Finite Group Databasebeta

← C107×#18503 #41044467

Subgroups — C107×#18503 #41044467

Order 27392.

922 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3482C211yesmaximal, characteristic
2C107×#3160C211yesmaximal, characteristic, complemented
3C107×#3107C211yesmaximal, characteristic, complemented
4C107×#3107C211yesmaximal, characteristic, complemented
5C107×#1654C211yesmaximal, characteristic, complemented
6C107×#1653C211yesmaximal, characteristic, complemented
7C107×#1652C211yesmaximal, characteristic, complemented
8C107×#1651C211yesmaximal, characteristic, complemented
9C107×#1650C211yesmaximal, characteristic, complemented
10C107×#1649C211yesmaximal, characteristic, complemented
11C107×#1648C211yesmaximal, characteristic, complemented
12C107×#1647C211yesmaximal, characteristic, complemented
13C107×#1544C211yesmaximal, characteristic, complemented
14C107×#1476C211yesmaximal, characteristic, complemented
15C107×#1476C211yesmaximal, characteristic, complemented
16#557×C107C2211yescharacteristic
17#556×C107—21no—
18#556×C107C2211yescharacteristic
19#552×C107—22no—
20#552×C107—21no—
21D4×Q8×C107C2211yescharacteristic
22#548×C107—21no—
23#547×C107—21no—
24#547×C107C2211yescharacteristic
25#533×C107—21no—
26#533×C107C2211yescharacteristic
27#533×C107C2211yescharacteristic
28#529×C107—21no—
29#529×C107—22no—
30C4×#41×C107—21no—
31C4×#41×C107C2211yescharacteristic
32C4×#41×C107C2211yescharacteristic
33C2×C4×Q8×C107—21no—
34#500×C107C2211yescharacteristic
35#500×C107C2211yescharacteristic
36#499×C107—22no—
37#498×C107C2211yescharacteristic
38#498×C107C2211yescharacteristic
39#485×C107—21no—
40#485×C107—21no—
41#475×C107C2211yescharacteristic
42#475×C107C2211yescharacteristic
43#474×C107C2211yescharacteristic
44#474×C107C2211yescharacteristic
45#462×C107C2211yescharacteristic
46#462×C107C2211yescharacteristic
47#461×C107C2211yescharacteristic
48#461×C107C2211yescharacteristic
49#452×C107—21no—
50#452×C107—21no—
51C4×Q16×C107—21no—
52C4×Q16×C107—21no—
53C4×SD16×C107—21no—
54C4×SD16×C107—21no—
55#431×C107C2211yescharacteristic
56#431×C107C2211yescharacteristic
57#427×C107—22no—
58C2×C4×C8×C107C2211yescharacteristic
59#332×C107C2211yescharacteristic
60#332×C107C2211yescharacteristic
61#332×C107C2211yescharacteristic
62#332×C107C2211yescharacteristic
63Q8⋊C8×C107C2211yescharacteristic
64Q8⋊C8×C107C2211yescharacteristic
65Q8⋊C8×C107C2211yescharacteristic
66Q8⋊C8×C107C2211yescharacteristic
67D4⋊C8×C107C2211yescharacteristic
68D4⋊C8×C107C2211yescharacteristic
69D4⋊C8×C107C2211yescharacteristic
70D4⋊C8×C107C2211yescharacteristic
71C2×#41×C107—21no—
72C2×#41×C107D411yescharacteristic
73C2×#41×C107D411yescharacteristic
74C22×Q8×C107—21no—
75C2×Q16×C107—21no—
76C2×Q16×C107—21no—
77C2×SD16×C107—21no—
78C2×SD16×C107—21no—
79C22×C8×C107—21no—
80C4⋊Q8×C107—21no—
81C4⋊Q8×C107—21no—
82C4⋊Q8×C107C2311yescharacteristic
