Finite Group Databasebeta

← C2×#22574321 #31764116

Subgroups — C2×#22574321 #31764116

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#22574321C2132yesmaximal, direct product factor
2C2×#16864131C213yesmaximal, complemented
3C2×#16864112C213yesmaximal, complemented
4C2×#16864099C213yesmaximal, complemented
5C2×#16864084C213yesmaximal, complemented
6C2×#16864068C211yesmaximal, characteristic, complemented
7C2×#16864058C211yesmaximal, characteristic, complemented
8C2×#16864058C211yesmaximal, characteristic, complemented
9C2×#16864020C213yesmaximal, complemented
10C2×#16864002C213yesmaximal, complemented
11C2×#16863933C213yesmaximal, complemented
12C2×#16863931C213yesmaximal, complemented
13C2×#16863878C211yesmaximal, characteristic, complemented
14C2×#16863872C211yesmaximal, characteristic, complemented
15C2×C4×#11761629C211yesmaximal, characteristic, complemented
16C2×#557×C67C211yesmaximal, characteristic, complemented
17C22×#11761629C2211yescharacteristic
18C22×#11761629C2211yescharacteristic
19C22×Q8×D67C2211yescharacteristic
20#16864131C22148yescomplemented
21#16864112C22148yescomplemented
22#16864099C22148yescomplemented
23#16864084C22148yescomplemented
24#16864068C22116yescomplemented
25#16864058C22116yescomplemented
26#16864058C22116yescomplemented
27#16864020C22148yescomplemented
28#16864002C22148yescomplemented
29C2×#14524040C2213yes—
30#16863933C22148yescomplemented
31#16863931C22148yescomplemented
32C2×#14524038C2216yes—
33C2×#14524038C2213yes—
34C2×#14524038C2211yescharacteristic
35C2×#14524034C2213yes—
36C2×#14524032C2216yes—
37C2×#14524032C2213yes—
38C2×#14524031C2213yes—
39C2×#14524031C2213yes—
40C2×#14524028C2216yes—
41C2×#14524028C2216yes—
42C2×#14524028C2213yes—
43C2×#14524028C2213yes—
44C2×#14524023C2213yes—
45C2×#14524023C2213yes—
46C2×#14524019C2213yes—
47C2×#14524018C2213yes—
48C2×#14524018C2213yes—
49C2×#14524018C2213yes—
50C2×#14524018C2216yes—
51C2×#14524018C2213yes—
52C2×#14524018C2213yes—
53#16863878C22116yescomplemented
54#16863872C22116yescomplemented
55C4×#11761629C22116yescomplemented
56C2×Q8×Dic67C2211yescharacteristic
57C2×C4×Dic134C2213yes—
58C2×#14524008C2213yes—
59C2×C4×D268C2213yes—
60C2×C4×D268C2213yes—
61C2×C4×D268C2213yes—
62C2×C4×D268C2213yes—
63C2×C4×D268C2213yes—
64C2×#14524005C2213yes—
65C2×#14524005C2213yes—
66C2×#14524005C2216yes—
67C2×#14524001C2213yes—
68C2×#14524001C2213yes—
69C2×#14524001C2216yes—
70C2×#14524000C2213yes—
71C2×#14524000C2213yes—
72C2×C4⋊C4×D67C2213yes—
73C2×C42×D67C2213yes—
74#557×C67C22116yescomplemented
75C2×C4⋊Q8×C67C2213yes—
76C2×#125×C67C2213yes—
77C2×#125×C67C2213yes—
78C2×C4×Q8×C67C2211yescharacteristic
79C2×C4×Q8×C67C2211yescharacteristic
80C2×C4×Q8×C67C2211yescharacteristic
