Finite Group Databasebeta

← #6394040

Subgroups — #6394040

Order 512.

3084 conjugacy classes of subgroups.

The subgroup lattice has 1287 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3495C211yesmaximal, characteristic
2#34180C211yesmaximal, characteristic, complemented
3#34109C211yesmaximal, characteristic, complemented
4#22513C214yesmaximal, complemented
5#22478C214yesmaximal, complemented
6#22477C218yesmaximal, complemented
7#21875C212yesmaximal, complemented
8#21874C211yesmaximal, characteristic
9#21826C212yesmaximal, complemented
10#21825C211yesmaximal, characteristic, complemented
11#21421C212yesmaximal, complemented
12#21420C211yesmaximal, characteristic
13#21332C212yesmaximal, complemented
14C2×#1996C211yesmaximal, characteristic, complemented
15#3495—22no—
16#3495—21no—
17#3495—22no—
18#3495—22no—
19#3495—21no—
20#3495—21no—
21#3495—21no—
22#3495—21no—
23#3495—21no—
24#3495—21no—
25#3495—21no—
26#3495—22no—
27C2×#556C412yescomplemented
28C2×#554C2212yes—
29C2×#552C414yescomplemented
30C2×#552C412yescomplemented
31C2×#552C2212yes—
32C2×#551C2214yes—
33C2×#544C411yescharacteristic, complemented
34C2×#542C412yescomplemented
35C2×#541C412yescomplemented
36C2×#536C411yescharacteristic, complemented
37C2×#533C2212yes—
38C2×#529C2212yes—
39C2×#525C2211yescharacteristic
40C22×C22⋊Q8C2211yescharacteristic
41C2×#520C411yescharacteristic, complemented
42C2×#519C411yescharacteristic, complemented
43C22×#117C2211yescharacteristic
44#2347—21no—
45#2347—21no—
46#2346—21no—
47#2346—21no—
48#2345C2212yes—
49#2345C2212yes—
50#2344C2212yes—
51#2344C2212yes—
52#2343—22no—
53#2343—22no—
54#2342C2214yes—
55#2342C2214yes—
56#2317—21no—
57#2314—22no—
58#2298—22no—
59#2296—21no—
60#2285C2212yes—
61#2283C2212yes—
62#2283C2212yes—
63#2280C2211yescharacteristic
64#2280C2211yescharacteristic
65C2×#380C2211yescharacteristic
66#2274—21no—
67C4×#117—21no—
68C4×#117C2212yes—
69C2×C4×C22⋊C4C2211yescharacteristic
70#1996C2212yes—
71#1996C2212yes—
72#1996C2214yes—
73#1996C2211yescharacteristic
74#1996C2212yes—
75#1996C2212yes—
76#1996C2218yes—
77#1996C2212yes—
78#1996C2214yes—
79#1996C2211yescharacteristic
80#1996C2218yes—
81#1964C2212yes—
82#1964C2211yescharacteristic
83#1964C2211yescharacteristic
84#1899C2218yes—
85#1899C2218yes—
86#1898C2214yes—
87#1898C2214yes—
88#1820C2218yes—
89#1819C2214yes—
90#1799C2214yes—
91#1799C2218yes—
92C4×#99C2214yes—
93C4×#99C2218yes—
94#1740C2218yes—
95C2×#342C2214yes—
96C22×#41C2×C411yescharacteristic
97C23×Q8C2×C411yescharacteristic
98C24×C4C2311yescharacteristic
99#556—22no—
100#556—22no—
101#556—22no—
102#556—22no—
103#556—24no—
104#556—24no—
105#554—22no—
106#554—22no—
107#554—24no—
108#554—24no—
109#554—22no—
110#554—22no—
111#552—24no—
112#552—24no—
113#552—24no—
114#552—24no—
115#552—24no—
116#552—24no—
117#552—24no—
118#552—24no—
119#552—22no—
120#552—22no—
121#552—22no—
122#552—22no—
123#552—24no—
124#552—24no—
125#552—22no—
126#552—22no—
127#552—24no—
128#552—24no—
129#552—22no—
130#552—22no—
131#551—24no—
132#551—24no—
133#551—24no—
134#551—24no—
135#551—24no—
136#551—24no—
137#551—24no—
138#551—24no—
139#544—22no—
