Finite Group Databasebeta

← C107×#18520 #41044484

Subgroups — C107×#18520 #41044484

Order 27392.

990 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3480C211yesmaximal, characteristic, complemented
2C107×#3169C211yesmaximal, characteristic, complemented
3C107×#3103C211yesmaximal, characteristic, complemented
4C107×#3035C211yesmaximal, characteristic, complemented
5C107×#1650C211yesmaximal, characteristic, complemented
6C107×#1648C211yesmaximal, characteristic, complemented
7C107×#1642C211yesmaximal, characteristic, complemented
8C107×#1640C211yesmaximal, characteristic, complemented
9C107×#1628C211yesmaximal, characteristic, complemented
10C107×#1626C211yesmaximal, characteristic, complemented
11C107×#1621C211yesmaximal, characteristic, complemented
12C107×#1620C211yesmaximal, characteristic, complemented
13C107×#1540C211yesmaximal, characteristic, complemented
14C107×#1476C211yesmaximal, characteristic, complemented
15C2×Q8⋊C8×C107C211yesmaximal, characteristic, complemented
16C2×#135×C107—21no—
17#559×C107—21no—
18#559×C107C2211yescharacteristic
19#557×C107C2211yescharacteristic
20#556×C107—21no—
21#556×C107C2211yescharacteristic
22#553×C107—22no—
23#553×C107—21no—
24#550×C107C2211yescharacteristic
25#548×C107—21no—
26#532×C107—21no—
27#532×C107C2211yescharacteristic
28#532×C107C2211yescharacteristic
29#529×C107—21no—
30#529×C107—22no—
31C4×#41×C107—21no—
32C4×#41×C107—21no—
33C4×#41×C107C2211yescharacteristic
34C2×C4×Q8×C107C2211yescharacteristic
35#500×C107C2211yescharacteristic
36#493×C107C2211yescharacteristic
37#486×C107C2211yescharacteristic
38#486×C107C2211yescharacteristic
39#481×C107—21no—
40#475×C107C2211yescharacteristic
41#475×C107C2211yescharacteristic
42#466×C107—22no—
43#464×C107—21no—
44#463×C107—21no—
45#462×C107C2211yescharacteristic
46#461×C107C2211yescharacteristic
47#460×C107C2211yescharacteristic
48#460×C107C2211yescharacteristic
49#460×C107C2211yescharacteristic
50#459×C107C2211yescharacteristic
51#448×C107—21no—
52C4×SD16×C107—21no—
53C4×SD16×C107—21no—
54C4×D8×C107—22no—
55#431×C107C2211yescharacteristic
56C2×C4⋊C8×C107C2211yescharacteristic
57#416×C107—21no—
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—
74C2×#41×C107D411yescharacteristic
75C22×Q8×C107D411yescharacteristic
76#135×C107—44no—
77C2×Q16×C107—21no—
78C2×SD16×C107—21no—
79C2×SD16×C107—21no—
80C2×SD16×C107—21no—
81C2×SD16×C107—21no—
82C2×D8×C107—22no—
83C2×D8×C107—21no—
84C22×C8×C107—21no—
85C22×C8×C107—21no—
86C4⋊Q8×C107—21no—
87C4⋊Q8×C107C2311yescharacteristic
88C4⋊Q8×C107C2311yescharacteristic
89#127×C107—21no—
90#127×C107C2311yescharacteristic
91#127×C107C2311yescharacteristic
92#126×C107—22no—
93#126×C107—22no—
94#126×C107—22no—
95#125×C107—22no—
96#125×C107—21no—
97#124×C107—22no—
98#124×C107—21no—
99#124×C107—21no—
100#124×C107—21no—
101#124×C107—21no—
102#124×C107—21no—
103#123×C107—22no—
104#123×C107—22no—
105#123×C107—22no—
106C22⋊Q8×C107—22no—
