Finite Group Databasebeta

← C107×#16263 #41042227

Subgroups — C107×#16263 #41042227

Order 27392.

2058 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊Q8×C107C211yesmaximal, characteristic, complemented
2C2×#394×C107C212yesmaximal
3C2×#393×C107C211yesmaximal, characteristic, complemented
4C2×#386×C107C211yesmaximal, characteristic
5C2×#381×C107C211yesmaximal, characteristic, complemented
6C107×#1446C211yesmaximal, characteristic, complemented
7C107×#1444C211yesmaximal, characteristic, complemented
8C107×#1441C212yesmaximal, complemented
9C107×#1440C212yesmaximal, complemented
10C107×#1439C212yesmaximal, complemented
11C107×#1439C211yesmaximal, characteristic, complemented
12C23×Q8×C107C2211yescharacteristic
13C23×D4×C107C2211yescharacteristic
14C24×C4×C107C2211yescharacteristic
15C2×C22⋊Q8×C107—24no—
16C2×C22⋊Q8×C107—28no—
17C22×C4⋊C4×C107C2212yes—
18C22×C4⋊C4×C107C2211yescharacteristic
19C22×C4⋊C4×C107C2212yes—
20C22×C22⋊C4×C107C2211yescharacteristic
21C22×C22⋊C4×C107C2212yes—
22C22×C22⋊C4×C107C2212yes—
23C22×C22⋊C4×C107C2212yes—
24C22×C22⋊C4×C107C2212yes—
25C22×C22⋊C4×C107C2211yescharacteristic
26C22×C22⋊C4×C107C2211yescharacteristic
27#394×C107—28no—
28#393×C107—24no—
29#386×C107—24no—
30#381×C107—24no—
31C2×#95×C107C2212yes—
32C2×#95×C107C2212yes—
33C2×#95×C107C2212yes—
34C2×#95×C107C2211yescharacteristic
35C2×#95×C107C2211yescharacteristic
36C2×#95×C107C2211yescharacteristic
37C2×#95×C107C2212yes—
38C2×#95×C107C2212yes—
39C2×#95×C107C2212yes—
40C2×#95×C107C2211yescharacteristic
41C25×C107C2311yescharacteristic
42C25×C107C2311yescharacteristic
43C22×Q8×C107—24no—
44C22×Q8×C107—22no—
45C22×Q8×C107—22no—
46C22×Q8×C107—22no—
47C22×Q8×C107—42no—
48C22×D4×C107—22no—
49C22×D4×C107—22no—
50C22×D4×C107—24no—
51C22×D4×C107—22no—
52C22×D4×C107—42no—
53C23×C4×C107—24no—
54C23×C4×C107—22no—
55C23×C4×C107—22no—
56C23×C4×C107—42no—
57C23×C4×C107D414yes—
58C23×C4×C107C2311yescharacteristic
59C23×C4×C107C2312yes—
60C23×C4×C107C2311yescharacteristic
61C23×C4×C107C2312yes—
62C23×C4×C107C2312yes—
63C23×C4×C107C2311yescharacteristic
64C23×C4×C107C2312yes—
65C23×C4×C107C2311yescharacteristic
66C23×C4×C107C2311yescharacteristic
67C22⋊Q8×C107—232no—
68C2×C4⋊C4×C107—24no—
69C2×C4⋊C4×C107—22no—
70C2×C4⋊C4×C107—24no—
71C2×C4⋊C4×C107—24no—
72C2×C4⋊C4×C107—24no—
73C2×C4⋊C4×C107—24no—
74C2×C4⋊C4×C107—24no—
75C2×C4⋊C4×C107—42no—
76C2×C22⋊C4×C107—24no—
77C2×C22⋊C4×C107—24no—
78C2×C22⋊C4×C107—22no—
79C2×C22⋊C4×C107—24no—
80C2×C22⋊C4×C107—24no—
81C2×C22⋊C4×C107—24no—
82C2×C22⋊C4×C107—22no—
83C2×C22⋊C4×C107—22no—
84C2×C22⋊C4×C107—24no—
85C2×C22⋊C4×C107—22no—
86C2×C22⋊C4×C107—24no—
87C2×C22⋊C4×C107—24no—
88C2×C22⋊C4×C107—22no—
89C2×C22⋊C4×C107—42no—
90C2×C22⋊C4×C107—42no—
91C2×C22⋊C4×C107—42no—
92C2×C22⋊C4×C107—42no—
93C2×C22⋊C4×C107—42no—
94C2×C22⋊C4×C107D418yes—
95#95×C107—24no—
96#95×C107—22no—
97#95×C107—22no—
98#95×C107—22no—
99#95×C107—24no—
100#95×C107—24no—
101#95×C107—42no—
102#95×C107—42no—
103#95×C107—42no—
104#95×C107D414yescomplemented
105C24×C107—21no—
106C24×C107—21no—
107C24×C107—21no—
108C24×C107—21no—
109C24×C107—22no—
110C24×C107—22no—
111C24×C107—22no—
112C24×C107—21no—
