Finite Group Databasebeta

← #7738228

Subgroups — #7738228

Order 512.

5702 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59820C214yesmaximal, complemented
2#59147C214yesmaximal, complemented
3#51093C214yesmaximal, complemented
4#50718C214yesmaximal, complemented
5#45421C212yesmaximal, complemented
6#45312C212yesmaximal, complemented
7#45070C212yesmaximal, complemented
8#44963C212yesmaximal, complemented
9#43905C218yesmaximal, complemented
10#39770C212yesmaximal, complemented
11#38985C212yesmaximal, complemented
12#38056C214yesmaximal, complemented
13#37336C214yesmaximal, complemented
14#36595C212yesmaximal, complemented
15#36300C212yesmaximal, complemented
16#36264C214yesmaximal, complemented
17#35562C214yesmaximal, complemented
18#35274C211yesmaximal, characteristic
19#35249C211yesmaximal, characteristic, complemented
20#34966C211yesmaximal, characteristic, complemented
21C2×#2548C211yesmaximal, characteristic, complemented
22#34364C211yesmaximal, characteristic, complemented
23#34236C211yesmaximal, characteristic, complemented
24#34128C211yesmaximal, characteristic, complemented
25C2×#559C2214yescomplemented
26C2×#551C2218yes—
27C2×#535C2214yes—
28C2×#532C2211yescharacteristic
29C22×#127C2211yescharacteristic
30C22×#124C2212yes—
31C22×C4×Q8C2211yescharacteristic
32#2867C2212yes—
33#2860C2214yescomplemented
34#2858C2212yes—
35#2858C2214yescomplemented
36#2854C2214yes—
37#2756C2218yescomplemented
38#2753C2218yescomplemented
39#2749C2218yescomplemented
40#2730C2218yescomplemented
41#2715C2218yescomplemented
42#2712C2218yescomplemented
43#2710C2218yescomplemented
44#2709C2218yescomplemented
45#2709C2218yescomplemented
46#2706C2218yescomplemented
47#2705C2218yescomplemented
48#2701C2218yescomplemented
49#2700C2218yescomplemented
50#2691C2218yescomplemented
51#2686C2218yescomplemented
52#2672C2218yescomplemented
53#2657C2212yes—
54#2657C2212yes—
55#2644C2214yescomplemented
56#2641C2214yescomplemented
57#2632C2214yescomplemented
58#2610C2218yescomplemented
59#2606C2212yescomplemented
60#2605C2212yescomplemented
61#2603C2218yescomplemented
62#2592C2214yescomplemented
63#2580C2214yescomplemented
64#2570C2212yescomplemented
65#2567C2211yescharacteristic, complemented
66#2567C2211yescharacteristic, complemented
67#2559C2218yescomplemented
68#2557C2218yescomplemented
69#2554C2218yescomplemented
70#2550C2212yescomplemented
71#2548C2212yes—
72#2548C2212yes—
73#2548C2214yes—
74#2548C2212yes—
75#2548C2212yes—
76#2548C2212yes—
77#2548C2212yes—
78#2548C2214yescomplemented
79#2548C2211yescharacteristic, complemented
80#2548C2214yescomplemented
81#2548C2211yescharacteristic, complemented
82#2544C2214yescomplemented
83#2544C2214yescomplemented
84#2544C2218yescomplemented
85#2541C2212yes—
86#2541C2212yes—
87#2541C2214yes—
88#2538C2214yescomplemented
89#2534C2218yes—
90#2521C2218yescomplemented
91#2513C2214yescomplemented
92#2512C2214yescomplemented
93#2512C2214yescomplemented
94#2512C2214yescomplemented
95#2501C2212yes—
96#2476C2218yescomplemented
97#2474C2218yescomplemented
98#2472C2218yes—
99#2471C2218yescomplemented
