Finite Group Databasebeta

← C107×#24140 #41050104

Subgroups — C107×#24140 #41050104

Order 27392.

1556 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3505C211yesmaximal, characteristic, complemented
2C107×#2848C211yesmaximal, characteristic, complemented
3C107×#2847C211yesmaximal, characteristic, complemented
4C4×#120×C107C211yesmaximal, characteristic, complemented
5C107×#2044C212yesmaximal, complemented
6C107×#2021C212yesmaximal, complemented
7C107×#1996C211yesmaximal, characteristic, complemented
8C107×#1964C211yesmaximal, characteristic, complemented
9C107×#1889C212yesmaximal, complemented
10C107×#1867C212yesmaximal, complemented
11C107×#1799C211yesmaximal, characteristic, complemented
12C24×C4×C107C2211yescharacteristic
13#553×C107—21no—
14#553×C107—22no—
15#552×C107—21no—
16#551×C107—22no—
17#548×C107—21no—
18#546×C107—21no—
19#539×C107—21no—
20#538×C107—21no—
21#534×C107C2212yes—
22#529×C107—21no—
23#525×C107—21no—
24C2×C22⋊Q8×C107—21no—
25C2×C22⋊Q8×C107C2211yescharacteristic
26C2×#121×C107—21no—
27C2×#121×C107C2211yescharacteristic
28C2×#120×C107C2211yescharacteristic
29C2×#120×C107C2212yes—
30#518×C107C2212yes—
31C2×C4×D4×C107—21no—
32C2×C4×D4×C107C2211yescharacteristic
33C2×#99×C107C2212yes—
34C2×#99×C107C2212yes—
35C2×#99×C107C2212yes—
36#386×C107—21no—
37#386×C107—22no—
38#386×C107C2212yes—
39#386×C107C2211yescharacteristic
40#385×C107—21no—
41#385×C107—22no—
42#385×C107C2211yescharacteristic
43#385×C107C2212yes—
44#380×C107—21no—
45#380×C107—21no—
46#380×C107C2211yescharacteristic
47#380×C107C2211yescharacteristic
48#379×C107C2211yescharacteristic
49#379×C107C2212yes—
50C4×C22⋊C4×C107—21no—
51C4×C22⋊C4×C107C2211yescharacteristic
52#342×C107C2212yes—
53#342×C107C2212yes—
54#342×C107C2212yes—
55C25×C107C2311yescharacteristic
56C2×#41×C107—21no—
57C22×Q8×C107D411yescharacteristic, complemented
58C22×D4×C107—21no—
59C22×D4×C107—22no—
60C22×D4×C107D411yescharacteristic, complemented
61C22×D4×C107C2311yescharacteristic
62C22×D4×C107C2312yes—
63C23×C4×C107—21no—
64C23×C4×C107—21no—
65C23×C4×C107—21no—
66C23×C4×C107—21no—
67C23×C4×C107—21no—
68C23×C4×C107—21no—
69C23×C4×C107—44no—
70C23×C4×C107D411yescharacteristic, complemented
71C23×C4×C107C2311yescharacteristic
72C23×C4×C107C2311yescharacteristic
73#126×C107—22no—
74#126×C107—22no—
75#126×C107—22no—
76#125×C107—21no—
77#125×C107—22no—
78#124×C107—21no—
79#124×C107—22no—
80#123×C107—22no—
81#123×C107—22no—
82#123×C107—22no—
83#123×C107—22no—
84#123×C107—22no—
85C22⋊Q8×C107—21no—
86C22⋊Q8×C107—22no—
87C22⋊Q8×C107—21no—
88C22⋊Q8×C107—21no—
89C22⋊Q8×C107—21no—
90C22⋊Q8×C107—21no—
91C22⋊Q8×C107—44no—
92#121×C107—21no—
93#121×C107—22no—
94#121×C107—21no—
95#121×C107—21no—
96#121×C107—21no—
97#121×C107—21no—
98#121×C107—22no—
99#121×C107—22no—
100#121×C107—44no—
