Finite Group Databasebeta

← #7631266

Subgroups — #7631266

Order 512.

5222 conjugacy classes of subgroups.

The subgroup lattice has 1089 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36640C211yesmaximal, characteristic, complemented
2#36638C214yesmaximal, complemented
3C2×#2861C211yesmaximal, characteristic, complemented
4#36527C214yesmaximal, complemented
5#36485C214yesmaximal, complemented
6#36421C214yesmaximal, complemented
7#36320C218yesmaximal, complemented
8#36253C214yesmaximal, complemented
9#36248C218yesmaximal, complemented
10#35340C214yesmaximal, complemented
11#35333C211yesmaximal, characteristic, complemented
12#35327C211yesmaximal, characteristic
13#35313C211yesmaximal, characteristic, complemented
14#35307C211yesmaximal, characteristic, complemented
15#35300C214yesmaximal, complemented
16#35269C214yesmaximal, complemented
17#35266C211yesmaximal, characteristic, complemented
18#35254C211yesmaximal, characteristic
19#34269C211yesmaximal, characteristic
20#34268C211yesmaximal, characteristic, complemented
21#34255C211yesmaximal, characteristic, complemented
22#34254C211yesmaximal, characteristic, complemented
23#34217C211yesmaximal, characteristic, complemented
24#34211C211yesmaximal, characteristic, complemented
25C42×#41C211yesmaximal, characteristic, complemented
26C2×#536C2211yescharacteristic
27C2×#535C2211yescharacteristic
28C22×#125C2211yescharacteristic
29C22×#124C2211yescharacteristic
30C2×#519C2211yescharacteristic
31C2×#518C2211yescharacteristic
32C2×C4×#41C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35#2866C2218yescomplemented
36#2865C2218yescomplemented
37#2864C2212yescomplemented
38#2864C2212yescomplemented
39#2863C2214yescomplemented
40#2861C2212yes—
41#2861C2212yes—
42#2861C2214yes—
43#2861C2214yes—
44#2861C2212yes—
45#2861C2212yes—
46#2860C2214yes—
47#2859C2212yescomplemented
48#2859C2212yescomplemented
49#2855C2214yescomplemented
50#2854C2214yes—
51#2853C2218yescomplemented
52#2852C2218yescomplemented
53#2851C2214yes—
54#2851C2214yes—
55#2851C2214yescomplemented
56#2850C2214yes—
57#2645C2214yescomplemented
58#2644C2214yes—
59#2629C2214yescomplemented
60#2625C2214yescomplemented
61#2624C2214yes—
62#2620C2214yes—
63#2597C2218yescomplemented
64#2596C2218yescomplemented
65#2595C2218yescomplemented
66#2594C2218yescomplemented
67#2594C2218yescomplemented
68#2587C2218yescomplemented
69#2579C2214yes—
70#2579C2214yes—
71#2578C2218yescomplemented
72#2577C2218yescomplemented
73#2576C2218yescomplemented
74#2576C2218yescomplemented
75#2575C2218yescomplemented
76#2566C2212yescomplemented
77#2566C2212yescomplemented
78#2565C2212yescomplemented
79#2565C2212yescomplemented
80#2558C2218yescomplemented
81#2545C2212yes—
82#2545C2212yes—
83#2544C2212yes—
84#2544C2212yes—
85#2534C2214yes—
86#2534C2214yes—
87#2529C2218yescomplemented
88#2526C2218yescomplemented
89#2525C2218yescomplemented
90#2522C2218yescomplemented
91#2519C2218yescomplemented
92#2518C2218yescomplemented
93#2518C2218yescomplemented
94#2515C2218yescomplemented
95#2514C2214yescomplemented
96#2513C2214yes—
97#2512C2214yes—
98#2511C2214yescomplemented
99#2493C2218yes—
100#2480C2218yes—
101#2475C2218yescomplemented
102#2470C2218yescomplemented
