Finite Group Databasebeta

← C2×#22574318 #31764115

Subgroups — C2×#22574318 #31764115

Order 17152.

7226 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574318C2132yesmaximal, direct product factor
2C2×#16864129C213yesmaximal, complemented
3C2×#16864122C211yesmaximal, characteristic, complemented
4C2×#16864109C213yesmaximal, complemented
5C2×#16864096C213yesmaximal, complemented
6C2×#16864085C213yesmaximal, complemented
7C2×#16864065C211yesmaximal, characteristic, complemented
8C2×#16864058C211yesmaximal, characteristic, complemented
9C2×#16864053C211yesmaximal, characteristic, complemented
10C2×#16864011C213yesmaximal, complemented
11C2×#16863997C213yesmaximal, complemented
12C2×#16863930C213yesmaximal, complemented
13C2×#16863930C213yesmaximal, complemented
14C2×#16863878C211yesmaximal, characteristic, complemented
15C2×#16863872C211yesmaximal, characteristic, complemented
16C2×C4×#41×C67C211yesmaximal, characteristic, complemented
17C22×#11761629C2211yescharacteristic
18C22×Q8×D67C2211yescharacteristic
19#16864129C22148yescomplemented
20#16864122C22116yescomplemented
21#16864109C22148yescomplemented
22#16864096C22148yescomplemented
23#16864085C22148yescomplemented
24#16864065C22116yescomplemented
25#16864058C22116yescomplemented
26#16864053C22116yescomplemented
27#16864011C22148yescomplemented
28#16863997C22148yescomplemented
29C2×#14524042C2213yes—
30C2×#14524039C2213yes—
31#16863930C22148yescomplemented
32#16863930C22148yescomplemented
33C2×#14524037C2211yescharacteristic
34C2×#14524037C2213yes—
35C2×#14524036C2216yes—
36C2×#14524035C2213yes—
37C2×#14524035C2213yes—
38C2×#14524034C2213yes—
39C2×#14524031C2213yes—
40C2×#14524031C2213yes—
41C2×#14524030C2213yes—
42C2×#14524029C2216yes—
43C2×#14524026C2216yes—
44C2×#14524026C2213yes—
45C2×#14524026C2213yes—
46C2×#14524025C2216yes—
47C2×#14524023C2213yes—
48C2×#14524022C2213yes—
49C2×#14524022C2213yes—
50C2×#14524018C2213yes—
51C2×#14524017C2213yes—
52C2×#14524017C2213yes—
53C2×#14524016C2216yes—
54C2×#14524014C2213yes—
55C2×#14524014C2213yes—
56#16863878C22116yescomplemented
57#16863872C22116yescomplemented
58C2×Q8×Dic67C2211yescharacteristic
59C2×Q8×Dic67C2211yescharacteristic
60C2×C4×Dic134C2213yes—
61C2×C4×Dic134C2213yes—
62C2×#14524008C2213yes—
63C2×C4×D268C2213yes—
64C2×C4×D268C2213yes—
65C2×#14524005C2213yes—
66C2×C4×C22⋊D67C2213yes—
67C2×C4×C22⋊D67C2213yes—
68C2×C4×C22⋊D67C2216yes—
69C2×#14524001C2213yes—
70C2×#14524000C2213yes—
