Finite Group Databasebeta

← C107×#18708 #41044672

Subgroups — C107×#18708 #41044672

Order 27392.

908 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3554C211yesmaximal, characteristic, complemented
2C107×#3251C211yesmaximal, characteristic, complemented
3C107×#3216C211yesmaximal, characteristic, complemented
4C107×#3169C211yesmaximal, characteristic, complemented
5C107×#1649C211yesmaximal, characteristic, complemented
6C107×#1648C211yesmaximal, characteristic, complemented
7C107×#1641C211yesmaximal, characteristic, complemented
8C107×#1640C211yesmaximal, characteristic, complemented
9C107×#1627C211yesmaximal, characteristic, complemented
10C107×#1626C211yesmaximal, characteristic, complemented
11C107×#1621C211yesmaximal, characteristic, complemented
12C107×#1620C211yesmaximal, characteristic, complemented
13C107×#1557C211yesmaximal, characteristic, complemented
14C107×#1494C211yesmaximal, characteristic, complemented
15C107×#1493C211yesmaximal, characteristic, complemented
16#562×C107—22no—
17#559×C107—21no—
18#559×C107C2211yescharacteristic
19#557×C107C2211yescharacteristic
20#554×C107—21no—
21#550×C107C2211yescharacteristic
22D4×Q8×C107C2211yescharacteristic
23#548×C107—21no—
24#547×C107—21no—
25#542×C107—21no—
26#542×C107—21no—
27#540×C107—21no—
28#539×C107—22no—
29#536×C107—21no—
30#533×C107C2211yescharacteristic
31#532×C107C2211yescharacteristic
32#532×C107C2211yescharacteristic
33#529×C107C2211yescharacteristic
34#500×C107C2211yescharacteristic
35#497×C107—21no—
36#493×C107C2211yescharacteristic
37#489×C107—21no—
38#486×C107C2211yescharacteristic
39#486×C107C2211yescharacteristic
40#478×C107—21no—
41#475×C107C2211yescharacteristic
42#474×C107C2211yescharacteristic
43#469×C107—21no—
44#468×C107—21no—
45#466×C107—22no—
46#463×C107—21no—
47#462×C107C2211yescharacteristic
48#462×C107C2211yescharacteristic
49#460×C107C2211yescharacteristic
50#460×C107C2211yescharacteristic
51#460×C107C2211yescharacteristic
52#459×C107C2211yescharacteristic
53#452×C107—21no—
54#452×C107—21no—
55C4×D8×C107—22no—
56#432×C107C2211yescharacteristic
57#423×C107C2211yescharacteristic
58C2×C4×C8×C107C2211yescharacteristic
59#332×C107C2211yescharacteristic
60#332×C107C2211yescharacteristic
61#331×C107C2211yescharacteristic
62#331×C107C2211yescharacteristic
63Q8⋊C8×C107C2211yescharacteristic
64Q8⋊C8×C107C2211yescharacteristic
65Q8⋊C8×C107C2211yescharacteristic
66Q8⋊C8×C107C2211yescharacteristic
67Q8⋊C8×C107C2211yescharacteristic
68Q8⋊C8×C107C2211yescharacteristic
69D4⋊C8×C107C2211yescharacteristic
70D4⋊C8×C107C2211yescharacteristic
71C2×#41×C107—21no—
72C2×#41×C107—21no—
73C2×#41×C107—21no—
74C22×Q8×C107—21no—
75C2×Q16×C107—21no—
76C2×Q16×C107—21no—
77C2×SD16×C107—21no—
78C2×SD16×C107—21no—
79C2×SD16×C107—21no—
80C2×D8×C107—22no—
81C2×D8×C107—21no—
82C2×M16×C107—21no—
83C22×C8×C107—21no—
84C4⋊Q8×C107—21no—
85C4⋊Q8×C107—21no—
86C4⋊Q8×C107D411yescharacteristic
87C4⋊Q8×C107D411yescharacteristic
88C4⋊Q8×C107C2311yescharacteristic
89C4⋊Q8×C107C2311yescharacteristic
90#127×C107—21no—
91#127×C107C2311yescharacteristic
92#127×C107C2311yescharacteristic
93#126×C107—22no—
94#126×C107—21no—
95#125×C107—22no—
96#125×C107—21no—
97#125×C107—21no—
98#125×C107D411yescharacteristic
99#124×C107—22no—
100#124×C107—22no—
101#124×C107—21no—
102#124×C107—21no—
103#124×C107—21no—
104#124×C107—21no—
