Finite Group Databasebeta

← C2×#22573859 #31763995

Subgroups — C2×#22573859 #31763995

Order 17152.

11254 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524091C211yesmaximal, characteristic, complemented
2C23×Q8×D67C211yesmaximal, characteristic, complemented
3#22573859C2132yesmaximal, direct product factor
4C2×#16864061C213yesmaximal, complemented
5C2×Q8×C22⋊D67C211yesmaximal, characteristic, complemented
6C2×#16864059C213yesmaximal, complemented
7C2×#16864058C211yesmaximal, characteristic, complemented
8C2×#16864057C211yesmaximal, characteristic, complemented
9C2×#16864056C213yesmaximal, complemented
10C2×#16864055C213yesmaximal, complemented
11C2×#16863971C213yesmaximal, complemented
12C2×#16863969C213yesmaximal, complemented
13C2×#16863909C213yesmaximal, complemented
14C2×#16863905C213yesmaximal, complemented
15C2×#16863872C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C67C211yesmaximal, characteristic, complemented
17C2×#14524091—216no—
18C2×#14524091C22116yescomplemented
19C22×#11761629C2213yes—
20C22×#11761629C2211yescharacteristic, complemented
21C22×#11761628C2213yes—
22C22×#11761628C2213yescomplemented
23C23×Dic134C2213yes—
24C22×Q8×D67—216no—
25C22×Q8×D67C2213yes—
26C22×Q8×D67C2211yescharacteristic
27C22×Q8×D67C2213yes—
28C22×Q8×D67C2211yescharacteristic
29C22×Q8×D67C22116yescomplemented
30C22×Q8×D67C2213yescomplemented
31C23×C4×D67C2213yes—
32#16864061C22148yescomplemented
33Q8×C22⋊D67C22116yescomplemented
34#16864059C22148yescomplemented
35#16864058C22116yescomplemented
36#16864057C22116yescomplemented
37#16864056C22148yescomplemented
38#16864055C22148yescomplemented
39#16863971C22148yescomplemented
40#16863969C22148yescomplemented
41C2×#14524042C2216yescomplemented
42C2×#14524041C2213yescomplemented
43C2×#14524032C2213yescomplemented
44C2×#14524031C2213yescomplemented
45C2×#14524029C2216yescomplemented
46#16863909C22148yescomplemented
47#16863905C22148yescomplemented
48C2×#14524028C2213yes—
49C2×#14524028C2216yes—
50C2×#14524025C2213yes—
51C2×#14524023C2213yescomplemented
52C2×#14524022C2213yescomplemented
53C2×#14524021C2213yes—
54C2×#14524021C2216yescomplemented
55C2×#14524021C2216yescomplemented
56C2×#14524020C2213yes—
57C2×#14524019C2213yes—
58C2×#14524019C2213yescomplemented
59C2×#14524018C2213yes—
60C2×#14524017C2213yes—
61C2×#14524016C2213yes—
62C2×#14524015C2213yes—
63C2×#14524013C2213yes—
64C2×#14524011C2211yescharacteristic
65#16863872C22116yescomplemented
66C2×Q8×Dic67C2211yescharacteristic, complemented
67C2×C4×Dic134C2213yescomplemented
68C2×#14524008C2213yescomplemented
69C2×C4×D268C2213yes—
70C2×#14524005C2216yes—
71C2×C4×C22⋊D67C2213yes—
72C2×C4×C22⋊D67C2213yes—
73C2×(C22⋊D67)⋊C4C2216yes—
