Finite Group Databasebeta

← C2×#22573826 #31762923

Subgroups — C2×#22573826 #31762923

Order 17152.

7706 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22573826C2132yesmaximal, direct product factor
2C2×#16864122C211yesmaximal, characteristic, complemented
3C2×#16864118C213yesmaximal, complemented
4C2×#16864087C213yesmaximal, complemented
5C2×#16864081C213yesmaximal, complemented
6C2×Q8×C22⋊D67C211yesmaximal, characteristic, complemented
7C2×#16864058C211yesmaximal, characteristic, complemented
8C2×#16864057C211yesmaximal, characteristic, complemented
9C2×#16864047C213yesmaximal, complemented
10C2×#16863950C213yesmaximal, complemented
11C2×#16863933C213yesmaximal, complemented
12C2×#16863930C213yesmaximal, complemented
13C2×C4×#11761629C211yesmaximal, characteristic, complemented
14C2×C4×#11761628C213yesmaximal, complemented
15C2×C4×Q8×D67C211yesmaximal, characteristic, complemented
16C22×C4×Q8×C67C211yesmaximal, characteristic, complemented
17C22×#11761629C2211yescharacteristic
18C22×#11761628C2213yes—
19C22×Q8×D67C2211yescharacteristic
20#16864122C22116yescomplemented
21#16864118C22148yescomplemented
22#16864087C22148yescomplemented
23#16864081C22148yescomplemented
24Q8×C22⋊D67C22116yescomplemented
25#16864058C22116yescomplemented
26#16864057C22116yescomplemented
27#16864047C22148yescomplemented
28#16863950C22148yescomplemented
29C2×#14524042C2213yes—
30C2×#14524041C2213yes—
31#16863933C22148yescomplemented
32#16863930C22148yescomplemented
33C2×#14524038C2216yes—
34C2×#14524037C2216yes—
35C2×#14524035C2213yes—
36C2×#14524034C2213yes—
37C2×#14524033C2216yes—
38C2×#14524032C2213yes—
39C2×#14524031C2213yes—
40C2×#14524028C2216yes—
41C2×#14524026C2216yes—
42C2×#14524023C2213yes—
43C2×#14524022C2213yes—
44C2×#14524021C2216yes—
45C2×#14524019C2213yes—
46C2×#14524019C2213yes—
47C2×#14524018C2213yes—
48C2×#14524017C2213yes—
49C4×#11761629C22116yescomplemented
50C4×#11761628C22148yescomplemented
51C2×Q8×Dic67C2211yescharacteristic
52C2×Q8×Dic67C2211yescharacteristic
53C2×C4×Dic134C2213yes—
54C2×C4×Dic134C2213yes—
55C2×C4×Dic134C2213yes—
56C2×#14524008C2213yes—
57C4×Q8×D67C22116yescomplemented
58C2×C4×D268C2213yes—
59C2×C4×D268C2213yes—
60C2×C4×D268C2213yes—
61C2×#14524005C2213yes—
62C2×C4×C22⋊D67C2211yescharacteristic
63C2×C4×C22⋊D67C2213yes—
64C2×C4×C22⋊D67C2213yes—
65C2×C4×C22⋊D67C2213yes—
66C2×#14524002C2213yes—
67C2×#14524001C2213yes—
68C2×#14524000C2213yes—
69C2×#14524000C2213yes—
70C2×#14524000C2216yes—
71C2×C4⋊C4×D67C2213yes—
72C2×C42×D67C2213yes—
73C2×C42×D67C2213yes—
