Finite Group Databasebeta

← #7657757

Subgroups — #7657757

Order 512.

8535 conjugacy classes of subgroups.

The subgroup lattice has 1086 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3489C211yesmaximal, characteristic, complemented
2C2×D4×#41C211yesmaximal, characteristic, complemented
3#42943C213yesmaximal, complemented
4#42942C213yesmaximal, complemented
5#42917C213yesmaximal, complemented
6#42916C213yesmaximal, complemented
7#42673C216yesmaximal, complemented
8#42474C216yesmaximal, complemented
9#39889C216yesmaximal, complemented
10#39884C216yesmaximal, complemented
11#37449C213yesmaximal, complemented
12#37445C213yesmaximal, complemented
13#36432C212yesmaximal, complemented
14#36428C212yesmaximal, complemented
15#36076C211yesmaximal, characteristic, complemented
16#35996C211yesmaximal, characteristic, complemented
17#35771C212yesmaximal, complemented
18#35757C211yesmaximal, characteristic, complemented
19#35700C212yesmaximal, complemented
20#35687C211yesmaximal, characteristic, complemented
21#35084C213yesmaximal, complemented
22#34562C213yesmaximal, complemented
23#34174C211yesmaximal, characteristic, complemented
24C22×2−1+4C2211yescharacteristic, complemented
25C23×#41C2211yescharacteristic
26C23×#41C2211yescharacteristic
27#3489—216no—
28D4×#41—216no—
29C2×#550C2211yescharacteristic
30C2×D4×Q8C2211yescharacteristic
31C2×D4×Q8C2212yescomplemented
32C2×D4×Q8C2212yescomplemented
33C2×#548C2212yes—
34C2×#548C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#548C2212yescomplemented
37C2×#547C2213yes—
38C2×#547C2216yescomplemented
39C2×#546C2213yes—
40C2×#546C2213yes—
41C2×#546C2216yescomplemented
42C2×D42C2213yes—
43C2×#537C2213yescomplemented
44C2×#536C2213yescomplemented
45C2×#532C2213yes—
46C2×#525C2213yes—
47C2×#525C2213yes—
48C2×#525C2213yescomplemented
49C22×C22⋊Q8C2213yescomplemented
50C2×#520C2211yescharacteristic, complemented
51C2×#519C2212yescomplemented
52C2×C4×#41C2211yescharacteristic
53C22×C4×D4C2213yes—
54#2855C2216yescomplemented
55#2848C2216yescomplemented
56#2814C2216yescomplemented
57#2814C2216yescomplemented
58#2812C22112yescomplemented
59#2724C22112yescomplemented
60#2701C22112yescomplemented
61#2701C22112yescomplemented
62#2701C22112yescomplemented
63#2699C22112yescomplemented
64#2697C22112yescomplemented
65#2682C22112yescomplemented
66#2678C22112yescomplemented
67#2663C2216yescomplemented
68#2661C2216yescomplemented
69#2638C2213yes—
70#2638C2213yescomplemented
71#2638C2216yescomplemented
72#2635C2211yescharacteristic
73#2635C2213yescomplemented
74#2630C2216yescomplemented
75#2630C2216yescomplemented
76#2627C2213yescomplemented
77#2626C2213yescomplemented
78#2625C2213yescomplemented
79#2624C2213yescomplemented
80#2622C2216yescomplemented
81#2622C22112yescomplemented
82#2621C2216yescomplemented
83#2620C2216yescomplemented
84#2618C2213yescomplemented
85#2617C2213yescomplemented
86#2616C2213yescomplemented
87#2615C2213yescomplemented
88#2613C2216yes—
89#2602C22112yescomplemented
90#2583C2216yescomplemented
91#2579C22112yescomplemented
92#2561C2216yescomplemented
93#2546C2216yescomplemented
94#2545C2216yescomplemented