71C2×#14524000C2213yes—
72C2×#14524000C2216yes—
73C2×C4⋊C4×D67C2213yes—
74C22×#41×C67C2211yescharacteristic
75C4×#41×C67C22116yescomplemented
76C2×C4×Q8×C67C2211yescharacteristic
77C2×C4×Q8×C67C2211yescharacteristic
78C2×C4×D4×C67C2213yes—
79C2×C4×D4×C67C2213yes—
80C2×#117×C67C2213yes—
81C22×C42×C67C2213yes—
82C2×#11761629—28no—
83C2×#11761629C2318yes—
84C22×Dic134C2313yes—
85C22×Dic134C2313yes—
86C2×Q8×D67—28no—
87C2×Q8×D67C2318yes—
88C22×D268C2313yes—
89C22×D268C2313yes—
90C22×C22⋊D67C2313yes—
91C22×C22⋊D67C2316yes—
92C22×C22⋊D67C2313yes—
93C22×C4×D67C2313yes—
94C22×C4×D67C2313yes—
95C22×C4×D67C2316yes—
96#14524042C23124yes—
97#14524039C23124yes—
98#14524037C2318yes—
99#14524037C23124yes—
100#14524036C23148yes—
101#14524035C23124yes—
102#14524035C23124yes—
103#14524034C23124yes—
104#14524031C23124yes—
105#14524031C23124yes—
106#14524030C23124yes—
107#14524029C23148yes—
108#14524026C23148yes—
109#14524026C23124yes—
110#14524026C23124yes—
111#14524025C23148yes—
112#14524023C23124yes—
113#14524022C23124yes—
114#14524022C23124yes—
115#14524018C23124yes—
116#14524017C23124yes—
117#14524017C23124yes—
118#14524016C23148yes—
119#14524014C23124yes—
120#14524014C23124yes—
121Q8×Dic67C2318yes—
122Q8×Dic67C2318yes—
123C4×Dic134C23124yes—
124C4×Dic134C23124yes—
125#14524008C23124yes—
126C4×D268C23124yes—
127C4×D268C23124yes—
128#14524005C23124yes—
129C4×C22⋊D67C23124yes—
130C4×C22⋊D67C23124yes—
131C4×C22⋊D67C23148yes—
132#14524001C23124yes—
133#14524000C23124yes—
134#14524000C23148yes—
135#14524000C23124yes—
136C2×C4⋊Dic67C2313yes—
137C2×C4⋊Dic67C2313yes—
138C2×C4⋊Dic67C2313yes—
139C2×C4⋊Dic67C2313yes—
140C2×Dic67⋊C4C2313yes—
141C2×Dic67⋊C4C2311yescharacteristic
142C2×Dic67⋊C4C2313yes—
143C2×Dic67⋊C4C2313yes—
144C2×Dic67⋊C4C2313yes—
145C2×Dic67⋊C4C2316yes—
146C2×Dic67⋊C4C2311yescharacteristic
147C2×Dic67⋊C4C2313yes—
148C2×Dic67⋊C4C2311yescharacteristic
149C4⋊C4×D67C23124yes—
150C2×C22⋊Dic67C2313yes—
151C2×C22⋊Dic67C2316yes—
152C2×C22⋊Dic67C2313yes—
153C2×(C2×D67)⋊C4C2311yescharacteristic
154C2×(C2×D67)⋊C4C2313yes—
155C2×(C2×D67)⋊C4C2313yes—
156C2×(C2×D67)⋊C4C2313yes—
157C2×(C2×D67)⋊C4C2313yes—
158C2×(C2×D67)⋊C4C2316yes—
159C2×(C2×D67)⋊C4C2311yescharacteristic
160C2×(C2×D67)⋊C4C2313yes—
161C2×(C2×D67)⋊C4C2311yescharacteristic
162C2×C4×Dic67C2316yes—
163C2×C4×Dic67C2313yes—
164C2×C4×Dic67C2313yes—
165C2×#41×C67—28no—
166C2×#41×C67C2318yes—
167C22×Q8×C67C2311yescharacteristic
168C22×D4×C67C2313yes—