74C23×Q8×C67C2211yescharacteristic
75C2×C4×Q8×C67C2211yescharacteristic
76C2×C4×Q8×C67C2211yescharacteristic
77C2×C4×Q8×C67C2213yes—
78C2×C4×Q8×C67C2213yes—
79C2×C4×Q8×C67C22116yescomplemented
80C22×C4⋊C4×C67C2213yes—
81C22×C42×C67C2213yes—
82C2×#11761629—28no—
83C2×#11761629C2318yes—
84C2×#11761628—224no—
85C2×#11761628C23124yes—
86C22×Dic134C2313yes—
87C22×Dic134C2313yes—
88C2×Q8×D67—28no—
89C2×Q8×D67C2318yes—
90C22×D268C2313yes—
91C22×D268C2313yes—
92C22×C22⋊D67C2313yes—
93C22×C22⋊D67C2311yescharacteristic
94C22×C4×D67C2311yescharacteristic
95C22×C4×D67C2313yes—
96C22×C4×D67C2313yes—
97C22×C4×D67C2313yes—
98C22×C4×D67C2313yes—
99C22×C4×D67C2313yes—
100#14524042C23124yes—
101#14524041C23124yes—
102#14524038C23148yes—
103#14524037C23148yes—
104#14524035C23124yes—
105#14524034C23124yes—
106#14524033C23148yes—
107#14524032C23124yes—
108#14524031C23124yes—
109#14524028C23148yes—
110#14524026C23148yes—
111#14524023C23124yes—
112#14524022C23124yes—
113#14524021C23148yes—
114#14524019C23124yes—
115#14524019C23124yes—
116#14524018C23124yes—
117#14524017C23124yes—
118Q8×Dic67C2318yes—
119Q8×Dic67C2318yes—
120C4×Dic134C23124yes—
121C4×Dic134C23124yes—
122C4×Dic134C23124yes—
123#14524008C23124yes—
124C4×D268C23124yes—
125C4×D268C23124yes—
126C4×D268C23124yes—
127#14524005C23124yes—
128C4×C22⋊D67C23124yes—
129C4×C22⋊D67C23124yes—
130C4×C22⋊D67C2318yes—
131C4×C22⋊D67C23124yes—
132#14524002C23124yes—
133#14524001C23124yes—
134#14524000C23124yes—
135#14524000C23124yes—
136#14524000C23148yes—
137C2×C4⋊Dic67C2313yes—
138C2×C4⋊Dic67C2313yes—
139C2×C4⋊Dic67C2313yes—
140C2×C4⋊Dic67C2313yes—
141C2×Dic67⋊C4C2316yes—
142C2×Dic67⋊C4C2311yescharacteristic
143C2×Dic67⋊C4C2313yes—
144C2×Dic67⋊C4C2313yes—
145C2×Dic67⋊C4C2313yes—
146C2×Dic67⋊C4C2316yes—
147C2×Dic67⋊C4C2316yes—
148C4⋊C4×D67C23124yes—
149C2×C22⋊Dic67C2311yescharacteristic
150C2×C22⋊Dic67C2313yes—
151C2×(C2×D67)⋊C4C2311yescharacteristic
152C2×(C2×D67)⋊C4C2313yes—
153C2×(C2×D67)⋊C4C2313yes—
154C2×(C2×D67)⋊C4C2313yes—
155C2×(C2×D67)⋊C4C2316yes—
156C2×(C2×D67)⋊C4C2316yes—
157C2×(C2×D67)⋊C4C2316yes—
158C2×C4×Dic67C2311yescharacteristic
159C2×C4×Dic67C2313yes—
160C2×C4×Dic67C2313yes—
161C2×C4×Dic67C2313yes—
162C2×C4×Dic67C2313yes—
163C2×C4×Dic67C2313yes—
164C42×D67C23124yes—
165C42×D67C23124yes—
166C22×Q8×C67—28no—
167C22×Q8×C67C2318yes—
168C22×Q8×C67C2313yes—
169C22×Q8×C67C2311yescharacteristic
170C23×C4×C67C2311yescharacteristic
171C23×C4×C67C2313yes—
172C23×C4×C67C2313yes—
173C4×Q8×C67C2318yes—
174C4×Q8×C67C23124yes—
175C4×Q8×C67C2318yes—
176C4×Q8×C67C23124yes—
