Finite Group Databasebeta

← C2×#22574202 #31764028

Subgroups — C2×#22574202 #31764028

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#22574202C2132yesmaximal, direct product factor
2C2×#16864122C211yesmaximal, characteristic, complemented
3C2×#16864118C213yesmaximal, complemented
4C2×#16864101C213yesmaximal, complemented
5C2×#16864094C213yesmaximal, complemented
6C2×#16864087C213yesmaximal, complemented
7C2×Q8×C22⋊D67C211yesmaximal, characteristic, complemented
8C2×#16864058C211yesmaximal, characteristic, complemented
9C2×#16864057C211yesmaximal, characteristic, complemented
10C2×#16864018C213yesmaximal, complemented
11C2×#16864004C213yesmaximal, complemented
12C2×#16863930C213yesmaximal, complemented
13C2×#16863930C213yesmaximal, complemented
14C2×#16863878C211yesmaximal, characteristic, complemented
15C2×#16863872C211yesmaximal, characteristic, complemented
16C22×C4×Q8×C67C211yesmaximal, characteristic, complemented
17C22×#11761629C2211yescharacteristic
18C22×Q8×D67C2211yescharacteristic
19#16864122C22116yescomplemented
20#16864118C22148yescomplemented
21#16864101C22148yescomplemented
22#16864094C22148yescomplemented
23#16864087C22148yescomplemented
24Q8×C22⋊D67C22116yescomplemented
25#16864058C22116yescomplemented
26#16864057C22116yescomplemented
27#16864018C22148yescomplemented
28#16864004C22148yescomplemented
29C2×#14524042C2213yes—
30C2×#14524041C2213yes—
31#16863930C22148yescomplemented
32#16863930C22148yescomplemented
33C2×#14524038C2216yes—
34C2×#14524037C2216yes—
35C2×#14524037C2213yes—
36C2×#14524037C2213yes—
37C2×#14524035C2213yes—
38C2×#14524035C2213yes—
39C2×#14524034C2213yes—
40C2×#14524033C2216yes—
41C2×#14524032C2213yes—
42C2×#14524031C2213yes—
43C2×#14524031C2213yes—
44C2×#14524028C2216yes—
45C2×#14524026C2211yescharacteristic
46C2×#14524026C2213yes—
47C2×#14524023C2213yes—
48C2×#14524022C2213yes—
49C2×#14524022C2213yes—
50C2×#14524021C2216yes—
51C2×#14524019C2213yes—
52C2×#14524019C2213yes—
53C2×#14524018C2213yes—
54C2×#14524017C2213yes—
55C2×#14524017C2213yes—
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—
74C23×Q8×C67C2211yescharacteristic
75C2×C4×Q8×C67C2213yes—
76C2×C4×Q8×C67C2211yescharacteristic
77C2×C4×Q8×C67C2211yescharacteristic
78C2×C4×Q8×C67C2213yes—
79C2×C4×Q8×C67C22116yescomplemented
80C22×C4⋊C4×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⋊D67C2311yescharacteristic
92C22×C4×D67C2313yes—
93C22×C4×D67C2313yes—
94C22×C4×D67C2316yes—
95#14524042C23124yes—
96#14524041C23124yes—
97#14524038C23148yes—
98#14524037C23148yes—
99#14524037C23124yes—
100#14524037C23124yes—
101#14524035C23124yes—