74C2×#14524001C2213yes—
75C2×#14524000C2213yes—
76C23×Q8×C67C2211yescharacteristic
77C23×Q8×C67C2211yescharacteristic, complemented
78D4×Q8×C67C22116yescomplemented
79C2×C4⋊Q8×C67C2213yescomplemented
80C2×C22⋊Q8×C67C2213yes—
81C2×C22⋊Q8×C67C2213yescomplemented
82C2×C4×Q8×C67C2211yescharacteristic, complemented
83C2×C4×D4×C67C2213yes—
84C24×D67C2311yescharacteristic
85#14524091—2128no—
86C2×#11761629—224no—
87C2×#11761629—28no—
88C2×#11761629C23124yes—
89C2×#11761629C2318yescomplemented
90C2×#11761628—224no—
91C2×#11761628—224no—
92C2×#11761628C23124yes—
93C2×#11761628C23124yescomplemented
94C22×Dic134—224no—
95C22×Dic134C23124yes—
96C22×Dic134C2313yes—
97C22×Dic134C2316yes—
98C22×Dic134C2313yes—
99C22×Dic134C2313yes—
100C2×Q8×D67—224no—
101C2×Q8×D67—224no—
102C2×Q8×D67—2128no—
103C2×Q8×D67—224no—
104C2×Q8×D67—28no—
105C2×Q8×D67D4116yescomplemented
106C2×Q8×D67C23124yes—
107C2×Q8×D67C2318yes—
108C2×Q8×D67C23124yes—
109C2×Q8×D67C2318yes—
110C2×Q8×D67C23124yescomplemented
111C22×D268C2313yes—
112C22×D268C2313yes—
113C22×D268C2313yes—
114C22×C22⋊D67C2313yes—
115C22×C22⋊D67C2311yescharacteristic
116C22×C22⋊D67C2311yescharacteristic
117C22×C22⋊D67C2313yes—
118C23×Dic67C2313yes—
119C22×C4×D67—224no—
120C22×C4×D67C2316yes—
121C22×C4×D67C2313yes—
122C22×C4×D67C2313yes—
123C22×C4×D67C2313yes—
124C22×C4×D67C2313yes—
125C22×C4×D67C23124yes—
126C22×C4×D67C2313yes—
127#14524042C23148yescomplemented
128#14524041C23124yescomplemented
129#14524032C23124yescomplemented
130#14524031C23124yescomplemented
131#14524029C23148yescomplemented
132#14524028C23124yes—
133#14524028C23148yes—
134#14524025C23124yes—
135#14524023C23124yescomplemented
136#14524022C23124yescomplemented
137#14524021C23124yes—
138#14524021C23148yescomplemented
139#14524021C23148yescomplemented
140#14524020C23124yes—
141#14524019C23124yes—
142#14524019C23124yescomplemented
143#14524018C23124yes—
144#14524017C23124yes—
145#14524016C23124yes—
146#14524015C23124yes—
147#14524013C23124yes—
148#14524011C2318yes—
149Q8×Dic67C2318yescomplemented
150C4×Dic134C23124yescomplemented
151#14524008C23124yescomplemented
152C4×D268C23124yes—
153#14524005C23148yes—
154C4×C22⋊D67C23124yes—
155C4×C22⋊D67C23124yes—
156(C22⋊D67)⋊C4C23148yes—
157#14524001C23124yes—
158#14524000C23124yes—
159C2×C4⋊Dic67C2313yes—
160C2×C4⋊Dic67C2313yes—
161C2×Dic67⋊C4C2313yes—
162C2×Dic67⋊C4C2313yes—
163C2×Dic67⋊C4C2316yes—
164C2×Dic67⋊C4C2313yes—
165C2×Dic67⋊C4C2313yes—
166C2×C22⋊Dic67C2311yescharacteristic
167C2×C22⋊Dic67C2313yes—
168C2×(C2×D67)⋊C4C2311yescharacteristic
169C2×(C2×D67)⋊C4C2313yes—
170C2×(C2×D67)⋊C4C2316yes—
171C2×(C2×D67)⋊C4C2313yes—
172C2×(C2×D67)⋊C4C2313yes—
173C2×(C2×D67)⋊C4C2316yes—
174C2×(C2×D67)⋊C4C2311yescharacteristic
