Finite Group Databasebeta

← C2×#22574194 #31764022

Subgroups — C2×#22574194 #31764022

Order 17152.

7130 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574194C2132yesmaximal, direct product factor
2C2×#16864122C211yesmaximal, characteristic, complemented
3C2×#16864116C213yesmaximal, complemented
4C2×#16864101C213yesmaximal, complemented
5C2×#16864096C213yesmaximal, complemented
6C2×#16864081C213yesmaximal, complemented
7C2×Q8×D268C211yesmaximal, characteristic, complemented
8C2×#16864053C211yesmaximal, characteristic, complemented
9C2×#16864053C211yesmaximal, characteristic, complemented
10C2×#16864011C213yesmaximal, complemented
11C2×#16864008C213yesmaximal, complemented
12C2×#16863928C213yesmaximal, complemented
13C2×#16863924C213yesmaximal, complemented
14C2×#16863872C211yesmaximal, characteristic, complemented
15C2×C4×Q8×D67C211yesmaximal, characteristic, complemented
16C2×#520×C67C211yesmaximal, characteristic, complemented
17C22×Q8×D67C2211yescharacteristic
18C22×Q8×D67C2211yescharacteristic
19#16864122C22116yescomplemented
20#16864116C22148yescomplemented
21#16864101C22148yescomplemented
22#16864096C22148yescomplemented
23#16864081C22148yescomplemented
24Q8×D268C22116yescomplemented
25#16864053C22116yescomplemented
26#16864053C22116yescomplemented
27#16864011C22148yescomplemented
28#16864008C22148yescomplemented
29C2×#14524043C2213yes—
30C2×#14524042C2213yes—
31#16863928C22148yescomplemented
32#16863924C22148yescomplemented
33C2×#14524038C2213yes—
34C2×#14524036C2216yes—
35C2×#14524036C2216yes—
36C2×#14524036C2213yes—
37C2×#14524035C2213yes—
38C2×#14524034C2213yes—
39C2×#14524033C2213yes—
40C2×#14524033C2216yes—
41C2×#14524030C2213yes—
42C2×#14524030C2213yes—
43C2×#14524029C2213yes—
44C2×#14524028C2211yescharacteristic
45C2×#14524026C2216yes—
46C2×#14524025C2213yes—
47C2×#14524023C2213yes—
48C2×#14524023C2213yes—
49C2×#14524022C2213yes—
50C2×#14524022C2213yes—
51C2×#14524022C2216yes—
52C2×#14524021C2213yes—
53C2×#14524016C2213yes—
54C2×#14524014C2213yes—
55C2×#14524014C2213yes—
56#16863872C22116yescomplemented
57C2×Q8×Dic67C2211yescharacteristic
58C2×Q8×Dic67C2211yescharacteristic
59C2×C4×Dic134C2213yes—
60C2×C4×Dic134C2213yes—
61C2×C4×Dic134C2213yes—
62C2×#14524008C2213yes—
63C2×#14524008C2213yes—
64C4×Q8×D67C22116yescomplemented
65C2×C4×D268C2213yes—
66C2×C4×C22⋊D67C2213yes—
67C2×C4×C22⋊D67C2213yes—
68C2×C4×C22⋊D67C2216yes—
69C2×#14524002C2216yes—
70C2×#14524001C2213yes—
71C2×#14524000C2213yes—
72C2×C4⋊C4×D67C2213yes—
73C2×C42×D67C2213yes—
74C22×#41×C67C2211yescharacteristic
75#520×C67C22116yescomplemented
76C2×C4×Q8×C67C2211yescharacteristic
77C2×C4×Q8×C67C2211yescharacteristic
78C2×C4×D4×C67C2213yes—
79C2×C4×D4×C67C2213yes—
80C2×#117×C67C2213yes—
81C22×C4⋊C4×C67C2213yes—
82C22×Dic134C2313yes—
83C22×Dic134C2313yes—