105#124×C107D411yescharacteristic
106#123×C107—22no—
107#123×C107—22no—
108#123×C107—22no—
109#123×C107—22no—
110#123×C107—22no—
111#123×C107—22no—
112#123×C107—21no—
113C22⋊Q8×C107—22no—
114C22⋊Q8×C107—22no—
115C22⋊Q8×C107—22no—
116C22⋊Q8×C107—22no—
117C22⋊Q8×C107—21no—
118C22⋊Q8×C107—22no—
119C22⋊Q8×C107—21no—
120C22⋊Q8×C107D411yescharacteristic
121C22⋊Q8×C107D411yescharacteristic
122C22⋊Q8×C107D411yescharacteristic
123#121×C107—22no—
124#121×C107—22no—
125#121×C107—22no—
126#121×C107—21no—
127#121×C107—21no—
128#121×C107—21no—
129#121×C107—21no—
130#121×C107D412yes—
131#121×C107D411yescharacteristic
132C4×Q8×C107—21no—
133C4×Q8×C107—21no—
134C4×Q8×C107—21no—
135C4×Q8×C107C2311yescharacteristic
136C4×Q8×C107C2311yescharacteristic
137C4×Q8×C107C2311yescharacteristic
138C4×D4×C107—22no—
139C4×D4×C107—21no—
140C4×D4×C107—21no—
141C4×D4×C107—21no—
142C4×D4×C107—21no—
143C4×D4×C107—21no—
144C4×D4×C107—21no—
145C4×D4×C107—21no—
146C4×D4×C107—21no—
147C4×D4×C107D412yes—
148C4×D4×C107C2311yescharacteristic
149#117×C107—21no—
150#117×C107—21no—
151C2×C4⋊C4×C107—22no—
152C2×C42×C107C2311yescharacteristic
153#107×C107—22no—
154#107×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—21no—
163#103×C107—21no—
164#102×C107—22no—
165#102×C107—21no—
166#102×C107—22no—
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
176#41×C107—81no—
177#41×C107—81no—
178#41×C107—81no—
179#41×C107—81no—
180#41×C107—81no—
181#41×C107—81no—
182C2×Q8×C107—22no—
183C2×Q8×C107—21no—
184C2×Q8×C107—21no—
185C2×Q8×C107—21no—
186C2×Q8×C107—81no—
187C2×Q8×C107—81no—
188C2×Q8×C107C2×D411yescharacteristic
189C2×Q8×C107C2×D411yescharacteristic
190C2×Q8×C107C2×D411yescharacteristic
191C2×D4×C107—22no—
192C2×D4×C107—22no—
193C2×D4×C107—21no—
194C2×D4×C107—22no—
195C2×D4×C107—21no—
196C2×D4×C107—21no—
197C2×D4×C107—21no—
198C2×D4×C107—21no—
199C2×D4×C107—21no—
200C2×D4×C107—41no—
201C2×D4×C107C2×D411yescharacteristic
202C2×D4×C107C2×D412yes—
203C22×C4×C107—22no—
204C22×C4×C107—22no—
205C22×C4×C107—22no—
206C22×C4×C107—21no—
207C22×C4×C107—22no—
208C22×C4×C107—41no—
209C22×C4×C107C2×D411yescharacteristic
210C22×C4×C107C2×D411yescharacteristic
211C22×C4×C107C2×D411yescharacteristic
212Q16×C107—81no—
213Q16×C107—81no—
214SD16×C107—81no—
215SD16×C107—81no—
216SD16×C107—81no—
217D8×C107—44no—
218D8×C107—81no—
219M16×C107—81no—
220C2×C8×C107—21no—
221C2×C8×C107—21no—
222C2×C8×C107—21no—
223C2×C8×C107—21no—
224C2×C8×C107—21no—
225C2×C8×C107—21no—
226C2×C8×C107—42no—
227C4⋊C4×C107—22no—
228C4⋊C4×C107—22no—
229C4⋊C4×C107—22no—
230C4⋊C4×C107—22no—
231C4⋊C4×C107—21no—
232C4⋊C4×C107—21no—
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—21no—
244C4⋊C4×C107—21no—
245C4⋊C4×C107C2×D411yescharacteristic
246C4⋊C4×C107C2×D411yescharacteristic
247C4⋊C4×C107C2×D411yescharacteristic
248C4⋊C4×C107C2×D411yescharacteristic
249C4⋊C4×C107C2×D412yes—
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—41no—
265C22⋊C4×C107—41no—
266C42×C107—22no—
267C42×C107—21no—
268C42×C107—21no—
269C42×C107—21no—
270C42×C107C2×D411yescharacteristic
271C42×C107C2×D411yescharacteristic
272C42×C107C2×D411yescharacteristic
273C42×C107C2411yescharacteristic
274C23×C107—21no—
275C23×C107—22no—
276C23×C107—41no—
277C23×C107#12011yescharacteristic
278Q8×C107—21no—
279Q8×C107—21no—
280Q8×C107—21no—
281Q8×C107—21no—
282Q8×C107—21no—
283Q8×C107—21no—
284Q8×C107—41no—