100#2467C2218yescomplemented
101#2461C2218yescomplemented
102#2459C2218yescomplemented
103#2454C2214yescomplemented
104#2452C2214yescomplemented
105#2448C2214yescomplemented
106#2447C2214yescomplemented
107#2445C2214yescomplemented
108#2445C2218yescomplemented
109#2445C2214yescomplemented
110#2445C2214yescomplemented
111#2445C2214yescomplemented
112#2445C2214yescomplemented
113#2445C2214yescomplemented
114#2444C2218yescomplemented
115#2442C2212yes—
116#2440C2212yes—
117#2438C2214yes—
118#2436C2212yes—
119#2433C2214yes—
120#2433C2212yes—
121#2433C2212yes—
122#2425C2218yescomplemented
123#2418C2218yes—
124#2412C2218yes—
125#2412C2218yes—
126#2411C2218yes—
127#2406C2214yes—
128#2402C2212yescomplemented
129#2399C2212yescomplemented
130C2×#394C2214yes—
131#2380C2214yes—
132#2369C2212yescomplemented
133#2367C2214yescomplemented
134#2366C2212yes—
135#2366C2212yes—
136#2366C2214yescomplemented
137#2366C2212yescomplemented
138#2361C2214yes—
139#2358C2218yes—
140#2357C2212yescomplemented
141#2356C2211yescharacteristic, complemented
142#2356C2212yescomplemented
143#2356C2212yescomplemented
144#2356C2211yescharacteristic, complemented
145#2354C2214yescomplemented
146#2351C2211yescharacteristic, complemented
147#2351C2211yescharacteristic, complemented
148#2349C2212yescomplemented
149#2344C2214yes—
150#2344C2212yes—
151Q8×C22⋊C4C2212yes—
152#2339C2214yes—
153D4×C22⋊C4C2214yes—
154D4×C22⋊C4C2214yes—
155#2337C2214yescomplemented
156#2328C2212yes—
157#2328C2212yes—
158#2328C2214yes—
159#2328C2214yescomplemented
160#2326C2212yescomplemented
161#2326C2212yescomplemented
162#2319C2214yescomplemented
163#2319C2212yescomplemented
164#2308C2214yes—
165C4×C4⋊Q8C2212yescomplemented
166C4×#127C2214yescomplemented
167C4×#125C2212yescomplemented
168C4×C22⋊Q8C2214yes—
169C4×#121C2214yes—
170#2295C2212yescomplemented
171#2295C2214yescomplemented
172#2293C2214yescomplemented
173C2×#390C2214yes—
174C2×#390C2212yes—
175#2283C2211yescharacteristic
176#2283C2211yescharacteristic
177#2283C2212yes—
178#2275C2212yescomplemented
179C42×Q8C2212yescomplemented
180C4×#117C2211yescharacteristic
181C4×#117C2212yes—
182C2×C4×C4⋊C4C2211yescharacteristic
183C22×#41C2312yes—
184C23×Q8C2311yescharacteristic
185C23×D4C2312yes—
186C23×D4C2312yes—
187C23×D4C2312yes—
188#559—416no—
189#551—432no—
190#535—416no—
191#532—28no—
192C2×C4⋊Q8C2311yescharacteristic
193C2×C4⋊Q8C2312yes—
194C2×#127—28no—
195C2×#127C2312yes—
196C2×#127C2312yes—
197C2×#127C2312yes—
198C2×#127C2311yescharacteristic
199C2×#127C2312yes—
200C2×#127C2314yes—
201C2×#127C2314yes—
202C2×#127C2314yes—
203C2×#127C2314yes—
204C2×#127C2314yes—
205C2×#127C2314yes—
206C2×#126C2318yes—
207C2×#126C2318yes—
208C2×#125C2312yes—
209C2×#124—48no—
210C2×#124C2312yes—
211C2×#124C2312yes—
212C2×#124C2314yes—
213C2×#124C2312yes—
214C2×#124C2314yes—
215C2×#124C2314yes—
216C2×#124C2314yes—
217C2×#124C2318yes—
218C2×#124C2318yes—
219C2×#124C2314yes—
220C2×#124C2314yes—
221C2×#123C2318yes—
222C2×#123C2318yes—
223C2×#123C2318yes—
224C2×#123C2318yes—
225C2×#123C2318yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2318yes—