84C22×Dic134C2313yes—
85C2×Q8×D67—28no—
86C2×Q8×D67—28no—
87C2×Q8×D67C2318yes—
88C2×Q8×D67C2318yes—
89C22×D268C2311yescharacteristic
90C22×C22⋊D67C2313yes—
91C22×C22⋊D67C2313yes—
92C22×C4×D67C2311yescharacteristic
93C22×C4×D67C2313yes—
94C22×C4×D67C2313yes—
95C22×C4×D67C2313yes—
96#14524043C23124yes—
97#14524042C23124yes—
98#14524038C23124yes—
99#14524036C23148yes—
100#14524036C23148yes—
101#14524036C23124yes—
102#14524035C23124yes—
103#14524034C23124yes—
104#14524033C23124yes—
105#14524033C23148yes—
106#14524030C23124yes—
107#14524030C23124yes—
108#14524029C23124yes—
109#14524028C2318yes—
110#14524026C23148yes—
111#14524025C23124yes—
112#14524023C23124yes—
113#14524023C23124yes—
114#14524022C23124yes—
115#14524022C23124yes—
116#14524022C23148yes—
117#14524021C23124yes—
118#14524016C23124yes—
119#14524014C23124yes—
120#14524014C23124yes—
121Q8×Dic67C2318yes—
122Q8×Dic67C2318yes—
123C4×Dic134C23124yes—
124C4×Dic134C23124yes—
125C4×Dic134C23124yes—
126#14524008C23124yes—
127#14524008C23124yes—
128C4×D268C23124yes—
129C4×C22⋊D67C23124yes—
130C4×C22⋊D67C23124yes—
131C4×C22⋊D67C23148yes—
132#14524002C23148yes—
133#14524001C23124yes—
134#14524000C23124yes—
135C2×C4⋊Dic67C2313yes—
136C2×C4⋊Dic67C2313yes—
137C2×C4⋊Dic67C2313yes—
138C2×C4⋊Dic67C2316yes—
139C2×C4⋊Dic67C2313yes—
140C2×Dic67⋊C4C2316yes—
141C2×Dic67⋊C4C2313yes—
142C2×Dic67⋊C4C2313yes—
143C2×Dic67⋊C4C2313yes—
144C2×Dic67⋊C4C2313yes—
145C2×Dic67⋊C4C2316yes—
146C2×Dic67⋊C4C2311yescharacteristic
147C2×Dic67⋊C4C2313yes—
148C4⋊C4×D67C23124yes—
149C2×C22⋊Dic67C2313yes—
150C2×C22⋊Dic67C2316yes—
151C2×C22⋊Dic67C2316yes—
152C2×C22⋊Dic67C2313yes—
153C2×(C2×D67)⋊C4C2311yescharacteristic
154C2×(C2×D67)⋊C4C2313yes—
155C2×(C2×D67)⋊C4C2311yescharacteristic
156C2×(C2×D67)⋊C4C2311yescharacteristic
157C2×(C2×D67)⋊C4C2313yes—
158C2×(C2×D67)⋊C4C2313yes—
159C2×C4×Dic67C2313yes—
160C2×C4×Dic67C2313yes—
161C2×C4×Dic67C2313yes—
162C2×C4×Dic67C2313yes—
163C2×C4×Dic67C2316yes—
164C42×D67C23124yes—
165C2×#41×C67—28no—
166C2×#41×C67C2318yes—
167C22×Q8×C67C2311yescharacteristic
168C22×D4×C67C2313yes—
169C23×C4×C67C2313yes—
170C23×C4×C67C2316yes—
171C4×Q8×C67C2318yes—
172C4×Q8×C67C2318yes—
173C4×D4×C67C23124yes—
174C4×D4×C67C23124yes—
175#117×C67C23124yes—
176C2×C4⋊C4×C67C2313yes—
177C2×C4⋊C4×C67C2313yes—
178C2×C4⋊C4×C67C2313yes—
179C2×C4⋊C4×C67C23124yes—
180C2×C4⋊C4×C67C2311yescharacteristic
181C2×C22⋊C4×C67C2313yes—
182C2×C22⋊C4×C67C2313yes—
183C2×C42×C67C2313yes—
184C2×C42×C67C2313yes—
185C23×D67C2411yescharacteristic
186C23×D67C2411yescharacteristic
187C2×Dic134—212no—
188C2×Dic134—212no—
189C2×Dic134—46no—
190C2×Dic134C24112yes—
191C2×Dic134C24112yes—
192C2×Dic134C24112yes—
193Q8×D67—232no—
194Q8×D67—232no—
195C2×D268—24no—
196C2×D268C2414yes—
197C2×C22⋊D67—212no—
198C2×C22⋊D67—46no—