101#120×C107—22no—
102#120×C107—22no—
103#120×C107—22no—
104#120×C107—22no—
105#120×C107—24no—
106#120×C107—42no—
107C4×Q8×C107—21no—
108C4×D4×C107—22no—
109C4×D4×C107—21no—
110C4×D4×C107—21no—
111C4×D4×C107—21no—
112C4×D4×C107—21no—
113C4×D4×C107—21no—
114C4×D4×C107—22no—
115C4×D4×C107—22no—
116C4×D4×C107—22no—
117C4×D4×C107—22no—
118C4×D4×C107—44no—
119#117×C107—21no—
120#117×C107—22no—
121#117×C107—22no—
122C2×C4⋊C4×C107—21no—
123C2×C4⋊C4×C107—21no—
124C2×C4⋊C4×C107—21no—
125C2×C4⋊C4×C107—22no—
126C2×C4⋊C4×C107D411yescharacteristic, complemented
127C2×C4⋊C4×C107D411yescharacteristic, complemented
128C2×C4⋊C4×C107D411yescharacteristic, complemented
129C2×C4⋊C4×C107D412yescomplemented
130C2×C22⋊C4×C107—22no—
131C2×C22⋊C4×C107—21no—
132C2×C22⋊C4×C107—21no—
133C2×C22⋊C4×C107—22no—
134C2×C22⋊C4×C107—21no—
135C2×C22⋊C4×C107—22no—
136C2×C22⋊C4×C107—21no—
137C2×C22⋊C4×C107—22no—
138C2×C22⋊C4×C107—22no—
139C2×C22⋊C4×C107D411yescharacteristic, complemented
140C2×C22⋊C4×C107D412yescomplemented
141C2×C22⋊C4×C107C2312yes—
142C2×C22⋊C4×C107C2311yescharacteristic
143C2×C22⋊C4×C107C2312yes—
144C2×C22⋊C4×C107C2311yescharacteristic
145C2×C22⋊C4×C107C2312yes—
146C2×C22⋊C4×C107C2311yescharacteristic
147C2×C42×C107—21no—
148C2×C42×C107D411yescharacteristic, complemented
149#99×C107—24no—
150#99×C107—42no—
151#99×C107—42no—
152#95×C107—21no—
153#95×C107—21no—
154#95×C107—21no—
155#95×C107—22no—
156#95×C107—22no—
157#95×C107—21no—
158#95×C107—21no—
159C24×C107—21no—
160C24×C107—21no—
161C24×C107—21no—
162C24×C107—21no—
163C24×C107—21no—
164C24×C107—21no—
165C24×C107—42no—
166C24×C107—42no—
167C24×C107C2×D412yes—
168C24×C107C2×D411yescharacteristic
169C24×C107#4112yescomplemented
170C24×C107C2411yescharacteristic
171#41×C107—82no—
172C2×Q8×C107—21no—
173C2×Q8×C107—21no—
174C2×Q8×C107—42no—
175C2×D4×C107—24no—
176C2×D4×C107—21no—
177C2×D4×C107—22no—
178C2×D4×C107—21no—
179C2×D4×C107—22no—
180C2×D4×C107—22no—
181C2×D4×C107—21no—
182C2×D4×C107—21no—
183C2×D4×C107—22no—
184C2×D4×C107—21no—
185C2×D4×C107—22no—
186C2×D4×C107—21no—
187C2×D4×C107—22no—
188C2×D4×C107—22no—
189C2×D4×C107—22no—
190C2×D4×C107—21no—
191C2×D4×C107—21no—
192C2×D4×C107—42no—
193C2×D4×C107—42no—
194C2×D4×C107—42no—
195C2×D4×C107—44no—
196C2×D4×C107—44no—
197C2×D4×C107—44no—
198C22×C4×C107—24no—
199C22×C4×C107—24no—
200C22×C4×C107—24no—
201C22×C4×C107—21no—
202C22×C4×C107—21no—
203C22×C4×C107—21no—
204C22×C4×C107—21no—
205C22×C4×C107—22no—
206C22×C4×C107—22no—
207C22×C4×C107—21no—
208C22×C4×C107—21no—
209C22×C4×C107—21no—
210C22×C4×C107—22no—
211C22×C4×C107—22no—
212C22×C4×C107—42no—
213C22×C4×C107—42no—
214C22×C4×C107—42no—
215C22×C4×C107—42no—
216C22×C4×C107—42no—
217C22×C4×C107—42no—
218C22×C4×C107—42no—
219C22×C4×C107—42no—
220C22×C4×C107—42no—
221C22×C4×C107—42no—
