Finite Group Databasebeta

← #6343540

Subgroups — #6343540

Order 512.

2950 conjugacy classes of subgroups.

The subgroup lattice has 1291 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62830C211yesmaximal, characteristic
2#60290C211yesmaximal, characteristic, complemented
3#34229C211yesmaximal, characteristic, complemented
4#17631C211yesmaximal, characteristic, complemented
5#17630C211yesmaximal, characteristic, complemented
6#17628C211yesmaximal, characteristic, complemented
7#17626C211yesmaximal, characteristic, complemented
8#17618C211yesmaximal, characteristic, complemented
9#17617C211yesmaximal, characteristic, complemented
10#17616C211yesmaximal, characteristic, complemented
11#17613C211yesmaximal, characteristic, complemented
12#17610C214yesmaximal, complemented
13#17604C214yesmaximal, complemented
14#17597C214yesmaximal, complemented
15#17588C211yesmaximal, characteristic, complemented
16C2×#1517C211yesmaximal, characteristic, complemented
17#17547C214yesmaximal, complemented
18#17544C211yesmaximal, characteristic, complemented
19#17533C211yesmaximal, characteristic, complemented
20#3562—22no—
21#3560—22no—
22#3552C412yescomplemented
23#3551—22no—
24#3547C412yescomplemented
25#3546C412yescomplemented
26#3543C412yescomplemented
27#3534—22no—
28#3520C412yescomplemented
29#3519C412yescomplemented
30#3519C2214yes—
31#3517C412yescomplemented
32#3514—22no—
33#3514C412yescomplemented
34#3512—21no—
35#3507C2211yescharacteristic
36#3506C2211yescharacteristic
37#3505—22no—
38#3500—21no—
39#3497C2211yescharacteristic
40#3496C2211yescharacteristic
41#3494C2214yes—
42#3489—21no—
43#3488—21no—
44#3444C2211yescharacteristic
45C2×#532C2211yescharacteristic
46C2×#529C2211yescharacteristic
47#2994—22no—
48#2993—22no—
49#2983C2211yescharacteristic, complemented
50#2982C2211yescharacteristic, complemented
51#2975C2211yescharacteristic, complemented
52#2974C2214yescomplemented
53#2972C2211yescharacteristic, complemented
54#2969—22no—
55#2966—22no—
56#2924C2214yescomplemented
57#2920C2211yescharacteristic, complemented
58C2×#431C2211yescharacteristic, complemented
59#2361—21no—
60#2360—21no—
61#2359—22no—
62#2357C2211yescharacteristic, complemented
63#2356C2211yescharacteristic, complemented
64#2351C2211yescharacteristic, complemented
65#2349C2211yescharacteristic, complemented
66#2346C2212yescomplemented
67#2343C2212yescomplemented
68#2334—22no—
69#2318C2212yescomplemented
70C4×#125—21no—
71C4×#124—21no—
72C2×#382C2211yescharacteristic, complemented
73#2275C2212yescomplemented
74C4×#117C2211yescharacteristic, complemented
75#1521C2214yescomplemented
76#1519C2214yescomplemented
77#1518C2211yescharacteristic, complemented
78#1518C2211yescharacteristic, complemented
79#1517C2211yescharacteristic
80#1517C2211yescharacteristic
81#1517C2214yescomplemented
82#1517C2211yescharacteristic, complemented
83#1517C2211yescharacteristic, complemented
84#1517C2211yescharacteristic, complemented
85#1517C2211yescharacteristic, complemented
86#1517C2214yescomplemented
87#1516C2214yescomplemented
88#1514C2214yescomplemented
89#1513C2214yescomplemented
90#1512C2214yescomplemented
91#1512C2214yescomplemented
92#1510C2214yescomplemented
93#1509C2214yescomplemented
94#1507C2212yescomplemented
95#1507C2212yescomplemented
96#1507C2214yescomplemented
97#1505C2212yescomplemented
98#1505C2212yescomplemented
99#1505C2214yescomplemented
100#1504C2214yescomplemented
101#1504C2214yescomplemented
102#1503C2211yescharacteristic, complemented
103#1503C2211yescharacteristic, complemented
104#1502C2211yescharacteristic
105#1502C2211yescharacteristic
