Finite Group Databasebeta

← C107×#18705 #41044669

Subgroups — C107×#18705 #41044669

Order 27392.

938 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3546C211yesmaximal, characteristic
2C107×#3252C211yesmaximal, characteristic, complemented
3C107×#3235C211yesmaximal, characteristic, complemented
4C107×#3167C211yesmaximal, characteristic, complemented
5C107×#1654C211yesmaximal, characteristic, complemented
6C107×#1652C211yesmaximal, characteristic, complemented
7C107×#1641C211yesmaximal, characteristic, complemented
8C107×#1639C211yesmaximal, characteristic, complemented
9C107×#1638C211yesmaximal, characteristic, complemented
10C107×#1635C211yesmaximal, characteristic, complemented
11C107×#1631C211yesmaximal, characteristic, complemented
12C107×#1629C211yesmaximal, characteristic, complemented
13C107×#1557C211yesmaximal, characteristic, complemented
14C107×#1494C211yesmaximal, characteristic, complemented
15C107×#1492C211yesmaximal, 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#501×C107—21no—
35#498×C107C2211yescharacteristic, complemented
36#492×C107C2211yescharacteristic
37#490×C107—21no—
38#487×C107C2211yescharacteristic, complemented
39#486×C107C2211yescharacteristic
40#482×C107—21no—
41#482×C107—21no—
42#479×C107—21no—
43#477×C107C2211yescharacteristic, complemented
44#476×C107C2211yescharacteristic
45#476×C107C2211yescharacteristic
46#476×C107C2211yescharacteristic, complemented
47#474×C107C2211yescharacteristic
48#474×C107C2211yescharacteristic, complemented
49#470×C107—21no—
50#468×C107—21no—
51#465×C107—22no—
52#464×C107—21no—
53#462×C107C2211yescharacteristic, complemented
54#461×C107C2211yescharacteristic
55C4×SD16×C107—22no—
56#432×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—22no—
79C2×SD16×C107—21no—
80C2×M16×C107—21no—
81C22×C8×C107—21no—
82C4⋊Q8×C107D411yescharacteristic
83C4⋊Q8×C107C2311yescharacteristic
84C4⋊Q8×C107C2311yescharacteristic
85C4⋊Q8×C107C2311yescharacteristic
86#127×C107—22no—
87#127×C107—21no—
88#127×C107D411yescharacteristic
89#127×C107C2311yescharacteristic
90#126×C107—22no—
91#126×C107—22no—
92#126×C107—21no—
93#125×C107—21no—
94#125×C107D411yescharacteristic
95#124×C107—22no—
96#124×C107—21no—
97#124×C107—21no—
98#124×C107—21no—
99#124×C107D411yescharacteristic
100#123×C107—22no—
101#123×C107—22no—
102#123×C107—21no—
103#123×C107—22no—
104C22⋊Q8×C107—22no—
105C22⋊Q8×C107—21no—
106C22⋊Q8×C107—21no—
107C22⋊Q8×C107—21no—
108C22⋊Q8×C107—21no—
109C22⋊Q8×C107D411yescharacteristic
110#121×C107—22no—
111#121×C107—22no—
112#121×C107—22no—
113#121×C107—22no—
114#121×C107—22no—
115#121×C107—21no—
116#121×C107—22no—
117#121×C107—21no—
118#121×C107—21no—
119#121×C107—21no—
120#121×C107—21no—
121#121×C107—21no—
122#121×C107D412yes—
123#121×C107D411yescharacteristic
124#121×C107D411yescharacteristic
125#121×C107D411yescharacteristic
126#120×C107—22no—
127#120×C107—22no—
128#120×C107—22no—
129#120×C107—22no—
130C4×Q8×C107—21no—
131C4×Q8×C107—21no—
132C4×Q8×C107—21no—
133C4×Q8×C107C2311yescharacteristic
134C4×D4×C107—22no—
135C4×D4×C107—21no—
136C4×D4×C107—21no—
137C4×D4×C107—21no—
138C4×D4×C107—21no—
139C4×D4×C107D412yes—
140C4×D4×C107C2311yescharacteristic
141C4×D4×C107C2311yescharacteristic