222C22×C4×C107—42no—
223C22×C4×C107—42no—
224C22×C4×C107—41no—
225C22×C4×C107—41no—
226C22×C4×C107—41no—
227C22×C4×C107—41no—
228C22×C4×C107C2×D411yescharacteristic
229C22×C4×C107C2×D412yes—
230C22×C4×C107C2×D411yescharacteristic
231C22×C4×C107C2×D411yescharacteristic
232C22×C4×C107C2×D411yescharacteristic
233C22×C4×C107C2×D411yescharacteristic
234C22×C4×C107C2×D412yes—
235C22×C4×C107C2×D411yescharacteristic
236C22×C4×C107C2×D412yes—
237C22×C4×C107C2×D411yescharacteristic
238C22×C4×C107C2×D411yescharacteristic
239C22×C4×C107C2×D411yescharacteristic
240C4⋊C4×C107—22no—
241C4⋊C4×C107—22no—
242C4⋊C4×C107—22no—
243C4⋊C4×C107—22no—
244C4⋊C4×C107—21no—
245C4⋊C4×C107—22no—
246C4⋊C4×C107—21no—
247C4⋊C4×C107—21no—
248C4⋊C4×C107—21no—
249C4⋊C4×C107—21no—
250C4⋊C4×C107—22no—
251C4⋊C4×C107—21no—
252C4⋊C4×C107—42no—
253C4⋊C4×C107—42no—
254C4⋊C4×C107—42no—
255C4⋊C4×C107—44no—
256C22⋊C4×C107—22no—
257C22⋊C4×C107—22no—
258C22⋊C4×C107—24no—
259C22⋊C4×C107—22no—
260C22⋊C4×C107—22no—
261C22⋊C4×C107—22no—
262C22⋊C4×C107—22no—
263C22⋊C4×C107—21no—
264C22⋊C4×C107—22no—
265C22⋊C4×C107—21no—
266C22⋊C4×C107—22no—
267C22⋊C4×C107—21no—
268C22⋊C4×C107—22no—
269C22⋊C4×C107—21no—
270C22⋊C4×C107—21no—
271C22⋊C4×C107—22no—
272C22⋊C4×C107—22no—
273C22⋊C4×C107—22no—
274C22⋊C4×C107—21no—
275C22⋊C4×C107—22no—
276C22⋊C4×C107—22no—
277C22⋊C4×C107—21no—
278C22⋊C4×C107—44no—
279C22⋊C4×C107—42no—
280C22⋊C4×C107—44no—
281C22⋊C4×C107—44no—
282C22⋊C4×C107—42no—
283C22⋊C4×C107—42no—
284C22⋊C4×C107—44no—
285C22⋊C4×C107#4112yescomplemented
286C42×C107—22no—
287C42×C107—22no—
288C42×C107—21no—
289C42×C107—21no—
290C42×C107—42no—
291C23×C107—22no—
292C23×C107—22no—
293C23×C107—22no—
294C23×C107—22no—
295C23×C107—22no—
296C23×C107—22no—
297C23×C107—22no—
298C23×C107—22no—
299C23×C107—22no—
300C23×C107—21no—
301C23×C107—22no—
302C23×C107—21no—
303C23×C107—21no—
304C23×C107—22no—
305C23×C107—22no—
306C23×C107—41no—
307C23×C107—44no—
308C23×C107—41no—
309C23×C107—41no—
310C23×C107—41no—
311C23×C107—41no—
312C23×C107—41no—
313C23×C107—41no—
314C23×C107—41no—
315C23×C107—44no—
316C23×C107—44no—
317C23×C107—44no—
318C23×C107—41no—
319C23×C107—41no—
320C23×C107—42no—
321C23×C107—42no—
322C23×C107—41no—
323C23×C107—41no—
324C23×C107—41no—
325C23×C107—41no—
326C23×C107C22×D411yescharacteristic
327C23×C107C22×D411yescharacteristic
328C23×C107C22×D411yescharacteristic
329C23×C107C2×#4111yescharacteristic
330C23×C107C2×#4111yescharacteristic
331C23×C107H(5,𝔽2)11yescharacteristic
332C23×C1072−1+411yescharacteristic
333Q8×C107—42no—
334Q8×C107—81no—
335D4×C107—48no—
336D4×C107—42no—
337D4×C107—42no—
338D4×C107—41no—
339D4×C107—41no—
340D4×C107—41no—
341D4×C107—42no—
342D4×C107—42no—
343D4×C107—41no—
344D4×C107—42no—
345D4×C107—81no—
346D4×C107—82no—
347D4×C107—82no—
348D4×C107—88no—
349C2×C4×C107—22no—