228C2×#121C2312yes—
229C2×#121C2312yes—
230C2×#121C2318yes—
231C2×#121C2318yes—
232C2×#120C2318yes—
233C2×#120C2318yes—
234C2×C4×Q8—28no—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2312yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2318yes—
249C2×C4×D4C2318yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2318yes—
254C2×C4×D4C2314yes—
255C2×#117C2314yes—
256C2×#117C2312yes—
257C2×#117C2318yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2312yes—
261C22×C22⋊C4C2318yes—
262C22×C22⋊C4C2318yes—
263C22×C22⋊C4C2318yes—
264C22×C42C2312yes—
265C22×C42C2312yes—
266C22×C42C2311yescharacteristic
267#400C2314yes—
268#400C2314yes—
269#399C2318yes—
270#399C2318yes—
271#398C2314yes—
272#398C2314yes—
273#398C2314yes—
274#398C2314yes—
275#397C2318yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2318yes—
281#396C2318yes—
282#396C2318yes—
283#396C2318yes—
284#396C2318yes—
285#395C2314yes—
286#395C2314yes—
287#395C2314yes—
288#395C2314yes—
289#394C2318yes—
290#394C2318yes—
291#394C2314yes—
292#394C2314yes—
293#394C2318yes—
294#394C2318yes—
295#394C2318yes—
296#394C2318yes—
297#394C2314yes—
298#394C2314yes—
299#394C2314yes—
300#394C2314yes—
301#394C2318yes—
302#394C2318yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#394C2318yes—
308#394C2318yes—
309#393C2318yes—
310#393C2318yes—
311#392C2314yes—
312#392C2314yes—
313#392C2318yes—
314#392C2314yes—
315#392C2318yes—
316#392C2314yes—
317#391C2314yes—
318#391C2312yes—
319#391C2312yes—
320#391C2312yes—
321#391C2318yes—
322#391C2312yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#390C2314yes—
327#390C2318yes—
328#390C2318yes—
329#390C2314yes—
330#390C2314yes—
331#390C2314yes—
332#390C2314yes—
333#390C2314yes—
334#390C2312yes—
335#390C2312yes—
336#390C2314yes—
337#390C2314yes—
338#390C2314yes—
339#390C2314yes—
340#390C2314yes—
341#390C2314yes—
342#390C2314yes—
343#390C2318yes—
344#390C2314yes—
345#390C2318yes—
346#390C2318yes—
347#390C2314yes—
348#390C2314yes—
349#390C2314yes—
350#390C2314yes—
351#390C2314yes—
352#390C2318yes—
353#390C2314yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2314yes—
358#389C2312yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2312yes—
364#389C2312yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#387C2314yes—
383#387C2314yes—
384#387C2314yes—
385#387C2314yes—
386#387C2314yes—
387#387C2314yes—
388#387C2314yes—
389#387C2314yes—
390#387C2314yes—
391#387C2314yes—
392#386C2318yes—
393#386C2318yes—
394#386C2318yes—
395#386C2318yes—
396#386C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2318yes—
401#386C2318yes—
402#386C2318yes—
403#386C2318yes—
404#386C2318yes—
405#386C2318yes—
406#386C2318yes—
407#386C2318yes—
408#386C2318yes—
409#386C2318yes—
410#386C2318yes—
411#385C2318yes—
412#385C2318yes—
413#385C2318yes—
414#385C2318yes—
415#385C2314yes—
416#385C2318yes—
417#385C2314yes—
418#384C2312yes—
419#384C2312yes—
420#384C2312yes—
421#383C2312yes—
422#383C2312yes—
423#383C2312yes—
424#383C2312yes—
425#382C2312yes—
426#382C2312yes—
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2312yes—