169C23×C4×C67C2313yes—
170C23×C4×C67C2313yes—
171C23×C4×C67C2313yes—
172C4×Q8×C67C2318yes—
173C4×Q8×C67C2318yes—
174C4×D4×C67C23124yes—
175C4×D4×C67C23124yes—
176#117×C67C23124yes—
177C2×C4⋊C4×C67C2313yes—
178C2×C4⋊C4×C67C2313yes—
179C2×C22⋊C4×C67C2316yes—
180C2×C42×C67C2311yescharacteristic
181C2×C42×C67C2313yes—
182C2×C42×C67C2313yes—
183C2×C42×C67C2313yes—
184C2×C42×C67C23124yes—
185C23×D67C2411yescharacteristic
186C23×D67C2413yes—
187#11761629—232no—
188C2×Dic134—212no—
189C2×Dic134—46no—
190C2×Dic134C24112yes—
191C2×Dic134C24112yes—
192Q8×D67—232no—
193C2×D268—212no—
194C2×D268—46no—
195C2×D268C24112yes—
196C2×D268C24112yes—
197C2×C22⋊D67—46no—
198C2×C22⋊D67—46no—
199C2×C22⋊D67—412no—
200C2×C22⋊D67C24112yes—
201C2×C22⋊D67C24124yes—
202C2×C22⋊D67C24112yes—
203C22×Dic67C2411yescharacteristic
204C22×Dic67C2413yes—
205C22×Dic67C2411yescharacteristic
206C22×Dic67C2413yes—
207C22×Dic67C2413yes—
208C22×Dic67C2411yescharacteristic
209C2×C4×D67—212no—
210C2×C4×D67—212no—
211C2×C4×D67—412no—
212C2×C4×D67C24112yes—
213C2×C4×D67C24112yes—
214C2×C4×D67C24124yes—
215C4⋊Dic67C24112yes—
216C4⋊Dic67C24112yes—
217C4⋊Dic67C24112yes—
218C4⋊Dic67C24112yes—
219Dic67⋊C4C24112yes—
220Dic67⋊C4C2414yes—
221Dic67⋊C4C24112yes—
222Dic67⋊C4C24112yes—
223Dic67⋊C4C24112yes—
224Dic67⋊C4C24124yes—
225Dic67⋊C4C2414yes—
226Dic67⋊C4C24112yes—
227Dic67⋊C4C2414yes—
228C22⋊Dic67C24112yes—
229C22⋊Dic67C24124yes—
230C22⋊Dic67C24112yes—
231(C2×D67)⋊C4C2414yes—
232(C2×D67)⋊C4C24112yes—
233(C2×D67)⋊C4C24112yes—
234(C2×D67)⋊C4C24112yes—
235(C2×D67)⋊C4C24112yes—
236(C2×D67)⋊C4C24124yes—
237(C2×D67)⋊C4C2414yes—
238(C2×D67)⋊C4C24112yes—
239(C2×D67)⋊C4C2414yes—
240C4×Dic67C24124yes—
241C4×Dic67C24112yes—
242C4×Dic67C24112yes—
243C24×C67C2413yes—
244#41×C67—232no—
245C2×Q8×C67#4118yes—
246C2×Q8×C67C2414yes—
247C2×D4×C67—212no—
248C2×D4×C67C24112yes—
249C22×C4×C67—212no—
250C22×C4×C67—46no—
251C22×C4×C67—46no—
252C22×C4×C67C2411yescharacteristic
253C22×C4×C67C2411yescharacteristic
254C22×C4×C67C2411yescharacteristic
255C22×C4×C67C2413yes—
256C22×C4×C67C2413yes—
257C22×C4×C67C24112yes—
258C22×C4×C67C24112yes—
259C22×C4×C67C24112yes—
260C22×C4×C67C2413yes—
261C4⋊C4×C67C24112yes—
262C4⋊C4×C67C24112yes—
263C22⋊C4×C67C24124yes—
264C42×C67C2414yes—
265C42×C67C24112yes—
266C42×C67C24112yes—
267C42×C67C24112yes—
268C23×C67—26no—
269C23×C67—26no—
270C23×C67—26no—
271C23×C67C2516yes—
272C23×C67C2511yescharacteristic
273C22×D67—22no—