350C2×C4×C107—22no—
351C2×C4×C107—22no—
352C2×C4×C107—22no—
353C2×C4×C107—22no—
354C2×C4×C107—22no—
355C2×C4×C107—21no—
356C2×C4×C107—22no—
357C2×C4×C107—21no—
358C2×C4×C107—21no—
359C2×C4×C107—22no—
360C2×C4×C107—22no—
361C2×C4×C107—21no—
362C2×C4×C107—22no—
363C2×C4×C107—21no—
364C2×C4×C107—22no—
365C2×C4×C107—22no—
366C2×C4×C107—41no—
367C2×C4×C107—41no—
368C2×C4×C107—41no—
369C2×C4×C107—44no—
370C2×C4×C107—44no—
371C2×C4×C107—44no—
372C2×C4×C107—41no—
373C2×C4×C107—41no—
374C2×C4×C107—41no—
375C2×C4×C107—41no—
376C2×C4×C107—41no—
377C2×C4×C107—41no—
378C2×C4×C107—44no—
379C2×C4×C107—42no—
380C2×C4×C107—41no—
381C2×C4×C107—42no—
382C2×C4×C107—41no—
383C2×C4×C107—42no—
384C2×C4×C107—41no—
385C2×C4×C107—42no—
386C2×C4×C107—42no—
387C2×C4×C107—42no—
388C2×C4×C107—41no—
389C2×C4×C107—42no—
390C2×C4×C107—41no—
391C2×C4×C107—42no—
392C2×C4×C107—42no—
393C2×C4×C107—81no—
394C2×C4×C107—82no—
395C2×C4×C107—82no—
396C2×C4×C107#12011yescharacteristic
397C2×C4×C107#12011yescharacteristic
398C2×C4×C107#12011yescharacteristic
399C2×C4×C107#12011yescharacteristic
400C22×C107—21no—
401C22×C107—21no—
402C22×C107—21no—
403C22×C107—21no—
404C22×C107—21no—
405C22×C107—21no—
406C22×C107—24no—
407C22×C107—24no—
408C22×C107—24no—
409C22×C107—41no—
410C22×C107—41no—
411C22×C107—41no—
412C22×C107—41no—
413C22×C107—42no—
414C22×C107—42no—
415C22×C107—42no—
416C22×C107—42no—
417C22×C107—42no—
418C22×C107—42no—
419C22×C107—42no—
420C22×C107—42no—
421C22×C107—42no—
422C22×C107—42no—
423C22×C107—42no—
424C22×C107—42no—
425C22×C107—42no—
426C22×C107—41no—
427C22×C107—42no—
428C22×C107—41no—
429C22×C107—42no—
430C22×C107—42no—
431C22×C107—41no—
432C22×C107—82no—
433C22×C107—81no—
434C22×C107—82no—
435C22×C107C2×#12011yescharacteristic
436C22×C107#52511yescharacteristic
437C22×C107#53711yescharacteristic
438C22×C107#54611yescharacteristic
439C22×C107#54711yescharacteristic
440C22×C107#54811yescharacteristic
441C22×C107#55011yescharacteristic
442C4×C107—21no—
443C4×C107—21no—
444C4×C107—21no—
445C4×C107—42no—
446C4×C107—41no—
447C4×C107—42no—
448C4×C107—42no—
449C4×C107—41no—
450C4×C107—42no—
451C4×C107—41no—
452C4×C107—42no—
453C4×C107—82no—
454C4×C107—81no—
455C4×C107—82no—
456C4×C107B(4,𝔽2)12yes—
457#24140C10711yesmaximal, characteristic, direct product factor, Sylow
458C2×C107—21no—
459C2×C107—21no—
460C2×C107—21no—
461C2×C107—21no—
462C2×C107—21no—
463C2×C107—21no—
464C2×C107—44no—
465C2×C107—81no—
466C2×C107—82no—
467C2×C107#240711yescharacteristic
468C2×C107C2×B(4,𝔽2)11yescharacteristic
469C2×C107#302511yescharacteristic
470#3505C2×C10711yescharacteristic, complemented
471#2848C2×C10711yescharacteristic, complemented
472#2847C2×C10711yescharacteristic, complemented
473C4×#120C2×C10711yescharacteristic, complemented
474#2044C2×C10712yescomplemented