177C2×C4⋊C4×C67C23124yes—
178C2×C4⋊C4×C67C2313yes—
179C2×C4⋊C4×C67C2313yes—
180C2×C4⋊C4×C67C2316yes—
181C2×C42×C67C2313yes—
182C2×C42×C67C2313yes—
183C2×C42×C67C2313yes—
184C2×C42×C67C2313yes—
185C2×C42×C67C23124yes—
186C23×D67C2413yes—
187C23×D67C2411yescharacteristic
188#11761629—232no—
189#11761628—296no—
190C2×Dic134—212no—
191C2×Dic134—212no—
192C2×Dic134C24112yes—
193C2×Dic134C24112yes—
194Q8×D67—232no—
195C2×D268—212no—
196C2×D268—212no—
197C2×D268C24112yes—
198C2×D268C24112yes—
199C2×C22⋊D67—212no—
200C2×C22⋊D67#4118yescomplemented
201C2×C22⋊D67C24112yes—
202C2×C22⋊D67C2414yes—
203C22×Dic67C2411yescharacteristic
204C22×Dic67C2411yescharacteristic
205C22×Dic67C2413yes—
206C22×Dic67C2413yes—
207C22×Dic67C2413yes—
208C22×Dic67C2411yescharacteristic
209C2×C4×D67—212no—
210C2×C4×D67—212no—
211C2×C4×D67—212no—
212C2×C4×D67—24no—
213C2×C4×D67—212no—
214C2×C4×D67—212no—
215C2×C4×D67C2414yes—
216C2×C4×D67C24112yes—
217C2×C4×D67C24112yes—
218C2×C4×D67C24112yes—
219C2×C4×D67C24112yes—
220C2×C4×D67C24112yes—
221C4⋊Dic67C24112yes—
222C4⋊Dic67C24112yes—
223C4⋊Dic67C24112yes—
224C4⋊Dic67C24112yes—
225Dic67⋊C4C24124yes—
226Dic67⋊C4C2414yes—
227Dic67⋊C4C24112yes—
228Dic67⋊C4C24112yes—
229Dic67⋊C4C24112yes—
230Dic67⋊C4C24124yes—
231Dic67⋊C4C24124yes—
232C22⋊Dic67C2414yes—
233C22⋊Dic67C24112yes—
234(C2×D67)⋊C4C2414yes—
235(C2×D67)⋊C4C24112yes—
236(C2×D67)⋊C4C24112yes—
237(C2×D67)⋊C4C24112yes—
238(C2×D67)⋊C4C24124yes—
239(C2×D67)⋊C4C24124yes—
240(C2×D67)⋊C4C24124yes—
241C4×Dic67C2414yes—
242C4×Dic67C24112yes—
243C4×Dic67C24112yes—
244C4×Dic67C24112yes—
245C4×Dic67C24112yes—
246C4×Dic67C24112yes—
247C24×C67C2411yescharacteristic
248C2×Q8×C67—232no—
249C2×Q8×C67—212no—
250C2×Q8×C67#4118yescomplemented
251C2×Q8×C67C24112yes—
252C2×Q8×C67C2414yes—
253C22×C4×C67—212no—
254C22×C4×C67—212no—
255C22×C4×C67—24no—
256C22×C4×C67C2411yescharacteristic
257C22×C4×C67C2414yes—
258C22×C4×C67C2413yes—
259C22×C4×C67C2413yes—
260C22×C4×C67C24112yes—
261C22×C4×C67C2413yes—
262C22×C4×C67C24112yes—
263C22×C4×C67C2413yes—
264C22×C4×C67C2411yescharacteristic
265C4⋊C4×C67C24112yes—
266C4⋊C4×C67C24112yes—
267C4⋊C4×C67C24124yes—
268C42×C67C24112yes—
269C42×C67C24112yes—
270C42×C67C24112yes—
271C42×C67C24112yes—
272C23×C67—22no—
273C23×C67—22no—
274C23×C67C2×#4114yes—
275C23×C67C2512yes—
276C23×C67C2511yescharacteristic
277C22×D67—22no—
278C22×D67—22no—
279C22×D67—26no—
280C22×D67—26no—
281C22×D67—26no—
282C22×D67C2×#4114yes—
283C22×D67C2516yes—
284C22×D67C2512yes—
285Q8×C67—224no—
286Q8×C67C2×#41116yescomplemented