142C4×D4×C107C2311yescharacteristic
143#117×C107—21no—
144#117×C107—21no—
145#117×C107—21no—
146C2×C4⋊C4×C107—21no—
147C2×C22⋊C4×C107—22no—
148C2×C42×C107C2311yescharacteristic
149#107×C107—21no—
150#107×C107—21no—
151#107×C107—21no—
152#106×C107—22no—
153#106×C107—21no—
154#106×C107—21no—
155#106×C107—21no—
156C4⋊C8×C107—21no—
157C4⋊C8×C107C2311yescharacteristic
158C4⋊C8×C107C2311yescharacteristic
159C4⋊C8×C107C2311yescharacteristic
160C4⋊C8×C107C2311yescharacteristic
161#103×C107—21no—
162#103×C107—22no—
163#103×C107—21no—
164#103×C107—21no—
165#102×C107—22no—
166#102×C107—21no—
167#102×C107—21no—
168#102×C107—21no—
169#102×C107—21no—
170#102×C107—21no—
171C22⋊C8×C107—21no—
172#97×C107—21no—
173C4×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—44no—
222SD16×C107—81no—
223M16×C107—81no—
224C2×C8×C107—21no—
225C2×C8×C107—21no—
226C2×C8×C107—21no—
227C2×C8×C107—21no—
228C2×C8×C107—21no—
229C2×C8×C107—21no—
230C2×C8×C107—42no—
231C4⋊C4×C107—22no—
232C4⋊C4×C107—22no—
233C4⋊C4×C107—21no—
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—41no—
244C4⋊C4×C107—41no—
245C4⋊C4×C107C2×D411yescharacteristic
246C4⋊C4×C107C2×D412yes—
247C4⋊C4×C107C2×D411yescharacteristic
248C4⋊C4×C107C2×D411yescharacteristic
249C4⋊C4×C107C2×D411yescharacteristic
250C22⋊C4×C107—22no—
251C22⋊C4×C107—22no—
252C22⋊C4×C107—22no—
253C22⋊C4×C107—22no—
254C22⋊C4×C107—22no—
255C22⋊C4×C107—21no—
256C22⋊C4×C107—21no—
257C22⋊C4×C107—21no—
258C22⋊C4×C107—21no—
259C22⋊C4×C107—21no—
260C22⋊C4×C107—21no—
261C22⋊C4×C107—22no—
262C22⋊C4×C107—22no—
263C22⋊C4×C107—21no—
264C22⋊C4×C107—21no—
265C22⋊C4×C107—21no—
266C22⋊C4×C107—41no—
267C42×C107—22no—
268C42×C107—21no—
269C42×C107—41no—
270C42×C107C2×D411yescharacteristic
271C42×C107C2×D411yescharacteristic
272C42×C107C2×D411yescharacteristic
273C42×C107C2411yescharacteristic
274C23×C107—21no—
275C23×C107—21no—
276C23×C107—22no—
277C23×C107—21no—
278C23×C107—82no—
279C23×C107—82no—
280C23×C107—82no—
281C23×C107#12011yescharacteristic
282Q8×C107—21no—
283Q8×C107—21no—
284Q8×C107—42no—
285Q8×C107—41no—
286Q8×C107—41no—
287Q8×C107—41no—
288Q8×C107—41no—
289Q8×C107—81no—
290D4×C107—21no—
291D4×C107—21no—
292D4×C107—21no—
293D4×C107—21no—
294D4×C107—21no—
295D4×C107—21no—
296D4×C107—42no—
297D4×C107—41no—
298D4×C107—41no—
299D4×C107—41no—
300D4×C107—41no—
301D4×C107—81no—
302D4×C107—81no—
303D4×C107—81no—
304D4×C107—82no—
305D4×C107—81no—
306D4×C107—81no—
307D4×C107—82no—
308D4×C107—82no—
309D4×C107—82no—
310D4×C107—82no—
311D4×C107—82no—
312C2×C4×C107—21no—
313C2×C4×C107—21no—
314C2×C4×C107—21no—
315C2×C4×C107—21no—
316C2×C4×C107—21no—
317C2×C4×C107—21no—
318C2×C4×C107—21no—
319C2×C4×C107—22no—
320C2×C4×C107—21no—
321C2×C4×C107—21no—
322C2×C4×C107—41no—
323C2×C4×C107—41no—
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—82no—
332C2×C4×C107—82no—
333C2×C4×C107—82no—
334C2×C4×C107#12011yescharacteristic
335C2×C4×C107#12011yescharacteristic
336C2×C4×C107#12011yescharacteristic
337C2×C4×C107C22×D411yescharacteristic
338C2×C4×C107C22×D411yescharacteristic
339C2×C4×C107C22×D411yescharacteristic
340C8×C107—22no—
341C8×C107—41no—
342C8×C107—41no—
343C8×C107—41no—
344C8×C107—41no—
345C8×C107—41no—
346C22×C107—21no—
347C22×C107—21no—
