Finite Group Databasebeta

← C2×#22574000 #31764299

Subgroups — C2×#22574000 #31764299

Order 17152.

11534 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524091C211yesmaximal, characteristic, complemented
2C22×#14524089C211yesmaximal, characteristic, complemented
3#22574000C2132yesmaximal, direct product factor
4C2×#16864058C211yesmaximal, characteristic, complemented
5C2×#16864057C211yesmaximal, characteristic, complemented
6C2×#16864053C211yesmaximal, characteristic, complemented
7C2×#16864043C213yesmaximal, complemented
8C2×#16864042C213yesmaximal, complemented
9C2×#16864039C213yesmaximal, complemented
10C2×#16864037C213yesmaximal, complemented
11C2×#16863969C213yesmaximal, complemented
12C2×#16863962C213yesmaximal, complemented
13C2×#16863943C213yesmaximal, complemented
14C2×#124×D67C213yesmaximal, complemented
15C2×C4×#11761629C211yesmaximal, characteristic, complemented
16C2×#548×C67C211yesmaximal, characteristic, complemented
17C2×#14524091—216no—
18C2×#14524091C22116yescomplemented
19C2×#14524089—216no—
20C2×#14524089C22116yescomplemented
21C22×#11761629C2211yescharacteristic
22C22×#11761629C2211yescharacteristic
23C22×#11761629C2213yescomplemented
24C22×#11761628C2213yes—
25C22×#11761628C2213yescomplemented
26C22×#11761628C2213yescomplemented
27C22×Q8×D67C2211yescharacteristic, complemented
28C22×Q8×D67C2213yescomplemented
29C23×D268C2213yes—
30C22×D4×D67C2213yes—
31C22×D4×D67C2213yes—
32#16864058C22116yescomplemented
33#16864057C22116yescomplemented
34#16864053C22116yescomplemented
35#16864043C22148yescomplemented
36#16864042C22148yescomplemented
37#16864039C22148yescomplemented
38#16864037C22148yescomplemented
39#16863969C22148yescomplemented
40#16863962C22148yescomplemented
41#16863943C22148yescomplemented
42C2×#14524042C2213yescomplemented
43C2×#14524039C2213yescomplemented
44C2×#14524032C2213yescomplemented
45C2×#14524031C2213yescomplemented
46C2×#14524030C2213yescomplemented
47C2×#14524029C2213yescomplemented
48C2×#14524029C2216yescomplemented
49C2×#14524029C2211yescharacteristic, complemented
50#124×D67C22148yescomplemented
51C2×#14524028C2216yescomplemented
52C2×#14524025C2216yescomplemented
53C2×#14524023C2213yescomplemented
54C2×#14524022C2213yescomplemented
55C2×#14524019C2213yescomplemented
56C2×#14524018C2213yescomplemented
57C2×#14524018C2213yescomplemented
58C2×#14524017C2213yescomplemented
59C2×#14524016C2213yescomplemented
60C2×#14524016C2213yescomplemented
61C2×#14524014C2213yescomplemented
62C2×#14524014C2213yescomplemented
63C2×#14524013C2216yescomplemented
64C2×#14524011C2216yescomplemented
65C4×#11761629C22116yescomplemented
66C2×Q8×Dic67C2211yescharacteristic, complemented
67C2×C4×D268C2213yescomplemented
68C2×C4×D268C2213yescomplemented
69C2×#14524005C2213yescomplemented
70C2×C4×C22⋊D67C2213yescomplemented
71C2×C4×C22⋊D67C2213yescomplemented
72C2×#14524001C2213yescomplemented
73C2×C22⋊C4×D67C2216yescomplemented