95#2538C2216yescomplemented
96#2536C2216yescomplemented
97#2504C2213yescomplemented
98#2502C2213yescomplemented
99#2499C2216yescomplemented
100#2486C2213yescomplemented
101#2486C2213yescomplemented
102#2485C2216yescomplemented
103#2483C2216yescomplemented
104#2447C2216yescomplemented
105#2447C2216yescomplemented
106#2447C2216yescomplemented
107#2445C2216yescomplemented
108#2436C2213yescomplemented
109#2435C2216yescomplemented
110#2434C2213yescomplemented
111#2432C2216yescomplemented
112#2432C2216yescomplemented
113#2432C2216yescomplemented
114#2431C2216yescomplemented
115#2429C2216yescomplemented
116#2429C2216yescomplemented
117#2429C2216yescomplemented
118#2426C2216yescomplemented
119#2422C2216yescomplemented
120#2422C2216yescomplemented
121#2420C2216yescomplemented
122#2420C2216yescomplemented
123#2415C2216yes—
124#2415C2216yescomplemented
125#2415C2216yescomplemented
126#2414C2216yescomplemented
127#2409C2213yescomplemented
128#2409C2213yescomplemented
129#2408C2216yescomplemented
130#2407C2216yescomplemented
131#2407C2216yescomplemented
132#2407C2216yescomplemented
133#2407C2216yescomplemented
134#2405C2216yes—
135#2395C2213yescomplemented
136#2395C2213yescomplemented
137#2392C2216yes—
138#2392C2216yescomplemented
139#2388C2213yescomplemented
140#2388C2213yescomplemented
141#2351C2212yescomplemented
142Q8×C4⋊C4C2212yescomplemented
143#2341C2212yes—
144#2341C2212yescomplemented
145#2341C2211yescharacteristic, complemented
146#2341C2211yescharacteristic, complemented
147#2341C2213yescomplemented
148#2341C2213yescomplemented
149#2341C2216yescomplemented
150Q8×C22⋊C4C2212yescomplemented
151Q8×C22⋊C4C2212yescomplemented
152Q8×C22⋊C4C2212yescomplemented
153#2322C2216yescomplemented
154#2322C2216yescomplemented
155#2309C2216yescomplemented
156C4×#123C2216yescomplemented
157C4×#120C2216yescomplemented
158#2280C2213yescomplemented
159#2280C2213yescomplemented
160C2×2−1+4—28no—
161C2×2−1+4—48no—
162C22×#41—28no—
163C22×#41—48no—
164C22×#41—48no—
165C22×#41D4116yescomplemented
166C22×#41C2311yescharacteristic
167C22×#41C2311yescharacteristic
168C22×#41C2311yescharacteristic
169C22×#41C2313yes—
170C22×#41C2313yes—
171C22×#41C2313yes—
172C22×#41C2316yes—
173C22×#41C2313yes—
174C22×#41C2313yes—
175C23×Q8C2311yescharacteristic
176C23×Q8C2312yes—
177C23×Q8C2311yescharacteristic
178C23×Q8C2313yes—
179C23×D4C2313yes—
180C23×D4C2313yes—
181C23×D4C2313yes—
182C24×C4C2313yes—
183C24×C4C2313yes—
184#550—28no—
185D4×Q8—28no—
186D4×Q8—216no—
187D4×Q8—48no—
188#548—28no—
189#548—216no—
190#548—28no—
191#548—48no—
192#547—224no—
193#547—248no—
194#546—224no—
195#546—224no—
196#546—248no—
197D42—224no—
198#537—224no—
199#536—224no—
200#532—224no—
201C2×C4⋊Q8C2313yes—
202C2×C4⋊Q8C2316yes—
203C2×C4⋊Q8C2316yes—
204C2×#127C2313yes—
205C2×#124C2313yes—
206C2×#124C2313yes—
207C2×#124C2316yes—
208C2×#124C2316yes—
209#525—224no—
210#525—224no—
211#525—224no—
212C2×#123C2316yes—
213C2×#123C2316yes—
214C2×#123C2316yes—
215C2×#123C23112yes—
216C2×#123C2316yes—
217C2×#123C2316yes—
218C2×#123C2316yes—
219C2×C22⋊Q8—224no—
220C2×C22⋊Q8C2316yes—
221C2×C22⋊Q8C2316yes—
222C2×C22⋊Q8C2313yes—
223C2×C22⋊Q8C2316yes—