348C22×C107—21no—
349C22×C107—41no—
350C22×C107—41no—
351C22×C107—42no—
352C22×C107—41no—
353C22×C107—41no—
354C22×C107—41no—
355C22×C107—42no—
356C22×C107—41no—
357C22×C107—42no—
358C22×C107—41no—
359C22×C107—41no—
360C22×C107—41no—
361C22×C107—164no—
362C22×C107C2×#12011yescharacteristic
363C4×C107—21no—
364C4×C107—21no—
365C4×C107—21no—
366C4×C107—21no—
367C4×C107—41no—
368C4×C107—42no—
369C4×C107—41no—
370C4×C107—41no—
371C4×C107—41no—
372C4×C107—41no—
373C4×C107—81no—
374C4×C107—81no—
375C4×C107#57611yescharacteristic
376C4×C107#57711yescharacteristic
377C4×C107#57711yescharacteristic
378C4×C107#57711yescharacteristic
379#18705C10711yesmaximal, characteristic, direct product factor, Sylow
380C2×C107—41no—
381C2×C107—81no—
382C2×C107—82no—
383C2×C107—81no—
384C2×C107—81no—
385C2×C107#300911yescharacteristic
386C2×C107#301211yescharacteristic
387C2×C107#301811yescharacteristic
388#3546C2×C10711yescharacteristic
389#3252C2×C10711yescharacteristic, complemented
390#3235C2×C10711yescharacteristic, complemented
391#3167C2×C10711yescharacteristic, complemented
392#1654C2×C10711yescharacteristic, complemented
393#1652C2×C10711yescharacteristic, complemented
394#1641C2×C10711yescharacteristic, complemented
395#1639C2×C10711yescharacteristic, complemented
396#1638C2×C10711yescharacteristic, complemented
397#1635C2×C10711yescharacteristic, complemented
398#1631C2×C10711yescharacteristic, complemented
399#1629C2×C10711yescharacteristic, complemented
400#1557C2×C10711yescharacteristic, complemented
401#1494C2×C10711yescharacteristic, complemented
402#1492C2×C10711yescharacteristic, complemented
403C107#1870511yescharacteristic, direct product factor, Sylow
404#560—22no—
405#556C22×C10711yescharacteristic
406#553—21no—
407#550—21no—
408#550C22×C10711yescharacteristic
409#547C22×C10711yescharacteristic
410#546—21no—
411#546—21no—
412D42C22×C10711yescharacteristic
413#542—21no—
414#538—22no—
415#537—21no—
416#535—21no—
417#535—21no—
418#533C22×C10711yescharacteristic, complemented
419#532C22×C10711yescharacteristic
420#532C22×C10711yescharacteristic
421#529C22×C10711yescharacteristic
422#501—21no—
423#498C22×C10711yescharacteristic, complemented
424#492C22×C10711yescharacteristic
425#490—21no—
426#487C22×C10711yescharacteristic, complemented
427#486C22×C10711yescharacteristic
428#482—21no—
429#482—21no—
430#479—21no—
431#477C22×C10711yescharacteristic, complemented
432#476C22×C10711yescharacteristic
433#476C22×C10711yescharacteristic
434#476C22×C10711yescharacteristic, complemented
435#474C22×C10711yescharacteristic
436#474C22×C10711yescharacteristic, complemented
437#470—21no—
438#468—21no—
439#465—22no—
440#464—21no—
441#462C22×C10711yescharacteristic, complemented
442#461C22×C10711yescharacteristic
443C4×SD16—22no—
444#432C22×C10711yescharacteristic, complemented
445#423C22×C10711yescharacteristic, complemented
446C2×C4×C8C22×C10711yescharacteristic, complemented
447#332C22×C10711yescharacteristic, complemented
448#332C22×C10711yescharacteristic, complemented
449#331C22×C10711yescharacteristic
450#331C22×C10711yescharacteristic
451Q8⋊C8C22×C10711yescharacteristic, complemented
452Q8⋊C8C22×C10711yescharacteristic, complemented
453D4⋊C8C22×C10711yescharacteristic
