Finite Group Databasebeta

← C2×#22573886 #31764231

Subgroups — C2×#22573886 #31764231

Order 17152.

11438 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524091C211yesmaximal, characteristic, complemented
2C23×#11761629C211yesmaximal, characteristic, complemented
3#22573886C2132yesmaximal, direct product factor
4C2×Q8×C22⋊D67C211yesmaximal, characteristic, complemented
5C2×#16864058C211yesmaximal, characteristic, complemented
6C2×#16864057C211yesmaximal, characteristic, complemented
7C2×#16864049C213yesmaximal, complemented
8C2×#16864048C213yesmaximal, complemented
9C2×#16864042C213yesmaximal, complemented
10C2×#16864037C213yesmaximal, complemented
11C2×#16863976C213yesmaximal, complemented
12C2×#16863971C213yesmaximal, complemented
13C2×#16863905C213yesmaximal, complemented
14C2×C22⋊Q8×D67C213yesmaximal, complemented
15C2×#16863878C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C67C211yesmaximal, characteristic, complemented
17C2×#14524091—216no—
18C2×#14524091C22116yescomplemented
19C22×#11761629—216no—
20C22×#11761629C2213yes—
21C22×#11761629C2211yescharacteristic
22C22×#11761629C2213yes—
23C22×#11761629C2211yescharacteristic
24C22×#11761629C22116yescomplemented
25C22×#11761629C2213yescomplemented
26C22×#11761628C2213yescomplemented
27C22×#11761628C2213yescomplemented
28C22×Q8×D67C2211yescharacteristic, complemented
29C22×Q8×D67C2213yescomplemented
30C23×D268C2213yes—
31C23×C4×D67C2213yes—
32Q8×C22⋊D67C22116yescomplemented
33#16864058C22116yescomplemented
34#16864057C22116yescomplemented
35#16864049C22148yescomplemented
36#16864048C22148yescomplemented
37#16864042C22148yescomplemented
38#16864037C22148yescomplemented
39#16863976C22148yescomplemented
40#16863971C22148yescomplemented
41C2×#14524041C2213yescomplemented
42C2×#14524032C2213yescomplemented
43C2×#14524031C2213yescomplemented
44#16863905C22148yescomplemented
45C2×#14524028C2216yescomplemented
46C2×#14524028C2216yescomplemented
47C2×#14524028C2213yescomplemented
48C2×#14524025C2213yescomplemented
49C2×#14524023C2213yescomplemented
50C2×#14524022C2213yes—
51C2×#14524021C2216yescomplemented
52C2×#14524021C2213yescomplemented
53C2×#14524020C2213yes—
54C2×#14524019C2213yescomplemented
55C2×#14524019C2213yescomplemented
56C22⋊Q8×D67C22148yescomplemented
57C2×#14524018C2216yescomplemented
58C2×#14524018C2213yescomplemented
59C2×#14524017C2213yescomplemented
60C2×#14524016C2216yescomplemented
61C2×#14524016C2213yescomplemented
62C2×#14524015C2211yescharacteristic
63C2×#14524013C2213yes—
64C2×#14524011C2213yes—
65#16863878C22116yescomplemented
66C2×Q8×Dic67C2211yescharacteristic, complemented
67C2×C4×D268C2213yescomplemented
68C2×C4×D268C2213yescomplemented
69C2×#14524005C2213yescomplemented