74C2×C22⋊C4×D67C2216yescomplemented
75C2×C42×D67C2213yescomplemented
76C22×#41×C67C2211yescharacteristic
77C23×Q8×C67C2211yescharacteristic, complemented
78#548×C67C22116yescomplemented
79C2×#124×C67C2213yescomplemented
80C2×C22⋊Q8×C67C2213yescomplemented
81C2×#121×C67C2213yescomplemented
82C2×C4×Q8×C67C2211yescharacteristic, complemented
83C2×C4×D4×C67C2213yescomplemented
84C24×D67C2316yes—
85#14524091—2128no—
86#14524089—2128no—
87C2×#11761629—224no—
88C2×#11761629—28no—
89C2×#11761629D4116yescomplemented
90C2×#11761629C2318yes—
91C2×#11761629C2318yes—
92C2×#11761629C23124yescomplemented
93C2×#11761628—224no—
94C2×#11761628—224no—
95C2×#11761628—224no—
96C2×#11761628C23124yes—
97C2×#11761628C23124yescomplemented
98C2×#11761628C23124yescomplemented
99C22×Dic134C2313yes—
100C22×Dic134C2313yes—
101C22×Dic134C2311yescharacteristic
102C2×Q8×D67—224no—
103C2×Q8×D67—28no—
104C2×Q8×D67C2318yescomplemented
105C2×Q8×D67C23124yescomplemented
106C22×D268—224no—
107C22×D268C23124yes—
108C22×D268C2313yes—
109C22×D268C2313yes—
110C22×D268C2313yes—
111C22×D268C2313yes—
112C22×D268C2313yes—
113C22×C22⋊D67C2313yes—
114C22×C22⋊D67C2313yes—
115C22×C22⋊D67C2313yes—
116C22×C22⋊D67C2311yescharacteristic
117C22×C22⋊D67C2313yes—
118C22×C22⋊D67C2313yes—
119C2×D4×D67—224no—
120C2×D4×D67—224no—
121C2×D4×D67C23124yes—
122C2×D4×D67C23124yes—
123C22×C4×D67C2316yes—
124C22×C4×D67C2313yes—
125C22×C4×D67C2313yes—
126C22×C4×D67C2313yes—
127C22×C4×D67C2313yes—
128C22×C4×D67C2313yes—
129#14524042C23124yescomplemented
130#14524039C23124yescomplemented
131#14524032C23124yescomplemented
132#14524031C23124yescomplemented
133#14524030C23124yescomplemented
134#14524029C23124yescomplemented
135#14524029C23148yescomplemented
136#14524029C2318yescomplemented
137#14524028C23148yescomplemented
138#14524025C23148yescomplemented
139#14524023C23124yescomplemented
140#14524022C23124yescomplemented
141#14524019C23124yescomplemented
142#14524018C23124yescomplemented
143#14524018C23124yescomplemented
144#14524017C23124yescomplemented
145#14524016C23124yescomplemented
146#14524016C23124yescomplemented
147#14524014C23124yescomplemented
148#14524014C23124yescomplemented
149#14524013C23148yescomplemented
150#14524011C23148yescomplemented
151Q8×Dic67C2318yescomplemented
152C4×D268C23124yescomplemented
153C4×D268C23124yescomplemented
154#14524005C23124yescomplemented
155C4×C22⋊D67C23124yescomplemented
156C4×C22⋊D67C23124yescomplemented
157#14524001C23124yescomplemented
158C2×C4⋊Dic67C2313yes—
159C2×C4⋊Dic67C2313yes—
160C2×Dic67⋊C4C2313yes—
161C2×Dic67⋊C4C2313yes—
162C2×C22⋊Dic67C2313yes—
163C2×C22⋊Dic67C2316yes—
164C2×C22⋊Dic67C2311yescharacteristic
165C2×(C2×D67)⋊C4C2313yes—
166C2×(C2×D67)⋊C4C2313yes—
167C2×(C2×D67)⋊C4C2316yes—
168C2×(C2×D67)⋊C4C2316yes—
169C2×(C2×D67)⋊C4C2316yes—
170C2×(C2×D67)⋊C4C2311yescharacteristic
171C2×(C2×D67)⋊C4C2311yescharacteristic
172C22⋊C4×D67C23148yescomplemented
173C22⋊C4×D67C23148yescomplemented
