Finite Group Databasebeta

← C107×#18704 #41044668

Subgroups — C107×#18704 #41044668

Order 27392.

972 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3546C211yesmaximal, characteristic, complemented
2C107×#3251C211yesmaximal, characteristic, complemented
3C107×#3214C211yesmaximal, characteristic, complemented
4C107×#3169C211yesmaximal, characteristic, complemented
5C107×#1650C211yesmaximal, characteristic, complemented
6C107×#1647C211yesmaximal, characteristic, complemented
7C107×#1642C211yesmaximal, characteristic, complemented
8C107×#1639C211yesmaximal, characteristic, complemented
9C107×#1628C211yesmaximal, characteristic, complemented
10C107×#1625C211yesmaximal, characteristic, complemented
11C107×#1621C211yesmaximal, characteristic, complemented
12C107×#1619C211yesmaximal, 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#532×C107C2211yescharacteristic
31#532×C107C2211yescharacteristic
32#532×C107C2211yescharacteristic, complemented
33#529×C107C2211yescharacteristic
34#500×C107C2211yescharacteristic, complemented
35#496×C107—21no—
36#493×C107C2211yescharacteristic
37#489×C107—21no—
38#486×C107C2211yescharacteristic
39#486×C107C2211yescharacteristic, complemented
40#478×C107—21no—
41#475×C107C2211yescharacteristic, complemented
42#474×C107C2211yescharacteristic
43#469×C107—21no—
44#468×C107—21no—
45#466×C107—22no—
46#463×C107—21no—
47#461×C107C2211yescharacteristic
48#461×C107C2211yescharacteristic, complemented
49#460×C107C2211yescharacteristic, complemented
50#459×C107C2211yescharacteristic
51#459×C107C2211yescharacteristic
52#459×C107C2211yescharacteristic, complemented
53#449×C107—21no—
54#449×C107—21no—
55C4×D8×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—
75C2×#41×C107—21no—
76C22×D4×C107—21no—
77C22×D4×C107—21no—
78C2×SD16×C107—21no—
79C2×SD16×C107—21no—
80C2×SD16×C107—21no—
81C2×D8×C107—22no—
82C2×D8×C107—21no—
83C2×D8×C107—21no—
84C2×D8×C107—21no—
85C2×M16×C107—21no—
86C22×C8×C107—21no—
87C4⋊Q8×C107D411yescharacteristic
88C4⋊Q8×C107C2311yescharacteristic
89C4⋊Q8×C107C2311yescharacteristic
90#127×C107—22no—
91#127×C107—21no—
92#127×C107D411yescharacteristic
93#127×C107C2311yescharacteristic
94#127×C107C2311yescharacteristic
95#126×C107—22no—
96#126×C107—22no—
97#126×C107—21no—
98#125×C107D411yescharacteristic
99#124×C107—22no—
100#124×C107—21no—
101#124×C107—21no—
102#124×C107—21no—
103#124×C107—21no—
104#124×C107D411yescharacteristic
105#123×C107—22no—
106#123×C107—22no—
107#123×C107—21no—
108#123×C107—22no—
109C22⋊Q8×C107—22no—
110C22⋊Q8×C107—21no—
111C22⋊Q8×C107—21no—
112C22⋊Q8×C107D411yescharacteristic
113#121×C107—22no—
114#121×C107—22no—
115#121×C107—22no—
116#121×C107—22no—
117#121×C107—22no—
118#121×C107—21no—
119#121×C107—22no—
120#121×C107—21no—
121#121×C107—21no—
122#121×C107—21no—
123#121×C107—21no—
124#121×C107—21no—
125#121×C107—21no—
126#121×C107—21no—
127#121×C107D411yescharacteristic
