2×C10711yescharacteristic, complemented
383#1850C2×C10711yescharacteristic, complemented
384#1798C2×C10711yescharacteristic, complemented
385#1771C2×C10711yescharacteristic, complemented
386C107#2214211yescharacteristic, direct product factor, Sylow
387C22×M16C22×C10711yescharacteristic
388C23×C8C22×C10711yescharacteristic
389C2×C4×D4C22×C10711yescharacteristic
390C2×C4×D4C22×C10711yescharacteristic
391C2×C4×D4C22×C10711yescharacteristic
392C2×#117C22×C10711yescharacteristic
393#435—24no—
394#433—24no—
395C2×C4⋊C8C22×C10711yescharacteristic
396C2×C4⋊C8C22×C10711yescharacteristic
397C2×C4⋊C8C22×C10711yescharacteristic
398C2×C4⋊C8C22×C10711yescharacteristic
399C2×C4⋊C8C22×C10711yescharacteristic
400C2×C4⋊C8C22×C10711yescharacteristic
401C2×C22⋊C8C22×C10711yescharacteristic
402C2×C22⋊C8C22×C10711yescharacteristic
403C2×C22⋊C8C22×C10711yescharacteristic
404C2×C22⋊C8C22×C10711yescharacteristic
405C2×C22⋊C8C22×C10711yescharacteristic
406C2×C22⋊C8C22×C10711yescharacteristic
407C2×C22⋊C8C22×C10711yescharacteristic
408C2×C22⋊C8C22×C10711yescharacteristic
409C2×C22⋊C8C22×C10711yescharacteristic
410C2×C22⋊C8C22×C10711yescharacteristic
411C2×#97C22×C10711yescharacteristic
412C2×#97C22×C10711yescharacteristic
413C2×C4×C8C22×C10711yescharacteristic
414C2×C4×C8C22×C10711yescharacteristic
415#398C4×C10711yescharacteristic
416#397C4×C10711yescharacteristic
417#396C4×C10711yescharacteristic
418#396C4×C10711yescharacteristic
419#394C4×C10711yescharacteristic
420#394C4×C10711yescharacteristic
421#394C4×C10711yescharacteristic
422#392C4×C10711yescharacteristic
423C4×C4⋊C4C22×C10711yescharacteristic
424C4×C22⋊C4C22×C10711yescharacteristic
425C4×C22⋊C4C22×C10711yescharacteristic
426#336C22×C10711yescharacteristic
427#336C22×C10711yescharacteristic
428#336C22×C10711yescharacteristic
429#336C22×C10711yescharacteristic
430#336C22×C10711yescharacteristic
431#336C22×C10711yescharacteristic
432C22×D4C2×C4×C10711yescharacteristic
433C22×D4C2×C4×C10711yescharacteristic
434C22×D4C2×C4×C10711yescharacteristic
435C23×C4C23×C10711yescharacteristic
436C23×C4C23×C10711yescharacteristic
437C23×C4C23×C10711yescharacteristic
438C2×M16—22no—
439C2×M16—41no—
440C2×M16—41no—
441C22×C8—22no—
442C22×C8—41no—
443C22×C8—41no—
444C22×C8C23×C10711yescharacteristic
445C22×C8C23×C10711yescharacteristic
446C22×C8C23×C10711yescharacteristic
447C22×C8C23×C10711yescharacteristic
448C22×C8C23×C10711yescharacteristic
449C22×C8C23×C10711yescharacteristic
450C22×C8C23×C10711yescharacteristic
451C22×C8C23×C10711yescharacteristic
452C4×D4—22no—
453C4×D4—22no—
454C4×D4—41no—
455C4×D4—41no—
456C4×D4—41no—
457C4×D4—41no—
458#117—22no—
459#117—22no—
460C2×C4⋊C4C2×C4×C10711yescharacteristic
461C2×C4⋊C4C2×C4×C10711yescharacteristic
462C2×C4⋊C4C2×C4×C10711yescharacteristic
463C2×C4⋊C4C2×C4×C10711yescharacteristic
464C2×C4⋊C4C2×C4×C10711yescharacteristic
465C2×C4⋊C4C2×C4×C10711yescharacteristic
466C2×C4⋊C4C2×C4×C10711yescharacteristic
467C2×C22⋊C4C2×C4×C10711yescharacteristic
468C2×C22⋊C4C2×C4×C10711yescharacteristic
469C2×C22⋊C4C2×C4×C10711yescharacteristic
470C2×C22⋊C4C2×C4×C10711yescharacteristic
471C2×C22⋊C4C2×C4×C10711yescharacteristic
472C2×C22⋊C4C2×C4×C10711yescharacteristic
473C2×C22⋊C4C2×C4×C10711yescharacteristic
474C2×C22⋊C4C2×C4×C10711yescharacteristic
475C2×C22⋊C4C2×C4×C10711yescharacteristic
476C2×C22⋊C4C2×C4×C10711yescharacteristic
477C2×C22⋊C4C2×C4×C10711yescharacteristic
478C2×C22⋊C4C2×C4×C10711yescharacteristic
479C2×C42C23×C10711yescharacteristic
480C2×C42C23×C10711yescharacteristic
481C2×C42C23×C10711yescharacteristic
482C2×C42C23×C10711yescharacteristic
483C4⋊C8—22no—
484C4⋊C8—22no—
485C4⋊C8—22no—
486C4⋊C8—22no—
487C4⋊C8—41no—
488C4⋊C8—41no—
489C22⋊C8—22no—
490C22⋊C8—22no—
491C22⋊C8—22no—
492C22⋊C8—22no—
493C22⋊C8—41no—
494C22⋊C8—41no—
495C22⋊C8—41no—
496C22⋊C8—41no—
497C22⋊C8—41no—
498C22⋊C8—41no—
499#97—41no—
500#97D4×C10714yescomplemented
501C4×C8—22no—
502C4×C8—41no—
503#95C2×C4×C10711yescharacteristic
504#95C2×C4×C10711yescharacteristic
505#95C2×C4×C10711yescharacteristic
