Finite Group Databasebeta

← C107×#18974 #41044938

Subgroups — C107×#18974 #41044938

Order 27392.

930 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3546C211yesmaximal, characteristic
2C107×#3254C211yesmaximal, characteristic, complemented
3C107×#3248C211yesmaximal, characteristic, complemented
4C107×#3228C211yesmaximal, characteristic, complemented
5C107×#1654C211yesmaximal, characteristic, complemented
6C107×#1652C211yesmaximal, characteristic, complemented
7C107×#1650C211yesmaximal, characteristic, complemented
8C107×#1647C211yesmaximal, characteristic, complemented
9C107×#1642C211yesmaximal, characteristic, complemented
10C107×#1641C211yesmaximal, characteristic, complemented
11C107×#1639C211yesmaximal, characteristic, complemented
12C107×#1639C211yesmaximal, characteristic, complemented
13C107×#1547C211yesmaximal, characteristic, complemented
14C107×#1495C211yesmaximal, characteristic, complemented
15C107×#1480C211yesmaximal, characteristic, complemented
16#560×C107—22no—
17#556×C107C2211yescharacteristic
18#553×C107—21no—
19#550×C107—21no—
20#550×C107C2211yescharacteristic
21#547×C107C2211yescharacteristic
22#546×C107—21no—
23#546×C107—21no—
24D42×C107C2211yescharacteristic
25#542×C107—21no—
26#538×C107—22no—
27#537×C107—21no—
28#535×C107—21no—
29#535×C107—21no—
30#533×C107C2211yescharacteristic, complemented
31#532×C107C2211yescharacteristic
32#532×C107C2211yescharacteristic
33#529×C107C2211yescharacteristic
34#500×C107C2211yescharacteristic, complemented
35#498×C107C2211yescharacteristic, complemented
36#486×C107C2211yescharacteristic
37#486×C107C2211yescharacteristic
38#482×C107—22no—
39#479×C107—21no—
40#478×C107—22no—
41#477×C107—21no—
42#475×C107C2211yescharacteristic, complemented
43#474×C107C2211yescharacteristic
44#474×C107C2211yescharacteristic
45#474×C107C2211yescharacteristic, complemented
46#468×C107—21no—
47#468×C107—21no—
48#467×C107—21no—
49#465×C107—21no—
50#464×C107—21no—
51#462×C107C2211yescharacteristic, complemented
52#461×C107C2211yescharacteristic
53#461×C107C2211yescharacteristic
54#461×C107C2211yescharacteristic, complemented
55#460×C107—21no—
56#431×C107C2211yescharacteristic, complemented
57#423×C107C2211yescharacteristic, complemented
58C2×C4⋊C8×C107C2211yescharacteristic, complemented
59#332×C107C2211yescharacteristic, complemented
60#332×C107C2211yescharacteristic, complemented
61#331×C107C2211yescharacteristic
62#331×C107C2211yescharacteristic
63Q8⋊C8×C107C2211yescharacteristic, complemented
64Q8⋊C8×C107C2211yescharacteristic, complemented
65D4⋊C8×C107C2211yescharacteristic
66D4⋊C8×C107C2211yescharacteristic
67D4⋊C8×C107C2211yescharacteristic
68D4⋊C8×C107C2211yescharacteristic
69D4⋊C8×C107C2211yescharacteristic, complemented
70D4⋊C8×C107C2211yescharacteristic, complemented
71C2×#41×C107—21no—
72C2×#41×C107—21no—
73C2×#41×C107—21no—
74C2×#41×C107—21no—
75C22×D4×C107—21no—
76C22×D4×C107—21no—
77C2×Q16×C107—21no—
78C2×SD16×C107—21no—
79C2×SD16×C107—21no—
80C2×SD16×C107—21no—
81C2×M16×C107—21no—
82C22×C8×C107—21no—
83C4⋊Q8×C107D411yescharacteristic
84C4⋊Q8×C107C2311yescharacteristic
85C4⋊Q8×C107C2311yescharacteristic