224C2×C22⋊Q8C2313yes—
225C2×C22⋊Q8C2313yes—
226C2×C22⋊Q8C2313yes—
227C2×C22⋊Q8C2313yes—
228C2×C22⋊Q8C2313yes—
229C2×C22⋊Q8C2316yes—
230C2×C22⋊Q8C2316yes—
231C2×C22⋊Q8C2316yes—
232C2×C22⋊Q8C2316yes—
233C2×#121C2313yes—
234C2×#121C2313yes—
235C2×#121C2313yes—
236C2×#121C2311yescharacteristic
237C2×#121C2313yes—
238C2×#121C2313yes—
239C2×#121C2316yes—
240C2×#121C2316yes—
241C2×#121C2316yes—
242C2×#121C23112yes—
243C2×#121C2316yes—
244C2×#120C2316yes—
245C2×#120C2316yes—
246C2×#120C2316yes—
247C2×#120C2316yes—
248#520—28no—
249#519—48no—
250C4×#41—28no—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2312yes—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2316yes—
257C2×C4×Q8C2316yes—
258C2×C4×D4—224no—
259C2×C4×D4C2313yes—
260C2×C4×D4C2313yes—
261C2×C4×D4C2316yes—
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2313yes—
264C2×C4×D4C2313yes—
265C2×C4×D4C2313yes—
266C2×C4×D4C2313yes—
267C2×C4×D4C2316yes—
268C2×C4×D4C2313yes—
269C2×C4×D4C2313yes—
270C2×C4×D4C2313yes—
271C2×C4×D4C2316yes—
272C2×C4×D4C2316yes—
273C2×C4×D4C2316yes—
274C2×C4×D4C2316yes—
275C2×#117C2313yes—
276C2×#117C2313yes—
277C2×#117C2316yes—
278C2×#117C2316yes—
279C22×C4⋊C4C2316yes—
280C22×C4⋊C4C2313yes—
281C22×C4⋊C4C2313yes—
282C22×C22⋊C4C2313yes—
283C22×C22⋊C4C2313yes—
284C22×C22⋊C4C2316yes—
285C22×C42C2313yes—
286#400C2313yes—
287#400C2311yescharacteristic
288#399C2313yes—
289#399C2311yescharacteristic
290#398C23112yes—
291#398C23112yes—
292#398C2313yes—
293#398C2316yes—
294#398C2313yes—
295#398C2316yes—
296#398C2316yes—
297#397C2313yes—
298#397C2316yes—
299#397C23112yes—
300#397C2313yes—
301#397C2316yes—
302#397C23112yes—
303#397C2316yes—
304#397C2316yes—
305#397C2316yes—
306#397C23112yes—
307#397C23112yes—
308#397C23112yes—
309#396C23112yes—
310#396C23112yes—
311#396C2316yes—
312#396C2316yes—
313#396C2316yes—
314#396C2316yes—
315#395C2313yes—
316#395C2316yes—
317#395C2313yes—
318#394C23112yes—
319#394C23112yes—
320#394C2316yes—
321#394C2316yes—
322#394C2316yes—
323#394C2316yes—
324#394C2313yes—
325#394C2316yes—
326#394C2316yes—
327#394C2311yescharacteristic
328#394C23112yes—
329#394C2312yes—
330#394C2316yes—
331#394C2316yes—
332#394C2316yes—
333#394C23112yes—
334#394C23112yes—
335#394C23112yes—
336#394C23112yes—
337#393C2313yes—
338#393C2316yes—
339#393C2313yes—
340#392C23112yes—
341#392C2312yes—
342#392C2316yes—
343#392C2316yes—
344#392C2316yes—
345#392C2313yes—
346#392C2311yescharacteristic
347#392C23112yes—
348#391C2316yes—
349#391C2316yes—
350#391C2316yes—
351#391C2316yes—
352#391C2316yes—
353#391C2316yes—
354#390C2316yes—
355#390C2316yes—
356#390C2316yes—
357#390C2316yes—
358#390C23112yes—
359#390C23112yes—
360#390C2316yes—
361#390C2316yes—
362#390C23112yes—
363#389C23112yes—
364#389C23112yes—
365#389C2316yes—
366#389C2316yes—
367#389C23112yes—
368#389C2316yes—
369#389C2316yes—
370#388C23112yes—
371#388C23112yes—
372#388C2316yes—
373#388C23112yes—
374#388C23112yes—
375#388C2312yes—
376#387C2316yes—
377#387C23112yes—
378#387C2316yes—
379#386C2316yes—
380#386C2316yes—
381#386C23112yes—
382#386C23112yes—
383#386C2316yes—
384#386C2316yes—
385#386C2316yes—
386#386C2312yes—