103#2466C2218yescomplemented
104#2460C2218yescomplemented
105#2448C2214yes—
106#2447C2214yescomplemented
107#2446C2214yescomplemented
108#2445C2214yes—
109#2419C2218yes—
110#2418C2218yes—
111#2370C2214yescomplemented
112#2370C2214yescomplemented
113#2367C2214yes—
114#2367C2214yes—
115#2367C2214yes—
116#2367C2214yescomplemented
117#2366C2214yes—
118#2365C2214yescomplemented
119#2359C2218yes—
120#2358C2218yes—
121#2357C2214yes—
122#2356C2214yescomplemented
123#2355C2214yescomplemented
124#2354C2214yes—
125#2345C2214yes—
126#2345C2214yes—
127#2343C2218yes—
128#2342C2214yes—
129#2342C2218yes—
130#2342C2214yes—
131#2330C2214yescomplemented
132#2326C2214yes—
133#2324C2214yes—
134#2323C2214yescomplemented
135#2320C2214yescomplemented
136#2319C2214yes—
137#2317C2211yescharacteristic
138#2317C2211yescharacteristic
139#2316C2211yescharacteristic
140#2316C2211yescharacteristic
141#2311C2211yescharacteristic
142#2311C2211yescharacteristic
143#2310C2211yescharacteristic
144#2310C2211yescharacteristic
145#2309C2211yescharacteristic
146#2309C2211yescharacteristic
147C4×#125C2214yescomplemented
148C4×#125C2214yescomplemented
149C4×#125C2214yescomplemented
150C4×#126C2218yescomplemented
151C4×#124C2214yes—
152C4×C22⋊Q8C2214yescomplemented
153C4×#123C2218yescomplemented
154C4×#121C2214yes—
155#2298C2218yescomplemented
156#2296C2211yescharacteristic
157#2296C2211yescharacteristic
158#2296C2211yescharacteristic
159#2296C2211yescharacteristic
160#2295C2214yescomplemented
161C2×#391C2211yescharacteristic
162C2×#391C2211yescharacteristic
163#2293C2214yes—
164C2×#390C2211yescharacteristic
165C2×#390C2211yescharacteristic
166#2290C2218yescomplemented
167C2×#388C2214yes—
168C2×#388C2214yes—
169#2285C2211yescharacteristic
170#2285C2211yescharacteristic
171#2274C2211yescharacteristic
172#2274C2211yescharacteristic
173C42×Q8C2212yescomplemented
174C42×Q8C2212yescomplemented
175C42×D4C2214yes—
176C42×D4C2214yes—
177C42×D4C2212yescomplemented
178C42×D4C2212yescomplemented
179C4×#117C2211yescharacteristic
180C4×#117C2211yescharacteristic
181C4×#117C2211yescharacteristic
182C4×#117C2212yescomplemented
183C4×#117C2212yescomplemented
184C4×#117C2212yescomplemented
185C2×C43C2211yescharacteristic
186C2×C43C2212yescomplemented
187C22×#41C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189C23×D4C2311yescharacteristic
190#536—28no—
191#535—28no—
192C2×C4⋊Q8C2312yes—
193C2×#127C2312yes—
194C2×#126C2318yes—
195C2×#125—28no—
196C2×#125C2312yes—
197C2×#125C2312yes—
198C2×#125C2312yes—
199C2×#125C2312yes—
200C2×#125C2314yes—
201C2×#125C2314yes—
202C2×#124—28no—
203C2×#124C2312yes—
204C2×#124C2312yes—
205C2×#124C2312yes—
206C2×#124C2312yes—
207C2×#124C2312yes—
208C2×#124C2312yes—
209C2×#123C2314yes—
210C2×#123C2318yes—
211C2×C22⋊Q8C2314yes—
212C2×#121C2314yes—
213C2×#120C2314yes—
214#519—28no—
215#518—28no—
216C4×#41—28no—
217C4×#41—28no—
218C4×#41—28no—
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2314yes—
222C2×C4×Q8C2314yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2312yes—
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2314yes—
228C2×C4×D4C2312yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2312yes—
235C2×C4×D4C2318yes—
