Finite Group Databasebeta

← #7633152

Subgroups — #7633152

Order 512.

11221 conjugacy classes of subgroups.

The subgroup lattice has 1242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3489C211yesmaximal, characteristic, complemented
2C2×#3489C211yesmaximal, characteristic, complemented
3C2×D4×#41C211yesmaximal, characteristic, complemented
4C22×#520C211yesmaximal, characteristic, complemented
5Q8×#121C212yesmaximal, complemented
6#36434C212yesmaximal, complemented
7#36214C216yesmaximal, complemented
8#36153C216yesmaximal, complemented
9#36020C216yesmaximal, complemented
10#35831C212yesmaximal, complemented
11#35821C216yesmaximal, complemented
12#35737C212yesmaximal, complemented
13#35633C213yesmaximal, complemented
14#35621C213yesmaximal, complemented
15#35564C213yesmaximal, complemented
16#35518C213yesmaximal, complemented
17#35306C213yesmaximal, complemented
18#35223C213yesmaximal, complemented
19#34737C213yesmaximal, complemented
20C2×#2417C213yesmaximal, complemented
21#34259C211yesmaximal, characteristic, complemented
22#34250C211yesmaximal, characteristic, complemented
23#34175C211yesmaximal, characteristic, complemented
24C22×2−1+4C2211yescharacteristic
25C23×#41C2211yescharacteristic
26C23×#41C2211yescharacteristic
27#3489—216no—
28#3489—216no—
29D4×#41—216no—
30C2×#550C2211yescharacteristic
31C2×D4×Q8C2211yescharacteristic
32C2×D4×Q8C2212yescomplemented
33C2×D4×Q8C2212yescomplemented
34C2×#548C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#548C2212yescomplemented
37C2×#548C2212yescomplemented
38C2×#547C2213yes—
39C2×#547C2216yescomplemented
40C2×#547C2216yescomplemented
41C2×#546C2213yes—
42C2×#546C2213yes—
43C2×#546C2216yescomplemented
44C2×#546C2216yescomplemented
45C2×D42C2213yes—
46C2×#537C2213yescomplemented
47C2×#537C2213yescomplemented
48C2×#536C2213yescomplemented
49C2×#536C2213yescomplemented
50C2×#532C2213yes—
51C2×#525C2213yes—
52C2×#525C2213yes—
53C2×#525C2213yescomplemented
54C2×#525C2213yescomplemented
55C22×C22⋊Q8C2213yescomplemented
56C22×C22⋊Q8C2213yescomplemented
57C2×#520—216no—
58C2×#520C2211yescharacteristic
59C2×#520C2211yescharacteristic
60C2×#520C2211yescharacteristic
61C2×#520C2213yescomplemented
62C2×#520C2213yescomplemented
63C2×#520C2212yescomplemented
64C2×#520C2216yescomplemented
65C2×C4×#41C2211yescharacteristic
66C22×C4×Q8C2212yescomplemented
67C22×C4×D4C2213yes—
68C22×C4×D4C2216yescomplemented
69C22×#117C2213yescomplemented
70C23×C4⋊C4C2213yescomplemented
71#2857C2216yescomplemented
72#2850C2216yescomplemented
73#2847C22112yescomplemented
74#2621C2216yescomplemented
75#2620C2216yescomplemented
76#2618C22112yescomplemented
77#2547C2216yescomplemented
78#2546C2216yescomplemented
79#2545C2216yescomplemented
80#2544C2216yescomplemented
81#2543C22112yescomplemented
82#2538C2216yescomplemented
83#2537C2216yescomplemented
84#2536C2216yescomplemented
85#2535C2216yescomplemented
86#2534C22112yescomplemented
87#2486C22112yescomplemented
88#2429C2216yescomplemented
89#2429C2216yescomplemented
90#2429C2216yescomplemented
91#2428C2216yescomplemented
92#2427C2216yescomplemented
93#2427C2216yescomplemented
94#2427C2216yescomplemented
95#2426C2216yescomplemented
96#2425C22112yescomplemented
97#2425C22112yescomplemented
98#2425C22112yescomplemented
99#2424C22112yescomplemented
100#2417C2216yes—
101#2417C2213yes—
102#2417C2216yescomplemented
103#2417C2216yescomplemented
104#2417C2216yescomplemented
105#2417C2216yescomplemented
106#2417C2216yescomplemented
107#2417C2216yescomplemented
108#2417C2216yescomplemented