113C24×C107—21no—
114C24×C107—21no—
115C24×C107—21no—
116C24×C107—22no—
117C24×C107—21no—
118C24×C107—21no—
119C24×C107—22no—
120C24×C107—22no—
121C24×C107—22no—
122C24×C107—21no—
123C24×C107—21no—
124C24×C107C2×D412yes—
125C24×C107C2×D414yes—
126C24×C107#4112yes—
127C24×C107C2411yescharacteristic
128C2×Q8×C107—28no—
129C2×Q8×C107—48no—
130C2×Q8×C107—48no—
131C2×Q8×C107—44no—
132C2×Q8×C107—44no—
133C2×D4×C107—28no—
134C2×D4×C107—48no—
135C2×D4×C107—48no—
136C2×D4×C107—44no—
137C2×D4×C107—44no—
138C22×C4×C107—22no—
139C22×C4×C107—22no—
140C22×C4×C107—28no—
141C22×C4×C107—21no—
142C22×C4×C107—21no—
143C22×C4×C107—22no—
144C22×C4×C107—22no—
145C22×C4×C107—22no—
146C22×C4×C107—22no—
147C22×C4×C107—22no—
148C22×C4×C107—22no—
149C22×C4×C107—22no—
150C22×C4×C107—22no—
151C22×C4×C107—22no—
152C22×C4×C107—22no—
153C22×C4×C107—22no—
154C22×C4×C107—21no—
155C22×C4×C107—21no—
156C22×C4×C107—22no—
157C22×C4×C107—22no—
158C22×C4×C107—22no—
159C22×C4×C107—22no—
160C22×C4×C107—22no—
161C22×C4×C107—22no—
162C22×C4×C107—22no—
163C22×C4×C107—22no—
164C22×C4×C107—22no—
165C22×C4×C107—22no—
166C22×C4×C107—22no—
167C22×C4×C107—28no—
168C22×C4×C107—21no—
169C22×C4×C107—22no—
170C22×C4×C107—21no—
171C22×C4×C107—21no—
172C22×C4×C107—22no—
173C22×C4×C107—21no—
174C22×C4×C107—22no—
175C22×C4×C107—22no—
176C22×C4×C107—22no—
177C22×C4×C107—22no—
178C22×C4×C107—22no—
179C22×C4×C107—22no—
180C22×C4×C107—22no—
181C22×C4×C107—22no—
182C22×C4×C107—22no—
183C22×C4×C107—21no—
184C22×C4×C107—21no—
185C22×C4×C107—44no—
186C22×C4×C107—48no—
187C22×C4×C107—48no—
188C22×C4×C107C2×D414yes—
189C22×C4×C107C2×D414yes—
190C22×C4×C107C2×D412yes—
191C22×C4×C107C2×D414yes—
192C22×C4×C107C2×D412yes—
193C22×C4×C107C2×D412yes—
194C22×C4×C107#4112yes—
195C22×C4×C107#4112yes—
196C4⋊C4×C107—28no—
197C4⋊C4×C107—216no—
198C4⋊C4×C107—48no—
199C22⋊C4×C107—216no—
200C22⋊C4×C107—48no—
201C22⋊C4×C107—48no—
202C22⋊C4×C107—48no—
203C22⋊C4×C107—44no—
204C22⋊C4×C107—44no—
205C22⋊C4×C107—44no—
206C23×C107—22no—
207C23×C107—22no—
208C23×C107—22no—
209C23×C107—22no—
210C23×C107—22no—
211C23×C107—22no—
212C23×C107—24no—
213C23×C107—24no—
214C23×C107—24no—
215C23×C107—24no—
216C23×C107—24no—
217C23×C107—24no—
218C23×C107—22no—
219C23×C107—24no—
220C23×C107—24no—
221C23×C107—22no—
222C23×C107—22no—
223C23×C107—42no—
224C23×C107—42no—
225C23×C107—42no—
226C23×C107—42no—
227C23×C107—41no—
228C23×C107—41no—
229C23×C107—41no—
230C23×C107—41no—
231C23×C107—42no—
232C23×C107—42no—
233C23×C107—41no—
234C23×C107—41no—
235C23×C107—41no—
236C23×C107—41no—
237C23×C107—41no—
238C23×C107—41no—
239C23×C107—42no—
240C23×C107—42no—
241C23×C107—42no—
242C23×C107—42no—
243C23×C107—42no—
244C23×C107—42no—
245C23×C107—42no—
246C23×C107—42no—
247C23×C107—41no—
248C23×C107—41no—
249C23×C107—42no—
250C23×C107—42no—
251C23×C107#12014yes—
252C23×C107C22×D411yescharacteristic
253C23×C107C22×D412yes—
254C23×C107C22×D411yescharacteristic
255C23×C107C2×#4111yescharacteristic
256C23×C107C2×#4111yescharacteristic
257C23×C107C2×#4111yescharacteristic
258C23×C107H(5,𝔽2)12yes—
259C23×C107H(5,𝔽2)12yes—
260C23×C1072−1+412yes—
261C23×C1072−1+411yescharacteristic
