Finite Group Databasebeta

← C2×#22574191 #31764017

Subgroups — C2×#22574191 #31764017

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#22574191C2132yesmaximal, direct product factor
2C2×#16864125C211yesmaximal, characteristic, complemented
3C2×#16864115C213yesmaximal, complemented
4C2×#16864103C213yesmaximal, complemented
5C2×#16864098C213yesmaximal, complemented
6C2×#16864088C213yesmaximal, complemented
7C2×Q8×C22⋊D67C211yesmaximal, characteristic, complemented
8C2×#16864053C211yesmaximal, characteristic, complemented
9C2×#16864015C213yesmaximal, complemented
10C2×#16864006C213yesmaximal, complemented
11C2×#16863927C213yesmaximal, complemented
12C2×#16863926C213yesmaximal, complemented
13C2×#16863879C211yesmaximal, characteristic, complemented
14C2×#16863872C211yesmaximal, characteristic, complemented
15C22×Q8×Dic67C211yesmaximal, characteristic, complemented
16C2×#548×C67C211yesmaximal, characteristic, complemented
17C22×Q8×D67C2211yescharacteristic
18#16864125C22116yescomplemented
19#16864115C22148yescomplemented
20#16864103C22148yescomplemented
21#16864098C22148yescomplemented
22#16864088C22148yescomplemented
23Q8×C22⋊D67C22116yescomplemented
24#16864053C22116yescomplemented
25#16864015C22148yescomplemented
26#16864006C22148yescomplemented
27C2×#14524043C2213yes—
28C2×#14524041C2213yes—
29#16863927C22148yescomplemented
30#16863926C22148yescomplemented
31C2×#14524038C2213yes—
32C2×#14524036C2216yes—
33C2×#14524036C2216yes—
34C2×#14524036C2213yes—
35C2×#14524034C2216yes—
36C2×#14524034C2213yes—
37C2×#14524034C2213yes—
38C2×#14524033C2213yes—
39C2×#14524030C2213yes—
40C2×#14524029C2213yes—
41C2×#14524027C2216yes—
42C2×#14524027C2211yescharacteristic
43C2×#14524024C2213yes—
44C2×#14524022C2213yes—
45C2×#14524022C2213yes—
46C2×#14524020C2216yes—
47C2×#14524020C2213yes—
48C2×#14524019C2213yes—
49C2×#14524015C2213yes—
50C2×#14524014C2213yes—
51#16863879C22116yescomplemented
52#16863872C22116yescomplemented
53C2×Q8×Dic67C2213yes—
54C2×Q8×Dic67C2211yescharacteristic
55C2×Q8×Dic67C2211yescharacteristic
56C2×Q8×Dic67C2213yes—
57C2×Q8×Dic67C2211yescharacteristic
58C2×Q8×Dic67C22116yescomplemented
59C2×C4×Dic134C2213yes—
60C2×C4×Dic134C2213yes—
61C2×#14524008C2213yes—
62C2×D4×Dic67C2213yes—
63C2×D4×Dic67C2213yes—
64C2×D4×Dic67C2216yes—
65C2×C4×C22⋊D67C2213yes—
66C2×C4×C22⋊D67C2213yes—
67C2×#14524002C2213yes—
68C2×#14524001C2213yes—
69C2×#14524000C2213yes—
70C2×#14523999C2216yes—
71C22×C4⋊Dic67C2213yes—
72C22×C4⋊Dic67C2213yes—
73C22×C4×Dic67C2213yes—
74C22×#41×C67C2211yescharacteristic
75C23×Q8×C67C2211yescharacteristic
76#548×C67C22116yescomplemented
77C2×#124×C67C2213yes—
78C2×C22⋊Q8×C67C2213yes—
79C2×#121×C67C2213yes—
80C2×C4×Q8×C67C2211yescharacteristic