109#2417C2216yescomplemented
110#2417C2216yescomplemented
111#2417C2213yescomplemented
112#2416C2211yescharacteristic
113#2416C22112yescomplemented
114#2416C2216yescomplemented
115#2416C2213yescomplemented
116#2416C2216yescomplemented
117#2416C2216yescomplemented
118#2415C2213yescomplemented
119#2415C2216yescomplemented
120#2415C2213yescomplemented
121#2415C2216yescomplemented
122#2414C2213yescomplemented
123#2414C2213yescomplemented
124#2413C2216yescomplemented
125#2413C22112yescomplemented
126#2412C2216yescomplemented
127#2412C22112yescomplemented
128#2411C2216yescomplemented
129#2410C2216yes—
130#2392C2216yescomplemented
131#2392C2216yescomplemented
132C2×#398C2216yescomplemented
133C2×#396C2216yescomplemented
134#2351C2212yescomplemented
135Q8×C4⋊C4C2212yescomplemented
136#2349C2216yescomplemented
137D4×C4⋊C4C2216yescomplemented
138#2341C2212yescomplemented
139Q8×C22⋊C4C2212yescomplemented
140Q8×C22⋊C4C2212yescomplemented
141Q8×C22⋊C4C2212yescomplemented
142#2339C2216yescomplemented
143#2339C2216yescomplemented
144#2339C2216yescomplemented
145D4×C22⋊C4C2216yescomplemented
146#2317C2213yescomplemented
147#2316C2213yescomplemented
148#2311C2213yescomplemented
149#2311C2213yescomplemented
150#2311C2213yescomplemented
151#2310C2213yescomplemented
152C4×#121C2216yes—
153C4×#121C2216yescomplemented
154#2297C2213yescomplemented
155#2296C2213yescomplemented
156C2×#391C2213yescomplemented
157C2×#389C2213yescomplemented
158C2×#386C2216yes—
159#2280C2213yescomplemented
160C2×#380C2216yescomplemented
161C2×#380C2213yescomplemented
162C2×2−1+4—28no—
163C2×2−1+4—28no—
164C2×2−1+4—28no—
165C22×#41—28no—
166C22×#41—28no—
167C22×#41—28no—
168C22×#41—28no—
169C22×#41—28no—
170C22×#41D4116yescomplemented
171C22×#41C2313yes—
172C22×#41C2313yes—
173C22×#41C2311yescharacteristic
174C22×#41C2313yes—
175C22×#41C2316yes—
176C22×#41C2313yes—
177C22×#41C2313yes—
178C22×#41C2311yescharacteristic
179C22×#41C2311yescharacteristic
180C23×Q8C2313yes—
181C23×Q8C2311yescharacteristic
182C23×Q8C2312yes—
183C23×Q8C2311yescharacteristic
184C23×D4C2313yes—
185C23×D4C2313yes—
186C23×D4C2313yes—
187C24×C4C2313yes—
188C24×C4C2313yes—
189C24×C4C2316yes—
190#550—28no—
191D4×Q8—28no—
192D4×Q8—216no—
193D4×Q8—216no—
194#548—28no—
195#548—216no—
196#548—28no—
197#548—216no—
198#547—224no—
199#547—248no—
200#547—248no—
201#546—224no—
202#546—224no—
203#546—248no—
204#546—248no—
205D42—224no—
206#537—224no—
207#537—224no—
208#536—224no—
209#536—224no—
210#532—224no—
211C2×C4⋊Q8C2316yes—
212C2×C4⋊Q8C2313yes—
213C2×C4⋊Q8C2316yes—
214C2×#127C2313yes—
215C2×#124C2316yes—
216C2×#124C2313yes—
217C2×#124C2313yes—
218C2×#124C2316yes—
219#525—224no—
220#525—224no—
221#525—224no—
222#525—224no—
223C2×#123C2316yes—
224C2×#123C2316yes—
225C2×#123C2316yes—
226C2×#123C2316yes—
227C2×#123C23112yes—
228C2×#123C23112yes—
229C2×C22⋊Q8—224no—
230C2×C22⋊Q8—224no—
231C2×C22⋊Q8C2316yes—
232C2×C22⋊Q8C2313yes—
233C2×C22⋊Q8C2316yes—
234C2×C22⋊Q8C2313yes—
235C2×C22⋊Q8C2313yes—
236C2×C22⋊Q8C2313yes—
237C2×C22⋊Q8C2316yes—
238C2×C22⋊Q8C2316yes—
239C2×C22⋊Q8C2316yes—
240C2×C22⋊Q8C2316yes—
241C2×C22⋊Q8C2313yes—
242C2×C22⋊Q8C2313yes—
243C2×C22⋊Q8C2313yes—
244C2×C22⋊Q8C2313yes—
245C2×C22⋊Q8C2316yes—
246C2×C22⋊Q8C2316yes—
247C2×#121C23112yes—
248C2×#121C2313yes—
249C2×#121C2313yes—
250C2×#121C2312yes—
251C2×#121C2313yes—
252C2×#121C2313yes—
253C2×#121C2311yescharacteristic
254C2×#121C2311yescharacteristic
255C2×#121C2313yes—
256C2×#121C2313yes—
257C2×#121C2316yes—
258C2×#121C2316yes—
259C2×#121C23112yes—
260C2×#121C2316yes—
261C2×#121C2316yes—
262C2×#121C2316yes—