86C4⋊Q8×C107C2311yescharacteristic
87#127×C107—22no—
88#127×C107—21no—
89#127×C107D411yescharacteristic
90#127×C107C2311yescharacteristic
91#126×C107—22no—
92#126×C107—22no—
93#126×C107—21no—
94#125×C107—21no—
95#125×C107D411yescharacteristic
96#124×C107—22no—
97#124×C107—21no—
98#124×C107—21no—
99#124×C107—21no—
100#124×C107D411yescharacteristic
101#123×C107—22no—
102#123×C107—22no—
103#123×C107—21no—
104#123×C107—22no—
105C22⋊Q8×C107—22no—
106C22⋊Q8×C107—21no—
107C22⋊Q8×C107—21no—
108C22⋊Q8×C107—21no—
109C22⋊Q8×C107—21no—
110C22⋊Q8×C107D411yescharacteristic
111#121×C107—22no—
112#121×C107—22no—
113#121×C107—22no—
114#121×C107—22no—
115#121×C107—22no—
116#121×C107—21no—
117#121×C107—22no—
118#121×C107—21no—
119#121×C107—21no—
120#121×C107—21no—
121#121×C107—21no—
122#121×C107—21no—
123#121×C107D411yescharacteristic
124#121×C107D411yescharacteristic
125#121×C107D411yescharacteristic
126#121×C107D412yes—
127#120×C107—22no—
128#120×C107—22no—
129#120×C107—22no—
130#120×C107—22no—
131C4×Q8×C107—21no—
132C4×Q8×C107—21no—
133C4×Q8×C107—21no—
134C4×Q8×C107C2311yescharacteristic
135C4×D4×C107—22no—
136C4×D4×C107—21no—
137C4×D4×C107—21no—
138C4×D4×C107—21no—
139C4×D4×C107—21no—
140C4×D4×C107D412yes—
141C4×D4×C107C2311yescharacteristic
142C4×D4×C107C2311yescharacteristic
143C4×D4×C107C2311yescharacteristic
144#117×C107—21no—
145#117×C107—21no—
146#117×C107—21no—
147C2×C4⋊C4×C107—21no—
148C2×C22⋊C4×C107—22no—
149C2×C42×C107C2311yescharacteristic
150#107×C107—21no—
151#107×C107—21no—
152#107×C107—21no—
153#107×C107—22no—
154#106×C107—21no—
155#106×C107—22no—
156C4⋊C8×C107—21no—
157C4⋊C8×C107—21no—
158C4⋊C8×C107—21no—
159C4⋊C8×C107C2311yescharacteristic
160C4⋊C8×C107C2311yescharacteristic
161C4⋊C8×C107C2311yescharacteristic
162C4⋊C8×C107C2311yescharacteristic
163#103×C107—21no—
164#103×C107—21no—
165#103×C107—21no—
166#103×C107—21no—
167#103×C107—21no—
168#102×C107—21no—
169#102×C107—21no—
170#102×C107—21no—
171#102×C107—22no—
172#102×C107—22no—
173C22⋊C8×C107—21no—
174C4×C8×C107C2311yescharacteristic
175C4×C8×C107C2311yescharacteristic
176C24×C107—22no—
177#41×C107—81no—
178#41×C107—81no—
179#41×C107—81no—
180#41×C107—81no—
181#41×C107—81no—
182#41×C107—81no—
183#41×C107—81no—
184#41×C107—81no—
185C2×Q8×C107—21no—
186C2×Q8×C107—21no—
187C2×Q8×C107—21no—
188C2×Q8×C107—21no—
189C2×Q8×C107C2×D411yescharacteristic
190C2×D4×C107—22no—
191C2×D4×C107—22no—
192C2×D4×C107—22no—
193C2×D4×C107—22no—
194C2×D4×C107—22no—
195C2×D4×C107—21no—
196C2×D4×C107—21no—
197C2×D4×C107—22no—
198C2×D4×C107—21no—
199C2×D4×C107—21no—
200C2×D4×C107—21no—
201C2×D4×C107—21no—
202C2×D4×C107—21no—
203C2×D4×C107—81no—
204C2×D4×C107—81no—
205C2×D4×C107—81no—
206C2×D4×C107—81no—
207C2×D4×C107C2×D411yescharacteristic
208C2×D4×C107C2×D411yescharacteristic
209C2×D4×C107C2×D411yescharacteristic
210C2×D4×C107C2×D412yes—
211C22×C4×C107—22no—
212C22×C4×C107—22no—
213C22×C4×C107—21no—
214C22×C4×C107—21no—
215C22×C4×C107—21no—
216C22×C4×C107—22no—
217C22×C4×C107C2×D411yescharacteristic
218C22×C4×C107C2×D411yescharacteristic
219C22×C4×C107C2×D411yescharacteristic
220Q16×C107—81no—
221SD16×C107—81no—
222SD16×C107—81no—
223SD16×C107—81no—