287C2×C4×C67—26no—
288C2×C4×C67—26no—
289C2×C4×C67—26no—
290C2×C4×C67—224no—
291C2×C4×C67—22no—
292C2×C4×C67—224no—
293C2×C4×C67—28no—
294C2×C4×C67C2×#41112yes—
295C2×C4×C672−1+414yes—
296C2×C4×C67C2512yes—
297C2×C4×C67C2516yes—
298C2×C4×C67C2516yes—
299C2×C4×C67C2516yes—
300C2×C4×C67C2516yes—
301C2×C4×C67C2512yes—
302C22⋊D67—224no—
303C22⋊D67C2×#41116yescomplemented
304C2×Dic67—22no—
305C2×Dic67—26no—
306C2×Dic67—26no—
307C2×Dic67—22no—
308C2×Dic67—26no—
309C2×Dic67C2×#4114yes—
310C2×Dic67C2512yes—
311C2×Dic67C2512yes—
312C2×Dic67C2516yes—
313C2×Dic67C2516yes—
314C2×Dic67C2516yes—
315C2×Dic67C2512yes—
316D268—224no—
317D268—224no—
318C4×D67—224no—
319C4×D67—224no—
320C4×D67—224no—
321C4×D67—28no—
322C4×D67—224no—
323C4×D67—224no—
324Dic134—224no—
325Dic134—224no—
326C22×C67—22no—
327C22×C67—22no—
328C22×C67—28no—
329C22×C67C22×#4114yes—
330C22×C67C22×#4112yes—
331C22×C67C22×#4112yes—
332C22×C67C2×2−1+412yes—
333C22×C67C2611yescharacteristic
334C2×D67—22no—
335C2×D67—22no—
336C2×D67—28no—
337C2×D67—26no—
338C2×D67—26no—
339C2×D67—26no—
340C2×D67—412no—
341C2×D67C22×#4114yes—
342C4×C67—26no—
343C4×C67—26no—
344C4×C67—26no—
345C4×C67—22no—
346C4×C67C22×#41112yes—
347C4×C67C2×2−1+414yes—
348Dic67—26no—
349Dic67—26no—
350Dic67—22no—
351Dic67—22no—
352Dic67—26no—
353Dic67C22×#4114yes—
354C2×#3482—671nomaximal, Sylow
355C2×C67—24no—
356C2×C67#348214yescomplemented
357C2×C67C23×#4111yescharacteristic
358C2×C67C23×#4111yescharacteristic
359C2×C67C22×2−1+411yescharacteristic
360D67—24no—
361D67—46no—
362#3482—6732no—
363C2×#557—671no—
364C2×#556—673no—
365C2×#552—673no—
366C2×#552—673no—
367C2×D4×Q8—671no—
368C2×#548—671no—
369C2×#548—671no—
370C2×#547—673no—
371C2×#533—673no—
372C2×#529—673no—
373C2×#529—673no—
374C2×C4×#41—673no—
375C2×C4×#41—671no—
376C22×C4×Q8—671no—
377C22×C4×Q8D6711yescharacteristic, complemented
378C67C2×#348211yescharacteristic, complemented, Sylow
379C22×#41—671no—
380C22×#41—673no—
381C23×Q8—671no—
382C23×Q8C2×D6711yescharacteristic
383#557—6716no—
384#556—6748no—
385#552—6748no—
386#552—6748no—
387D4×Q8—6716no—
388#548—6716no—
389#548—6716no—
390#547—6748no—
391#533—6748no—
392C2×C4⋊Q8—673no—
393C2×C4⋊Q8—673no—
394#529—6748no—
395#529—6748no—
396C2×#126—676no—
397C2×#126—676no—
398C2×#125—673no—
399C2×#125—676no—
400C2×#125—673no—
401C2×#124—673no—
402C2×#124—673no—
403C2×#123—676no—
404C2×#123—676no—
405C2×C22⋊Q8—673no—
406C2×C22⋊Q8—673no—
407C2×C22⋊Q8—673no—
408C2×C22⋊Q8—676no—
409C2×C22⋊Q8—673no—
410C2×#121—673no—
411C2×#121—673no—
412C4×#41—6716no—