106#1502C2211yescharacteristic, complemented
107#1502C2211yescharacteristic, complemented
108#1502C2211yescharacteristic, complemented
109#1502C2211yescharacteristic, complemented
110#1502C2214yescomplemented
111#1501C2212yescomplemented
112#1501C2212yescomplemented
113#1501C2214yescomplemented
114#1500C2212yescomplemented
115#1500C2212yescomplemented
116#1500C2214yescomplemented
117C2×#327C2214yescomplemented
118C2×#327C2214yescomplemented
119C2×2−1+4—21no—
120C2×H(5,𝔽2)—21no—
121C22×#41—21no—
122#563—24no—
123#562—24no—
124#560—24no—
125#560—24no—
126#559—22no—
127#559C2×C412yescomplemented
128#557C2×C412yescomplemented
129#556—22no—
130#556C2×C412yescomplemented
131#556C2×C412yescomplemented
132#555—24no—
133#555C2×C412yescomplemented
134#555C2×C414yescomplemented
135#554C2×C412yescomplemented
136#554C2×C414yescomplemented
137#553—24no—
138#553—22no—
139#553—22no—
140#553—22no—
141#553—24no—
142#553—24no—
143#553—24no—
144#553C2×C414yescomplemented
145#553C2×C414yescomplemented
146#552—22no—
147#552—22no—
148#552—22no—
149#551—24no—
150#551—24no—
151#551—24no—
152#551—24no—
153#550—22no—
154#550C2×C412yescomplemented
155#550C2×C414yescomplemented
156#550C2×C412yescomplemented
157#550C2×C412yescomplemented
158D4×Q8—22no—
159D4×Q8C2×C412yescomplemented
160D4×Q8C2×C412yescomplemented
161#548—22no—
162#548—22no—
163#548—22no—
164#548—22no—
165#548—22no—
166#548—22no—
167#547—22no—
168#547—24no—
169#547C2×C412yescomplemented
170#547C2×C412yescomplemented
171#547C2×C412yescomplemented
172#546—22no—
173#546—22no—
174#546—24no—
175#546—22no—
176#546—22no—
177#546—22no—
178#546—22no—
179#546—24no—
180#546—24no—
181#546—24no—
182#546—24no—
183#546C2×C414yescomplemented
184#546C2×C414yescomplemented
185D42—24no—
186D42—22no—
187D42C2×C412yescomplemented
188D42C2×C412yescomplemented
189D42C2×C414yescomplemented
190#544C2×C414yescomplemented
191#542—24no—
192#542C2×C414yescomplemented
193#542C2×C414yescomplemented
194#541—22no—
195#540—22no—
196#540—24no—
197#540—24no—
198#540C2×C414yescomplemented
199#540C2×C414yescomplemented
200#539—24no—
201#539—24no—
202#539—22no—
203#538—24no—
204#538—24no—
205#538—24no—
206#538—24no—
207#538—24no—
208#538—22no—
209#537—22no—
210#537—22no—
211#537—21no—
212#537—21no—
213#537—22no—
214#536—21no—
215#536—22no—
216#536—22no—
217#535—21no—
218#535—22no—
219#535—22no—
220#535C2×C414yescomplemented
221#534—24no—
222#534—22no—
223#533C2×C411yescharacteristic, complemented
224#533C2×C411yescharacteristic, complemented
225#533C2311yescharacteristic
226#532—22no—
227#532—21no—
228#532—21no—
229#532—21no—
230#532—21no—
231#532C2×C411yescharacteristic, complemented
232#532C2×C411yescharacteristic, complemented
233#532C2×C411yescharacteristic, complemented
234#532C2×C412yescomplemented
235#532C2×C411yescharacteristic, complemented
236#532C2312yes—
237#532C2311yescharacteristic
238#532C2311yescharacteristic
239#532C2311yescharacteristic
240#532C2314yes—
241C2×C4⋊Q8C2×C411yescharacteristic, complemented
242C2×#127C2×C411yescharacteristic, complemented
243#529—22no—
244#529—22no—
245#529—21no—
246#529—21no—
247#529—21no—
248#529—21no—
249#529C2×C412yes—
250#529C2×C412yes—
251#529C2×C412yes—
252#529C2×C412yes—
253#529C2×C412yescomplemented
254#529D412yes—
255#529D412yes—
256#529D412yes—
257#529D412yes—
258#529C2312yes—
259#529C2314yes—
260C2×#126D412yes—
261C2×#125D411yescharacteristic
262C2×#124—22no—
263C2×#124—21no—
264C2×#124D411yescharacteristic
265#525—21no—
266#525—21no—
267#525—22no—
268#525—22no—
269#525C2312yes—
270#525C2314yes—
271C2×#123D412yes—
272C2×C22⋊Q8—22no—