140#544—22no—
141#544—21no—
142#544—21no—
143#544—21no—
144#544—21no—
145#542—22no—
146#542—22no—
147#542—22no—
148#542—22no—
149#542—22no—
150#542—22no—
151#542—22no—
152#542—22no—
153#541—22no—
154#541—22no—
155#541—22no—
156#541—22no—
157#541—22no—
158#541—22no—
159#541—22no—
160#541—22no—
161#536—22no—
162#536—22no—
163#536—21no—
164#536—21no—
165#536—21no—
166#536—21no—
167#533—22no—
168#533—22no—
169#533—22no—
170#533—22no—
171#533—22no—
172#533—22no—
173#533—22no—
174#533—22no—
175C2×C4⋊Q8C2×C412yescomplemented
176C2×C4⋊Q8C2×C412yescomplemented
177C2×C4⋊Q8C2×C412yescomplemented
178#529—22no—
179#529—22no—
180#529—22no—
181#529—22no—
182#529—22no—
183#529—22no—
184#529—22no—
185#529—22no—
186C2×#126C2×C414yes—
187C2×#126C2×C414yes—
188C2×#126C2×C414yescomplemented
189C2×#126C2×C414yescomplemented
190C2×#125C2×C412yescomplemented
191C2×#125C2×C414yescomplemented
192C2×#125C2×C414yescomplemented
193C2×#125C2×C414yescomplemented
194C2×#125C2×C412yescomplemented
195C2×#124C2×C414yes—
196C2×#124C2×C412yescomplemented
197#525—21no—
198#525—21no—
199#525—21no—
200#525—21no—
201#525—21no—
202#525—21no—
203#525—21no—
204#525—21no—
205C2×#123C2×C412yes—
206C2×#123C2×C414yes—
207C2×#123C2×C414yes—
208C2×#123C2314yes—
209C2×C22⋊Q8—21no—
210C2×C22⋊Q8—21no—
211C2×C22⋊Q8—21no—
212C2×C22⋊Q8—21no—
213C2×C22⋊Q8—21no—
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8C2×C412yes—
218C2×C22⋊Q8C2×C412yes—
219C2×C22⋊Q8C2×C411yescharacteristic
220C2×C22⋊Q8C2×C414yes—
221C2×C22⋊Q8C2×C412yescomplemented
222C2×C22⋊Q8C2×C412yescomplemented
223C2×C22⋊Q8C2×C414yescomplemented
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2314yes—
228C2×#121C2×C411yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#120C2312yes—
231#520—22no—
232#520—22no—
233#520—21no—
234#520—21no—
235#520—21no—
236#520—21no—
237#519—22no—
238#519—22no—
239#519—21no—
240#519—21no—
241#519—21no—
242#519—21no—
243C2×C4×Q8C2×C412yescomplemented
244C2×C4×Q8C2×C412yescomplemented
245C2×C4×Q8C2×C412yescomplemented
246C2×C4×Q8C2×C412yescomplemented
247C2×C4×Q8C2×C412yescomplemented
248C2×C4×Q8C2×C414yescomplemented
249C2×C4×D4C2×C414yes—
250C2×C4×D4C2×C412yes—
251C2×C4×D4C2×C412yescomplemented
252C2×C4×D4C2312yes—
253C2×C4×D4C2314yes—
254C2×#117—21no—
255C2×#117—21no—
256C2×#117C2×C411yescharacteristic
257C2×#117C2×C414yes—
258C2×#117C2×C411yescharacteristic
259C2×#117C2×C411yescharacteristic
260C2×#117C2×C412yes—
261C2×#117C2×C411yescharacteristic
262C2×#117C2×C412yes—
263C2×#117C2×C411yescharacteristic
264C2×#117C2×C412yescomplemented
265C2×#117C2×C414yescomplemented
266C2×#117D412yes—
267C2×#117D411yescharacteristic
268C2×#117D412yes—
269C2×#117D412yes—
270C2×#117D411yescharacteristic
271C2×#117D411yescharacteristic
272C2×#117D411yescharacteristic
273C2×#117D411yescharacteristic
274C2×#117D411yescharacteristic
275C2×#117D411yescharacteristic
276C2×#117D411yescharacteristic
277C2×#117D412yes—
278C2×#117C2314yes—
279C2×#117C2314yes—
280C2×#117C2314yes—
281C22×C4⋊C4—21no—
282C22×C4⋊C4C2×C411yescharacteristic
283C22×C4⋊C4C2×C412yes—
284C22×C4⋊C4C2×C412yescomplemented
285C22×C4⋊C4C2311yescharacteristic