175C2×(C2×D67)⋊C4C2313yes—
176C2×C4×Dic67C2313yes—
177C2×C4×Dic67C2316yes—
178C22×Q8×C67—28no—
179C22×Q8×C67—28no—
180C22×Q8×C67C2318yes—
181C22×Q8×C67C2313yes—
182C22×Q8×C67C2313yes—
183C22×Q8×C67C2311yescharacteristic
184C22×Q8×C67C2318yescomplemented
185C22×D4×C67C2311yescharacteristic
186C23×C4×C67C2313yes—
187C23×C4×C67C2313yes—
188C4⋊Q8×C67C23124yescomplemented
189C22⋊Q8×C67C23124yes—
190C22⋊Q8×C67C23124yescomplemented
191C4×Q8×C67C2318yescomplemented
192C4×D4×C67C23124yes—
193C2×C4⋊C4×C67C2313yes—
194C2×C4⋊C4×C67C2313yes—
195C2×C4⋊C4×C67C2316yes—
196C2×C22⋊C4×C67C2313yes—
197C2×C22⋊C4×C67C2313yes—
198C2×C42×C67C2313yes—
199C23×D67—24no—
200C23×D67—24no—
201C23×D67—24no—
202C23×D67C2413yes—
203C23×D67C2414yes—
204C23×D67C2411yescharacteristic
205C23×D67C2411yescharacteristic
206#11761629—232no—
207#11761629—296no—
208#11761628—296no—
209#11761628—296no—
210C2×Dic134—212no—
211C2×Dic134—224no—
212C2×Dic134—212no—
213C2×Dic134—296no—
214C2×Dic134C2×D4124yes—
215C2×Dic134C24112yes—
216C2×Dic134C24124yes—
217C2×Dic134C24112yes—
218C2×Dic134C24112yes—
219Q8×D67—232no—
220Q8×D67—296no—
221Q8×D67—296no—
222Q8×D67—296no—
223Q8×D67C2×D4164yescomplemented
224C2×D268—212no—
225C2×D268—212no—
226C2×D268—212no—
227C2×D268C24112yes—
228C2×D268C24112yes—
229C2×D268C24112yes—
230C2×C22⋊D67—212no—
231C2×C22⋊D67—24no—
232C2×C22⋊D67—24no—
233C2×C22⋊D67—212no—
234C2×C22⋊D67C24112yes—
235C2×C22⋊D67C2414yes—
236C2×C22⋊D67C2414yes—
237C2×C22⋊D67C24112yes—
238C22×Dic67—212no—
239C22×Dic67C2411yescharacteristic
240C22×Dic67C2413yes—
241C22×Dic67C2413yes—
242C22×Dic67C2411yescharacteristic
243C22×Dic67C24112yes—
244C22×Dic67C2413yes—
245C2×C4×D67—212no—
246C2×C4×D67—212no—
247C2×C4×D67—212no—
248C2×C4×D67—212no—
249C2×C4×D67—224no—
250C2×C4×D67—296no—
251C2×C4×D67C2×D4124yes—
252C2×C4×D67C24124yes—
253C2×C4×D67C24112yes—
254C2×C4×D67C24112yes—
255C2×C4×D67C24112yes—
256C2×C4×D67C24112yes—
257C2×C4×D67C24112yes—
258C4⋊Dic67C24112yes—
259C4⋊Dic67C24112yes—
260Dic67⋊C4C24112yes—
261Dic67⋊C4C24112yes—
262Dic67⋊C4C24124yes—
263Dic67⋊C4C24112yes—
264Dic67⋊C4C24112yes—
265C22⋊Dic67C2414yes—
266C22⋊Dic67C24112yes—
267(C2×D67)⋊C4C2414yes—
268(C2×D67)⋊C4C24112yes—
269(C2×D67)⋊C4C24124yes—
270(C2×D67)⋊C4C24112yes—
271(C2×D67)⋊C4C24112yes—
272(C2×D67)⋊C4C24124yes—
273(C2×D67)⋊C4C2414yes—
274(C2×D67)⋊C4C24112yes—
275C4×Dic67C24112yes—
276C4×Dic67C24124yes—
277C24×C67C2411yescharacteristic
278C24×C67C2411yescharacteristic
279C2×Q8×C67—232no—
280C2×Q8×C67—232no—
281C2×Q8×C67—212no—
282C2×Q8×C67—212no—
283C2×Q8×C67C2×D418yes—
284C2×Q8×C67C24112yes—
285C2×Q8×C67C24112yes—
286C2×Q8×C67C2414yes—
287C2×D4×C67—24no—
288C2×D4×C67C2414yes—
289C22×C4×C67—212no—