81C2×C4×D4×C67C2213yes—
82C22×Dic134C2313yes—
83C22×Dic134C2313yes—
84C2×Q8×D67—28no—
85C2×Q8×D67C2318yes—
86C22×C22⋊D67C2311yescharacteristic
87C22×C22⋊D67C2313yes—
88C23×Dic67C2311yescharacteristic
89C23×Dic67C2313yes—
90C23×Dic67C2316yes—
91C22×C4×D67C2313yes—
92#14524043C23124yes—
93#14524041C23124yes—
94#14524038C23124yes—
95#14524036C23148yes—
96#14524036C23148yes—
97#14524036C23124yes—
98#14524034C23148yes—
99#14524034C23124yes—
100#14524034C23124yes—
101#14524033C23124yes—
102#14524030C23124yes—
103#14524029C23124yes—
104#14524027C23148yes—
105#14524027C2318yes—
106#14524024C23124yes—
107#14524022C23124yes—
108#14524022C23124yes—
109#14524020C23148yes—
110#14524020C23124yes—
111#14524019C23124yes—
112#14524015C23124yes—
113#14524014C23124yes—
114Q8×Dic67C23124yes—
115Q8×Dic67C2318yes—
116Q8×Dic67C2318yes—
117Q8×Dic67C23124yes—
118Q8×Dic67C2318yes—
119C4×Dic134C23124yes—
120C4×Dic134C23124yes—
121#14524008C23124yes—
122D4×Dic67C23124yes—
123D4×Dic67C23148yes—
124D4×Dic67C23124yes—
125C4×C22⋊D67C23124yes—
126C4×C22⋊D67C23124yes—
127#14524002C23124yes—
128#14524001C23124yes—
129#14524000C23124yes—
130#14523999C23148yes—
131C2×C4⋊Dic67C23124yes—
132C2×C4⋊Dic67C23124yes—
133C2×C4⋊Dic67C2313yes—
134C2×C4⋊Dic67C2313yes—
135C2×C4⋊Dic67C2313yes—
136C2×C4⋊Dic67C2313yes—
137C2×C4⋊Dic67C2316yes—
138C2×C4⋊Dic67C2311yescharacteristic
139C2×C4⋊Dic67C2316yes—
140C2×C4⋊Dic67C2311yescharacteristic
141C2×Dic67⋊C4C2313yes—
142C2×Dic67⋊C4C2316yes—
143C2×Dic67⋊C4C2313yes—
144C2×Dic67⋊C4C2313yes—
145C2×Dic67⋊C4C2313yes—
146C2×Dic67⋊C4C2313yes—
147C2×Dic67⋊C4C2313yes—
148C2×C22⋊Dic67C2313yes—
149C2×C22⋊Dic67C2313yes—
150C2×C22⋊Dic67C2313yes—
151C2×C22⋊Dic67C2313yes—
152C2×C22⋊Dic67C2316yes—
153C2×(C2×D67)⋊C4C2311yescharacteristic
154C2×(C2×D67)⋊C4C2313yes—
155C2×(C2×D67)⋊C4C2311yescharacteristic
156C2×(C2×D67)⋊C4C2313yes—
157C2×C4×Dic67C2313yes—
158C2×C4×Dic67C2313yes—
159C2×C4×Dic67C2313yes—
160C2×C4×Dic67C2313yes—
161C2×C4×Dic67C23124yes—
162C2×C4×Dic67C2316yes—
163C2×C4×Dic67C2313yes—
164C2×#41×C67—28no—
165C2×#41×C67C2318yes—
166C22×Q8×C67—28no—
167C22×Q8×C67C2318yes—
168C22×Q8×C67C2313yes—
169C22×Q8×C67C2311yescharacteristic
170C22×D4×C67C2313yes—
171C22×D4×C67C2313yes—
172C23×C4×C67C2313yes—
173C23×C4×C67C2313yes—
174#124×C67C23124yes—
175C22⋊Q8×C67C23124yes—
176#121×C67C23124yes—
177C4×Q8×C67C2318yes—
178C4×D4×C67C23124yes—
179C2×C4⋊C4×C67C2313yes—
180C2×C4⋊C4×C67C2313yes—
181C2×C22⋊C4×C67C2311yescharacteristic
182C2×C22⋊C4×C67C2313yes—
183C2×C22⋊C4×C67C2316yes—
184C2×C42×C67C2313yes—
185C23×D67C2411yescharacteristic
186C2×Dic134—212no—
187C2×Dic134—46no—
188C2×Dic134C24112yes—
189C2×Dic134C24112yes—
190Q8×D67—232no—
191C2×C22⋊D67—24no—