102#14524035C23124yes—
103#14524034C23124yes—
104#14524033C23148yes—
105#14524032C23124yes—
106#14524031C23124yes—
107#14524031C23124yes—
108#14524028C23148yes—
109#14524026C2318yes—
110#14524026C23124yes—
111#14524023C23124yes—
112#14524022C23124yes—
113#14524022C23124yes—
114#14524021C23148yes—
115#14524019C23124yes—
116#14524019C23124yes—
117#14524018C23124yes—
118#14524017C23124yes—
119#14524017C23124yes—
120Q8×Dic67C2318yes—
121Q8×Dic67C2318yes—
122C4×Dic134C23124yes—
123C4×Dic134C23124yes—
124#14524008C23124yes—
125C4×D268C23124yes—
126C4×D268C23124yes—
127#14524005C23124yes—
128C4×C22⋊D67C23124yes—
129C4×C22⋊D67C23124yes—
130C4×C22⋊D67C23148yes—
131#14524001C23124yes—
132#14524000C23124yes—
133#14524000C23124yes—
134#14524000C23148yes—
135C2×C4⋊Dic67C2313yes—
136C2×C4⋊Dic67C2313yes—
137C2×C4⋊Dic67C2313yes—
138C2×C4⋊Dic67C2313yes—
139C2×Dic67⋊C4C2313yes—
140C2×Dic67⋊C4C2311yescharacteristic
141C2×Dic67⋊C4C2313yes—
142C2×Dic67⋊C4C2313yes—
143C2×Dic67⋊C4C2313yes—
144C2×Dic67⋊C4C2316yes—
145C2×Dic67⋊C4C2313yes—
146C2×Dic67⋊C4C2316yes—
147C2×Dic67⋊C4C2313yes—
148C2×Dic67⋊C4C2311yescharacteristic
149C4⋊C4×D67C23124yes—
150C2×C22⋊Dic67C2311yescharacteristic
151C2×C22⋊Dic67C2313yes—
152C2×(C2×D67)⋊C4C2311yescharacteristic
153C2×(C2×D67)⋊C4C2313yes—
154C2×(C2×D67)⋊C4C2313yes—
155C2×(C2×D67)⋊C4C2313yes—
156C2×(C2×D67)⋊C4C2313yes—
157C2×(C2×D67)⋊C4C2316yes—
158C2×(C2×D67)⋊C4C2316yes—
159C2×(C2×D67)⋊C4C2313yes—
160C2×(C2×D67)⋊C4C2313yes—
161C2×(C2×D67)⋊C4C2311yescharacteristic
162C2×C4×Dic67C2316yes—
163C2×C4×Dic67C2313yes—
164C2×C4×Dic67C2313yes—
165C22×Q8×C67—28no—
166C22×Q8×C67C2318yes—
167C22×Q8×C67C2313yes—
168C22×Q8×C67C2311yescharacteristic
169C23×C4×C67C2311yescharacteristic
170C23×C4×C67C2313yes—
171C23×C4×C67C2313yes—
172C4×Q8×C67C23124yes—
173C4×Q8×C67C2318yes—
174C4×Q8×C67C23124yes—
175C4×Q8×C67C2318yes—
176C2×C4⋊C4×C67C2313yes—
177C2×C4⋊C4×C67C2313yes—
178C2×C4⋊C4×C67C2316yes—
179C2×C4⋊C4×C67C23124yes—
180C2×C42×C67C2313yes—
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—212no—
198C2×C22⋊D67—24no—
199C2×C22⋊D67C24112yes—
200C2×C22⋊D67C2414yes—
201C22×Dic67C2411yescharacteristic
202C22×Dic67C2413yes—
203C22×Dic67C2411yescharacteristic
204C22×Dic67C2413yes—
205C22×Dic67C2413yes—
206C22×Dic67C2411yescharacteristic
207C2×C4×D67—212no—
208C2×C4×D67—212no—
209C2×C4×D67—412no—
210C2×C4×D67C24112yes—
211C2×C4×D67C24112yes—
212C2×C4×D67C24124yes—
213C4⋊Dic67C24112yes—
214C4⋊Dic67C24112yes—
215C4⋊Dic67C24112yes—
216C4⋊Dic67C24112yes—
217Dic67⋊C4C24112yes—
218Dic67⋊C4C2414yes—
219Dic67⋊C4C24112yes—
220Dic67⋊C4C24112yes—
221Dic67⋊C4C24112yes—