430#382C2312yes—
431#381C2312yes—
432#381C2312yes—
433#381C2314yes—
434#381C2318yes—
435#381C2314yes—
436#380C2314yes—
437#380C2318yes—
438#380C2312yes—
439#380C2312yes—
440#380C2314yes—
441#380C2318yes—
442#380C2314yes—
443#379C2318yes—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2312yes—
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2312yes—
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C22⋊C4C2318yes—
469C4×C22⋊C4C2312yes—
470C4×C22⋊C4C2312yes—
471C4×C22⋊C4C2314yes—
472C4×C22⋊C4C2314yes—
473C4×C22⋊C4C2312yes—
474C4×C22⋊C4C2318yes—
475C4×C22⋊C4C2311yescharacteristic
476C4×C22⋊C4C2311yescharacteristic
477#376C2312yes—
478#376C2314yes—
479#376C2312yes—
480#376C2312yes—
481#376C2311yescharacteristic
482#376C2311yescharacteristic
483#376C2312yes—
484C2×#95C2312yes—
485C2×#95C2314yes—
486C43C2312yes—
487C43C2314yes—
488C25C2414yes—
489C2×#41—28no—
490C2×#41—48no—
491C22×Q8—24no—
492C22×Q8—24no—
493C22×Q8—42no—
494C22×Q8C2411yescharacteristic
495C22×Q8C2412yes—
496C22×Q8C2411yescharacteristic
497C22×Q8C2414yes—
498C22×Q8C2412yes—
499C22×D4—28no—
500C22×D4—28no—
501C22×D4—28no—
502C22×D4—44no—
503C22×D4—48no—
504C22×D4—44no—
505C22×D4—48no—
506C22×D4C2412yes—
507C22×D4C2412yes—
508C22×D4C2414yes—
509C22×D4C2414yes—
510C22×D4C2414yes—
511C22×D4C2418yes—
512C22×D4C2418yes—
513C22×D4C2414yes—
514C22×D4C2414yes—
515C22×D4C2414yes—
516C22×D4C2412yes—
517C22×D4C2414yes—
518C22×D4C2418yes—
519C22×D4C2418yes—
520C23×C4C2412yes—
521C23×C4C2412yes—
522C23×C4C2411yescharacteristic
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C23×C4C2414yes—
526C23×C4C2414yes—
527C23×C4C2418yes—
528C23×C4C2418yes—
529C23×C4C2418yes—
530C4⋊Q8—24no—
531C4⋊Q8—44no—
532#127—28no—
533#127—28no—
534#127—28no—
535#127—28no—
536#127—24no—
537#127—48no—
538#127—48no—
539#127—48no—
540#127—48no—
541#127—48no—
542#127—48no—
543#126—416no—
544#126—416no—
545#125—44no—
546#124—216no—
547#124—28no—
548#124—28no—
549#124—48no—
550#124—48no—
551#124—416no—
552#124—48no—
553#124—44no—
554#124—416no—
555#124—48no—
556#124—48no—
557#123—416no—
558#123—416no—
559#123—416no—
560#123—416no—
561#123—416no—
562C22⋊Q8—216no—
563C22⋊Q8—416no—
564#121—28no—
565#121—28no—
566#121—416no—
567#121—416no—
568#120—232no—
569#120—416no—
570C4×Q8—28no—
571C4×Q8—24no—
572C4×Q8—28no—
573C4×Q8—24no—
574C4×Q8—28no—
575C4×Q8—24no—
576C4×Q8—24no—
577C4×Q8—48no—
578C4×Q8—44no—
579C4×D4—28no—
580C4×D4—28no—
581C4×D4—416no—
582C4×D4—48no—
583C4×D4—48no—
584C4×D4—48no—
585C4×D4—48no—
586C4×D4—416no—
587C4×D4—48no—
588C4×D4—48no—
589C4×D4—416no—
590#117—28no—
591#117—216no—
592#117—416no—
593C2×C4⋊C4—24no—
594C2×C4⋊C4—28no—
595C2×C4⋊C4—44no—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C22⋊C4—416no—
631C2×C22⋊C4—416no—
632C2×C22⋊C4—416no—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2412yes—
664C2×C42—28no—
665C2×C42—44no—
666C2×C42#4118yes—
667C2×C42C2414yes—
668C2×C42C2414yes—
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2414yes—
672C2×C42C2412yes—
673C2×C42C2414yes—
674C2×C42C2412yes—
675C2×C42C2414yes—