274C22×D67—26no—
275C22×D67—26no—
276C22×D67—22no—
277C22×D67—26no—
278C22×D67—22no—
279C22×D67C2512yes—
280C22×D67C2516yes—
281Q8×C67C2×#41116yes—
282D4×C67—224no—
283C2×C4×C67—22no—
284C2×C4×C67—22no—
285C2×C4×C67—22no—
286C2×C4×C67—26no—
287C2×C4×C67—26no—
288C2×C4×C67—224no—
289C2×C4×C67—412no—
290C2×C4×C67—412no—
291C2×C4×C67C2×#41112yes—
292C2×C4×C67C2512yes—
293C2×C4×C67C2512yes—
294C2×C4×C67C2512yes—
295C2×C4×C67C2516yes—
296C2×C4×C67C2516yes—
297C2×C4×C67C2516yes—
298C22⋊D67—424no—
299C22⋊D67—412no—
300C22⋊D67—412no—
301C2×Dic67—22no—
302C2×Dic67—26no—
303C2×Dic67—26no—
304C2×Dic67—22no—
305C2×Dic67—26no—
306C2×Dic67—22no—
307C2×Dic67C2512yes—
308C2×Dic67C2516yes—
309C2×Dic67C2512yes—
310C2×Dic67C2516yes—
311C2×Dic67C2516yes—
312C2×Dic67C2512yes—
313D268—224no—
314D268—412no—
315C4×D67—224no—
316C4×D67—224no—
317C4×D67—424no—
318Dic134—224no—
319Dic134—412no—
320C22×C67—26no—
321C22×C67—26no—
322C22×C67—26no—
323C22×C67—412no—
324C22×C67C22×#4112yes—
325C22×C67#58512yes—
326C22×C67#58512yes—
327C22×C67C2611yescharacteristic
328C2×D67—22no—
329C2×D67—26no—
330C2×D67—26no—
331C2×D67—22no—
332C2×D67—26no—
333C2×D67—22no—
334C2×D67—44no—
335C2×D67—412no—
336C4×C67—22no—
337C4×C67—26no—
338C4×C67—26no—
339C4×C67—22no—
340C4×C67—22no—
341C4×C67C22×#41112yes—
342Dic67—26no—
343Dic67—22no—
344Dic67—22no—
345Dic67—26no—
346Dic67—26no—
347Dic67—22no—
348C2×#3524—671nomaximal, Sylow
349C2×C67—46no—
350C2×C67#352414yescomplemented
351C2×C67C23×#4111yescharacteristic
352C2×C67C2×#58511yescharacteristic
353C2×C67C2×#58511yescharacteristic
354D67—42no—
355D67—46no—
356#3524—6732no—
357C2×#559—673no—
358C2×#557—671no—
359C2×#555—673no—
360C2×#553—673no—
361C2×#552—673no—
362C2×#550—671no—
363C2×#548—671no—
364C2×#548—671no—
365C2×#542—673no—
366C2×#540—673no—
367C2×#529—673no—
368C2×#529—673no—
369C2×#520—671no—
370C2×#519—671no—
371C2×C4×#41D6711yescharacteristic, complemented
372C67C2×#352411yescharacteristic, complemented, Sylow
373C22×#41—671no—
374C22×#41C2×D6711yescharacteristic
375C23×Q8—671no—
376#559—6748no—
377#557—6716no—
378#555—6748no—
379#553—6748no—
380#552—6748no—
381#550—6716no—
382#548—6716no—
383#548—6716no—
384#542—6748no—
385#540—6748no—
386C2×C4⋊Q8—673no—
387C2×#127—673no—
388#529—6748no—
389#529—6748no—
390C2×#126—676no—
391C2×#126—671no—
392C2×#126—673no—
393C2×#125—673no—
394C2×#125—673no—
395C2×#125—673no—
396C2×#124—673no—
397C2×#124—676no—
398C2×#124—673no—