387#385C2316yes—
388#385C23112yes—
389#385C2316yes—
390#385C2316yes—
391#385C2316yes—
392#385C23112yes—
393#385C23112yes—
394#385C23112yes—
395#385C23112yes—
396#385C2316yes—
397#385C2316yes—
398#384C2316yes—
399#382C2316yes—
400#381C23112yes—
401#381C2316yes—
402#381C2316yes—
403#381C2316yes—
404#381C2311yescharacteristic
405#381C2313yes—
406#380C2316yes—
407#380C2316yes—
408#380C2316yes—
409#380C2316yes—
410#380C2316yes—
411#380C2316yes—
412#380C2313yes—
413#380C2313yes—
414#380C2313yes—
415#380C2313yes—
416#379C23112yes—
417#379C2316yes—
418#379C2316yes—
419#379C2316yes—
420C4×C4⋊C4C2316yes—
421C4×C4⋊C4C2316yes—
422C4×C22⋊C4C2316yes—
423C4×C22⋊C4C2316yes—
424C4×C22⋊C4C2316yes—
425C4×C22⋊C4C2316yes—
426C4×C22⋊C4C2316yes—
427C4×C22⋊C4C2316yes—
428C4×C22⋊C4C2313yes—
429C4×C22⋊C4C2313yes—
430C4×C22⋊C4C2316yes—
431C25C2413yes—
432C25C2413yes—
4332−1+4—464no—
434C2×#41—24no—
435C2×#41—28no—
436C2×#41—28no—
437C2×#41—28no—
438C2×#41—212no—
439C2×#41—224no—
440C2×#41—212no—
441C2×#41—212no—
442C2×#41—412no—
443C2×#41—412no—
444C2×#41—412no—
445C2×#41—412no—
446C2×#41—412no—
447C2×#41—412no—
448C2×#41—412no—
449C2×#41—464no—
450C2×#41—464no—
451C2×#41C2×D418yes—
452C2×#41C2×D418yes—
453C2×#41C2×D4124yes—
454C2×#41C2×D4124yes—
455C22×Q8—28no—
456C22×Q8—24no—
457C22×Q8—28no—
458C22×Q8—28no—
459C22×Q8—28no—
460C22×Q8—28no—
461C22×Q8—212no—
462C22×Q8—412no—
463C22×Q8C2×D418yes—
464C22×Q8C2416yes—
465C22×Q8C2413yes—
466C22×Q8C2413yes—
467C22×Q8C2413yes—
468C22×Q8C2411yescharacteristic
469C22×D4—212no—
470C22×D4—212no—
471C22×D4—46no—
472C22×D4—412no—
473C22×D4—412no—
474C22×D4—46no—
475C22×D4C2×D4124yes—
476C22×D4C2411yescharacteristic
477C22×D4C2413yes—
478C22×D4C2413yes—
479C22×D4C2413yes—
480C22×D4C2413yes—
481C22×D4C2413yes—
482C22×D4C2412yes—
483C22×D4C2412yes—
484C22×D4C2413yes—
485C22×D4C2416yes—
486C22×D4C2416yes—
487C22×D4C2416yes—
488C22×D4C2416yes—
489C22×D4C2411yescharacteristic
490C22×D4C2416yes—
491C22×D4C2416yes—
492C23×C4—212no—
493C23×C4—412no—
494C23×C4—412no—
495C23×C4C2×D4124yes—
496C23×C4C2416yes—
497C23×C4C2413yes—
498C23×C4C2413yes—
499C23×C4C2413yes—
500C23×C4C2413yes—
501C23×C4C2413yes—
502C23×C4C2413yes—
503C23×C4C2413yes—
504C23×C4C2416yes—
505C23×C4C2413yes—
506C23×C4C2416yes—
507C23×C4C2411yescharacteristic
508C23×C4C2413yes—
509C23×C4C2413yes—
510C23×C4C2413yes—
511C23×C4C2411yescharacteristic
512C4⋊Q8—212no—
513C4⋊Q8—224no—
514C4⋊Q8—412no—
515#127—212no—
516#124—212no—
517#124—212no—
518#124—224no—
519#124—412no—
520#123—224no—
521#123—248no—
522#123—224no—
523#123—224no—
524#123—412no—
525#123—412no—
526#123—412no—
527C22⋊Q8—212no—
528C22⋊Q8—212no—
529C22⋊Q8—224no—
530C22⋊Q8—212no—
531C22⋊Q8—224no—
532C22⋊Q8—224no—
533C22⋊Q8—224no—
534C22⋊Q8—212no—
535C22⋊Q8—212no—
536C22⋊Q8—212no—
537C22⋊Q8—412no—
538C22⋊Q8—412no—
539C22⋊Q8—412no—
540#121—212no—
541#121—212no—
542#121—224no—
543#121—224no—
544#121—248no—
545#121—224no—
546#121—24no—
547#121—212no—
548#121—212no—
549#121—212no—
550#121—412no—
551#120—224no—
552#120—224no—
553#120—224no—
554#120—412no—
555C4×Q8—24no—
556C4×Q8—24no—
557C4×Q8—28no—
558C4×Q8—28no—
559C4×Q8—28no—
560C4×Q8—412no—
