Finite Group Databasebeta

← C107×#18465 #41044429

Subgroups — C107×#18465 #41044429

Order 27392.

870 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3564C211yesmaximal, characteristic
2C107×#3218C211yesmaximal, characteristic, complemented
3C107×#3209C211yesmaximal, characteristic, complemented
4C107×#2821C211yesmaximal, characteristic, complemented
5C107×#1606C212yesmaximal
6C107×#1605C212yesmaximal, complemented
7C107×#1603C212yesmaximal, complemented
8C107×#1602C212yesmaximal, complemented
9C107×#1521C211yesmaximal, characteristic, complemented
10C107×#1515C211yesmaximal, characteristic, complemented
11C107×#1473C211yesmaximal, characteristic, complemented
12#563×C107—21no—
13#563×C107—21no—
14#556×C107—21no—
15#554×C107—21no—
16#552×C107—21no—
17#552×C107—21no—
18#551×C107—21no—
19#551×C107—21no—
20#544×C107C2211yescharacteristic
21#543×C107C2211yescharacteristic
22#542×C107—21no—
23#541×C107—21no—
24#541×C107—21no—
25#539×C107—21no—
26#539×C107C2211yescharacteristic
27#538×C107C2211yescharacteristic
28#533×C107C2211yescharacteristic
29C2×C4⋊Q8×C107C2211yescharacteristic
30#529×C107C2211yescharacteristic
31C2×#126×C107C2211yescharacteristic
32#497×C107—21no—
33#494×C107—21no—
34#491×C107—21no—
35#487×C107—21no—
36#462×C107—21no—
37#462×C107—21no—
38#462×C107—21no—
39#461×C107—21no—
40#451×C107C2212yes—
41#451×C107C2212yes—
42#451×C107C2212yes—
43#448×C107C2212yes—
44#432×C107C2211yescharacteristic
45#431×C107C2211yescharacteristic
46#400×C107—21no—
47#399×C107—21no—
48#398×C107—21no—
49#397×C107—21no—
50#395×C107C2212yes—
51#393×C107C2212yes—
52#383×C107C2211yescharacteristic
53#328×C107C2212yes—
54#328×C107C2212yes—
55#328×C107C2212yes—
56#327×C107C2212yes—
57#324×C107C2212yes—
58#323×C107C2212yes—
59C22×Q8×C107C2312yes—
60C2×Q16×C107—22no—
61C2×Q16×C107—22no—
62C2×Q16×C107—22no—
63C2×SD16×C107—22no—
64C4⋊Q8×C107—21no—
65C4⋊Q8×C107—21no—
66C4⋊Q8×C107—21no—
67C4⋊Q8×C107—21no—
68C4⋊Q8×C107—21no—
69C4⋊Q8×C107—21no—
70C4⋊Q8×C107—21no—
71C4⋊Q8×C107D411yescharacteristic
72C4⋊Q8×C107D411yescharacteristic
73#126×C107—21no—
74#126×C107—21no—
75#126×C107—21no—
76#126×C107—21no—
77#126×C107—21no—
78#126×C107—21no—
79#126×C107—21no—
80#126×C107—21no—
81#126×C107—21no—
82#126×C107—21no—
83#126×C107—21no—
84#126×C107—21no—
85#126×C107—21no—
86#125×C107—21no—
87#125×C107—21no—
88#125×C107—21no—
89#125×C107—21no—
90#125×C107—21no—
91#125×C107—21no—
92#125×C107—21no—
93#125×C107—21no—
94#125×C107—21no—
95#125×C107D411yescharacteristic
96#124×C107—21no—
97#124×C107—21no—
98#124×C107—21no—
99#124×C107D411yescharacteristic
100#123×C107—21no—
101#123×C107—21no—
102#123×C107—21no—
103#123×C107—21no—
104#123×C107—21no—
105#123×C107—21no—
106#123×C107—21no—
107#123×C107—21no—
108C22⋊Q8×C107—21no—
109C22⋊Q8×C107—21no—
110C22⋊Q8×C107—21no—
111C22⋊Q8×C107—21no—
112C22⋊Q8×C107—21no—
113C22⋊Q8×C107—21no—
114C22⋊Q8×C107—21no—
115C22⋊Q8×C107—21no—
116C22⋊Q8×C107—21no—
117C22⋊Q8×C107—21no—
118C22⋊Q8×C107—21no—
119C22⋊Q8×C107—21no—
120C22⋊Q8×C107—21no—
121C22⋊Q8×C107—21no—
122C22⋊Q8×C107C2311yescharacteristic