192C2×C22⋊D67—46no—
193C2×C22⋊D67C2414yes—
194C2×C22⋊D67C24112yes—
195C22×Dic67—24no—
196C22×Dic67—412no—
197C22×Dic67—46no—
198C22×Dic67C2411yescharacteristic
199C22×Dic67C2411yescharacteristic
200C22×Dic67C2414yes—
201C22×Dic67C2413yes—
202C22×Dic67C2411yescharacteristic
203C22×Dic67C2413yes—
204C22×Dic67C2413yes—
205C22×Dic67C2413yes—
206C22×Dic67C24112yes—
207C22×Dic67C24124yes—
208C2×C4×D67—212no—
209C2×C4×D67C24112yes—
210C4⋊Dic67C24112yes—
211C4⋊Dic67C24112yes—
212C4⋊Dic67C24112yes—
213C4⋊Dic67C24112yes—
214C4⋊Dic67C24124yes—
215C4⋊Dic67C2414yes—
216C4⋊Dic67C24124yes—
217C4⋊Dic67C2414yes—
218Dic67⋊C4C24112yes—
219Dic67⋊C4C24124yes—
220Dic67⋊C4C24112yes—
221Dic67⋊C4C24112yes—
222Dic67⋊C4C24112yes—
223Dic67⋊C4C24112yes—
224Dic67⋊C4C24112yes—
225C22⋊Dic67C24112yes—
226C22⋊Dic67C24112yes—
227C22⋊Dic67C24112yes—
228C22⋊Dic67C24112yes—
229C22⋊Dic67C24124yes—
230(C2×D67)⋊C4C2414yes—
231(C2×D67)⋊C4C24112yes—
232(C2×D67)⋊C4C2414yes—
233(C2×D67)⋊C4C24112yes—
234C4×Dic67C24112yes—
235C4×Dic67C24112yes—
236C4×Dic67C24112yes—
237C4×Dic67C24112yes—
238C4×Dic67C24124yes—
239C4×Dic67C24112yes—
240C24×C67C2413yes—
241C24×C67C2411yescharacteristic
242#41×C67—232no—
243C2×Q8×C67—232no—
244C2×Q8×C67—212no—
245C2×Q8×C67#4118yes—
246C2×Q8×C67C24112yes—
247C2×Q8×C67C2414yes—
248C2×D4×C67—212no—
249C2×D4×C67—212no—
250C2×D4×C67C24112yes—
251C2×D4×C67C24112yes—
252C22×C4×C67—212no—
253C22×C4×C67—212no—
254C22×C4×C67C2411yescharacteristic
255C22×C4×C67C2413yes—
256C22×C4×C67C2413yes—
257C22×C4×C67C2411yescharacteristic
258C22×C4×C67C24112yes—
259C22×C4×C67C24112yes—
260C22×C4×C67C2413yes—
261C4⋊C4×C67C24112yes—
262C4⋊C4×C67C24112yes—
263C22⋊C4×C67C2414yes—
264C22⋊C4×C67C24112yes—
265C22⋊C4×C67C24124yes—
266C42×C67C24112yes—
267C23×C67—22no—
268C23×C67—22no—
269C23×C67—26no—
270C23×C67—26no—
271C23×C67—26no—
272C23×C672−1+414yes—
273C23×C67C2516yes—
274C23×C67C2512yes—
275C23×C67C2511yescharacteristic
276C22×D67—22no—
277C22×D67—22no—
278C22×D67—22no—
279C22×D67C2512yes—
280Q8×C67—224no—
281Q8×C67C2×#41116yes—
282D4×C67—224no—
283D4×C67—224no—
284C2×C4×C67—22no—
285C2×C4×C67—26no—
286C2×C4×C67—26no—
287C2×C4×C67—22no—
288C2×C4×C67—224no—
289C2×C4×C67—224no—
290C2×C4×C67C2×#41112yes—
291C2×C4×C67C2512yes—
292C2×C4×C67C2516yes—
293C2×C4×C67C2516yes—
294C2×C4×C67C2512yes—
295C2×C4×C67C2516yes—
296C22⋊D67—28no—
297C22⋊D67—412no—
298C2×Dic67—26no—
299C2×Dic67—28no—
300C2×Dic67—22no—
301C2×Dic67—22no—
302C2×Dic67—22no—
303C2×Dic67—26no—
304C2×Dic67—26no—
305C2×Dic67—26no—
306C2×Dic67—424no—
307C2×Dic67—412no—
308C2×Dic67C2512yes—
309C2×Dic67C2512yes—
310C2×Dic67C2516yes—
311C2×Dic67C2512yes—
312C2×Dic67C2516yes—
313C2×Dic67C2516yes—
314C2×Dic67C2516yes—