174C2×C4×Dic67C2311yescharacteristic
175C2×C4×Dic67C2313yes—
176C2×C4×Dic67C2313yes—
177C42×D67C23124yescomplemented
178C2×#41×C67—28no—
179C2×#41×C67C2318yes—
180C22×Q8×C67—28no—
181C22×Q8×C67C2313yes—
182C22×Q8×C67C2311yescharacteristic
183C22×Q8×C67C2318yescomplemented
184C22×D4×C67C2313yes—
185C22×D4×C67C2313yes—
186C23×C4×C67C2313yes—
187C23×C4×C67C2313yes—
188#124×C67C23124yescomplemented
189C22⋊Q8×C67C23124yescomplemented
190#121×C67C23124yescomplemented
191C4×Q8×C67C2318yescomplemented
192C4×D4×C67C23124yescomplemented
193C2×C4⋊C4×C67C2313yes—
194C2×C4⋊C4×C67C2313yes—
195C2×C22⋊C4×C67C2311yescharacteristic
196C2×C22⋊C4×C67C2313yes—
197C2×C22⋊C4×C67C2316yes—
198C2×C42×C67C2313yes—
199C23×D67—224no—
200C23×D67—412no—
201C23×D67—412no—
202C23×D67C2413yes—
203C23×D67C2411yescharacteristic
204C23×D67C2413yes—
205C23×D67C24124yes—
206#11761629—232no—
207#11761629—296no—
208#11761629C2×D4164yescomplemented
209#11761628—296no—
210#11761628—296no—
211#11761628—296no—
212C2×Dic134—212no—
213C2×Dic134—212no—
214C2×Dic134—24no—
215C2×Dic134C24112yes—
216C2×Dic134C24112yes—
217C2×Dic134C2414yes—
218Q8×D67—232no—
219Q8×D67—296no—
220C2×D268—212no—
221C2×D268—212no—
222C2×D268—212no—
223C2×D268—296no—
224C2×D268—46no—
225C2×D268C2×D4124yes—
226C2×D268C24112yes—
227C2×D268C24112yes—
228C2×D268C24112yes—
229C2×D268C24112yes—
230C2×D268C24112yes—
231C2×C22⋊D67—212no—
232C2×C22⋊D67—212no—
233C2×C22⋊D67—212no—
234C2×C22⋊D67—24no—
235C2×C22⋊D67—46no—
236C2×C22⋊D67—46no—
237C2×C22⋊D67C24112yes—
238C2×C22⋊D67C24112yes—
239C2×C22⋊D67C24112yes—
240C2×C22⋊D67C2414yes—
241C2×C22⋊D67C24112yes—
242C2×C22⋊D67C24112yes—
243D4×D67—296no—
244D4×D67—296no—
245C22×Dic67C2411yescharacteristic
246C22×Dic67C2413yes—
247C22×Dic67C2413yes—
248C22×Dic67C2411yescharacteristic
249C22×Dic67C2411yescharacteristic
250C2×C4×D67—224no—
251C2×C4×D67—212no—
252C2×C4×D67—212no—
253C2×C4×D67—46no—
254C2×C4×D67—46no—
255C2×C4×D67C2×D4124yes—
256C2×C4×D67C24124yes—
257C2×C4×D67C24112yes—
258C2×C4×D67C24112yes—
259C2×C4×D67C24112yes—
260C2×C4×D67C24112yes—
261C2×C4×D67C24112yes—
262C4⋊Dic67C24112yes—
263C4⋊Dic67C24112yes—
264Dic67⋊C4C24112yes—
265Dic67⋊C4C24112yes—
266C22⋊Dic67C24112yes—
267C22⋊Dic67C24124yes—
268C22⋊Dic67C2414yes—
269(C2×D67)⋊C4C24112yes—
270(C2×D67)⋊C4C24112yes—
271(C2×D67)⋊C4C24124yes—
272(C2×D67)⋊C4C24124yes—
273(C2×D67)⋊C4C24124yes—
274(C2×D67)⋊C4C2414yes—
275(C2×D67)⋊C4C2414yes—
276C4×Dic67C2414yes—
277C4×Dic67C24112yes—
278C4×Dic67C24112yes—
279C24×C67C2413yes—
280C24×C67C2411yescharacteristic
281#41×C67—232no—
282C2×Q8×C67—232no—
283C2×Q8×C67—212no—
284C2×Q8×C67C2×D418yes—
285C2×Q8×C67C24112yes—
286C2×Q8×C67C2414yes—
287C2×D4×C67—212no—
288C2×D4×C67—46no—
289C2×D4×C67C24112yes—
290C2×D4×C67C24112yes—
291C22×C4×C67—212no—
292C22×C4×C67—212no—
293C22×C4×C67C2411yescharacteristic
294C22×C4×C67C2413yes—
295C22×C4×C67C2413yes—
296C22×C4×C67C2411yescharacteristic
297C22×C4×C67C24112yes—