561C4×Q8—412no—
562C4×D4—212no—
563C4×D4—212no—
564C4×D4—224no—
565C4×D4—24no—
566C4×D4—212no—
567C4×D4—212no—
568C4×D4—212no—
569C4×D4—212no—
570C4×D4—212no—
571C4×D4—212no—
572C4×D4—212no—
573C4×D4—224no—
574C4×D4—224no—
575C4×D4—224no—
576C4×D4—412no—
577C4×D4—412no—
578#117—212no—
579#117—212no—
580#117—412no—
581#117—412no—
582C2×C4⋊C4—212no—
583C2×C4⋊C4—212no—
584C2×C4⋊C4—224no—
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2413yes—
587C2×C4⋊C4C2416yes—
588C2×C4⋊C4C2413yes—
589C2×C4⋊C4C2413yes—
590C2×C4⋊C4C2413yes—
591C2×C4⋊C4C2416yes—
592C2×C4⋊C4C24112yes—
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2413yes—
595C2×C4⋊C4C2413yes—
596C2×C4⋊C4C2416yes—
597C2×C4⋊C4C2416yes—
598C2×C4⋊C4C2416yes—
599C2×C4⋊C4C2416yes—
600C2×C4⋊C4C2416yes—
601C2×C4⋊C4C2416yes—
602C2×C4⋊C4C2416yes—
603C2×C4⋊C4C2416yes—
604C2×C4⋊C4C2416yes—
605C2×C4⋊C4C24112yes—
606C2×C4⋊C4C2416yes—
607C2×C4⋊C4C24112yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2416yes—
610C2×C22⋊C4—212no—
611C2×C22⋊C4—224no—
612C2×C22⋊C4—212no—
613C2×C22⋊C4C2411yescharacteristic
614C2×C22⋊C4C2411yescharacteristic
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C2413yes—
617C2×C22⋊C4C2413yes—
618C2×C22⋊C4C2413yes—
619C2×C22⋊C4C2413yes—
620C2×C22⋊C4C2413yes—
621C2×C22⋊C4C2413yes—
622C2×C22⋊C4C24112yes—
623C2×C22⋊C4C2416yes—
624C2×C22⋊C4C2416yes—
625C2×C22⋊C4C2412yes—
626C2×C22⋊C4C2416yes—
627C2×C22⋊C4C2416yes—
628C2×C22⋊C4C2416yes—
629C2×C22⋊C4C2416yes—
630C2×C22⋊C4C2416yes—
631C2×C22⋊C4C2412yes—
632C2×C22⋊C4C2412yes—
633C2×C22⋊C4C2416yes—
634C2×C22⋊C4C2412yes—
635C2×C22⋊C4C2416yes—
636C2×C22⋊C4C2416yes—
637C2×C22⋊C4C2416yes—
638C2×C22⋊C4C2416yes—
639C2×C22⋊C4C2416yes—
640C2×C22⋊C4C24112yes—
641C2×C22⋊C4C2416yes—
642C2×C22⋊C4C2416yes—
643C2×C22⋊C4C2416yes—
644C2×C22⋊C4C2416yes—
645C2×C22⋊C4C24112yes—
646C2×C22⋊C4C2412yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C24112yes—
649C2×C22⋊C4C2416yes—
650C2×C22⋊C4C2416yes—
651C2×C22⋊C4C2416yes—
652C2×C22⋊C4C2416yes—
653C2×C42—212no—
654C2×C42C2413yes—
655C2×C42C2416yes—
656C2×C42C2416yes—
657C2×C42C2416yes—
658C2×C42C2411yescharacteristic
659C2×C42C2413yes—
660C2×C42C2413yes—
661C2×C42C24112yes—
662#95C2416yes—
663#95C2412yes—
664#95C2413yes—
665#95C2411yescharacteristic
666#95C2411yescharacteristic
667#95C2413yes—
668#95C2412yes—
669#95C2416yes—
670#95C2416yes—
671#95C2416yes—
672#95C2416yes—
673#95C2416yes—
674#95C2416yes—
675#95C2416yes—
676#95C2412yes—
677#95C2416yes—
678#95C2416yes—
679#95C2416yes—
680#95C24112yes—
681#95C24112yes—
682#95C24112yes—
683#95C24112yes—
684C24—26no—
685C24—26no—
686C24—46no—
687C24—46no—
688C24—43no—
689C24—43no—
690C24—43no—
691C24—46no—
692C24—46no—
693C24C22×D4112yes—
694C24C2513yes—
695C24C2512yes—
696C24C2511yescharacteristic
697C24C2513yes—
698C24C2513yes—
699C24C2511yescharacteristic
700#41—232no—
701#41—232no—
702#41—448no—
703#41—448no—
704#41—448no—
705#41—448no—
706#41—448no—
707#41—496no—
708#41—416no—
709C2×Q8—232no—
710C2×Q8—26no—
711C2×Q8—212no—
712C2×Q8—26no—
713C2×Q8—212no—
714C2×Q8—212no—
715C2×Q8—212no—
716C2×Q8—212no—
717C2×Q8—46no—
718C2×Q8—448no—
719C2×Q8—416no—
720C2×Q8—432no—