123C22⋊Q8×C107C2311yescharacteristic
124C22⋊Q8×C107C2311yescharacteristic
125#121×C107—21no—
126#121×C107C2311yescharacteristic
127#120×C107—21no—
128C4×Q8×C107—21no—
129C4×Q8×C107—21no—
130C4×Q8×C107—21no—
131C4×Q8×C107D411yescharacteristic
132C4×Q8×C107D411yescharacteristic
133C4×Q8×C107D411yescharacteristic
134C4×D4×C107—21no—
135C4×D4×C107—21no—
136C4×D4×C107—21no—
137C4×D4×C107—21no—
138C4×D4×C107—21no—
139C4×D4×C107D411yescharacteristic
140#117×C107—21no—
141#117×C107—21no—
142#117×C107—21no—
143#117×C107—21no—
144#117×C107—21no—
145#117×C107—21no—
146C2×C4⋊C4×C107—21no—
147C2×C4⋊C4×C107—21no—
148C2×C4⋊C4×C107—21no—
149C2×C4⋊C4×C107—22no—
150C2×C4⋊C4×C107D411yescharacteristic
151C2×C4⋊C4×C107D411yescharacteristic
152C2×C4⋊C4×C107C2311yescharacteristic
153C2×C22⋊C4×C107—21no—
154C2×C22⋊C4×C107—22no—
155C2×C22⋊C4×C107D411yescharacteristic
156C2×C22⋊C4×C107D411yescharacteristic
157C2×C22⋊C4×C107C2311yescharacteristic
158C2×C42×C107C2311yescharacteristic
159C4⋊C8×C107—21no—
160C4⋊C8×C107—21no—
161#103×C107—22no—
162#103×C107—22no—
163#103×C107—22no—
164#103×C107—22no—
165C22⋊C8×C107C2312yes—
166C22⋊C8×C107C2312yes—
167#97×C107—21no—
168C4×C8×C107—21no—
169#95×C107—21no—
170#95×C107—21no—
171#95×C107—22no—
172#95×C107—22no—
173#95×C107C2312yes—
174C24×C107C2×D411yescharacteristic
175C2×Q8×C107—21no—
176C2×Q8×C107—21no—
177C2×Q8×C107—21no—
178C2×Q8×C107—22no—
179C2×Q8×C107—22no—
180C2×Q8×C107—82no—
181C2×Q8×C107C2×D411yescharacteristic
182C2×Q8×C107C2×D411yescharacteristic
183C2×Q8×C107C2×D411yescharacteristic
184C2×D4×C107—21no—
185C2×D4×C107—21no—
186C2×D4×C107—21no—
187C2×D4×C107C2×D411yescharacteristic
188C22×C4×C107—21no—
189C22×C4×C107—21no—
190C22×C4×C107—21no—
191C22×C4×C107—21no—
192C22×C4×C107—21no—
193C22×C4×C107—22no—
194C22×C4×C107—22no—
195C22×C4×C107C2×D411yescharacteristic
196C22×C4×C107C2×D411yescharacteristic
197C22×C4×C107C2×D411yescharacteristic
198C22×C4×C107C2×D411yescharacteristic
199C22×C4×C107C2×D411yescharacteristic
200C22×C4×C107C2411yescharacteristic
201Q16×C107—82no—
202Q16×C107—82no—
203Q16×C107—82no—
204SD16×C107—82no—
205C2×C8×C107—22no—
206C2×C8×C107—22no—
207C4⋊C4×C107—21no—
208C4⋊C4×C107—21no—
209C4⋊C4×C107—21no—
210C4⋊C4×C107—21no—
211C4⋊C4×C107—21no—
212C4⋊C4×C107—21no—
213C4⋊C4×C107—21no—
214C4⋊C4×C107—21no—
215C4⋊C4×C107—21no—
216C4⋊C4×C107—21no—
217C4⋊C4×C107—21no—
218C4⋊C4×C107—21no—
219C4⋊C4×C107—21no—
220C4⋊C4×C107—21no—
221C4⋊C4×C107—21no—
222C4⋊C4×C107—21no—
223C4⋊C4×C107—21no—
224C4⋊C4×C107—21no—
225C4⋊C4×C107—21no—
226C4⋊C4×C107—21no—
227C4⋊C4×C107—21no—
228C4⋊C4×C107—21no—
229C4⋊C4×C107—21no—
230C4⋊C4×C107—21no—
231C4⋊C4×C107—21no—
232C4⋊C4×C107—21no—
233C4⋊C4×C107—21no—
234C4⋊C4×C107—21no—
235C4⋊C4×C107—21no—
236C4⋊C4×C107—41no—
237C4⋊C4×C107—41no—
238C4⋊C4×C107—41no—
239C4⋊C4×C107—41no—
240C4⋊C4×C107—82no—
241C4⋊C4×C107C2×D411yescharacteristic
242C4⋊C4×C107C2×D411yescharacteristic
243C4⋊C4×C107C2×D411yescharacteristic
244C4⋊C4×C107C2×D411yescharacteristic
245C22⋊C4×C107—21no—
246C22⋊C4×C107—21no—
247C22⋊C4×C107—21no—
248C22⋊C4×C107—21no—
249C22⋊C4×C107—21no—
