Finite Group Databasebeta

← C107×#14114 #41040078

Subgroups — C107×#14114 #41040078

Order 27392.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#388×C107C211yesmaximal, characteristic
2C2×#388×C107C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C107C211yesmaximal, characteristic
4C107×#1442C211yesmaximal, characteristic, complemented
5C107×#1441C211yesmaximal, characteristic, complemented
6C107×#1439C211yesmaximal, characteristic
7C107×#1439C211yesmaximal, characteristic
8C107×#1436C211yesmaximal, characteristic, complemented
9C107×#1436C211yesmaximal, characteristic, complemented
10C107×#1436C211yesmaximal, characteristic, complemented
11C107×C4⋊#95C211yesmaximal, characteristic, complemented
12C107×#1434C211yesmaximal, characteristic, complemented
13C107×C22⋊#95C211yesmaximal, characteristic
14C107×C22⋊#95C211yesmaximal, characteristic
15C4×#95×C107C211yesmaximal, characteristic, complemented
16C24×C4×C107C2211yescharacteristic
17C22×C4⋊C4×C107C2211yescharacteristic
18C22×C4⋊C4×C107C2211yescharacteristic
19C22×C4⋊C4×C107C2211yescharacteristic
20C22×C4⋊C4×C107C2211yescharacteristic
21C22×C22⋊C4×C107C2211yescharacteristic
22C22×C22⋊C4×C107C2211yescharacteristic
23C22×C22⋊C4×C107C2211yescharacteristic
24C22×C22⋊C4×C107C2211yescharacteristic
25C22×C22⋊C4×C107C2211yescharacteristic
26C22×C22⋊C4×C107C2211yescharacteristic
27C22×C42×C107C2211yescharacteristic
28C22×C42×C107C2211yescharacteristic
29C22×C42×C107C2211yescharacteristic
30C22×C42×C107C2211yescharacteristic
31#388×C107—24no—
32#388×C107C418yescomplemented
33C4×C22⋊C4×C107—24no—
34C2×#95×C107C2211yescharacteristic
35C2×#95×C107C2211yescharacteristic
36C2×#95×C107C2211yescharacteristic
37C2×#95×C107C2211yescharacteristic
38C2×#95×C107C2211yescharacteristic
39C2×#95×C107C2211yescharacteristic
40C2×#95×C107C2211yescharacteristic
41C2×#95×C107C2211yescharacteristic
42C2×#95×C107C2211yescharacteristic
43C2×#95×C107C2211yescharacteristic
44C2×#95×C107C2211yescharacteristic
45C2×#95×C107C2211yescharacteristic
46C2×#95×C107C2211yescharacteristic
47C2×#95×C107C2211yescharacteristic
48C2×#95×C107C2211yescharacteristic
49C2×#95×C107C2211yescharacteristic
50C2×#95×C107C2211yescharacteristic
51C2×#95×C107C2211yescharacteristic
52C2×#95×C107C2211yescharacteristic
53C2×#95×C107C2211yescharacteristic
54C25×C107C2311yescharacteristic
55C23×C4×C107—22no—
56C23×C4×C107—22no—
57C23×C4×C107—22no—
58C23×C4×C107—22no—
59C23×C4×C107—22no—
60C23×C4×C107—41no—
61C23×C4×C107—41no—
62C23×C4×C107C2311yescharacteristic
63C23×C4×C107C2311yescharacteristic
64C23×C4×C107C2311yescharacteristic
65C23×C4×C107C2311yescharacteristic
66C23×C4×C107C2311yescharacteristic
67C23×C4×C107C2311yescharacteristic
68C23×C4×C107C2311yescharacteristic
69C23×C4×C107C2311yescharacteristic
70C23×C4×C107C2311yescharacteristic
71C23×C4×C107C2311yescharacteristic
72C23×C4×C107C2311yescharacteristic
73C23×C4×C107C2311yescharacteristic
74C23×C4×C107C2311yescharacteristic
75C23×C4×C107C2311yescharacteristic
76C2×C4⋊C4×C107—22no—
77C2×C4⋊C4×C107—22no—
78C2×C4⋊C4×C107—22no—
