Finite Group Databasebeta

← C107×#25585 #41051549

Subgroups — C107×#25585 #41051549

Order 27392.

1636 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3505C211yesmaximal, characteristic, complemented
2C107×#2435C211yesmaximal, characteristic, complemented
3C107×#2433C211yesmaximal, characteristic, complemented
4C107×#2408C211yesmaximal, characteristic, complemented
5C107×#2021C214yesmaximal, complemented
6C107×#1996C211yesmaximal, characteristic, complemented
7C107×#1964C211yesmaximal, characteristic, complemented
8C107×#1889C214yesmaximal, complemented
9C4×#99×C107C211yesmaximal, characteristic, complemented
10C23×D4×C107C2211yescharacteristic
11#553×C107—21no—
12#553×C107—22no—
13#552×C107—21no—
14#551×C107—22no—
15#548×C107—21no—
16#546×C107—21no—
17#539×C107—21no—
18#538×C107—21no—
19#534×C107C2212yes—
20C2×#127×C107—21no—
21#529×C107—21no—
22C2×#124×C107—21no—
23#525×C107—21no—
24C2×C22⋊Q8×C107C2211yescharacteristic
25C2×#121×C107—21no—
26C2×#121×C107C2211yescharacteristic
27C2×#120×C107C2214yes—
28C2×#120×C107C2212yes—
29#518×C107C2212yes—
30C2×C4×D4×C107C2211yescharacteristic
31C2×#99×C107C2212yes—
32C2×#99×C107C2214yes—
33#394×C107—21no—
34#394×C107—22no—
35#392×C107—21no—
36#392×C107—22no—
37#390×C107—21no—
38#390×C107—21no—
39#390×C107—21no—
40#380×C107C2211yescharacteristic
41#379×C107C2212yes—
42#379×C107C2214yes—
43C4×C22⋊C4×C107C2211yescharacteristic
44C4×C22⋊C4×C107C2211yescharacteristic
45#342×C107C2212yes—
46#342×C107C2214yes—
47C25×C107C2312yes—
48C2×#41×C107—21no—
49C22×Q8×C107D411yescharacteristic, complemented
50C22×D4×C107—22no—
51C22×D4×C107—24no—
52C22×D4×C107—21no—
53C22×D4×C107—21no—
54C22×D4×C107—21no—
55C22×D4×C107—21no—
56C22×D4×C107—21no—
57C22×D4×C107—21no—
58C22×D4×C107—44no—
59C22×D4×C107D411yescharacteristic, complemented
60C22×D4×C107C2311yescharacteristic
61C22×D4×C107C2312yes—
62C23×C4×C107D411yescharacteristic, complemented
63C23×C4×C107C2311yescharacteristic
64#127×C107—44no—
65#126×C107—22no—
66#126×C107—22no—
67#126×C107—22no—
68#125×C107—21no—
69#125×C107—22no—
70#124×C107—21no—
71#124×C107—22no—
72#124×C107—44no—
73#123×C107—22no—
74#123×C107—22no—
75#123×C107—22no—
76#123×C107—22no—
77#123×C107—22no—
78C22⋊Q8×C107—21no—
79C22⋊Q8×C107—22no—
80C22⋊Q8×C107—21no—
81C22⋊Q8×C107—21no—
82C22⋊Q8×C107—21no—
83C22⋊Q8×C107—21no—
84#121×C107—21no—
85#121×C107—22no—
86#121×C107—21no—
87#121×C107—21no—
88#121×C107—21no—
89#121×C107—21no—
90#121×C107—22no—
91#121×C107—22no—
92#121×C107—44no—
93#120×C107—22no—
94#120×C107—22no—
95#120×C107—28no—
96#120×C107—44no—
97#120×C107—44no—
98C4×Q8×C107—21no—
99C4×D4×C107—22no—
100C4×D4×C107—21no—
101C4×D4×C107—21no—
102C4×D4×C107—21no—
103C4×D4×C107—21no—
104C4×D4×C107—21no—
105C4×D4×C107—22no—
106C4×D4×C107—22no—