263C2×#121C23112yes—
264C2×#120C2316yes—
265C2×#120C2316yes—
266C2×#120C2316yes—
267C2×#120C2316yes—
268#520—28no—
269#520—28no—
270#520—216no—
271#520—248no—
272#520—224no—
273#520—224no—
274#520D4116yescomplemented
275C4×#41—28no—
276C2×C4×Q8—216no—
277C2×C4×Q8C2312yes—
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2316yes—
282C2×C4×Q8C2316yes—
283C2×C4×Q8C2312yes—
284C2×C4×D4—224no—
285C2×C4×D4—248no—
286C2×C4×D4C2316yes—
287C2×C4×D4C2316yes—
288C2×C4×D4C2313yes—
289C2×C4×D4C2313yes—
290C2×C4×D4C2313yes—
291C2×C4×D4C2313yes—
292C2×C4×D4C2316yes—
293C2×C4×D4C2316yes—
294C2×C4×D4C2316yes—
295C2×C4×D4C2311yescharacteristic
296C2×C4×D4C2313yes—
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C23112yes—
302C2×C4×D4C23112yes—
303C2×C4×D4C2316yes—
304C2×C4×D4C2316yes—
305C2×C4×D4C2316yes—
306C2×C4×D4C2316yes—
307C2×C4×D4C2316yes—
308C2×#117—224no—
309C2×#117C2313yes—
310C2×#117C2313yes—
311C2×#117C2313yes—
312C2×#117C2316yes—
313C2×#117C2316yes—
314C2×#117C2313yes—
315C2×#117C2313yes—
316C2×#117C2313yes—
317C22×C4⋊C4—224no—
318C22×C4⋊C4C2313yes—
319C22×C4⋊C4C2313yes—
320C22×C4⋊C4C2316yes—
321C22×C4⋊C4C2316yes—
322C22×C4⋊C4C2313yes—
323C22×C4⋊C4C2316yes—
324C22×C4⋊C4C2313yes—
325C22×C4⋊C4C2316yes—
326C22×C4⋊C4C2316yes—
327C22×C4⋊C4C2316yes—
328C22×C4⋊C4C2311yescharacteristic
329C22×C4⋊C4C2316yes—
330C22×C4⋊C4C2313yes—
331C22×C22⋊C4C2313yes—
332C22×C22⋊C4C2316yes—
333C22×C22⋊C4C2316yes—
334C22×C22⋊C4C2313yes—
335C22×C22⋊C4C2316yes—
336C22×C22⋊C4C2316yes—
337C22×C42C2316yes—
338C22×C42C2313yes—
339#398C23112yes—
340#398C23112yes—
341#398C2316yes—
342#398C2316yes—
343#398C23112yes—
344#398C23112yes—
345#397C23112yes—
346#397C23112yes—
347#397C2316yes—
348#397C2316yes—
349#396C2316yes—
350#396C23112yes—
351#396C23112yes—
352#396C23112yes—
353#396C2316yes—
354#396C2316yes—
355#396C23112yes—
356#396C23112yes—
357#396C2312yes—
358#394C2316yes—
359#394C23112yes—
360#394C23112yes—
361#394C23112yes—
362#394C2312yes—
363#394C2316yes—
364#394C2316yes—
365#394C2316yes—
366#394C2316yes—
367#392C2316yes—
368#392C2316yes—
369#391C2313yes—
370#391C2316yes—
371#391C2316yes—
372#391C2316yes—
373#391C2316yes—
374#391C2316yes—
375#391C2316yes—
376#391C2316yes—
377#391C2313yes—
378#390C2313yes—
379#390C2316yes—
380#390C2316yes—
381#390C2316yes—
382#390C2316yes—
383#390C2311yescharacteristic
384#389C2313yes—
385#389C2316yes—
386#389C2316yes—
387#389C2316yes—
388#389C2313yes—
389#389C23112yes—
390#389C23112yes—
391#389C2316yes—
392#389C2316yes—
393#389C2316yes—
394#389C2316yes—
395#389C2313yes—
396#389C2311yescharacteristic
397#388C23112yes—
398#388C23112yes—
399#388C2316yes—
400#388C2316yes—
401#388C2316yes—
402#388C2316yes—
403#386C23112yes—
404#386C23112yes—
405#386C23112yes—
406#386C2316yes—
407#386C23112yes—
408#386C23112yes—
409#386C23112yes—
410#386C2316yes—
411#386C2316yes—
412#386C2316yes—
413#386C2316yes—
414#386C2312yes—
415#386C23112yes—
416#386C23112yes—
417#385C23112yes—
418#385C2316yes—
419#385C2316yes—
420#384C2316yes—
421#382C2316yes—
422#381C23112yes—
423#381C2316yes—
424#380C2313yes—
425#380C2316yes—
426#380C2313yes—
427#380C2316yes—
428#380C2316yes—
429#380C23112yes—
430#380C23112yes—
431#380C23112yes—
432#380C2316yes—
433#380C2316yes—
434#380C2316yes—
435#380C2316yes—
436#380C2313yes—
437#380C2311yescharacteristic
438#380C23112yes—
439#380C23112yes—
440#379C2316yes—
441C4×C4⋊C4C2316yes—
442C4×C4⋊C4C2316yes—
443C4×C22⋊C4C2316yes—
444C4×C22⋊C4C2316yes—
445C4×C22⋊C4C2316yes—
446C4×C22⋊C4C2316yes—
447C2×#95C2316yes—
448C2×#95C2316yes—
449C2×#95C2316yes—