262C23×C1072−1+411yescharacteristic
263Q8×C107—416no—
264D4×C107—416no—
265C2×C4×C107—22no—
266C2×C4×C107—22no—
267C2×C4×C107—24no—
268C2×C4×C107—24no—
269C2×C4×C107—24no—
270C2×C4×C107—24no—
271C2×C4×C107—22no—
272C2×C4×C107—22no—
273C2×C4×C107—22no—
274C2×C4×C107—22no—
275C2×C4×C107—24no—
276C2×C4×C107—24no—
277C2×C4×C107—24no—
278C2×C4×C107—24no—
279C2×C4×C107—24no—
280C2×C4×C107—24no—
281C2×C4×C107—24no—
282C2×C4×C107—24no—
283C2×C4×C107—416no—
284C2×C4×C107—41no—
285C2×C4×C107—42no—
286C2×C4×C107—42no—
287C2×C4×C107—42no—
288C2×C4×C107—42no—
289C2×C4×C107—41no—
290C2×C4×C107—42no—
291C2×C4×C107—42no—
292C2×C4×C107—42no—
293C2×C4×C107—42no—
294C2×C4×C107—42no—
295C2×C4×C107—42no—
296C2×C4×C107—42no—
297C2×C4×C107—42no—
298C2×C4×C107—42no—
299C2×C4×C107—42no—
300C2×C4×C107—42no—
301C2×C4×C107—41no—
302C2×C4×C107—41no—
303C2×C4×C107—41no—
304C2×C4×C107—41no—
305C2×C4×C107—41no—
306C2×C4×C107—41no—
307C2×C4×C107—42no—
308C2×C4×C107—42no—
309C2×C4×C107—42no—
310C2×C4×C107—42no—
311C2×C4×C107—42no—
312C2×C4×C107—42no—
313C2×C4×C107—42no—
314C2×C4×C107—42no—
315C2×C4×C107—42no—
316C2×C4×C107—42no—
317C2×C4×C107—42no—
318C2×C4×C107#12114yes—
319C22×C107—24no—
320C22×C107—24no—
321C22×C107—24no—
322C22×C107—42no—
323C22×C107—42no—
324C22×C107—42no—
325C22×C107—42no—
326C22×C107—44no—
327C22×C107—44no—
328C22×C107—44no—
329C22×C107—44no—
330C22×C107—42no—
331C22×C107—42no—
332C22×C107—42no—
333C22×C107—44no—
334C22×C107—44no—
335C22×C107—81no—
336C22×C107—81no—
337C22×C107—81no—
338C22×C107—81no—
339C22×C107—82no—
340C22×C107—82no—
341C22×C107C2×#12011yescharacteristic
342C22×C107C2×#12111yescharacteristic
343C22×C107#52511yescharacteristic
344C22×C107#53411yescharacteristic
345C22×C107#53511yescharacteristic
346C22×C107#53611yescharacteristic
347C22×C107#53611yescharacteristic
348C22×C107#53612yes—
349C22×C107#53612yes—
350C22×C107#53712yes—
351C22×C107#53912yes—
352C22×C107#54212yes—
353C22×C107#54212yes—
354C22×C107D4212yes—
355C22×C107#54612yes—
356C22×C107#54612yes—
357C22×C107#54612yes—
358C22×C107#54711yescharacteristic
359C22×C107#54811yescharacteristic
360C22×C107#55211yescharacteristic
361C22×C107#55611yescharacteristic
362C22×C107#56212yes—
363C22×C107#56212yes—
364C4×C107—24no—
365C4×C107—44no—
366C4×C107—42no—
367C4×C107—42no—
368C4×C107—44no—
369C4×C107—44no—
370C4×C107—81no—
371C4×C107—81no—
372C4×C107—82no—
373#16263C10711yesmaximal, characteristic, direct product factor, Sylow
374C2×C107—44no—
375C2×C107—82no—
376C2×C107#240411yescharacteristic
377C2×C107#241011yescharacteristic
378C2×C107#241511yescharacteristic
379C2×C107#261411yescharacteristic
380C2×C107#262011yescharacteristic
381C2×C107#263811yescharacteristic
382C2×C107#267212yes—
383C2×C107#268112yes—
384C2×C107#268712yes—
385C2×C107#270012yes—
386C2×C107#281611yescharacteristic
387C22×C22⋊Q8C2×C10711yescharacteristic, complemented
388C2×#394C2×C10712yes—
389C2×#393C2×C10711yescharacteristic, complemented
390C2×#386C2×C10711yescharacteristic
391C2×#381C2×C10711yescharacteristic, complemented
392#1446C2×C10711yescharacteristic, complemented
393#1444C2×C10711yescharacteristic, complemented