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2312yes—
243C2×#117C2314yes—
244C2×#117C2312yes—
245C2×#117C2312yes—
246C2×#117C2318yes—
247C2×#117C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2312yes—
252C22×C22⋊C4C2314yes—
253C22×C22⋊C4C2312yes—
254C22×C22⋊C4C2312yes—
255C22×C22⋊C4C2314yes—
256C22×C22⋊C4C2314yes—
257C22×C42C2312yes—
258C22×C42C2312yes—
259C22×C42C2311yescharacteristic
260C22×C42C2311yescharacteristic
261C22×C42C2312yes—
262C22×C42C2312yes—
263C22×C42C2312yes—
264C22×C42C2314yes—
265C22×C42C2314yes—
266C22×C42C2311yescharacteristic
267#401C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#399C2318yes—
273#398C2318yes—
274#398C2318yes—
275#398C2318yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2318yes—
281#397C2318yes—
282#396C2318yes—
283#396C2318yes—
284#396C2318yes—
285#396C2318yes—
286#396C2318yes—
287#394C2318yes—
288#394C2318yes—
289#394C2318yes—
290#394C2318yes—
291#391C2312yes—
292#391C2312yes—
293#391C2314yes—
294#391C2314yes—
295#391C2312yes—
296#391C2312yes—
297#391C2314yes—
298#391C2312yes—
299#391C2312yes—
300#391C2312yes—
301#391C2312yes—
302#391C2314yes—
303#391C2314yes—
304#390C2314yes—
305#390C2314yes—
306#390C2312yes—
307#390C2312yes—
308#390C2314yes—
309#390C2312yes—
310#390C2312yes—
311#390C2312yes—
312#390C2312yes—
313#390C2318yes—
314#390C2312yes—
315#390C2312yes—
316#390C2314yes—
317#390C2314yes—
318#389C2314yes—
319#389C2314yes—
320#389C2314yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2312yes—
329#389C2312yes—
330#389C2312yes—
331#389C2318yes—
332#389C2312yes—
333#389C2318yes—
334#389C2318yes—
335#389C2312yes—
336#389C2312yes—
337#389C2312yes—
338#389C2312yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#387C2314yes—
367#387C2318yes—
368#387C2318yes—
369#387C2314yes—
370#387C2318yes—
371#387C2314yes—
372#387C2318yes—
373#387C2314yes—
374#387C2314yes—
375#387C2314yes—
376#387C2314yes—
377#387C2314yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#386C2314yes—
392#386C2314yes—
393#386C2318yes—
394#386C2318yes—
395#386C2318yes—
396#386C2318yes—
397#386C2318yes—
398#385C2318yes—
399#385C2318yes—
400#385C2314yes—
401#385C2314yes—
402#385C2318yes—
403#385C2318yes—
404#385C2318yes—
405#385C2314yes—
406#385C2314yes—
407#385C2314yes—
408#385C2314yes—
409#385C2318yes—
410#385C2318yes—
411#384C2312yes—
412#384C2312yes—
413#384C2312yes—
414#384C2312yes—
415#383C2318yes—
416#383C2318yes—
417#382C2312yes—
418#382C2314yes—
419#382C2314yes—
420#382C2312yes—
421#382C2312yes—
422#382C2318yes—
423#382C2312yes—
424#381C2314yes—
425#381C2314yes—
426#381C2318yes—
427#381C2318yes—
428#380C2314yes—
429#380C2314yes—
430#380C2314yes—
431#380C2314yes—
432#380C2318yes—
433#380C2312yes—
434#380C2312yes—
435#380C2312yes—
436#380C2312yes—
437#379C2314yes—
438#379C2314yes—
439C4×C4⋊C4C2318yes—
440C4×C4⋊C4C2318yes—
441C4×C4⋊C4C2318yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2318yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C22⋊C4C2318yes—
468C4×C22⋊C4C2318yes—
469C4×C22⋊C4C2318yes—
470C4×C22⋊C4C2314yes—
471C4×C22⋊C4C2314yes—
472C4×C22⋊C4C2318yes—
473C4×C22⋊C4C2314yes—
474C4×C22⋊C4C2314yes—
475C4×C22⋊C4C2314yes—
476C4×C22⋊C4C2312yes—
477C4×C22⋊C4C2312yes—
478C4×C22⋊C4C2314yes—
479C4×C22⋊C4C2318yes—