399C2×#124—673no—
400C2×#123—676no—
401C2×#123—673no—
402C2×#123—673no—
403C2×#123—676no—
404C2×C22⋊Q8—673no—
405C2×C22⋊Q8—673no—
406C2×C22⋊Q8—673no—
407C2×#121—673no—
408C2×#121—673no—
409C2×#121—673no—
410C2×#121—673no—
411C2×#121—673no—
412C2×#121—676no—
413#520—6716no—
414#519—6716no—
415C4×#41C2×D67116yescomplemented
416C2×C4×Q8—671no—
417C2×C4×Q8—671no—
418C2×C4×Q8—673no—
419C2×C4×Q8—673no—
420C2×C4×Q8—673no—
421C2×C4×Q8C2×D6711yescharacteristic
422C2×C4×Q8C2×D6711yescharacteristic
423C2×C4×D4—673no—
424C2×C4×D4—673no—
425C2×C4×D4—676no—
426C2×C4×D4—673no—
427C2×C4×D4—673no—
428C2×C4×D4—673no—
429C2×C4×D4C2×D6713yes—
430C2×C4×D4C2×D6713yes—
431C2×#117—673no—
432C2×#117—673no—
433C2×#117—673no—
434C2×#117—676no—
435C2×#117C2×D6713yes—
436C22×C4⋊C4—673no—
437C22×C42C2×D6713yes—
438C2×#41—28no—
439C2×#41—678no—
440C2×#41—1348no—
441C2×#41C22×D6718yes—
442C22×Q8—678no—
443C22×Q8—673no—
444C22×Q8—673no—
445C22×Q8—1348no—
446C22×Q8C22×D6711yescharacteristic
447C22×D4—673no—
448C22×D4—676no—
449C22×D4—673no—
450C22×D4—673no—
451C22×D4—673no—
452C22×D4C22×D6713yes—
453C23×C4—676no—
454C23×C4—673no—
455C23×C4—673no—
456C23×C4C22×D6713yes—
457C23×C4C22×D6713yes—
458C23×C4C22×D6713yes—
459C4⋊Q8—6724no—
460#127—6724no—
461#126—6748no—
462#126—678no—
463#126—6724no—
464#125—6724no—
465#125—6724no—
466#125—6724no—
467#124—6724no—
468#124—6748no—
469#124—6724no—
470#124—6724no—
471#123—6748no—
472#123—6724no—
473#123—6724no—
474#123—6748no—
475C22⋊Q8—6724no—
476C22⋊Q8—6724no—
477C22⋊Q8—6724no—
478#121—6724no—
479#121—6724no—
480#121—6724no—
481#121—6724no—
482#121—6724no—
483#121—6748no—
484C4×Q8—678no—
485C4×Q8—678no—
486C4×Q8—6724no—
487C4×Q8—6724no—
488C4×Q8—6724no—
489C4×Q8C22×D6718yes—
490C4×Q8C22×D6718yes—
491C4×D4—6724no—
492C4×D4—6724no—
493C4×D4—6748no—
494C4×D4—6724no—
495C4×D4—6724no—
496C4×D4—6724no—
497C4×D4C22×D67124yes—
498C4×D4C22×D67124yes—
499#117—6724no—
500#117—6724no—
501#117—6724no—
502#117—6748no—
503#117C22×D67124yes—
504C2×C4⋊C4—673no—
505C2×C4⋊C4—673no—
506C2×C4⋊C4—671no—
507C2×C4⋊C4—673no—
508C2×C4⋊C4—673no—
509C2×C4⋊C4—673no—
510C2×C4⋊C4—673no—
511C2×C4⋊C4—676no—
512C2×C4⋊C4—671no—
513C2×C4⋊C4—673no—
514C2×C4⋊C4—673no—
515C2×C4⋊C4—671no—
516C2×C4⋊C4—673no—
517C2×C4⋊C4—6724no—
518C2×C4⋊C4C22×D6713yes—
519C2×C4⋊C4C22×D6713yes—
520C2×C22⋊C4—673no—
521C2×C22⋊C4—676no—
522C2×C22⋊C4—673no—
523C2×C22⋊C4—671no—
524C2×C22⋊C4—673no—
525C2×C22⋊C4—673no—
526C2×C22⋊C4—673no—
527C2×C22⋊C4—673no—