273C2×C22⋊Q8D411yescharacteristic
274C2×#121—21no—
275C2×#121—22no—
276C2×#121D411yescharacteristic
277C2×#121C2312yes—
278C2×#121C2314yes—
279#520—21no—
280#520—21no—
281#520C2×C414yescomplemented
282#518—24no—
283#518C2×C414yescomplemented
284C4×#41—21no—
285C4×#41—21no—
286C4×#41C2×C412yescomplemented
287C2×C4×Q8—21no—
288C2×C4×Q8C2311yescharacteristic
289C2×C4×D4—22no—
290C2×C4×D4—21no—
291C2×C4×D4—21no—
292C2×C4×D4C2×C412yescomplemented
293C2×C4×D4C2312yes—
294C2×C4×D4C2311yescharacteristic
295C2×#117—21no—
296C2×#117C2312yes—
297C22×C4⋊C4—21no—
298C22×C42C2311yescharacteristic
299#446—22no—
300#446—22no—
301C8×Q8—22no—
302C8×Q8—22no—
303#436—22no—
304#436—24no—
305#436—22no—
306#435—24no—
307#435—24no—
308C8×D4—22no—
309C8×D4—24no—
310C8×D4—22no—
311#433—24no—
312#433—24no—
313#432—21no—
314#432C2312yes—
315#432C2314yes—
316#431—21no—
317#431—21no—
318#431—21no—
319#431C2312yes—
320#431C2311yescharacteristic
321#431C2311yescharacteristic
322#431C2311yescharacteristic
323#431C2311yescharacteristic
324#431C2314yes—
325#424—24no—
326#423—21no—
327C2×C4⋊C8—21no—
328#407C2312yes—
329#407C2314yes—
330C2×C22⋊C8C2312yes—
331C2×C22⋊C8C2314yes—
332#405—24no—
333C4×M16—21no—
334C2×C4×C8—21no—
335#391—21no—
336#390—21no—
337#389—21no—
338#389—21no—
339#389—22no—
340#389—22no—
341#388—22no—
342#388—22no—
343#388—22no—
344#388—22no—
345#387—22no—
346#387—22no—
347#387—22no—
348#387—22no—
349#386—22no—
350#385—22no—
351#385—22no—
352#385—22no—
353#383C2312yes—
354#382—21no—
355#382—21no—
356#382C2312yes—
357#382C2312yes—
358#382C2311yescharacteristic
359#382C2311yescharacteristic
360#381C2312yes—
361#380C2312yes—
362C4×C4⋊C4—22no—
363C4×C4⋊C4—22no—
364C4×C4⋊C4—21no—
365C4×C4⋊C4—21no—
366C4×C4⋊C4—21no—
367C4×C4⋊C4C2312yes—
368C4×C4⋊C4C2311yescharacteristic
369C4×C4⋊C4C2311yescharacteristic
370C4×C22⋊C4—21no—
371C4×C22⋊C4—22no—
372C4×C22⋊C4—22no—
373C4×C22⋊C4—22no—
374C4×C22⋊C4C2311yescharacteristic
375C4×C22⋊C4C2312yes—
376C4×C22⋊C4C2311yescharacteristic
377#376C2311yescharacteristic
378#376C2311yescharacteristic
379#376C2312yes—
380C2×#95—21no—
381C2×#95C2312yes—
382C2×#95C2312yes—
383C43—21no—
384#328C2312yes—
385#328C2312yes—
386#328C2312yes—
387#328C2312yes—
388#328C2314yes—
389#328C2314yes—
390#327C2312yes—
391#327C2314yes—
392#327C2312yes—
393#327C2314yes—
394#327C2314yes—
395#327C2314yes—
396#327C2314yes—
397#327C2312yes—
398#327C2312yes—
399#327C2312yes—
400#327C2312yes—
401#327C2312yes—
402#327C2312yes—
403#327C2312yes—
404#327C2312yes—
405#327C2314yes—
406#327C2312yes—
407#327C2312yes—
4082−1+4—82no—
4092−1+4—82no—
410H(5,𝔽2)—82no—
411H(5,𝔽2)—82no—
412C2×#41—22no—
413C2×#41—22no—
414C2×#41—22no—
415C2×#41—22no—
416C2×#41—21no—
417C2×#41—22no—
418C2×#41—21no—
419C2×#41—21no—
420C2×#41—21no—
421C2×#41—21no—
422C2×#41—21no—
423C2×#41—22no—
424C2×#41—24no—
425C2×#41—82no—
426C2×#41—82no—
427C2×#41C22×C412yes—
428C2×#41C22×C414yes—
429C22×Q8—22no—
430C22×Q8—22no—
431C22×Q8—21no—
432C22×Q8C2×D411yescharacteristic
433C22×D4—22no—
434C22×D4—24no—
435C22×D4—24no—
436C22×D4—22no—
437C22×D4—22no—
438C22×D4—21no—
439C22×D4—21no—
440C22×D4C22×C412yes—
441C22×D4C22×C414yes—
442C22×D4C2×D411yescharacteristic
443C22×D4C2×D412yes—
444C23×C4—22no—
445C23×C4—22no—
446C23×C4—22no—
447C23×C4C2×D411yescharacteristic
448C23×C4C2×D411yescharacteristic
449C23×C4C2412yes—
450C23×C4C2411yescharacteristic
451C2×M16—22no—
452C2×M16—24no—
453C22×C8—22no—
454C22×C8—24no—
455C4⋊Q8—22no—
456C4⋊Q8—24no—
457C4⋊Q8—21no—
458C4⋊Q8—21no—
459C4⋊Q8C22×C411yescharacteristic
460C4⋊Q8C22×C412yes—
461C4⋊Q8C22×C411yescharacteristic