298C22×C4×C67C24112yes—
299C22×C4×C67C2413yes—
300C4⋊C4×C67C24112yes—
301C4⋊C4×C67C24112yes—
302C22⋊C4×C67C2414yes—
303C22⋊C4×C67C24112yes—
304C22⋊C4×C67C24124yes—
305C42×C67C24112yes—
306C23×C67—22no—
307C23×C67—26no—
308C23×C67—22no—
309C23×C67—26no—
310C23×C67—22no—
311C23×C67—26no—
312C23×C67C2516yes—
313C23×C67C2512yes—
314C23×C67C2511yescharacteristic
315C22×D67—26no—
316C22×D67—26no—
317C22×D67—22no—
318C22×D67—26no—
319C22×D67—22no—
320C22×D67—26no—
321C22×D67—22no—
322C22×D67—26no—
323C22×D67—248no—
324C22×D67—424no—
325C22×D67—424no—
326C22×D67—848no—
327C22×D67C22×D4112yes—
328C22×D67C2516yes—
329C22×D67C2512yes—
330C22×D67C2516yes—
331Q8×C67—224no—
332Q8×C67C22×D4116yes—
333D4×C67—224no—
334D4×C67—412no—
335C2×C4×C67—22no—
336C2×C4×C67—26no—
337C2×C4×C67—26no—
338C2×C4×C67—22no—
339C2×C4×C67—224no—
340C2×C4×C67—224no—
341C2×C4×C67C22×D4112yes—
342C2×C4×C67C2512yes—
343C2×C4×C67C2516yes—
344C2×C4×C67C2516yes—
345C2×C4×C67C2512yes—
346C2×C4×C67C2516yes—
347C22⋊D67—224no—
348C22⋊D67—224no—
349C22⋊D67—224no—
350C22⋊D67—28no—
351C22⋊D67—412no—
352C22⋊D67—412no—
353C2×Dic67—22no—
354C2×Dic67—26no—
355C2×Dic67—22no—
356C2×Dic67—26no—
357C2×Dic67C22×D414yes—
358C2×Dic67C2512yes—
359C2×Dic67C2516yes—
360C2×Dic67C2516yes—
361C2×Dic67C2512yes—
362C2×Dic67C2512yes—
363D268—224no—
364D268—224no—
365D268—224no—
366D268—412no—
367D268C22×D4148yes—
368C4×D67—248no—
369C4×D67—224no—
370C4×D67—224no—
371C4×D67—412no—
372C4×D67—412no—
373C4×D67C22×D4148yes—
374Dic134—224no—
375Dic134—224no—
376Dic134—28no—
377C22×C67—22no—
378C22×C67—26no—
379C22×C67—22no—
380C22×C67—26no—
381C22×C67—22no—
382C22×C67—26no—
383C22×C67—412no—
384C22×C67—44no—
385C22×C67C23×D412yes—
386C22×C67#58512yes—
387C22×C67#58512yes—
388C22×C67C2611yescharacteristic
389C2×D67—26no—
390C2×D67—26no—
391C2×D67—224no—
392C2×D67—22no—
393C2×D67—26no—
394C2×D67—22no—
395C2×D67—26no—
396C2×D67—22no—
397C2×D67—26no—
398C2×D67—44no—
399C2×D67—412no—
400C2×D67—848no—
401C2×D67C23×D4112yes—
402C4×C67—26no—
403C4×C67—22no—
404C4×C67—22no—
405C4×C67—26no—
406C4×C67C23×D4112yes—
407Dic67—26no—
408Dic67—22no—
409Dic67—22no—
410Dic67—26no—
411Dic67C23×D414yes—
412C2×#3500—671nomaximal, Sylow
413C2×C67—46no—
414C2×C67—42no—
415C2×C67#350014yescomplemented
416C2×C67C24×D411yescharacteristic
417C2×C67C2×#58511yescharacteristic
418C2×C67C2×#58511yescharacteristic
419D67—212no—
420D67—42no—
421D67—46no—
422C22×2−1+4—671no—
423C22×H(5,𝔽2)—671no—
424#3500—6732no—
425C2×#548—671no—
426C2×#548—671no—
427C2×#548—671no—
428C2×#548D6711yescharacteristic, complemented
429C2×#546—673no—
430C2×#546—673no—
431C2×#546—673no—
432C2×#546—673no—
433C2×#536—673no—
434C2×#535—673no—
435C2×#532—673no—
436C22×#124—673no—
437C2×C4×#41—671no—
438C67C2×#350011yescharacteristic, complemented, Sylow
439C2×2−1+4—6716no—
440C2×2−1+4—13416no—
441C2×H(5,𝔽2)—6716no—
442C2×H(5,𝔽2)—13416no—
443C22×#41—671no—
444C22×#41—671no—
445C22×#41—673no—
446C22×#41—673no—