250C22⋊C4×C107—21no—
251C22⋊C4×C107—21no—
252C22⋊C4×C107—21no—
253C22⋊C4×C107—21no—
254C22⋊C4×C107—21no—
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—21no—
262C22⋊C4×C107—21no—
263C22⋊C4×C107—21no—
264C22⋊C4×C107—21no—
265C22⋊C4×C107—21no—
266C22⋊C4×C107—82no—
267C42×C107—21no—
268C42×C107—21no—
269C42×C107—21no—
270C42×C107—21no—
271C42×C107—21no—
272C42×C107—21no—
273C42×C107—21no—
274C42×C107C2×D411yescharacteristic
275C42×C107C2×D411yescharacteristic
276C42×C107C2×D411yescharacteristic
277C42×C107C2×D411yescharacteristic
278C23×C107—21no—
279C23×C107—21no—
280C23×C107—22no—
281C23×C107—41no—
282C23×C107—41no—
283C23×C107C22×D411yescharacteristic
284Q8×C107—41no—
285Q8×C107—41no—
286Q8×C107—41no—
287Q8×C107—42no—
288Q8×C107—42no—
289Q8×C107—42no—
290Q8×C107—42no—
291Q8×C107—81no—
292Q8×C107—81no—
293Q8×C107—81no—
294D4×C107—41no—
295D4×C107—42no—
296D4×C107—81no—
297D4×C107—81no—
298C2×C4×C107—22no—
299C2×C4×C107—21no—
300C2×C4×C107—21no—
301C2×C4×C107—21no—
302C2×C4×C107—21no—
303C2×C4×C107—21no—
304C2×C4×C107—21no—
305C2×C4×C107—21no—
306C2×C4×C107—21no—
307C2×C4×C107—21no—
308C2×C4×C107—21no—
309C2×C4×C107—22no—
310C2×C4×C107—41no—
311C2×C4×C107—41no—
312C2×C4×C107—41no—
313C2×C4×C107—41no—
314C2×C4×C107—42no—
315C2×C4×C107—42no—
316C2×C4×C107—42no—
317C2×C4×C107—42no—
318C2×C4×C107—42no—
319C2×C4×C107—42no—
320C2×C4×C107—81no—
321C2×C4×C107—81no—
322C2×C4×C107—81no—
323C2×C4×C107—81no—
324C2×C4×C107—81no—
325C2×C4×C107#12011yescharacteristic
326C2×C4×C107#12011yescharacteristic
327C2×C4×C107#12011yescharacteristic
328C2×C4×C107#12011yescharacteristic
329C2×C4×C107C22×D411yescharacteristic
330C2×C4×C107C22×D411yescharacteristic
331C8×C107—42no—
332C8×C107—42no—
333C22×C107—21no—
334C22×C107—21no—
335C22×C107—41no—
336C22×C107—41no—
337C22×C107—41no—
338C22×C107—41no—
339C22×C107—41no—
340C22×C107—41no—
341C22×C107—82no—
342C22×C107C2×#12011yescharacteristic
343C22×C107#57812yes—
344C4×C107—21no—
345C4×C107—21no—
346C4×C107—21no—
347C4×C107—21no—
348C4×C107—21no—
349C4×C107—21no—
350C4×C107—41no—
351C4×C107—41no—
352C4×C107—41no—
353C4×C107—41no—
354C4×C107—41no—
355C4×C107—41no—
356C4×C107—41no—
357C4×C107—41no—
358C4×C107—41no—
359C4×C107—41no—
360C4×C107—82no—
361C4×C107—82no—
362#18465C10711yesmaximal, characteristic, direct product factor, Sylow
363C2×C107—22no—
364C2×C107—81no—
365C2×C107—81no—
366C2×C107#301111yescharacteristic
367C2×C107#302211yescharacteristic
368C2×C107#302711yescharacteristic
369#3564C2×C10711yescharacteristic
370#3218C2×C10711yescharacteristic, complemented
371#3209C2×C10711yescharacteristic, complemented
372#2821C2×C10711yescharacteristic, complemented
373#1606C2×C10712yes—
374#1605C2×C10712yescomplemented
375#1603C2×C10712yescomplemented
376#1602C2×C10712yescomplemented
377#1521C2×C10711yescharacteristic, complemented
378#1515C2×C10711yescharacteristic, complemented
379#1473C2×C10711yescharacteristic, complemented
380C107#1846511yescharacteristic, direct product factor, Sylow
381#563—21no—
382#563—21no—
383#556—21no—
384#554—21no—
385#552—21no—
386#552—21no—
387#551—21no—