199C2×C22⋊D67C24112yes—
200C2×C22⋊D67C24112yes—
201C22×Dic67C2411yescharacteristic
202C22×Dic67C2411yescharacteristic
203C22×Dic67C2413yes—
204C22×Dic67C2413yes—
205C22×Dic67C2413yes—
206C22×Dic67C2413yes—
207C2×C4×D67—24no—
208C2×C4×D67—212no—
209C2×C4×D67—212no—
210C2×C4×D67—46no—
211C2×C4×D67C2414yes—
212C2×C4×D67C24112yes—
213C2×C4×D67C24112yes—
214C2×C4×D67C24112yes—
215C4⋊Dic67C24112yes—
216C4⋊Dic67C24112yes—
217C4⋊Dic67C24112yes—
218C4⋊Dic67C24124yes—
219C4⋊Dic67C24112yes—
220Dic67⋊C4C24124yes—
221Dic67⋊C4C24112yes—
222Dic67⋊C4C24112yes—
223Dic67⋊C4C24112yes—
224Dic67⋊C4C24112yes—
225Dic67⋊C4C24124yes—
226Dic67⋊C4C2414yes—
227Dic67⋊C4C24112yes—
228C22⋊Dic67C24112yes—
229C22⋊Dic67C24124yes—
230C22⋊Dic67C24124yes—
231C22⋊Dic67C24112yes—
232(C2×D67)⋊C4C2414yes—
233(C2×D67)⋊C4C24112yes—
234(C2×D67)⋊C4C2414yes—
235(C2×D67)⋊C4C2414yes—
236(C2×D67)⋊C4C24112yes—
237(C2×D67)⋊C4C24112yes—
238C4×Dic67C24112yes—
239C4×Dic67C24112yes—
240C4×Dic67C24112yes—
241C4×Dic67C24112yes—
242C4×Dic67C24124yes—
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—412no—
251C22×C4×C67C2411yescharacteristic
252C22×C4×C67C2411yescharacteristic
253C22×C4×C67C2413yes—
254C22×C4×C67C2413yes—
255C22×C4×C67C2411yescharacteristic
256C22×C4×C67C24112yes—
257C22×C4×C67C24124yes—
258C22×C4×C67C2413yes—
259C4⋊C4×C67C24112yes—
260C4⋊C4×C67C24112yes—
261C4⋊C4×C67C24112yes—
262C4⋊C4×C67C2414yes—
263C22⋊C4×C67C24112yes—
264C22⋊C4×C67C24112yes—
265C42×C67C24112yes—
266C42×C67C24112yes—
267C23×C67—26no—
268C23×C67—26no—
269C23×C67—26no—
270C23×C67C2516yes—
271C23×C67C2511yescharacteristic
272C22×D67—22no—
273C22×D67—22no—
274C22×D67—22no—
275C22×D67—22no—
276C22×D67—22no—
277C22×D672−1+414yes—
278C22×D67C2512yes—
279C22×D67C2512yes—
280Q8×C67C2×#41116yes—
281D4×C67—224no—
282C2×C4×C67—22no—
283C2×C4×C67—22no—
284C2×C4×C67—22no—
285C2×C4×C67—26no—
286C2×C4×C67—26no—
287C2×C4×C67—224no—
288C2×C4×C67—424no—
289C2×C4×C67C2×#41112yes—
290C2×C4×C67C2512yes—
291C2×C4×C67C2512yes—
292C2×C4×C67C2516yes—
293C2×C4×C67C2516yes—
294C2×C4×C67C2512yes—
295C2×C4×C67C2516yes—
296C22⋊D67—224no—
297C22⋊D67—412no—
298C2×Dic67—26no—
299C2×Dic67—26no—
300C2×Dic67—22no—
301C2×Dic67—26no—
302C2×Dic67—26no—
303C2×Dic67—22no—
304C2×Dic67C2512yes—
305C2×Dic67C2512yes—
306C2×Dic67C2516yes—
307C2×Dic67C2516yes—
308C2×Dic67C2516yes—
309C2×Dic67C2516yes—
310D268—28no—
311C4×D67—28no—
312C4×D67—224no—
313C4×D67—224no—
314C4×D67—412no—
315Dic134—224no—
316Dic134—224no—
317Dic134—412no—
318C22×C67—26no—
319C22×C67—26no—
320C22×C67—26no—
321C22×C67—412no—
322C22×C67C22×#4112yes—
323C22×C67C2×2−1+412yes—
324C22×C67#58512yes—
325C22×C67C2611yescharacteristic
326C2×D67—22no—
327C2×D67—22no—
328C2×D67—28no—
329C2×D67—22no—
330C2×D67—22no—
331C2×D67—22no—
332C2×D67—44no—
333C2×D67C2×2−1+414yes—
334C4×C67—22no—