286C22×C4⋊C4C2311yescharacteristic
287C22×C22⋊C4C2312yes—
288C22×C22⋊C4C2312yes—
289C22×C22⋊C4C2312yes—
290C22×C22⋊C4C2312yes—
291C22×C42—21no—
292C22×C42C2312yes—
293C2×#99C2314yes—
294C2×#99C2318yes—
295C2×#99C2314yes—
296#389—22no—
297#389—22no—
298#389—22no—
299#389—22no—
300#388—24no—
301#388—24no—
302#388—24no—
303#388—24no—
304#387—24no—
305#387—24no—
306#387—24no—
307#387—24no—
308#385—24no—
309#385—24no—
310#384—22no—
311#383—22no—
312#383—22no—
313#382—22no—
314#382—22no—
315#382—22no—
316#381—21no—
317#381—21no—
318#381C2314yes—
319#381C2314yes—
320#380—21no—
321#380—21no—
322#380—21no—
323#380—21no—
324#380C2314yes—
325#380C2314yes—
326#380C2312yes—
327#380C2312yes—
328#380C2312yes—
329#380C2311yescharacteristic
330#380C2311yescharacteristic
331#379C2312yes—
332#379C2312yes—
333C4×C4⋊C4—22no—
334C4×C4⋊C4—22no—
335C4×C4⋊C4—22no—
336C4×C4⋊C4—22no—
337C4×C4⋊C4—22no—
338C4×C4⋊C4—22no—
339C4×C4⋊C4—22no—
340C4×C4⋊C4—22no—
341C4×C4⋊C4—22no—
342C4×C4⋊C4—22no—
343C4×C22⋊C4—21no—
344C4×C22⋊C4—21no—
345C4×C22⋊C4—21no—
346C4×C22⋊C4—21no—
347C4×C22⋊C4—24no—
348C4×C22⋊C4—24no—
349C4×C22⋊C4C2314yes—
350C4×C22⋊C4C2314yes—
351C4×C22⋊C4C2312yes—
352C4×C22⋊C4C2312yes—
353C4×C22⋊C4C2311yescharacteristic
354C4×C22⋊C4C2311yescharacteristic
355C4×C22⋊C4C2312yes—
356#376—22no—
357#376—22no—
358#376—22no—
359C2×#95—21no—
360C2×#95—21no—
361C43—22no—
362#342C2318yes—
363#342C2318yes—
364#342C2318yes—
365#342C2318yes—
366#342C2314yes—
367#342C2314yes—
368#342C2318yes—
369C25C2411yescharacteristic
370C2×#41—21no—
371C2×#41—21no—
372C2×#41—21no—
373C2×#41—21no—
374C2×#41—44no—
375C22×Q8—21no—
376C22×Q8—21no—
377C22×Q8—21no—
378C22×Q8—21no—
379C22×Q8—44no—
380C22×Q8C22×C412yes—
381C22×Q8C22×C412yes—
382C22×Q8C22×C411yescharacteristic
383C22×Q8C22×C414yes—
384C22×D4C22×C412yes—
385C22×D4C22×C411yescharacteristic
386C22×D4C22×C412yes—
387C22×D4C2412yes—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—44no—
391C23×C4C22×C411yescharacteristic
392C23×C4C22×C412yes—
393C23×C4C22×C412yes—
394C23×C4C22×C412yes—
395C23×C4C22×C414yes—
396C23×C4C22×C411yescharacteristic
397C23×C4C22×C411yescharacteristic
398C23×C4C22×C411yescharacteristic
399C23×C4C2×D411yescharacteristic
400C23×C4C2×D411yescharacteristic
401C23×C4C2×D411yescharacteristic
402C23×C4C2×D411yescharacteristic
403C23×C4C2×D411yescharacteristic
404C23×C4C2×D411yescharacteristic
405C23×C4C2×D411yescharacteristic
406C23×C4C2×D411yescharacteristic
407C23×C4C2412yes—
408C23×C4C2411yescharacteristic
409C23×C4C2411yescharacteristic
410C23×C4C2412yes—
411C4⋊Q8—24no—
412C4⋊Q8—22no—
413C4⋊Q8—22no—
414C4⋊Q8—22no—
415C4⋊Q8—22no—
416C4⋊Q8—22no—
417C4⋊Q8—22no—
418C4⋊Q8—22no—
419C4⋊Q8—22no—
420C4⋊Q8—22no—
421C4⋊Q8—22no—
422#126—24no—
423#126—24no—
424#126—24no—
425#126—24no—
426#126—24no—
427#126—24no—
428#126—24no—
429#126—24no—
430#126—24no—
431#126—24no—
432#126—24no—
433#126—24no—
434#126—24no—
435#126—24no—
436#126—24no—
437#126—24no—
438#125—24no—
439#125—24no—
440#125—24no—
441#125—24no—
442#125—24no—
443#125—24no—
444#125—24no—
445#125—24no—
446#125—24no—
447#125—22no—
448#125—22no—
449#125—22no—
450#125—22no—
451#125—22no—