447C22×#41—673no—
448C22×#41—673no—
449C22×#41C2×D6711yescharacteristic
450C23×Q8—673no—
451C23×Q8—671no—
452C23×Q8C2×D6711yescharacteristic, complemented
453C23×D4—673no—
454C23×D4—673no—
455C23×D4—673no—
456#548—6716no—
457#548—6716no—
458#548—6716no—
459#548C2×D67116yescomplemented
460#546—6748no—
461#546—6748no—
462#546—6748no—
463#546—6748no—
464#536—6748no—
465#535—6748no—
466#532—6748no—
467C2×C4⋊Q8—673no—
468C2×#127—673no—
469C2×#124—673no—
470C2×#124—673no—
471C2×#124—6748no—
472C2×#124—673no—
473C2×#124—676no—
474C2×#124—671no—
475C2×#124—673no—
476C2×#124C2×D6713yescomplemented
477C2×#123—676no—
478C2×#123—676no—
479C2×C22⋊Q8—673no—
480C2×C22⋊Q8—673no—
481C2×C22⋊Q8—673no—
482C2×C22⋊Q8C2×D6713yescomplemented
483C2×#121—673no—
484C2×#121—673no—
485C2×#121—673no—
486C2×#121—673no—
487C2×#121—673no—
488C2×#121—673no—
489C2×#121—673no—
490C2×#121C2×D6713yescomplemented
491C2×#120—676no—
492C2×#120—676no—
493C4×#41—6716no—
494C2×C4×Q8—671no—
495C2×C4×Q8C2×D6711yescharacteristic, complemented
496C2×C4×D4—673no—
497C2×C4×D4—673no—
498C2×C4×D4—673no—
499C2×C4×D4—673no—
500C2×C4×D4—673no—
501C2×C4×D4C2×D6713yescomplemented
502C2×#117—673no—
503C22×C22⋊C4—676no—
504C22×C22⋊C4—676no—
505C22×C42—673no—
506C25—676no—
5072−1+4—134128no—
508H(5,𝔽2)—134128no—
509C2×#41—28no—
510C2×#41—6716no—
511C2×#41—678no—
512C2×#41—6724no—
513C2×#41—678no—
514C2×#41—6724no—
515C2×#41—6724no—
516C2×#41—6724no—
517C2×#41—13424no—
518C2×#41—13424no—
519C2×#41—13424no—
520C2×#41—13424no—
521C2×#41—1348no—
522C2×#41C22×D6718yes—
523C22×Q8—28no—
524C22×Q8—6724no—
525C22×Q8—678no—
526C22×Q8—673no—
527C22×Q8—673no—
528C22×Q8—671no—
529C22×Q8—13424no—
530C22×Q8—1348no—
531C22×Q8C22×D6713yes—
532C22×Q8C22×D6711yescharacteristic
533C22×Q8C22×D6718yescomplemented
534C22×D4—673no—
535C22×D4—673no—
536C22×D4—673no—
537C22×D4—673no—
538C22×D4—673no—
539C22×D4—671no—
540C22×D4—6724no—
541C22×D4—6724no—
542C22×D4—673no—
543C22×D4—673no—
544C22×D4—673no—
545C22×D4—673no—
546C22×D4—673no—
547C22×D4—6724no—
548C22×D4—13424no—
549C22×D4—13424no—
550C22×D4—13424no—
551C22×D4C22×D6713yes—
552C22×D4C22×D6713yes—
553C23×C4—673no—
554C23×C4—673no—
555C23×C4—673no—
556C23×C4—676no—
557C23×C4—673no—
558C23×C4—673no—
559C23×C4C22×D6713yes—
560C23×C4C22×D6713yes—
561C4⋊Q8—6724no—
562#127—6724no—
563#124—6724no—
564#124—6724no—
565#124—6724no—
566#124—6748no—
567#124—678no—
568#124—6724no—
569#124C22×D67124yescomplemented
570#123—6748no—
571#123—6748no—
572C22⋊Q8—6724no—
573C22⋊Q8—6724no—
574C22⋊Q8—6724no—
575C22⋊Q8C22×D67124yescomplemented
576#121—6724no—
577#121—6724no—
578#121—6724no—
579#121—6724no—
580#121—6724no—
581#121—6724no—
582#121—6724no—
583#121C22×D67124yescomplemented
584#120—6748no—
585#120—6748no—
586C4×Q8—678no—
587C4×Q8C22×D6718yescomplemented
588C4×D4—6724no—
589C4×D4—6724no—
590C4×D4—6724no—
591C4×D4—6724no—
592C4×D4—6724no—
593C4×D4C22×D67124yescomplemented
594#117—6724no—
595C2×C4⋊C4—673no—