79C2×C4⋊C4×C107—22no—
80C2×C4⋊C4×C107—22no—
81C2×C4⋊C4×C107—41no—
82C2×C4⋊C4×C107—41no—
83C2×C4⋊C4×C107—41no—
84C2×C4⋊C4×C107—41no—
85C2×C4⋊C4×C107—41no—
86C2×C4⋊C4×C107—41no—
87C2×C4⋊C4×C107C2×C414yescomplemented
88C2×C22⋊C4×C107—22no—
89C2×C22⋊C4×C107—22no—
90C2×C22⋊C4×C107—22no—
91C2×C22⋊C4×C107—22no—
92C2×C22⋊C4×C107—22no—
93C2×C22⋊C4×C107—22no—
94C2×C22⋊C4×C107—22no—
95C2×C22⋊C4×C107—41no—
96C2×C22⋊C4×C107—41no—
97C2×C22⋊C4×C107—41no—
98C2×C22⋊C4×C107—41no—
99C2×C22⋊C4×C107—41no—
100C2×C22⋊C4×C107—41no—
101C2×C22⋊C4×C107C2×C414yes—
102C2×C22⋊C4×C107C2×C414yes—
103C2×C22⋊C4×C107C2×C414yes—
104C2×C22⋊C4×C107D414yes—
105C2×C22⋊C4×C107Q814yes—
106C2×C42×C107—22no—
107C2×C42×C107—22no—
108C2×C42×C107—22no—
109C2×C42×C107—22no—
110C2×C42×C107—22no—
111C2×C42×C107—22no—
112C2×C42×C107—41no—
113C2×C42×C107—41no—
114C2×C42×C107—41no—
115C2×C42×C107—41no—
116C2×C42×C107—41no—
117C2×C42×C107C2×C414yescomplemented
118#95×C107—22no—
119#95×C107—22no—
120#95×C107—22no—
121#95×C107—22no—
122#95×C107—22no—
123#95×C107—22no—
124#95×C107—22no—
125#95×C107—22no—
126#95×C107—22no—
127#95×C107—22no—
128#95×C107—22no—
129#95×C107—22no—
130#95×C107—22no—
131#95×C107—41no—
132#95×C107—41no—
133#95×C107—41no—
134#95×C107—41no—
135#95×C107—41no—
136#95×C107C2×C414yescomplemented
137#95×C107C2×C414yescomplemented
138C24×C107—21no—
139C24×C107—21no—
140C24×C107—21no—
141C24×C107—21no—
142C24×C107—21no—
143C24×C107—21no—
144C24×C107—21no—
145C24×C107—21no—
146C24×C107—21no—
147C24×C107—21no—
148C24×C107—21no—
149C24×C107—21no—
150C24×C107C22×C412yes—
151C24×C107C2×D412yes—
152C24×C107C2×Q812yes—
153C24×C107C2411yescharacteristic
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—28no—
167C22×C4×C107—21no—
168C22×C4×C107—21no—
169C22×C4×C107—21no—
170C22×C4×C107—21no—
171C22×C4×C107—21no—
172C22×C4×C107—21no—
173C22×C4×C107—21no—
174C22×C4×C107—21no—
175C22×C4×C107—21no—
176C22×C4×C107—21no—
177C22×C4×C107—21no—
178C22×C4×C107—21no—
179C22×C4×C107—21no—
180C22×C4×C107—21no—
181C22×C4×C107—21no—
182C22×C4×C107—21no—
183C22×C4×C107—21no—
184C22×C4×C107—21no—
185C22×C4×C107—21no—
186C22×C4×C107—21no—
187C22×C4×C107—21no—
188C22×C4×C107—21no—
189C22×C4×C107—21no—
190C22×C4×C107—21no—
191C22×C4×C107—21no—
192C22×C4×C107—21no—
193C22×C4×C107—21no—
194C22×C4×C107—21no—
195C22×C4×C107—21no—
196C22×C4×C107—21no—
197C22×C4×C107—21no—
198C22×C4×C107—21no—
199C22×C4×C107—21no—
200C22×C4×C107—21no—
201C22×C4×C107—21no—
202C22×C4×C107—21no—
203C22×C4×C107—21no—
204C22×C4×C107—21no—
205C22×C4×C107—21no—
206C22×C4×C107—21no—
207C22×C4×C107—21no—
208C22×C4×C107—21no—
209C22×C4×C107—21no—
210C22×C4×C107—21no—
211C22×C4×C107—21no—
212C22×C4×C107—21no—
213C22×C4×C107—21no—
214C22×C4×C107—21no—
215C22×C4×C107—21no—
216C22×C4×C107—21no—
217C22×C4×C107—21no—
218C22×C4×C107—21no—
219C22×C4×C107—21no—
220C22×C4×C107—21no—
221C22×C4×C107—21no—
222C22×C4×C107—21no—
223C22×C4×C107—21no—
224C22×C4×C107—21no—
225C22×C4×C107—21no—
226C22×C4×C107—21no—
227C22×C4×C107—21no—
228C22×C4×C107—21no—
229C22×C4×C107—21no—
230C22×C4×C107—21no—