128#121×C107D411yescharacteristic
129#121×C107D412yes—
130#121×C107D411yescharacteristic
131#120×C107—22no—
132#120×C107—22no—
133#120×C107—22no—
134#120×C107—22no—
135C4×Q8×C107—21no—
136C4×Q8×C107C2311yescharacteristic
137C4×D4×C107—22no—
138C4×D4×C107—21no—
139C4×D4×C107—21no—
140C4×D4×C107—21no—
141C4×D4×C107—21no—
142C4×D4×C107—21no—
143C4×D4×C107—21no—
144C4×D4×C107D412yes—
145C4×D4×C107C2311yescharacteristic
146C4×D4×C107C2311yescharacteristic
147C4×D4×C107C2311yescharacteristic
148#117×C107—21no—
149#117×C107—21no—
150C2×C4⋊C4×C107—21no—
151C2×C22⋊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
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—
185#41×C107—81no—
186#41×C107—81no—
187C2×Q8×C107—21no—
188C2×Q8×C107—21no—
189C2×Q8×C107—21no—
190C2×Q8×C107C2×D411yescharacteristic
191C2×D4×C107—22no—
192C2×D4×C107—22no—
193C2×D4×C107—22no—
194C2×D4×C107—22no—
195C2×D4×C107—22no—
196C2×D4×C107—21no—
197C2×D4×C107—21no—
198C2×D4×C107—22no—
199C2×D4×C107—21no—
200C2×D4×C107—21no—
201C2×D4×C107—21no—
202C2×D4×C107—21no—
203C2×D4×C107—21no—
204C2×D4×C107—21no—
205C2×D4×C107—21no—
206C2×D4×C107—21no—
207C2×D4×C107—41no—
208C2×D4×C107—81no—
209C2×D4×C107—81no—
210C2×D4×C107—81no—
211C2×D4×C107—81no—
212C2×D4×C107C2×D411yescharacteristic
213C2×D4×C107C2×D411yescharacteristic
214C2×D4×C107C2×D411yescharacteristic
215C2×D4×C107C2×D412yes—
216C22×C4×C107—22no—
217C22×C4×C107—22no—
218C22×C4×C107—21no—
219C22×C4×C107—21no—
220C22×C4×C107—21no—
221C22×C4×C107—22no—
222C22×C4×C107—41no—
223C22×C4×C107C2×D411yescharacteristic
224C22×C4×C107C2×D411yescharacteristic
225C22×C4×C107C2×D411yescharacteristic
226SD16×C107—81no—
227SD16×C107—81no—
228SD16×C107—81no—
229D8×C107—44no—
230D8×C107—81no—
231D8×C107—81no—
232D8×C107—81no—
233M16×C107—81no—
234C2×C8×C107—21no—
235C2×C8×C107—21no—
236C2×C8×C107—21no—
237C2×C8×C107—21no—
238C2×C8×C107—21no—
239C2×C8×C107—21no—
240C2×C8×C107—42no—
241C4⋊C4×C107—22no—
242C4⋊C4×C107—22no—
243C4⋊C4×C107—21no—
244C4⋊C4×C107—21no—
245C4⋊C4×C107—21no—
246C4⋊C4×C107—21no—
247C4⋊C4×C107—21no—
248C4⋊C4×C107—21no—
249C4⋊C4×C107—21no—
250C4⋊C4×C107—21no—
251C4⋊C4×C107C2×D411yescharacteristic
252C4⋊C4×C107C2×D411yescharacteristic
253C4⋊C4×C107C2×D411yescharacteristic
254C4⋊C4×C107C2×D411yescharacteristic
255C4⋊C4×C107C2×D412yes—
256C22⋊C4×C107—22no—
257C22⋊C4×C107—22no—
258C22⋊C4×C107—22no—
259C22⋊C4×C107—22no—
260C22⋊C4×C107—22no—
261C22⋊C4×C107—21no—
262C22⋊C4×C107—21no—
263C22⋊C4×C107—21no—
264C22⋊C4×C107—21no—
265C22⋊C4×C107—21no—
266C22⋊C4×C107—21no—
267C22⋊C4×C107—22no—
268C22⋊C4×C107—22no—
269C22⋊C4×C107—21no—
270C22⋊C4×C107—21no—
271C22⋊C4×C107—21no—
272C22⋊C4×C107—41no—
273C22⋊C4×C107—41no—
274C42×C107—22no—
275C42×C107—21no—
276C42×C107C2×D411yescharacteristic
277C42×C107C2×D411yescharacteristic
278C42×C107C2×D411yescharacteristic
279C42×C107C2411yescharacteristic
280C23×C107—21no—
281C23×C107—21no—
282C23×C107—22no—