450C2×#95C2316yes—
451C25C2413yes—
452C25C2413yes—
4532−1+4—464no—
454C2×#41—2128no—
455C2×#41—24no—
456C2×#41—24no—
457C2×#41—24no—
458C2×#41—24no—
459C2×#41—24no—
460C2×#41—212no—
461C2×#41—212no—
462C2×#41—224no—
463C2×#41—224no—
464C2×#41—212no—
465C2×#41—212no—
466C2×#41—212no—
467C2×#41—224no—
468C2×#41—212no—
469C2×#41—212no—
470C2×#41—212no—
471C2×#41—212no—
472C2×#41—212no—
473C2×#41—212no—
474C2×#41—212no—
475C2×#41—212no—
476C2×#41—464no—
477C2×#41C2×D4124yes—
478C2×#41C2×D4124yes—
479C2×#41C2×D418yes—
480C2×#41C2×D418yes—
481C2×#41C2×D418yes—
482C2×#41#4118yes—
483C22×Q8—24no—
484C22×Q8—24no—
485C22×Q8—24no—
486C22×Q8—28no—
487C22×Q8—28no—
488C22×Q8—24no—
489C22×Q8—24no—
490C22×Q8—28no—
491C22×Q8—212no—
492C22×Q8—212no—
493C22×Q8—212no—
494C22×Q8C2×D418yes—
495C22×Q8C2413yes—
496C22×Q8C2416yes—
497C22×Q8C2413yes—
498C22×Q8C2413yes—
499C22×Q8C2411yescharacteristic
500C22×D4—212no—
501C22×D4—212no—
502C22×D4—212no—
503C22×D4—212no—
504C22×D4—212no—
505C22×D4—212no—
506C22×D4—212no—
507C22×D4—46no—
508C22×D4C2×D4124yes—
509C22×D4C2412yes—
510C22×D4C2413yes—
511C22×D4C2416yes—
512C22×D4C2416yes—
513C22×D4C2411yescharacteristic
514C22×D4C2413yes—
515C22×D4C2412yes—
516C22×D4C2413yes—
517C22×D4C2413yes—
518C22×D4C2416yes—
519C22×D4C2413yes—
520C22×D4C2411yescharacteristic
521C22×D4C2416yes—
522C22×D4C2416yes—
523C22×D4C2416yes—
524C22×D4C2413yes—
525C23×C4—212no—
526C23×C4—212no—
527C23×C4—212no—
528C23×C4—212no—
529C23×C4—212no—
530C23×C4—224no—
531C23×C4—412no—
532C23×C4—86no—
533C23×C4C2×D4124yes—
534C23×C4C2416yes—
535C23×C4C2413yes—
536C23×C4C2416yes—
537C23×C4C2411yescharacteristic
538C23×C4C2413yes—
539C23×C4C2413yes—
540C23×C4C2413yes—
541C23×C4C2412yes—
542C23×C4C2416yes—
543C23×C4C2413yes—
544C23×C4C2413yes—
545C23×C4C2411yescharacteristic
546C23×C4C2413yes—
547C23×C4C2413yes—
548C23×C4C2413yes—
549C23×C4C2416yes—
550C23×C4C2413yes—
551C23×C4C2416yes—
552C23×C4C24112yes—
553C23×C4C2416yes—
554C23×C4C2413yes—
555C4⋊Q8—212no—
556C4⋊Q8—224no—
557C4⋊Q8—224no—
558#127—212no—
559#124—212no—
560#124—212no—
561#124—224no—
562#124—224no—
563#123—224no—
564#123—248no—
565#123—224no—
566#123—224no—
567#123—224no—
568#123—248no—
569C22⋊Q8—212no—
570C22⋊Q8—212no—
571C22⋊Q8—224no—
572C22⋊Q8—212no—
573C22⋊Q8—224no—
574C22⋊Q8—224no—
575C22⋊Q8—224no—
576C22⋊Q8—212no—
577C22⋊Q8—212no—
578C22⋊Q8—212no—
579C22⋊Q8—212no—
580C22⋊Q8—224no—
581C22⋊Q8—224no—
582C22⋊Q8—224no—
583C22⋊Q8—212no—
584C22⋊Q8—224no—
585#121—212no—
586#121—212no—
587#121—224no—
588#121—224no—
589#121—248no—
590#121—224no—
591#121—28no—
592#121—24no—
593#121—212no—
594#121—212no—
595#121—212no—
596#121—248no—
597#121—24no—
598#121—212no—
599#121—224no—
600#121—412no—
601#121—812no—
602#120—224no—
603#120—224no—
604#120—224no—
605#120—224no—
606C4×Q8—28no—
607C4×Q8—24no—
608C4×Q8—24no—
609C4×Q8—28no—
610C4×Q8—224no—
611C4×Q8—224no—
612C4×Q8C2×D4116yescomplemented
613C4×D4—224no—
614C4×D4—212no—
615C4×D4—212no—
616C4×D4—224no—
617C4×D4—24no—
618C4×D4—248no—
619C4×D4—212no—
620C4×D4—212no—
621C4×D4—212no—
622C4×D4—212no—
623C4×D4—212no—
624C4×D4—212no—
625C4×D4—212no—
626C4×D4—224no—
627C4×D4—224no—
628C4×D4—224no—
629C4×D4—224no—
630C4×D4—248no—
631C4×D4—224no—
632C4×D4—224no—
633C4×D4—224no—
634C4×D4C2×D4148yescomplemented
635#117—212no—
636#117—212no—
637#117—212no—
638#117—212no—
639#117—212no—
640#117—224no—
641#117—224no—
642#117C2×D4124yescomplemented
643C2×C4⋊C4—224no—
644C2×C4⋊C4—212no—
645C2×C4⋊C4—212no—
646C2×C4⋊C4—212no—
647C2×C4⋊C4—224no—
648C2×C4⋊C4—224no—
649C2×C4⋊C4—212no—
650C2×C4⋊C4—224no—