462C4⋊Q8C22×C411yescharacteristic
463C4⋊Q8C22×C411yescharacteristic
464C4⋊Q8C22×C411yescharacteristic
465C4⋊Q8C22×C414yes—
466#127—22no—
467#127—24no—
468#127—21no—
469#127—21no—
470#127C22×C412yes—
471#127C22×C411yescharacteristic
472#127C22×C411yescharacteristic
473#127C22×C411yescharacteristic
474#127C22×C414yes—
475#126—24no—
476#126—24no—
477#126—24no—
478#126—24no—
479#126—24no—
480#126—24no—
481#126—22no—
482#126—22no—
483#126—24no—
484#126C22⋊C414yes—
485#126C22⋊C414yes—
486#126C22⋊C414yes—
487#126C22⋊C414yes—
488#125—24no—
489#125—24no—
490#125—24no—
491#125—21no—
492#125—21no—
493#125C22⋊C412yes—
494#125C22⋊C412yes—
495#125C22⋊C412yes—
496#125C22⋊C412yes—
497#125C22×C412yes—
498#125C22×C414yes—
499#124—22no—
500#124—22no—
501#124—24no—
502#124—24no—
503#124—24no—
504#124—24no—
505#124—24no—
506#124—21no—
507#124—21no—
508#124—22no—
509#124—21no—
510#124—21no—
511#124—21no—
512#124—22no—
513#124—21no—
514#124—24no—
515#124C22⋊C412yes—
516#124C22⋊C412yes—
517#124C22⋊C412yes—
518#124C22⋊C412yes—
519#124C22×C412yes—
520#124C22×C414yes—
521#123—22no—
522#123—22no—
523#123—22no—
524#123—24no—
525#123—24no—
526#123—24no—
527#123—24no—
528#123—24no—
529#123—24no—
530#123—24no—
531#123—24no—
532#123—24no—
533#123—24no—
534#123—24no—
535#123—24no—
536#123—24no—
537#123—24no—
538#123—24no—
539#123—24no—
540#123C22⋊C414yes—
541#123C22⋊C414yes—
542#123C22⋊C414yes—
543#123C22⋊C414yes—
544C22⋊Q8—22no—
545C22⋊Q8—22no—
546C22⋊Q8—21no—
547C22⋊Q8—21no—
548C22⋊Q8—21no—
549C22⋊Q8—21no—
550C22⋊Q8—22no—
551C22⋊Q8—24no—
552C22⋊Q8—22no—
553C22⋊Q8—22no—
554C22⋊Q8—22no—
555C22⋊Q8—24no—
556C22⋊Q8—24no—
557C22⋊Q8—24no—
558C22⋊Q8—24no—
559C22⋊Q8—24no—
560C22⋊Q8—24no—
561C22⋊Q8—24no—
562C22⋊Q8—24no—
563C22⋊Q8C22⋊C412yes—
564C22⋊Q8C22⋊C412yes—
565C22⋊Q8C22⋊C412yes—
566C22⋊Q8C22⋊C412yes—
567C22⋊Q8C22×C412yes—
568C22⋊Q8C22×C414yes—
569C22⋊Q8C2412yes—
570#121—22no—
571#121—24no—
572#121—22no—
573#121—24no—
574#121—24no—
575#121—21no—
576#121—21no—
577#121—21no—
578#121—22no—
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
583#121—22no—
584#121—22no—
585#121—22no—
586#121—24no—
587#121—24no—
588#121—21no—
589#121—24no—
590#121—22no—
591#121—22no—
592#121—22no—
593#121—22no—
594#121—24no—
595#121—24no—
596#121—24no—
597#121—24no—
598#121—24no—
599#121—24no—
600#121—24no—
601#121—24no—
602#121—24no—
603#121—24no—
604#121—24no—
605#121—24no—
606#121—24no—
607#121—24no—
608#121C22⋊C412yes—
609#121C22⋊C412yes—
610#121C22⋊C412yes—
611#121C22⋊C412yes—
612#121C22×C412yes—
613#121C22×C412yes—
614#121C22×C414yes—
615#121C22×C414yes—
616#121C22×C412yes—
617#121C22×C414yes—
618#121C2412yes—
619#121C2412yes—
620#121C2412yes—
621#120—22no—
622#120—24no—
623#120—24no—
624#120—24no—
625#120—24no—
626#120—24no—
627#120—24no—
628#120—24no—
629#120—24no—
630#120—24no—
631C4×Q8—22no—
632C4×Q8—22no—
633C4×Q8—21no—
634C4×Q8—21no—
635C4×Q8—21no—
636C4×Q8—21no—
637C4×Q8—82no—
638C4×Q8C22×C412yes—
639C4×Q8C22×C412yes—
640C4×Q8C22×C414yes—
641C4×Q8C22×C412yes—
642C4×Q8C22×C412yes—
643C4×Q8C2×D412yes—
644C4×Q8C2×D412yes—
645C4×D4—24no—
646C4×D4—22no—
647C4×D4—22no—
648C4×D4—22no—
649C4×D4—22no—
650C4×D4—22no—
651C4×D4—22no—
652C4×D4—24no—
653C4×D4—24no—
654C4×D4—24no—
655C4×D4—24no—
656C4×D4—24no—
657C4×D4—24no—
658C4×D4—22no—
659C4×D4—22no—
660C4×D4—24no—
661C4×D4—24no—
662C4×D4—24no—
663C4×D4—24no—
664C4×D4—22no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—22no—
668C4×D4—22no—
669C4×D4—21no—
670C4×D4—21no—
671C4×D4—21no—
672C4×D4—21no—
673C4×D4—21no—
674C4×D4—22no—
675C4×D4—21no—
676C4×D4—24no—
677C4×D4—48no—
678C4×D4—82no—