388#551—21no—
389#544C22×C10711yescharacteristic
390#543C22×C10711yescharacteristic
391#542—21no—
392#541—21no—
393#541—21no—
394#539—21no—
395#539C22×C10711yescharacteristic
396#538C22×C10711yescharacteristic
397#533C22×C10711yescharacteristic
398C2×C4⋊Q8C22×C10711yescharacteristic
399#529C22×C10711yescharacteristic
400C2×#126C22×C10711yescharacteristic
401#497—21no—
402#494—21no—
403#491—21no—
404#487—21no—
405#462—21no—
406#462—21no—
407#462—21no—
408#461—21no—
409#451C22×C10712yes—
410#451C22×C10712yes—
411#451C22×C10712yes—
412#448C22×C10712yes—
413#432C22×C10711yescharacteristic
414#431C22×C10711yescharacteristic
415#400—21no—
416#399—21no—
417#398—21no—
418#397—21no—
419#395C22×C10712yes—
420#393C22×C10712yes—
421#383C22×C10711yescharacteristic
422#328C22×C10712yes—
423#328C22×C10712yes—
424#328C22×C10712yes—
425#327C22×C10712yes—
426#324C22×C10712yes—
427#323C22×C10712yes—
428C22×Q8C23×C10712yes—
429C2×Q16—22no—
430C2×Q16—22no—
431C2×Q16—22no—
432C2×SD16—22no—
433C4⋊Q8—21no—
434C4⋊Q8—21no—
435C4⋊Q8—21no—
436C4⋊Q8—21no—
437C4⋊Q8—21no—
438C4⋊Q8—21no—
439C4⋊Q8—21no—
440C4⋊Q8D4×C10711yescharacteristic
441C4⋊Q8D4×C10711yescharacteristic
442#126—21no—
443#126—21no—
444#126—21no—
445#126—21no—
446#126—21no—
447#126—21no—
448#126—21no—
449#126—21no—
450#126—21no—
451#126—21no—
452#126—21no—
453#126—21no—
454#126—21no—
455#125—21no—
456#125—21no—
457#125—21no—
458#125—21no—
459#125—21no—
460#125—21no—
461#125—21no—
462#125—21no—
463#125—21no—
464#125D4×C10711yescharacteristic
465#124—21no—
466#124—21no—
467#124—21no—
468#124D4×C10711yescharacteristic
469#123—21no—
470#123—21no—
471#123—21no—
472#123—21no—
473#123—21no—
474#123—21no—
475#123—21no—
476#123—21no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482C22⋊Q8—21no—
483C22⋊Q8—21no—
484C22⋊Q8—21no—
485C22⋊Q8—21no—
486C22⋊Q8—21no—
487C22⋊Q8—21no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8C23×C10711yescharacteristic
492C22⋊Q8C23×C10711yescharacteristic
493C22⋊Q8C23×C10711yescharacteristic
494#121—21no—
495#121C23×C10711yescharacteristic
496#120—21no—
497C4×Q8—21no—
498C4×Q8—21no—
499C4×Q8—21no—
500C4×Q8D4×C10711yescharacteristic
501C4×Q8D4×C10711yescharacteristic
502C4×Q8D4×C10711yescharacteristic
503C4×D4—21no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4D4×C10711yescharacteristic
509#117—21no—
510#117—21no—
511#117—21no—
512#117—21no—
513#117—21no—
514#117—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4D4×C10711yescharacteristic
520C2×C4⋊C4D4×C10711yescharacteristic
521C2×C4⋊C4C23×C10711yescharacteristic
522C2×C22⋊C4—21no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4D4×C10711yescharacteristic
525C2×C22⋊C4D4×C10711yescharacteristic
526C2×C22⋊C4C23×C10711yescharacteristic
527C2×C42C23×C10711yescharacteristic
528C4⋊C8—21no—
529C4⋊C8—21no—
530#103—22no—
531#103—22no—
532#103—22no—
533#103—22no—
534C22⋊C8C23×C10712yes—
535C22⋊C8C23×C10712yes—
536#97—21no—
537C4×C8—21no—
538#95—21no—
539#95—21no—
540#95—22no—
541#95—22no—
542#95C23×C10712yes—
543C24C2×D4×C10711yescharacteristic
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—82no—