528C2×C22⋊C4—676no—
529C2×C22⋊C4—671no—
530C2×C22⋊C4—673no—
531C2×C22⋊C4—671no—
532C2×C22⋊C4C22×D6716yes—
533C2×C42—676no—
534C2×C42—673no—
535C2×C42—673no—
536C2×C42C22×D6713yes—
537C2×C42C22×D6713yes—
538C2×C42C22×D6713yes—
539C2×C42C22×D67124yes—
540C2×C42C22×D6711yescharacteristic
541C24—671no—
542C24—673no—
543C24C23×D6713yes—
544#41—232no—
545#41—13432no—
546C2×Q8—2686no—
547C2×Q8—6712no—
548C2×Q8—6712no—
549C2×Q8—13432no—
550C2×Q8—13412no—
551C2×Q8#1176162818yes—
552C2×Q8C23×D6714yes—
553C2×D4—212no—
554C2×D4—2686no—
555C2×D4—2686no—
556C2×D4—2686no—
557C2×D4—26812no—
558C2×D4—6712no—
559C2×D4—6724no—
560C2×D4—6712no—
561C2×D4—6712no—
562C2×D4—6712no—
563C2×D4—13412no—
564C2×D4C23×D67112yes—
565C22×C4—212no—
566C22×C4—46no—
567C22×C4—46no—
568C22×C4—26812no—
569C22×C4—6724no—
570C22×C4—671no—
571C22×C4—673no—
572C22×C4—671no—
573C22×C4—673no—
574C22×C4—673no—
575C22×C4—671no—
576C22×C4—6712no—
577C22×C4—6712no—
578C22×C4—13412no—
579C22×C4—13412no—
580C22×C4C23×D67112yes—
581C22×C4C23×D6713yes—
582C22×C4C23×D6711yescharacteristic
583C22×C4C23×D6711yescharacteristic
584C22×C4C23×D6711yescharacteristic
585C22×C4C23×D6713yes—
586C22×C4C23×D67112yes—
587C22×C4C23×D67112yes—
588C22×C4C23×D6713yes—
589C4⋊C4—6712no—
590C4⋊C4—6712no—
591C4⋊C4—674no—
592C4⋊C4—6712no—
593C4⋊C4—6712no—
594C4⋊C4—6712no—
595C4⋊C4—6712no—
596C4⋊C4—6724no—
597C4⋊C4—674no—
598C4⋊C4—6712no—
599C4⋊C4—6712no—
600C4⋊C4—674no—
601C4⋊C4—6712no—
602C4⋊C4C23×D67112yes—
603C4⋊C4C23×D67112yes—
604C22⋊C4—6712no—
605C22⋊C4—6724no—
606C22⋊C4—6712no—
607C22⋊C4—674no—
608C22⋊C4—6712no—
609C22⋊C4—6712no—
610C22⋊C4—6712no—
611C22⋊C4—6712no—
612C22⋊C4—6724no—
613C22⋊C4—674no—
614C22⋊C4—6712no—
615C22⋊C4—674no—
616C22⋊C4C23×D67124yes—
617C42—6724no—
618C42—6712no—
619C42—6712no—
620C42C23×D6714yes—
621C42C23×D67112yes—
622C42C23×D67112yes—
623C42C23×D67112yes—
624C23—26no—
625C23—26no—
626C23—26no—
627C23—672no—
628C23—676no—
629C23—1342no—
630C23—1346no—
631C23—1346no—
632C23—1342no—
633C23—1346no—
634C23—1342no—
635C23C24×D6716yes—
636C23C24×D6711yescharacteristic
637Q8—26812no—
638Q8—13424no—
639Q8C2×#11761628116yes—
640D4—224no—
641D4—26812no—
642D4—26812no—
643D4—26812no—
644D4—26824no—
645D4—13424no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—26no—
650C2×C4—26no—
651C2×C4—224no—
652C2×C4—412no—
653C2×C4—412no—
654C2×C4—26824no—
655C2×C4—672no—
656C2×C4—676no—
657C2×C4—672no—
658C2×C4—676no—
659C2×C4—676no—