70C2×C4×C22⋊D67C2213yes—
71C2×C4×C22⋊D67C2213yescomplemented
72C2×#14524000C2213yescomplemented
73C2×C4⋊C4×D67C2213yescomplemented
74C2×C4⋊C4×D67C2216yescomplemented
75C2×C22⋊C4×D67C2216yes—
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×D67C2313yes—
85#14524091—2128no—
86C2×#11761629—2128no—
87C2×#11761629—224no—
88C2×#11761629—224no—
89C2×#11761629—224no—
90C2×#11761629—28no—
91C2×#11761629D4116yescomplemented
92C2×#11761629C23124yes—
93C2×#11761629C2318yes—
94C2×#11761629C23124yes—
95C2×#11761629C2318yes—
96C2×#11761629C23124yescomplemented
97C2×#11761628—224no—
98C2×#11761628—224no—
99C2×#11761628C23124yescomplemented
100C2×#11761628C23124yescomplemented
101C22×Dic134C2313yes—
102C22×Dic134C2313yes—
103C2×Q8×D67—224no—
104C2×Q8×D67—28no—
105C2×Q8×D67C2318yescomplemented
106C2×Q8×D67C23124yescomplemented
107C22×D268—224no—
108C22×D268C23124yes—
109C22×D268C2313yes—
110C22×D268C2316yes—
111C22×D268C2313yes—
112C22×D268C2313yes—
113C22×D268C2313yes—
114C22×C22⋊D67C2311yescharacteristic
115C22×C22⋊D67C2313yes—
116C22×C22⋊D67C2311yescharacteristic
117C22×C22⋊D67C2313yes—
118C23×Dic67C2311yescharacteristic
119C22×C4×D67—224no—
120C22×C4×D67C2316yes—
121C22×C4×D67C2313yes—
122C22×C4×D67C2313yes—
123C22×C4×D67C2313yes—
124C22×C4×D67C2313yes—
125C22×C4×D67C23124yes—
126C22×C4×D67C2316yes—
127C22×C4×D67C2313yes—
128#14524041C23124yescomplemented
129#14524032C23124yescomplemented
130#14524031C23124yescomplemented
131#14524028C23148yescomplemented
132#14524028C23148yescomplemented
133#14524028C23124yescomplemented
134#14524025C23124yescomplemented
135#14524023C23124yescomplemented
136#14524022C23124yes—
137#14524021C23148yescomplemented
138#14524021C23124yescomplemented
139#14524020C23124yes—
140#14524019C23124yescomplemented
141#14524019C23124yescomplemented
142#14524018C23148yescomplemented
143#14524018C23124yescomplemented
144#14524017C23124yescomplemented
145#14524016C23148yescomplemented
146#14524016C23124yescomplemented
147#14524015C2318yes—
148#14524013C23124yes—
149#14524011C23124yes—
150Q8×Dic67C2318yescomplemented
151C4×D268C23124yescomplemented
152C4×D268C23124yescomplemented
153#14524005C23124yescomplemented
154C4×C22⋊D67C23124yes—
155C4×C22⋊D67C23124yescomplemented
156#14524000C23124yescomplemented
157C2×C4⋊Dic67C2313yes—
158C2×C4⋊Dic67C2313yes—
159C2×Dic67⋊C4C2313yes—
160C2×Dic67⋊C4C2313yes—
161C2×Dic67⋊C4C2316yes—
162C2×Dic67⋊C4C2311yescharacteristic
163C2×Dic67⋊C4C2313yes—
164C4⋊C4×D67C23148yescomplemented
165C4⋊C4×D67C23124yescomplemented
166C2×C22⋊Dic67C2313yes—
167C2×C22⋊Dic67C2311yescharacteristic
168C2×(C2×D67)⋊C4C2316yes—
169C2×(C2×D67)⋊C4C2316yes—
170C2×(C2×D67)⋊C4C2313yes—
171C2×(C2×D67)⋊C4C2313yes—
172C2×(C2×D67)⋊C4C2313yes—
173C2×(C2×D67)⋊C4C2313yes—