413C4×#41—6748no—
414C2×C4×Q8—671no—
415C2×C4×Q8—671no—
416C2×C4×Q8—6716no—
417C2×C4×Q8—673no—
418C2×C4×Q8—673no—
419C2×C4×Q8—673no—
420C2×C4×Q8—673no—
421C2×C4×Q8C2×D6711yescharacteristic
422C2×C4×Q8C2×D6713yes—
423C2×C4×Q8C2×D6711yescharacteristic
424C2×C4×Q8C2×D6713yes—
425C2×C4×Q8C2×D67116yescomplemented
426C2×C4×D4—671no—
427C2×C4×D4—673no—
428C2×C4×D4—673no—
429C2×C4×D4—673no—
430C2×C4×D4—673no—
431C2×C4×D4—673no—
432C2×C4×D4—673no—
433C2×C4×D4—673no—
434C2×#117—673no—
435C2×#117—673no—
436C2×#117—673no—
437C2×#117—673no—
438C2×#117—676no—
439C22×C4⋊C4—673no—
440C22×C4⋊C4C2×D6713yes—
441C22×C42—673no—
442C22×C42—673no—
443C22×C42C2×D6713yes—
444C2×#41—678no—
445C2×#41—6724no—
446C2×#41—13424no—
447C2×#41—1348no—
448C22×Q8—28no—
449C22×Q8—678no—
450C22×Q8—673no—
451C22×Q8—673no—
452C22×Q8—1348no—
453C22×Q8C22×D6713yes—
454C22×Q8C22×D6718yes—
455C22×Q8C22×D6711yescharacteristic
456C22×D4—671no—
457C22×D4—673no—
458C22×D4—673no—
459C22×D4—673no—
460C23×C4—673no—
461C23×C4—673no—
462C23×C4—673no—
463C23×C4—673no—
464C23×C4—673no—
465C23×C4—671no—
466C23×C4C22×D6713yes—
467C23×C4C22×D6713yes—
468C23×C4C22×D6711yescharacteristic
469C4⋊Q8—6724no—
470C4⋊Q8—6724no—
471#126—6748no—
472#126—6748no—
473#125—6724no—
474#125—6748no—
475#125—6724no—
476#124—6724no—
477#124—6724no—
478#123—6748no—
479#123—6748no—
480C22⋊Q8—6724no—
481C22⋊Q8—6724no—
482C22⋊Q8—6724no—
483C22⋊Q8—6748no—
484C22⋊Q8—6724no—
485#121—6724no—
486#121—6724no—
487C4×Q8—678no—
488C4×Q8—678no—
489C4×Q8—6724no—
490C4×Q8—6724no—
491C4×Q8—6724no—
492C4×Q8—6724no—
493C4×Q8C22×D6718yes—
494C4×Q8C22×D67124yes—
495C4×Q8C22×D6718yes—
496C4×Q8C22×D67124yes—
497C4×D4—678no—
498C4×D4—6724no—
499C4×D4—6724no—
500C4×D4—6724no—
501C4×D4—6724no—
502C4×D4—6724no—
503C4×D4—6724no—
504C4×D4—6724no—
505#117—6724no—
506#117—6724no—
507#117—6724no—
508#117—6724no—
509#117—6748no—
510C2×C4⋊C4—673no—
511C2×C4⋊C4—676no—
512C2×C4⋊C4—671no—
513C2×C4⋊C4—673no—
514C2×C4⋊C4—673no—
515C2×C4⋊C4—673no—
516C2×C4⋊C4—673no—
517C2×C4⋊C4—673no—
518C2×C4⋊C4—673no—
519C2×C4⋊C4—676no—
520C2×C4⋊C4—676no—
521C2×C4⋊C4—6724no—
522C2×C4⋊C4C22×D6713yes—
523C2×C4⋊C4C22×D6713yes—
524C2×C4⋊C4C22×D6716yes—
525C2×C4⋊C4C22×D67124yes—
526C2×C22⋊C4—671no—
527C2×C22⋊C4—673no—
528C2×C22⋊C4—671no—
529C2×C22⋊C4—673no—
530C2×C22⋊C4—676no—
531C2×C22⋊C4—673no—
532C2×C22⋊C4—673no—
533C2×C22⋊C4—676no—
534C2×C22⋊C4—676no—
535C2×C42—673no—
536C2×C42—673no—
537C2×C42—673no—
538C2×C42—673no—
539C2×C42—673no—
540C2×C42—671no—
541C2×C42—6724no—
542C2×C42—6724no—
543C2×C42C22×D6713yes—