480C4×C22⋊C4C2314yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2314yes—
483C4×C22⋊C4C2314yes—
484#376C2312yes—
485#376C2312yes—
486#376C2318yes—
487#376C2312yes—
488C2×#95C2314yes—
489C2×#95C2314yes—
490C43C2314yes—
491C43C2312yes—
492C43C2312yes—
493C43C2312yes—
494C43C2311yescharacteristic
495C43C2311yescharacteristic
496C43C2312yes—
497C43C2311yescharacteristic
498C43C2311yescharacteristic
499C43C2314yes—
500C43C2312yes—
501C25C2412yes—
502C2×#41—24no—
503C2×#41—24no—
504C2×#41#4118yes—
505C22×Q8—24no—
506C22×Q8—24no—
507C22×Q8—24no—
508C22×Q8C2412yes—
509C22×Q8C2412yes—
510C22×Q8C2411yescharacteristic
511C22×D4—24no—
512C22×D4—24no—
513C22×D4—24no—
514C22×D4C2412yes—
515C22×D4C2412yes—
516C22×D4C2412yes—
517C22×D4C2411yescharacteristic
518C22×D4C2418yes—
519C23×C4C2412yes—
520C23×C4C2412yes—
521C23×C4C2412yes—
522C23×C4C2414yes—
523C23×C4C2414yes—
524C23×C4C2412yes—
525C23×C4C2412yes—
526C23×C4C2412yes—
527C23×C4C2418yes—
528C23×C4C2412yes—
529C23×C4C2412yes—
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C4⋊Q8—28no—
534#127—28no—
535#126—416no—
536#125—28no—
537#125—28no—
538#125—28no—
539#125—28no—
540#125—48no—
541#125—48no—
542#124—28no—
543#124—28no—
544#124—28no—
545#124—28no—
546#124—28no—
547#124—28no—
548#123—216no—
549#123—416no—
550C22⋊Q8—216no—
551#121—216no—
552#120—216no—
553C4×Q8—28no—
554C4×Q8—28no—
555C4×Q8—216no—
556C4×Q8—24no—
557C4×Q8—24no—
558C4×Q8—216no—
559C4×D4—216no—
560C4×D4—28no—
561C4×D4—28no—
562C4×D4—28no—
563C4×D4—28no—
564C4×D4—216no—
565C4×D4—216no—
566C4×D4—24no—
567C4×D4—24no—
568C4×D4—216no—
569C4×D4—416no—
570#117—28no—
571#117—24no—
572#117—24no—
573#117—24no—
574#117—24no—
575#117—24no—
576#117—24no—
577#117—216no—
578#117—28no—
579#117—28no—
580#117—416no—
581#117#4118yes—
582C2×C4⋊C4—28no—
583C2×C4⋊C4—28no—
584C2×C4⋊C4—24no—
585C2×C4⋊C4—24no—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2412yes—
624C2×C22⋊C4—28no—
625C2×C22⋊C4—28no—
626C2×C22⋊C4—216no—
627C2×C22⋊C4—48no—
628C2×C22⋊C4—48no—
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2412yes—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
657C2×C42—28no—
658C2×C42—24no—
659C2×C42—24no—
660C2×C42—28no—
661C2×C42—28no—
662C2×C42—48no—
663C2×C42—44no—
664C2×C42—44no—
665C2×C42—48no—
666C2×C42#4118yes—
667C2×C42C2414yes—
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2412yes—
673C2×C42C2418yes—
674C2×C42C2412yes—
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2414yes—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2414yes—
683C2×C42C2412yes—
684C2×C42C2412yes—
685C2×C42C2414yes—
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2418yes—
691C2×C42C2418yes—
692C2×C42C2414yes—
693C2×C42C2414yes—
694C2×C42C2414yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2414yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2418yes—
717#95C2418yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729#95C2414yes—
730#95C2414yes—
731#95C2418yes—
732#95C2418yes—
733#95C2418yes—
734#95C2414yes—
735#95C2418yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739C24—24no—
740C24—24no—
741C24—24no—
742C24—44no—
743C24—44no—
744C24C2514yes—
745C24C2512yes—
746C24C2511yescharacteristic
747#41—232no—