174C2×(C2×D67)⋊C4C2311yescharacteristic
175C2×(C2×D67)⋊C4C2313yes—
176C22⋊C4×D67C23148yes—
177C2×C4×Dic67C2313yes—
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—212no—
200C23×D67—212no—
201C23×D67—46no—
202C23×D67C2413yes—
203C23×D67C2411yescharacteristic
204C23×D67C24112yes—
205C23×D67C2413yes—
206#11761629—232no—
207#11761629—296no—
208#11761629—296no—
209#11761629—296no—
210#11761629C2×D4164yescomplemented
211#11761628—296no—
212#11761628—296no—
213C2×Dic134—212no—
214C2×Dic134—212no—
215C2×Dic134C24112yes—
216C2×Dic134C24112yes—
217Q8×D67—232no—
218Q8×D67—296no—
219C2×D268—224no—
220C2×D268—212no—
221C2×D268—212no—
222C2×D268—296no—
223C2×D268—46no—
224C2×D268C2×D4124yes—
225C2×D268C24112yes—
226C2×D268C24124yes—
227C2×D268C24112yes—
228C2×D268C24112yes—
229C2×D268C24112yes—
230C2×C22⋊D67—24no—
231C2×C22⋊D67—212no—
232C2×C22⋊D67—24no—
233C2×C22⋊D67—46no—
234C2×C22⋊D67C2414yes—
235C2×C22⋊D67C24112yes—
236C2×C22⋊D67C2414yes—
237C2×C22⋊D67C24112yes—
238C22×Dic67—24no—
239C22×Dic67C2411yescharacteristic
240C22×Dic67C2413yes—
241C22×Dic67C2413yes—
242C22×Dic67C2411yescharacteristic
243C22×Dic67C2414yes—
244C22×Dic67C2411yescharacteristic
245C2×C4×D67—212no—
246C2×C4×D67—224no—
247C2×C4×D67—212no—
248C2×C4×D67—212no—
249C2×C4×D67—212no—
250C2×C4×D67—296no—
251C2×C4×D67—412no—
252C2×C4×D67C2×D4124yes—
253C2×C4×D67C24124yes—
254C2×C4×D67C24112yes—
255C2×C4×D67C24112yes—
256C2×C4×D67C24112yes—
257C2×C4×D67C24112yes—
258C2×C4×D67C24124yes—
259C2×C4×D67C24112yes—
260C4⋊Dic67C24112yes—
261C4⋊Dic67C24112yes—
262Dic67⋊C4C24112yes—
263Dic67⋊C4C24112yes—
264Dic67⋊C4C24124yes—
265Dic67⋊C4C2414yes—
266Dic67⋊C4C24112yes—
267C22⋊Dic67C24112yes—
268C22⋊Dic67C2414yes—
269(C2×D67)⋊C4C24124yes—
270(C2×D67)⋊C4C24124yes—
271(C2×D67)⋊C4C24112yes—
272(C2×D67)⋊C4C24112yes—
273(C2×D67)⋊C4C24112yes—
274(C2×D67)⋊C4C24112yes—
275(C2×D67)⋊C4C2414yes—
276(C2×D67)⋊C4C24112yes—
277C4×Dic67C24112yes—
278C24×C67C2411yescharacteristic
279C24×C67C2411yescharacteristic
280C2×Q8×C67—232no—
281C2×Q8×C67—232no—
282C2×Q8×C67—212no—
283C2×Q8×C67—212no—
284C2×Q8×C67C2×D418yes—
285C2×Q8×C67C24112yes—
286C2×Q8×C67C24112yes—
287C2×Q8×C67C2414yes—
288C2×D4×C67—24no—
289C2×D4×C67C2414yes—
290C22×C4×C67—212no—
291C22×C4×C67—212no—
292C22×C4×C67C2411yescharacteristic
293C22×C4×C67C2413yes—
294C22×C4×C67C2413yes—
295C22×C4×C67C2413yes—
296C22×C4×C67C24112yes—
297C22×C4×C67C24112yes—
298C22×C4×C67C2413yes—
299C4⋊C4×C67C24112yes—
300C4⋊C4×C67C24112yes—
301C4⋊C4×C67C24124yes—
302C22⋊C4×C67C24112yes—
303C22⋊C4×C67C24112yes—
304C42×C67C24112yes—
305C23×C67—22no—
306C23×C67—22no—
307C23×C67—22no—
308C23×C67—22no—
309C23×C67—22no—
310C23×C672−1+414yescomplemented
311C23×C67C2512yes—
312C23×C67C2512yes—
313C23×C67C2511yescharacteristic