452#125—22no—
453#125—24no—
454#125—24no—
455#125—24no—
456#125—24no—
457#124—24no—
458#124—24no—
459#124—24no—
460#124—24no—
461#124—22no—
462#124—22no—
463#124—22no—
464#124—22no—
465#123—22no—
466#123—22no—
467#123—22no—
468#123—22no—
469#123—24no—
470#123—24no—
471#123—24no—
472#123—24no—
473#123—24no—
474#123—24no—
475#123—24no—
476#123—24no—
477#123—24no—
478#123—24no—
479#123—24no—
480#123—24no—
481C22⋊Q8—22no—
482C22⋊Q8—22no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488C22⋊Q8—22no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493C22⋊Q8—22no—
494C22⋊Q8—22no—
495C22⋊Q8—22no—
496C22⋊Q8—22no—
497C22⋊Q8—22no—
498C22⋊Q8—22no—
499C22⋊Q8—22no—
500C22⋊Q8—22no—
501C22⋊Q8—21no—
502C22⋊Q8—21no—
503C22⋊Q8—21no—
504C22⋊Q8—21no—
505C22⋊Q8—24no—
506C22⋊Q8—24no—
507C22⋊Q8—24no—
508C22⋊Q8—24no—
509C22⋊Q8—24no—
510C22⋊Q8—22no—
511C22⋊Q8—22no—
512C22⋊Q8—24no—
513C22⋊Q8—22no—
514C22⋊Q8—22no—
515C22⋊Q8—24no—
516C22⋊Q8—24no—
517C22⋊Q8—24no—
518C22⋊Q8—24no—
519C22⋊Q8—24no—
520C22⋊Q8—24no—
521C22⋊Q8—24no—
522C22⋊Q8—24no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—21no—
531#120—22no—
532#120—22no—
533#120—22no—
534#120—22no—
535C4×Q8—24no—
536C4×Q8—22no—
537C4×Q8—22no—
538C4×Q8—24no—
539C4×Q8—22no—
540C4×Q8—22no—
541C4×Q8—22no—
542C4×Q8—22no—
543C4×Q8—22no—
544C4×Q8—22no—
545C4×Q8—22no—
546C4×Q8—22no—
547C4×Q8—22no—
548C4×Q8—22no—
549C4×Q8—22no—
550C4×Q8—22no—
551C4×Q8—22no—
552C4×Q8—22no—
553C4×Q8—24no—
554C4×Q8—24no—
555C4×Q8—24no—
556C4×Q8—24no—
557C4×D4—22no—
558C4×D4—22no—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—22no—
562C4×D4—22no—
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—24no—
566C4×D4—24no—
567C4×D4—24no—
568C4×D4—24no—
569C4×D4—24no—
570C4×D4—24no—
571C4×D4—24no—
572C4×D4—24no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—22no—
577#117—21no—
578#117—21no—
579#117—21no—
580#117—21no—
581#117—24no—
582#117—24no—
583#117—24no—
584#117—24no—
585#117—24no—
586#117—22no—
587#117—22no—
588#117—24no—
589#117—24no—
590#117—24no—
591#117—24no—
592#117—24no—
593#117—24no—
594#117—24no—
595#117—24no—
596#117—28no—
597#117—44no—
598#117—44no—
599#117—44no—
600#117—48no—
601#117C22⋊C412yes—
602#117C22⋊C412yes—
603#117C22⋊C411yescharacteristic
604#117C22⋊C411yescharacteristic
605#117C22⋊C411yescharacteristic
606#117C22⋊C411yescharacteristic
607#117C22⋊C412yes—
608#117C22⋊C412yes—
609#117C22⋊C411yescharacteristic
610#117C22⋊C411yescharacteristic
611#117C22⋊C411yescharacteristic
612#117C22⋊C411yescharacteristic
613#117C22⋊C412yes—
614#117C22⋊C412yes—
615#117C22⋊C412yes—
616#117C22⋊C412yes—
617#117C22⋊C412yes—
618#117C22⋊C412yes—
619#117C22⋊C412yes—
620#117C22⋊C412yes—
621#117C22⋊C411yescharacteristic
622#117C22⋊C411yescharacteristic
623#117C22⋊C411yescharacteristic
624#117C22⋊C411yescharacteristic
625#117C22⋊C412yes—
626#117C22⋊C412yes—
627#117C22⋊C412yes—
628#117C22⋊C412yes—
629#117C22⋊C412yes—
630#117C22⋊C412yes—
631#117C22⋊C412yes—
632#117C22⋊C412yes—
633#117C22⋊C412yes—
634#117C22⋊C412yes—
635#117C22⋊C411yescharacteristic
636#117C22⋊C411yescharacteristic
637#117C22⋊C411yescharacteristic
638#117C22⋊C411yescharacteristic