107C4×D4×C107—22no—
108C4×D4×C107—22no—
109#117×C107—21no—
110#117×C107—22no—
111#117×C107—22no—
112C2×C4⋊C4×C107—21no—
113C2×C4⋊C4×C107D411yescharacteristic, complemented
114C2×C4⋊C4×C107D411yescharacteristic, complemented
115C2×C4⋊C4×C107D411yescharacteristic, complemented
116C2×C4⋊C4×C107D412yescomplemented
117C2×C22⋊C4×C107—22no—
118C2×C22⋊C4×C107—22no—
119C2×C22⋊C4×C107—24no—
120C2×C22⋊C4×C107—24no—
121C2×C22⋊C4×C107—22no—
122C2×C22⋊C4×C107—22no—
123C2×C22⋊C4×C107—24no—
124C2×C22⋊C4×C107D411yescharacteristic, complemented
125C2×C22⋊C4×C107D412yescomplemented
126C2×C22⋊C4×C107C2312yes—
127C2×C22⋊C4×C107C2312yes—
128C2×C22⋊C4×C107C2311yescharacteristic
129C2×C22⋊C4×C107C2312yes—
130C2×C22⋊C4×C107C2312yes—
131C2×C42×C107—21no—
132C2×C42×C107—21no—
133C2×C42×C107D411yescharacteristic, complemented
134#99×C107—24no—
135#99×C107—44no—
136#95×C107—21no—
137#95×C107—21no—
138#95×C107—21no—
139C24×C107—22no—
140C24×C107—22no—
141C24×C107—22no—
142C24×C107—24no—
143C24×C107—24no—
144C24×C107—44no—
145C24×C107—82no—
146C24×C107C2×D412yes—
147C24×C107C2×D411yescharacteristic
148C24×C107C2411yescharacteristic
149#41×C107—82no—
150C2×Q8×C107—21no—
151C2×Q8×C107—21no—
152C2×Q8×C107—42no—
153C2×D4×C107—24no—
154C2×D4×C107—24no—
155C2×D4×C107—24no—
156C2×D4×C107—21no—
157C2×D4×C107—22no—
158C2×D4×C107—21no—
159C2×D4×C107—22no—
160C2×D4×C107—22no—
161C2×D4×C107—24no—
162C2×D4×C107—24no—
163C2×D4×C107—22no—
164C2×D4×C107—22no—
165C2×D4×C107—22no—
166C2×D4×C107—21no—
167C2×D4×C107—21no—
168C2×D4×C107—42no—
169C2×D4×C107—42no—
170C2×D4×C107—42no—
171C2×D4×C107—42no—
172C2×D4×C107—48no—
173C2×D4×C107—44no—
174C2×D4×C107—44no—
175C2×D4×C107—44no—
176C2×D4×C107—44no—
177C2×D4×C107—44no—
178C2×D4×C107—48no—
179C2×D4×C107—41no—
180C2×D4×C107—41no—
181C2×D4×C107—41no—
182C2×D4×C107—41no—
183C2×D4×C107—84no—
184C2×D4×C107—82no—
185C22×C4×C107—22no—
186C22×C4×C107—22no—
187C22×C4×C107—22no—
188C22×C4×C107—21no—
189C22×C4×C107—21no—
190C22×C4×C107—22no—
191C22×C4×C107—22no—
192C22×C4×C107—42no—
193C22×C4×C107—42no—
194C22×C4×C107C2×D411yescharacteristic
195C22×C4×C107C2×D412yes—
196C22×C4×C107C2×D411yescharacteristic
197C22×C4×C107C2×D411yescharacteristic
198C22×C4×C107C2×D411yescharacteristic
199C22×C4×C107C2×D411yescharacteristic
200C22×C4×C107C2×D412yes—
201C22×C4×C107C2×D411yescharacteristic
202C22×C4×C107C2×D412yes—
203C22×C4×C107C2×D411yescharacteristic
204C22×C4×C107C2×D411yescharacteristic
205C22×C4×C107C2×D411yescharacteristic
206C4⋊C4×C107—22no—
207C4⋊C4×C107—22no—
208C4⋊C4×C107—22no—
209C4⋊C4×C107—22no—
210C4⋊C4×C107—21no—
211C4⋊C4×C107—22no—
212C4⋊C4×C107—21no—
213C4⋊C4×C107—21no—
214C4⋊C4×C107—21no—
215C4⋊C4×C107—21no—
216C4⋊C4×C107—22no—
217C4⋊C4×C107—21no—
218C4⋊C4×C107—42no—
219C22⋊C4×C107—22no—