83C4⋊Q8×C107C2311yescharacteristic
84C4⋊Q8×C107C2311yescharacteristic
85C4⋊Q8×C107C2311yescharacteristic
86#126×C107—22no—
87#126×C107—22no—
88#126×C107—22no—
89#125×C107—22no—
90#125×C107—22no—
91#125×C107—21no—
92#125×C107—21no—
93#125×C107D412yes—
94#124×C107—22no—
95#124×C107—21no—
96#123×C107—22no—
97#123×C107—22no—
98#123×C107—22no—
99C22⋊Q8×C107—22no—
100C22⋊Q8×C107—21no—
101C22⋊Q8×C107—21no—
102C22⋊Q8×C107—21no—
103C22⋊Q8×C107—21no—
104C22⋊Q8×C107—22no—
105C22⋊Q8×C107—21no—
106C22⋊Q8×C107—21no—
107C22⋊Q8×C107—21no—
108#121×C107—22no—
109#121×C107—21no—
110C4×Q8×C107—22no—
111C4×Q8×C107—22no—
112C4×Q8×C107—21no—
113C4×Q8×C107—21no—
114C4×Q8×C107—21no—
115C4×Q8×C107—21no—
116C4×Q8×C107—21no—
117C4×Q8×C107—21no—
118C4×Q8×C107—21no—
119C4×Q8×C107D411yescharacteristic
120C4×Q8×C107D411yescharacteristic
121C4×Q8×C107C2311yescharacteristic
122C4×Q8×C107C2311yescharacteristic
123C4×D4×C107—22no—
124C4×D4×C107—22no—
125C4×D4×C107—21no—
126C4×D4×C107—21no—
127C4×D4×C107—21no—
128C4×D4×C107—21no—
129C4×D4×C107—21no—
130C4×D4×C107D411yescharacteristic
131C4×D4×C107D411yescharacteristic
132C4×D4×C107C2311yescharacteristic
133C4×D4×C107C2311yescharacteristic
134#117×C107—22no—
135#117×C107—22no—
136#117×C107—21no—
137#117×C107—21no—
138#117×C107—21no—
139#117×C107—21no—
140#117×C107D412yes—
141#117×C107D411yescharacteristic
142#117×C107D411yescharacteristic
143C2×C4⋊C4×C107—22no—
144C2×C4⋊C4×C107—21no—
145C2×C42×C107—22no—
146C2×C42×C107—21no—
147C2×C42×C107—21no—
148C2×C42×C107C2311yescharacteristic
149#107×C107—22no—
150#107×C107—22no—
151#107×C107—21no—
152#107×C107—21no—
153#106×C107—22no—
154#106×C107—22no—
155#106×C107—21no—
156#106×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#103×C107—21no—
165#103×C107—21no—
166#103×C107—21no—
167#102×C107—21no—
168#102×C107—21no—
169C22⋊C8×C107—21no—
170C22⋊C8×C107—21no—
171C4×C8×C107—21no—
172C4×C8×C107—21no—
173C4×C8×C107—21no—
174C4×C8×C107C2311yescharacteristic
175C4×C8×C107C2311yescharacteristic
176#41×C107—22no—
177#41×C107—22no—
178#41×C107—41no—
179#41×C107—41no—
180#41×C107—42no—
181#41×C107—42no—
182C2×Q8×C107—22no—
183C2×Q8×C107—21no—
184C2×Q8×C107—21no—
185C2×Q8×C107—21no—
186C2×Q8×C107—21no—
187C2×Q8×C107—42no—
188C2×Q8×C107—42no—
189C2×Q8×C107C2×D411yescharacteristic
190C2×Q8×C107C2×D411yescharacteristic
191C2×D4×C107—22no—
192C2×D4×C107—21no—
193C2×D4×C107—21no—
194C2×D4×C107C2×D411yescharacteristic
195C2×D4×C107C2×D411yescharacteristic
196C22×C4×C107—22no—
197C22×C4×C107—22no—
198C22×C4×C107—21no—
199C22×C4×C107—21no—
200C22×C4×C107—21no—
201C22×C4×C107—21no—
202C22×C4×C107—21no—
203C22×C4×C107—21no—
204C22×C4×C107C2×D411yescharacteristic
205C22×C4×C107C2×D411yescharacteristic
206C22×C4×C107C2×D411yescharacteristic
207Q16×C107—42no—
208Q16×C107—42no—
209SD16×C107—42no—
210SD16×C107—42no—
211C2×C8×C107—24no—
212C2×C8×C107—21no—