315C4×D67—224no—
316Dic134—224no—
317Dic134—412no—
318C22×C67—22no—
319C22×C67—22no—
320C22×C67—28no—
321C22×C67—26no—
322C22×C67—26no—
323C22×C67—26no—
324C22×C67—412no—
325C22×C67C22×#4112yes—
326C22×C67C2×2−1+414yes—
327C22×C67C2×2−1+412yes—
328C22×C67#58512yes—
329C22×C67C2611yescharacteristic
330C2×D67—22no—
331C2×D67—22no—
332C2×D67—22no—
333C2×D67—44no—
334C4×C67—22no—
335C4×C67—26no—
336C4×C67—26no—
337C4×C67—22no—
338C4×C67C22×#41112yes—
339Dic67—26no—
340Dic67—22no—
341Dic67—22no—
342Dic67—22no—
343Dic67—26no—
344Dic67—26no—
345Dic67—26no—
346C2×#3516—671nomaximal, Sylow
347C2×C67—24no—
348C2×C67—46no—
349C2×C67#351614yescomplemented
350C2×C67C23×#4111yescharacteristic
351C2×C67C22×2−1+411yescharacteristic
352C2×C67C2×#58511yescharacteristic
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×#548D6711yescharacteristic, complemented
363C2×#542—673no—
364C2×#541—673no—
365C2×#529—673no—
366C2×#529—673no—
367C2×#520—671no—
368C2×#519—671no—
369C22×C4×Q8—671no—
370C67C2×#351611yescharacteristic, complemented, Sylow
371C22×#41C2×D6711yescharacteristic
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#548C2×D67116yescomplemented
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×#124C2×D6713yes—
399C2×#123—673no—
400C2×#123—671no—
401C2×#123—676no—
402C2×C22⋊Q8—673no—
403C2×C22⋊Q8—673no—
404C2×C22⋊Q8—673no—
405C2×C22⋊Q8—673no—
406C2×C22⋊Q8—676no—
407C2×C22⋊Q8C2×D6713yes—
408C2×#121—673no—
409C2×#121—673no—
410C2×#121C2×D6713yes—
411#520—6716no—
412#519—6716no—
413C2×C4×Q8—671no—
414C2×C4×Q8—673no—
415C2×C4×Q8—671no—
416C2×C4×Q8—673no—
417C2×C4×Q8—6716no—
418C2×C4×Q8—671no—
419C2×C4×Q8—673no—
420C2×C4×Q8—673no—
421C2×C4×Q8—673no—
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×D4C2×D6713yes—
429C2×#117—673no—
430C2×#117—673no—
431C2×#117—676no—
432C2×#117—673no—
433C22×C4⋊C4—673no—
434C22×C4⋊C4—673no—
435C22×C42—673no—
436C2×#41—28no—
437C2×#41C22×D6718yes—
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×D4C22×D6713yes—
449C22×D4C22×D6713yes—
450C23×C4—673no—
451C23×C4—676no—
452C23×C4—671no—
453C23×C4—673no—
454C23×C4C22×D6713yes—
455C23×C4C22×D6713yes—
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#124C22×D67124yes—
469#123—6724no—
470#123—678no—
471#123—6748no—
472C22⋊Q8—6724no—
473C22⋊Q8—6724no—
474C22⋊Q8—6724no—
475C22⋊Q8—6724no—
476C22⋊Q8—6748no—
477C22⋊Q8C22×D67124yes—
478#121—6724no—
479#121—6724no—
480#121C22×D67124yes—
481C4×Q8—678no—
482C4×Q8—6724no—
483C4×Q8—678no—
484C4×Q8—6724no—
485C4×Q8—678no—
486C4×Q8—6724no—
487C4×Q8—6724no—
488C4×Q8—6724no—
489C4×Q8C22×D6718yes—
490C4×D4—6724no—
491C4×D4—6724no—
492C4×D4—6748no—
493C4×D4—6724no—
494C4×D4—6724no—
495C4×D4C22×D67124yes—
496#117—6724no—