506#95C2×C4×C10711yescharacteristic
507#95C2×C4×C10711yescharacteristic
508#95C2×C4×C10711yescharacteristic
509C24C22×C4×C10711yescharacteristic
510C24C22×C4×C10711yescharacteristic
511C24C22×C4×C10711yescharacteristic
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—41no—
517C2×D4—41no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—41no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4C22×C4×C10711yescharacteristic
540C22×C4C22×C4×C10711yescharacteristic
541C22×C4C22×C4×C10711yescharacteristic
542C22×C4C22×C4×C10711yescharacteristic
543C22×C4C22×C4×C10711yescharacteristic
544C22×C4C22×C4×C10711yescharacteristic
545C22×C4C22×C4×C10711yescharacteristic
546C22×C4C22×C4×C10711yescharacteristic
547C22×C4C22×C4×C10711yescharacteristic
548C22×C4C22×C4×C10711yescharacteristic
549C22×C4C22×C4×C10711yescharacteristic
550C22×C4C24×C10711yescharacteristic
551M16—44no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—44no—
575C2×C8C2×D4×C10712yes—
576C2×C8C2×D4×C10712yes—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—41no—
582C4⋊C4—41no—
583C4⋊C4—41no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—41no—
591C22⋊C4—41no—
592C22⋊C4—41no—
593C22⋊C4—41no—
594C22⋊C4—41no—
595C22⋊C4—41no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—21no—
602C42C2×D4×C10712yes—
603C42#41×C10712yes—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23#131×C10712yes—
625C23C23×C4×C10711yescharacteristic
626D4—44no—
627D4—44no—
628D4—44no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4C4×D4×C10712yes—
672C2×C4C4×D4×C10712yes—
673C2×C4#131×C10712yes—
674C2×C4C22×D4×C10711yescharacteristic
675C2×C4C2×#41×C10711yescharacteristic
676C2×C4H(5,𝔽2)×C10711yescharacteristic
677C2×C4H(5,𝔽2)×C10711yescharacteristic
678C2×C4H(5,𝔽2)×C10711yescharacteristic
679C2×C42−1+4×C10711yescharacteristic
680C8—22no—
681C8—22no—
682C8—41no—
683C8—41no—
684C8—41no—
685C8—41no—
686C8—41no—
687C8—41no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22C2×C4×D4×C10711yescharacteristic
710C22#518×C10711yescharacteristic
711C22#520×C10711yescharacteristic
712C22C2×#131×C10711yescharacteristic
713C22C2×#131×C10711yescharacteristic
714C22#568×C10711yescharacteristic
715C22#568×C10711yescharacteristic
716C4—22no—
717C4—22no—
718C4—22no—
719C4—41no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4#535×C10711yescharacteristic
728C4#537×C10711yescharacteristic
729C4#540×C10711yescharacteristic
730C4#542×C10711yescharacteristic
731C2—42no—
732C2—81no—
733C2—81no—
734C2C107×#232411yescharacteristic
735C2C107×#293311yescharacteristic
736C2C107×#293511yescharacteristic
737C2C107×#297611yescharacteristic
738C2C107×#297611yescharacteristic
739C2C107×#299411yescharacteristic
740C2C107×#299511yescharacteristic
subgroupG/H
centerC22×C4×C107C24
commutatorC23C23×C4×C107
Frattini, cosocleC22×C4C24×C107
socleC23×C107C23×C4
prime radical#392×C107C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#435×C107C2semidirect
2. C2×#433×C107C2semidirect
4. C107×#1955C2semidirect
5. C107×#1954C2semidirect
6. C107×#1954C2semidirect
7. C107×#1939C2semidirect
8. C107×#1924C2semidirect
9. C107×#1923C2semidirect
10. C107×#1870C2semidirect
11. C107×#1869C2semidirect
12. C107×#1851C2semidirect
13. C107×#1850C2semidirect
14. C107×#1798C2semidirect
15. C107×#1771C2semidirect
129. #97×C107D4semidirect
360. #22142C107direct (N × H)
371. C2×#435C2×C107semidirect
372. C2×#433C2×C107semidirect
374. #1955C2×C107semidirect
375. #1954C2×C107semidirect
376. #1954C2×C107semidirect
377. #1939C2×C107semidirect
378. #1924C2×C107semidirect
379. #1923C2×C107semidirect
380. #1870C2×C107semidirect
381. #1869C2×C107semidirect
382. #1851C2×C107semidirect
383. #1850C2×C107semidirect
384. #1798C2×C107semidirect
385. #1771C2×C107semidirect
386. C107#22142direct (N × H)
500. #97D4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#435×C1072
C2×#433×C1072
C107×#23922
C107×#19552
C107×#19542
C107×#19392
C107×#19242
C107×#19232
C107×#18702
C107×#18692
C107×#18512
C107×#18502
C107×#17982
C107×#17712
#22142107