231C22×C4×C107—21no—
232C22×C4×C107—21no—
233C22×C4×C107—21no—
234C22×C4×C107—21no—
235C22×C4×C107—44no—
236C22×C4×C107—44no—
237C22×C4×C107—44no—
238C22×C4×C107—44no—
239C22×C4×C107—44no—
240C22×C4×C107—44no—
241C22×C4×C107C22×C412yes—
242C22×C4×C107C22×C412yes—
243C22×C4×C107C22×C412yes—
244C22×C4×C107C22×C412yes—
245C22×C4×C107C22×C412yes—
246C22×C4×C107C22×C412yes—
247C22×C4×C107C2×D412yes—
248C22×C4×C107C2×D412yes—
249C22×C4×C107C2×Q812yes—
250C22×C4×C107C2×Q812yes—
251C22×C4×C107#4112yes—
252C22×C4×C107#4112yes—
253C22×C4×C107#4112yes—
254C22×C4×C107#4112yes—
255C22×C4×C107#4112yes—
256C22×C4×C107#4112yes—
257C22×C4×C107#4112yes—
258C22×C4×C107#4112yes—
259C4⋊C4×C107—44no—
260C4⋊C4×C107—44no—
261C4⋊C4×C107—44no—
262C4⋊C4×C107—44no—
263C22⋊C4×C107—28no—
264C22⋊C4×C107—44no—
265C22⋊C4×C107—44no—
266C22⋊C4×C107—44no—
267C22⋊C4×C107—44no—
268C22⋊C4×C107C4⋊C4116yescomplemented
269C42×C107—44no—
270C42×C107—44no—
271C42×C107—44no—
272C42×C107—44no—
273C23×C107—22no—
274C23×C107—22no—
275C23×C107—22no—
276C23×C107—22no—
277C23×C107—22no—
278C23×C107—22no—
279C23×C107—22no—
280C23×C107—22no—
281C23×C107—22no—
282C23×C107—22no—
283C23×C107—22no—
284C23×C107—22no—
285C23×C107—22no—
286C23×C107—22no—
287C23×C107—22no—
288C23×C107—22no—
289C23×C107—22no—
290C23×C107—22no—
291C23×C107—41no—
292C23×C107—41no—
293C23×C107—41no—
294C23×C107—41no—
295C23×C107—41no—
296C23×C107—41no—
297C23×C107—41no—
298C23×C107—41no—
299C23×C107—41no—
300C23×C107—41no—
301C23×C107—41no—
302C23×C107—41no—
303C23×C107—41no—
304C23×C107—41no—
305C23×C107—41no—
306C23×C107—41no—
307C23×C107C2×C4⋊C414yes—
308C23×C107C23×C411yescharacteristic
309C23×C107C22×D411yescharacteristic
310C23×C107C22×Q811yescharacteristic
311C23×C107C2×#4111yescharacteristic
312C23×C107C2×#4111yescharacteristic
313C23×C107C2×#4111yescharacteristic
314C23×C107C2×#4111yescharacteristic
315C23×C107C2×#4111yescharacteristic
316C23×C107C2×#4111yescharacteristic
317C23×C107C2×#4111yescharacteristic
318C23×C107C2×#4111yescharacteristic
319C23×C107H(5,𝔽2)11yescharacteristic
320C23×C107H(5,𝔽2)11yescharacteristic
321C23×C107H(5,𝔽2)11yescharacteristic
322C23×C107H(5,𝔽2)11yescharacteristic
323C2×C4×C107—22no—
324C2×C4×C107—22no—
325C2×C4×C107—22no—
326C2×C4×C107—22no—
327C2×C4×C107—22no—
328C2×C4×C107—22no—
329C2×C4×C107—22no—
330C2×C4×C107—22no—
331C2×C4×C107—22no—
332C2×C4×C107—22no—
333C2×C4×C107—22no—
334C2×C4×C107—22no—
335C2×C4×C107—22no—
336C2×C4×C107—22no—
337C2×C4×C107—22no—
338C2×C4×C107—22no—
339C2×C4×C107—22no—
340C2×C4×C107—22no—
341C2×C4×C107—22no—
342C2×C4×C107—22no—
343C2×C4×C107—22no—
344C2×C4×C107—22no—
345C2×C4×C107—22no—
346C2×C4×C107—22no—
347C2×C4×C107—22no—
348C2×C4×C107—22no—
349C2×C4×C107—22no—
350C2×C4×C107—22no—
351C2×C4×C107—22no—
352C2×C4×C107—22no—
353C2×C4×C107—22no—
354C2×C4×C107—22no—
355C2×C4×C107—22no—
356C2×C4×C107—22no—
357C2×C4×C107—22no—
358C2×C4×C107—22no—
359C2×C4×C107—22no—
360C2×C4×C107—22no—
361C2×C4×C107—22no—
362C2×C4×C107—22no—
363C2×C4×C107—22no—
364C2×C4×C107—22no—
365C2×C4×C107—22no—
366C2×C4×C107—22no—
367C2×C4×C107—22no—