285Q8×C107—41no—
286Q8×C107—41no—
287Q8×C107—41no—
288Q8×C107—81no—
289Q8×C107—82no—
290D4×C107—21no—
291D4×C107—21no—
292D4×C107—42no—
293D4×C107—42no—
294D4×C107—41no—
295D4×C107—41no—
296D4×C107—41no—
297D4×C107—41no—
298D4×C107—41no—
299D4×C107—41no—
300D4×C107—41no—
301D4×C107—41no—
302D4×C107—81no—
303D4×C107—82no—
304D4×C107—82no—
305D4×C107—82no—
306D4×C107—82no—
307C2×C4×C107—21no—
308C2×C4×C107—21no—
309C2×C4×C107—21no—
310C2×C4×C107—21no—
311C2×C4×C107—21no—
312C2×C4×C107—21no—
313C2×C4×C107—21no—
314C2×C4×C107—21no—
315C2×C4×C107—21no—
316C2×C4×C107—22no—
317C2×C4×C107—21no—
318C2×C4×C107—21no—
319C2×C4×C107—41no—
320C2×C4×C107—41no—
321C2×C4×C107—41no—
322C2×C4×C107—41no—
323C2×C4×C107—82no—
324C2×C4×C107—82no—
325C2×C4×C107—82no—
326C2×C4×C107—82no—
327C2×C4×C107—82no—
328C2×C4×C107#12011yescharacteristic
329C2×C4×C107#12011yescharacteristic
330C2×C4×C107#12011yescharacteristic
331C2×C4×C107C22×D411yescharacteristic
332C2×C4×C107C22×D411yescharacteristic
333C2×C4×C107C22×D411yescharacteristic
334C8×C107—22no—
335C8×C107—41no—
336C8×C107—41no—
337C8×C107—41no—
338C8×C107—41no—
339C8×C107—41no—
340C22×C107—21no—
341C22×C107—21no—
342C22×C107—21no—
343C22×C107—41no—
344C22×C107—42no—
345C22×C107—41no—
346C22×C107—42no—
347C22×C107—42no—
348C22×C107—41no—
349C22×C107—81no—
350C22×C107—81no—
351C22×C107—81no—
352C22×C107C2×#12011yescharacteristic
353C4×C107—21no—
354C4×C107—21no—
355C4×C107—21no—
356C4×C107—21no—
357C4×C107—41no—
358C4×C107—41no—
359C4×C107—42no—
360C4×C107—41no—
361C4×C107—41no—
362C4×C107—41no—
363C4×C107—41no—
364C4×C107—41no—
365C4×C107—81no—
366C4×C107#57611yescharacteristic
367C4×C107#57611yescharacteristic
368C4×C107#57711yescharacteristic
369C4×C107#57811yescharacteristic
370#18708C10711yesmaximal, characteristic, direct product factor, Sylow
371C2×C107—41no—
372C2×C107—81no—
373C2×C107—82no—
374C2×C107—161no—
375C2×C107#300811yescharacteristic
376C2×C107#301311yescharacteristic
377C2×C107#301811yescharacteristic
378#3554C2×C10711yescharacteristic, complemented
379#3251C2×C10711yescharacteristic, complemented
380#3216C2×C10711yescharacteristic, complemented
381#3169C2×C10711yescharacteristic, complemented
382#1649C2×C10711yescharacteristic, complemented
383#1648C2×C10711yescharacteristic, complemented
384#1641C2×C10711yescharacteristic, complemented
385#1640C2×C10711yescharacteristic, complemented
386#1627C2×C10711yescharacteristic, complemented
387#1626C2×C10711yescharacteristic, complemented
388#1621C2×C10711yescharacteristic, complemented
389#1620C2×C10711yescharacteristic, complemented
390#1557C2×C10711yescharacteristic, complemented
391#1494C2×C10711yescharacteristic, complemented
392#1493C2×C10711yescharacteristic, complemented
393C107#1870811yescharacteristic, direct product factor, Sylow
394#562—22no—
395#559—21no—
396#559C22×C10711yescharacteristic
397#557C22×C10711yescharacteristic
398#554—21no—
399#550C22×C10711yescharacteristic
400D4×Q8C22×C10711yescharacteristic
401#548—21no—
402#547—21no—
403#542—21no—
404#542—21no—
405#540—21no—
406#539—22no—
407#536—21no—
408#533C22×C10711yescharacteristic
409#532C22×C10711yescharacteristic
410#532C22×C10711yescharacteristic
411#529C22×C10711yescharacteristic
412#500C22×C10711yescharacteristic
413#497—21no—
414#493C22×C10711yescharacteristic
415#489—21no—
416#486C22×C10711yescharacteristic