679C4×D4C22×C412yes—
680C4×D4C22×C412yes—
681C4×D4C22×C412yes—
682C4×D4C22×C412yes—
683C4×D4C22×C412yes—
684C4×D4C22×C412yes—
685C4×D4C22×C414yes—
686C4×D4C22×C414yes—
687C4×D4C22×C414yes—
688C4×D4C22×C414yes—
689C4×D4C22×C412yes—
690C4×D4C22×C412yes—
691C4×D4C22×C414yes—
692C4×D4C2×D414yes—
693C4×D4C2×D414yes—
694C4×D4C2×D412yes—
695C4×D4C2×D412yes—
696#117—21no—
697#117—21no—
698#117—24no—
699#117—22no—
700#117—22no—
701#117—24no—
702#117—22no—
703#117—22no—
704#117—22no—
705#117—24no—
706#117—44no—
707#117C22×C412yes—
708#117C22×C414yes—
709#117C22×C414yes—
710#117C22×C414yes—
711#117C2×D414yes—
712#117C2×D414yes—
713C2×C4⋊C4—21no—
714C2×C4⋊C4—22no—
715C2×C4⋊C4—22no—
716C2×C4⋊C4—24no—
717C2×C4⋊C4—21no—
718C2×C4⋊C4—21no—
719C2×C4⋊C4—21no—
720C2×C4⋊C4—21no—
721C2×C4⋊C4—22no—
722C2×C4⋊C4—22no—
723C2×C4⋊C4—22no—
724C2×C4⋊C4—22no—
725C2×C4⋊C4—82no—
726C2×C4⋊C4C22×C412yes—
727C2×C4⋊C4C22×C414yes—
728C2×C4⋊C4C2×D412yes—
729C2×C4⋊C4C2×D412yes—
730C2×C4⋊C4C2×D411yescharacteristic
731C2×C4⋊C4C2×D412yes—
732C2×C4⋊C4C2×D411yescharacteristic
733C2×C4⋊C4C2×D412yes—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—22no—
736C2×C22⋊C4—22no—
737C2×C22⋊C4—24no—
738C2×C22⋊C4—24no—
739C2×C22⋊C4—24no—
740C2×C22⋊C4—24no—
741C2×C22⋊C4—24no—
742C2×C22⋊C4—21no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4C2×D412yes—
747C2×C22⋊C4C2×D412yes—
748C2×C22⋊C4C2×D412yes—
749C2×C22⋊C4C2×D412yes—
750C2×C22⋊C4C2×D412yes—
751C2×C42—22no—
752C2×C42—21no—
753C2×C42—21no—
754C2×C42—21no—
755C2×C42—22no—
756C2×C42—21no—
757C2×C42—22no—
758C2×C42—21no—
759C2×C42—21no—
760C2×C42—22no—
761C2×C42C22×C411yescharacteristic
762C2×C42C22×C411yescharacteristic
763C2×C42C22×C411yescharacteristic
764C2×C42C22×C411yescharacteristic
765C2×C42C2×D411yescharacteristic
766C2×C42C2×D411yescharacteristic
767C2×C42C2×D411yescharacteristic
768C2×C42C2×D411yescharacteristic
769C2×C42C2×D411yescharacteristic
770C2×C42C2×D411yescharacteristic
771C2×C42C2411yescharacteristic
772C2×C42C2412yes—
773C2×C42C2411yescharacteristic
774C4⋊C8—22no—
775C4⋊C8—21no—
776C4⋊C8—21no—
777C4⋊C8—22no—
778C4⋊C8—21no—
779C4⋊C8—21no—
780C4⋊C8—24no—
781C4⋊C8—24no—
782C22⋊C8—22no—
783C22⋊C8—24no—
784C22⋊C8—22no—
785C22⋊C8—24no—
786C22⋊C8C2412yes—
787C22⋊C8C2412yes—
788C22⋊C8C2412yes—
789C22⋊C8C2412yes—
790#97—22no—
791#97—24no—
792C4×C8—22no—
793C4×C8—21no—
794C4×C8—21no—
795C4×C8—21no—
796C4×C8—21no—
797C4×C8—24no—
798#95—22no—
799#95—21no—
800#95—21no—
801#95—22no—
802#95—22no—
803#95—22no—
804#95—21no—
805#95—21no—
806#95—22no—
807#95—22no—
808#95—22no—
809#95—22no—
810#95C2411yescharacteristic
811#95C2412yes—
812#95C2412yes—
813#95C2411yescharacteristic
814#95C2411yescharacteristic
815#95C2411yescharacteristic
816C24—22no—
817C24—24no—
818C24C22×D411yescharacteristic
819C24C22×D412yes—
820#41—42no—
821#41—42no—
822#41—42no—
823#41—42no—
824#41—42no—
825#41—42no—
826#41—84no—
827#41—82no—
828#41—82no—
829#41—82no—
830#41—84no—
831#41—84no—
832#41—82no—
833#41—82no—
834#41—84no—
835#41—84no—
836#41—84no—
837#41—84no—
838#41—84no—
839#41—82no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—24no—
845C2×Q8—22no—
846C2×Q8—22no—
847C2×Q8—22no—
848C2×Q8—82no—
849C2×Q8—84no—
850C2×Q8—84no—
851C2×Q8C2×C22⋊C412yes—
852C2×Q8C2×C22⋊C412yes—
853C2×Q8C23×C412yes—
854C2×D4—22no—
855C2×D4—22no—
856C2×D4—22no—
857C2×D4—22no—
858C2×D4—24no—
859C2×D4—22no—
860C2×D4—24no—
861C2×D4—22no—
862C2×D4—24no—
863C2×D4—24no—
864C2×D4—22no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—24no—
871C2×D4—22no—
872C2×D4—22no—
873C2×D4—24no—
874C2×D4—21no—
875C2×D4—24no—
876C2×D4—22no—
877C2×D4—22no—