222Dic67⋊C4C24124yes—
223Dic67⋊C4C24112yes—
224Dic67⋊C4C24124yes—
225Dic67⋊C4C24112yes—
226Dic67⋊C4C2414yes—
227C22⋊Dic67C2414yes—
228C22⋊Dic67C24112yes—
229(C2×D67)⋊C4C2414yes—
230(C2×D67)⋊C4C24112yes—
231(C2×D67)⋊C4C24112yes—
232(C2×D67)⋊C4C24112yes—
233(C2×D67)⋊C4C24112yes—
234(C2×D67)⋊C4C24124yes—
235(C2×D67)⋊C4C24124yes—
236(C2×D67)⋊C4C24112yes—
237(C2×D67)⋊C4C24112yes—
238(C2×D67)⋊C4C2414yes—
239C4×Dic67C24124yes—
240C4×Dic67C24112yes—
241C4×Dic67C24112yes—
242C24×C67C2411yescharacteristic
243C2×Q8×C67—232no—
244C2×Q8×C67—212no—
245C2×Q8×C67#4118yes—
246C2×Q8×C67C24112yes—
247C2×Q8×C67C2414yes—
248C22×C4×C67—24no—
249C22×C4×C67—212no—
250C22×C4×C67—46no—
251C22×C4×C67C2411yescharacteristic
252C22×C4×C67C2411yescharacteristic
253C22×C4×C67C2414yes—
254C22×C4×C67C2413yes—
255C22×C4×C67C2413yes—
256C22×C4×C67C2413yes—
257C22×C4×C67C24112yes—
258C22×C4×C67C24112yes—
259C22×C4×C67C2413yes—
260C4⋊C4×C67C24112yes—
261C4⋊C4×C67C24112yes—
262C4⋊C4×C67C24124yes—
263C42×C67C24112yes—
264C42×C67C24112yes—
265C42×C67C24112yes—
266C42×C67C24112yes—
267C23×C67—22no—
268C23×C67—22no—
269C23×C672−1+414yes—
270C23×C67C2512yes—
271C23×C67C2511yescharacteristic
272C22×D67—22no—
273C22×D67—26no—
274C22×D67—22no—
275C22×D67—26no—
276C22×D67—26no—
277C22×D67—22no—
278C22×D67C2512yes—
279C22×D67C2516yes—
280Q8×C67—224no—
281Q8×C67C2×#41116yes—
282C2×C4×C67—26no—
283C2×C4×C67—28no—
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×C67C2×#41112yes—
291C2×C4×C67C2512yes—
292C2×C4×C67C2512yes—
293C2×C4×C67C2516yes—
294C2×C4×C67C2516yes—
295C2×C4×C67C2516yes—
296C2×C4×C67C2516yes—
297C22⋊D67—224no—
298C22⋊D67—28no—
299C2×Dic67—22no—
300C2×Dic67—26no—
301C2×Dic67—26no—
302C2×Dic67—22no—
303C2×Dic67—26no—
304C2×Dic67—22no—
305C2×Dic67C2512yes—
306C2×Dic67C2516yes—
307C2×Dic67C2512yes—
308C2×Dic67C2516yes—
309C2×Dic67C2516yes—
310C2×Dic67C2512yes—
311D268—224no—
312D268—412no—
313C4×D67—224no—
314C4×D67—224no—
315C4×D67—424no—
316Dic134—224no—
317Dic134—412no—
318C22×C67—22no—
319C22×C67—22no—
320C22×C67—28no—
321C22×C67C22×#4112yes—
322C22×C67C2×2−1+414yes—
323C22×C67C2×2−1+412yes—
324C22×C67#58512yes—
325C22×C67C2611yescharacteristic
326C2×D67—22no—
327C2×D67—26no—
328C2×D67—22no—
329C2×D67—26no—
330C2×D67—26no—
331C2×D67—22no—
332C2×D67—44no—
333C2×D67—412no—
334C4×C67—26no—
335C4×C67—22no—
336C4×C67—22no—
337C4×C67—26no—
338C4×C67—26no—
339C4×C67C22×#41112yes—
340Dic67—26no—
341Dic67—22no—
342Dic67—26no—
343Dic67—22no—
344Dic67—22no—
345Dic67—26no—
346C2×#3516—671nomaximal, Sylow
347C2×C67—24no—
348C2×C67#351614yescomplemented
349C2×C67C23×#4111yescharacteristic