290C22×C4×C67—212no—
291C22×C4×C67C2411yescharacteristic
292C22×C4×C67C2413yes—
293C22×C4×C67C2413yes—
294C22×C4×C67C2413yes—
295C22×C4×C67C24112yes—
296C22×C4×C67C24112yes—
297C22×C4×C67C2413yes—
298C4⋊C4×C67C24112yes—
299C4⋊C4×C67C24112yes—
300C4⋊C4×C67C24124yes—
301C22⋊C4×C67C24112yes—
302C22⋊C4×C67C24112yes—
303C42×C67C24112yes—
304C23×C67—22no—
305C23×C67—22no—
306C23×C67—22no—
307C23×C67—22no—
308C23×C67—22no—
309C23×C672−1+414yescomplemented
310C23×C67C2512yes—
311C23×C67C2512yes—
312C23×C67C2511yescharacteristic
313C22×D67—232no—
314C22×D67—22no—
315C22×D67—22no—
316C22×D67—22no—
317C22×D67—22no—
318C22×D67—28no—
319C22×D67—28no—
320C22×D67—28no—
321C22×D67—26no—
322C22×D67—26no—
323C22×D67—26no—
324C22×D67C22×D414yes—
325C22×D672−1+414yescomplemented
326C22×D67C2516yes—
327C22×D67C2512yes—
328C22×D67C2512yes—
329Q8×C67—224no—
330Q8×C67—224no—
331Q8×C67C22×D4116yes—
332D4×C67—28no—
333C2×C4×C67—26no—
334C2×C4×C67—26no—
335C2×C4×C67—22no—
336C2×C4×C67—26no—
337C2×C4×C67—224no—
338C2×C4×C67—224no—
339C2×C4×C67C22×D4112yes—
340C2×C4×C67C2512yes—
341C2×C4×C67C2516yes—
342C2×C4×C67C2516yes—
343C2×C4×C67C2516yes—
344C2×C4×C67C2516yes—
345C22⋊D67—224no—
346C22⋊D67—28no—
347C22⋊D67—28no—
348C22⋊D67—224no—
349C2×Dic67—22no—
350C2×Dic67—26no—
351C2×Dic67—22no—
352C2×Dic67—26no—
353C2×Dic67—224no—
354C2×Dic67C22×D4112yes—
355C2×Dic67C2512yes—
356C2×Dic67C2516yes—
357C2×Dic67C2516yes—
358C2×Dic67C2512yes—
359C2×Dic67C2516yes—
360D268—224no—
361D268—224no—
362D268—224no—
363C4×D67—224no—
364C4×D67—224no—
365C4×D67—224no—
366C4×D67—224no—
367C4×D67—248no—
368C4×D67C22×D4148yes—
369Dic134—224no—
370Dic134—248no—
371Dic134—224no—
372Dic134C22×D4148yes—
373C22×C67—22no—
374C22×C67—22no—
375C22×C67—28no—
376C22×C67—22no—
377C22×C67—22no—
378C22×C67—22no—
379C22×C67—44no—
380C22×C67C23×D412yes—
381C22×C67C2×2−1+412yes—
382C22×C67C2×2−1+412yes—
383C22×C67C2×2−1+414yescomplemented
384C22×C67C2611yescharacteristic
385C2×D67—232no—
386C2×D67—22no—
387C2×D67—22no—
388C2×D67—22no—
389C2×D67—22no—
390C2×D67—28no—
391C2×D67—28no—
392C2×D67—26no—
393C2×D67—26no—
394C2×D67—26no—
395C2×D67—412no—
396C2×D67C23×D414yes—
397C2×D67C2×2−1+414yescomplemented
398C4×C67—26no—
399C4×C67—26no—
400C4×C67—26no—
401C4×C67—22no—
402C4×C67C23×D4112yes—
403Dic67—26no—
404Dic67—22no—
405Dic67—22no—
406Dic67—26no—
407Dic67C23×D4112yes—
408C2×#3486—671nomaximal, Sylow
409C2×C67—24no—
410C2×C67—42no—
411C2×C67#348614yescomplemented
412C2×C67C24×D411yescharacteristic
413C2×C67C22×2−1+411yescharacteristic
414C2×C67C22×2−1+411yescharacteristic
415D67—24no—
416D67—24no—
417D67—46no—
418C22×2−1+4—671no—
419C24×Q8—671no—
420#3486—6732no—
421C2×D4×Q8—671no—
422C2×D4×Q8—673no—