878C2×D4—22no—
879C2×D4—44no—
880C2×D4—82no—
881C2×D4—82no—
882C2×D4—84no—
883C2×D4—84no—
884C2×D4—82no—
885C2×D4—84no—
886C2×D4—88no—
887C2×D4—82no—
888C2×D4—82no—
889C2×D4—84no—
890C2×D4—84no—
891C2×D4C2×C22⋊C414yes—
892C2×D4C2×C22⋊C412yes—
893C2×D4C2×C22⋊C412yes—
894C2×D4C2×C22⋊C414yes—
895C2×D4C23×C412yes—
896C2×D4C23×C412yes—
897C2×D4C23×C412yes—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—22no—
903C22×C4—24no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—22no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—24no—
911C22×C4—24no—
912C22×C4—24no—
913C22×C4—24no—
914C22×C4—22no—
915C22×C4—21no—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—21no—
919C22×C4—42no—
920C22×C4—44no—
921C22×C4—44no—
922C22×C4—84no—
923C22×C4—81no—
924C22×C4—82no—
925C22×C4—82no—
926C22×C4—82no—
927C22×C4—82no—
928C22×C4—82no—
929C22×C4C2×C22⋊C411yescharacteristic
930C22×C4C2×C22⋊C411yescharacteristic
931C22×C4C2×C22⋊C411yescharacteristic
932C22×C4C2×C22⋊C411yescharacteristic
933C22×C4C2×C22⋊C411yescharacteristic
934C22×C4C2×C22⋊C411yescharacteristic
935C22×C4C2×C22⋊C411yescharacteristic
936C22×C4C2×C22⋊C411yescharacteristic
937C22×C4C23×C411yescharacteristic
938C22×C4C23×C411yescharacteristic
939C22×C4C23×C414yes—
940C22×C4C22×D412yes—
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D412yes—
945C22×C4C22×D412yes—
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D414yes—
950C22×C4C22×D411yescharacteristic
951C22×C4C2511yescharacteristic
952M16—82no—
953M16—84no—
954C2×C8—22no—
955C2×C8—22no—
956C2×C8—22no—
957C2×C8—22no—
958C2×C8—84no—
959C2×C8—82no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—22no—
963C4⋊C4—24no—
964C4⋊C4—21no—
965C4⋊C4—22no—
966C4⋊C4—21no—
967C4⋊C4—24no—
968C4⋊C4—24no—
969C4⋊C4—24no—
970C4⋊C4—22no—
971C4⋊C4—24no—
972C4⋊C4—24no—
973C4⋊C4—22no—
974C4⋊C4—22no—
975C4⋊C4—22no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—22no—
979C4⋊C4—22no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—44no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—82no—
986C4⋊C4—82no—
987C4⋊C4—82no—
988C4⋊C4C2×C22⋊C412yes—
989C4⋊C4C2×C22⋊C412yes—
990C4⋊C4C2×C22⋊C414yes—
991C4⋊C4C2×C22⋊C414yes—
992C4⋊C4C2×C22⋊C414yes—
993C4⋊C4C2×C22⋊C414yes—
994C4⋊C4C2×C22⋊C414yes—
995C4⋊C4C2×C22⋊C412yes—
996C4⋊C4C2×C22⋊C412yes—
997C4⋊C4C2×C22⋊C414yes—
998C4⋊C4C2×C22⋊C414yes—
999C4⋊C4C2×C22⋊C414yes—
1000C4⋊C4C23×C412yes—
1001C4⋊C4C23×C412yes—
1002C4⋊C4C23×C412yes—
1003C4⋊C4C23×C412yes—
1004C22⋊C4—24no—
1005C22⋊C4—22no—
1006C22⋊C4—24no—
1007C22⋊C4—24no—
1008C22⋊C4—22no—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—22no—
1012C22⋊C4—22no—
1013C22⋊C4—24no—
1014C22⋊C4—24no—
1015C22⋊C4—22no—
1016C22⋊C4—22no—
1017C22⋊C4—24no—
1018C22⋊C4—22no—
1019C22⋊C4—24no—
1020C22⋊C4—24no—
1021C22⋊C4—22no—
1022C22⋊C4—24no—
1023C22⋊C4—22no—
1024C22⋊C4—22no—
1025C22⋊C4—22no—
1026C22⋊C4—24no—
1027C22⋊C4—22no—
1028C22⋊C4—24no—
1029C22⋊C4—22no—
1030C22⋊C4—22no—
1031C22⋊C4—22no—
1032C22⋊C4—44no—
1033C22⋊C4—42no—
1034C22⋊C4—82no—
1035C22⋊C4—82no—
1036C22⋊C4C2×C22⋊C414yes—
1037C22⋊C4C2×C22⋊C414yes—
1038C22⋊C4C2×C22⋊C414yes—
1039C22⋊C4C2×C22⋊C414yes—
1040C22⋊C4C2×C22⋊C414yes—
1041C22⋊C4C2×C22⋊C414yes—
1042C22⋊C4C2×C22⋊C414yes—
1043C22⋊C4C2×C22⋊C414yes—
1044C22⋊C4C2×C22⋊C414yes—
1045C22⋊C4C2×C22⋊C414yes—
1046C42—22no—
1047C42—22no—
1048C42—22no—
1049C42—24no—
1050C42—24no—
1051C42—42no—
1052C42—42no—
1053C42—44no—
1054C42—42no—
1055C42—42no—
1056C42—82no—
1057C42—81no—
1058C42—81no—
1059C42—82no—
1060C42C2×C22⋊C411yescharacteristic
1061C42C2×C22⋊C411yescharacteristic
1062C42C2×C22⋊C411yescharacteristic