314C22×D67—26no—
315C22×D67—26no—
316C22×D67—22no—
317C22×D67—26no—
318C22×D67—22no—
319C22×D67—26no—
320C22×D67—224no—
321C22×D67—26no—
322C22×D67—22no—
323C22×D67—224no—
324C22×D67—412no—
325C22×D67—448no—
326C22×D67C22×D4112yes—
327C22×D67C2516yes—
328C22×D67C2512yes—
329C22×D67C2516yes—
330Q8×C67—224no—
331Q8×C67—224no—
332Q8×C67C22×D4116yes—
333D4×C67—28no—
334C2×C4×C67—26no—
335C2×C4×C67—26no—
336C2×C4×C67—22no—
337C2×C4×C67—26no—
338C2×C4×C67—224no—
339C2×C4×C67—224no—
340C2×C4×C67C22×D4112yes—
341C2×C4×C67C2512yes—
342C2×C4×C67C2516yes—
343C2×C4×C67C2516yes—
344C2×C4×C67C2516yes—
345C2×C4×C67C2516yes—
346C22⋊D67—28no—
347C22⋊D67—224no—
348C22⋊D67—28no—
349C22⋊D67—412no—
350C2×Dic67—22no—
351C2×Dic67—26no—
352C2×Dic67—22no—
353C2×Dic67—26no—
354C2×Dic67—28no—
355C2×Dic67C22×D414yes—
356C2×Dic67C2512yes—
357C2×Dic67C2516yes—
358C2×Dic67C2516yes—
359C2×Dic67C2512yes—
360C2×Dic67C2512yes—
361D268—248no—
362D268—224no—
363D268—224no—
364D268—412no—
365D268C22×D4148yes—
366C4×D67—224no—
367C4×D67—248no—
368C4×D67—224no—
369C4×D67—224no—
370C4×D67—224no—
371C4×D67—424no—
372C4×D67C22×D4148yes—
373Dic134—224no—
374Dic134—224no—
375C22×C67—22no—
376C22×C67—22no—
377C22×C67—28no—
378C22×C67—22no—
379C22×C67—22no—
380C22×C67—22no—
381C22×C67—44no—
382C22×C67C23×D412yes—
383C22×C67C2×2−1+412yes—
384C22×C67C2×2−1+414yescomplemented
385C22×C67#58512yes—
386C22×C67C2611yescharacteristic
387C2×D67—26no—
388C2×D67—26no—
389C2×D67—224no—
390C2×D67—22no—
391C2×D67—26no—
392C2×D67—22no—
393C2×D67—26no—
394C2×D67—22no—
395C2×D67—26no—
396C2×D67—448no—
397C2×D67—44no—
398C2×D67—412no—
399C2×D67C23×D4112yes—
400C4×C67—26no—
401C4×C67—26no—
402C4×C67—22no—
403C4×C67—26no—
404C4×C67C23×D4112yes—
405Dic67—26no—
406Dic67—22no—
407Dic67—22no—
408Dic67—26no—
409Dic67C23×D414yes—
410C2×#3489—671nomaximal, Sylow
411C2×C67—24no—
412C2×C67—42no—
413C2×C67#348914yescomplemented
414C2×C67C24×D411yescharacteristic
415C2×C67C22×2−1+411yescharacteristic
416C2×C67C2×#58511yescharacteristic
417D67—212no—
418D67—42no—
419D67—46no—
420C22×2−1+4—671no—
421C23×#41—671no—
422#3489—6732no—
423C2×D4×Q8—671no—
424C2×D4×Q8D6711yescharacteristic, complemented
425C2×#548—671no—
426C2×#548—671no—
427C2×#547—673no—
428C2×#547—673no—
429C2×#546—673no—
430C2×#546—673no—
431C2×#537—673no—
432C2×#536—673no—
433C2×#525—673no—
434C22×C22⋊Q8—673no—
435C2×#520—671no—
436C67C2×#348911yescharacteristic, complemented, Sylow
437C2×2−1+4—6716no—
438C2×2−1+4—13416no—
439C22×#41—671no—
440C22×#41—673no—
441C22×#41—673no—
442C22×#41—671no—
443C22×#41—6716no—
444C22×#41—673no—
445C22×#41—673no—
446C22×#41—673no—
447C22×#41—13416no—
448C23×Q8—673no—
449C23×Q8—671no—
450C23×Q8C2×D6711yescharacteristic