748C2×Q8—22no—
749C2×Q8—22no—
750C2×Q8—24no—
751C2×Q8—24no—
752C2×Q8—24no—
753C2×Q8—24no—
754C2×Q8—24no—
755C2×Q8—24no—
756C2×Q8—416no—
757C2×Q8C2×#4114yes—
758C2×D4—24no—
759C2×D4—24no—
760C2×D4—216no—
761C2×D4—22no—
762C2×D4—22no—
763C2×D4—24no—
764C2×D4—24no—
765C2×D4—24no—
766C2×D4—24no—
767C2×D4—24no—
768C2×D4—24no—
769C2×D4—48no—
770C2×D4—48no—
771C2×D4—416no—
772C2×D4C2×#4118yes—
773C2×D4C2×#4114yes—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—28no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—28no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—28no—
790C22×C4—28no—
791C22×C4—216no—
792C22×C4—44no—
793C22×C4—42no—
794C22×C4—42no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—42no—
799C22×C4—42no—
800C22×C4—44no—
801C22×C4—44no—
802C22×C4—48no—
803C22×C4—48no—
804C22×C4C2×#4118yes—
805C22×C4C2×#4114yes—
806C22×C4C2×#4114yes—
807C22×C4C2×#4114yes—
808C22×C4C2×#4114yes—
809C22×C4C2×#4114yes—
810C22×C4C2514yes—
811C22×C4C2514yes—
812C22×C4C2514yes—
813C22×C4C2512yes—
814C22×C4C2512yes—
815C22×C4C2514yes—
816C22×C4C2512yes—
817C22×C4C2512yes—
818C22×C4C2514yes—
819C22×C4C2514yes—
820C22×C4C2514yes—
821C22×C4C2514yes—
822C22×C4C2511yescharacteristic
823C22×C4C2511yescharacteristic
824C22×C4C2514yes—
825C22×C4C2512yes—
826C22×C4C2511yescharacteristic
827C22×C4C2511yescharacteristic
828C22×C4C2512yes—
829C22×C4C2512yes—
830C22×C4C2511yescharacteristic
831C22×C4C2511yescharacteristic
832C4⋊C4—28no—
833C4⋊C4—28no—
834C4⋊C4—28no—
835C4⋊C4—28no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—28no—
842C4⋊C4—24no—
843C4⋊C4—24no—
844C4⋊C4—28no—
845C4⋊C4—24no—
846C4⋊C4—22no—
847C4⋊C4—22no—
848C4⋊C4—24no—
849C4⋊C4—216no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—216no—
853C4⋊C4—28no—
854C4⋊C4—28no—
855C4⋊C4—28no—
856C4⋊C4—28no—
857C4⋊C4—48no—
858C4⋊C4—48no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—48no—
868C4⋊C4—48no—
869C4⋊C4C2×#4118yes—
870C22⋊C4—24no—
871C22⋊C4—24no—
872C22⋊C4—28no—
873C22⋊C4—24no—
874C22⋊C4—24no—
875C22⋊C4—24no—
876C22⋊C4—24no—
877C22⋊C4—216no—
878C22⋊C4—216no—
879C22⋊C4—28no—
880C22⋊C4—28no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—24no—
885C22⋊C4—24no—
886C22⋊C4—216no—
887C22⋊C4—216no—
888C22⋊C4—216no—
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⋊C4C2×#4118yes—
898C42—22no—
899C42—22no—
900C42—24no—
901C42—22no—
902C42—22no—
903C42—24no—
904C42—28no—
905C42—28no—
906C42—24no—
907C42—24no—
908C42—24no—
909C42—24no—
910C42—24no—
911C42—24no—
912C42—216no—
913C42—24no—
914C42—24no—
915C42—24no—
916C42—24no—
917C42—28no—
918C42—24no—
919C42—24no—
920C42—28no—
921C42—44no—
922C42—42no—
923C42—42no—
924C42—44no—
925C42—44no—
926C42—44no—
927C42—42no—
928C42—42no—
929C42—48no—
930C42—48no—
931C42C2×#4114yes—
932C42C2×#4118yes—
933C42C2×#4114yes—
934C42C2×#4114yes—
935C42C2×#4114yes—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—24no—
941C23—24no—
942C23—24no—
943C23—24no—
944C23—24no—
945C23—28no—
946C23—28no—
947C23—48no—
948C23—88no—
949C23—88no—
950C23—84no—
951C23—84no—
952C23C22×#4114yes—
953C23C22×#4112yes—
954C23C22×#4112yes—
955C23C22×#4112yes—
956C23C2611yescharacteristic
957Q8—28no—
958Q8—48no—
959Q8—48no—
960D4—216no—
961D4—28no—
962D4—48no—