639#117C22⋊C412yes—
640#117C22⋊C412yes—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—22no—
648C2×C4⋊C4—22no—
649C2×C4⋊C4—24no—
650C2×C4⋊C4—22no—
651C2×C4⋊C4—22no—
652C2×C4⋊C4—22no—
653C2×C4⋊C4—22no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—24no—
658C2×C4⋊C4—24no—
659C2×C4⋊C4—24no—
660C2×C4⋊C4—24no—
661C2×C4⋊C4—44no—
662C2×C4⋊C4C22×C412yes—
663C2×C4⋊C4C22×C414yes—
664C2×C4⋊C4C22×C412yes—
665C2×C4⋊C4C22×C414yes—
666C2×C4⋊C4C22×C414yes—
667C2×C4⋊C4C22×C411yescharacteristic
668C2×C4⋊C4C22×C411yescharacteristic
669C2×C4⋊C4C22×C414yes—
670C2×C4⋊C4C22×C414yes—
671C2×C4⋊C4C22×C414yes—
672C2×C4⋊C4C22×C414yes—
673C2×C4⋊C4C22×C414yes—
674C2×C4⋊C4C22×C412yes—
675C2×C4⋊C4C22×C412yes—
676C2×C4⋊C4C22×C414yes—
677C2×C4⋊C4C22×C414yes—
678C2×C4⋊C4C22×C411yescharacteristic
679C2×C4⋊C4C22×C411yescharacteristic
680C2×C4⋊C4C22×C411yescharacteristic
681C2×C4⋊C4C22×C412yes—
682C2×C4⋊C4C22×C411yescharacteristic
683C2×C4⋊C4C22×C412yes—
684C2×C4⋊C4C2×D411yescharacteristic
685C2×C4⋊C4C2×D411yescharacteristic
686C2×C4⋊C4C2×D412yes—
687C2×C4⋊C4C2×D412yes—
688C2×C4⋊C4C2×D411yescharacteristic
689C2×C4⋊C4C2×D411yescharacteristic
690C2×C4⋊C4C2×D411yescharacteristic
691C2×C4⋊C4C2×D411yescharacteristic
692C2×C4⋊C4C2×D412yes—
693C2×C4⋊C4C2×D412yes—
694C2×C4⋊C4C2×D411yescharacteristic
695C2×C4⋊C4C2×D411yescharacteristic
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—24no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—42no—
708C2×C22⋊C4—44no—
709C2×C22⋊C4C22×C414yes—
710C2×C22⋊C4C22×C412yes—
711C2×C22⋊C4C22×C412yes—
712C2×C22⋊C4C22×C414yes—
713C2×C22⋊C4C22×C414yes—
714C2×C22⋊C4C22×C412yes—
715C2×C22⋊C4C22×C412yes—
716C2×C22⋊C4C22×C414yes—
717C2×C22⋊C4C22×C412yes—
718C2×C22⋊C4C22×C412yes—
719C2×C22⋊C4C22×C412yes—
720C2×C22⋊C4C22×C412yes—
721C2×C22⋊C4C2×D412yes—
722C2×C22⋊C4C2×D412yes—
723C2×C22⋊C4C2×D412yes—
724C2×C22⋊C4C2×D412yes—
725C2×C22⋊C4C2×D412yes—
726C2×C22⋊C4C2×D412yes—
727C2×C22⋊C4C2×D412yes—
728C2×C22⋊C4C2×D412yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2412yes—
731C2×C22⋊C4C2412yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2412yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2412yes—
736C2×C22⋊C4C2412yes—
737C2×C42—22no—
738C2×C42—22no—
739C2×C42—24no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—22no—
743C2×C42—24no—
744C2×C42—24no—
745C2×C42—24no—
746C2×C42—44no—
747C2×C42C22×C414yes—
748C2×C42C22×C414yes—
749C2×C42C22×C412yes—
750C2×C42C22×C414yes—
751C2×C42C22×C412yes—
752C2×C42C22×C412yes—
753C2×C42C22×C412yes—
754C2×C42C22×C412yes—
755C2×C42C2×D412yes—
756C2×C42C2×D412yes—
757C2×C42C2×D412yes—
758C2×C42C2×D412yes—
759C2×C42C2×D412yes—
760C2×C42C2×D412yes—
761C2×C42C2×D412yes—
762C2×C42C2×D412yes—
763#99—28no—
764#99—44no—
765#99—48no—
766#95—21no—
767#95—22no—
768#95—21no—
769#95—22no—
770#95—22no—
771#95—21no—
772#95—24no—
773#95—24no—
774#95—22no—
775#95—24no—
776#95—24no—
777#95—21no—
778#95—24no—
779#95—24no—
780#95—22no—
781#95—22no—
782#95—24no—
783#95—24no—
784C24—22no—
785C24—22no—
786C24—42no—
787C24—81no—
788C24C23×C411yescharacteristic
789C24C23×C412yes—
790C24C23×C411yescharacteristic