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2418yes—
685C2×C42C2414yes—
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692#95C2412yes—
693#95C2412yes—
694#95C2418yes—
695#95C2412yes—
696#95C2414yes—
697#95C2411yescharacteristic
698#95C2411yescharacteristic
699#95C2414yes—
700#95C2412yes—
701#95C2412yes—
702#95C2412yes—
703#95C2411yescharacteristic
704#95C2411yescharacteristic
705#95C2414yes—
706#95C2414yes—
707#95C2412yes—
708#95C2412yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2418yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2418yes—
723#95C2414yes—
724#95C2412yes—
725#95C2412yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2418yes—
730C24—28no—
731C24—216no—
732C24—44no—
733C24—48no—
734C24—44no—
735C24C2518yes—
736C24C2514yes—
737C24C2511yescharacteristic
738#41—816no—
739C2×Q8—22no—
740C2×Q8—24no—
741C2×Q8—22no—
742C2×Q8—24no—
743C2×Q8—24no—
744C2×Q8—22no—
745C2×Q8—28no—
746C2×Q8—22no—
747C2×Q8—22no—
748C2×Q8—42no—
749C2×Q8—44no—
750C2×Q8—44no—
751C2×Q8—44no—
752C2×Q8—416no—
753C2×Q8H(5,𝔽2)14yes—
754C2×D4—28no—
755C2×D4—216no—
756C2×D4—24no—
757C2×D4—24no—
758C2×D4—28no—
759C2×D4—28no—
760C2×D4—24no—
761C2×D4—28no—
762C2×D4—28no—
763C2×D4—28no—
764C2×D4—28no—
765C2×D4—24no—
766C2×D4—28no—
767C2×D4—216no—
768C2×D4—216no—
769C2×D4—28no—
770C2×D4—28no—
771C2×D4—28no—
772C2×D4—28no—
773C2×D4—24no—
774C2×D4—48no—
775C2×D4—48no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—48no—
781C2×D4—48no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—44no—
785C2×D4—48no—
786C2×D4—48no—
787C2×D4—48no—
788C2×D4—48no—
789C2×D4—48no—
790C2×D4—48no—
791C2×D4—816no—
792C2×D4—816no—
793C2×D4—816no—
794C22×C4—24no—
795C22×C4—22no—
796C22×C4—24no—
797C22×C4—22no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—28no—
801C22×C4—28no—
802C22×C4—24no—
803C22×C4—28no—
804C22×C4—42no—
805C22×C4—44no—
806C22×C4—48no—
807C22×C4—44no—
808C22×C4—48no—
809C22×C4—48no—
810C22×C4—48no—
811C22×C4—48no—
812C22×C4—48no—
813C22×C4—48no—
814C22×C4—48no—
815C22×C4—48no—
816C22×C4—48no—
817C22×C4C2×#4114yes—
818C22×C4C2×#4114yes—
819C22×C4C2×#4114yes—
820C22×C4C2512yes—
821C22×C4C2512yes—
822C22×C4C2514yes—
823C22×C4C2514yes—
824C22×C4C2512yes—
825C22×C4C2514yes—
826C22×C4C2514yes—
827C22×C4C2514yes—
828C22×C4C2514yes—
829C22×C4C2514yes—
830C22×C4C2512yes—
831C22×C4C2512yes—
832C22×C4C2511yescharacteristic
833C22×C4C2511yescharacteristic
834C22×C4C2511yescharacteristic
835C22×C4C2511yescharacteristic
836C22×C4C2512yes—
837C22×C4C2512yes—
838C22×C4C2512yes—
839C22×C4C2511yescharacteristic
840C22×C4C2511yescharacteristic
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—24no—
844C4⋊C4—22no—
845C4⋊C4—22no—
846C4⋊C4—24no—
847C4⋊C4—24no—
848C4⋊C4—24no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—28no—
853C4⋊C4—28no—
854C4⋊C4—28no—
855C4⋊C4—24no—
856C4⋊C4—28no—
857C4⋊C4—28no—
858C4⋊C4—28no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—44no—
865C4⋊C4—48no—
866C4⋊C4—44no—
867C4⋊C4—48no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—48no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—24no—