497#117—6724no—
498#117—6748no—
499#117—6724no—
500C2×C4⋊C4—673no—
501C2×C4⋊C4—673no—
502C2×C4⋊C4—673no—
503C2×C4⋊C4—673no—
504C2×C4⋊C4—676no—
505C2×C4⋊C4—6724no—
506C2×C4⋊C4—6724no—
507C2×C4⋊C4—671no—
508C2×C4⋊C4—673no—
509C2×C4⋊C4—673no—
510C2×C4⋊C4—673no—
511C2×C4⋊C4—676no—
512C2×C4⋊C4—673no—
513C2×C4⋊C4—676no—
514C2×C4⋊C4—673no—
515C2×C4⋊C4—671no—
516C2×C4⋊C4—673no—
517C2×C4⋊C4C22×D6713yes—
518C2×C4⋊C4C22×D6713yes—
519C2×C22⋊C4—673no—
520C2×C22⋊C4—673no—
521C2×C22⋊C4—673no—
522C2×C22⋊C4—673no—
523C2×C22⋊C4—676no—
524C2×C22⋊C4—673no—
525C2×C22⋊C4—671no—
526C2×C22⋊C4—671no—
527C2×C22⋊C4—673no—
528C2×C22⋊C4C22×D6716yes—
529C2×C22⋊C4C22×D6711yescharacteristic
530C2×C22⋊C4C22×D6713yes—
531C2×C42—673no—
532C2×C42—676no—
533C2×C42—673no—
534C2×C42—673no—
535C2×C42—673no—
536C2×C42—673no—
537C2×C42—6724no—
538C2×C42C22×D6713yes—
539C24—671no—
540C24C23×D6713yes—
541C24C23×D6711yescharacteristic
542#41—232no—
543C2×Q8—232no—
544C2×Q8—212no—
545C2×Q8—2686no—
546C2×Q8—6712no—
547C2×Q8—6712no—
548C2×Q8—13432no—
549C2×Q8—13412no—
550C2×Q8#1176162718yes—
551C2×Q8C23×D67112yes—
552C2×Q8C23×D6714yes—
553C2×D4—212no—
554C2×D4—212no—
555C2×D4—2686no—
556C2×D4—6712no—
557C2×D4—674no—
558C2×D4—1344no—
559C2×D4C23×D67112yes—
560C2×D4C23×D67112yes—
561C22×C4—212no—
562C22×C4—212no—
563C22×C4—26812no—
564C22×C4—2686no—
565C22×C4—6712no—
566C22×C4—6724no—
567C22×C4—674no—
568C22×C4—671no—
569C22×C4—671no—
570C22×C4—673no—
571C22×C4—671no—
572C22×C4—673no—
573C22×C4—673no—
574C22×C4—673no—
575C22×C4—6712no—
576C22×C4—1344no—
577C22×C4—13412no—
578C22×C4C23×D67112yes—
579C22×C4C23×D67112yes—
580C22×C4C23×D6713yes—
581C22×C4C23×D6713yes—
582C22×C4C23×D6711yescharacteristic
583C22×C4C23×D6711yescharacteristic
584C22×C4C23×D6713yes—
585C4⋊C4—6712no—
586C4⋊C4—6712no—
587C4⋊C4—6712no—
588C4⋊C4—6712no—
589C4⋊C4—6724no—
590C4⋊C4—674no—
591C4⋊C4—6712no—
592C4⋊C4—6712no—
593C4⋊C4—6712no—
594C4⋊C4—6724no—
595C4⋊C4—6712no—
596C4⋊C4—6724no—
597C4⋊C4—6712no—
598C4⋊C4—674no—
599C4⋊C4—6712no—
600C4⋊C4C23×D67112yes—
601C4⋊C4C23×D67112yes—
602C22⋊C4—6712no—
603C22⋊C4—6712no—
604C22⋊C4—6712no—
605C22⋊C4—6712no—
606C22⋊C4—6724no—
607C22⋊C4—6712no—
608C22⋊C4—674no—
609C22⋊C4—674no—
610C22⋊C4—6712no—
611C22⋊C4C23×D67124yes—
612C22⋊C4C23×D6714yes—
613C22⋊C4C23×D67112yes—
614C42—6712no—
615C42—6712no—
616C42—6712no—
617C42—6712no—
618C42—6724no—
619C42—6712no—
620C42C23×D67112yes—
621C23—22no—
622C23—22no—
623C23—26no—
624C23—26no—
625C23—26no—
626C23—672no—
627C23—1342no—
628C23—1342no—
629C23—1342no—
630C23#1452409014yes—
631C23C24×D6716yes—
632C23C24×D6712yes—
633C23C24×D6711yescharacteristic
634Q8—224no—
635Q8—26812no—
636Q8—13424no—
637Q8C2×#11761627116yes—
638D4—224no—
639D4—224no—