451C23×Q8C2×D6711yescharacteristic, complemented
452C23×D4—673no—
453C24×C4—673no—
454D4×Q8—6716no—
455D4×Q8C2×D67116yescomplemented
456#548—6716no—
457#548—6716no—
458#547—6748no—
459#547—6748no—
460#546—6748no—
461#546—6748no—
462#537—6748no—
463#536—6748no—
464C2×C4⋊Q8—673no—
465C2×C4⋊Q8C2×D6713yescomplemented
466C2×#124—673no—
467C2×#124—673no—
468#525—6748no—
469C2×#123—673no—
470C2×#123—676no—
471C2×#123—676no—
472C2×#123—673no—
473C2×C22⋊Q8—673no—
474C2×C22⋊Q8—673no—
475C2×C22⋊Q8—673no—
476C2×C22⋊Q8—6748no—
477C2×C22⋊Q8—676no—
478C2×C22⋊Q8—673no—
479C2×C22⋊Q8—673no—
480C2×C22⋊Q8—673no—
481C2×C22⋊Q8C2×D6713yes—
482C2×C22⋊Q8C2×D6713yescomplemented
483C2×#121—671no—
484C2×#121—673no—
485C2×#121—676no—
486C2×#121—673no—
487C2×#121—673no—
488C2×#121—676no—
489C2×#120—673no—
490C2×#120—673no—
491#520—6716no—
492C2×C4×Q8—671no—
493C2×C4×Q8C2×D6711yescharacteristic, complemented
494C2×C4×D4—673no—
495C2×C4×D4—673no—
496C2×C4×D4—673no—
497C2×C4×D4—673no—
498C2×C4×D4—673no—
499C2×C4×D4C2×D6713yes—
500C2×#117—673no—
501C22×C4⋊C4—673no—
502C22×C4⋊C4—676no—
503C22×C22⋊C4—676no—
504C25—673no—
5052−1+4—134128no—
506C2×#41—6716no—
507C2×#41—678no—
508C2×#41—6724no—
509C2×#41—6724no—
510C2×#41—6724no—
511C2×#41—678no—
512C2×#41—6724no—
513C2×#41—6724no—
514C2×#41—13424no—
515C2×#41—13424no—
516C2×#41—13424no—
517C2×#41—13424no—
518C2×#41—13424no—
519C2×#41—134128no—
520C2×#41—1348no—
521C22×Q8—28no—
522C22×Q8—28no—
523C22×Q8—6724no—
524C22×Q8—678no—
525C22×Q8—673no—
526C22×Q8—673no—
527C22×Q8—13424no—
528C22×Q8—1348no—
529C22×Q8C22×D6713yes—
530C22×Q8C22×D6713yes—
531C22×Q8C22×D6718yes—
532C22×Q8C22×D6711yescharacteristic
533C22×Q8C22×D6718yescomplemented
534C22×D4—673no—
535C22×D4—671no—
536C22×D4—673no—
537C22×D4—671no—
538C22×D4—673no—
539C22×D4—673no—
540C22×D4—673no—
541C22×D4—676no—
542C22×D4—673no—
543C22×D4—6724no—
544C22×D4—13424no—
545C22×D4C22×D6711yescharacteristic
546C23×C4—676no—
547C23×C4—673no—
548C23×C4—671no—
549C23×C4—676no—
550C23×C4—673no—
551C23×C4—673no—
552C23×C4—673no—
553C23×C4—673no—
554C23×C4—6724no—
555C23×C4—13424no—
556C23×C4C22×D6713yes—
557C23×C4C22×D6713yes—
558C4⋊Q8—6724no—
559C4⋊Q8C22×D67124yescomplemented
560#124—6724no—
561#124—6724no—
562#123—6724no—
563#123—6748no—
564#123—6748no—
565#123—6724no—
566C22⋊Q8—6724no—
567C22⋊Q8—6724no—
568C22⋊Q8—6724no—
569C22⋊Q8—6748no—
570C22⋊Q8—6724no—
571C22⋊Q8—6724no—
572C22⋊Q8—6724no—
573C22⋊Q8C22×D67124yes—
574C22⋊Q8C22×D67124yescomplemented
575#121—678no—
576#121—6724no—
577#121—6748no—
578#121—6724no—
579#121—6724no—
580#121—6748no—
581#120—6724no—
582#120—6724no—
583C4×Q8—678no—
584C4×Q8C22×D6718yescomplemented
585C4×D4—6724no—
586C4×D4—6724no—
587C4×D4—6724no—
588C4×D4—6724no—
589C4×D4—6724no—
590C4×D4C22×D67124yes—