791C24C22×D411yescharacteristic
792C24C22×D411yescharacteristic
793C24C22×D411yescharacteristic
794C24C22×D411yescharacteristic
795C24C2511yescharacteristic
796#41—44no—
797#41—44no—
798#41—44no—
799#41—44no—
800C2×Q8—22no—
801C2×Q8—22no—
802C2×Q8—22no—
803C2×Q8—22no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—24no—
807C2×Q8—24no—
808C2×Q8—44no—
809C2×Q8—44no—
810C2×Q8—42no—
811C2×Q8—44no—
812C2×Q8—44no—
813C2×Q8—44no—
814C2×Q8—44no—
815C2×Q8—84no—
816C2×D4—22no—
817C2×D4—22no—
818C2×D4—22no—
819C2×D4—22no—
820C2×D4—24no—
821C2×D4—24no—
822C2×D4—22no—
823C2×D4—22no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—42no—
827C2×D4—44no—
828C2×D4—82no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—24no—
846C22×C4—24no—
847C22×C4—22no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—82no—
865C22×C4—82no—
866C22×C4—84no—
867C22×C4—82no—
868C22×C4—82no—
869C22×C4—82no—
870C22×C4C2×C22⋊C411yescharacteristic
871C22×C4C2×C22⋊C411yescharacteristic
872C22×C4C2×C22⋊C411yescharacteristic
873C22×C4C2×C22⋊C411yescharacteristic
874C22×C4C2×C22⋊C411yescharacteristic
875C22×C4C2×C22⋊C411yescharacteristic
876C22×C4C2×C22⋊C411yescharacteristic
877C22×C4C2×C22⋊C411yescharacteristic
878C22×C4C2×C22⋊C411yescharacteristic
879C22×C4C2×C22⋊C411yescharacteristic
880C22×C4C2×C22⋊C411yescharacteristic
881C22×C4C2×C22⋊C411yescharacteristic
882C22×C4C2×C22⋊C411yescharacteristic
883C22×C4C2×C22⋊C411yescharacteristic
884C22×C4C2×C22⋊C411yescharacteristic
885C22×C4C2×C22⋊C411yescharacteristic
886C22×C4C23×C412yes—
887C22×C4C23×C412yes—
888C22×C4C23×C411yescharacteristic
889C22×C4C23×C412yes—
890C22×C4C23×C411yescharacteristic
891C22×C4C23×C412yes—
892C22×C4C23×C414yes—
893C22×C4C23×C412yes—
894C22×C4C23×C414yes—
895C22×C4C23×C411yescharacteristic
896C22×C4C23×C412yes—
897C22×C4C23×C412yes—
898C22×C4C23×C411yescharacteristic
899C22×C4C22×D412yes—
900C22×C4C22×D412yes—
901C22×C4C22×D412yes—
902C22×C4C22×D412yes—
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D412yes—
912C22×C4C22×D412yes—
913C22×C4C22×D412yes—
914C22×C4C22×D412yes—
915C4⋊C4—22no—
916C4⋊C4—22no—
917C4⋊C4—24no—
918C4⋊C4—24no—
919C4⋊C4—22no—
920C4⋊C4—22no—
921C4⋊C4—24no—
922C4⋊C4—24no—
923C4⋊C4—24no—
924C4⋊C4—24no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—24no—
930C4⋊C4—24no—
931C4⋊C4—24no—
932C4⋊C4—24no—
933C4⋊C4—24no—
934C4⋊C4—24no—
935C4⋊C4—24no—
936C4⋊C4—24no—
937C4⋊C4—24no—
938C4⋊C4—24no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—22no—
943C4⋊C4—24no—
944C4⋊C4—24no—
945C4⋊C4—24no—
946C4⋊C4—24no—
947C4⋊C4—48no—
948C4⋊C4—44no—
949C4⋊C4—44no—
950C4⋊C4—44no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—84no—
954C4⋊C4—84no—
955C4⋊C4—84no—
956C4⋊C4C2×C22⋊C412yes—
957C4⋊C4C2×C22⋊C411yescharacteristic
958C4⋊C4C2×C22⋊C411yescharacteristic
959C4⋊C4C2×C22⋊C412yes—
960C4⋊C4C2×C22⋊C411yescharacteristic
961C4⋊C4C2×C22⋊C411yescharacteristic
962C4⋊C4C2×C22⋊C412yes—
963C4⋊C4C2×C22⋊C412yes—
964C4⋊C4C2×C22⋊C412yes—
965C4⋊C4C2×C22⋊C412yes—
966C4⋊C4C2×C22⋊C412yes—
967C4⋊C4C2×C22⋊C411yescharacteristic
968C4⋊C4C2×C22⋊C411yescharacteristic
969C4⋊C4C2×C22⋊C412yes—
970C4⋊C4C2×C22⋊C411yescharacteristic