1063C42C2×C22⋊C411yescharacteristic
1064C42C2×C22⋊C411yescharacteristic
1065C42C2×C22⋊C411yescharacteristic
1066C42C2×C22⋊C411yescharacteristic
1067C42C2×C22⋊C411yescharacteristic
1068C42C23×C411yescharacteristic
1069C42C23×C411yescharacteristic
1070C42C23×C411yescharacteristic
1071C42C23×C411yescharacteristic
1072C42C23×C414yes—
1073C42C22×D411yescharacteristic
1074C42C22×D411yescharacteristic
1075C42C22×D411yescharacteristic
1076C42C22×D414yes—
1077C42C22×D411yescharacteristic
1078C23—22no—
1079C23—21no—
1080C23—21no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—41no—
1087C23—42no—
1088C23—42no—
1089C23—44no—
1090C23—82no—
1091C23—82no—
1092C23—84no—
1093C23—84no—
1094C23—84no—
1095C23C22×C22⋊C414yes—
1096C23C22×C22⋊C411yescharacteristic
1097C23C22×C22⋊C411yescharacteristic
1098C23C23×D411yescharacteristic
1099Q8—24no—
1100Q8—24no—
1101Q8—42no—
1102Q8—42no—
1103Q8—42no—
1104Q8—42no—
1105Q8—84no—
1106Q8—82no—
1107Q8—81no—
1108D4—28no—
1109D4—24no—
1110D4—24no—
1111D4—44no—
1112D4—42no—
1113D4—42no—
1114D4—42no—
1115D4—44no—
1116D4—42no—
1117D4—42no—
1118D4—42no—
1119D4—42no—
1120D4—42no—
1121D4—42no—
1122D4—42no—
1123D4—42no—
1124D4—42no—
1125D4—84no—
1126D4—82no—
1127D4—81no—
1128D4—82no—
1129D4—81no—
1130D4—84no—
1131D4—82no—
1132D4—81no—
1133D4—84no—
1134D4—84no—
1135D4—84no—
1136D4—84no—
1137D4—82no—
1138D4—82no—
1139D4—82no—
1140D4—84no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—41no—
1159C2×C4—42no—
1160C2×C4—41no—
1161C2×C4—42no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—44no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—44no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—44no—
1177C2×C4—44no—
1178C2×C4—44no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—42no—
1182C2×C4—41no—
1183C2×C4—42no—
1184C2×C4—41no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—41no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—41no—
1191C2×C4—82no—
1192C2×C4—82no—
1193C2×C4—84no—
1194C2×C4—84no—
1195C2×C4—84no—
1196C2×C4—82no—
1197C2×C4—84no—
1198C2×C4—82no—
1199C2×C4—82no—
1200C2×C4—84no—
1201C2×C4—164no—
1202C2×C4—164no—
1203C2×C4C22×C22⋊C411yescharacteristic
1204C2×C4C22×C22⋊C411yescharacteristic
1205C2×C4C22×C22⋊C414yes—
1206C2×C4C22×C22⋊C414yes—
1207C2×C4C22×C22⋊C411yescharacteristic
1208C2×C4C22×C22⋊C411yescharacteristic
1209C2×C4C22×C22⋊C411yescharacteristic
1210C2×C4C22×C22⋊C411yescharacteristic
1211C2×C4C22×C22⋊C411yescharacteristic
1212C2×C4C22×C22⋊C411yescharacteristic
1213C2×C4C22×C22⋊C414yes—
1214C2×C4C22×C22⋊C411yescharacteristic
1215C2×C4C22×C22⋊C411yescharacteristic
1216C2×C4#57612yes—
1217C2×C4#57712yes—
1218C2×C4C24×C411yescharacteristic
1219C2×C4C23×D411yescharacteristic
1220C8—42no—
1221C8—42no—
1222C8—42no—
1223C8—42no—
1224C22—21no—
1225C22—21no—
1226C22—21no—
1227C22—21no—
1228C22—21no—
1229C22—24no—
1230C22—21no—
1231C22—24no—
1232C22—21no—
1233C22—24no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—82no—
1246C22—82no—
1247C22—164no—
1248C22—324no—
1249C22#290112yes—
1250C22C23×C22⋊C411yescharacteristic
1251C22C2×#57611yescharacteristic
1252C22C2×#57711yescharacteristic
1253C4—21no—
1254C4—21no—
1255C4—21no—
1256C4—24no—
1257C4—21no—
1258C4—21no—
1259C4—21no—
1260C4—24no—
1261C4—21no—
1262C4—21no—
1263C4—21no—
1264C4—21no—
1265C4—24no—
1266C4—42no—
1267C4—42no—
1268C4—42no—
1269C4—42no—
1270C4—42no—
1271C4—42no—
1272C4—42no—
1273C4—81no—
1274C4—81no—
1275C4—82no—
1276C4—82no—
1277C4#289712yes—
1278C4#289712yes—
1279C2—21no—
1280C2—21no—
1281C2—22no—
1282C2—41no—
1283C2—44no—
1284C2—82no—
1285C2—82no—
1286C2—82no—