721C2×Q8C22×D4112yes—
722C2×Q8C22×D414yes—
723C2×Q8H(5,𝔽2)18yes—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—24no—
727C2×D4—26no—
728C2×D4—26no—
729C2×D4—26no—
730C2×D4—212no—
731C2×D4—212no—
732C2×D4—24no—
733C2×D4—26no—
734C2×D4—212no—
735C2×D4—212no—
736C2×D4—22no—
737C2×D4—26no—
738C2×D4—212no—
739C2×D4—212no—
740C2×D4—212no—
741C2×D4—22no—
742C2×D4—26no—
743C2×D4—448no—
744C2×D4—42no—
745C2×D4—43no—
746C2×D4—43no—
747C2×D4—43no—
748C2×D4—43no—
749C2×D4—412no—
750C2×D4—412no—
751C2×D4—42no—
752C2×D4—42no—
753C2×D4—42no—
754C2×D4—42no—
755C2×D4—46no—
756C2×D4—46no—
757C2×D4—46no—
758C2×D4—46no—
759C2×D4—46no—
760C2×D4—46no—
761C2×D4—46no—
762C2×D4—412no—
763C2×D4—448no—
764C2×D4—448no—
765C2×D4C22×D4112yes—
766C2×D4C22×D4112yes—
767C2×D4C22×D4124yes—
768C22×C4—212no—
769C22×C4—212no—
770C22×C4—212no—
771C22×C4—26no—
772C22×C4—26no—
773C22×C4—212no—
774C22×C4—26no—
775C22×C4—212no—
776C22×C4—22no—
777C22×C4—26no—
778C22×C4—26no—
779C22×C4—26no—
780C22×C4—212no—
781C22×C4—212no—
782C22×C4—212no—
783C22×C4—212no—
784C22×C4—212no—
785C22×C4—26no—
786C22×C4—448no—
787C22×C4—42no—
788C22×C4—42no—
789C22×C4—46no—
790C22×C4—46no—
791C22×C4—46no—
792C22×C4—46no—
793C22×C4—43no—
794C22×C4—412no—
795C22×C4—46no—
796C22×C4—46no—
797C22×C4—46no—
798C22×C4—448no—
799C22×C4C22×D4112yes—
800C22×C4C22×D4112yes—
801C22×C4C22×D4112yes—
802C22×C4C22×D4112yes—
803C22×C4C22×D4112yes—
804C22×C4C22×D414yes—
805C22×C4C2511yescharacteristic
806C22×C4C2513yes—
807C22×C4C2512yes—
808C22×C4C2516yes—
809C22×C4C2512yes—
810C22×C4C2516yes—
811C22×C4C2512yes—
812C22×C4C2513yes—
813C22×C4C2516yes—
814C22×C4C2516yes—
815C22×C4C2511yescharacteristic
816C22×C4C2513yes—
817C22×C4C2511yescharacteristic
818C22×C4C2511yescharacteristic
819C22×C4C2513yes—
820C22×C4C2511yescharacteristic
821C22×C4C2513yes—
822C4⋊C4—22no—
823C4⋊C4—26no—
824C4⋊C4—212no—
825C4⋊C4—26no—
826C4⋊C4—26no—
827C4⋊C4—26no—
828C4⋊C4—212no—
829C4⋊C4—224no—
830C4⋊C4—22no—
831C4⋊C4—26no—
832C4⋊C4—26no—
833C4⋊C4—212no—
834C4⋊C4—212no—
835C4⋊C4—212no—
836C4⋊C4—212no—
837C4⋊C4—212no—
838C4⋊C4—42no—
839C4⋊C4—46no—
840C4⋊C4—46no—
841C4⋊C4—46no—
842C4⋊C4—46no—
843C4⋊C4—46no—
844C4⋊C4—412no—
845C4⋊C4—46no—
846C4⋊C4—412no—
847C22⋊C4—22no—
848C22⋊C4—212no—
849C22⋊C4—26no—
850C22⋊C4—26no—
851C22⋊C4—26no—
852C22⋊C4—224no—
853C22⋊C4—212no—
854C22⋊C4—212no—
855C22⋊C4—212no—
856C22⋊C4—212no—
857C22⋊C4—212no—
858C22⋊C4—22no—
859C22⋊C4—26no—
860C22⋊C4—26no—
861C22⋊C4—26no—
862C22⋊C4—24no—
863C22⋊C4—212no—
864C22⋊C4—212no—
865C22⋊C4—24no—
866C22⋊C4—412no—
867C22⋊C4—46no—
868C22⋊C4—46no—
869C22⋊C4—46no—
870C22⋊C4—42no—
871C22⋊C4—42no—
872C22⋊C4—46no—
873C22⋊C4—42no—
874C22⋊C4—46no—
875C22⋊C4—42no—
876C22⋊C4—46no—
877C22⋊C4—46no—
878C22⋊C4—46no—
879C22⋊C4—46no—
880C22⋊C4—46no—
881C22⋊C4—412no—
882C22⋊C4—46no—
883C22⋊C4—46no—
884C22⋊C4—46no—
885C22⋊C4—412no—
886C22⋊C4—46no—
887C42—22no—
888C42—26no—
889C42—26no—
890C42—26no—
891C42—212no—
892C42—212no—
893C42—212no—
894C42—412no—
895C23—21no—
896C23—22no—
897C23—22no—
898C23—26no—
899C23—26no—
900C23—23no—
901C23—23no—
902C23—23no—
903C23—23no—
904C23—21no—
905C23—21no—
906C23—21no—
907C23—26no—