220C22⋊C4×C107—22no—
221C22⋊C4×C107—22no—
222C22⋊C4×C107—22no—
223C22⋊C4×C107—22no—
224C22⋊C4×C107—22no—
225C22⋊C4×C107—21no—
226C22⋊C4×C107—22no—
227C22⋊C4×C107—21no—
228C22⋊C4×C107—22no—
229C22⋊C4×C107—22no—
230C22⋊C4×C107—22no—
231C22⋊C4×C107—21no—
232C22⋊C4×C107—21no—
233C22⋊C4×C107—22no—
234C22⋊C4×C107—22no—
235C22⋊C4×C107—22no—
236C22⋊C4×C107—24no—
237C22⋊C4×C107—48no—
238C22⋊C4×C107—44no—
239C22⋊C4×C107—44no—
240C22⋊C4×C107—48no—
241C22⋊C4×C107—84no—
242C22⋊C4×C107—82no—
243C22⋊C4×C107#4114yescomplemented
244C42×C107—22no—
245C42×C107—22no—
246C42×C107—21no—
247C42×C107—21no—
248C42×C107—42no—
249C42×C107—42no—
250C23×C107—24no—
251C23×C107—24no—
252C23×C107—24no—
253C23×C107—21no—
254C23×C107—22no—
255C23×C107—21no—
256C23×C107—21no—
257C23×C107—24no—
258C23×C107—41no—
259C23×C107—41no—
260C23×C107—41no—
261C23×C107—41no—
262C23×C107—44no—
263C23×C107—42no—
264C23×C107—42no—
265C23×C107—42no—
266C23×C107—42no—
267C23×C107—42no—
268C23×C107—44no—
269C23×C107—42no—
270C23×C107—42no—
271C23×C107—42no—
272C23×C107—42no—
273C23×C107—42no—
274C23×C107—44no—
275C23×C107—44no—
276C23×C107—88no—
277C23×C107—88no—
278C23×C107C22×D411yescharacteristic
279C23×C107C22×D411yescharacteristic
280C23×C107C22×D411yescharacteristic
281C23×C107C2×#4112yes—
282C23×C107H(5,𝔽2)12yes—
283Q8×C107—42no—
284Q8×C107—81no—
285D4×C107—44no—
286D4×C107—44no—
287D4×C107—44no—
288D4×C107—42no—
289D4×C107—42no—
290D4×C107—42no—
291D4×C107—42no—
292D4×C107—44no—
293D4×C107—44no—
294D4×C107—42no—
295D4×C107—81no—
296D4×C107—82no—
297D4×C107—82no—
298D4×C107—816no—
299D4×C107—88no—
300C2×C4×C107—22no—
301C2×C4×C107—22no—
302C2×C4×C107—22no—
303C2×C4×C107—21no—
304C2×C4×C107—22no—
305C2×C4×C107—21no—
306C2×C4×C107—21no—
307C2×C4×C107—22no—
308C2×C4×C107—22no—
309C2×C4×C107—21no—
310C2×C4×C107—21no—
311C2×C4×C107—24no—
312C2×C4×C107—24no—
313C2×C4×C107—41no—
314C2×C4×C107—41no—
315C2×C4×C107—41no—
316C2×C4×C107—42no—
317C2×C4×C107—42no—
318C2×C4×C107—42no—
319C2×C4×C107—41no—
320C2×C4×C107—42no—
321C2×C4×C107—41no—
322C2×C4×C107—42no—
323C2×C4×C107—42no—
324C2×C4×C107—42no—
325C2×C4×C107—42no—
326C2×C4×C107—42no—
327C2×C4×C107—42no—
328C2×C4×C107—42no—
329C2×C4×C107—81no—
330C2×C4×C107—82no—
331C2×C4×C107—82no—
332C2×C4×C107#12011yescharacteristic
333C2×C4×C107#12011yescharacteristic
334C2×C4×C107#12011yescharacteristic
335C2×C4×C107#12011yescharacteristic
336C22×C107—21no—
337C22×C107—21no—
338C22×C107—21no—
339C22×C107—21no—
340C22×C107—21no—
341C22×C107—21no—
342C22×C107—42no—
343C22×C107—42no—
344C22×C107—42no—
345C22×C107—48no—
346C22×C107—44no—
347C22×C107—48no—
348C22×C107—44no—
349C22×C107—41no—
350C22×C107—42no—
351C22×C107—41no—
352C22×C107—42no—
353C22×C107—44no—
354C22×C107—42no—
355C22×C107—41no—