651C2×C4⋊C4—224no—
652C2×C4⋊C4—224no—
653C2×C4⋊C4—24no—
654C2×C4⋊C4—86no—
655C2×C4⋊C4C2×D4124yescomplemented
656C2×C4⋊C4C2413yes—
657C2×C4⋊C4C2416yes—
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2416yes—
660C2×C4⋊C4C24112yes—
661C2×C4⋊C4C2413yes—
662C2×C4⋊C4C2416yes—
663C2×C4⋊C4C2416yes—
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2413yes—
667C2×C4⋊C4C2413yes—
668C2×C4⋊C4C2413yes—
669C2×C4⋊C4C2416yes—
670C2×C4⋊C4C24112yes—
671C2×C4⋊C4C24112yes—
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2413yes—
674C2×C4⋊C4C2413yes—
675C2×C4⋊C4C2416yes—
676C2×C4⋊C4C2416yes—
677C2×C4⋊C4C2416yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2416yes—
680C2×C4⋊C4C24112yes—
681C2×C4⋊C4C2416yes—
682C2×C4⋊C4C2416yes—
683C2×C4⋊C4C2413yes—
684C2×C4⋊C4C2416yes—
685C2×C4⋊C4C2411yescharacteristic
686C2×C22⋊C4—212no—
687C2×C22⋊C4—224no—
688C2×C22⋊C4—212no—
689C2×C22⋊C4—224no—
690C2×C22⋊C4—224no—
691C2×C22⋊C4—86no—
692C2×C22⋊C4C2411yescharacteristic
693C2×C22⋊C4C2411yescharacteristic
694C2×C22⋊C4C2416yes—
695C2×C22⋊C4C2416yes—
696C2×C22⋊C4C2416yes—
697C2×C22⋊C4C2416yes—
698C2×C22⋊C4C2416yes—
699C2×C22⋊C4C2413yes—
700C2×C22⋊C4C2413yes—
701C2×C22⋊C4C2413yes—
702C2×C22⋊C4C2413yes—
703C2×C22⋊C4C2413yes—
704C2×C22⋊C4C2413yes—
705C2×C22⋊C4C24112yes—
706C2×C22⋊C4C24112yes—
707C2×C22⋊C4C2416yes—
708C2×C22⋊C4C2416yes—
709C2×C22⋊C4C2412yes—
710C2×C22⋊C4C2412yes—
711C2×C22⋊C4C2416yes—
712C2×C22⋊C4C2416yes—
713C2×C22⋊C4C2416yes—
714C2×C22⋊C4C2416yes—
715C2×C22⋊C4C2416yes—
716C2×C22⋊C4C2416yes—
717C2×C22⋊C4C2412yes—
718C2×C22⋊C4C2412yes—
719C2×C22⋊C4C2416yes—
720C2×C22⋊C4C24112yes—
721C2×C22⋊C4C2416yes—
722C2×C22⋊C4C2416yes—
723C2×C22⋊C4C2416yes—
724C2×C22⋊C4C2412yes—
725C2×C22⋊C4C2416yes—
726C2×C22⋊C4C2416yes—
727C2×C42—212no—
728C2×C42—224no—
729C2×C42C2413yes—
730C2×C42C2416yes—
731C2×C42C2416yes—
732C2×C42C2416yes—
733C2×C42C2416yes—
734C2×C42C2411yescharacteristic
735C2×C42C2413yes—
736C2×C42C2413yes—
737C2×C42C2416yes—
738#95C2416yes—
739#95C2416yes—
740#95C2416yes—
741#95C2416yes—
742#95C24112yes—
743#95C24112yes—
744#95C24112yes—
745#95C24112yes—
746#95C2412yes—
747#95C2416yes—
748#95C2416yes—
749#95C2416yes—
750#95C2416yes—
751#95C2412yes—
752#95C2416yes—
753#95C2416yes—
754C24—26no—
755C24—26no—
756C24—26no—
757C24—26no—
758C24—26no—
759C24—26no—
760C24—26no—
761C24—26no—
762C24—43no—
763C24—43no—
764C24—43no—
765C24—43no—
766C24—43no—
767C24C22×D4112yes—
768C24C2513yes—
769C24C2512yes—
770C24C2513yes—
771C24C2511yescharacteristic
772C24C2513yes—
773C24C2511yescharacteristic
774#41—232no—
775#41—296no—
776#41—296no—
777#41—416no—
778#41—448no—
779#41—496no—
780#41—448no—
781#41—448no—
782#41#121164yescomplemented
783C2×Q8—232no—
784C2×Q8—26no—
785C2×Q8—26no—
786C2×Q8—26no—
787C2×Q8—212no—
788C2×Q8—212no—
789C2×Q8—26no—
790C2×Q8—26no—
791C2×Q8—26no—
792C2×Q8—26no—
793C2×Q8—212no—
794C2×Q8—26no—
795C2×Q8—416no—
796C2×Q8—432no—
797C2×Q8—448no—
798C2×Q8C22×D4112yes—
799C2×Q8C22×D414yes—
800C2×Q8C22×D414yes—
801C2×Q8C2×#4114yes—
802C2×D4—22no—
803C2×D4—212no—
804C2×D4—212no—
805C2×D4—22no—
806C2×D4—296no—
807C2×D4—24no—
808C2×D4—26no—
809C2×D4—26no—
810C2×D4—26no—
811C2×D4—212no—
812C2×D4—212no—
813C2×D4—212no—
814C2×D4—212no—
815C2×D4—212no—
816C2×D4—212no—
817C2×D4—24no—
818C2×D4—24no—
819C2×D4—26no—
820C2×D4—26no—
821C2×D4—24no—
822C2×D4—26no—
823C2×D4—212no—
824C2×D4—212no—
825C2×D4—26no—
826C2×D4—24no—
827C2×D4—22no—
828C2×D4—22no—
829C2×D4—26no—
830C2×D4—26no—
831C2×D4—212no—
832C2×D4—26no—
833C2×D4—26no—
834C2×D4—22no—
835C2×D4—26no—
836C2×D4—43no—
837C2×D4—43no—