81C2×C4×Q8×C67C2213yes—
82C2×#11761629—28no—
83C2×#11761629—28no—
84C2×#11761629C2318yes—
85C2×#11761629C2318yes—
86C22×Dic134C2313yes—
87C2×Q8×D67—28no—
88C2×Q8×D67C2318yes—
89C22×D268C2313yes—
90C22×D268C2313yes—
91C22×D268C2316yes—
92C22×D268C2313yes—
93C22×D268C2313yes—
94C22×D268C2313yes—
95C22×C4×D67C2313yes—
96C22×C4×D67C2313yes—
97C22×C4×D67C2313yes—
98C22×C4×D67C2313yes—
99C22×C4×D67C2313yes—
100C22×C4×D67C2316yes—
101#14524040C23124yes—
102#14524038C23148yes—
103#14524038C23124yes—
104#14524038C2318yes—
105#14524034C23124yes—
106#14524032C23148yes—
107#14524032C23124yes—
108#14524031C23124yes—
109#14524031C23124yes—
110#14524028C23148yes—
111#14524028C23148yes—
112#14524028C23124yes—
113#14524028C23124yes—
114#14524023C23124yes—
115#14524023C23124yes—
116#14524019C23124yes—
117#14524018C23124yes—
118#14524018C23124yes—
119#14524018C23124yes—
120#14524018C23148yes—
121#14524018C23124yes—
122#14524018C23124yes—
123Q8×Dic67C2318yes—
124C4×Dic134C23124yes—
125#14524008C23124yes—
126C4×D268C23124yes—
127C4×D268C23124yes—
128C4×D268C23124yes—
129C4×D268C23124yes—
130C4×D268C23124yes—
131#14524005C23124yes—
132#14524005C23124yes—
133#14524005C23148yes—
134#14524001C23124yes—
135#14524001C23148yes—
136#14524001C23124yes—
137#14524000C23124yes—
138#14524000C23124yes—
139C2×C4⋊Dic67C2313yes—
140C2×C4⋊Dic67C2313yes—
141C2×C4⋊Dic67C2311yescharacteristic
142C2×C4⋊Dic67C2313yes—
143C2×Dic67⋊C4C2313yes—
144C2×Dic67⋊C4C2311yescharacteristic
145C2×Dic67⋊C4C2313yes—
146C2×Dic67⋊C4C2313yes—
147C4⋊C4×D67C23124yes—
148C2×(C2×D67)⋊C4C2311yescharacteristic
149C2×(C2×D67)⋊C4C2313yes—
150C2×(C2×D67)⋊C4C2313yes—
151C2×(C2×D67)⋊C4C2313yes—
152C2×(C2×D67)⋊C4C2313yes—
153C2×(C2×D67)⋊C4C2316yes—
154C2×(C2×D67)⋊C4C2316yes—
155C2×(C2×D67)⋊C4C2313yes—
156C2×(C2×D67)⋊C4C2316yes—
157C2×(C2×D67)⋊C4C2311yescharacteristic
158C2×(C2×D67)⋊C4C2311yescharacteristic
159C2×(C2×D67)⋊C4C2313yes—
160C2×(C2×D67)⋊C4C2313yes—
161C2×C4×Dic67C2311yescharacteristic
162C2×C4×Dic67C2313yes—
163C2×C4×Dic67C2313yes—
164C2×C4×Dic67C2316yes—
165C42×D67C23124yes—
166C22×Q8×C67C2313yes—
167C22×Q8×C67C2311yescharacteristic
168C4⋊Q8×C67C23124yes—
169#125×C67C23124yes—
170#125×C67C23124yes—
171C4×Q8×C67C2318yes—
172C4×Q8×C67C2318yes—
173C4×Q8×C67C2318yes—
174C4×Q8×C67C23124yes—
175C2×C4⋊C4×C67C2311yescharacteristic
176C2×C4⋊C4×C67C2313yes—
177C2×C4⋊C4×C67C2313yes—
178C2×C4⋊C4×C67C2313yes—
179C2×C4⋊C4×C67C2313yes—
180C2×C4⋊C4×C67C2313yes—
181C2×C4⋊C4×C67C2316yes—
182C2×C42×C67C2313yes—
183C2×C42×C67C2313yes—
184C2×C42×C67C2313yes—
185C23×D67C2411yescharacteristic
186C23×D67C2413yes—
187C23×D67C2413yes—
188#11761629—232no—
189#11761629—232no—
190C2×Dic134—212no—
191C2×Dic134C24112yes—