350C2×C67C22×2−1+411yescharacteristic
351C2×C67C2×#58511yescharacteristic
352D67—42no—
353D67—46no—
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×#520—671no—
368C2×#519—671no—
369C22×C4×Q8D6711yescharacteristic, complemented
370C67C2×#351611yescharacteristic, complemented, Sylow
371C22×#41—671no—
372C23×Q8—671no—
373C23×Q8C2×D6711yescharacteristic
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—676no—
389C2×#126—676no—
390C2×#126—673no—
391C2×#126—673no—
392C2×#125—676no—
393C2×#125—673no—
394C2×#125—673no—
395C2×#125—673no—
396C2×#124—673no—
397C2×#124—673no—
398C2×#124—673no—
399C2×#123—671no—
400C2×#123—673no—
401C2×#123—676no—
402C2×C22⋊Q8—673no—
403C2×C22⋊Q8—673no—
404C2×C22⋊Q8—673no—
405C2×C22⋊Q8—673no—
406C2×C22⋊Q8—673no—
407C2×C22⋊Q8—676no—
408C2×#121—673no—
409C2×#121—673no—
410C2×#121—673no—
411#520—6716no—
412#519—6716no—
413C2×C4×Q8—671no—
414C2×C4×Q8—671no—
415C2×C4×Q8—673no—
416C2×C4×Q8—673no—
417C2×C4×Q8—673no—
418C2×C4×Q8C2×D6711yescharacteristic
419C2×C4×Q8C2×D6713yes—
420C2×C4×Q8C2×D6711yescharacteristic
421C2×C4×Q8C2×D6713yes—
422C2×C4×Q8C2×D67116yescomplemented
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×#117—673no—
430C2×#117—673no—
431C2×#117—673no—
432C2×#117—676no—
433C22×C4⋊C4—673no—
434C22×C4⋊C4C2×D6713yes—
435C22×C42C2×D6713yes—
436C2×#41—678no—
437C2×#41—1348no—
438C22×Q8—28no—
439C22×Q8—678no—
440C22×Q8—673no—
441C22×Q8—673no—
442C22×Q8—1348no—
443C22×Q8C22×D6713yes—
444C22×Q8C22×D6718yes—
445C22×Q8C22×D6711yescharacteristic
446C22×D4—673no—
447C22×D4—671no—
448C22×D4—673no—
449C22×D4—673no—
450C23×C4—676no—
451C23×C4—673no—
452C23×C4—673no—
453C23×C4C22×D6713yes—
454C23×C4C22×D6711yescharacteristic
455C23×C4C22×D6713yes—
456C4⋊Q8—6724no—
457C4⋊Q8—6724no—
458#126—6748no—
459#126—6748no—
460#126—6724no—
461#126—6724no—
462#125—6748no—
463#125—6724no—
464#125—6724no—
465#125—6724no—
466#124—6724no—
467#124—6724no—
468#124—6724no—
469#123—678no—
470#123—6724no—
471#123—6748no—
472C22⋊Q8—6724no—
473C22⋊Q8—6724no—
474C22⋊Q8—6724no—
475C22⋊Q8—6724no—
476C22⋊Q8—6724no—
477C22⋊Q8—6748no—
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×Q8C22×D6718yes—
487C4×Q8C22×D67124yes—
488C4×Q8C22×D6718yes—
489C4×Q8C22×D67124yes—
490C4×D4—6724no—
491C4×D4—6724no—
492C4×D4—6748no—
493C4×D4—6724no—
494C4×D4—6724no—
495C4×D4—6724no—
496#117—6724no—
497#117—6724no—
498#117—6724no—
499#117—6748no—
500C2×C4⋊C4—673no—
501C2×C4⋊C4—673no—
502C2×C4⋊C4—671no—
503C2×C4⋊C4—673no—
504C2×C4⋊C4—673no—
505C2×C4⋊C4—673no—
506C2×C4⋊C4—673no—
507C2×C4⋊C4—676no—
508C2×C4⋊C4—673no—
509C2×C4⋊C4—673no—
510C2×C4⋊C4—676no—