335C4×C67—22no—
336C4×C67—22no—
337C4×C67—26no—
338C4×C67—26no—
339C4×C67C22×#41112yes—
340Dic67—26no—
341Dic67—26no—
342Dic67—22no—
343Dic67—26no—
344Dic67—22no—
345Dic67—26no—
346C2×#3516—671nomaximal, Sylow
347C2×C67—46no—
348C2×C67#351614yescomplemented
349C2×C67C23×#4111yescharacteristic
350C2×C67C22×2−1+411yescharacteristic
351C2×C67C2×#58511yescharacteristic
352D67—24no—
353D67—42no—
354#3516—6732no—
355C2×#557—671no—
356C2×#556—673no—
357C2×#554—673no—
358C2×#553—673no—
359C2×#552—673no—
360C2×D4×Q8—671no—
361C2×#548—671no—
362C2×#548—671no—
363C2×#542—673no—
364C2×#541—673no—
365C2×#529—673no—
366C2×#529—673no—
367C2×#520D6711yescharacteristic, complemented
368C2×#519—671no—
369C22×C4×Q8—671no—
370C67C2×#351611yescharacteristic, complemented, Sylow
371C22×#41C2×D6711yescharacteristic
372C23×Q8—671no—
373C23×Q8—671no—
374#557—6716no—
375#556—6748no—
376#554—6748no—
377#553—6748no—
378#552—6748no—
379D4×Q8—6716no—
380#548—6716no—
381#548—6716no—
382#542—6748no—
383#541—6748no—
384C2×C4⋊Q8—673no—
385C2×C4⋊Q8—673no—
386#529—6748no—
387#529—6748no—
388C2×#126—673no—
389C2×#126—676no—
390C2×#126—673no—
391C2×#126—676no—
392C2×#125—673no—
393C2×#125—673no—
394C2×#125—676no—
395C2×#125—673no—
396C2×#124—673no—
397C2×#124—673no—
398C2×#124—673no—
399C2×#123—676no—
400C2×#123—671no—
401C2×#123—673no—
402C2×C22⋊Q8—673no—
403C2×C22⋊Q8—673no—
404C2×C22⋊Q8—676no—
405C2×C22⋊Q8—673no—
406C2×C22⋊Q8—673no—
407C2×C22⋊Q8—673no—
408C2×#121—673no—
409C2×#121—673no—
410C2×#121—673no—
411#520C2×D67116yescomplemented
412#519—6716no—
413C2×C4×Q8—671no—
414C2×C4×Q8—671no—
415C2×C4×Q8—6716no—
416C2×C4×Q8—673no—
417C2×C4×Q8—673no—
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×D4C2×D6713yes—
428C2×C4×D4C2×D6713yes—
429C2×#117—676no—
430C2×#117—673no—
431C2×#117—673no—
432C2×#117C2×D6713yes—
433C22×C4⋊C4—673no—
434C22×C4⋊C4C2×D6713yes—
435C22×C42—673no—
436C2×#41—28no—
437C2×#41C22×D6718yes—
438C22×Q8—678no—
439C22×Q8—678no—
440C22×Q8—673no—
441C22×Q8—673no—
442C22×Q8—673no—
443C22×Q8—1348no—
444C22×Q8—1348no—
445C22×Q8C22×D6711yescharacteristic
446C22×D4—673no—
447C22×D4—673no—
448C22×D4—671no—
449C22×D4C22×D6713yes—
450C23×C4—673no—
451C23×C4—673no—
452C23×C4—673no—
453C23×C4—671no—
454C23×C4C22×D6713yes—
455C23×C4C22×D6716yes—
456C4⋊Q8—6724no—
457C4⋊Q8—6724no—
458#126—6724no—
459#126—6748no—
460#126—6724no—
461#126—6748no—
462#125—6724no—
463#125—6724no—
464#125—6748no—
465#125—6724no—
466#124—6724no—
467#124—6724no—
468#124—6724no—
469#123—6748no—
470#123—678no—
471#123—6724no—
472C22⋊Q8—6724no—
473C22⋊Q8—6724no—
474C22⋊Q8—6748no—
475C22⋊Q8—6724no—
476C22⋊Q8—6724no—
477C22⋊Q8—6724no—
478#121—6724no—
479#121—6724no—
480#121—6724no—
481C4×Q8—678no—
482C4×Q8—678no—
483C4×Q8—6724no—
484C4×Q8—6724no—
485C4×Q8—6724no—
486C4×Q8—6724no—