423C2×D4×Q8—673no—
424C2×D4×Q8D6711yescharacteristic, complemented
425C2×#548—671no—
426C2×#548—673no—
427C2×#548—671no—
428C2×#548—673no—
429C2×#536—673no—
430C2×#536—673no—
431C2×#525—673no—
432C2×#525—673no—
433C2×#519—671no—
434C67C2×#348611yescharacteristic, complemented, Sylow
435C2×2−1+4—6716no—
436C2×2−1+4—13416no—
437C22×#41—673no—
438C22×#41—671no—
439C22×#41—673no—
440C22×#41—673no—
441C23×Q8—671no—
442C23×Q8—673no—
443C23×Q8—673no—
444C23×Q8—671no—
445C23×Q8—6716no—
446C23×Q8—673no—
447C23×Q8—673no—
448C23×Q8—13416no—
449C23×Q8C2×D6711yescharacteristic
450C23×Q8C2×D6711yescharacteristic, complemented
451C24×C4—673no—
452D4×Q8—6716no—
453D4×Q8—6748no—
454D4×Q8—6748no—
455D4×Q8C2×D67116yescomplemented
456#548—6716no—
457#548—6748no—
458#548—6716no—
459#548—6748no—
460#536—6748no—
461#536—6748no—
462C2×C4⋊Q8—673no—
463C2×C4⋊Q8—676no—
464C2×C4⋊Q8C2×D6713yescomplemented
465C2×#124—673no—
466C2×#124—676no—
467C2×#124—673no—
468#525—6748no—
469#525—6748no—
470C2×#123—676no—
471C2×#123—673no—
472C2×#123—673no—
473C2×C22⋊Q8—673no—
474C2×C22⋊Q8—673no—
475C2×C22⋊Q8—673no—
476C2×C22⋊Q8—673no—
477C2×C22⋊Q8—676no—
478C2×C22⋊Q8—676no—
479C2×C22⋊Q8—673no—
480C2×C22⋊Q8—673no—
481C2×C22⋊Q8C2×D6713yes—
482C2×C22⋊Q8C2×D6713yescomplemented
483C2×#121—673no—
484C2×#121—673no—
485C2×#121—673no—
486C2×#121—673no—
487C2×#120—671no—
488C2×#120—673no—
489#519—6716no—
490C2×C4×Q8—671no—
491C2×C4×Q8—673no—
492C2×C4×Q8—673no—
493C2×C4×Q8C2×D6711yescharacteristic, complemented
494C2×C4×D4—673no—
495C2×C4×D4—673no—
496C2×C4×D4—676no—
497C2×C4×D4—676no—
498C2×C4×D4—673no—
499C2×C4×D4C2×D6713yes—
500C2×#117—673no—
501C2×#117—673no—
502C25—671no—
5032−1+4—134128no—
504C2×#41—6724no—
505C2×#41—678no—
506C2×#41—6724no—
507C2×#41—6724no—
508C2×#41—13424no—
509C2×#41—13424no—
510C2×#41—13424no—
511C2×#41—1348no—
512C22×Q8—28no—
513C22×Q8—28no—
514C22×Q8—6716no—
515C22×Q8—678no—
516C22×Q8—6724no—
517C22×Q8—6724no—
518C22×Q8—678no—
519C22×Q8—6724no—
520C22×Q8—673no—
521C22×Q8—676no—
522C22×Q8—673no—
523C22×Q8—673no—
524C22×Q8—6724no—
525C22×Q8—13424no—
526C22×Q8—13424no—
527C22×Q8—134128no—
528C22×Q8—13424no—
529C22×Q8—13424no—
530C22×Q8—1348no—
531C22×Q8C22×D6713yes—
532C22×Q8C22×D6713yes—
533C22×Q8C22×D6718yes—
534C22×Q8C22×D6711yescharacteristic
535C22×Q8C22×D6718yescomplemented
536C22×D4—671no—
537C22×D4—673no—
538C22×D4—671no—
539C22×D4—673no—
540C22×D4—673no—
541C22×D4—673no—
542C22×D4—673no—
543C22×D4C22×D6711yescharacteristic
544C23×C4—673no—
545C23×C4—673no—
546C23×C4—673no—
547C23×C4—673no—
548C23×C4—676no—
549C23×C4—673no—
550C23×C4—673no—
551C23×C4—6724no—
552C23×C4—13424no—
553C23×C4C22×D6713yes—
554C23×C4C22×D6713yes—
555C4⋊Q8—6724no—
556C4⋊Q8—6748no—