283C23×C107—21no—
284C23×C107—41no—
285C23×C107—82no—
286C23×C107—82no—
287C23×C107—82no—
288C23×C107#12011yescharacteristic
289Q8×C107—21no—
290Q8×C107—21no—
291Q8×C107—41no—
292Q8×C107—41no—
293Q8×C107—41no—
294Q8×C107—41no—
295Q8×C107—81no—
296D4×C107—21no—
297D4×C107—21no—
298D4×C107—21no—
299D4×C107—21no—
300D4×C107—21no—
301D4×C107—21no—
302D4×C107—42no—
303D4×C107—42no—
304D4×C107—41no—
305D4×C107—41no—
306D4×C107—41no—
307D4×C107—41no—
308D4×C107—41no—
309D4×C107—41no—
310D4×C107—41no—
311D4×C107—41no—
312D4×C107—81no—
313D4×C107—81no—
314D4×C107—81no—
315D4×C107—82no—
316D4×C107—81no—
317D4×C107—81no—
318D4×C107—82no—
319D4×C107—82no—
320D4×C107—82no—
321D4×C107—82no—
322D4×C107—82no—
323D4×C107—82no—
324C2×C4×C107—21no—
325C2×C4×C107—21no—
326C2×C4×C107—21no—
327C2×C4×C107—21no—
328C2×C4×C107—21no—
329C2×C4×C107—21no—
330C2×C4×C107—21no—
331C2×C4×C107—22no—
332C2×C4×C107—21no—
333C2×C4×C107—21no—
334C2×C4×C107—41no—
335C2×C4×C107—41no—
336C2×C4×C107—41no—
337C2×C4×C107—41no—
338C2×C4×C107—41no—
339C2×C4×C107—41no—
340C2×C4×C107—41no—
341C2×C4×C107—41no—
342C2×C4×C107—82no—
343C2×C4×C107—82no—
344C2×C4×C107—82no—
345C2×C4×C107—82no—
346C2×C4×C107#12011yescharacteristic
347C2×C4×C107#12011yescharacteristic
348C2×C4×C107#12011yescharacteristic
349C2×C4×C107C22×D411yescharacteristic
350C2×C4×C107C22×D411yescharacteristic
351C2×C4×C107C22×D411yescharacteristic
352C8×C107—22no—
353C8×C107—41no—
354C8×C107—41no—
355C8×C107—41no—
356C8×C107—41no—
357C8×C107—41no—
358C22×C107—21no—
359C22×C107—21no—
360C22×C107—21no—
361C22×C107—41no—
362C22×C107—41no—
363C22×C107—42no—
364C22×C107—41no—
365C22×C107—41no—
366C22×C107—41no—
367C22×C107—42no—
368C22×C107—41no—
369C22×C107—42no—
370C22×C107—41no—
371C22×C107—41no—
372C22×C107—41no—
373C22×C107—81no—
374C22×C107—81no—
375C22×C107—81no—
376C22×C107—164no—
377C22×C107C2×#12011yescharacteristic
378C4×C107—21no—
379C4×C107—21no—
380C4×C107—21no—
381C4×C107—21no—
382C4×C107—41no—
383C4×C107—42no—
384C4×C107—41no—
385C4×C107—41no—
386C4×C107—41no—
387C4×C107—41no—
388C4×C107—81no—
389C4×C107#57611yescharacteristic
390C4×C107#57611yescharacteristic
391C4×C107#57611yescharacteristic
392C4×C107#57711yescharacteristic
393#18704C10711yesmaximal, characteristic, direct product factor, Sylow
394C2×C107—41no—
395C2×C107—81no—
396C2×C107—82no—
397C2×C107—81no—
398C2×C107—81no—
399C2×C107—161no—
400C2×C107#300811yescharacteristic
401C2×C107#301211yescharacteristic
402C2×C107#301811yescharacteristic
403#3546C2×C10711yescharacteristic, complemented
404#3251C2×C10711yescharacteristic, complemented
405#3214C2×C10711yescharacteristic, complemented
406#3169C2×C10711yescharacteristic, complemented
407#1650C2×C10711yescharacteristic, complemented
408#1647C2×C10711yescharacteristic, complemented
409#1642C2×C10711yescharacteristic, complemented
410#1639C2×C10711yescharacteristic, complemented
411#1628C2×C10711yescharacteristic, complemented