192Q8×D67—232no—
193C2×D268—212no—
194C2×D268—212no—
195C2×D268—46no—
196C2×D268—412no—
197C2×D268—46no—
198C2×D268—46no—
199C2×D268C24112yes—
200C2×D268C24112yes—
201C2×D268C24124yes—
202C2×D268C24112yes—
203C2×D268C24112yes—
204C2×D268C24112yes—
205C22×Dic67C2411yescharacteristic
206C22×Dic67C2413yes—
207C22×Dic67C2411yescharacteristic
208C22×Dic67C2413yes—
209C22×Dic67C2411yescharacteristic
210C2×C4×D67—212no—
211C2×C4×D67—212no—
212C2×C4×D67—212no—
213C2×C4×D67—46no—
214C2×C4×D67—46no—
215C2×C4×D67—412no—
216C2×C4×D67C24112yes—
217C2×C4×D67C24112yes—
218C2×C4×D67C24112yes—
219C2×C4×D67C24112yes—
220C2×C4×D67C24112yes—
221C2×C4×D67C24124yes—
222C4⋊Dic67C24112yes—
223C4⋊Dic67C24112yes—
224C4⋊Dic67C2414yes—
225C4⋊Dic67C24112yes—
226Dic67⋊C4C24112yes—
227Dic67⋊C4C2414yes—
228Dic67⋊C4C24112yes—
229Dic67⋊C4C24112yes—
230(C2×D67)⋊C4C2414yes—
231(C2×D67)⋊C4C24112yes—
232(C2×D67)⋊C4C24112yes—
233(C2×D67)⋊C4C24112yes—
234(C2×D67)⋊C4C24112yes—
235(C2×D67)⋊C4C24124yes—
236(C2×D67)⋊C4C24124yes—
237(C2×D67)⋊C4C24112yes—
238(C2×D67)⋊C4C24124yes—
239(C2×D67)⋊C4C2414yes—
240(C2×D67)⋊C4C2414yes—
241(C2×D67)⋊C4C24112yes—
242(C2×D67)⋊C4C24112yes—
243C4×Dic67C2414yes—
244C4×Dic67C24112yes—
245C4×Dic67C24112yes—
246C4×Dic67C24124yes—
247C2×Q8×C67—46no—
248C2×Q8×C67#4118yes—
249C2×Q8×C67C24112yes—
250C2×Q8×C67C2414yes—
251C22×C4×C67C2411yescharacteristic
252C22×C4×C67C2411yescharacteristic
253C22×C4×C67C2411yescharacteristic
254C22×C4×C67C2413yes—
255C22×C4×C67C2413yes—
256C22×C4×C67C2413yes—
257C22×C4×C67C2413yes—
258C4⋊C4×C67C2414yes—
259C4⋊C4×C67C24112yes—
260C4⋊C4×C67C24112yes—
261C4⋊C4×C67C24112yes—
262C4⋊C4×C67C24112yes—
263C4⋊C4×C67C24112yes—
264C4⋊C4×C67C24124yes—
265C42×C67C24112yes—
266C42×C67C24112yes—
267C42×C67C24112yes—
268C23×C67C2511yescharacteristic
269C22×D67—22no—
270C22×D67—26no—
271C22×D67—26no—
272C22×D67—26no—
273C22×D67—26no—
274C22×D67—26no—
275C22×D67—22no—
276C22×D67—26no—
277C22×D67—22no—
278C22×D67C2512yes—
279C22×D67C2516yes—
280C22×D67C2516yes—
281Q8×C67—412no—
282Q8×C67C2×#41116yes—
283C2×C4×C67—22no—
284C2×C4×C67—26no—
285C2×C4×C67—26no—
286C2×C4×C67—22no—
287C2×C4×C67—26no—
288C2×C4×C67—22no—
289C2×C4×C67C2×#41112yes—
290C2×C4×C67C2512yes—
291C2×C4×C67C2512yes—
292C2×C4×C67C2512yes—
293C2×C4×C67C2516yes—
294C2×C4×C67C2516yes—
295C2×C4×C67C2516yes—
296C2×C4×C67C2516yes—
297C2×Dic67—22no—
298C2×Dic67—22no—
299C2×Dic67—26no—
300C2×Dic67—22no—
301C2×Dic67—26no—
302C2×Dic67C2512yes—
303C2×Dic67C2516yes—
304C2×Dic67C2512yes—
305C2×Dic67C2516yes—
306C2×Dic67C2512yes—
307D268—224no—
308D268—224no—
309D268—412no—
310D268—412no—
311D268—412no—
312D268—424no—
313C4×D67—224no—
314C4×D67—224no—
315C4×D67—224no—
316C4×D67—412no—
317C4×D67—424no—