475#2021C2×C10712yescomplemented
476#1996C2×C10711yescharacteristic, complemented
477#1964C2×C10711yescharacteristic, complemented
478#1889C2×C10712yescomplemented
479#1867C2×C10712yescomplemented
480#1799C2×C10711yescharacteristic, complemented
481C107#2414011yescharacteristic, direct product factor, Sylow
482C24×C4C22×C10711yescharacteristic
483#553—21no—
484#553—22no—
485#552—21no—
486#551—22no—
487#548—21no—
488#546—21no—
489#539—21no—
490#538—21no—
491#534C22×C10712yes—
492#529—21no—
493#525—21no—
494C2×C22⋊Q8—21no—
495C2×C22⋊Q8C22×C10711yescharacteristic
496C2×#121—21no—
497C2×#121C22×C10711yescharacteristic
498C2×#120C22×C10711yescharacteristic
499C2×#120C22×C10712yes—
500#518C22×C10712yes—
501C2×C4×D4—21no—
502C2×C4×D4C22×C10711yescharacteristic
503C2×#99C22×C10712yes—
504C2×#99C22×C10712yes—
505C2×#99C22×C10712yes—
506#386—22no—
507#386—21no—
508#386C22×C10712yes—
509#386C22×C10711yescharacteristic
510#385—22no—
511#385—21no—
512#385C22×C10712yes—
513#385C22×C10711yescharacteristic
514#380—21no—
515#380—21no—
516#380C22×C10711yescharacteristic
517#380C22×C10711yescharacteristic
518#379C22×C10712yes—
519#379C22×C10711yescharacteristic
520C4×C22⋊C4—21no—
521C4×C22⋊C4C22×C10711yescharacteristic
522#342C22×C10712yes—
523#342C22×C10712yes—
524#342C22×C10712yes—
525C25C23×C10711yescharacteristic
526C2×#41—21no—
527C22×Q8D4×C10711yescharacteristic, complemented
528C22×D4—21no—
529C22×D4—22no—
530C22×D4D4×C10711yescharacteristic, complemented
531C22×D4C23×C10711yescharacteristic
532C22×D4C23×C10712yes—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—44no—
540C23×C4D4×C10711yescharacteristic, complemented
541C23×C4C23×C10711yescharacteristic
542C23×C4C23×C10711yescharacteristic
543#126—22no—
544#126—22no—
545#126—22no—
546#125—21no—
547#125—22no—
548#124—21no—
549#124—22no—
550#123—22no—
551#123—22no—
552#123—22no—
553#123—22no—
554#123—22no—
555C22⋊Q8—21no—
556C22⋊Q8—22no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—44no—
562#121—21no—
563#121—22no—
564#121—21no—
565#121—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—44no—
571#120—22no—
572#120—22no—
573#120—22no—
574#120—22no—
575#120—24no—
576#120—42no—
577C4×Q8—21no—
578C4×D4—22no—
579C4×D4—21no—
580C4×D4—21no—
581C4×D4—21no—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—44no—
589#117—21no—
590#117—22no—
591#117—22no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4D4×C10711yescharacteristic, complemented
597C2×C4⋊C4D4×C10711yescharacteristic, complemented
598C2×C4⋊C4D4×C10711yescharacteristic, complemented
599C2×C4⋊C4D4×C10712yescomplemented
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4D4×C10711yescharacteristic, complemented
610C2×C22⋊C4D4×C10712yescomplemented
611C2×C22⋊C4C23×C10712yes—
612C2×C22⋊C4C23×C10711yescharacteristic