412#1625C2×C10711yescharacteristic, complemented
413#1621C2×C10711yescharacteristic, complemented
414#1619C2×C10711yescharacteristic, complemented
415#1557C2×C10711yescharacteristic, complemented
416#1494C2×C10711yescharacteristic, complemented
417#1492C2×C10711yescharacteristic, complemented
418C107#1870411yescharacteristic, direct product factor, Sylow
419#560—22no—
420#556C22×C10711yescharacteristic
421#553—21no—
422#550—21no—
423#550C22×C10711yescharacteristic
424#547C22×C10711yescharacteristic
425#546—21no—
426#546—21no—
427D42C22×C10711yescharacteristic
428#542—21no—
429#538—22no—
430#537—21no—
431#535—21no—
432#535—21no—
433#532C22×C10711yescharacteristic
434#532C22×C10711yescharacteristic
435#532C22×C10711yescharacteristic, complemented
436#529C22×C10711yescharacteristic
437#500C22×C10711yescharacteristic, complemented
438#496—21no—
439#493C22×C10711yescharacteristic
440#489—21no—
441#486C22×C10711yescharacteristic
442#486C22×C10711yescharacteristic, complemented
443#478—21no—
444#475C22×C10711yescharacteristic, complemented
445#474C22×C10711yescharacteristic
446#469—21no—
447#468—21no—
448#466—22no—
449#463—21no—
450#461C22×C10711yescharacteristic
451#461C22×C10711yescharacteristic, complemented
452#460C22×C10711yescharacteristic, complemented
453#459C22×C10711yescharacteristic
454#459C22×C10711yescharacteristic
455#459C22×C10711yescharacteristic, complemented
456#449—21no—
457#449—21no—
458C4×D8—22no—
459#432C22×C10711yescharacteristic, complemented
460#423C22×C10711yescharacteristic, complemented
461C2×C4×C8C22×C10711yescharacteristic, complemented
462#332C22×C10711yescharacteristic, complemented
463#332C22×C10711yescharacteristic, complemented
464#331C22×C10711yescharacteristic
465#331C22×C10711yescharacteristic
466Q8⋊C8C22×C10711yescharacteristic, complemented
467Q8⋊C8C22×C10711yescharacteristic, complemented
468D4⋊C8C22×C10711yescharacteristic
469D4⋊C8C22×C10711yescharacteristic
470D4⋊C8C22×C10711yescharacteristic
471D4⋊C8C22×C10711yescharacteristic
472D4⋊C8C22×C10711yescharacteristic, complemented
473D4⋊C8C22×C10711yescharacteristic, complemented
474C2×#41—21no—
475C2×#41—21no—
476C2×#41—21no—
477C2×#41—21no—
478C2×#41—21no—
479C22×D4—21no—
480C22×D4—21no—
481C2×SD16—21no—
482C2×SD16—21no—
483C2×SD16—21no—
484C2×D8—22no—
485C2×D8—21no—
486C2×D8—21no—
487C2×D8—21no—
488C2×M16—21no—
489C22×C8—21no—
490C4⋊Q8D4×C10711yescharacteristic
491C4⋊Q8C23×C10711yescharacteristic
492C4⋊Q8C23×C10711yescharacteristic
493#127—22no—
494#127—21no—
495#127D4×C10711yescharacteristic
496#127C23×C10711yescharacteristic
497#127C23×C10711yescharacteristic
498#126—22no—
499#126—22no—
500#126—21no—
501#125D4×C10711yescharacteristic
502#124—22no—
503#124—21no—
504#124—21no—
505#124—21no—
506#124—21no—
507#124D4×C10711yescharacteristic
508#123—22no—
509#123—22no—
510#123—21no—
511#123—22no—
512C22⋊Q8—22no—
513C22⋊Q8—21no—
514C22⋊Q8—21no—