318C4×D67—412no—
319Dic134—224no—
320C22×C67C22×#4112yes—
321C22×C67#58512yes—
322C22×C67#58512yes—
323C22×C67C2611yescharacteristic
324C2×D67—22no—
325C2×D67—26no—
326C2×D67—26no—
327C2×D67—26no—
328C2×D67—26no—
329C2×D67—26no—
330C2×D67—22no—
331C2×D67—26no—
332C2×D67—22no—
333C2×D67—44no—
334C2×D67—412no—
335C2×D67—412no—
336C4×C67—22no—
337C4×C67—26no—
338C4×C67—26no—
339C4×C67—22no—
340C4×C67—26no—
341C4×C67—22no—
342C4×C67C22×#41112yes—
343Dic67—26no—
344Dic67—22no—
345Dic67—22no—
346Dic67—22no—
347Dic67—26no—
348C2×#3524—671nomaximal, Sylow
349C2×C67#352414yescomplemented
350C2×C67C23×#4111yescharacteristic
351C2×C67C2×#58511yescharacteristic
352C2×C67C2×#58511yescharacteristic
353D67—42no—
354D67—46no—
355D67—46no—
356#3524—6732no—
357C2×#559—673no—
358C2×#557D6711yescharacteristic, complemented
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×#41—671no—
372C67C2×#352411yescharacteristic, complemented, Sylow
373C22×#41—671no—
374C22×#41—671no—
375C23×Q8—671no—
376#559—6748no—
377#557C2×D67116yescomplemented
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⋊Q8C2×D6713yes—
387C2×#127—673no—
388#529—6748no—
389#529—6748no—
390C2×#126—671no—
391C2×#126—673no—
392C2×#126—676no—
393C2×#125—673no—
394C2×#125C2×D6713yes—
395C2×#125C2×D6713yes—
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—676no—
412C2×#121—673no—
413#520—6716no—
414#519—6716no—
415C4×#41—6716no—
416C2×C4×Q8—671no—
417C2×C4×Q8—673no—
418C2×C4×Q8—673no—
419C2×C4×Q8C2×D6711yescharacteristic
420C2×C4×Q8C2×D6711yescharacteristic
421C2×C4×Q8C2×D6711yescharacteristic
422C2×C4×Q8C2×D6713yes—
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×D4—673no—
430C2×C4×D4—673no—
431C2×#117—673no—
432C2×#117—673no—
433C2×#117—676no—
434C2×#117—673no—
435C2×#117—673no—
436C22×C4⋊C4—673no—
437C22×C42—673no—
438C2×#41—678no—
439C2×#41—678no—
440C2×#41—1348no—
441C2×#41—1348no—
442C22×Q8—678no—
443C22×Q8—673no—
444C22×Q8—1348no—
445C22×Q8C22×D6713yes—
446C22×Q8C22×D6711yescharacteristic
447C22×D4—673no—
448C22×D4—673no—
449C22×D4—676no—
450C22×D4—673no—
451C22×D4—673no—
452C22×D4—673no—
453C23×C4—676no—
454C23×C4—673no—
455C23×C4—673no—
456C23×C4—673no—
457C23×C4—673no—
458C23×C4—673no—
459C4⋊Q8C22×D67124yes—
460#127—6724no—
461#126—678no—
462#126—6724no—
463#126—6748no—
464#125—6724no—
465#125C22×D67124yes—
466#125C22×D67124yes—
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—6748no—
483#121—6724no—
484C4×Q8—678no—
485C4×Q8—6724no—
486C4×Q8—6724no—
487C4×Q8C22×D6718yes—
488C4×Q8C22×D6718yes—
489C4×Q8C22×D6718yes—
490C4×Q8C22×D67124yes—
491C4×D4—6724no—
492C4×D4—6724no—
493C4×D4—6748no—
494C4×D4—6724no—
495C4×D4—6724no—
496C4×D4—6724no—
497C4×D4—6724no—
498C4×D4—6724no—