613C2×C22⋊C4C23×C10712yes—
614C2×C22⋊C4C23×C10711yescharacteristic
615C2×C22⋊C4C23×C10712yes—
616C2×C22⋊C4C23×C10711yescharacteristic
617C2×C42—21no—
618C2×C42D4×C10711yescharacteristic, complemented
619#99—24no—
620#99—42no—
621#99—42no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—22no—
626#95—22no—
627#95—21no—
628#95—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—42no—
636C24—42no—
637C24C2×D4×C10712yes—
638C24C2×D4×C10711yescharacteristic
639C24#41×C10712yescomplemented
640C24C24×C10711yescharacteristic
641#41—82no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—42no—
645C2×D4—24no—
646C2×D4—21no—
647C2×D4—22no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—44no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—41no—
695C22×C4—41no—
696C22×C4—41no—
697C22×C4—41no—
698C22×C4C2×D4×C10711yescharacteristic
699C22×C4C2×D4×C10712yes—
700C22×C4C2×D4×C10711yescharacteristic
701C22×C4C2×D4×C10711yescharacteristic
702C22×C4C2×D4×C10711yescharacteristic
703C22×C4C2×D4×C10711yescharacteristic
704C22×C4C2×D4×C10712yes—
705C22×C4C2×D4×C10711yescharacteristic
706C22×C4C2×D4×C10712yes—
707C22×C4C2×D4×C10711yescharacteristic
708C22×C4C2×D4×C10711yescharacteristic
709C22×C4C2×D4×C10711yescharacteristic
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—21no—
715C4⋊C4—22no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—22no—
721C4⋊C4—21no—
722C4⋊C4—42no—
723C4⋊C4—42no—
724C4⋊C4—42no—
725C4⋊C4—44no—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—24no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—21no—
734C22⋊C4—22no—
735C22⋊C4—21no—
736C22⋊C4—22no—
737C22⋊C4—21no—
738C22⋊C4—22no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—22no—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—21no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—21no—
748C22⋊C4—44no—
749C22⋊C4—42no—
750C22⋊C4—44no—
751C22⋊C4—42no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—42no—
755C22⋊C4#41×C10712yescomplemented
756C42—22no—
757C42—22no—
758C42—21no—
759C42—21no—
760C42—42no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—21no—
771C23—22no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—22no—
776C23—41no—
777C23—44no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—42no—
791C23—42no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23C22×D4×C10711yescharacteristic
797C23C22×D4×C10711yescharacteristic
798C23C22×D4×C10711yescharacteristic
799C23C2×#41×C10711yescharacteristic
800C23C2×#41×C10711yescharacteristic
801C23H(5,𝔽2)×C10711yescharacteristic
802C232−1+4×C10711yescharacteristic
803Q8—42no—
804Q8—81no—
805D4—48no—
806D4—42no—
807D4—42no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—42no—
812D4—42no—
813D4—41no—
814D4—42no—
815D4—81no—
816D4—82no—
817D4—82no—