368C2×C4×C107—416no—
369C2×C4×C107—41no—
370C2×C4×C107—41no—
371C2×C4×C107—41no—
372C2×C4×C107—41no—
373C2×C4×C107—41no—
374C2×C4×C107—41no—
375C2×C4×C107—41no—
376C2×C4×C107—41no—
377C2×C4×C107—41no—
378C2×C4×C107—41no—
379C2×C4×C107—41no—
380C2×C4×C107—41no—
381C2×C4×C107—41no—
382C2×C4×C107—41no—
383C2×C4×C107—41no—
384C2×C4×C107—41no—
385C2×C4×C107—41no—
386C2×C4×C107—41no—
387C2×C4×C107—41no—
388C2×C4×C107—41no—
389C2×C4×C107—41no—
390C2×C4×C107—41no—
391C2×C4×C107—41no—
392C2×C4×C107—41no—
393C2×C4×C107—41no—
394C2×C4×C107—41no—
395C2×C4×C107—41no—
396C2×C4×C107—41no—
397C2×C4×C107—41no—
398C2×C4×C107—41no—
399C2×C4×C107—41no—
400C2×C4×C107—41no—
401C2×C4×C107—41no—
402C2×C4×C107—41no—
403C2×C4×C107—41no—
404C2×C4×C107—41no—
405C2×C4×C107—41no—
406C2×C4×C107—41no—
407C2×C4×C107—41no—
408C2×C4×C107—41no—
409C2×C4×C107—41no—
410C2×C4×C107—41no—
411C2×C4×C107—41no—
412C2×C4×C107—41no—
413C2×C4×C107—41no—
414C2×C4×C107—41no—
415C2×C4×C107—41no—
416C2×C4×C107—41no—
417C2×C4×C107—41no—
418C2×C4×C107—41no—
419C2×C4×C107C2×C4⋊C414yes—
420C2×C4×C107C2×C4⋊C414yes—
421C2×C4×C107#12614yes—
422C22×C107—24no—
423C22×C107—24no—
424C22×C107—24no—
425C22×C107—42no—
426C22×C107—42no—
427C22×C107—42no—
428C22×C107—42no—
429C22×C107—42no—
430C22×C107—42no—
431C22×C107—42no—
432C22×C107—42no—
433C22×C107—42no—
434C22×C107—42no—
435C22×C107—42no—
436C22×C107—42no—
437C22×C107C22×C4⋊C411yescharacteristic
438C22×C107C4×#4111yescharacteristic
439C22×C107C4×#4111yescharacteristic
440C22×C107C4×#4111yescharacteristic
441C22×C107C4×#4111yescharacteristic
442C22×C107#51811yescharacteristic
443C22×C107#51811yescharacteristic
444C22×C107#52511yescharacteristic
445C22×C107#52511yescharacteristic
446C22×C107C2×#12611yescharacteristic
447C22×C107#52911yescharacteristic
448C22×C107#52911yescharacteristic
449C22×C107#52911yescharacteristic
450C22×C107#53311yescharacteristic
451C22×C107#53311yescharacteristic
452C22×C107#53811yescharacteristic
453C22×C107#53811yescharacteristic
454C22×C107#54011yescharacteristic
455C22×C107#54011yescharacteristic
456C22×C107#54611yescharacteristic
457C22×C107#54611yescharacteristic
458C22×C107#54611yescharacteristic
459C22×C107#54611yescharacteristic
460C22×C107#55111yescharacteristic
461C22×C107#55111yescharacteristic
462C22×C107#55111yescharacteristic
463C22×C107#55311yescharacteristic
464C22×C107#55311yescharacteristic
465C22×C107#55411yescharacteristic
466C22×C107#55411yescharacteristic
467C22×C107#55411yescharacteristic
468C22×C107#55411yescharacteristic
469C22×C107#55511yescharacteristic
470C22×C107#55511yescharacteristic
471C22×C107#55911yescharacteristic
472C4×C107—24no—
473C4×C107—24no—
474C4×C107—24no—
475C4×C107—42no—
476C4×C107—42no—
477C4×C107—42no—
478C4×C107—42no—
479C4×C107—42no—
480C4×C107—42no—
481C4×C107—42no—
482C4×C107—42no—
483C4×C107—42no—
484C4×C107—81no—
485C4×C107—81no—
486#14114C10711yesmaximal, characteristic, direct product factor, Sylow
487C2×C107—44no—
488C2×C107#229611yescharacteristic
489C2×C107C4×#12611yescharacteristic
490C2×C107#233311yescharacteristic