107C22⋊Q8×C107—21no—
108#121×C107—22no—
109#121×C107—22no—
110#121×C107—22no—
111#121×C107—21no—
112#121×C107—21no—
113#121×C107—21no—
114#121×C107—21no—
115#121×C107D412yes—
116C4×Q8×C107—21no—
117C4×Q8×C107—21no—
118C4×Q8×C107—21no—
119C4×Q8×C107—21no—
120C4×Q8×C107—21no—
121C4×Q8×C107D411yescharacteristic
122C4×Q8×C107D411yescharacteristic
123C4×Q8×C107D411yescharacteristic
124C4×Q8×C107C2311yescharacteristic
125C4×Q8×C107C2311yescharacteristic
126C4×Q8×C107C2311yescharacteristic
127C4×D4×C107—22no—
128C4×D4×C107—22no—
129C4×D4×C107—22no—
130C4×D4×C107—22no—
131C4×D4×C107—22no—
132C4×D4×C107—21no—
133C4×D4×C107—21no—
134C4×D4×C107—21no—
135C4×D4×C107—21no—
136C4×D4×C107—21no—
137C4×D4×C107—21no—
138C4×D4×C107—21no—
139C4×D4×C107—21no—
140C4×D4×C107D412yes—
141C4×D4×C107D411yescharacteristic
142C4×D4×C107C2311yescharacteristic
143#117×C107—22no—
144#117×C107—22no—
145#117×C107—21no—
146#117×C107—21no—
147#117×C107D411yescharacteristic
148C2×C4⋊C4×C107—21no—
149C2×C4⋊C4×C107D411yescharacteristic
150C2×C42×C107—22no—
151C2×C42×C107—21no—
152C2×C42×C107—21no—
153C2×C42×C107C2311yescharacteristic
154#107×C107—22no—
155#106×C107—21no—
156#106×C107—21no—
157C4⋊C8×C107—21no—
158C4⋊C8×C107C2311yescharacteristic
159C4⋊C8×C107C2311yescharacteristic
160C4⋊C8×C107C2311yescharacteristic
161C4⋊C8×C107C2311yescharacteristic
162#103×C107—21no—
163#103×C107—21no—
164#103×C107—21no—
165#103×C107—21no—
166#102×C107—22no—
167#102×C107—21no—
168#102×C107—21no—
169#102×C107—22no—
170#102×C107—21no—
171#102×C107—21no—
172C22⋊C8×C107—21no—
173C4×C8×C107—21no—
174C4×C8×C107—21no—
175C4×C8×C107C2311yescharacteristic
176C4×C8×C107C2311yescharacteristic
177#41×C107—22no—
178#41×C107—22no—
179#41×C107—42no—
180#41×C107—42no—
181#41×C107—42no—
182#41×C107—42no—
183#41×C107—42no—
184#41×C107—42no—
185C2×Q8×C107—21no—
186C2×Q8×C107—21no—
187C2×Q8×C107—22no—
188C2×Q8×C107—21no—
189C2×Q8×C107—41no—
190C2×Q8×C107C2×D411yescharacteristic
191C2×Q8×C107C2×D411yescharacteristic
192C2×Q8×C107C2×D411yescharacteristic
193C2×D4×C107—22no—
194C2×D4×C107—21no—
195C2×D4×C107—22no—
196C2×D4×C107—22no—
197C2×D4×C107—21no—
198C2×D4×C107—21no—
199C2×D4×C107—21no—
200C2×D4×C107—21no—
201C2×D4×C107—21no—
202C2×D4×C107—41no—
203C2×D4×C107C2×D411yescharacteristic
204C2×D4×C107C2×D412yes—
205C22×C4×C107—22no—
206C22×C4×C107—21no—
207C22×C4×C107—22no—
208C22×C4×C107—21no—
209C22×C4×C107—21no—
210C22×C4×C107—22no—
211C22×C4×C107—21no—
212C22×C4×C107—21no—
213C22×C4×C107—41no—
214C22×C4×C107C2×D411yescharacteristic
215C22×C4×C107C2×D411yescharacteristic
216C22×C4×C107C2×D411yescharacteristic
217Q16×C107—42no—
218SD16×C107—42no—
219SD16×C107—42no—
220SD16×C107—42no—
221SD16×C107—42no—
222D8×C107—44no—
223D8×C107—42no—
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—
231C2×C8×C107—42no—
232C4⋊C4×C107—22no—
233C4⋊C4×C107—22no—
234C4⋊C4×C107—22no—
235C4⋊C4×C107—22no—