1287C2#6007011yescharacteristic
1288C2C2×#289711yescharacteristic
1289C2C2×#290111yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radical#62830C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×#529 ◁ G
LECSG ▷ C22×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60290C2semidirect
3. #34229C2semidirect
4. #17631C2semidirect
5. #17630C2semidirect
6. #17628C2semidirect
7. #17626C2semidirect
8. #17618C2semidirect
9. #17617C2semidirect
10. #17616C2semidirect
11. #17613C2semidirect
12. #17610C2semidirect
13. #17604C2semidirect
14. #17597C2semidirect
15. #17588C2semidirect
16. C2×#1517C2semidirect
17. #17547C2semidirect
18. #17544C2semidirect
19. #17533C2semidirect
22. #3552C4semidirect
24. #3547C4semidirect
25. #3546C4semidirect
26. #3543C4semidirect
28. #3520C4semidirect
29. #3519C4semidirect
31. #3517C4semidirect
33. #3514C4semidirect
49. #2983C22semidirect
50. #2982C22semidirect
51. #2975C22semidirect
52. #2974C22semidirect
53. #2972C22semidirect
56. #2924C22semidirect
57. #2920C22semidirect
58. C2×#431C22semidirect
62. #2357C22semidirect
63. #2356C22semidirect
64. #2351C22semidirect
65. #2349C22semidirect
66. #2346C22semidirect
67. #2343C22semidirect
69. #2318C22semidirect
72. C2×#382C22semidirect
73. #2275C22semidirect
74. C4×#117C22semidirect
75. #1521C22semidirect
76. #1519C22semidirect
77. #1518C22semidirect
78. #1518C22semidirect
81. #1517C22semidirect
82. #1517C22semidirect
83. #1517C22semidirect
84. #1517C22semidirect
85. #1517C22semidirect
86. #1517C22semidirect
87. #1516C22semidirect
88. #1514C22semidirect
89. #1513C22semidirect
90. #1512C22semidirect
91. #1512C22semidirect
92. #1510C22semidirect
93. #1509C22semidirect
94. #1507C22semidirect
95. #1507C22semidirect
96. #1507C22semidirect
97. #1505C22semidirect
98. #1505C22semidirect
99. #1505C22semidirect
100. #1504C22semidirect
101. #1504C22semidirect
102. #1503C22semidirect
103. #1503C22semidirect
106. #1502C22semidirect
107. #1502C22semidirect
108. #1502C22semidirect
109. #1502C22semidirect
110. #1502C22semidirect
111. #1501C22semidirect
112. #1501C22semidirect
113. #1501C22semidirect
114. #1500C22semidirect
115. #1500C22semidirect
116. #1500C22semidirect
117. C2×#327C22semidirect
118. C2×#327C22semidirect
127. #559C2×C4semidirect
128. #557C2×C4semidirect
130. #556C2×C4semidirect
131. #556C2×C4semidirect
133. #555C2×C4semidirect
134. #555C2×C4semidirect
135. #554C2×C4semidirect
136. #554C2×C4semidirect
144. #553C2×C4semidirect
145. #553C2×C4semidirect
154. #550C2×C4semidirect
155. #550C2×C4semidirect
156. #550C2×C4semidirect
157. #550C2×C4semidirect
159. D4×Q8C2×C4semidirect
160. D4×Q8C2×C4semidirect
169. #547C2×C4semidirect
170. #547C2×C4semidirect
171. #547C2×C4semidirect
183. #546C2×C4semidirect
184. #546C2×C4semidirect
187. D42C2×C4semidirect
188. D42C2×C4semidirect
189. D42C2×C4semidirect
190. #544C2×C4semidirect
192. #542C2×C4semidirect
193. #542C2×C4semidirect
198. #540C2×C4semidirect
199. #540C2×C4semidirect
220. #535C2×C4semidirect
223. #533C2×C4semidirect
224. #533C2×C4semidirect
231. #532C2×C4semidirect
232. #532C2×C4semidirect
233. #532C2×C4semidirect
234. #532C2×C4semidirect
235. #532C2×C4semidirect
241. C2×C4⋊Q8C2×C4semidirect
242. C2×#127C2×C4semidirect
253. #529C2×C4semidirect
281. #520C2×C4semidirect
283. #518C2×C4semidirect
286. C4×#41C2×C4semidirect
292. C2×C4×D4C2×C4semidirect

Maximal subgroups

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

subgroupindex
#628302
#602902
#342292
#176312
#176302
#176282
#176262
#176182
#176172
#176162
#176132
#176102
#176042
#175972
#175882
C2×#15172
#175472
#175442
#175332