224M16×C107—81no—
225C2×C8×C107—21no—
226C2×C8×C107—21no—
227C2×C8×C107—21no—
228C2×C8×C107—21no—
229C2×C8×C107—21no—
230C2×C8×C107—21no—
231C2×C8×C107—81no—
232C4⋊C4×C107—22no—
233C4⋊C4×C107—22no—
234C4⋊C4×C107—21no—
235C4⋊C4×C107—21no—
236C4⋊C4×C107—21no—
237C4⋊C4×C107—21no—
238C4⋊C4×C107—21no—
239C4⋊C4×C107—21no—
240C4⋊C4×C107—21no—
241C4⋊C4×C107—21no—
242C4⋊C4×C107—21no—
243C4⋊C4×C107—21no—
244C4⋊C4×C107—41no—
245C4⋊C4×C107—41no—
246C4⋊C4×C107C2×D411yescharacteristic
247C4⋊C4×C107C2×D411yescharacteristic
248C4⋊C4×C107C2×D411yescharacteristic
249C4⋊C4×C107C2×D411yescharacteristic
250C4⋊C4×C107C2×D412yes—
251C22⋊C4×C107—22no—
252C22⋊C4×C107—22no—
253C22⋊C4×C107—22no—
254C22⋊C4×C107—22no—
255C22⋊C4×C107—22no—
256C22⋊C4×C107—21no—
257C22⋊C4×C107—21no—
258C22⋊C4×C107—21no—
259C22⋊C4×C107—21no—
260C22⋊C4×C107—21no—
261C22⋊C4×C107—21no—
262C22⋊C4×C107—22no—
263C22⋊C4×C107—22no—
264C22⋊C4×C107—21no—
265C22⋊C4×C107—21no—
266C22⋊C4×C107—21no—
267C22⋊C4×C107—41no—
268C42×C107—22no—
269C42×C107—21no—
270C42×C107—41no—
271C42×C107C2×D411yescharacteristic
272C42×C107C2×D411yescharacteristic
273C42×C107C2×D411yescharacteristic
274C42×C107C2411yescharacteristic
275C23×C107—21no—
276C23×C107—21no—
277C23×C107—22no—
278C23×C107—21no—
279C23×C107—82no—
280C23×C107—82no—
281C23×C107—82no—
282C23×C107#12011yescharacteristic
283Q8×C107—21no—
284Q8×C107—21no—
285Q8×C107—41no—
286Q8×C107—41no—
287Q8×C107—41no—
288Q8×C107—41no—
289Q8×C107—41no—
290Q8×C107—41no—
291Q8×C107—81no—
292D4×C107—21no—
293D4×C107—21no—
294D4×C107—21no—
295D4×C107—21no—
296D4×C107—21no—
297D4×C107—21no—
298D4×C107—42no—
299D4×C107—41no—
300D4×C107—41no—
301D4×C107—41no—
302D4×C107—41no—
303D4×C107—81no—
304D4×C107—81no—
305D4×C107—81no—
306D4×C107—81no—
307D4×C107—81no—
308D4×C107—82no—
309D4×C107—82no—
310D4×C107—82no—
311D4×C107—82no—
312D4×C107—82no—
313D4×C107—82no—
314C2×C4×C107—21no—
315C2×C4×C107—21no—
316C2×C4×C107—21no—
317C2×C4×C107—21no—
318C2×C4×C107—21no—
319C2×C4×C107—21no—
320C2×C4×C107—21no—
321C2×C4×C107—22no—
322C2×C4×C107—21no—
323C2×C4×C107—21no—
324C2×C4×C107—41no—
325C2×C4×C107—41no—
326C2×C4×C107—41no—
327C2×C4×C107—41no—
328C2×C4×C107—41no—
329C2×C4×C107—41no—
330C2×C4×C107—41no—
331C2×C4×C107—41no—
332C2×C4×C107—41no—
333C2×C4×C107—82no—
334C2×C4×C107—82no—
335C2×C4×C107—82no—
336C2×C4×C107#12011yescharacteristic
337C2×C4×C107#12011yescharacteristic
338C2×C4×C107#12011yescharacteristic
339C2×C4×C107C22×D411yescharacteristic
340C2×C4×C107C22×D411yescharacteristic
341C2×C4×C107C22×D411yescharacteristic
342C8×C107—41no—
343C8×C107—41no—
344C8×C107—41no—
345C8×C107—41no—
346C8×C107—41no—
347C8×C107—41no—
348C22×C107—21no—
349C22×C107—21no—
350C22×C107—21no—
351C22×C107—41no—
352C22×C107—41no—
353C22×C107—41no—
354C22×C107—41no—
355C22×C107—42no—
356C22×C107—42no—
357C22×C107—41no—
358C22×C107—41no—
359C22×C107—42no—
360C22×C107—41no—
361C22×C107—41no—
362C22×C107—41no—
363C22×C107—164no—
364C22×C107C2×#12011yescharacteristic
365C4×C107—21no—
366C4×C107—21no—
367C4×C107—21no—
368C4×C107—21no—
369C4×C107—41no—
370C4×C107—41no—
371C4×C107—41no—
372C4×C107—41no—
373C4×C107—42no—
374C4×C107—41no—
375C4×C107—81no—