394#1441C2×C10712yescomplemented
395#1440C2×C10712yescomplemented
396#1439C2×C10711yescharacteristic, complemented
397#1439C2×C10712yescomplemented
398C107#1626311yescharacteristic, direct product factor, Sylow
399C23×Q8C22×C10711yescharacteristic
400C23×D4C22×C10711yescharacteristic
401C24×C4C22×C10711yescharacteristic
402C2×C22⋊Q8—24no—
403C2×C22⋊Q8—28no—
404C22×C4⋊C4C22×C10712yes—
405C22×C4⋊C4C22×C10711yescharacteristic
406C22×C4⋊C4C22×C10712yes—
407C22×C22⋊C4C22×C10711yescharacteristic
408C22×C22⋊C4C22×C10712yes—
409C22×C22⋊C4C22×C10712yes—
410C22×C22⋊C4C22×C10712yes—
411C22×C22⋊C4C22×C10712yes—
412C22×C22⋊C4C22×C10711yescharacteristic
413C22×C22⋊C4C22×C10711yescharacteristic
414#394—28no—
415#393—24no—
416#386—24no—
417#381—24no—
418C2×#95C22×C10712yes—
419C2×#95C22×C10712yes—
420C2×#95C22×C10712yes—
421C2×#95C22×C10711yescharacteristic
422C2×#95C22×C10711yescharacteristic
423C2×#95C22×C10711yescharacteristic
424C2×#95C22×C10712yes—
425C2×#95C22×C10712yes—
426C2×#95C22×C10712yes—
427C2×#95C22×C10711yescharacteristic
428C25C23×C10711yescharacteristic
429C25C23×C10711yescharacteristic
430C22×Q8—24no—
431C22×Q8—22no—
432C22×Q8—22no—
433C22×Q8—22no—
434C22×Q8—42no—
435C22×D4—22no—
436C22×D4—22no—
437C22×D4—24no—
438C22×D4—22no—
439C22×D4—42no—
440C23×C4—24no—
441C23×C4—22no—
442C23×C4—22no—
443C23×C4—42no—
444C23×C4D4×C10714yes—
445C23×C4C23×C10711yescharacteristic
446C23×C4C23×C10712yes—
447C23×C4C23×C10711yescharacteristic
448C23×C4C23×C10712yes—
449C23×C4C23×C10712yes—
450C23×C4C23×C10712yes—
451C23×C4C23×C10711yescharacteristic
452C23×C4C23×C10711yescharacteristic
453C23×C4C23×C10711yescharacteristic
454C22⋊Q8—232no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—42no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—42no—
477C2×C22⋊C4—42no—
478C2×C22⋊C4—42no—
479C2×C22⋊C4—42no—
480C2×C22⋊C4—42no—
481C2×C22⋊C4D4×C10718yes—
482#95—24no—
483#95—22no—
484#95—22no—
485#95—22no—
486#95—24no—
487#95—24no—
488#95—42no—
489#95—42no—
490#95—42no—
491#95D4×C10714yescomplemented
492C24—21no—
493C24—21no—
494C24—21no—
495C24—21no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—21no—
500C24—21no—
501C24—21no—
502C24—21no—
503C24—22no—
504C24—21no—
505C24—21no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—21no—
510C24—21no—
511C24C2×D4×C10712yes—
512C24C2×D4×C10714yes—
513C24#41×C10712yes—
514C24C24×C10711yescharacteristic
515C2×Q8—28no—
516C2×Q8—48no—
517C2×Q8—48no—
518C2×Q8—44no—
519C2×Q8—44no—
520C2×D4—28no—
521C2×D4—48no—
522C2×D4—48no—
523C2×D4—44no—
524C2×D4—44no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—28no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—28no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—44no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4C2×D4×C10714yes—
576C22×C4C2×D4×C10714yes—
577C22×C4C2×D4×C10712yes—
578C22×C4C2×D4×C10714yes—
579C22×C4C2×D4×C10712yes—
580C22×C4C2×D4×C10712yes—
581C22×C4#41×C10712yes—
582C22×C4#41×C10712yes—
583C4⋊C4—28no—
584C4⋊C4—216no—
585C4⋊C4—48no—
586C22⋊C4—216no—
587C22⋊C4—48no—
588C22⋊C4—48no—
589C22⋊C4—48no—
590C22⋊C4—44no—
591C22⋊C4—44no—
592C22⋊C4—44no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—22no—