544C2×C42C22×D6713yes—
545C2×C42C22×D67124yes—
546C2×C42C22×D6713yes—
547C2×C42C22×D6713yes—
548C24—671no—
549C24—673no—
550C24C23×D6711yescharacteristic
551#41—13496no—
552#41—13432no—
553C2×Q8—232no—
554C2×Q8—212no—
555C2×Q8—6712no—
556C2×Q8—6712no—
557C2×Q8—13412no—
558C2×Q8—13432no—
559C2×Q8—13412no—
560C2×Q8#1176162818yescomplemented
561C2×Q8C23×D67112yes—
562C2×Q8C23×D6714yes—
563C2×D4—678no—
564C2×D4—674no—
565C2×D4—6712no—
566C2×D4—6712no—
567C2×D4—6712no—
568C2×D4—13412no—
569C2×D4—13412no—
570C2×D4—13412no—
571C22×C4—212no—
572C22×C4—212no—
573C22×C4—24no—
574C22×C4—671no—
575C22×C4—671no—
576C22×C4—671no—
577C22×C4—673no—
578C22×C4—673no—
579C22×C4—673no—
580C22×C4—674no—
581C22×C4—6712no—
582C22×C4—6712no—
583C22×C4—6712no—
584C22×C4—6712no—
585C22×C4—6712no—
586C22×C4—13412no—
587C22×C4—13412no—
588C22×C4—13412no—
589C22×C4—13412no—
590C22×C4—13412no—
591C22×C4—1344no—
592C22×C4C23×D6713yes—
593C22×C4C23×D6711yescharacteristic
594C22×C4C23×D6714yes—
595C22×C4C23×D6713yes—
596C22×C4C23×D6713yes—
597C22×C4C23×D67112yes—
598C22×C4C23×D67112yes—
599C22×C4C23×D6713yes—
600C22×C4C23×D6711yescharacteristic
601C4⋊C4—6712no—
602C4⋊C4—6724no—
603C4⋊C4—674no—
604C4⋊C4—6712no—
605C4⋊C4—6712no—
606C4⋊C4—6712no—
607C4⋊C4—6712no—
608C4⋊C4—6712no—
609C4⋊C4—6712no—
610C4⋊C4—6724no—
611C4⋊C4—6724no—
612C4⋊C4C23×D67112yes—
613C4⋊C4C23×D67112yes—
614C4⋊C4C23×D67124yes—
615C22⋊C4—674no—
616C22⋊C4—6712no—
617C22⋊C4—674no—
618C22⋊C4—6712no—
619C22⋊C4—6724no—
620C22⋊C4—6712no—
621C22⋊C4—6712no—
622C22⋊C4—6724no—
623C22⋊C4—6724no—
624C42—674no—
625C42—6712no—
626C42—6712no—
627C42—6712no—
628C42—6712no—
629C42—6712no—
630C42C23×D67112yes—
631C42C23×D67112yes—
632C42C23×D67112yes—
633C42C23×D67112yes—
634C23—22no—
635C23—22no—
636C23—674no—
637C23—672no—
638C23—676no—
639C23—1346no—
640C23—1346no—
641C23—1346no—
642C23—1342no—
643C23—1342no—
644C23#41×D6714yes—
645C23C24×D6712yes—
646C23C24×D6711yescharacteristic
647Q8—224no—
648Q8—13424no—
649Q8—13424no—
650Q8C2×#11761628116yescomplemented
651D4—6716no—
652D4—13424no—
653D4—13424no—
654D4—13424no—
655C2×C4—26no—
656C2×C4—26no—
657C2×C4—224no—
658C2×C4—26no—
659C2×C4—22no—
660C2×C4—224no—
661C2×C4—28no—
662C2×C4—674no—
663C2×C4—672no—
664C2×C4—672no—
665C2×C4—672no—
666C2×C4—676no—
667C2×C4—676no—
668C2×C4—676no—
669C2×C4—13424no—
670C2×C4—13424no—
671C2×C4—1346no—
672C2×C4—1342no—
673C2×C4—1346no—
674C2×C4—1342no—
675C2×C4—1346no—
676C2×C4—13424no—
677C2×C4—13424no—
678C2×C4—13424no—
679C2×C4—1348no—
680C2×C4C2×#11761628112yes—
681C2×C4#1452409114yes—