499#117—6724no—
500#117—6724no—
501#117—6748no—
502#117—6724no—
503#117—6724no—
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—671no—
511C2×C4⋊C4—673no—
512C2×C4⋊C4—6724no—
513C2×C4⋊C4C22×D6713yes—
514C2×C4⋊C4C22×D6713yes—
515C2×C4⋊C4C22×D6713yes—
516C2×C4⋊C4C22×D6716yes—
517C2×C4⋊C4C22×D6713yes—
518C2×C4⋊C4C22×D6711yescharacteristic
519C2×C4⋊C4C22×D6713yes—
520C2×C22⋊C4—671no—
521C2×C22⋊C4—673no—
522C2×C22⋊C4—673no—
523C2×C22⋊C4—673no—
524C2×C22⋊C4—676no—
525C2×C22⋊C4—673no—
526C2×C22⋊C4—676no—
527C2×C22⋊C4—671no—
528C2×C22⋊C4—673no—
529C2×C22⋊C4—671no—
530C2×C22⋊C4—673no—
531C2×C22⋊C4—676no—
532C2×C22⋊C4—673no—
533C2×C42—673no—
534C2×C42—673no—
535C2×C42—676no—
536C2×C42—671no—
537C2×C42—6724no—
538C2×C42C22×D6713yes—
539C2×C42C22×D6713yes—
540C2×C42C22×D6713yes—
541C24—671no—
542C24—673no—
543C24—673no—
544#41—13432no—
545#41—13432no—
546C2×Q8—46no—
547C2×Q8—6712no—
548C2×Q8—13432no—
549C2×Q8—13412no—
550C2×Q8#1176162918yes—
551C2×Q8C23×D67112yes—
552C2×Q8C23×D6714yes—
553C2×D4—2686no—
554C2×D4—26812no—
555C2×D4—2686no—
556C2×D4—2686no—
557C2×D4—6712no—
558C2×D4—6712no—
559C2×D4—6724no—
560C2×D4—6712no—
561C2×D4—6712no—
562C2×D4—6712no—
563C2×D4—13412no—
564C2×D4—13412no—
565C22×C4—2686no—
566C22×C4—2686no—
567C22×C4—26812no—
568C22×C4—6712no—
569C22×C4—6712no—
570C22×C4—6724no—
571C22×C4—671no—
572C22×C4—671no—
573C22×C4—673no—
574C22×C4—673no—
575C22×C4—671no—
576C22×C4—6712no—
577C22×C4—6712no—
578C22×C4—6712no—
579C22×C4—13412no—
580C22×C4—13412no—
581C22×C4—13412no—
582C22×C4C23×D6713yes—
583C22×C4C23×D6711yescharacteristic
584C22×C4C23×D6713yes—
585C22×C4C23×D6711yescharacteristic
586C22×C4C23×D6711yescharacteristic
587C22×C4C23×D6713yes—
588C22×C4C23×D6713yes—
589C4⋊C4—6712no—
590C4⋊C4—6712no—
591C4⋊C4—674no—
592C4⋊C4—6712no—
593C4⋊C4—6712no—
594C4⋊C4—6712no—
595C4⋊C4—674no—
596C4⋊C4—6712no—
597C4⋊C4C23×D67112yes—
598C4⋊C4C23×D67112yes—
599C4⋊C4C23×D67112yes—
600C4⋊C4C23×D67124yes—
601C4⋊C4C23×D67112yes—
602C4⋊C4C23×D6714yes—
603C4⋊C4C23×D67112yes—
604C22⋊C4—674no—
605C22⋊C4—6712no—
606C22⋊C4—6712no—
607C22⋊C4—6712no—
608C22⋊C4—6724no—
609C22⋊C4—6712no—
610C22⋊C4—6724no—
611C22⋊C4—674no—
612C22⋊C4—6712no—
613C22⋊C4—674no—
614C22⋊C4—6712no—
615C22⋊C4—6724no—
616C22⋊C4—6712no—
617C42—674no—
618C42—6712no—
619C42—6712no—
620C42—6724no—
621C42C23×D67112yes—
622C42C23×D67112yes—
623C42C23×D67112yes—
624C23—672no—
625C23—676no—
626C23—676no—
627C23—1342no—
628C23—1346no—
629C23—1346no—
630C23—1346no—
631C23—1342no—
632C23—1346no—
633C23—1346no—
634C23—1346no—
635C23—1342no—
636C23C24×D6711yescharacteristic
637Q8—412no—
638Q8—13424no—
639Q8C2×#11761629116yes—
640D4—26812no—
641D4—26824no—
642D4—26812no—
643D4—26812no—
644D4—13424no—