838C2×D4—42no—
839C2×D4—46no—
840C2×D4—46no—
841C2×D4—46no—
842C2×D4—46no—
843C2×D4—46no—
844C2×D4—46no—
845C2×D4—448no—
846C2×D4—448no—
847C2×D4C22×D4124yes—
848C2×D4C22×D4112yes—
849C2×D4C22×D4112yes—
850C2×D4C22×D4112yes—
851C2×D4C2×#41112yes—
852C2×D42−1+414yescomplemented
853C22×C4—26no—
854C22×C4—26no—
855C22×C4—296no—
856C22×C4—26no—
857C22×C4—22no—
858C22×C4—26no—
859C22×C4—26no—
860C22×C4—22no—
861C22×C4—26no—
862C22×C4—26no—
863C22×C4—26no—
864C22×C4—26no—
865C22×C4—26no—
866C22×C4—212no—
867C22×C4—212no—
868C22×C4—26no—
869C22×C4—26no—
870C22×C4—212no—
871C22×C4—24no—
872C22×C4—212no—
873C22×C4—26no—
874C22×C4—212no—
875C22×C4—212no—
876C22×C4—24no—
877C22×C4—212no—
878C22×C4—22no—
879C22×C4—26no—
880C22×C4—26no—
881C22×C4—26no—
882C22×C4—212no—
883C22×C4—212no—
884C22×C4—26no—
885C22×C4—26no—
886C22×C4—22no—
887C22×C4—26no—
888C22×C4—22no—
889C22×C4—26no—
890C22×C4—26no—
891C22×C4—26no—
892C22×C4—212no—
893C22×C4—26no—
894C22×C4—224no—
895C22×C4—46no—
896C22×C4—46no—
897C22×C4—46no—
898C22×C4—42no—
899C22×C4—43no—
900C22×C4—46no—
901C22×C4—46no—
902C22×C4—43no—
903C22×C4—412no—
904C22×C4—412no—
905C22×C4—46no—
906C22×C4—43no—
907C22×C4—46no—
908C22×C4—448no—
909C22×C4—848no—
910C22×C4C22×D4112yes—
911C22×C4C22×D414yes—
912C22×C4C22×D4112yes—
913C22×C4C22×D4112yes—
914C22×C4C22×D4112yes—
915C22×C4C22×D4124yes—
916C22×C4C22×D4112yes—
917C22×C4C22×D4112yes—
918C22×C4C2×#41112yes—
919C22×C4C2513yes—
920C22×C4C2512yes—
921C22×C4C2516yes—
922C22×C4C2511yescharacteristic
923C22×C4C2512yes—
924C22×C4C2513yes—
925C22×C4C2516yes—
926C22×C4C2516yes—
927C22×C4C2511yescharacteristic
928C22×C4C2513yes—
929C22×C4C2512yes—
930C22×C4C2516yes—
931C22×C4C2513yes—
932C22×C4C2511yescharacteristic
933C22×C4C2511yescharacteristic
934C22×C4C2513yes—
935C22×C4C2511yescharacteristic
936C4⋊C4—212no—
937C4⋊C4—26no—
938C4⋊C4—22no—
939C4⋊C4—224no—
940C4⋊C4—212no—
941C4⋊C4—26no—
942C4⋊C4—212no—
943C4⋊C4—212no—
944C4⋊C4—24no—
945C4⋊C4—22no—
946C4⋊C4—26no—
947C4⋊C4—26no—
948C4⋊C4—26no—
949C4⋊C4—212no—
950C4⋊C4—224no—
951C4⋊C4—224no—
952C4⋊C4—22no—
953C4⋊C4—26no—
954C4⋊C4—26no—
955C4⋊C4—212no—
956C4⋊C4—212no—
957C4⋊C4—212no—
958C4⋊C4—24no—
959C4⋊C4—46no—
960C4⋊C4—412no—
961C4⋊C4—46no—
962C4⋊C4—46no—
963C4⋊C4C22×D4112yes—
964C4⋊C4C22×D4124yes—
965C4⋊C4C22×D414yes—
966C22⋊C4—22no—
967C22⋊C4—212no—
968C22⋊C4—212no—
969C22⋊C4—26no—
970C22⋊C4—26no—
971C22⋊C4—26no—
972C22⋊C4—224no—
973C22⋊C4—212no—
974C22⋊C4—212no—
975C22⋊C4—212no—
976C22⋊C4—212no—
977C22⋊C4—24no—
978C22⋊C4—22no—
979C22⋊C4—212no—
980C22⋊C4—212no—
981C22⋊C4—212no—
982C22⋊C4—26no—
983C22⋊C4—26no—
984C22⋊C4—26no—
985C22⋊C4—224no—
986C22⋊C4—24no—
987C22⋊C4—24no—
988C22⋊C4—212no—
989C22⋊C4—212no—
990C22⋊C4—212no—
991C22⋊C4—212no—
992C22⋊C4—24no—
993C22⋊C4—46no—
994C22⋊C4—412no—
995C22⋊C4—42no—
996C22⋊C4—46no—
997C22⋊C4—46no—
998C22⋊C4—46no—
999C22⋊C4—46no—
1000C22⋊C4C22×D4124yes—
1001C42—22no—
1002C42—26no—
1003C42—212no—
1004C42—212no—
1005C42—212no—
1006C42—26no—
1007C42—26no—
1008C42—212no—
1009C42C22×D4124yes—
1010C23—21no—
1011C23—21no—
1012C23—23no—
1013C23—23no—
1014C23—23no—
1015C23—21no—
1016C23—23no—
1017C23—21no—
1018C23—21no—
1019C23—23no—
1020C23—21no—
1021C23—21no—
1022C23—23no—
1023C23—23no—
1024C23—23no—
1025C23—21no—
1026C23—21no—
1027C23—23no—
1028C23—23no—
1029C23—21no—
1030C23—224no—
1031C23—224no—
1032C23—23no—
1033C23—22no—
1034C23—22no—
1035C23—23no—
1036C23—22no—
1037C23—23no—
1038C23—22no—
1039C23—23no—
1040C23—22no—
1041C23—23no—
1042C23—23no—
1043C23—22no—
1044C23—23no—
1045C23—22no—
1046C23—412no—
1047C23—412no—