596C2×C4⋊C4—673no—
597C2×C4⋊C4—673no—
598C2×C4⋊C4—673no—
599C2×C4⋊C4C22×D6713yes—
600C2×C4⋊C4C22×D6713yes—
601C2×C22⋊C4—673no—
602C2×C22⋊C4—676no—
603C2×C22⋊C4—671no—
604C2×C22⋊C4—673no—
605C2×C22⋊C4—673no—
606C2×C22⋊C4—676no—
607C2×C22⋊C4—676no—
608C2×C22⋊C4—676no—
609C2×C22⋊C4—671no—
610C2×C22⋊C4—671no—
611C2×C22⋊C4—6748no—
612C2×C22⋊C4—6748no—
613C2×C22⋊C4C22×D6713yes—
614C2×C22⋊C4C22×D6716yes—
615C2×C22⋊C4C22×D6711yescharacteristic
616C2×C42—673no—
617C2×C42—673no—
618C2×C42—671no—
619C2×C42—6724no—
620C2×C42C22×D6713yes—
621C24—26812no—
622C24—26812no—
623C24—6724no—
624C24—673no—
625C24—673no—
626C24—671no—
627C24—13424no—
628C24C23×D6713yes—
629C24C23×D6711yescharacteristic
630#41—232no—
631#41—6764no—
632#41—13496no—
633#41—13496no—
634#41—13496no—
635#41—13496no—
636#41—13432no—
637C2×Q8—232no—
638C2×Q8—212no—
639C2×Q8—6712no—
640C2×Q8—6712no—
641C2×Q8—674no—
642C2×Q8—13412no—
643C2×Q8—1344no—
644C2×Q8—13496no—
645C2×Q8—13432no—
646C2×Q8—13412no—
647C2×Q8D4×D6718yes—
648C2×Q8C23×D67112yes—
649C2×Q8C23×D6714yes—
650C2×D4—212no—
651C2×D4—46no—
652C2×D4—2686no—
653C2×D4—2686no—
654C2×D4—2686no—
655C2×D4—6712no—
656C2×D4—6712no—
657C2×D4—6712no—
658C2×D4—6712no—
659C2×D4—6712no—
660C2×D4—674no—
661C2×D4—6724no—
662C2×D4—6712no—
663C2×D4—6712no—
664C2×D4—6712no—
665C2×D4—6712no—
666C2×D4—6712no—
667C2×D4—13496no—
668C2×D4—13412no—
669C2×D4—13412no—
670C2×D4—13496no—
671C2×D4—13412no—
672C2×D4—1344no—
673C2×D4—13496no—
674C2×D4—13412no—
675C2×D4—13412no—
676C2×D4—13412no—
677C2×D4C23×D67112yes—
678C2×D4C23×D67112yes—
679C22×C4—212no—
680C22×C4—212no—
681C22×C4—2686no—
682C22×C4—2686no—
683C22×C4—6712no—
684C22×C4—6712no—
685C22×C4—671no—
686C22×C4—6724no—
687C22×C4—6712no—
688C22×C4—671no—
689C22×C4—673no—
690C22×C4—673no—
691C22×C4—671no—
692C22×C4—6724no—
693C22×C4—6712no—
694C22×C4—6712no—
695C22×C4—13424no—
696C22×C4—13412no—
697C22×C4—13412no—
698C22×C4C23×D67112yes—
699C22×C4C23×D67112yes—
700C22×C4C23×D6711yescharacteristic
701C22×C4C23×D6713yes—
702C22×C4C23×D6713yes—
703C22×C4C23×D6711yescharacteristic
704C22×C4C23×D6713yes—
705C4⋊C4—6712no—
706C4⋊C4—6712no—
707C4⋊C4—6712no—
708C4⋊C4—6712no—
709C4⋊C4C23×D67112yes—
710C4⋊C4C23×D67112yes—
711C22⋊C4—6712no—
712C22⋊C4—6724no—
713C22⋊C4—674no—
714C22⋊C4—6712no—
715C22⋊C4—6712no—
716C22⋊C4—6724no—
717C22⋊C4—6724no—
718C22⋊C4—6724no—
719C22⋊C4—674no—
720C22⋊C4—674no—
721C22⋊C4C23×D67112yes—
722C22⋊C4C23×D67124yes—
723C22⋊C4C23×D6714yes—
724C42—674no—
725C42—6712no—
726C42—6712no—
727C42C23×D67112yes—
728C23—22no—
729C23—26no—
730C23—22no—
731C23—26no—
732C23—22no—
733C23—26no—
734C23—26824no—
735C23—26824no—
736C23—53648no—
737C23—6712no—
738C23—676no—
739C23—676no—
740C23—672no—
741C23—13448no—
742C23—1342no—
743C23—1346no—
744C23—1342no—
745C23—1346no—
746C23—1342no—
747C23—1346no—
748C23—1346no—
749C23—1346no—
750C23C24×D6716yes—
751C23C24×D6712yes—
752C23C24×D6711yescharacteristic
753Q8—224no—