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×C107—21no—
246C4⋊C4×C107C2×D411yescharacteristic
247C4⋊C4×C107C2×D411yescharacteristic
248C4⋊C4×C107C2×D411yescharacteristic
249C4⋊C4×C107C2×D411yescharacteristic
250C4⋊C4×C107C2×D412yes—
251C22⋊C4×C107—22no—
252C22⋊C4×C107—22no—
253C22⋊C4×C107—22no—
254C22⋊C4×C107—22no—
255C22⋊C4×C107—22no—
256C22⋊C4×C107—22no—
257C22⋊C4×C107—21no—
258C22⋊C4×C107—22no—
259C22⋊C4×C107—21no—
260C22⋊C4×C107—22no—
261C22⋊C4×C107—21no—
262C22⋊C4×C107—41no—
263C22⋊C4×C107—41no—
264C42×C107—22no—
265C42×C107—22no—
266C42×C107—21no—
267C42×C107—21no—
268C42×C107—21no—
269C42×C107—21no—
270C42×C107—21no—
271C42×C107—21no—
272C42×C107—21no—
273C42×C107C2×D411yescharacteristic
274C42×C107C2×D411yescharacteristic
275C42×C107C2×D411yescharacteristic
276C42×C107C2411yescharacteristic
277C23×C107—21no—
278C23×C107—22no—
279C23×C107—41no—
280C23×C107#12011yescharacteristic
281Q8×C107—21no—
282Q8×C107—21no—
283Q8×C107—21no—
284Q8×C107—21no—
285Q8×C107—21no—
286Q8×C107—42no—
287Q8×C107—41no—
288Q8×C107—41no—
289Q8×C107—41no—
290Q8×C107—41no—
291Q8×C107#13512yescomplemented
292D4×C107—21no—
293D4×C107—21no—
294D4×C107—42no—
295D4×C107—44no—
296D4×C107—42no—
297D4×C107—42no—
298D4×C107—44no—
299D4×C107—41no—
300D4×C107—41no—
301D4×C107—41no—
302D4×C107—41no—
303D4×C107—41no—
304D4×C107—41no—
305D4×C107—41no—
306D4×C107—41no—
307D4×C107—82no—
308D4×C107—82no—
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—21no—
317C2×C4×C107—22no—
318C2×C4×C107—21no—
319C2×C4×C107—41no—
320C2×C4×C107—42no—
321C2×C4×C107—44no—
322C2×C4×C107—41no—
323C2×C4×C107—41no—
324C2×C4×C107—42no—
325C2×C4×C107—44no—
326C2×C4×C107—41no—
327C2×C4×C107—81no—
328C2×C4×C107—81no—
329C2×C4×C107—82no—
330C2×C4×C107—82no—
331C2×C4×C107#12011yescharacteristic
332C2×C4×C107#12011yescharacteristic
333C2×C4×C107#12011yescharacteristic
334C2×C4×C107#13512yes—
335C2×C4×C107AGL(1,ℤ/8)12yes—
336C2×C4×C107C22×D411yescharacteristic
337C2×C4×C107C22×D411yescharacteristic
338C2×C4×C107C22×D411yescharacteristic
339C8×C107—22no—
340C8×C107—41no—
341C8×C107—41no—
342C8×C107—41no—
343C8×C107—41no—
344C8×C107—41no—
345C22×C107—21no—
346C22×C107—21no—
347C22×C107—41no—
348C22×C107—42no—
349C22×C107—42no—
350C22×C107—41no—
351C22×C107—42no—
352C22×C107—41no—
353C22×C107—81no—
354C22×C107—81no—
355C22×C107—81no—
356C22×C107#44912yes—
357C22×C107C2×#12011yescharacteristic
358C4×C107—21no—
359C4×C107—22no—
360C4×C107—21no—
361C4×C107—21no—
362C4×C107—41no—
363C4×C107—42no—
364C4×C107—41no—
365C4×C107—41no—
366C4×C107—41no—
367C4×C107—41no—
368C4×C107—41no—
369C4×C107—81no—
370C4×C107#44912yes—
371C4×C107C2×#13511yescharacteristic
372C4×C107C2×#13511yescharacteristic
373C4×C107C2×AGL(1,ℤ/8)11yescharacteristic
374C4×C107#57511yescharacteristic
375#18520C10711yesmaximal, characteristic, direct product factor, Sylow
376C2×C107—22no—
377C2×C107—81no—
378C2×C107—82no—
379C2×C107—161no—
380C2×C107C2×#44911yescharacteristic