515C22⋊Q8D4×C10711yescharacteristic
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—21no—
522#121—22no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121D4×C10711yescharacteristic
531#121D4×C10711yescharacteristic
532#121D4×C10711yescharacteristic
533#121D4×C10712yes—
534#120—22no—
535#120—22no—
536#120—22no—
537#120—22no—
538C4×Q8—21no—
539C4×Q8C23×C10711yescharacteristic
540C4×D4—22no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—21no—
547C4×D4D4×C10712yes—
548C4×D4C23×C10711yescharacteristic
549C4×D4C23×C10711yescharacteristic
550C4×D4C23×C10711yescharacteristic
551#117—21no—
552#117—21no—
553C2×C4⋊C4—21no—
554C2×C22⋊C4—22no—
555C2×C42C23×C10711yescharacteristic
556#107—22no—
557#107—21no—
558#106—21no—
559C4⋊C8—21no—
560C4⋊C8C23×C10711yescharacteristic
561C4⋊C8C23×C10711yescharacteristic
562C4⋊C8C23×C10711yescharacteristic
563C4⋊C8C23×C10711yescharacteristic
564#103—21no—
565#103—21no—
566#103—21no—
567#102—22no—
568#102—21no—
569#102—22no—
570#102—21no—
571#102—21no—
572#102—21no—
573#102—21no—
574C22⋊C8—21no—
575#97—21no—
576C4×C8—21no—
577C4×C8C23×C10711yescharacteristic
578C4×C8C23×C10711yescharacteristic
579C24—22no—
580#41—81no—
581#41—81no—
582#41—81no—
583#41—81no—
584#41—81no—
585#41—81no—
586#41—81no—
587#41—81no—
588#41—81no—
589#41—81no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8C2×D4×C10711yescharacteristic
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—41no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4—81no—
615C2×D4C2×D4×C10711yescharacteristic
616C2×D4C2×D4×C10711yescharacteristic
617C2×D4C2×D4×C10711yescharacteristic
618C2×D4C2×D4×C10712yes—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—22no—
625C22×C4—41no—
626C22×C4C2×D4×C10711yescharacteristic
627C22×C4C2×D4×C10711yescharacteristic
628C22×C4C2×D4×C10711yescharacteristic
629SD16—81no—
630SD16—81no—
631SD16—81no—
632D8—44no—
633D8—81no—
634D8—81no—
635D8—81no—
636M16—81no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—42no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4C2×D4×C10711yescharacteristic
655C4⋊C4C2×D4×C10711yescharacteristic
656C4⋊C4C2×D4×C10711yescharacteristic
657C4⋊C4C2×D4×C10711yescharacteristic
658C4⋊C4C2×D4×C10712yes—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C42—22no—
678C42—21no—
679C42C2×D4×C10711yescharacteristic
680C42C2×D4×C10711yescharacteristic
681C42C2×D4×C10711yescharacteristic
682C42C24×C10711yescharacteristic
683C23—21no—
684C23—21no—
685C23—22no—
686C23—21no—
687C23—41no—
688C23—82no—
689C23—82no—
690C23—82no—
691C23#120×C10711yescharacteristic
692Q8—21no—
693Q8—21no—
694Q8—41no—
695Q8—41no—
696Q8—41no—
697Q8—41no—
698Q8—81no—
699D4—21no—
700D4—21no—
701D4—21no—
702D4—21no—
703D4—21no—
704D4—21no—
705D4—42no—
706D4—42no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—81no—
716D4—81no—
717D4—82no—
718D4—81no—
719D4—81no—
720D4—81no—
721D4—82no—
722D4—82no—
723D4—82no—