1048C23—412no—
1049C23—412no—
1050C23—412no—
1051C23—412no—
1052C23—412no—
1053C23—412no—
1054C23—412no—
1055C23—86no—
1056C23—86no—
1057C23—86no—
1058C23C23×D416yes—
1059C23C23×D416yes—
1060C23C23×D416yes—
1061C23C23×D412yes—
1062C23C22×#4116yes—
1063C23C2×2−1+412yes—
1064C23C2×2−1+412yes—
1065C23#58512yes—
1066C23C2611yescharacteristic
1067Q8—224no—
1068Q8—412no—
1069Q8—424no—
1070Q8—412no—
1071Q8C2×#121116yes—
1072D4—248no—
1073D4—28no—
1074D4—224no—
1075D4—48no—
1076D4—412no—
1077D4—412no—
1078D4—424no—
1079D4—424no—
1080D4—48no—
1081D4—412no—
1082D4—412no—
1083D4—44no—
1084D4—812no—
1085D4—812no—
1086D4—812no—
1087D4C2×#121148yes—
1088C2×C4—21no—
1089C2×C4—23no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—23no—
1093C2×C4—22no—
1094C2×C4—26no—
1095C2×C4—21no—
1096C2×C4—26no—
1097C2×C4—22no—
1098C2×C4—224no—
1099C2×C4—28no—
1100C2×C4—224no—
1101C2×C4—224no—
1102C2×C4—224no—
1103C2×C4—22no—
1104C2×C4—21no—
1105C2×C4—22no—
1106C2×C4—23no—
1107C2×C4—23no—
1108C2×C4—26no—
1109C2×C4—26no—
1110C2×C4—21no—
1111C2×C4—23no—
1112C2×C4—26no—
1113C2×C4—26no—
1114C2×C4—21no—
1115C2×C4—23no—
1116C2×C4—21no—
1117C2×C4—23no—
1118C2×C4—26no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—23no—
1122C2×C4—22no—
1123C2×C4—23no—
1124C2×C4—26no—
1125C2×C4—26no—
1126C2×C4—26no—
1127C2×C4—23no—
1128C2×C4—21no—
1129C2×C4—22no—
1130C2×C4—21no—
1131C2×C4—26no—
1132C2×C4—23no—
1133C2×C4—424no—
1134C2×C4—48no—
1135C2×C4—424no—
1136C2×C4—412no—
1137C2×C4—412no—
1138C2×C4—424no—
1139C2×C4—44no—
1140C2×C4—412no—
1141C2×C4—412no—
1142C2×C4—412no—
1143C2×C4—424no—
1144C2×C4—824no—
1145C2×C4—86no—
1146C2×C4—812no—
1147C2×C4—812no—
1148C2×C4C2×#121148yes—
1149C2×C4C23×D414yes—
1150C2×C4C23×D4112yes—
1151C2×C4C23×D412yes—
1152C2×C4C23×D416yes—
1153C2×C4C23×D412yes—
1154C2×C4C23×D416yes—
1155C2×C4C23×D416yes—
1156C2×C4C23×D412yes—
1157C2×C4C22×#4112yes—
1158C2×C4C22×#4116yes—
1159C2×C4C2×2−1+412yes—
1160C22—22no—
1161C22—26no—
1162C22—22no—
1163C22—26no—
1164C22—22no—
1165C22—26no—
1166C22—22no—
1167C22—26no—
1168C22—26no—
1169C22—26no—
1170C22—22no—
1171C22—22no—
1172C22—22no—
1173C22—22no—
1174C22—22no—
1175C22—26no—
1176C22—26no—
1177C22—26no—
1178C22—448no—
1179C22—43no—
1180C22—41no—
1181C22—43no—
1182C22—41no—
1183C22—43no—
1184C22—43no—
1185C22—41no—
1186C22—41no—
1187C22—42no—
1188C22—43no—
1189C22—42no—
1190C22—43no—
1191C22—42no—
1192C22—43no—
1193C22—42no—
1194C22—43no—
1195C22—43no—
1196C22—42no—
1197C22—42no—
1198C22—43no—
1199C22—42no—
1200C22—43no—
1201C22—824no—
1202C22C22×#121112yes—
1203C22#348914yescomplemented
1204C22C24×D411yescharacteristic
1205C22C24×D411yescharacteristic
1206C22C23×#4111yescharacteristic
1207C22C22×2−1+411yescharacteristic
1208C22C2×#58511yescharacteristic
1209C22H(7,𝔽2)11yescharacteristic
1210C222−1+611yescharacteristic
1211C4—212no—
1212C4—24no—
1213C4—22no—
1214C4—22no—
1215C4—26no—
1216C4—46no—
1217C4—42no—
1218C4—43no—
1219C4—42no—
1220C4—41no—
1221C4—46no—
1222C4—43no—
1223C4—41no—
1224C4—43no—
1225C4—46no—
1226C4C22×#12114yes—
1227C4C22×#121112yes—
1228C2—24no—
1229C2—212no—
1230C2—46no—
1231C2—42no—
1232C2—82no—
1233C2—83no—
1234C2C23×#12111yescharacteristic
1235C2C2×#348911yescharacteristic
1236C2#6285311yescharacteristic
1237C2#6298711yescharacteristic
1238C2#6299311yescharacteristic
1239C2D4×2−1+411yescharacteristic
1240C2#6300011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3489C2semidirect
2. C2×#3489C2semidirect
3. C2×D4×#41C2semidirect
4. C22×#520C2semidirect
5. Q8×#121C2semidirect
6. #36434C2semidirect
7. #36214C2semidirect