454D4⋊C8C22×C10711yescharacteristic
455D4⋊C8C22×C10711yescharacteristic
456D4⋊C8C22×C10711yescharacteristic
457D4⋊C8C22×C10711yescharacteristic, complemented
458D4⋊C8C22×C10711yescharacteristic, complemented
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C22×D4—21no—
464C22×D4—21no—
465C2×Q16—21no—
466C2×SD16—22no—
467C2×SD16—21no—
468C2×M16—21no—
469C22×C8—21no—
470C4⋊Q8D4×C10711yescharacteristic
471C4⋊Q8C23×C10711yescharacteristic
472C4⋊Q8C23×C10711yescharacteristic
473C4⋊Q8C23×C10711yescharacteristic
474#127—22no—
475#127—21no—
476#127D4×C10711yescharacteristic
477#127C23×C10711yescharacteristic
478#126—22no—
479#126—22no—
480#126—21no—
481#125—21no—
482#125D4×C10711yescharacteristic
483#124—22no—
484#124—21no—
485#124—21no—
486#124—21no—
487#124D4×C10711yescharacteristic
488#123—22no—
489#123—22no—
490#123—21no—
491#123—22no—
492C22⋊Q8—22no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8D4×C10711yescharacteristic
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—21no—
504#121—22no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121D4×C10711yescharacteristic
511#121D4×C10711yescharacteristic
512#121D4×C10711yescharacteristic
513#121D4×C10712yes—
514#120—22no—
515#120—22no—
516#120—22no—
517#120—22no—
518C4×Q8—21no—
519C4×Q8—21no—
520C4×Q8—21no—
521C4×Q8C23×C10711yescharacteristic
522C4×D4—22no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4D4×C10712yes—
528C4×D4C23×C10711yescharacteristic
529C4×D4C23×C10711yescharacteristic
530C4×D4C23×C10711yescharacteristic
531#117—21no—
532#117—21no—
533#117—21no—
534C2×C4⋊C4—21no—
535C2×C22⋊C4—22no—
536C2×C42C23×C10711yescharacteristic
537#107—21no—
538#107—21no—
539#107—21no—
540#106—22no—
541#106—21no—
542#106—21no—
543#106—21no—
544C4⋊C8—21no—
545C4⋊C8C23×C10711yescharacteristic
546C4⋊C8C23×C10711yescharacteristic
547C4⋊C8C23×C10711yescharacteristic
548C4⋊C8C23×C10711yescharacteristic
549#103—21no—
550#103—22no—
551#103—21no—
552#103—21no—
553#102—22no—
554#102—21no—
555#102—21no—
556#102—21no—
557#102—21no—
558#102—21no—
559C22⋊C8—21no—
560#97—21no—
561C4×C8—21no—
562C4×C8C23×C10711yescharacteristic
563C4×C8C23×C10711yescharacteristic
564C24—22no—
565#41—81no—
566#41—81no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8C2×D4×C10711yescharacteristic
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4C2×D4×C10711yescharacteristic
596C2×D4C2×D4×C10711yescharacteristic
597C2×D4C2×D4×C10711yescharacteristic
598C2×D4C2×D4×C10712yes—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4C2×D4×C10711yescharacteristic
606C22×C4C2×D4×C10711yescharacteristic
607C22×C4C2×D4×C10711yescharacteristic
608Q16—81no—
609SD16—44no—
610SD16—81no—
611M16—81no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—42no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4C2×D4×C10711yescharacteristic
634C4⋊C4C2×D4×C10712yes—
635C4⋊C4C2×D4×C10711yescharacteristic
636C4⋊C4C2×D4×C10711yescharacteristic
637C4⋊C4C2×D4×C10711yescharacteristic
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—41no—
655C42—22no—
656C42—21no—
657C42—41no—
658C42C2×D4×C10711yescharacteristic
659C42C2×D4×C10711yescharacteristic
660C42C2×D4×C10711yescharacteristic
661C42C24×C10711yescharacteristic