724D4—82no—
725D4—82no—
726D4—82no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—82no—
746C2×C4—82no—
747C2×C4—82no—
748C2×C4—82no—
749C2×C4#120×C10711yescharacteristic
750C2×C4#120×C10711yescharacteristic
751C2×C4#120×C10711yescharacteristic
752C2×C4C22×D4×C10711yescharacteristic
753C2×C4C22×D4×C10711yescharacteristic
754C2×C4C22×D4×C10711yescharacteristic
755C8—22no—
756C8—41no—
757C8—41no—
758C8—41no—
759C8—41no—
760C8—41no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—41no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—42no—
771C22—41no—
772C22—42no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—164no—
780C22C2×#120×C10711yescharacteristic
781C4—21no—
782C4—21no—
783C4—21no—
784C4—21no—
785C4—41no—
786C4—42no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4#576×C10711yescharacteristic
793C4#576×C10711yescharacteristic
794C4#576×C10711yescharacteristic
795C4#577×C10711yescharacteristic
796C2—41no—
797C2—81no—
798C2—81no—
799C2—82no—
800C2—81no—
801C2—161no—
802C2C107×#300811yescharacteristic
803C2C107×#301211yescharacteristic
804C2C107×#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×#3546C2semidirect
2. C107×#3251C2semidirect
3. C107×#3214C2semidirect
4. C107×#3169C2semidirect
5. C107×#1650C2semidirect
6. C107×#1647C2semidirect
7. C107×#1642C2semidirect
8. C107×#1639C2semidirect
9. C107×#1628C2semidirect
10. C107×#1625C2semidirect
11. C107×#1621C2semidirect
12. C107×#1619C2semidirect
13. C107×#1557C2semidirect
14. C107×#1494C2semidirect
15. C107×#1492C2semidirect
32. #532×C107C22semidirect
34. #500×C107C22semidirect
39. #486×C107C22semidirect
41. #475×C107C22semidirect
48. #461×C107C22semidirect
49. #460×C107C22semidirect
52. #459×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
393. #18704C107direct (N × H)
403. #3546C2×C107semidirect
404. #3251C2×C107semidirect
405. #3214C2×C107semidirect
406. #3169C2×C107semidirect
407. #1650C2×C107semidirect
408. #1647C2×C107semidirect
409. #1642C2×C107semidirect
410. #1639C2×C107semidirect
411. #1628C2×C107semidirect
412. #1625C2×C107semidirect
413. #1621C2×C107semidirect
414. #1619C2×C107semidirect
415. #1557C2×C107semidirect
416. #1494C2×C107semidirect
417. #1492C2×C107semidirect
418. C107#18704direct (N × H)
435. #532C22×C107semidirect
437. #500C22×C107semidirect
442. #486C22×C107semidirect
444. #475C22×C107semidirect
451. #461C22×C107semidirect
452. #460C22×C107semidirect
455. #459C22×C107semidirect
459. #432C22×C107semidirect
460. #423C22×C107semidirect
461. C2×C4×C8C22×C107semidirect
462. #332C22×C107semidirect
463. #332C22×C107semidirect
466. Q8⋊C8C22×C107semidirect
467. Q8⋊C8C22×C107semidirect
472. D4⋊C8C22×C107semidirect
473. 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×#32512
C107×#32142
C107×#31692
C107×#16502
C107×#16472
C107×#16422
C107×#16392
C107×#16282
C107×#16252
C107×#16212
C107×#16192
C107×#15572
C107×#14942
C107×#14922
#18704107