908C23—26no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—23no—
913C23—22no—
914C23—26no—
915C23—22no—
916C23—22no—
917C23—23no—
918C23—23no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—26no—
923C23—412no—
924C23—412no—
925C23—412no—
926C23—412no—
927C23—412no—
928C23—86no—
929C23—812no—
930C23—812no—
931C23—812no—
932C23—812no—
933C23C23×D412yes—
934C23C23×D416yes—
935C23C23×D416yes—
936C23#58512yes—
937C23C2611yescharacteristic
938Q8—224no—
939Q8—412no—
940Q8—424no—
941Q8—412no—
942Q8#534116yes—
943D4—28no—
944D4—224no—
945D4—224no—
946D4—424no—
947D4—412no—
948D4—44no—
949D4—412no—
950D4—48no—
951D4—48no—
952D4—412no—
953D4—424no—
954D4—424no—
955D4—412no—
956D4—812no—
957D4—812no—
958D4—812no—
959C2×C4—21no—
960C2×C4—26no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—21no—
964C2×C4—224no—
965C2×C4—224no—
966C2×C4—224no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—23no—
970C2×C4—23no—
971C2×C4—26no—
972C2×C4—21no—
973C2×C4—23no—
974C2×C4—26no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—26no—
978C2×C4—26no—
979C2×C4—26no—
980C2×C4—22no—
981C2×C4—26no—
982C2×C4—26no—
983C2×C4—22no—
984C2×C4—26no—
985C2×C4—26no—
986C2×C4—26no—
987C2×C4—22no—
988C2×C4—26no—
989C2×C4—23no—
990C2×C4—23no—
991C2×C4—22no—
992C2×C4—26no—
993C2×C4—22no—
994C2×C4—26no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—26no—
999C2×C4—44no—
1000C2×C4—412no—
1001C2×C4—412no—
1002C2×C4—412no—
1003C2×C4—44no—
1004C2×C4—412no—
1005C2×C4—412no—
1006C2×C4—424no—
1007C2×C4—412no—
1008C2×C4—412no—
1009C2×C4—424no—
1010C2×C4—812no—
1011C2×C4—86no—
1012C2×C4C23×D412yes—
1013C2×C4C23×D416yes—
1014C2×C4C23×D412yes—
1015C2×C4C23×D416yes—
1016C2×C4C2×H(5,𝔽2)112yes—
1017C2×C4#58512yes—
1018C22—26no—
1019C22—26no—
1020C22—22no—
1021C22—22no—
1022C22—26no—
1023C22—22no—
1024C22—26no—
1025C22—24no—
1026C22—22no—
1027C22—26no—
1028C22—26no—
1029C22—41no—
1030C22—46no—
1031C22—46no—
1032C22—42no—
1033C22—46no—
1034C22—46no—
1035C22—42no—
1036C22—42no—
1037C22—41no—
1038C22—43no—
1039C22—42no—
1040C22—42no—
1041C22—43no—
1042C22—42no—
1043C22—42no—
1044C22—46no—
1045C22—42no—
1046C22—42no—
1047C22—46no—
1048C22—42no—
1049C22—43no—
1050C22—824no—
1051C22—824no—
1052C22C24×D411yescharacteristic
1053C22C22×H(5,𝔽2)12yes—
1054C22C2×#58511yescharacteristic
1055C22C2×#58511yescharacteristic
1056C222−1+612yes—
1057C4—22no—
1058C4—22no—
1059C4—22no—
1060C4—26no—
1061C4—43no—
1062C4—46no—
1063C4—41no—
1064C4—43no—
1065C4—42no—
1066C4—42no—
1067C4—46no—
1068C4—42no—
1069C4—46no—
1070C4—41no—
1071C4—43no—
1072C4—46no—
1073C4C2×#534112yes—
1074C2—46no—
1075C2—46no—
1076C2—42no—
1077C2—42no—
1078C2—82no—
1079C2—83no—
1080C2C22×#53411yescharacteristic
1081C2#6281111yescharacteristic
1082C2#6285911yescharacteristic
1083C2#6289712yes—
1084C2#6292212yes—
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×D4×#41C2semidirect
3. #42943C2semidirect
4. #42942C2semidirect
5. #42917C2semidirect
6. #42916C2semidirect
7. #42673C2semidirect
8. #42474C2semidirect
9. #39889C2semidirect
10. #39884C2semidirect
11. #37449C2semidirect
12. #37445C2semidirect
13. #36432C2semidirect
14. #36428C2semidirect