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—671no—
598C2×C4⋊C4—673no—
599C2×C4⋊C4—6724no—
600C2×C4⋊C4—6748no—
601C2×C4⋊C4C22×D6713yes—
602C2×C4⋊C4C22×D6716yes—
603C2×C4⋊C4C22×D6713yes—
604C2×C22⋊C4—673no—
605C2×C22⋊C4—671no—
606C2×C22⋊C4—676no—
607C2×C22⋊C4—676no—
608C2×C22⋊C4—673no—
609C2×C22⋊C4—673no—
610C2×C22⋊C4—671no—
611C2×C22⋊C4—673no—
612C2×C22⋊C4—673no—
613C2×C22⋊C4—673no—
614C2×C22⋊C4—6748no—
615C2×C22⋊C4C22×D6713yes—
616C2×C22⋊C4C22×D6713yes—
617C2×C42—673no—
618C2×C42C22×D6713yes—
619C24—2686no—
620C24—6712no—
621C24—673no—
622C24—673no—
623C24—671no—
624C24—13412no—
625C24—13412no—
626C24C23×D6711yescharacteristic
627C24C23×D6711yescharacteristic
628#41—6764no—
629#41—13496no—
630#41—13496no—
631#41—13496no—
632#41—13496no—
633#41—13496no—
634#41—13432no—
635C2×Q8—232no—
636C2×Q8—232no—
637C2×Q8—212no—
638C2×Q8—212no—
639C2×Q8—6712no—
640C2×Q8—6712no—
641C2×Q8—13412no—
642C2×Q8—13496no—
643C2×Q8—13432no—
644C2×Q8—13412no—
645C2×Q8D4×D6718yes—
646C2×Q8C23×D67112yes—
647C2×Q8C23×D67112yes—
648C2×Q8C23×D6714yes—
649C2×D4—24no—
650C2×D4—2686no—
651C2×D4—2686no—
652C2×D4—6712no—
653C2×D4—674no—
654C2×D4—6712no—
655C2×D4—674no—
656C2×D4—6724no—
657C2×D4—6712no—
658C2×D4—6712no—
659C2×D4—6712no—
660C2×D4—6724no—
661C2×D4—6712no—
662C2×D4—13496no—
663C2×D4—13424no—
664C2×D4—13412no—
665C2×D4—1344no—
666C2×D4—13412no—
667C2×D4—1344no—
668C2×D4—13412no—
669C2×D4C23×D6714yes—
670C22×C4—212no—
671C22×C4—212no—
672C22×C4—26812no—
673C22×C4—6724no—
674C22×C4—671no—
675C22×C4—6724no—
676C22×C4—6712no—
677C22×C4—674no—
678C22×C4—671no—
679C22×C4—673no—
680C22×C4—673no—
681C22×C4—671no—
682C22×C4—6724no—
683C22×C4—6712no—
684C22×C4—6712no—
685C22×C4—6712no—
686C22×C4—6712no—
687C22×C4—13412no—
688C22×C4—13496no—
689C22×C4—13412no—
690C22×C4—13424no—
691C22×C4—1344no—
692C22×C4—13412no—
693C22×C4—13412no—
694C22×C4C23×D67112yes—
695C22×C4C23×D67112yes—
696C22×C4C23×D6711yescharacteristic
697C22×C4C23×D6713yes—
698C22×C4C23×D6713yes—
699C22×C4C23×D6713yes—
700C22×C4C23×D6713yes—
701C4⋊C4—6712no—
702C4⋊C4—6712no—
703C4⋊C4—6712no—
704C4⋊C4—6712no—
705C4⋊C4—6724no—
706C4⋊C4—674no—
707C4⋊C4—6712no—
708C4⋊C4C23×D67112yes—
709C4⋊C4C23×D67124yes—
710C4⋊C4C23×D67112yes—
711C22⋊C4—6712no—
712C22⋊C4—674no—
713C22⋊C4—6724no—
714C22⋊C4—6724no—
715C22⋊C4—6712no—
716C22⋊C4—6712no—
717C22⋊C4—674no—
718C22⋊C4—6712no—
719C22⋊C4—6712no—
720C22⋊C4—6712no—
721C22⋊C4C23×D67112yes—
722C22⋊C4C23×D67112yes—
723C42—6712no—
724C42C23×D67112yes—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—26848no—
731C23—26812no—
732C23—6712no—
733C23—676no—
734C23—676no—
735C23—672no—
736C23—13424no—
737C23—1342no—
738C23—1346no—
739C23—1342no—
740C23—1346no—
741C23—13424no—
742C23—1342no—
743C23—1346no—