878C22⋊C4—28no—
879C22⋊C4—28no—
880C22⋊C4—216no—
881C22⋊C4—216no—
882C22⋊C4—216no—
883C22⋊C4—216no—
884C22⋊C4—216no—
885C22⋊C4—48no—
886C22⋊C4—48no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—48no—
890C22⋊C4—48no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—48no—
897C22⋊C4—48no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—48no—
902C22⋊C4—48no—
903C22⋊C4—48no—
904C22⋊C4—48no—
905C22⋊C4H(5,𝔽2)18yes—
906C42—24no—
907C42—24no—
908C42—24no—
909C42—24no—
910C42—28no—
911C42—28no—
912C42—28no—
913C42—24no—
914C42—24no—
915C42—28no—
916C42—24no—
917C42—24no—
918C42—28no—
919C42—24no—
920C42—24no—
921C42—24no—
922C42—24no—
923C42—42no—
924C42—42no—
925C42—48no—
926C42—44no—
927C42C2×#4114yes—
928C42C2×#4114yes—
929C42C2×#4114yes—
930C42C2×#4114yes—
931C23—21no—
932C23—22no—
933C23—21no—
934C23—24no—
935C23—28no—
936C23—28no—
937C23—24no—
938C23—28no—
939C23—28no—
940C23—28no—
941C23—24no—
942C23—28no—
943C23—28no—
944C23—28no—
945C23—28no—
946C23—416no—
947C23—88no—
948C23—88no—
949C23—816no—
950C23—816no—
951C23C22×#4112yes—
952C23C2×H(5,𝔽2)14yes—
953C23C2611yescharacteristic
954Q8—28no—
955Q8—48no—
956Q8—44no—
957Q8—88no—
958Q8—84no—
959D4—416no—
960D4—48no—
961D4—416no—
962D4—48no—
963D4—416no—
964D4—816no—
965D4—816no—
966D4—88no—
967D4—88no—
968D4—88no—
969D4—88no—
970D4—84no—
971D4—168no—
972D4—168no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—21no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—21no—
984C2×C4—28no—
985C2×C4—28no—
986C2×C4—28no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—28no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—22no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—22no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—48no—
1021C2×C4—48no—
1022C2×C4—88no—
1023C2×C4—88no—
1024C2×C4—816no—
1025C2×C4—168no—
1026C2×C4—168no—
1027C2×C4C22×#4112yes—
1028C2×C4C22×#4112yes—
1029C2×C4C22×#4112yes—
1030C2×C4C22×#4112yes—
1031C2×C4C22×#4112yes—
1032C2×C4C22×#4112yes—
1033C2×C4C2×H(5,𝔽2)14yes—
1034C2×C4C2×H(5,𝔽2)14yes—
1035C2×C4C2×H(5,𝔽2)14yes—
1036C2×C4C2×H(5,𝔽2)12yes—
1037C2×C4#58512yes—
1038C2×C4#58514yes—
1039C22—24no—
1040C22—24no—
1041C22—22no—
1042C22—22no—
1043C22—48no—
1044C22—48no—
1045C22—48no—
1046C22—48no—
1047C22—48no—
1048C22—48no—
1049C22—48no—
1050C22—44no—
1051C22—44no—
1052C22—48no—
1053C22—48no—
1054C22—44no—
1055C22—1616no—
1056C22#350814yes—
1057C22C23×#4111yescharacteristic
1058C22C22×H(5,𝔽2)11yescharacteristic
1059C22C22×H(5,𝔽2)12yes—
1060C22C2×#58512yes—
1061C22C2×#58511yescharacteristic
1062C4—24no—
1063C4—24no—
1064C4—22no—
1065C4—24no—
1066C4—22no—
1067C4—22no—
1068C4—22no—
1069C4—44no—
1070C4—44no—
1071C4—44no—
1072C4—44no—
1073C4—42no—
1074C4—44no—
1075C4—44no—
1076C4—42no—
1077C4—42no—
1078C4—42no—
1079C4—42no—
1080C4—44no—
1081C4#349414yes—
1082C4#351014yes—
1083C2—24no—
1084C2—84no—
1085C2—88no—
1086C2C2×#349411yescharacteristic
1087C2C2×#350811yescharacteristic
1088C2C2×#351011yescharacteristic
1089C2#6301412yes—
1090C2#6302112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35274C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59820C2semidirect