491C2×C107#234911yescharacteristic
492C2×C107#234911yescharacteristic
493C2×C107#237211yescharacteristic
494C2×C107#237411yescharacteristic
495C2×C107#245711yescharacteristic
496C2×C107#245911yescharacteristic
497C2×C107#247611yescharacteristic
498C2×C107#248011yescharacteristic
499C2×C107#249711yescharacteristic
500C2×C107#252211yescharacteristic
501C2×C107#257411yescharacteristic
502C2×C107#258911yescharacteristic
503C2×#388C2×C10711yescharacteristic
504C2×#388C2×C10711yescharacteristic
505C2×C4×C22⋊C4C2×C10711yescharacteristic
506#1442C2×C10711yescharacteristic, complemented
507#1441C2×C10711yescharacteristic, complemented
508#1439C2×C10711yescharacteristic
509#1439C2×C10711yescharacteristic
510#1436C2×C10711yescharacteristic, complemented
511#1436C2×C10711yescharacteristic, complemented
512#1436C2×C10711yescharacteristic, complemented
513C4⋊#95C2×C10711yescharacteristic, complemented
514#1434C2×C10711yescharacteristic, complemented
515C22⋊#95C2×C10711yescharacteristic
516C22⋊#95C2×C10711yescharacteristic
517C4×#95C2×C10711yescharacteristic, complemented
518C107#1411411yescharacteristic, direct product factor, Sylow
519C24×C4C22×C10711yescharacteristic
520C22×C4⋊C4C22×C10711yescharacteristic
521C22×C4⋊C4C22×C10711yescharacteristic
522C22×C4⋊C4C22×C10711yescharacteristic
523C22×C4⋊C4C22×C10711yescharacteristic
524C22×C22⋊C4C22×C10711yescharacteristic
525C22×C22⋊C4C22×C10711yescharacteristic
526C22×C22⋊C4C22×C10711yescharacteristic
527C22×C22⋊C4C22×C10711yescharacteristic
528C22×C22⋊C4C22×C10711yescharacteristic
529C22×C22⋊C4C22×C10711yescharacteristic
530C22×C42C22×C10711yescharacteristic
531C22×C42C22×C10711yescharacteristic
532C22×C42C22×C10711yescharacteristic
533C22×C42C22×C10711yescharacteristic
534#388—24no—
535#388C4×C10718yescomplemented
536C4×C22⋊C4—24no—
537C2×#95C22×C10711yescharacteristic
538C2×#95C22×C10711yescharacteristic
539C2×#95C22×C10711yescharacteristic
540C2×#95C22×C10711yescharacteristic
541C2×#95C22×C10711yescharacteristic
542C2×#95C22×C10711yescharacteristic
543C2×#95C22×C10711yescharacteristic
544C2×#95C22×C10711yescharacteristic
545C2×#95C22×C10711yescharacteristic
546C2×#95C22×C10711yescharacteristic
547C2×#95C22×C10711yescharacteristic
548C2×#95C22×C10711yescharacteristic
549C2×#95C22×C10711yescharacteristic
550C2×#95C22×C10711yescharacteristic
551C2×#95C22×C10711yescharacteristic
552C2×#95C22×C10711yescharacteristic
553C2×#95C22×C10711yescharacteristic
554C2×#95C22×C10711yescharacteristic
555C2×#95C22×C10711yescharacteristic
556C2×#95C22×C10711yescharacteristic
557C25C23×C10711yescharacteristic
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—22no—
561C23×C4—22no—
562C23×C4—22no—
563C23×C4—41no—
564C23×C4—41no—
565C23×C4C23×C10711yescharacteristic
566C23×C4C23×C10711yescharacteristic
567C23×C4C23×C10711yescharacteristic
568C23×C4C23×C10711yescharacteristic
569C23×C4C23×C10711yescharacteristic
570C23×C4C23×C10711yescharacteristic
571C23×C4C23×C10711yescharacteristic
572C23×C4C23×C10711yescharacteristic
573C23×C4C23×C10711yescharacteristic