213C2×C8×C107—21no—
214C2×C8×C107—21no—
215C2×C8×C107—21no—
216C2×C8×C107—21no—
217C2×C8×C107—21no—
218C4⋊C4×C107—22no—
219C4⋊C4×C107—22no—
220C4⋊C4×C107—22no—
221C4⋊C4×C107—22no—
222C4⋊C4×C107—22no—
223C4⋊C4×C107—22no—
224C4⋊C4×C107—21no—
225C4⋊C4×C107—22no—
226C4⋊C4×C107—22no—
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×C107C2×D411yescharacteristic
239C4⋊C4×C107C2×D411yescharacteristic
240C4⋊C4×C107C2×D411yescharacteristic
241C4⋊C4×C107C2×D411yescharacteristic
242C4⋊C4×C107C2×D412yes—
243C4⋊C4×C107C2×D412yes—
244C22⋊C4×C107—22no—
245C22⋊C4×C107—22no—
246C22⋊C4×C107—22no—
247C22⋊C4×C107—22no—
248C22⋊C4×C107—21no—
249C22⋊C4×C107—21no—
250C22⋊C4×C107—22no—
251C22⋊C4×C107—21no—
252C22⋊C4×C107—21no—
253C22⋊C4×C107—21no—
254C22⋊C4×C107—21no—
255C22⋊C4×C107—41no—
256C42×C107—22no—
257C42×C107—22no—
258C42×C107—21no—
259C42×C107—21no—
260C42×C107—21no—
261C42×C107—21no—
262C42×C107—22no—
263C42×C107—21no—
264C42×C107—21no—
265C42×C107—41no—
266C42×C107C2×D411yescharacteristic
267C42×C107C2×D411yescharacteristic
268C42×C107C2×D411yescharacteristic
269C42×C107C2411yescharacteristic
270C23×C107—21no—
271C23×C107—21no—
272C23×C107#12011yescharacteristic
273Q8×C107—21no—
274Q8×C107—21no—
275Q8×C107—21no—
276Q8×C107—44no—
277Q8×C107—41no—
278Q8×C107—41no—
279Q8×C107—41no—
280Q8×C107—41no—
281Q8×C107—41no—
282Q8×C107—41no—
283Q8×C107—41no—
284Q8×C107—41no—
285Q8×C107#13512yes—
286D4×C107—21no—
287D4×C107—21no—
288D4×C107—21no—
289D4×C107—42no—
290D4×C107—42no—
291D4×C107—44no—
292D4×C107#13512yes—
293C2×C4×C107—21no—
294C2×C4×C107—21no—
295C2×C4×C107—21no—
296C2×C4×C107—21no—
297C2×C4×C107—21no—
298C2×C4×C107—22no—
299C2×C4×C107—21no—
300C2×C4×C107—21no—
301C2×C4×C107—21no—
302C2×C4×C107—22no—
303C2×C4×C107—21no—
304C2×C4×C107—21no—
305C2×C4×C107—22no—
306C2×C4×C107—42no—
307C2×C4×C107—42no—
308C2×C4×C107—44no—
309C2×C4×C107—44no—
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—41no—
317C2×C4×C107—41no—
318C2×C4×C107#12011yescharacteristic
319C2×C4×C107#12011yescharacteristic
320C2×C4×C107#12011yescharacteristic
321C2×C4×C107C22×D411yescharacteristic
322C2×C4×C107C22×D411yescharacteristic
323C2×C4×C107C22×D411yescharacteristic
324C8×C107—22no—
325C8×C107—22no—
326C8×C107—41no—
327C8×C107—41no—
328C8×C107—41no—
329C8×C107—41no—
330C22×C107—21no—
331C22×C107—21no—
332C22×C107—22no—
333C22×C107—21no—
334C22×C107—41no—
335C22×C107—41no—
336C22×C107—41no—
337C22×C107—41no—
338C22×C107—41no—
339C22×C107C2×#12011yescharacteristic
340C4×C107—21no—
341C4×C107—21no—
342C4×C107—22no—
343C4×C107—21no—
344C4×C107—41no—
345C4×C107—41no—
346C4×C107—42no—
347C4×C107—42no—
348C4×C107—41no—
349C4×C107—41no—
350C4×C107—41no—
351C4×C107—81no—
352C4×C107—81no—
353C4×C107#45612yes—
354C4×C107C2×#13511yescharacteristic
355C4×C107C2×#13511yescharacteristic
356C4×C107#57511yescharacteristic