971C4⋊C4C2×C22⋊C411yescharacteristic
972C4⋊C4C2×C22⋊C412yes—
973C4⋊C4C2×C22⋊C412yes—
974C4⋊C4C2×C22⋊C412yes—
975C4⋊C4C2×C22⋊C412yes—
976C22⋊C4—24no—
977C22⋊C4—24no—
978C22⋊C4—22no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—24no—
983C22⋊C4—24no—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—24no—
990C22⋊C4—24no—
991C22⋊C4—24no—
992C22⋊C4—24no—
993C22⋊C4—22no—
994C22⋊C4—22no—
995C22⋊C4—24no—
996C22⋊C4—24no—
997C22⋊C4—24no—
998C22⋊C4—22no—
999C22⋊C4—24no—
1000C22⋊C4—22no—
1001C22⋊C4—24no—
1002C22⋊C4—28no—
1003C22⋊C4—24no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—82no—
1008C22⋊C4—82no—
1009C22⋊C4—82no—
1010C22⋊C4C2×C22⋊C412yes—
1011C22⋊C4C2×C22⋊C412yes—
1012C22⋊C4C2×C22⋊C412yes—
1013C22⋊C4C2×C22⋊C412yes—
1014C22⋊C4C2×C22⋊C412yes—
1015C22⋊C4C2×C22⋊C412yes—
1016C22⋊C4C2×C22⋊C412yes—
1017C22⋊C4C2×C22⋊C412yes—
1018C22⋊C4C2×C22⋊C412yes—
1019C22⋊C4C2×C22⋊C412yes—
1020C22⋊C4C2×C22⋊C412yes—
1021C22⋊C4C2×C22⋊C412yes—
1022C22⋊C4C2×C22⋊C412yes—
1023C22⋊C4C2×C22⋊C412yes—
1024C22⋊C4C2×C22⋊C412yes—
1025C22⋊C4C2×C22⋊C412yes—
1026C22⋊C42−1+414yes—
1027C42—24no—
1028C42—24no—
1029C42—24no—
1030C42—24no—
1031C42—24no—
1032C42—24no—
1033C42—22no—
1034C42—22no—
1035C42—48no—
1036C42—42no—
1037C42—42no—
1038C42—44no—
1039C42—44no—
1040C42—44no—
1041C42—84no—
1042C42—84no—
1043C42—84no—
1044C42C2×C22⋊C412yes—
1045C42C2×C22⋊C412yes—
1046C42C2×C22⋊C412yes—
1047C42C2×C22⋊C412yes—
1048C42C2×C22⋊C412yes—
1049C42C2×C22⋊C412yes—
1050C42C2×C22⋊C412yes—
1051C42C2×C22⋊C412yes—
1052C42C2×C22⋊C412yes—
1053C42C2×C22⋊C412yes—
1054C42C2×C22⋊C412yes—
1055C42C2×C22⋊C412yes—
1056C42C2×C22⋊C412yes—
1057C42C2×C22⋊C412yes—
1058C42C2×C22⋊C412yes—
1059C42C2×C22⋊C412yes—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—21no—
1066C23—21no—
1067C23—22no—
1068C23—22no—
1069C23—21no—
1070C23—21no—
1071C23—22no—
1072C23—24no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—42no—
1085C23—42no—
1086C23—84no—
1087C23—84no—
1088C23C22×C22⋊C411yescharacteristic
1089C23C22×C22⋊C411yescharacteristic
1090C23C22×C22⋊C411yescharacteristic
1091C23C22×C22⋊C411yescharacteristic
1092C23C24×C411yescharacteristic
1093C23C23×D411yescharacteristic
1094C23C23×D411yescharacteristic
1095C23C2×2−1+412yes—
1096C23#58512yes—
1097Q8—44no—
1098Q8—44no—
1099Q8—42no—
1100Q8—44no—
1101Q8—44no—
1102Q8—42no—
1103Q8—84no—
1104Q8—84no—
1105D4—42no—
1106D4—44no—
1107D4—44no—
1108D4—44no—
1109D4—42no—
1110D4—42no—
1111D4—42no—
1112D4—82no—
1113D4—82no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—44no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—44no—
1166C2×C4—44no—
1167C2×C4—44no—
1168C2×C4—42no—
1169C2×C4—44no—
1170C2×C4—44no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—44no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—44no—
1178C2×C4—44no—
1179C2×C4—42no—
1180C2×C4—44no—
1181C2×C4—42no—
1182C2×C4—44no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—44no—
1187C2×C4—84no—
1188C2×C4—84no—
1189C2×C4—82no—
1190C2×C4—82no—
1191C2×C4—88no—
1192C2×C4—164no—
1193C2×C4#41014yes—
1194C2×C4C22×C22⋊C412yes—
1195C2×C4C22×C22⋊C412yes—
1196C2×C4C22×C22⋊C412yes—