381C2×C107#300211yescharacteristic
382C2×C107#301811yescharacteristic
383#3480C2×C10711yescharacteristic, complemented
384#3169C2×C10711yescharacteristic, complemented
385#3103C2×C10711yescharacteristic, complemented
386#3035C2×C10711yescharacteristic, complemented
387#1650C2×C10711yescharacteristic, complemented
388#1648C2×C10711yescharacteristic, complemented
389#1642C2×C10711yescharacteristic, complemented
390#1640C2×C10711yescharacteristic, complemented
391#1628C2×C10711yescharacteristic, complemented
392#1626C2×C10711yescharacteristic, complemented
393#1621C2×C10711yescharacteristic, complemented
394#1620C2×C10711yescharacteristic, complemented
395#1540C2×C10711yescharacteristic, complemented
396#1476C2×C10711yescharacteristic, complemented
397C2×Q8⋊C8C2×C10711yescharacteristic, complemented
398C107#1852011yescharacteristic, direct product factor, Sylow
399C2×#135—21no—
400#559—21no—
401#559C22×C10711yescharacteristic
402#557C22×C10711yescharacteristic
403#556—21no—
404#556C22×C10711yescharacteristic
405#553—22no—
406#553—21no—
407#550C22×C10711yescharacteristic
408#548—21no—
409#532—21no—
410#532C22×C10711yescharacteristic
411#532C22×C10711yescharacteristic
412#529—21no—
413#529—22no—
414C4×#41—21no—
415C4×#41—21no—
416C4×#41C22×C10711yescharacteristic
417C2×C4×Q8C22×C10711yescharacteristic
418#500C22×C10711yescharacteristic
419#493C22×C10711yescharacteristic
420#486C22×C10711yescharacteristic
421#486C22×C10711yescharacteristic
422#481—21no—
423#475C22×C10711yescharacteristic
424#475C22×C10711yescharacteristic
425#466—22no—
426#464—21no—
427#463—21no—
428#462C22×C10711yescharacteristic
429#461C22×C10711yescharacteristic
430#460C22×C10711yescharacteristic
431#460C22×C10711yescharacteristic
432#460C22×C10711yescharacteristic
433#459C22×C10711yescharacteristic
434#448—21no—
435C4×SD16—21no—
436C4×SD16—21no—
437C4×D8—22no—
438#431C22×C10711yescharacteristic
439C2×C4⋊C8C22×C10711yescharacteristic
440#416—21no—
441C2×C4×C8C22×C10711yescharacteristic
442#332C22×C10711yescharacteristic
443#332C22×C10711yescharacteristic
444#331C22×C10711yescharacteristic
445#331C22×C10711yescharacteristic
446Q8⋊C8C22×C10711yescharacteristic
447Q8⋊C8C22×C10711yescharacteristic
448Q8⋊C8C22×C10711yescharacteristic
449Q8⋊C8C22×C10711yescharacteristic
450Q8⋊C8C22×C10711yescharacteristic
451Q8⋊C8C22×C10711yescharacteristic
452D4⋊C8C22×C10711yescharacteristic
453D4⋊C8C22×C10711yescharacteristic
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41D4×C10711yescharacteristic
458C22×Q8D4×C10711yescharacteristic
459#135—44no—
460C2×Q16—21no—
461C2×SD16—21no—
462C2×SD16—21no—
463C2×SD16—21no—
464C2×SD16—21no—
465C2×D8—21no—
466C2×D8—22no—
467C22×C8—21no—
468C22×C8—21no—
469C4⋊Q8—21no—
470C4⋊Q8C23×C10711yescharacteristic
471C4⋊Q8C23×C10711yescharacteristic
472#127—21no—
473#127C23×C10711yescharacteristic
474#127C23×C10711yescharacteristic
475#126—22no—
476#126—22no—
477#126—22no—