511C2×C4⋊C4—673no—
512C2×C4⋊C4—671no—
513C2×C4⋊C4—673no—
514C2×C4⋊C4—6724no—
515C2×C4⋊C4C22×D6713yes—
516C2×C4⋊C4C22×D6713yes—
517C2×C4⋊C4C22×D6716yes—
518C2×C4⋊C4C22×D67124yes—
519C2×C22⋊C4—671no—
520C2×C22⋊C4—673no—
521C2×C22⋊C4—673no—
522C2×C22⋊C4—671no—
523C2×C22⋊C4—673no—
524C2×C22⋊C4—673no—
525C2×C22⋊C4—673no—
526C2×C22⋊C4—676no—
527C2×C22⋊C4—671no—
528C2×C22⋊C4—676no—
529C2×C22⋊C4—673no—
530C2×C22⋊C4—673no—
531C2×C42—676no—
532C2×C42—673no—
533C2×C42—673no—
534C2×C42C22×D6713yes—
535C2×C42C22×D6713yes—
536C2×C42C22×D6713yes—
537C2×C42C22×D6713yes—
538C2×C42C22×D67124yes—
539C24—671no—
540C24—673no—
541C24C23×D6711yescharacteristic
542#41—13432no—
543C2×Q8—232no—
544C2×Q8—212no—
545C2×Q8—2686no—
546C2×Q8—6712no—
547C2×Q8—6712no—
548C2×Q8—13432no—
549C2×Q8—13412no—
550C2×Q8#1176162818yes—
551C2×Q8C23×D67112yes—
552C2×Q8C23×D6714yes—
553C2×D4—2686no—
554C2×D4—6712no—
555C2×D4—674no—
556C2×D4—6712no—
557C2×D4—6712no—
558C2×D4—13412no—
559C2×D4—1344no—
560C2×D4—13412no—
561C22×C4—24no—
562C22×C4—212no—
563C22×C4—46no—
564C22×C4—26812no—
565C22×C4—6724no—
566C22×C4—671no—
567C22×C4—673no—
568C22×C4—671no—
569C22×C4—673no—
570C22×C4—673no—
571C22×C4—671no—
572C22×C4—6712no—
573C22×C4—6712no—
574C22×C4—13412no—
575C22×C4—13412no—
576C22×C4C23×D6714yes—
577C22×C4C23×D67112yes—
578C22×C4C23×D6713yes—
579C22×C4C23×D6711yescharacteristic
580C22×C4C23×D6711yescharacteristic
581C22×C4C23×D6713yes—
582C22×C4C23×D6713yes—
583C22×C4C23×D67112yes—
584C22×C4C23×D6713yes—
585C4⋊C4—6712no—
586C4⋊C4—6712no—
587C4⋊C4—674no—
588C4⋊C4—6712no—
589C4⋊C4—6712no—
590C4⋊C4—6712no—
591C4⋊C4—6712no—
592C4⋊C4—6724no—
593C4⋊C4—6712no—
594C4⋊C4—6712no—
595C4⋊C4—6724no—
596C4⋊C4—6712no—
597C4⋊C4—674no—
598C4⋊C4—6712no—
599C4⋊C4C23×D67112yes—
600C4⋊C4C23×D67112yes—
601C4⋊C4C23×D67124yes—
602C22⋊C4—674no—
603C22⋊C4—6712no—
604C22⋊C4—6712no—
605C22⋊C4—674no—
606C22⋊C4—6712no—
607C22⋊C4—6712no—
608C22⋊C4—6712no—
609C22⋊C4—6724no—
610C22⋊C4—674no—
611C22⋊C4—6724no—
612C22⋊C4—6712no—
613C22⋊C4—6712no—
614C42—6724no—
615C42—6712no—
616C42—6712no—
617C42C23×D67112yes—
618C42C23×D67112yes—
619C42C23×D67112yes—
620C42C23×D67112yes—
621C23—22no—
622C23—22no—
623C23—672no—
624C23—676no—
625C23—1342no—
626C23—1346no—
627C23—1342no—
628C23—1346no—
629C23—1346no—
630C23—1342no—
631C23#1452409114yes—
632C23C24×D6712yes—
633C23C24×D6711yescharacteristic
634Q8—224no—
635Q8—26812no—
636Q8—13424no—
637Q8C2×#11761628116yes—
638D4—26812no—
639D4—13424no—
640D4—1348no—
641D4—13424no—
642C2×C4—26no—
643C2×C4—28no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—26no—
647C2×C4—26no—