754Q8—13424no—
755Q8—1348no—
756Q8—13424no—
757Q8C2×D4×D67116yes—
758D4—224no—
759D4—412no—
760D4—26812no—
761D4—26812no—
762D4—26812no—
763D4—6748no—
764D4—13424no—
765D4—13424no—
766D4—13424no—
767D4—1348no—
768D4—13424no—
769D4—13424no—
770D4—13424no—
771C2×C4—22no—
772C2×C4—26no—
773C2×C4—26no—
774C2×C4—22no—
775C2×C4—224no—
776C2×C4—224no—
777C2×C4—26812no—
778C2×C4—26812no—
779C2×C4—674no—
780C2×C4—672no—
781C2×C4—6748no—
782C2×C4—672no—
783C2×C4—676no—
784C2×C4—676no—
785C2×C4—672no—
786C2×C4—13448no—
787C2×C4—1342no—
788C2×C4—1346no—
789C2×C4—1342no—
790C2×C4—1346no—
791C2×C4—13424no—
792C2×C4—13424no—
793C2×C4C2×D4×D67112yes—
794C2×C4C24×D6712yes—
795C2×C4C24×D6716yes—
796C2×C4C24×D6716yes—
797C2×C4C24×D6712yes—
798C2×C4C24×D6716yes—
799C22—22no—
800C22—26no—
801C22—22no—
802C22—26no—
803C22—22no—
804C22—26no—
805C22—412no—
806C22—44no—
807C22—26812no—
808C22—2684no—
809C22—53648no—
810C22—6712no—
811C22—1342no—
812C22—1346no—
813C22—1342no—
814C22—1346no—
815C22—1342no—
816C22—1346no—
817C22—1346no—
818C22—1346no—
819C22—13424no—
820C22C22×D4×D6712yes—
821C22#1686423212yes—
822C22#1686423312yes—
823C22C25×D6711yescharacteristic
824C4—22no—
825C4—26no—
826C4—26no—
827C4—22no—
828C4—674no—
829C4—1342no—
830C4—1346no—
831C4—1342no—
832C4—1346no—
833C4C22×D4×D67112yes—
834C2—46no—
835C2—42no—
836C2—2686no—
837C2—2682no—
838C2—13412no—
839C2#2257400014yesdirect product factor
840C2C23×D4×D6711yescharacteristic
841C2C2×#1686423211yescharacteristic
842C2C2×#1686423311yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#548×C67C2
socleC23×C67C25
hypercenterC2×#548D67
hypocenterC67C2×#3500
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#14524091C2semidirect
2. C22×#14524089C2semidirect
3. #22574000C2direct (N × H)
4. C2×#16864058C2semidirect
5. C2×#16864057C2semidirect
6. C2×#16864053C2semidirect
7. C2×#16864043C2semidirect
8. C2×#16864042C2semidirect
9. C2×#16864039C2semidirect
10. C2×#16864037C2semidirect
11. C2×#16863969C2semidirect
12. C2×#16863962C2semidirect
13. C2×#16863943C2semidirect
14. C2×#124×D67C2semidirect
15. C2×C4×#11761629C2semidirect
16. C2×#548×C67C2semidirect
18. C2×#14524091C22semidirect
20. C2×#14524089C22semidirect
23. C22×#11761629C22semidirect
25. C22×#11761628C22semidirect
26. C22×#11761628C22semidirect
27. C22×Q8×D67C22semidirect
28. C22×Q8×D67C22semidirect
32. #16864058C22semidirect
33. #16864057C22semidirect
34. #16864053C22semidirect
35. #16864043C22semidirect
36. #16864042C22semidirect
37. #16864039C22semidirect
38. #16864037C22semidirect
39. #16863969C22semidirect
40. #16863962C22semidirect
41. #16863943C22semidirect
42. C2×#14524042C22semidirect
43. C2×#14524039C22semidirect
44. C2×#14524032C22semidirect
45. C2×#14524031C22semidirect
46. C2×#14524030C22semidirect
47. C2×#14524029C22semidirect
48. C2×#14524029C22semidirect
49. C2×#14524029C22semidirect
50. #124×D67C22semidirect
51. C2×#14524028C22semidirect
52. C2×#14524025C22semidirect