574C23×C4C23×C10711yescharacteristic
575C23×C4C23×C10711yescharacteristic
576C23×C4C23×C10711yescharacteristic
577C23×C4C23×C10711yescharacteristic
578C23×C4C23×C10711yescharacteristic
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—41no—
585C2×C4⋊C4—41no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4C2×C4×C10714yescomplemented
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—41no—
599C2×C22⋊C4—41no—
600C2×C22⋊C4—41no—
601C2×C22⋊C4—41no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4C2×C4×C10714yes—
605C2×C22⋊C4C2×C4×C10714yes—
606C2×C22⋊C4C2×C4×C10714yes—
607C2×C22⋊C4D4×C10714yes—
608C2×C22⋊C4Q8×C10714yes—
609C2×C42—22no—
610C2×C42—22no—
611C2×C42—22no—
612C2×C42—22no—
613C2×C42—22no—
614C2×C42—22no—
615C2×C42—41no—
616C2×C42—41no—
617C2×C42—41no—
618C2×C42—41no—
619C2×C42—41no—
620C2×C42C2×C4×C10714yescomplemented
621#95—22no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—22no—
629#95—22no—
630#95—22no—
631#95—22no—
632#95—22no—
633#95—22no—
634#95—41no—
635#95—41no—
636#95—41no—
637#95—41no—
638#95—41no—
639#95C2×C4×C10714yescomplemented
640#95C2×C4×C10714yescomplemented
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C22×C4×C10712yes—
654C24C2×D4×C10712yes—
655C24C2×Q8×C10712yes—
656C24C24×C10711yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—28no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4C22×C4×C10712yes—
745C22×C4C22×C4×C10712yes—
746C22×C4C22×C4×C10712yes—
747C22×C4C22×C4×C10712yes—
748C22×C4C22×C4×C10712yes—
749C22×C4C22×C4×C10712yes—
750C22×C4C2×D4×C10712yes—
751C22×C4C2×D4×C10712yes—
752C22×C4C2×Q8×C10712yes—
753C22×C4C2×Q8×C10712yes—
754C22×C4#41×C10712yes—
755C22×C4#41×C10712yes—
756C22×C4#41×C10712yes—
757C22×C4#41×C10712yes—
758C22×C4#41×C10712yes—
759C22×C4#41×C10712yes—
760C22×C4#41×C10712yes—
761C22×C4#41×C10712yes—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—44no—
766C22⋊C4—28no—
767C22⋊C4—44no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—44no—
771C22⋊C4C4⋊C4×C107116yescomplemented
772C42—44no—
773C42—44no—
774C42—44no—
775C42—44no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C2×C4⋊C4×C10714yes—
811C23C23×C4×C10711yescharacteristic
812C23C22×D4×C10711yescharacteristic
813C23C22×Q8×C10711yescharacteristic
814C23C2×#41×C10711yescharacteristic
815C23C2×#41×C10711yescharacteristic
816C23C2×#41×C10711yescharacteristic
817C23C2×#41×C10711yescharacteristic
818C23C2×#41×C10711yescharacteristic
819C23C2×#41×C10711yescharacteristic
820C23C2×#41×C10711yescharacteristic
821C23C2×#41×C10711yescharacteristic
822C23H(5,𝔽2)×C10711yescharacteristic
823C23H(5,𝔽2)×C10711yescharacteristic
824C23H(5,𝔽2)×C10711yescharacteristic
825C23H(5,𝔽2)×C10711yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—416no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4C2×C4⋊C4×C10714yes—
923C2×C4C2×C4⋊C4×C10714yes—
924C2×C4#126×C10714yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C22×C4⋊C4×C10711yescharacteristic
941C22C4×#41×C10711yescharacteristic
942C22C4×#41×C10711yescharacteristic
943C22C4×#41×C10711yescharacteristic