356C22×C107—84no—
357C22×C107—81no—
358C22×C107—84no—
359C22×C107—82no—
360C22×C107—84no—
361C22×C107—82no—
362C22×C107—82no—
363C22×C107—82no—
364C22×C107C2×#12011yescharacteristic
365C22×C107#53211yescharacteristic
366C22×C107#53511yescharacteristic
367C22×C107#54612yes—
368C22×C107#55012yes—
369C4×C107—21no—
370C4×C107—21no—
371C4×C107—21no—
372C4×C107—44no—
373C4×C107—41no—
374C4×C107—42no—
375C4×C107—41no—
376C4×C107—42no—
377C4×C107—41no—
378C4×C107—42no—
379C4×C107—82no—
380C4×C107—82no—
381C4×C107B(4,𝔽2)12yes—
382#25585C10711yesmaximal, characteristic, direct product factor, Sylow
383C2×C107—22no—
384C2×C107—21no—
385C2×C107—22no—
386C2×C107—21no—
387C2×C107—84no—
388C2×C107—81no—
389C2×C107—82no—
390C2×C107#243111yescharacteristic
391C2×C107C2×B(4,𝔽2)11yescharacteristic
392C2×C107#302711yescharacteristic
393#3505C2×C10711yescharacteristic, complemented
394#2435C2×C10711yescharacteristic, complemented
395#2433C2×C10711yescharacteristic, complemented
396#2408C2×C10711yescharacteristic, complemented
397#2021C2×C10714yescomplemented
398#1996C2×C10711yescharacteristic, complemented
399#1964C2×C10711yescharacteristic, complemented
400#1889C2×C10714yescomplemented
401C4×#99C2×C10711yescharacteristic, complemented
402C107#2558511yescharacteristic, direct product factor, Sylow
403C23×D4C22×C10711yescharacteristic
404#553—21no—
405#553—22no—
406#552—21no—
407#551—22no—
408#548—21no—
409#546—21no—
410#539—21no—
411#538—21no—
412#534C22×C10712yes—
413C2×#127—21no—
414#529—21no—
415C2×#124—21no—
416#525—21no—
417C2×C22⋊Q8C22×C10711yescharacteristic
418C2×#121—21no—
419C2×#121C22×C10711yescharacteristic
420C2×#120C22×C10714yes—
421C2×#120C22×C10712yes—
422#518C22×C10712yes—
423C2×C4×D4C22×C10711yescharacteristic
424C2×#99C22×C10712yes—
425C2×#99C22×C10714yes—
426#394—21no—
427#394—22no—
428#392—21no—
429#392—22no—
430#390—21no—
431#390—21no—
432#390—21no—
433#380C22×C10711yescharacteristic
434#379C22×C10712yes—
435#379C22×C10714yes—
436C4×C22⋊C4C22×C10711yescharacteristic
437C4×C22⋊C4C22×C10711yescharacteristic
438#342C22×C10712yes—
439#342C22×C10714yes—
440C25C23×C10712yes—
441C2×#41—21no—
442C22×Q8D4×C10711yescharacteristic, complemented
443C22×D4—22no—
444C22×D4—24no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—44no—
452C22×D4D4×C10711yescharacteristic, complemented
453C22×D4C23×C10711yescharacteristic
454C22×D4C23×C10712yes—
455C23×C4D4×C10711yescharacteristic, complemented
456C23×C4C23×C10711yescharacteristic
457#127—44no—
458#126—22no—
459#126—22no—
460#126—22no—
461#125—21no—
462#125—22no—
463#124—21no—
464#124—22no—
465#124—44no—
466#123—22no—
467#123—22no—
468#123—22no—
469#123—22no—
470#123—22no—
471C22⋊Q8—21no—