744C23—1346no—
745C23—1346no—
746C23#1452409114yescomplemented
747C23C24×D6712yes—
748C23C24×D6712yes—
749C23C24×D6711yescharacteristic
750Q8—224no—
751Q8—224no—
752Q8—13424no—
753Q8—13424no—
754Q8C2×D4×D67116yes—
755D4—28no—
756D4—26812no—
757D4—26812no—
758D4—6748no—
759D4—13448no—
760D4—13424no—
761D4—1348no—
762D4—13424no—
763D4—1348no—
764D4—13424no—
765C2×C4—26no—
766C2×C4—26no—
767C2×C4—22no—
768C2×C4—26no—
769C2×C4—224no—
770C2×C4—224no—
771C2×C4—26824no—
772C2×C4—674no—
773C2×C4—672no—
774C2×C4—6748no—
775C2×C4—672no—
776C2×C4—676no—
777C2×C4—676no—
778C2×C4—672no—
779C2×C4—13424no—
780C2×C4—13424no—
781C2×C4—13448no—
782C2×C4—1348no—
783C2×C4—1342no—
784C2×C4—1346no—
785C2×C4—1342no—
786C2×C4—1346no—
787C2×C4—13424no—
788C2×C4—13424no—
789C2×C4C2×D4×D67112yes—
790C2×C4C24×D6712yes—
791C2×C4C24×D6716yes—
792C2×C4C24×D6716yes—
793C2×C4C24×D6716yes—
794C2×C4C24×D6716yes—
795C22—28no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—44no—
802C22—26848no—
803C22—26812no—
804C22—2684no—
805C22—6712no—
806C22—1342no—
807C22—1346no—
808C22—1342no—
809C22—1346no—
810C22—1342no—
811C22—1346no—
812C22—13424no—
813C22—1346no—
814C22—1346no—
815C22C22×D4×D6712yes—
816C22C2×#1452409112yes—
817C22C2×#1452409114yescomplemented
818C22#1686423312yes—
819C22C25×D6711yescharacteristic
820C4—26no—
821C4—26no—
822C4—22no—
823C4—26no—
824C4—674no—
825C4—1342no—
826C4—1346no—
827C4—1342no—
828C4—1346no—
829C4C22×D4×D67112yes—
830C2—24no—
831C2—42no—
832C2—2686no—
833C2—2682no—
834C2—13412no—
835C2#2257388614yesdirect product factor
836C2C23×D4×D6711yescharacteristic
837C2C22×#1452409111yescharacteristic
838C2C2×#1686423311yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×D4×Q8×C67C2
socleC23×C67C25
hypercenterC2×D4×Q8D67
hypocenterC67C2×#3489
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×#11761629C2semidirect
3. #22573886C2direct (N × H)
4. C2×Q8×C22⋊D67C2semidirect
5. C2×#16864058C2semidirect
6. C2×#16864057C2semidirect
7. C2×#16864049C2semidirect
8. C2×#16864048C2semidirect
9. C2×#16864042C2semidirect
10. C2×#16864037C2semidirect
11. C2×#16863976C2semidirect
12. C2×#16863971C2semidirect
13. C2×#16863905C2semidirect
14. C2×C22⋊Q8×D67C2semidirect
15. C2×#16863878C2semidirect
16. C2×D4×Q8×C67C2semidirect
18. C2×#14524091C22semidirect
24. C22×#11761629C22semidirect
25. C22×#11761629C22semidirect
26. C22×#11761628C22semidirect
27. C22×#11761628C22semidirect
28. C22×Q8×D67C22semidirect
29. C22×Q8×D67C22semidirect
32. Q8×C22⋊D67C22semidirect
33. #16864058C22semidirect
34. #16864057C22semidirect
35. #16864049C22semidirect
36. #16864048C22semidirect
37. #16864042C22semidirect
38. #16864037C22semidirect
39. #16863976C22semidirect
40. #16863971C22semidirect
41. C2×#14524041C22semidirect