487C4×Q8—6724no—
488C4×Q8C22×D6718yes—
489C4×Q8C22×D6718yes—
490C4×D4—6724no—
491C4×D4—6724no—
492C4×D4—6748no—
493C4×D4—6724no—
494C4×D4C22×D67124yes—
495C4×D4C22×D67124yes—
496#117—6748no—
497#117—6724no—
498#117—6724no—
499#117C22×D67124yes—
500C2×C4⋊C4—673no—
501C2×C4⋊C4—676no—
502C2×C4⋊C4—673no—
503C2×C4⋊C4—673no—
504C2×C4⋊C4—673no—
505C2×C4⋊C4—673no—
506C2×C4⋊C4—676no—
507C2×C4⋊C4—673no—
508C2×C4⋊C4—673no—
509C2×C4⋊C4—676no—
510C2×C4⋊C4—673no—
511C2×C4⋊C4—671no—
512C2×C4⋊C4—673no—
513C2×C4⋊C4—6724no—
514C2×C4⋊C4C22×D6713yes—
515C2×C4⋊C4C22×D6713yes—
516C2×C4⋊C4C22×D6713yes—
517C2×C4⋊C4C22×D67124yes—
518C2×C4⋊C4C22×D6711yescharacteristic
519C2×C22⋊C4—673no—
520C2×C22⋊C4—676no—
521C2×C22⋊C4—676no—
522C2×C22⋊C4—673no—
523C2×C22⋊C4—673no—
524C2×C22⋊C4—671no—
525C2×C22⋊C4—671no—
526C2×C22⋊C4—673no—
527C2×C22⋊C4—671no—
528C2×C22⋊C4—673no—
529C2×C22⋊C4C22×D6713yes—
530C2×C22⋊C4C22×D6713yes—
531C2×C42—676no—
532C2×C42—673no—
533C2×C42—673no—
534C2×C42—673no—
535C2×C42—673no—
536C2×C42—6724no—
537C2×C42C22×D6713yes—
538C2×C42C22×D6713yes—
539C24—671no—
540C24—671no—
541C24C23×D6713yes—
542#41—232no—
543C2×Q8—2686no—
544C2×Q8—6712no—
545C2×Q8—6712no—
546C2×Q8—6712no—
547C2×Q8—13432no—
548C2×Q8—13432no—
549C2×Q8—13412no—
550C2×Q8—13412no—
551C2×Q8#1176162818yes—
552C2×Q8C23×D6714yes—
553C2×D4—212no—
554C2×D4—2686no—
555C2×D4—6712no—
556C2×D4—6712no—
557C2×D4—674no—
558C2×D4—1344no—
559C2×D4—13412no—
560C2×D4C23×D67112yes—
561C22×C4—212no—
562C22×C4—412no—
563C22×C4—2686no—
564C22×C4—6712no—
565C22×C4—671no—
566C22×C4—671no—
567C22×C4—673no—
568C22×C4—673no—
569C22×C4—673no—
570C22×C4—673no—
571C22×C4—674no—
572C22×C4—6712no—
573C22×C4—6712no—
574C22×C4—1344no—
575C22×C4—13412no—
576C22×C4—13412no—
577C22×C4C23×D67112yes—
578C22×C4C23×D6711yescharacteristic
579C22×C4C23×D6713yes—
580C22×C4C23×D6711yescharacteristic
581C22×C4C23×D6713yes—
582C22×C4C23×D6711yescharacteristic
583C22×C4C23×D67124yes—
584C22×C4C23×D6713yes—
585C4⋊C4—6712no—
586C4⋊C4—6724no—
587C4⋊C4—6712no—
588C4⋊C4—6712no—
589C4⋊C4—6712no—
590C4⋊C4—6712no—
591C4⋊C4—6724no—
592C4⋊C4—6712no—
593C4⋊C4—6712no—
594C4⋊C4—6724no—
595C4⋊C4—6712no—
596C4⋊C4—674no—
597C4⋊C4—6712no—
598C4⋊C4C23×D67112yes—
599C4⋊C4C23×D67112yes—
600C4⋊C4C23×D67112yes—
601C4⋊C4C23×D6714yes—
602C22⋊C4—6712no—
603C22⋊C4—6724no—
604C22⋊C4—6724no—
605C22⋊C4—6712no—
606C22⋊C4—6712no—
607C22⋊C4—674no—
608C22⋊C4—674no—
609C22⋊C4—6712no—
610C22⋊C4—674no—
611C22⋊C4—6712no—
612C22⋊C4C23×D67112yes—
613C22⋊C4C23×D67112yes—
614C42—6712no—
615C42—6712no—
616C42—6712no—
617C42—6724no—
618C42—6712no—
619C42C23×D67112yes—
620C42C23×D67112yes—
621C23—26no—
622C23—26no—
623C23—26no—
624C23—674no—
625C23—672no—
626C23—672no—
627C23—1342no—
628C23—1342no—
629C23—1342no—
630C23—1342no—
631C23—1342no—
632C23C24×D6716yes—