376C4×C107—81no—
377C4×C107#57611yescharacteristic
378C4×C107#57611yescharacteristic
379C4×C107#57711yescharacteristic
380C4×C107#57711yescharacteristic
381#18974C10711yesmaximal, characteristic, direct product factor, Sylow
382C2×C107—41no—
383C2×C107—81no—
384C2×C107—82no—
385C2×C107—81no—
386C2×C107—81no—
387C2×C107#301211yescharacteristic
388C2×C107#301211yescharacteristic
389C2×C107#302211yescharacteristic
390#3546C2×C10711yescharacteristic
391#3254C2×C10711yescharacteristic, complemented
392#3248C2×C10711yescharacteristic, complemented
393#3228C2×C10711yescharacteristic, complemented
394#1654C2×C10711yescharacteristic, complemented
395#1652C2×C10711yescharacteristic, complemented
396#1650C2×C10711yescharacteristic, complemented
397#1647C2×C10711yescharacteristic, complemented
398#1642C2×C10711yescharacteristic, complemented
399#1641C2×C10711yescharacteristic, complemented
400#1639C2×C10711yescharacteristic, complemented
401#1639C2×C10711yescharacteristic, complemented
402#1547C2×C10711yescharacteristic, complemented
403#1495C2×C10711yescharacteristic, complemented
404#1480C2×C10711yescharacteristic, complemented
405C107#1897411yescharacteristic, direct product factor, Sylow
406#560—22no—
407#556C22×C10711yescharacteristic
408#553—21no—
409#550—21no—
410#550C22×C10711yescharacteristic
411#547C22×C10711yescharacteristic
412#546—21no—
413#546—21no—
414D42C22×C10711yescharacteristic
415#542—21no—
416#538—22no—
417#537—21no—
418#535—21no—
419#535—21no—
420#533C22×C10711yescharacteristic, complemented
421#532C22×C10711yescharacteristic
422#532C22×C10711yescharacteristic
423#529C22×C10711yescharacteristic
424#500C22×C10711yescharacteristic, complemented
425#498C22×C10711yescharacteristic, complemented
426#486C22×C10711yescharacteristic
427#486C22×C10711yescharacteristic
428#482—22no—
429#479—21no—
430#478—22no—
431#477—21no—
432#475C22×C10711yescharacteristic, complemented
433#474C22×C10711yescharacteristic
434#474C22×C10711yescharacteristic
435#474C22×C10711yescharacteristic, complemented
436#468—21no—
437#468—21no—
438#467—21no—
439#465—21no—
440#464—21no—
441#462C22×C10711yescharacteristic, complemented
442#461C22×C10711yescharacteristic
443#461C22×C10711yescharacteristic
444#461C22×C10711yescharacteristic, complemented
445#460—21no—
446#431C22×C10711yescharacteristic, complemented
447#423C22×C10711yescharacteristic, complemented
448C2×C4⋊C8C22×C10711yescharacteristic, complemented
449#332C22×C10711yescharacteristic, complemented
450#332C22×C10711yescharacteristic, complemented
451#331C22×C10711yescharacteristic
452#331C22×C10711yescharacteristic
453Q8⋊C8C22×C10711yescharacteristic, complemented
454Q8⋊C8C22×C10711yescharacteristic, complemented
455D4⋊C8C22×C10711yescharacteristic
456D4⋊C8C22×C10711yescharacteristic
457D4⋊C8C22×C10711yescharacteristic
458D4⋊C8C22×C10711yescharacteristic
459D4⋊C8C22×C10711yescharacteristic, complemented
460D4⋊C8C22×C10711yescharacteristic, complemented
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C22×D4—21no—
466C22×D4—21no—
467C2×Q16—21no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—21no—
471C2×M16—21no—
472C22×C8—21no—