818D4—88no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—21no—
832C2×C4—22no—
833C2×C4—21no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—44no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—81no—
864C2×C4—82no—
865C2×C4—82no—
866C2×C4#120×C10711yescharacteristic
867C2×C4#120×C10711yescharacteristic
868C2×C4#120×C10711yescharacteristic
869C2×C4#120×C10711yescharacteristic
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—41no—
897C22—42no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—82no—
903C22—81no—
904C22—82no—
905C22C2×#120×C10711yescharacteristic
906C22#525×C10711yescharacteristic
907C22#537×C10711yescharacteristic
908C22#546×C10711yescharacteristic
909C22#547×C10711yescharacteristic
910C22#548×C10711yescharacteristic
911C22#550×C10711yescharacteristic
912C4—21no—
913C4—21no—
914C4—21no—
915C4—42no—
916C4—41no—
917C4—42no—
918C4—42no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—42no—
923C4—82no—
924C4—82no—
925C4—81no—
926C4B(4,𝔽2)×C10712yes—
927C2—21no—
928C2—21no—
929C2—21no—
930C2—21no—
931C2—21no—
932C2—21no—
933C2—44no—
934C2—81no—
935C2—82no—
936C2C107×#240711yescharacteristic
937C2C2×B(4,𝔽2)×C10711yescharacteristic
938C2C107×#302511yescharacteristic
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×#2848C2semidirect
3. C107×#2847C2semidirect
4. C4×#120×C107C2semidirect
5. C107×#2044C2semidirect
6. C107×#2021C2semidirect
7. C107×#1996C2semidirect
8. C107×#1964C2semidirect
9. C107×#1889C2semidirect
10. C107×#1867C2semidirect
11. C107×#1799C2semidirect
57. C22×Q8×C107D4semidirect
60. C22×D4×C107D4semidirect
70. C23×C4×C107D4semidirect
126. C2×C4⋊C4×C107D4semidirect
127. C2×C4⋊C4×C107D4semidirect
128. C2×C4⋊C4×C107D4semidirect
129. C2×C4⋊C4×C107D4semidirect
139. C2×C22⋊C4×C107D4semidirect
140. C2×C22⋊C4×C107D4semidirect
148. C2×C42×C107D4semidirect
169. C24×C107#41semidirect
285. C22⋊C4×C107#41semidirect
457. #24140C107direct (N × H)
470. #3505C2×C107semidirect
471. #2848C2×C107semidirect
472. #2847C2×C107semidirect
473. C4×#120C2×C107semidirect
474. #2044C2×C107semidirect
475. #2021C2×C107semidirect
476. #1996C2×C107semidirect
477. #1964C2×C107semidirect
478. #1889C2×C107semidirect
479. #1867C2×C107semidirect
480. #1799C2×C107semidirect
481. C107#24140direct (N × H)
527. C22×Q8D4×C107semidirect
530. C22×D4D4×C107semidirect
540. C23×C4D4×C107semidirect
596. C2×C4⋊C4D4×C107semidirect
597. C2×C4⋊C4D4×C107semidirect
598. C2×C4⋊C4D4×C107semidirect
599. C2×C4⋊C4D4×C107semidirect
609. C2×C22⋊C4D4×C107semidirect
610. C2×C22⋊C4D4×C107semidirect
618. C2×C42D4×C107semidirect
639. C24#41×C107semidirect
755. 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×#28482
C107×#28472
C4×#120×C1072
C107×#20442
C107×#20212
C107×#19962
C107×#19642
C107×#18892
C107×#18672
C107×#17992
#24140107