478#125—22no—
479#125—21no—
480#124—22no—
481#124—21no—
482#124—21no—
483#124—21no—
484#124—21no—
485#124—21no—
486#123—22no—
487#123—22no—
488#123—22no—
489C22⋊Q8—22no—
490C22⋊Q8—21no—
491#121—22no—
492#121—22no—
493#121—22no—
494#121—21no—
495#121—21no—
496#121—21no—
497#121—21no—
498#121D4×C10712yes—
499C4×Q8—21no—
500C4×Q8—21no—
501C4×Q8—21no—
502C4×Q8—21no—
503C4×Q8—21no—
504C4×Q8D4×C10711yescharacteristic
505C4×Q8D4×C10711yescharacteristic
506C4×Q8D4×C10711yescharacteristic
507C4×Q8C23×C10711yescharacteristic
508C4×Q8C23×C10711yescharacteristic
509C4×Q8C23×C10711yescharacteristic
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—22no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4D4×C10711yescharacteristic
524C4×D4D4×C10712yes—
525C4×D4C23×C10711yescharacteristic
526#117—22no—
527#117—22no—
528#117—21no—
529#117—21no—
530#117D4×C10711yescharacteristic
531C2×C4⋊C4—21no—
532C2×C4⋊C4D4×C10711yescharacteristic
533C2×C42—22no—
534C2×C42—21no—
535C2×C42—21no—
536C2×C42C23×C10711yescharacteristic
537#107—22no—
538#106—21no—
539#106—21no—
540C4⋊C8—21no—
541C4⋊C8C23×C10711yescharacteristic
542C4⋊C8C23×C10711yescharacteristic
543C4⋊C8C23×C10711yescharacteristic
544C4⋊C8C23×C10711yescharacteristic
545#103—21no—
546#103—21no—
547#103—21no—
548#103—21no—
549#102—22no—
550#102—21no—
551#102—21no—
552#102—22no—
553#102—21no—
554#102—21no—
555C22⋊C8—21no—
556C4×C8—21no—
557C4×C8—21no—
558C4×C8C23×C10711yescharacteristic
559C4×C8C23×C10711yescharacteristic
560#41—22no—
561#41—22no—
562#41—42no—
563#41—42no—
564#41—42no—
565#41—42no—
566#41—42no—
567#41—42no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—22no—
571C2×Q8—21no—
572C2×Q8—41no—
573C2×Q8C2×D4×C10711yescharacteristic
574C2×Q8C2×D4×C10711yescharacteristic
575C2×Q8C2×D4×C10711yescharacteristic
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—41no—
586C2×D4C2×D4×C10711yescharacteristic
587C2×D4C2×D4×C10712yes—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—41no—
597C22×C4C2×D4×C10711yescharacteristic
598C22×C4C2×D4×C10711yescharacteristic
599C22×C4C2×D4×C10711yescharacteristic
600Q16—42no—
601SD16—42no—
602SD16—42no—
603SD16—42no—
604SD16—42no—
605D8—44no—
606D8—42no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—42no—
614C2×C8—42no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—21no—
620C4⋊C4—21no—
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⋊C4C2×D4×C10711yescharacteristic
630C4⋊C4C2×D4×C10711yescharacteristic
631C4⋊C4C2×D4×C10711yescharacteristic
632C4⋊C4C2×D4×C10711yescharacteristic
633C4⋊C4C2×D4×C10712yes—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—21no—
641C22⋊C4—22no—
642C22⋊C4—21no—
643C22⋊C4—22no—
644C22⋊C4—21no—
645C22⋊C4—41no—
646C22⋊C4—41no—
647C42—22no—
648C42—22no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42C2×D4×C10711yescharacteristic
657C42C2×D4×C10711yescharacteristic
658C42C2×D4×C10711yescharacteristic