557C4⋊Q8C22×D67124yescomplemented
558#124—6724no—
559#124—6748no—
560#124—6724no—
561#123—6748no—
562#123—6724no—
563#123—6724no—
564C22⋊Q8—6724no—
565C22⋊Q8—6724no—
566C22⋊Q8—6724no—
567C22⋊Q8—6724no—
568C22⋊Q8—6748no—
569C22⋊Q8—6748no—
570C22⋊Q8—6724no—
571C22⋊Q8—6724no—
572C22⋊Q8C22×D67124yes—
573C22⋊Q8C22×D67124yescomplemented
574#121—6724no—
575#121—6724no—
576#121—6724no—
577#121—6724no—
578#120—678no—
579#120—6724no—
580C4×Q8—678no—
581C4×Q8—6724no—
582C4×Q8—6724no—
583C4×Q8C22×D6718yescomplemented
584C4×D4—6724no—
585C4×D4—6724no—
586C4×D4—6748no—
587C4×D4—6748no—
588C4×D4—6724no—
589C4×D4C22×D67124yes—
590#117—6724no—
591#117—6724no—
592C2×C4⋊C4—673no—
593C2×C4⋊C4—673no—
594C2×C4⋊C4—673no—
595C2×C4⋊C4—673no—
596C2×C4⋊C4—676no—
597C2×C4⋊C4—673no—
598C2×C4⋊C4—673no—
599C2×C4⋊C4C22×D6713yes—
600C2×C4⋊C4C22×D6716yes—
601C2×C4⋊C4C22×D6713yes—
602C2×C22⋊C4—671no—
603C2×C22⋊C4—673no—
604C2×C22⋊C4—673no—
605C2×C22⋊C4—671no—
606C2×C22⋊C4—673no—
607C2×C22⋊C4—671no—
608C2×C22⋊C4—673no—
609C2×C22⋊C4—676no—
610C2×C22⋊C4—676no—
611C2×C22⋊C4—673no—
612C2×C22⋊C4C22×D6713yes—
613C2×C22⋊C4C22×D6713yes—
614C2×C42—676no—
615C2×C42—673no—
616C2×C42C22×D6713yes—
617C24—671no—
618C24—671no—
619C24—674no—
620C24—673no—
621C24—1344no—
622C24—1344no—
623C24—1344no—
624C24C23×D6711yescharacteristic
625C24C23×D6711yescharacteristic
626#41—13496no—
627#41—13496no—
628#41—13496no—
629#41—13432no—
630C2×Q8—232no—
631C2×Q8—232no—
632C2×Q8—212no—
633C2×Q8—212no—
634C2×Q8—6764no—
635C2×Q8—6724no—
636C2×Q8—6712no—
637C2×Q8—6724no—
638C2×Q8—6712no—
639C2×Q8—6712no—
640C2×Q8—13424no—
641C2×Q8—13412no—
642C2×Q8—13496no—
643C2×Q8—13496no—
644C2×Q8—13496no—
645C2×Q8—13496no—
646C2×Q8—13432no—
647C2×Q8—13412no—
648C2×Q8D4×D6718yes—
649C2×Q8C23×D67112yes—
650C2×Q8C23×D67112yes—
651C2×Q8C23×D6714yes—
652C2×D4—24no—
653C2×D4—674no—
654C2×D4—6712no—
655C2×D4—674no—
656C2×D4—6712no—
657C2×D4—6712no—
658C2×D4—6712no—
659C2×D4—6712no—
660C2×D4—13412no—
661C2×D4—13412no—
662C2×D4—13412no—
663C2×D4—1344no—
664C2×D4—1344no—
665C2×D4—13412no—
666C2×D4—13412no—
667C2×D4C23×D6714yes—
668C22×C4—212no—
669C22×C4—212no—
670C22×C4—673no—
671C22×C4—6724no—
672C22×C4—6712no—
673C22×C4—6712no—
674C22×C4—671no—
675C22×C4—673no—
676C22×C4—673no—
677C22×C4—671no—
678C22×C4—6712no—
679C22×C4—6712no—
680C22×C4—6724no—
681C22×C4—6712no—
682C22×C4—6712no—
683C22×C4—13412no—
684C22×C4—13496no—
685C22×C4—13424no—
686C22×C4—13412no—
687C22×C4—13412no—
688C22×C4—13412no—
689C22×C4—13412no—
690C22×C4C23×D67112yes—
691C22×C4C23×D67112yes—
692C22×C4C23×D6713yes—
693C22×C4C23×D6711yescharacteristic
694C22×C4C23×D6713yes—
695C22×C4C23×D6713yes—
696C22×C4C23×D6713yes—
697C4⋊C4—6712no—
698C4⋊C4—6712no—