2. #59147C2semidirect
3. #51093C2semidirect
4. #50718C2semidirect
5. #45421C2semidirect
6. #45312C2semidirect
7. #45070C2semidirect
8. #44963C2semidirect
9. #43905C2semidirect
10. #39770C2semidirect
11. #38985C2semidirect
12. #38056C2semidirect
13. #37336C2semidirect
14. #36595C2semidirect
15. #36300C2semidirect
16. #36264C2semidirect
17. #35562C2semidirect
19. #35249C2semidirect
20. #34966C2semidirect
21. C2×#2548C2semidirect
22. #34364C2semidirect
23. #34236C2semidirect
24. #34128C2semidirect
25. C2×#559C22semidirect
33. #2860C22semidirect
35. #2858C22semidirect
37. #2756C22semidirect
38. #2753C22semidirect
39. #2749C22semidirect
40. #2730C22semidirect
41. #2715C22semidirect
42. #2712C22semidirect
43. #2710C22semidirect
44. #2709C22semidirect
45. #2709C22semidirect
46. #2706C22semidirect
47. #2705C22semidirect
48. #2701C22semidirect
49. #2700C22semidirect
50. #2691C22semidirect
51. #2686C22semidirect
52. #2672C22semidirect
55. #2644C22semidirect
56. #2641C22semidirect
57. #2632C22semidirect
58. #2610C22semidirect
59. #2606C22semidirect
60. #2605C22semidirect
61. #2603C22semidirect
62. #2592C22semidirect
63. #2580C22semidirect
64. #2570C22semidirect
65. #2567C22semidirect
66. #2567C22semidirect
67. #2559C22semidirect
68. #2557C22semidirect
69. #2554C22semidirect
70. #2550C22semidirect
78. #2548C22semidirect
79. #2548C22semidirect
80. #2548C22semidirect
81. #2548C22semidirect
82. #2544C22semidirect
83. #2544C22semidirect
84. #2544C22semidirect
88. #2538C22semidirect
90. #2521C22semidirect
91. #2513C22semidirect
92. #2512C22semidirect
93. #2512C22semidirect
94. #2512C22semidirect
96. #2476C22semidirect
97. #2474C22semidirect
99. #2471C22semidirect
100. #2467C22semidirect
101. #2461C22semidirect
102. #2459C22semidirect
103. #2454C22semidirect
104. #2452C22semidirect
105. #2448C22semidirect
106. #2447C22semidirect
107. #2445C22semidirect
108. #2445C22semidirect
109. #2445C22semidirect
110. #2445C22semidirect
111. #2445C22semidirect
112. #2445C22semidirect
113. #2445C22semidirect
114. #2444C22semidirect
122. #2425C22semidirect
128. #2402C22semidirect
129. #2399C22semidirect
132. #2369C22semidirect
133. #2367C22semidirect
136. #2366C22semidirect
137. #2366C22semidirect
140. #2357C22semidirect
141. #2356C22semidirect
142. #2356C22semidirect
143. #2356C22semidirect
144. #2356C22semidirect
145. #2354C22semidirect
146. #2351C22semidirect
147. #2351C22semidirect
148. #2349C22semidirect
155. #2337C22semidirect
159. #2328C22semidirect
160. #2326C22semidirect
161. #2326C22semidirect
162. #2319C22semidirect
163. #2319C22semidirect
165. C4×C4⋊Q8C22semidirect
166. C4×#127C22semidirect
167. C4×#125C22semidirect
170. #2295C22semidirect
171. #2295C22semidirect
172. #2293C22semidirect
178. #2275C22semidirect
179. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#598202
#591472
#510932
#507182
#454212
#453122
#450702
#449632
#439052
#397702
#389852
#380562
#373362
#365952
#363002
#362642
#355622
#352742
#352492
#349662
C2×#25482
#343642
#342362
#341282