472C22⋊Q8—22no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477#121—21no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—21no—
483#121—22no—
484#121—22no—
485#121—44no—
486#120—22no—
487#120—22no—
488#120—28no—
489#120—44no—
490#120—44no—
491C4×Q8—21no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502#117—21no—
503#117—22no—
504#117—22no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4D4×C10711yescharacteristic, complemented
507C2×C4⋊C4D4×C10711yescharacteristic, complemented
508C2×C4⋊C4D4×C10711yescharacteristic, complemented
509C2×C4⋊C4D4×C10712yescomplemented
510C2×C22⋊C4—22no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4D4×C10711yescharacteristic, complemented
518C2×C22⋊C4D4×C10712yescomplemented
519C2×C22⋊C4C23×C10712yes—
520C2×C22⋊C4C23×C10712yes—
521C2×C22⋊C4C23×C10711yescharacteristic
522C2×C22⋊C4C23×C10712yes—
523C2×C22⋊C4C23×C10712yes—
524C2×C42—21no—
525C2×C42—21no—
526C2×C42D4×C10711yescharacteristic, complemented
527#99—24no—
528#99—44no—
529#95—21no—
530#95—21no—
531#95—21no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—24no—
536C24—24no—
537C24—44no—
538C24—82no—
539C24C2×D4×C10712yes—
540C24C2×D4×C10711yescharacteristic
541C24C24×C10711yescharacteristic
542#41—82no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—42no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—24no—
555C2×D4—24no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—48no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—48no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—84no—
577C2×D4—82no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4C2×D4×C10711yescharacteristic
588C22×C4C2×D4×C10712yes—
589C22×C4C2×D4×C10711yescharacteristic
590C22×C4C2×D4×C10711yescharacteristic
591C22×C4C2×D4×C10711yescharacteristic
592C22×C4C2×D4×C10711yescharacteristic
593C22×C4C2×D4×C10712yes—
594C22×C4C2×D4×C10711yescharacteristic
595C22×C4C2×D4×C10712yes—
596C22×C4C2×D4×C10711yescharacteristic
597C22×C4C2×D4×C10711yescharacteristic
598C22×C4C2×D4×C10711yescharacteristic
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—22no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—21no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—24no—
630C22⋊C4—48no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—48no—
634C22⋊C4—84no—
635C22⋊C4—82no—
636C22⋊C4#41×C10714yescomplemented
637C42—22no—
638C42—22no—
639C42—21no—
640C42—21no—
641C42—42no—
642C42—42no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—44no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—44no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—44no—
668C23—44no—
669C23—88no—
670C23—88no—
671C23C22×D4×C10711yescharacteristic
672C23C22×D4×C10711yescharacteristic
673C23C22×D4×C10711yescharacteristic
674C23C2×#41×C10712yes—
675C23H(5,𝔽2)×C10712yes—