699C4⋊C4—6712no—
700C4⋊C4—6712no—
701C4⋊C4—6724no—
702C4⋊C4—6712no—
703C4⋊C4—6712no—
704C4⋊C4C23×D67112yes—
705C4⋊C4C23×D67124yes—
706C4⋊C4C23×D67112yes—
707C22⋊C4—674no—
708C22⋊C4—6712no—
709C22⋊C4—6712no—
710C22⋊C4—674no—
711C22⋊C4—6712no—
712C22⋊C4—674no—
713C22⋊C4—6712no—
714C22⋊C4—6724no—
715C22⋊C4—6724no—
716C22⋊C4—6712no—
717C22⋊C4C23×D67112yes—
718C22⋊C4C23×D67112yes—
719C42—6724no—
720C42—6712no—
721C42C23×D67112yes—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—674no—
728C23—674no—
729C23—672no—
730C23—672no—
731C23—676no—
732C23—1348no—
733C23—1348no—
734C23—13432no—
735C23—1346no—
736C23—1346no—
737C23—1346no—
738C23—1342no—
739C23—1342no—
740C23—1342no—
741C23—1342no—
742C23—1348no—
743C23#1452409114yescomplemented
744C23C24×D6712yes—
745C23C24×D6712yes—
746C23C24×D6711yescharacteristic
747Q8—224no—
748Q8—224no—
749Q8—6748no—
750Q8—13448no—
751Q8—13424no—
752Q8—13424no—
753Q8C2×D4×D67116yes—
754D4—28no—
755D4—13424no—
756D4—13424no—
757D4—13424no—
758D4—1348no—
759D4—1348no—
760D4—13424no—
761D4—13424no—
762C2×C4—26no—
763C2×C4—26no—
764C2×C4—26no—
765C2×C4—22no—
766C2×C4—224no—
767C2×C4—224no—
768C2×C4—6712no—
769C2×C4—676no—
770C2×C4—6748no—
771C2×C4—672no—
772C2×C4—676no—
773C2×C4—676no—
774C2×C4—672no—
775C2×C4—13424no—
776C2×C4—13448no—
777C2×C4—13424no—
778C2×C4—13424no—
779C2×C4—1342no—
780C2×C4—1346no—
781C2×C4—1342no—
782C2×C4—1346no—
783C2×C4—13424no—
784C2×C4—13424no—
785C2×C4C2×D4×D67112yes—
786C2×C4C24×D6716yes—
787C2×C4C24×D6712yes—
788C2×C4C24×D6716yes—
789C2×C4C24×D6716yes—
790C2×C4C24×D6716yes—
791C22—28no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—44no—
798C22—26812no—
799C22—674no—
800C22—674no—
801C22—13432no—
802C22—1346no—
803C22—1346no—
804C22—1346no—
805C22—1348no—
806C22—1348no—
807C22—1342no—
808C22—1342no—
809C22—1342no—
810C22—1342no—
811C22C22×D4×D6712yes—
812C222−1+4×D6712yes—
813C22C2×#1452409112yes—
814C22C2×#1452409114yescomplemented
815C22C25×D6711yescharacteristic
816C4—26no—
817C4—26no—
818C4—26no—
819C4—22no—
820C4—6712no—
821C4—1342no—
822C4—1346no—
823C4—1342no—
824C4—1346no—
825C4C22×D4×D67112yes—
826C2—24no—
827C2—42no—
828C2—2686no—
829C2—1344no—
830C2—1344no—
831C2#2257385914yesdirect product factor
832C2C23×D4×D6711yescharacteristic
833C2C2×2−1+4×D6711yescharacteristic
834C2C22×#1452409111yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×D4×Q8×C67C2
socleC23×C67C25
hypercenterC2×D4×Q8D67
hypocenterC67C2×#3486
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14524091C2semidirect
2. C23×Q8×D67C2semidirect
3. #22573859C2direct (N × H)
4. C2×#16864061C2semidirect
5. C2×Q8×C22⋊D67C2semidirect
6. C2×#16864059C2semidirect
7. C2×#16864058C2semidirect
8. C2×#16864057C2semidirect