660C2×C4—672no—
661C2×C4—1342no—
662C2×C4—1346no—
663C2×C4—1346no—
664C2×C4—1342no—
665C2×C4—1346no—
666C2×C4—1342no—
667C2×C4—13424no—
668C2×C4—13424no—
669C2×C4C2×#11761628112yes—
670C2×C4C24×D6716yes—
671C2×C4C24×D6712yes—
672C2×C4C24×D6712yes—
673C2×C4C24×D6712yes—
674C2×C4C24×D6716yes—
675C2×C4C24×D6716yes—
676C22—26no—
677C22—26no—
678C22—26no—
679C22—412no—
680C22—2684no—
681C22—26812no—
682C22—1342no—
683C22—1346no—
684C22—1346no—
685C22—1342no—
686C22—1346no—
687C22—1342no—
688C22C22×#1176162812yes—
689C22#1686423212yes—
690C22#1686423212yes—
691C22C25×D6711yescharacteristic
692C4—22no—
693C4—22no—
694C4—22no—
695C4—26no—
696C4—26no—
697C4—1342no—
698C4—1346no—
699C4—1346no—
700C4—1342no—
701C4—1346no—
702C4—1342no—
703C4C22×#11761628112yes—
704C2—46no—
705C2—2682no—
706C2—2686no—
707C2#2257431814yesdirect product factor
708C2C23×#1176162811yescharacteristic
709C2C2×#1686423211yescharacteristic
710C2C2×#1686423211yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×C4×#41×C67C2
socleC23×C67C25
hypercenterC2×C4×#41D67
hypocenterC67C2×#3524
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #22574318C2direct (N × H)
2. C2×#16864129C2semidirect
3. C2×#16864122C2semidirect
4. C2×#16864109C2semidirect
5. C2×#16864096C2semidirect
6. C2×#16864085C2semidirect
7. C2×#16864065C2semidirect
8. C2×#16864058C2semidirect
9. C2×#16864053C2semidirect
10. C2×#16864011C2semidirect
11. C2×#16863997C2semidirect
12. C2×#16863930C2semidirect
13. C2×#16863930C2semidirect
14. C2×#16863878C2semidirect
15. C2×#16863872C2semidirect
16. C2×C4×#41×C67C2semidirect
19. #16864129C22semidirect
20. #16864122C22semidirect
21. #16864109C22semidirect
22. #16864096C22semidirect
23. #16864085C22semidirect
24. #16864065C22semidirect
25. #16864058C22semidirect
26. #16864053C22semidirect
27. #16864011C22semidirect
28. #16863997C22semidirect
31. #16863930C22semidirect
32. #16863930C22semidirect
56. #16863878C22semidirect
57. #16863872C22semidirect
75. C4×#41×C67C22semidirect
350. C2×C67#3524semidirect
371. C2×C4×#41D67semidirect
372. C67C2×#3524semidirect
415. C4×#41C2×D67semidirect
707. C2#22574318direct (N × H)

Maximal subgroups

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

subgroupindex
#225743182
C2×#168641292
C2×#168641222
C2×#168641092
C2×#168640962
C2×#168640852
C2×#168640652
C2×#168640582
C2×#168640532
C2×#168640112
C2×#168639972
C2×#168639302
C2×#168638782
C2×#168638722
C2×C4×#41×C672
C2×#352467