676Q8—42no—
677Q8—81no—
678D4—44no—
679D4—44no—
680D4—44no—
681D4—42no—
682D4—42no—
683D4—42no—
684D4—42no—
685D4—44no—
686D4—44no—
687D4—42no—
688D4—81no—
689D4—82no—
690D4—82no—
691D4—816no—
692D4—88no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—81no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4#120×C10711yescharacteristic
726C2×C4#120×C10711yescharacteristic
727C2×C4#120×C10711yescharacteristic
728C2×C4#120×C10711yescharacteristic
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—48no—
739C22—44no—
740C22—48no—
741C22—44no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—44no—
747C22—42no—
748C22—41no—
749C22—84no—
750C22—81no—
751C22—84no—
752C22—82no—
753C22—84no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22C2×#120×C10711yescharacteristic
758C22#532×C10711yescharacteristic
759C22#535×C10711yescharacteristic
760C22#546×C10712yes—
761C22#550×C10712yes—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—44no—
766C4—41no—
767C4—42no—
768C4—41no—
769C4—42no—
770C4—41no—
771C4—42no—
772C4—82no—
773C4—82no—
774C4B(4,𝔽2)×C10712yes—
775C2—22no—
776C2—21no—
777C2—22no—
778C2—21no—
779C2—84no—
780C2—81no—
781C2—82no—
782C2C107×#243111yescharacteristic
783C2C2×B(4,𝔽2)×C10711yescharacteristic
784C2C107×#302711yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC24C24×C107
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#3505C2semidirect
2. C107×#2435C2semidirect
3. C107×#2433C2semidirect
4. C107×#2408C2semidirect
5. C107×#2021C2semidirect
6. C107×#1996C2semidirect
7. C107×#1964C2semidirect
8. C107×#1889C2semidirect
9. C4×#99×C107C2semidirect
49. C22×Q8×C107D4semidirect
59. C22×D4×C107D4semidirect
62. C23×C4×C107D4semidirect
113. C2×C4⋊C4×C107D4semidirect
114. C2×C4⋊C4×C107D4semidirect
115. C2×C4⋊C4×C107D4semidirect
116. C2×C4⋊C4×C107D4semidirect
124. C2×C22⋊C4×C107D4semidirect
125. C2×C22⋊C4×C107D4semidirect
133. C2×C42×C107D4semidirect
243. C22⋊C4×C107#41semidirect
382. #25585C107direct (N × H)
393. #3505C2×C107semidirect
394. #2435C2×C107semidirect
395. #2433C2×C107semidirect
396. #2408C2×C107semidirect
397. #2021C2×C107semidirect
398. #1996C2×C107semidirect
399. #1964C2×C107semidirect
400. #1889C2×C107semidirect
401. C4×#99C2×C107semidirect
402. C107#25585direct (N × H)
442. C22×Q8D4×C107semidirect
452. C22×D4D4×C107semidirect
455. C23×C4D4×C107semidirect
506. C2×C4⋊C4D4×C107semidirect
507. C2×C4⋊C4D4×C107semidirect
508. C2×C4⋊C4D4×C107semidirect
509. C2×C4⋊C4D4×C107semidirect
517. C2×C22⋊C4D4×C107semidirect
518. C2×C22⋊C4D4×C107semidirect
526. C2×C42D4×C107semidirect
636. C22⋊C4#41×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#35052
C107×#24352
C107×#24332
C107×#24082
C107×#20212
C107×#19962
C107×#19642
C107×#18892
C4×#99×C1072
#25585107