15. #36076C2semidirect
16. #35996C2semidirect
17. #35771C2semidirect
18. #35757C2semidirect
19. #35700C2semidirect
20. #35687C2semidirect
21. #35084C2semidirect
22. #34562C2semidirect
23. #34174C2semidirect
24. C22×2−1+4C22semidirect
31. C2×D4×Q8C22semidirect
32. C2×D4×Q8C22semidirect
36. C2×#548C22semidirect
38. C2×#547C22semidirect
41. C2×#546C22semidirect
43. C2×#537C22semidirect
44. C2×#536C22semidirect
48. C2×#525C22semidirect
49. C22×C22⋊Q8C22semidirect
50. C2×#520C22semidirect
51. C2×#519C22semidirect
54. #2855C22semidirect
55. #2848C22semidirect
56. #2814C22semidirect
57. #2814C22semidirect
58. #2812C22semidirect
59. #2724C22semidirect
60. #2701C22semidirect
61. #2701C22semidirect
62. #2701C22semidirect
63. #2699C22semidirect
64. #2697C22semidirect
65. #2682C22semidirect
66. #2678C22semidirect
67. #2663C22semidirect
68. #2661C22semidirect
70. #2638C22semidirect
71. #2638C22semidirect
73. #2635C22semidirect
74. #2630C22semidirect
75. #2630C22semidirect
76. #2627C22semidirect
77. #2626C22semidirect
78. #2625C22semidirect
79. #2624C22semidirect
80. #2622C22semidirect
81. #2622C22semidirect
82. #2621C22semidirect
83. #2620C22semidirect
84. #2618C22semidirect
85. #2617C22semidirect
86. #2616C22semidirect
87. #2615C22semidirect
89. #2602C22semidirect
90. #2583C22semidirect
91. #2579C22semidirect
92. #2561C22semidirect
93. #2546C22semidirect
94. #2545C22semidirect
95. #2538C22semidirect
96. #2536C22semidirect
97. #2504C22semidirect
98. #2502C22semidirect
99. #2499C22semidirect
100. #2486C22semidirect
101. #2486C22semidirect
102. #2485C22semidirect
103. #2483C22semidirect
104. #2447C22semidirect
105. #2447C22semidirect
106. #2447C22semidirect
107. #2445C22semidirect
108. #2436C22semidirect
109. #2435C22semidirect
110. #2434C22semidirect
111. #2432C22semidirect
112. #2432C22semidirect
113. #2432C22semidirect
114. #2431C22semidirect
115. #2429C22semidirect
116. #2429C22semidirect
117. #2429C22semidirect
118. #2426C22semidirect
119. #2422C22semidirect
120. #2422C22semidirect
121. #2420C22semidirect
122. #2420C22semidirect
124. #2415C22semidirect
125. #2415C22semidirect
126. #2414C22semidirect
127. #2409C22semidirect
128. #2409C22semidirect
129. #2408C22semidirect
130. #2407C22semidirect
131. #2407C22semidirect
132. #2407C22semidirect
133. #2407C22semidirect
135. #2395C22semidirect
136. #2395C22semidirect
138. #2392C22semidirect
139. #2388C22semidirect
140. #2388C22semidirect
141. #2351C22semidirect
142. Q8×C4⋊C4C22semidirect
144. #2341C22semidirect
145. #2341C22semidirect
146. #2341C22semidirect
147. #2341C22semidirect
148. #2341C22semidirect
149. #2341C22semidirect
150. Q8×C22⋊C4C22semidirect
151. Q8×C22⋊C4C22semidirect
152. Q8×C22⋊C4C22semidirect
153. #2322C22semidirect
154. #2322C22semidirect
155. #2309C22semidirect
156. C4×#123C22semidirect
157. C4×#120C22semidirect
158. #2280C22semidirect
159. #2280C22semidirect
165. C22×#41D4semidirect

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
#429432
#429422
#429172
#429162
#426732
#424742
#398892
#398842
#374492
#374452
#364322
#364282
#360762
#359962
#357712
#357572
#357002
#356872
#350842
#345622
#341742