473C4⋊Q8D4×C10711yescharacteristic
474C4⋊Q8C23×C10711yescharacteristic
475C4⋊Q8C23×C10711yescharacteristic
476C4⋊Q8C23×C10711yescharacteristic
477#127—22no—
478#127—21no—
479#127D4×C10711yescharacteristic
480#127C23×C10711yescharacteristic
481#126—22no—
482#126—22no—
483#126—21no—
484#125—21no—
485#125D4×C10711yescharacteristic
486#124—22no—
487#124—21no—
488#124—21no—
489#124—21no—
490#124D4×C10711yescharacteristic
491#123—22no—
492#123—22no—
493#123—21no—
494#123—22no—
495C22⋊Q8—22no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8D4×C10711yescharacteristic
501#121—22no—
502#121—22no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—21no—
507#121—22no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121D4×C10711yescharacteristic
514#121D4×C10711yescharacteristic
515#121D4×C10711yescharacteristic
516#121D4×C10712yes—
517#120—22no—
518#120—22no—
519#120—22no—
520#120—22no—
521C4×Q8—21no—
522C4×Q8—21no—
523C4×Q8—21no—
524C4×Q8C23×C10711yescharacteristic
525C4×D4—22no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4D4×C10712yes—
531C4×D4C23×C10711yescharacteristic
532C4×D4C23×C10711yescharacteristic
533C4×D4C23×C10711yescharacteristic
534#117—21no—
535#117—21no—
536#117—21no—
537C2×C4⋊C4—21no—
538C2×C22⋊C4—22no—
539C2×C42C23×C10711yescharacteristic
540#107—21no—
541#107—21no—
542#107—21no—
543#107—22no—
544#106—21no—
545#106—22no—
546C4⋊C8—21no—
547C4⋊C8—21no—
548C4⋊C8—21no—
549C4⋊C8C23×C10711yescharacteristic
550C4⋊C8C23×C10711yescharacteristic
551C4⋊C8C23×C10711yescharacteristic
552C4⋊C8C23×C10711yescharacteristic
553#103—21no—
554#103—21no—
555#103—21no—
556#103—21no—
557#103—21no—
558#102—21no—
559#102—21no—
560#102—21no—
561#102—22no—
562#102—22no—
563C22⋊C8—21no—
564C4×C8C23×C10711yescharacteristic
565C4×C8C23×C10711yescharacteristic
566C24—22no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573#41—81no—
574#41—81no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8C2×D4×C10711yescharacteristic
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4C2×D4×C10711yescharacteristic
598C2×D4C2×D4×C10711yescharacteristic
599C2×D4C2×D4×C10711yescharacteristic
600C2×D4C2×D4×C10712yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4C2×D4×C10711yescharacteristic
608C22×C4C2×D4×C10711yescharacteristic
609C22×C4C2×D4×C10711yescharacteristic
610Q16—81no—
611SD16—81no—
612SD16—81no—
613SD16—81no—
614M16—81no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—81no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4C2×D4×C10711yescharacteristic
637C4⋊C4C2×D4×C10711yescharacteristic
638C4⋊C4C2×D4×C10711yescharacteristic
639C4⋊C4C2×D4×C10711yescharacteristic
640C4⋊C4C2×D4×C10712yes—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—41no—
658C42—22no—
659C42—21no—
660C42—41no—
661C42C2×D4×C10711yescharacteristic
662C42C2×D4×C10711yescharacteristic
663C42C2×D4×C10711yescharacteristic
664C42C24×C10711yescharacteristic
665C23—21no—
666C23—21no—
667C23—22no—
668C23—21no—
669C23—82no—
670C23—82no—
671C23—82no—
672C23#120×C10711yescharacteristic
673Q8—21no—
674Q8—21no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681Q8—81no—
682D4—21no—
683D4—21no—