662C23—21no—
663C23—21no—
664C23—22no—
665C23—21no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23#120×C10711yescharacteristic
670Q8—21no—
671Q8—21no—
672Q8—42no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—81no—
678D4—21no—
679D4—21no—
680D4—21no—
681D4—21no—
682D4—21no—
683D4—21no—
684D4—42no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—81no—
690D4—81no—
691D4—82no—
692D4—81no—
693D4—81no—
694D4—81no—
695D4—82no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4#120×C10711yescharacteristic
723C2×C4#120×C10711yescharacteristic
724C2×C4#120×C10711yescharacteristic
725C2×C4C22×D4×C10711yescharacteristic
726C2×C4C22×D4×C10711yescharacteristic
727C2×C4C22×D4×C10711yescharacteristic
728C8—22no—
729C8—41no—
730C8—41no—
731C8—41no—
732C8—41no—
733C8—41no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—41no—
738C22—41no—
739C22—42no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—164no—
750C22C2×#120×C10711yescharacteristic
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—41no—
756C4—42no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—81no—
762C4—81no—
763C4#576×C10711yescharacteristic
764C4#577×C10711yescharacteristic
765C4#577×C10711yescharacteristic
766C4#577×C10711yescharacteristic
767C2—41no—
768C2—81no—
769C2—81no—
770C2—82no—
771C2—81no—
772C2C107×#300911yescharacteristic
773C2C107×#301211yescharacteristic
774C2C107×#301811yescharacteristic
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×#3252C2semidirect
3. C107×#3235C2semidirect
4. C107×#3167C2semidirect
5. C107×#1654C2semidirect
6. C107×#1652C2semidirect
7. C107×#1641C2semidirect
8. C107×#1639C2semidirect
9. C107×#1638C2semidirect
10. C107×#1635C2semidirect
11. C107×#1631C2semidirect
12. C107×#1629C2semidirect
13. C107×#1557C2semidirect
14. C107×#1494C2semidirect
15. C107×#1492C2semidirect
30. #533×C107C22semidirect
35. #498×C107C22semidirect
38. #487×C107C22semidirect
43. #477×C107C22semidirect
46. #476×C107C22semidirect
48. #474×C107C22semidirect
53. #462×C107C22semidirect
56. #432×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
379. #18705C107direct (N × H)
389. #3252C2×C107semidirect
390. #3235C2×C107semidirect
391. #3167C2×C107semidirect
392. #1654C2×C107semidirect
393. #1652C2×C107semidirect
394. #1641C2×C107semidirect
395. #1639C2×C107semidirect
396. #1638C2×C107semidirect
397. #1635C2×C107semidirect
398. #1631C2×C107semidirect
399. #1629C2×C107semidirect
400. #1557C2×C107semidirect
401. #1494C2×C107semidirect
402. #1492C2×C107semidirect
403. C107#18705direct (N × H)
418. #533C22×C107semidirect
423. #498C22×C107semidirect
426. #487C22×C107semidirect
431. #477C22×C107semidirect
434. #476C22×C107semidirect
436. #474C22×C107semidirect
441. #462C22×C107semidirect
444. #432C22×C107semidirect
445. #423C22×C107semidirect
446. C2×C4×C8C22×C107semidirect
447. #332C22×C107semidirect
448. #332C22×C107semidirect
451. Q8⋊C8C22×C107semidirect
452. Q8⋊C8C22×C107semidirect
457. D4⋊C8C22×C107semidirect
458. 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×#32522
C107×#32352
C107×#31672
C107×#16542
C107×#16522
C107×#16412
C107×#16392
C107×#16382
C107×#16352
C107×#16312
C107×#16292
C107×#15572
C107×#14942
C107×#14922
#18705107