550C2×Q8C2×D4×C10711yescharacteristic
551C2×Q8C2×D4×C10711yescharacteristic
552C2×Q8C2×D4×C10711yescharacteristic
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4C2×D4×C10711yescharacteristic
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4C2×D4×C10711yescharacteristic
565C22×C4C2×D4×C10711yescharacteristic
566C22×C4C2×D4×C10711yescharacteristic
567C22×C4C2×D4×C10711yescharacteristic
568C22×C4C2×D4×C10711yescharacteristic
569C22×C4C24×C10711yescharacteristic
570Q16—82no—
571Q16—82no—
572Q16—82no—
573SD16—82no—
574C2×C8—22no—
575C2×C8—22no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—41no—
606C4⋊C4—41no—
607C4⋊C4—41no—
608C4⋊C4—41no—
609C4⋊C4—82no—
610C4⋊C4C2×D4×C10711yescharacteristic
611C4⋊C4C2×D4×C10711yescharacteristic
612C4⋊C4C2×D4×C10711yescharacteristic
613C4⋊C4C2×D4×C10711yescharacteristic
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—82no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42C2×D4×C10711yescharacteristic
644C42C2×D4×C10711yescharacteristic
645C42C2×D4×C10711yescharacteristic
646C42C2×D4×C10711yescharacteristic
647C23—21no—
648C23—21no—
649C23—22no—
650C23—41no—
651C23—41no—
652C23C22×D4×C10711yescharacteristic
653Q8—41no—
654Q8—41no—
655Q8—41no—
656Q8—42no—
657Q8—42no—
658Q8—42no—
659Q8—42no—
660Q8—81no—
661Q8—81no—
662Q8—81no—
663D4—41no—
664D4—42no—
665D4—81no—
666D4—81no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—81no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4—81no—
693C2×C4—81no—
694C2×C4#120×C10711yescharacteristic
695C2×C4#120×C10711yescharacteristic
696C2×C4#120×C10711yescharacteristic
697C2×C4#120×C10711yescharacteristic
698C2×C4C22×D4×C10711yescharacteristic
699C2×C4C22×D4×C10711yescharacteristic
700C8—42no—
701C8—42no—
702C22—21no—
703C22—21no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—82no—
711C22C2×#120×C10711yescharacteristic
712C22#578×C10712yes—
713C4—21no—
714C4—21no—
715C4—21no—
716C4—21no—
717C4—21no—
718C4—21no—
719C4—41no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4—82no—
730C4—82no—
731C2—22no—
732C2—81no—
733C2—81no—
734C2C107×#301111yescharacteristic
735C2C107×#302211yescharacteristic
736C2C107×#302711yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC22×C4C24×C107
prime radical#538×C107C22
LCSG ▷ C22×C4 ▷ 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×#3218C2semidirect
3. C107×#3209C2semidirect
4. C107×#2821C2semidirect
6. C107×#1605C2semidirect
7. C107×#1603C2semidirect
8. C107×#1602C2semidirect
9. C107×#1521C2semidirect
10. C107×#1515C2semidirect
11. C107×#1473C2semidirect
362. #18465C107direct (N × H)
370. #3218C2×C107semidirect
371. #3209C2×C107semidirect
372. #2821C2×C107semidirect
374. #1605C2×C107semidirect
375. #1603C2×C107semidirect
376. #1602C2×C107semidirect
377. #1521C2×C107semidirect
378. #1515C2×C107semidirect
379. #1473C2×C107semidirect
380. C107#18465direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#35642
C107×#32182
C107×#32092
C107×#28212
C107×#16062
C107×#16052
C107×#16032
C107×#16022
C107×#15212
C107×#15152
C107×#14732
#18465107