682C2×C4C24×D6716yes—
683C2×C4C24×D6712yes—
684C2×C4C24×D6716yes—
685C2×C4C24×D6716yes—
686C2×C4C24×D6716yes—
687C2×C4C24×D6712yes—
688C22—28no—
689C22—22no—
690C22—22no—
691C22—26812no—
692C22—674no—
693C22—1346no—
694C22—1346no—
695C22—1346no—
696C22—1348no—
697C22—1342no—
698C22—1342no—
699C22C2×#41×D6714yes—
700C22C2×#41×D6712yes—
701C22C22×#1176162812yes—
702C22C2×#1452409112yes—
703C22C25×D6711yescharacteristic
704C4—26no—
705C4—26no—
706C4—26no—
707C4—22no—
708C4—674no—
709C4—1346no—
710C4—1342no—
711C4—1346no—
712C4—1342no—
713C4—1346no—
714C4C22×#11761628112yes—
715C4C2×#1452409114yes—
716C2—24no—
717C2—2686no—
718C2—1344no—
719C2#2257382614yesdirect product factor
720C2C22×#41×D6711yescharacteristic
721C2C23×#1176162811yescharacteristic
722C2C22×#1452409111yescharacteristic
subgroupG/H
centerC22×C4C23×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC22×C4×Q8×C67C2
socleC23×C67C25
hypercenterC22×C4×Q8D67
hypocenterC67C2×#3482
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #22573826C2direct (N × H)
2. C2×#16864122C2semidirect
3. C2×#16864118C2semidirect
4. C2×#16864087C2semidirect
5. C2×#16864081C2semidirect
6. C2×Q8×C22⋊D67C2semidirect
7. C2×#16864058C2semidirect
8. C2×#16864057C2semidirect
9. C2×#16864047C2semidirect
10. C2×#16863950C2semidirect
11. C2×#16863933C2semidirect
12. C2×#16863930C2semidirect
13. C2×C4×#11761629C2semidirect
14. C2×C4×#11761628C2semidirect
15. C2×C4×Q8×D67C2semidirect
16. C22×C4×Q8×C67C2semidirect
20. #16864122C22semidirect
21. #16864118C22semidirect
22. #16864087C22semidirect
23. #16864081C22semidirect
24. Q8×C22⋊D67C22semidirect
25. #16864058C22semidirect
26. #16864057C22semidirect
27. #16864047C22semidirect
28. #16863950C22semidirect
31. #16863933C22semidirect
32. #16863930C22semidirect
49. C4×#11761629C22semidirect
50. C4×#11761628C22semidirect
57. C4×Q8×D67C22semidirect
79. C2×C4×Q8×C67C22semidirect
200. C2×C22⋊D67#41semidirect
250. C2×Q8×C67#41semidirect
286. Q8×C67C2×#41semidirect
303. C22⋊D67C2×#41semidirect
356. C2×C67#3482semidirect
377. C22×C4×Q8D67semidirect
378. C67C2×#3482semidirect
425. C2×C4×Q8C2×D67semidirect
560. C2×Q8#11761628semidirect
650. Q8C2×#11761628semidirect
719. C2#22573826direct (N × H)

Maximal subgroups

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

subgroupindex
#225738262
C2×#168641222
C2×#168641182
C2×#168640872
C2×#168640812
C2×Q8×C22⋊D672
C2×#168640582
C2×#168640572
C2×#168640472
C2×#168639502
C2×#168639332
C2×#168639302
C2×C4×#117616292
C2×C4×#117616282
C2×C4×Q8×D672
C22×C4×Q8×C672
C2×#348267