357C4×C107#57511yescharacteristic
358#18503C10711yesmaximal, characteristic, direct product factor, Sylow
359C2×C107—41no—
360C2×C107—42no—
361C2×C107—81no—
362C2×C107#300211yescharacteristic
363C2×C107#300211yescharacteristic
364C2×C107C2×#45611yescharacteristic
365#3482C2×C10711yescharacteristic
366#3160C2×C10711yescharacteristic, complemented
367#3107C2×C10711yescharacteristic, complemented
368#3107C2×C10711yescharacteristic, complemented
369#1654C2×C10711yescharacteristic, complemented
370#1653C2×C10711yescharacteristic, complemented
371#1652C2×C10711yescharacteristic, complemented
372#1651C2×C10711yescharacteristic, complemented
373#1650C2×C10711yescharacteristic, complemented
374#1649C2×C10711yescharacteristic, complemented
375#1648C2×C10711yescharacteristic, complemented
376#1647C2×C10711yescharacteristic, complemented
377#1544C2×C10711yescharacteristic, complemented
378#1476C2×C10711yescharacteristic, complemented
379#1476C2×C10711yescharacteristic, complemented
380C107#1850311yescharacteristic, direct product factor, Sylow
381#557C22×C10711yescharacteristic
382#556—21no—
383#556C22×C10711yescharacteristic
384#552—22no—
385#552—21no—
386D4×Q8C22×C10711yescharacteristic
387#548—21no—
388#547—21no—
389#547C22×C10711yescharacteristic
390#533—21no—
391#533C22×C10711yescharacteristic
392#533C22×C10711yescharacteristic
393#529—21no—
394#529—22no—
395C4×#41—21no—
396C4×#41C22×C10711yescharacteristic
397C4×#41C22×C10711yescharacteristic
398C2×C4×Q8—21no—
399#500C22×C10711yescharacteristic
400#500C22×C10711yescharacteristic
401#499—22no—
402#498C22×C10711yescharacteristic
403#498C22×C10711yescharacteristic
404#485—21no—
405#485—21no—
406#475C22×C10711yescharacteristic
407#475C22×C10711yescharacteristic
408#474C22×C10711yescharacteristic
409#474C22×C10711yescharacteristic
410#462C22×C10711yescharacteristic
411#462C22×C10711yescharacteristic
412#461C22×C10711yescharacteristic
413#461C22×C10711yescharacteristic
414#452—21no—
415#452—21no—
416C4×Q16—21no—
417C4×Q16—21no—
418C4×SD16—21no—
419C4×SD16—21no—
420#431C22×C10711yescharacteristic
421#431C22×C10711yescharacteristic
422#427—22no—
423C2×C4×C8C22×C10711yescharacteristic
424#332C22×C10711yescharacteristic
425#332C22×C10711yescharacteristic
426#332C22×C10711yescharacteristic
427#332C22×C10711yescharacteristic
428Q8⋊C8C22×C10711yescharacteristic
429Q8⋊C8C22×C10711yescharacteristic
430Q8⋊C8C22×C10711yescharacteristic
431Q8⋊C8C22×C10711yescharacteristic
432D4⋊C8C22×C10711yescharacteristic
433D4⋊C8C22×C10711yescharacteristic
434D4⋊C8C22×C10711yescharacteristic
435D4⋊C8C22×C10711yescharacteristic
436C2×#41—21no—
437C2×#41D4×C10711yescharacteristic
438C2×#41D4×C10711yescharacteristic
439C22×Q8—21no—
440C2×Q16—21no—
441C2×Q16—21no—
442C2×SD16—21no—
443C2×SD16—21no—
444C22×C8—21no—
445C4⋊Q8—21no—
446C4⋊Q8—21no—
447C4⋊Q8C23×C10711yescharacteristic
448C4⋊Q8C23×C10711yescharacteristic