944C22C4×#41×C10711yescharacteristic
945C22#518×C10711yescharacteristic
946C22#518×C10711yescharacteristic
947C22#525×C10711yescharacteristic
948C22#525×C10711yescharacteristic
949C22C2×#126×C10711yescharacteristic
950C22#529×C10711yescharacteristic
951C22#529×C10711yescharacteristic
952C22#529×C10711yescharacteristic
953C22#533×C10711yescharacteristic
954C22#533×C10711yescharacteristic
955C22#538×C10711yescharacteristic
956C22#538×C10711yescharacteristic
957C22#540×C10711yescharacteristic
958C22#540×C10711yescharacteristic
959C22#546×C10711yescharacteristic
960C22#546×C10711yescharacteristic
961C22#546×C10711yescharacteristic
962C22#546×C10711yescharacteristic
963C22#551×C10711yescharacteristic
964C22#551×C10711yescharacteristic
965C22#551×C10711yescharacteristic
966C22#553×C10711yescharacteristic
967C22#553×C10711yescharacteristic
968C22#554×C10711yescharacteristic
969C22#554×C10711yescharacteristic
970C22#554×C10711yescharacteristic
971C22#554×C10711yescharacteristic
972C22#555×C10711yescharacteristic
973C22#555×C10711yescharacteristic
974C22#559×C10711yescharacteristic
975C4—24no—
976C4—24no—
977C4—24no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—81no—
988C4—81no—
989C2—44no—
990C2C107×#229611yescharacteristic
991C2C4×#126×C10711yescharacteristic
992C2C107×#233311yescharacteristic
993C2C107×#234911yescharacteristic
994C2C107×#234911yescharacteristic
995C2C107×#237211yescharacteristic
996C2C107×#237411yescharacteristic
997C2C107×#245711yescharacteristic
998C2C107×#245911yescharacteristic
999C2C107×#247611yescharacteristic
1000C2C107×#248011yescharacteristic
1001C2C107×#249711yescharacteristic
1002C2C107×#252211yescharacteristic
1003C2C107×#257411yescharacteristic
1004C2C107×#258911yescharacteristic
subgroupG/H
center, socleC24×C107C24
commutatorC23C23×C4×C107
Frattini, cosocleC24C24×C107
prime radicalC25×C107C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C107 ◁ G

Complements

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

NH ≅ G/Ntype
4. C107×#1442C2semidirect
5. C107×#1441C2semidirect
8. C107×#1436C2semidirect
9. C107×#1436C2semidirect
10. C107×#1436C2semidirect
11. C107×C4⋊#95C2semidirect
12. C107×#1434C2semidirect
15. C4×#95×C107C2semidirect
32. #388×C107C4semidirect
87. C2×C4⋊C4×C107C2×C4semidirect
117. C2×C42×C107C2×C4semidirect
136. #95×C107C2×C4semidirect
137. #95×C107C2×C4semidirect
268. C22⋊C4×C107C4⋊C4semidirect
486. #14114C107direct (N × H)
506. #1442C2×C107semidirect
507. #1441C2×C107semidirect
510. #1436C2×C107semidirect
511. #1436C2×C107semidirect
512. #1436C2×C107semidirect
513. C4⋊#95C2×C107semidirect
514. #1434C2×C107semidirect
517. C4×#95C2×C107semidirect
518. C107#14114direct (N × H)
535. #388C4×C107semidirect
590. C2×C4⋊C4C2×C4×C107semidirect
620. C2×C42C2×C4×C107semidirect
639. #95C2×C4×C107semidirect
640. #95C2×C4×C107semidirect
771. C22⋊C4C4⋊C4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#388×C1072
C2×C4×C22⋊C4×C1072
C107×#14422
C107×#14412
C107×#14392
C107×#14362
C107×C4⋊#952
C107×#14342
C107×C22⋊#952
C4×#95×C1072
#14114107