659C42C24×C10711yescharacteristic
660C23—21no—
661C23—22no—
662C23—41no—
663C23#120×C10711yescharacteristic
664Q8—21no—
665Q8—21no—
666Q8—21no—
667Q8—21no—
668Q8—21no—
669Q8—42no—
670Q8—41no—
671Q8—41no—
672Q8—41no—
673Q8—41no—
674Q8#135×C10712yescomplemented
675D4—21no—
676D4—21no—
677D4—42no—
678D4—44no—
679D4—42no—
680D4—42no—
681D4—44no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—82no—
691D4—82no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—42no—
706C2×C4—44no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—82no—
713C2×C4—82no—
714C2×C4#120×C10711yescharacteristic
715C2×C4#120×C10711yescharacteristic
716C2×C4#120×C10711yescharacteristic
717C2×C4#135×C10712yes—
718C2×C4AGL(1,ℤ/8)×C10712yes—
719C2×C4C22×D4×C10711yescharacteristic
720C2×C4C22×D4×C10711yescharacteristic
721C2×C4C22×D4×C10711yescharacteristic
722C8—22no—
723C8—41no—
724C8—41no—
725C8—41no—
726C8—41no—
727C8—41no—
728C22—21no—
729C22—21no—
730C22—41no—
731C22—42no—
732C22—42no—
733C22—41no—
734C22—42no—
735C22—41no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22#449×C10712yes—
740C22C2×#120×C10711yescharacteristic
741C4—21no—
742C4—22no—
743C4—21no—
744C4—21no—
745C4—41no—
746C4—42no—
747C4—41no—
748C4—41no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—81no—
753C4#449×C10712yes—
754C4C2×#135×C10711yescharacteristic
755C4C2×#135×C10711yescharacteristic
756C4C2×AGL(1,ℤ/8)×C10711yescharacteristic
757C4#575×C10711yescharacteristic
758C2—22no—
759C2—81no—
760C2—82no—
761C2—161no—
762C2C2×#449×C10711yescharacteristic
763C2C107×#300211yescharacteristic
764C2C107×#301811yescharacteristic
subgroupG/H
centerC2×C4×C107#120
commutator, Frattini, cosocleC42C24×C107
socleC22×C107C2×#120
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
1. C107×#3480C2semidirect
2. C107×#3169C2semidirect
3. C107×#3103C2semidirect
4. C107×#3035C2semidirect
5. C107×#1650C2semidirect
6. C107×#1648C2semidirect
7. C107×#1642C2semidirect
8. C107×#1640C2semidirect
9. C107×#1628C2semidirect
10. C107×#1626C2semidirect
11. C107×#1621C2semidirect
12. C107×#1620C2semidirect
13. C107×#1540C2semidirect
14. C107×#1476C2semidirect
15. C2×Q8⋊C8×C107C2semidirect
291. Q8×C107#135semidirect
375. #18520C107direct (N × H)
383. #3480C2×C107semidirect
384. #3169C2×C107semidirect
385. #3103C2×C107semidirect
386. #3035C2×C107semidirect
387. #1650C2×C107semidirect
388. #1648C2×C107semidirect
389. #1642C2×C107semidirect
390. #1640C2×C107semidirect
391. #1628C2×C107semidirect
392. #1626C2×C107semidirect
393. #1621C2×C107semidirect
394. #1620C2×C107semidirect
395. #1540C2×C107semidirect
396. #1476C2×C107semidirect
397. C2×Q8⋊C8C2×C107semidirect
398. C107#18520direct (N × H)
674. Q8#135×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#34802
C107×#31692
C107×#31032
C107×#30352
C107×#16502
C107×#16482
C107×#16422
C107×#16402
C107×#16282
C107×#16262
C107×#16212
C107×#16202
C107×#15402
C107×#14762
C2×Q8⋊C8×C1072
#18520107