633C23C24×D6711yescharacteristic
634Q8—26812no—
635Q8—13424no—
636Q8—13424no—
637Q8C2×#11761628116yes—
638D4—224no—
639D4—26812no—
640D4—1348no—
641D4—13424no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—26no—
646C2×C4—26no—
647C2×C4—224no—
648C2×C4—424no—
649C2×C4—26812no—
650C2×C4—672no—
651C2×C4—672no—
652C2×C4—676no—
653C2×C4—676no—
654C2×C4—676no—
655C2×C4—676no—
656C2×C4—1348no—
657C2×C4—1346no—
658C2×C4—1346no—
659C2×C4—1342no—
660C2×C4—1346no—
661C2×C4—1346no—
662C2×C4—1342no—
663C2×C4—13424no—
664C2×C4—13424no—
665C2×C4C2×#11761628112yes—
666C2×C4C24×D6712yes—
667C2×C4C24×D6716yes—
668C2×C4C24×D6712yes—
669C2×C4C24×D6716yes—
670C2×C4C24×D6712yes—
671C2×C4C24×D6716yes—
672C22—26no—
673C22—26no—
674C22—26no—
675C22—412no—
676C22—2684no—
677C22—674no—
678C22—1342no—
679C22—1342no—
680C22—1342no—
681C22—1348no—
682C22—1342no—
683C22—1342no—
684C22C22×#1176162812yes—
685C222−1+4×D6712yes—
686C22#1686423112yes—
687C22C25×D6711yescharacteristic
688C4—22no—
689C4—22no—
690C4—22no—
691C4—26no—
692C4—26no—
693C4—1346no—
694C4—1346no—
695C4—1342no—
696C4—1346no—
697C4—1346no—
698C4—1342no—
699C4C22×#11761628112yes—
700C2—46no—
701C2—2682no—
702C2—1344no—
703C2#2257419414yesdirect product factor
704C2C23×#1176162811yescharacteristic
705C2C2×2−1+4×D6711yescharacteristic
706C2C2×#1686423111yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#520×C67C2
socleC23×C67C25
hypercenterC2×#520D67
hypocenterC67C2×#3516
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #22574194C2direct (N × H)
2. C2×#16864122C2semidirect
3. C2×#16864116C2semidirect
4. C2×#16864101C2semidirect
5. C2×#16864096C2semidirect
6. C2×#16864081C2semidirect
7. C2×Q8×D268C2semidirect
8. C2×#16864053C2semidirect
9. C2×#16864053C2semidirect
10. C2×#16864011C2semidirect
11. C2×#16864008C2semidirect
12. C2×#16863928C2semidirect
13. C2×#16863924C2semidirect
14. C2×#16863872C2semidirect
15. C2×C4×Q8×D67C2semidirect
16. C2×#520×C67C2semidirect
19. #16864122C22semidirect
20. #16864116C22semidirect
21. #16864101C22semidirect
22. #16864096C22semidirect
23. #16864081C22semidirect
24. Q8×D268C22semidirect
25. #16864053C22semidirect
26. #16864053C22semidirect
27. #16864011C22semidirect
28. #16864008C22semidirect
31. #16863928C22semidirect
32. #16863924C22semidirect
56. #16863872C22semidirect
64. C4×Q8×D67C22semidirect
75. #520×C67C22semidirect
348. C2×C67#3516semidirect
367. C2×#520D67semidirect
370. C67C2×#3516semidirect
411. #520C2×D67semidirect
703. C2#22574194direct (N × H)

Maximal subgroups

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

subgroupindex
#225741942
C2×#168641222
C2×#168641162
C2×#168641012
C2×#168640962
C2×#168640812
C2×Q8×D2682
C2×#168640532
C2×#168640112
C2×#168640082
C2×#168639282
C2×#168639242
C2×#168638722
C2×C4×Q8×D672
C2×#520×C672
C2×#351667