606C23—24no—
607C23—24no—
608C23—22no—
609C23—22no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—42no—
619C23—42no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—41no—
635C23—41no—
636C23—42no—
637C23—42no—
638C23#120×C10714yes—
639C23C22×D4×C10711yescharacteristic
640C23C22×D4×C10712yes—
641C23C22×D4×C10711yescharacteristic
642C23C2×#41×C10711yescharacteristic
643C23C2×#41×C10711yescharacteristic
644C23C2×#41×C10711yescharacteristic
645C23H(5,𝔽2)×C10712yes—
646C23H(5,𝔽2)×C10712yes—
647C232−1+4×C10712yes—
648C232−1+4×C10711yescharacteristic
649C232−1+4×C10711yescharacteristic
650Q8—416no—
651D4—416no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—416no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4#121×C10714yes—
706C22—24no—
707C22—24no—
708C22—24no—
709C22—42no—
710C22—42no—
711C22—44no—
712C22—44no—
713C22—44no—
714C22—44no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—44no—
721C22—44no—
722C22—81no—
723C22—82no—
724C22—82no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22C2×#120×C10711yescharacteristic
729C22C2×#121×C10711yescharacteristic
730C22#525×C10711yescharacteristic
731C22#534×C10711yescharacteristic
732C22#535×C10711yescharacteristic
733C22#536×C10711yescharacteristic
734C22#536×C10711yescharacteristic
735C22#536×C10712yes—
736C22#536×C10712yes—
737C22#537×C10712yes—
738C22#539×C10712yes—
739C22#542×C10712yes—
740C22#542×C10712yes—
741C22D42×C10712yes—
742C22#546×C10712yes—
743C22#546×C10712yes—
744C22#546×C10712yes—
745C22#547×C10711yescharacteristic
746C22#548×C10711yescharacteristic
747C22#552×C10711yescharacteristic
748C22#556×C10711yescharacteristic
749C22#562×C10712yes—
750C22#562×C10712yes—
751C4—24no—
752C4—42no—
753C4—44no—
754C4—42no—
755C4—44no—
756C4—44no—
757C4—82no—
758C4—81no—
759C4—81no—
760C2—44no—
761C2—82no—
762C2C107×#240411yescharacteristic
763C2C107×#241011yescharacteristic
764C2C107×#241511yescharacteristic
765C2C107×#261411yescharacteristic
766C2C107×#262011yescharacteristic
767C2C107×#263811yescharacteristic
768C2C107×#267212yes—
769C2C107×#268112yes—
770C2C107×#268712yes—
771C2C107×#270012yes—
772C2C107×#281611yescharacteristic
subgroupG/H
center, socleC24×C107C24
commutator, Frattini, cosocleC24C24×C107
prime radicalC23×D4×C107C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊Q8×C107C2semidirect
3. C2×#393×C107C2semidirect
5. C2×#381×C107C2semidirect
6. C107×#1446C2semidirect
7. C107×#1444C2semidirect
8. C107×#1441C2semidirect
9. C107×#1440C2semidirect
10. C107×#1439C2semidirect
11. C107×#1439C2semidirect
104. #95×C107D4semidirect
373. #16263C107direct (N × H)
387. C22×C22⋊Q8C2×C107semidirect
389. C2×#393C2×C107semidirect
391. C2×#381C2×C107semidirect
392. #1446C2×C107semidirect
393. #1444C2×C107semidirect
394. #1441C2×C107semidirect
395. #1440C2×C107semidirect
396. #1439C2×C107semidirect
397. #1439C2×C107semidirect
398. C107#16263direct (N × H)
491. #95D4×C107semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊Q8×C1072
C2×#394×C1072
C2×#393×C1072
C2×#386×C1072
C2×#381×C1072
C107×#14462
C107×#14442
C107×#14412
C107×#14402
C107×#14392
#16263107