417#486C22×C10711yescharacteristic
418#478—21no—
419#475C22×C10711yescharacteristic
420#474C22×C10711yescharacteristic
421#469—21no—
422#468—21no—
423#466—22no—
424#463—21no—
425#462C22×C10711yescharacteristic
426#462C22×C10711yescharacteristic
427#460C22×C10711yescharacteristic
428#460C22×C10711yescharacteristic
429#460C22×C10711yescharacteristic
430#459C22×C10711yescharacteristic
431#452—21no—
432#452—21no—
433C4×D8—22no—
434#432C22×C10711yescharacteristic
435#423C22×C10711yescharacteristic
436C2×C4×C8C22×C10711yescharacteristic
437#332C22×C10711yescharacteristic
438#332C22×C10711yescharacteristic
439#331C22×C10711yescharacteristic
440#331C22×C10711yescharacteristic
441Q8⋊C8C22×C10711yescharacteristic
442Q8⋊C8C22×C10711yescharacteristic
443Q8⋊C8C22×C10711yescharacteristic
444Q8⋊C8C22×C10711yescharacteristic
445Q8⋊C8C22×C10711yescharacteristic
446Q8⋊C8C22×C10711yescharacteristic
447D4⋊C8C22×C10711yescharacteristic
448D4⋊C8C22×C10711yescharacteristic
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C22×Q8—21no—
453C2×Q16—21no—
454C2×Q16—21no—
455C2×SD16—21no—
456C2×SD16—21no—
457C2×SD16—21no—
458C2×D8—22no—
459C2×D8—21no—
460C2×M16—21no—
461C22×C8—21no—
462C4⋊Q8—21no—
463C4⋊Q8—21no—
464C4⋊Q8D4×C10711yescharacteristic
465C4⋊Q8D4×C10711yescharacteristic
466C4⋊Q8C23×C10711yescharacteristic
467C4⋊Q8C23×C10711yescharacteristic
468#127—21no—
469#127C23×C10711yescharacteristic
470#127C23×C10711yescharacteristic
471#126—22no—
472#126—21no—
473#125—22no—
474#125—21no—
475#125—21no—
476#125D4×C10711yescharacteristic
477#124—22no—
478#124—22no—
479#124—21no—
480#124—21no—
481#124—21no—
482#124—21no—
483#124D4×C10711yescharacteristic
484#123—22no—
485#123—22no—
486#123—22no—
487#123—22no—
488#123—22no—
489#123—22no—
490#123—21no—
491C22⋊Q8—22no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—22no—
495C22⋊Q8—21no—
496C22⋊Q8—22no—
497C22⋊Q8—21no—
498C22⋊Q8D4×C10711yescharacteristic
499C22⋊Q8D4×C10711yescharacteristic
500C22⋊Q8D4×C10711yescharacteristic
501#121—22no—
502#121—22no—
503#121—22no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121D4×C10711yescharacteristic
509#121D4×C10712yes—
510C4×Q8—21no—
511C4×Q8—21no—
512C4×Q8—21no—
513C4×Q8C23×C10711yescharacteristic
514C4×Q8C23×C10711yescharacteristic
515C4×Q8C23×C10711yescharacteristic
516C4×D4—22no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4D4×C10712yes—
526C4×D4C23×C10711yescharacteristic
527#117—21no—
528#117—21no—
529C2×C4⋊C4—22no—
530C2×C42C23×C10711yescharacteristic
531#107—22no—
532#107—21no—
533#106—21no—
534C4⋊C8—21no—
535C4⋊C8C23×C10711yescharacteristic
536C4⋊C8C23×C10711yescharacteristic
537C4⋊C8C23×C10711yescharacteristic
538C4⋊C8C23×C10711yescharacteristic
539#103—21no—
540#103—21no—
541#103—21no—
542#102—22no—
543#102—21no—
544#102—22no—
545#102—21no—
546#102—21no—
547#102—21no—
548#102—21no—
549C22⋊C8—21no—
550#97—21no—
551C4×C8—21no—
552C4×C8C23×C10711yescharacteristic
553C4×C8C23×C10711yescharacteristic
554#41—81no—
555#41—81no—
556#41—81no—
557#41—81no—
558#41—81no—
559#41—81no—
560C2×Q8—22no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—81no—
565C2×Q8—81no—
566C2×Q8C2×D4×C10711yescharacteristic
567C2×Q8C2×D4×C10711yescharacteristic
568C2×Q8C2×D4×C10711yescharacteristic
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—41no—
579C2×D4C2×D4×C10711yescharacteristic