9. C2×#16864056C2semidirect
10. C2×#16864055C2semidirect
11. C2×#16863971C2semidirect
12. C2×#16863969C2semidirect
13. C2×#16863909C2semidirect
14. C2×#16863905C2semidirect
15. C2×#16863872C2semidirect
16. C2×D4×Q8×C67C2semidirect
18. C2×#14524091C22semidirect
20. C22×#11761629C22semidirect
22. C22×#11761628C22semidirect
29. C22×Q8×D67C22semidirect
30. C22×Q8×D67C22semidirect
32. #16864061C22semidirect
33. Q8×C22⋊D67C22semidirect
34. #16864059C22semidirect
35. #16864058C22semidirect
36. #16864057C22semidirect
37. #16864056C22semidirect
38. #16864055C22semidirect
39. #16863971C22semidirect
40. #16863969C22semidirect
41. C2×#14524042C22semidirect
42. C2×#14524041C22semidirect
43. C2×#14524032C22semidirect
44. C2×#14524031C22semidirect
45. C2×#14524029C22semidirect
46. #16863909C22semidirect
47. #16863905C22semidirect
51. C2×#14524023C22semidirect
52. C2×#14524022C22semidirect
54. C2×#14524021C22semidirect
55. C2×#14524021C22semidirect
58. C2×#14524019C22semidirect
65. #16863872C22semidirect
66. C2×Q8×Dic67C22semidirect
67. C2×C4×Dic134C22semidirect
68. C2×#14524008C22semidirect
77. C23×Q8×C67C22semidirect
78. D4×Q8×C67C22semidirect
79. C2×C4⋊Q8×C67C22semidirect
81. C2×C22⋊Q8×C67C22semidirect
82. C2×C4×Q8×C67C22semidirect
89. C2×#11761629C23semidirect
93. C2×#11761628C23semidirect
105. C2×Q8×D67D4semidirect
110. C2×Q8×D67C23semidirect
127. #14524042C23semidirect
128. #14524041C23semidirect
129. #14524032C23semidirect
130. #14524031C23semidirect
131. #14524029C23semidirect
135. #14524023C23semidirect
136. #14524022C23semidirect
138. #14524021C23semidirect
139. #14524021C23semidirect
142. #14524019C23semidirect
149. Q8×Dic67C23semidirect
150. C4×Dic134C23semidirect
151. #14524008C23semidirect
184. C22×Q8×C67C23semidirect
188. C4⋊Q8×C67C23semidirect
190. C22⋊Q8×C67C23semidirect
191. C4×Q8×C67C23semidirect
223. Q8×D67C2×D4semidirect
309. C23×C672−1+4semidirect
325. C22×D672−1+4semidirect
383. C22×C67C2×2−1+4semidirect
397. C2×D67C2×2−1+4semidirect
411. C2×C67#3486semidirect
424. C2×D4×Q8D67semidirect
434. C67C2×#3486semidirect
450. C23×Q8C2×D67semidirect
455. D4×Q8C2×D67semidirect
464. C2×C4⋊Q8C2×D67semidirect
482. C2×C22⋊Q8C2×D67semidirect
493. C2×C4×Q8C2×D67semidirect
535. C22×Q8C22×D67semidirect
557. C4⋊Q8C22×D67semidirect
573. C22⋊Q8C22×D67semidirect
583. C4×Q8C22×D67semidirect
743. C23#14524091semidirect
814. C22C2×#14524091semidirect
831. C2#22573859direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240912
C23×Q8×D672
#225738592
C2×#168640612
C2×Q8×C22⋊D672
C2×#168640592
C2×#168640582
C2×#168640572
C2×#168640562
C2×#168640552
C2×#168639712
C2×#168639692
C2×#168639092
C2×#168639052
C2×#168638722
C2×D4×Q8×C672
C2×#348667