684D4—21no—
685D4—21no—
686D4—21no—
687D4—21no—
688D4—42no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—81no—
694D4—81no—
695D4—81no—
696D4—81no—
697D4—82no—
698D4—81no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4#120×C10711yescharacteristic
727C2×C4#120×C10711yescharacteristic
728C2×C4#120×C10711yescharacteristic
729C2×C4C22×D4×C10711yescharacteristic
730C2×C4C22×D4×C10711yescharacteristic
731C2×C4C22×D4×C10711yescharacteristic
732C8—41no—
733C8—41no—
734C8—41no—
735C8—41no—
736C8—41no—
737C8—41no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—42no—
746C22—42no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—164no—
754C22C2×#120×C10711yescharacteristic
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—42no—
764C4—41no—
765C4—81no—
766C4—81no—
767C4#576×C10711yescharacteristic
768C4#576×C10711yescharacteristic
769C4#577×C10711yescharacteristic
770C4#577×C10711yescharacteristic
771C2—41no—
772C2—81no—
773C2—81no—
774C2—82no—
775C2—81no—
776C2C107×#301211yescharacteristic
777C2C107×#301211yescharacteristic
778C2C107×#302211yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC42C24×C107
prime radicalC107×#3546C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#3254C2semidirect
3. C107×#3248C2semidirect
4. C107×#3228C2semidirect
5. C107×#1654C2semidirect
6. C107×#1652C2semidirect
7. C107×#1650C2semidirect
8. C107×#1647C2semidirect
9. C107×#1642C2semidirect
10. C107×#1641C2semidirect
11. C107×#1639C2semidirect
12. C107×#1639C2semidirect
13. C107×#1547C2semidirect
14. C107×#1495C2semidirect
15. C107×#1480C2semidirect
30. #533×C107C22semidirect
34. #500×C107C22semidirect
35. #498×C107C22semidirect
42. #475×C107C22semidirect
45. #474×C107C22semidirect
51. #462×C107C22semidirect
54. #461×C107C22semidirect
56. #431×C107C22semidirect
57. #423×C107C22semidirect
58. C2×C4⋊C8×C107C22semidirect
59. #332×C107C22semidirect
60. #332×C107C22semidirect
63. Q8⋊C8×C107C22semidirect
64. Q8⋊C8×C107C22semidirect
69. D4⋊C8×C107C22semidirect
70. D4⋊C8×C107C22semidirect
381. #18974C107direct (N × H)
391. #3254C2×C107semidirect
392. #3248C2×C107semidirect
393. #3228C2×C107semidirect
394. #1654C2×C107semidirect
395. #1652C2×C107semidirect
396. #1650C2×C107semidirect
397. #1647C2×C107semidirect
398. #1642C2×C107semidirect
399. #1641C2×C107semidirect
400. #1639C2×C107semidirect
401. #1639C2×C107semidirect
402. #1547C2×C107semidirect
403. #1495C2×C107semidirect
404. #1480C2×C107semidirect
405. C107#18974direct (N × H)
420. #533C22×C107semidirect
424. #500C22×C107semidirect
425. #498C22×C107semidirect
432. #475C22×C107semidirect
435. #474C22×C107semidirect
441. #462C22×C107semidirect
444. #461C22×C107semidirect
446. #431C22×C107semidirect
447. #423C22×C107semidirect
448. C2×C4⋊C8C22×C107semidirect
449. #332C22×C107semidirect
450. #332C22×C107semidirect
453. Q8⋊C8C22×C107semidirect
454. Q8⋊C8C22×C107semidirect
459. D4⋊C8C22×C107semidirect
460. D4⋊C8C22×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#35462
C107×#32542
C107×#32482
C107×#32282
C107×#16542
C107×#16522
C107×#16502
C107×#16472
C107×#16422
C107×#16412
C107×#16392
C107×#15472
C107×#14952
C107×#14802
#18974107