8. #36153C2semidirect
9. #36020C2semidirect
10. #35831C2semidirect
11. #35821C2semidirect
12. #35737C2semidirect
13. #35633C2semidirect
14. #35621C2semidirect
15. #35564C2semidirect
16. #35518C2semidirect
17. #35306C2semidirect
18. #35223C2semidirect
19. #34737C2semidirect
20. C2×#2417C2semidirect
21. #34259C2semidirect
22. #34250C2semidirect
23. #34175C2semidirect
32. C2×D4×Q8C22semidirect
33. C2×D4×Q8C22semidirect
36. C2×#548C22semidirect
37. C2×#548C22semidirect
39. C2×#547C22semidirect
40. C2×#547C22semidirect
43. C2×#546C22semidirect
44. C2×#546C22semidirect
46. C2×#537C22semidirect
47. C2×#537C22semidirect
48. C2×#536C22semidirect
49. C2×#536C22semidirect
53. C2×#525C22semidirect
54. C2×#525C22semidirect
55. C22×C22⋊Q8C22semidirect
56. C22×C22⋊Q8C22semidirect
61. C2×#520C22semidirect
62. C2×#520C22semidirect
63. C2×#520C22semidirect
64. C2×#520C22semidirect
66. C22×C4×Q8C22semidirect
68. C22×C4×D4C22semidirect
69. C22×#117C22semidirect
70. C23×C4⋊C4C22semidirect
71. #2857C22semidirect
72. #2850C22semidirect
73. #2847C22semidirect
74. #2621C22semidirect
75. #2620C22semidirect
76. #2618C22semidirect
77. #2547C22semidirect
78. #2546C22semidirect
79. #2545C22semidirect
80. #2544C22semidirect
81. #2543C22semidirect
82. #2538C22semidirect
83. #2537C22semidirect
84. #2536C22semidirect
85. #2535C22semidirect
86. #2534C22semidirect
87. #2486C22semidirect
88. #2429C22semidirect
89. #2429C22semidirect
90. #2429C22semidirect
91. #2428C22semidirect
92. #2427C22semidirect
93. #2427C22semidirect
94. #2427C22semidirect
95. #2426C22semidirect
96. #2425C22semidirect
97. #2425C22semidirect
98. #2425C22semidirect
99. #2424C22semidirect
102. #2417C22semidirect
103. #2417C22semidirect
104. #2417C22semidirect
105. #2417C22semidirect
106. #2417C22semidirect
107. #2417C22semidirect
108. #2417C22semidirect
109. #2417C22semidirect
110. #2417C22semidirect
111. #2417C22semidirect
113. #2416C22semidirect
114. #2416C22semidirect
115. #2416C22semidirect
116. #2416C22semidirect
117. #2416C22semidirect
118. #2415C22semidirect
119. #2415C22semidirect
120. #2415C22semidirect
121. #2415C22semidirect
122. #2414C22semidirect
123. #2414C22semidirect
124. #2413C22semidirect
125. #2413C22semidirect
126. #2412C22semidirect
127. #2412C22semidirect
128. #2411C22semidirect
130. #2392C22semidirect
131. #2392C22semidirect
132. C2×#398C22semidirect
133. C2×#396C22semidirect
134. #2351C22semidirect
135. Q8×C4⋊C4C22semidirect
136. #2349C22semidirect
137. D4×C4⋊C4C22semidirect
138. #2341C22semidirect
139. Q8×C22⋊C4C22semidirect
140. Q8×C22⋊C4C22semidirect
141. Q8×C22⋊C4C22semidirect
142. #2339C22semidirect
143. #2339C22semidirect
144. #2339C22semidirect
145. D4×C22⋊C4C22semidirect
146. #2317C22semidirect
147. #2316C22semidirect
148. #2311C22semidirect
149. #2311C22semidirect
150. #2311C22semidirect
151. #2310C22semidirect
153. C4×#121C22semidirect
154. #2297C22semidirect
155. #2296C22semidirect
156. C2×#391C22semidirect
157. C2×#389C22semidirect
159. #2280C22semidirect
160. C2×#380C22semidirect
161. C2×#380C22semidirect
170. C22×#41D4semidirect
274. #520D4semidirect
612. C4×Q8C2×D4semidirect
634. C4×D4C2×D4semidirect
642. #117C2×D4semidirect
655. C2×C4⋊C4C2×D4semidirect
782. #41#121semidirect
852. C2×D42−1+4semidirect
1203. C22#3489semidirect

Maximal subgroups

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

subgroupindex
C2×#34892
C2×D4×#412
C22×#5202
Q8×#1212
#364342
#362142
#361532
#360202
#358312
#358212
#357372
#356332
#356212
#355642
#355182
#353062
#352232
#347372
C2×#24172
#342592
#342502
#341752