53. C2×#14524023C22semidirect
54. C2×#14524022C22semidirect
55. C2×#14524019C22semidirect
56. C2×#14524018C22semidirect
57. C2×#14524018C22semidirect
58. C2×#14524017C22semidirect
59. C2×#14524016C22semidirect
60. C2×#14524016C22semidirect
61. C2×#14524014C22semidirect
62. C2×#14524014C22semidirect
63. C2×#14524013C22semidirect
64. C2×#14524011C22semidirect
65. C4×#11761629C22semidirect
66. C2×Q8×Dic67C22semidirect
67. C2×C4×D268C22semidirect
68. C2×C4×D268C22semidirect
69. C2×#14524005C22semidirect
70. C2×C4×C22⋊D67C22semidirect
71. C2×C4×C22⋊D67C22semidirect
72. C2×#14524001C22semidirect
73. C2×C22⋊C4×D67C22semidirect
74. C2×C22⋊C4×D67C22semidirect
75. C2×C42×D67C22semidirect
77. C23×Q8×C67C22semidirect
78. #548×C67C22semidirect
79. C2×#124×C67C22semidirect
80. C2×C22⋊Q8×C67C22semidirect
81. C2×#121×C67C22semidirect
82. C2×C4×Q8×C67C22semidirect
83. C2×C4×D4×C67C22semidirect
89. C2×#11761629D4semidirect
92. C2×#11761629C23semidirect
97. C2×#11761628C23semidirect
98. C2×#11761628C23semidirect
104. C2×Q8×D67C23semidirect
105. C2×Q8×D67C23semidirect
129. #14524042C23semidirect
130. #14524039C23semidirect
131. #14524032C23semidirect
132. #14524031C23semidirect
133. #14524030C23semidirect
134. #14524029C23semidirect
135. #14524029C23semidirect
136. #14524029C23semidirect
137. #14524028C23semidirect
138. #14524025C23semidirect
139. #14524023C23semidirect
140. #14524022C23semidirect
141. #14524019C23semidirect
142. #14524018C23semidirect
143. #14524018C23semidirect
144. #14524017C23semidirect
145. #14524016C23semidirect
146. #14524016C23semidirect
147. #14524014C23semidirect
148. #14524014C23semidirect
149. #14524013C23semidirect
150. #14524011C23semidirect
151. Q8×Dic67C23semidirect
152. C4×D268C23semidirect
153. C4×D268C23semidirect
154. #14524005C23semidirect
155. C4×C22⋊D67C23semidirect
156. C4×C22⋊D67C23semidirect
157. #14524001C23semidirect
172. C22⋊C4×D67C23semidirect
173. C22⋊C4×D67C23semidirect
177. C42×D67C23semidirect
183. C22×Q8×C67C23semidirect
188. #124×C67C23semidirect
189. C22⋊Q8×C67C23semidirect
190. #121×C67C23semidirect
191. C4×Q8×C67C23semidirect
192. C4×D4×C67C23semidirect
208. #11761629C2×D4semidirect
415. C2×C67#3500semidirect
428. C2×#548D67semidirect
438. C67C2×#3500semidirect
452. C23×Q8C2×D67semidirect
459. #548C2×D67semidirect
476. C2×#124C2×D67semidirect
482. C2×C22⋊Q8C2×D67semidirect
490. C2×#121C2×D67semidirect
495. C2×C4×Q8C2×D67semidirect
501. C2×C4×D4C2×D67semidirect
533. C22×Q8C22×D67semidirect
569. #124C22×D67semidirect
575. C22⋊Q8C22×D67semidirect
583. #121C22×D67semidirect
587. C4×Q8C22×D67semidirect
593. C4×D4C22×D67semidirect
839. C2#22574000direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240912
C22×#145240892
#225740002
C2×#168640582
C2×#168640572
C2×#168640532
C2×#168640432
C2×#168640422
C2×#168640392
C2×#168640372
C2×#168639692
C2×#168639622
C2×#168639432
C2×#124×D672
C2×C4×#117616292
C2×#548×C672
C2×#350067