42. C2×#14524032C22semidirect
43. C2×#14524031C22semidirect
44. #16863905C22semidirect
45. C2×#14524028C22semidirect
46. C2×#14524028C22semidirect
47. C2×#14524028C22semidirect
48. C2×#14524025C22semidirect
49. C2×#14524023C22semidirect
51. C2×#14524021C22semidirect
52. C2×#14524021C22semidirect
54. C2×#14524019C22semidirect
55. C2×#14524019C22semidirect
56. C22⋊Q8×D67C22semidirect
57. C2×#14524018C22semidirect
58. C2×#14524018C22semidirect
59. C2×#14524017C22semidirect
60. C2×#14524016C22semidirect
61. C2×#14524016C22semidirect
65. #16863878C22semidirect
66. C2×Q8×Dic67C22semidirect
67. C2×C4×D268C22semidirect
68. C2×C4×D268C22semidirect
69. C2×#14524005C22semidirect
71. C2×C4×C22⋊D67C22semidirect
72. C2×#14524000C22semidirect
73. C2×C4⋊C4×D67C22semidirect
74. C2×C4⋊C4×D67C22semidirect
77. C23×Q8×C67C22semidirect
78. D4×Q8×C67C22semidirect
79. C2×C4⋊Q8×C67C22semidirect
81. C2×C22⋊Q8×C67C22semidirect
82. C2×C4×Q8×C67C22semidirect
91. C2×#11761629D4semidirect
96. C2×#11761629C23semidirect
99. C2×#11761628C23semidirect
100. C2×#11761628C23semidirect
105. C2×Q8×D67C23semidirect
106. C2×Q8×D67C23semidirect
128. #14524041C23semidirect
129. #14524032C23semidirect
130. #14524031C23semidirect
131. #14524028C23semidirect
132. #14524028C23semidirect
133. #14524028C23semidirect
134. #14524025C23semidirect
135. #14524023C23semidirect
137. #14524021C23semidirect
138. #14524021C23semidirect
140. #14524019C23semidirect
141. #14524019C23semidirect
142. #14524018C23semidirect
143. #14524018C23semidirect
144. #14524017C23semidirect
145. #14524016C23semidirect
146. #14524016C23semidirect
150. Q8×Dic67C23semidirect
151. C4×D268C23semidirect
152. C4×D268C23semidirect
153. #14524005C23semidirect
155. C4×C22⋊D67C23semidirect
156. #14524000C23semidirect
164. C4⋊C4×D67C23semidirect
165. C4⋊C4×D67C23semidirect
184. C22×Q8×C67C23semidirect
188. C4⋊Q8×C67C23semidirect
190. C22⋊Q8×C67C23semidirect
191. C4×Q8×C67C23semidirect
210. #11761629C2×D4semidirect
310. C23×C672−1+4semidirect
384. C22×C67C2×2−1+4semidirect
413. C2×C67#3489semidirect
424. C2×D4×Q8D67semidirect
436. C67C2×#3489semidirect
451. C23×Q8C2×D67semidirect
455. D4×Q8C2×D67semidirect
465. C2×C4⋊Q8C2×D67semidirect
482. C2×C22⋊Q8C2×D67semidirect
493. C2×C4×Q8C2×D67semidirect
533. C22×Q8C22×D67semidirect
559. C4⋊Q8C22×D67semidirect
574. C22⋊Q8C22×D67semidirect
584. C4×Q8C22×D67semidirect
746. C23#14524091semidirect
817. C22C2×#14524091semidirect
835. C2#22573886direct (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×#117616292
#225738862
C2×Q8×C22⋊D672
C2×#168640582
C2×#168640572
C2×#168640492
C2×#168640482
C2×#168640422
C2×#168640372
C2×#168639762
C2×#168639712
C2×#168639052
C2×C22⋊Q8×D672
C2×#168638782
C2×D4×Q8×C672
C2×#348967