1197C2×C4C22×C22⋊C412yes—
1198C2×C4C22×C22⋊C411yescharacteristic
1199C2×C4C22×C22⋊C411yescharacteristic
1200C2×C4C22×C22⋊C411yescharacteristic
1201C2×C4C22×C22⋊C411yescharacteristic
1202C2×C4C22×C22⋊C412yes—
1203C2×C4C22×C22⋊C412yes—
1204C2×C4C22×C22⋊C412yes—
1205C2×C4C22×C22⋊C412yes—
1206C2×C4C22×C22⋊C411yescharacteristic
1207C2×C4C22×C22⋊C411yescharacteristic
1208C2×C4C22×C22⋊C411yescharacteristic
1209C2×C4C22×C22⋊C411yescharacteristic
1210C22—21no—
1211C22—21no—
1212C22—21no—
1213C22—21no—
1214C22—21no—
1215C22—21no—
1216C22—21no—
1217C22—21no—
1218C22—21no—
1219C22—21no—
1220C22—21no—
1221C22—21no—
1222C22—21no—
1223C22—21no—
1224C22—21no—
1225C22—21no—
1226C22—21no—
1227C22—42no—
1228C22—42no—
1229C22—44no—
1230C22—42no—
1231C22—42no—
1232C22—44no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—82no—
1237C22—81no—
1238C22—81no—
1239C22—82no—
1240C22—84no—
1241C22C2×#41012yes—
1242C22C23×C22⋊C411yescharacteristic
1243C22C4×2−1+412yes—
1244C22#348912yes—
1245C22#349911yescharacteristic
1246C22#350011yescharacteristic
1247C4—21no—
1248C4—21no—
1249C4—21no—
1250C4—21no—
1251C4—21no—
1252C4—21no—
1253C4—22no—
1254C4—22no—
1255C4—22no—
1256C4—22no—
1257C4—22no—
1258C4—22no—
1259C4—22no—
1260C4—22no—
1261C4—44no—
1262C4—42no—
1263C4—44no—
1264C4—44no—
1265C4—42no—
1266C4—42no—
1267C4—84no—
1268C4—82no—
1269C4—82no—
1270C4—82no—
1271C4—84no—
1272C4C2×#41012yes—
1273C4C2×#41012yes—
1274C2—22no—
1275C2—21no—
1276C2—21no—
1277C2—22no—
1278C2—22no—
1279C2—41no—
1280C2—41no—
1281C2—41no—
1282C2—82no—
1283C2#3425911yescharacteristic
1284C2C22×#41011yescharacteristic
1285C2#6007011yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC23C24×C4
Frattini, cosocleC24C25
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×#117 ◁ G
LECSG ▷ C24 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34180C2semidirect
3. #34109C2semidirect
4. #22513C2semidirect
5. #22478C2semidirect
6. #22477C2semidirect
7. #21875C2semidirect
9. #21826C2semidirect
10. #21825C2semidirect
11. #21421C2semidirect
13. #21332C2semidirect
14. C2×#1996C2semidirect
27. C2×#556C4semidirect
29. C2×#552C4semidirect
30. C2×#552C4semidirect
33. C2×#544C4semidirect
34. C2×#542C4semidirect
35. C2×#541C4semidirect
36. C2×#536C4semidirect
41. C2×#520C4semidirect
42. C2×#519C4semidirect
175. C2×C4⋊Q8C2×C4semidirect
176. C2×C4⋊Q8C2×C4semidirect
177. C2×C4⋊Q8C2×C4semidirect
188. C2×#126C2×C4semidirect
189. C2×#126C2×C4semidirect
190. C2×#125C2×C4semidirect
191. C2×#125C2×C4semidirect
192. C2×#125C2×C4semidirect
193. C2×#125C2×C4semidirect
194. C2×#125C2×C4semidirect
196. C2×#124C2×C4semidirect
221. C2×C22⋊Q8C2×C4semidirect
222. C2×C22⋊Q8C2×C4semidirect
223. C2×C22⋊Q8C2×C4semidirect
243. C2×C4×Q8C2×C4semidirect
244. C2×C4×Q8C2×C4semidirect
245. C2×C4×Q8C2×C4semidirect
246. C2×C4×Q8C2×C4semidirect
247. C2×C4×Q8C2×C4semidirect
248. C2×C4×Q8C2×C4semidirect
251. C2×C4×D4C2×C4semidirect
264. C2×#117C2×C4semidirect
265. C2×#117C2×C4semidirect
284. C22×C4⋊C4C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#34952
#341802
#341092
#225132
#224782
#224772
#218752
#218742
#218262
#218252
#214212
#214202
#213322
C2×#19962