645D4—13424no—
646C2×C4—26no—
647C2×C4—26no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—26no—
651C2×C4—22no—
652C2×C4—26812no—
653C2×C4—26812no—
654C2×C4—26824no—
655C2×C4—672no—
656C2×C4—672no—
657C2×C4—676no—
658C2×C4—676no—
659C2×C4—672no—
660C2×C4—1342no—
661C2×C4—1342no—
662C2×C4—1346no—
663C2×C4—1342no—
664C2×C4—1346no—
665C2×C4—13424no—
666C2×C4—13424no—
667C2×C4—13424no—
668C2×C4C2×#11761629112yes—
669C2×C4C24×D6716yes—
670C2×C4C24×D6712yes—
671C2×C4C24×D6716yes—
672C2×C4C24×D6712yes—
673C2×C4C24×D6712yes—
674C2×C4C24×D6716yes—
675C2×C4C24×D6716yes—
676C22—2684no—
677C22—26812no—
678C22—26812no—
679C22—1342no—
680C22—1346no—
681C22—1346no—
682C22—1346no—
683C22—1342no—
684C22—1346no—
685C22—1346no—
686C22—1346no—
687C22—1342no—
688C22C22×#1176162912yes—
689C22#1686423212yes—
690C22#1686423312yes—
691C22C25×D6711yescharacteristic
692C4—26no—
693C4—26no—
694C4—22no—
695C4—22no—
696C4—26no—
697C4—22no—
698C4—1342no—
699C4—1342no—
700C4—1346no—
701C4—1342no—
702C4—1346no—
703C4C22×#11761629112yes—
704C2—2682no—
705C2—2686no—
706C2—2686no—
707C2#2257432114yesdirect product factor
708C2C23×#1176162911yescharacteristic
709C2C2×#1686423211yescharacteristic
710C2C2×#1686423311yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#557×C67C2
socleC23×C67C25
hypercenterC2×#557D67
hypocenterC67C2×#3524
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #22574321C2direct (N × H)
2. C2×#16864131C2semidirect
3. C2×#16864112C2semidirect
4. C2×#16864099C2semidirect
5. C2×#16864084C2semidirect
6. C2×#16864068C2semidirect
7. C2×#16864058C2semidirect
8. C2×#16864058C2semidirect
9. C2×#16864020C2semidirect
10. C2×#16864002C2semidirect
11. C2×#16863933C2semidirect
12. C2×#16863931C2semidirect
13. C2×#16863878C2semidirect
14. C2×#16863872C2semidirect
15. C2×C4×#11761629C2semidirect
16. C2×#557×C67C2semidirect
20. #16864131C22semidirect
21. #16864112C22semidirect
22. #16864099C22semidirect
23. #16864084C22semidirect
24. #16864068C22semidirect
25. #16864058C22semidirect
26. #16864058C22semidirect
27. #16864020C22semidirect
28. #16864002C22semidirect
30. #16863933C22semidirect
31. #16863931C22semidirect
53. #16863878C22semidirect
54. #16863872C22semidirect
55. C4×#11761629C22semidirect
74. #557×C67C22semidirect
349. C2×C67#3524semidirect
358. C2×#557D67semidirect
372. C67C2×#3524semidirect
377. #557C2×D67semidirect
707. C2#22574321direct (N × H)

Maximal subgroups

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

subgroupindex
#225743212
C2×#168641312
C2×#168641122
C2×#168640992
C2×#168640842
C2×#168640682
C2×#168640582
C2×#168640202
C2×#168640022
C2×#168639332
C2×#168639312
C2×#168638782
C2×#168638722
C2×C4×#117616292
C2×#557×C672
C2×#352467