640D4—26812no—
641D4—1348no—
642C2×C4—22no—
643C2×C4—26no—
644C2×C4—26no—
645C2×C4—22no—
646C2×C4—224no—
647C2×C4—224no—
648C2×C4—26824no—
649C2×C4—26812no—
650C2×C4—672no—
651C2×C4—672no—
652C2×C4—676no—
653C2×C4—672no—
654C2×C4—676no—
655C2×C4—676no—
656C2×C4—676no—
657C2×C4—1346no—
658C2×C4—1348no—
659C2×C4—1342no—
660C2×C4—1342no—
661C2×C4—1342no—
662C2×C4—1346no—
663C2×C4—1346no—
664C2×C4—1346no—
665C2×C4—13424no—
666C2×C4C2×#11761627112yes—
667C2×C4C24×D6716yes—
668C2×C4C24×D6716yes—
669C2×C4C24×D6712yes—
670C2×C4C24×D6712yes—
671C2×C4C24×D6716yes—
672C22—28no—
673C22—22no—
674C22—22no—
675C22—26no—
676C22—26no—
677C22—26no—
678C22—412no—
679C22—2684no—
680C22—1342no—
681C22—1342no—
682C22—1342no—
683C22C22×#1176162712yes—
684C22C2×#1452409014yes—
685C22C2×#1452409012yes—
686C22#1686423312yes—
687C22C25×D6711yescharacteristic
688C4—22no—
689C4—26no—
690C4—26no—
691C4—22no—
692C4—1346no—
693C4—1342no—
694C4—1342no—
695C4—1342no—
696C4—1346no—
697C4—1346no—
698C4—1346no—
699C4C22×#11761627112yes—
700C2—24no—
701C2—46no—
702C2—2682no—
703C2#2257419114yesdirect product factor
704C2C23×#1176162711yescharacteristic
705C2C22×#1452409011yescharacteristic
706C2C2×#1686423311yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#548×C67C2
socleC23×C67C25
hypercenterC2×#548D67
hypocenterC67C2×#3516
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #22574191C2direct (N × H)
2. C2×#16864125C2semidirect
3. C2×#16864115C2semidirect
4. C2×#16864103C2semidirect
5. C2×#16864098C2semidirect
6. C2×#16864088C2semidirect
7. C2×Q8×C22⋊D67C2semidirect
8. C2×#16864053C2semidirect
9. C2×#16864015C2semidirect
10. C2×#16864006C2semidirect
11. C2×#16863927C2semidirect
12. C2×#16863926C2semidirect
13. C2×#16863879C2semidirect
14. C2×#16863872C2semidirect
15. C22×Q8×Dic67C2semidirect
16. C2×#548×C67C2semidirect
18. #16864125C22semidirect
19. #16864115C22semidirect
20. #16864103C22semidirect
21. #16864098C22semidirect
22. #16864088C22semidirect
23. Q8×C22⋊D67C22semidirect
24. #16864053C22semidirect
25. #16864015C22semidirect
26. #16864006C22semidirect
29. #16863927C22semidirect
30. #16863926C22semidirect
51. #16863879C22semidirect
52. #16863872C22semidirect
58. C2×Q8×Dic67C22semidirect
76. #548×C67C22semidirect
349. C2×C67#3516semidirect
362. C2×#548D67semidirect
370. C67C2×#3516semidirect
381. #548C2×D67semidirect
703. C2#22574191direct (N × H)

Maximal subgroups

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

subgroupindex
#225741912
C2×#168641252
C2×#168641152
C2×#168641032
C2×#168640982
C2×#168640882
C2×Q8×C22⋊D672
C2×#168640532
C2×#168640152
C2×#168640062
C2×#168639272
C2×#168639262
C2×#168638792
C2×#168638722
C22×Q8×Dic672
C2×#548×C672
C2×#351667