449C4⋊Q8C23×C10711yescharacteristic
450C4⋊Q8C23×C10711yescharacteristic
451#126—22no—
452#126—22no—
453#126—22no—
454#125—22no—
455#125—22no—
456#125—21no—
457#125—21no—
458#125D4×C10712yes—
459#124—22no—
460#124—21no—
461#123—22no—
462#123—22no—
463#123—22no—
464C22⋊Q8—22no—
465C22⋊Q8—21no—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8—21no—
469C22⋊Q8—22no—
470C22⋊Q8—21no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473#121—22no—
474#121—21no—
475C4×Q8—22no—
476C4×Q8—22no—
477C4×Q8—21no—
478C4×Q8—21no—
479C4×Q8—21no—
480C4×Q8—21no—
481C4×Q8—21no—
482C4×Q8—21no—
483C4×Q8—21no—
484C4×Q8D4×C10711yescharacteristic
485C4×Q8D4×C10711yescharacteristic
486C4×Q8C23×C10711yescharacteristic
487C4×Q8C23×C10711yescharacteristic
488C4×D4—22no—
489C4×D4—22no—
490C4×D4—21no—
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4D4×C10711yescharacteristic
496C4×D4D4×C10711yescharacteristic
497C4×D4C23×C10711yescharacteristic
498C4×D4C23×C10711yescharacteristic
499#117—22no—
500#117—22no—
501#117—21no—
502#117—21no—
503#117—21no—
504#117—21no—
505#117D4×C10711yescharacteristic
506#117D4×C10711yescharacteristic
507#117D4×C10712yes—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—21no—
510C2×C42—22no—
511C2×C42—21no—
512C2×C42—21no—
513C2×C42C23×C10711yescharacteristic
514#107—22no—
515#107—22no—
516#107—21no—
517#107—21no—
518#106—22no—
519#106—22no—
520#106—21no—
521#106—21no—
522C4⋊C8C23×C10711yescharacteristic
523C4⋊C8C23×C10711yescharacteristic
524C4⋊C8C23×C10711yescharacteristic
525C4⋊C8C23×C10711yescharacteristic
526#103—21no—
527#103—21no—
528#103—21no—
529#103—21no—
530#103—21no—
531#103—21no—
532#102—21no—
533#102—21no—
534C22⋊C8—21no—
535C22⋊C8—21no—
536C4×C8—21no—
537C4×C8—21no—
538C4×C8—21no—
539C4×C8C23×C10711yescharacteristic
540C4×C8C23×C10711yescharacteristic
541#41—22no—
542#41—22no—
543#41—41no—
544#41—41no—
545#41—42no—
546#41—42no—
547C2×Q8—22no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—42no—
553C2×Q8—42no—
554C2×Q8C2×D4×C10711yescharacteristic
555C2×Q8C2×D4×C10711yescharacteristic
556C2×D4—22no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4C2×D4×C10711yescharacteristic
560C2×D4C2×D4×C10711yescharacteristic
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4C2×D4×C10711yescharacteristic
570C22×C4C2×D4×C10711yescharacteristic
571C22×C4C2×D4×C10711yescharacteristic
572Q16—42no—
573Q16—42no—
574SD16—42no—
575SD16—42no—
576C2×C8—24no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—21no—
590C4⋊C4—22no—
591C4⋊C4—22no—
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—41no—
602C4⋊C4—41no—
603C4⋊C4C2×D4×C10711yescharacteristic
604C4⋊C4C2×D4×C10711yescharacteristic
605C4⋊C4C2×D4×C10711yescharacteristic
606C4⋊C4C2×D4×C10711yescharacteristic
607C4⋊C4C2×D4×C10712yes—
608C4⋊C4C2×D4×C10712yes—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—22no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—41no—