648C2×C4—224no—
649C2×C4—412no—
650C2×C4—26824no—
651C2×C4—672no—
652C2×C4—676no—
653C2×C4—672no—
654C2×C4—676no—
655C2×C4—676no—
656C2×C4—672no—
657C2×C4—1342no—
658C2×C4—1346no—
659C2×C4—1346no—
660C2×C4—1342no—
661C2×C4—1346no—
662C2×C4—1342no—
663C2×C4—13424no—
664C2×C4—13424no—
665C2×C4C2×#11761628112yes—
666C2×C4C24×D6716yes—
667C2×C4C24×D6712yes—
668C2×C4C24×D6712yes—
669C2×C4C24×D6716yes—
670C2×C4C24×D6716yes—
671C2×C4C24×D6716yes—
672C22—28no—
673C22—22no—
674C22—22no—
675C22—2684no—
676C22—26812no—
677C22—1342no—
678C22—1346no—
679C22—1342no—
680C22—1346no—
681C22—1346no—
682C22—1342no—
683C22C22×#1176162812yes—
684C22C2×#1452409114yes—
685C22C2×#1452409112yes—
686C22#1686423212yes—
687C22C25×D6711yescharacteristic
688C4—26no—
689C4—22no—
690C4—22no—
691C4—26no—
692C4—26no—
693C4—1342no—
694C4—1346no—
695C4—1346no—
696C4—1342no—
697C4—1346no—
698C4—1342no—
699C4C22×#11761628112yes—
700C2—24no—
701C2—2682no—
702C2—2686no—
703C2#2257420214yesdirect product factor
704C2C23×#1176162811yescharacteristic
705C2C22×#1452409111yescharacteristic
706C2C2×#1686423211yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC22×C4×Q8×C67C2
socleC23×C67C25
hypercenterC22×C4×Q8D67
hypocenterC67C2×#3516
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #22574202C2direct (N × H)
2. C2×#16864122C2semidirect
3. C2×#16864118C2semidirect
4. C2×#16864101C2semidirect
5. C2×#16864094C2semidirect
6. C2×#16864087C2semidirect
7. C2×Q8×C22⋊D67C2semidirect
8. C2×#16864058C2semidirect
9. C2×#16864057C2semidirect
10. C2×#16864018C2semidirect
11. C2×#16864004C2semidirect
12. C2×#16863930C2semidirect
13. C2×#16863930C2semidirect
14. C2×#16863878C2semidirect
15. C2×#16863872C2semidirect
16. C22×C4×Q8×C67C2semidirect
19. #16864122C22semidirect
20. #16864118C22semidirect
21. #16864101C22semidirect
22. #16864094C22semidirect
23. #16864087C22semidirect
24. Q8×C22⋊D67C22semidirect
25. #16864058C22semidirect
26. #16864057C22semidirect
27. #16864018C22semidirect
28. #16864004C22semidirect
31. #16863930C22semidirect
32. #16863930C22semidirect
56. #16863878C22semidirect
57. #16863872C22semidirect
79. C2×C4×Q8×C67C22semidirect
348. C2×C67#3516semidirect
369. C22×C4×Q8D67semidirect
370. C67C2×#3516semidirect
422. C2×C4×Q8C2×D67semidirect
703. C2#22574202direct (N × H)

Maximal subgroups

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

subgroupindex
#225742022
C2×#168641222
C2×#168641182
C2×#168641012
C2×#168640942
C2×#168640872
C2×Q8×C22⋊D672
C2×#168640582
C2×#168640572
C2×#168640182
C2×#168640042
C2×#168639302
C2×#168638782
C2×#168638722
C22×C4×Q8×C672
C2×#351667