580C2×D4C2×D4×C10712yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—41no—
587C22×C4C2×D4×C10711yescharacteristic
588C22×C4C2×D4×C10711yescharacteristic
589C22×C4C2×D4×C10711yescharacteristic
590Q16—81no—
591Q16—81no—
592SD16—81no—
593SD16—81no—
594SD16—81no—
595D8—44no—
596D8—81no—
597M16—81no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—42no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4C2×D4×C10711yescharacteristic
624C4⋊C4C2×D4×C10711yescharacteristic
625C4⋊C4C2×D4×C10711yescharacteristic
626C4⋊C4C2×D4×C10711yescharacteristic
627C4⋊C4C2×D4×C10712yes—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—21no—
642C22⋊C4—41no—
643C22⋊C4—41no—
644C42—22no—
645C42—21no—
646C42—21no—
647C42—21no—
648C42C2×D4×C10711yescharacteristic
649C42C2×D4×C10711yescharacteristic
650C42C2×D4×C10711yescharacteristic
651C42C24×C10711yescharacteristic
652C23—21no—
653C23—22no—
654C23—41no—
655C23#120×C10711yescharacteristic
656Q8—21no—
657Q8—21no—
658Q8—21no—
659Q8—21no—
660Q8—21no—
661Q8—21no—
662Q8—41no—
663Q8—41no—
664Q8—41no—
665Q8—41no—
666Q8—81no—
667Q8—82no—
668D4—21no—
669D4—21no—
670D4—42no—
671D4—42no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—82no—
681D4—81no—
682D4—82no—
683D4—82no—
684D4—82no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4#120×C10711yescharacteristic
707C2×C4#120×C10711yescharacteristic
708C2×C4#120×C10711yescharacteristic
709C2×C4C22×D4×C10711yescharacteristic
710C2×C4C22×D4×C10711yescharacteristic
711C2×C4C22×D4×C10711yescharacteristic
712C8—22no—
713C8—41no—
714C8—41no—
715C8—41no—
716C8—41no—
717C8—41no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—41no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22C2×#120×C10711yescharacteristic
731C4—21no—
732C4—21no—
733C4—21no—
734C4—21no—
735C4—41no—
736C4—41no—
737C4—42no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—81no—
744C4#576×C10711yescharacteristic
745C4#576×C10711yescharacteristic
746C4#577×C10711yescharacteristic
747C4#578×C10711yescharacteristic
748C2—41no—
749C2—81no—
750C2—82no—
751C2—161no—
752C2C107×#300811yescharacteristic
753C2C107×#301311yescharacteristic
754C2C107×#301811yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC42C24×C107
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
1. C107×#3554C2semidirect
2. C107×#3251C2semidirect
3. C107×#3216C2semidirect
4. C107×#3169C2semidirect
5. C107×#1649C2semidirect
6. C107×#1648C2semidirect
7. C107×#1641C2semidirect
8. C107×#1640C2semidirect
9. C107×#1627C2semidirect
10. C107×#1626C2semidirect
11. C107×#1621C2semidirect
12. C107×#1620C2semidirect
13. C107×#1557C2semidirect
14. C107×#1494C2semidirect
15. C107×#1493C2semidirect
370. #18708C107direct (N × H)
378. #3554C2×C107semidirect
379. #3251C2×C107semidirect
380. #3216C2×C107semidirect
381. #3169C2×C107semidirect
382. #1649C2×C107semidirect
383. #1648C2×C107semidirect
384. #1641C2×C107semidirect
385. #1640C2×C107semidirect
386. #1627C2×C107semidirect
387. #1626C2×C107semidirect
388. #1621C2×C107semidirect
389. #1620C2×C107semidirect
390. #1557C2×C107semidirect
391. #1494C2×C107semidirect
392. #1493C2×C107semidirect
393. C107#18708direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#35542
C107×#32512
C107×#32162
C107×#31692
C107×#16492
C107×#16482
C107×#16412
C107×#16402
C107×#16272
C107×#16262
C107×#16212
C107×#16202
C107×#15572
C107×#14942
C107×#14932
#18708107