621C42—22no—
622C42—22no—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—22no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—41no—
631C42C2×D4×C10711yescharacteristic
632C42C2×D4×C10711yescharacteristic
633C42C2×D4×C10711yescharacteristic
634C42C24×C10711yescharacteristic
635C23—21no—
636C23—21no—
637C23#120×C10711yescharacteristic
638Q8—21no—
639Q8—21no—
640Q8—21no—
641Q8—44no—
642Q8—41no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8#135×C10712yes—
651D4—21no—
652D4—21no—
653D4—21no—
654D4—42no—
655D4—42no—
656D4—44no—
657D4#135×C10712yes—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—44no—
674C2×C4—44no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4#120×C10711yescharacteristic
684C2×C4#120×C10711yescharacteristic
685C2×C4#120×C10711yescharacteristic
686C2×C4C22×D4×C10711yescharacteristic
687C2×C4C22×D4×C10711yescharacteristic
688C2×C4C22×D4×C10711yescharacteristic
689C8—22no—
690C8—22no—
691C8—41no—
692C8—41no—
693C8—41no—
694C8—41no—
695C22—21no—
696C22—21no—
697C22—22no—
698C22—21no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22C2×#120×C10711yescharacteristic
705C4—21no—
706C4—21no—
707C4—22no—
708C4—21no—
709C4—41no—
710C4—41no—
711C4—42no—
712C4—42no—
713C4—41no—
714C4—41no—
715C4—41no—
716C4—81no—
717C4—81no—
718C4#456×C10712yes—
719C4C2×#135×C10711yescharacteristic
720C4C2×#135×C10711yescharacteristic
721C4#575×C10711yescharacteristic
722C4#575×C10711yescharacteristic
723C2—41no—
724C2—42no—
725C2—81no—
726C2C107×#300211yescharacteristic
727C2C107×#300211yescharacteristic
728C2C2×#456×C10711yescharacteristic
subgroupG/H
centerC2×C4×C107#120
commutator, Frattini, cosocleC42C24×C107
socleC22×C107C2×#120
prime radicalC107×#3482C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#3160C2semidirect
3. C107×#3107C2semidirect
4. C107×#3107C2semidirect
5. C107×#1654C2semidirect
6. C107×#1653C2semidirect
7. C107×#1652C2semidirect
8. C107×#1651C2semidirect
9. C107×#1650C2semidirect
10. C107×#1649C2semidirect
11. C107×#1648C2semidirect
12. C107×#1647C2semidirect
13. C107×#1544C2semidirect
14. C107×#1476C2semidirect
15. C107×#1476C2semidirect
358. #18503C107direct (N × H)
366. #3160C2×C107semidirect
367. #3107C2×C107semidirect
368. #3107C2×C107semidirect
369. #1654C2×C107semidirect
370. #1653C2×C107semidirect
371. #1652C2×C107semidirect
372. #1651C2×C107semidirect
373. #1650C2×C107semidirect
374. #1649C2×C107semidirect
375. #1648C2×C107semidirect
376. #1647C2×C107semidirect
377. #1544C2×C107semidirect
378. #1476C2×C107semidirect
379. #1476C2×C107semidirect
380. C107#18503direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#34822
C107×#31602
C107×#31072
C107×#16542
C107×#16532
C107×#16522
C107×#16512
C107×#16502
C107×#16492
C107×#16482
C107×#16472
C107×#15442
C107×#14762
#18503107