963D4—48no—
964D4—816no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—24no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—24no—
977C2×C4—216no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—28no—
1003C2×C4—28no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—44no—
1011C2×C4—44no—
1012C2×C4—416no—
1013C2×C4—48no—
1014C2×C4—48no—
1015C2×C4—416no—
1016C2×C4—48no—
1017C2×C4—48no—
1018C2×C4—48no—
1019C2×C4—816no—
1020C2×C4—84no—
1021C2×C4—84no—
1022C2×C4#529116yes—
1023C2×C4C22×#4118yes—
1024C2×C4C22×#4112yes—
1025C2×C4C22×#4112yes—
1026C2×C4C22×#4114yes—
1027C2×C4C22×#4112yes—
1028C2×C4C22×#4112yes—
1029C2×C4C22×#4112yes—
1030C2×C4C22×#4112yes—
1031C2×C4C22×#4112yes—
1032C2×C4C22×#4112yes—
1033C2×C4C22×#4112yes—
1034C2×C4C22×#4112yes—
1035C2×C4#58514yes—
1036C2×C4#58514yes—
1037C22—24no—
1038C22—24no—
1039C22—22no—
1040C22—22no—
1041C22—28no—
1042C22—24no—
1043C22—44no—
1044C22—42no—
1045C22—42no—
1046C22—48no—
1047C22—48no—
1048C22—44no—
1049C22—44no—
1050C22—44no—
1051C22—168no—
1052C22C2×#52914yes—
1053C22C23×#4111yescharacteristic
1054C22C23×#4111yescharacteristic
1055C22C23×#4111yescharacteristic
1056C22C2×#58512yes—
1057C22C2×#58512yes—
1058C4—24no—
1059C4—24no—
1060C4—28no—
1061C4—22no—
1062C4—22no—
1063C4—22no—
1064C4—22no—
1065C4—24no—
1066C4—44no—
1067C4—44no—
1068C4—42no—
1069C4—44no—
1070C4—42no—
1071C4—44no—
1072C4—44no—
1073C4—42no—
1074C4—42no—
1075C4—44no—
1076C4—44no—
1077C4—44no—
1078C4C2×#52914yes—
1079C4C2×#52914yes—
1080C2—24no—
1081C2—44no—
1082C2—84no—
1083C2C22×#52911yescharacteristic
1084C2#6281012yes—
1085C2#6281012yes—
1086C2#6281511yescharacteristic
1087C2#6281511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#535C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36640C2semidirect
2. #36638C2semidirect
3. C2×#2861C2semidirect
4. #36527C2semidirect
5. #36485C2semidirect
6. #36421C2semidirect
7. #36320C2semidirect
8. #36253C2semidirect
9. #36248C2semidirect
10. #35340C2semidirect
11. #35333C2semidirect
13. #35313C2semidirect
14. #35307C2semidirect
15. #35300C2semidirect
16. #35269C2semidirect
17. #35266C2semidirect
20. #34268C2semidirect
21. #34255C2semidirect
22. #34254C2semidirect
23. #34217C2semidirect
24. #34211C2semidirect
25. C42×#41C2semidirect
35. #2866C22semidirect
36. #2865C22semidirect
37. #2864C22semidirect
38. #2864C22semidirect
39. #2863C22semidirect
47. #2859C22semidirect
48. #2859C22semidirect
49. #2855C22semidirect
51. #2853C22semidirect
52. #2852C22semidirect
55. #2851C22semidirect
57. #2645C22semidirect
59. #2629C22semidirect
60. #2625C22semidirect
63. #2597C22semidirect
64. #2596C22semidirect
65. #2595C22semidirect
66. #2594C22semidirect
67. #2594C22semidirect
68. #2587C22semidirect
71. #2578C22semidirect
72. #2577C22semidirect
73. #2576C22semidirect
74. #2576C22semidirect
75. #2575C22semidirect
76. #2566C22semidirect
77. #2566C22semidirect
78. #2565C22semidirect
79. #2565C22semidirect
80. #2558C22semidirect
87. #2529C22semidirect
88. #2526C22semidirect
89. #2525C22semidirect
90. #2522C22semidirect
91. #2519C22semidirect
92. #2518C22semidirect
93. #2518C22semidirect
94. #2515C22semidirect
95. #2514C22semidirect
98. #2511C22semidirect
101. #2475C22semidirect
102. #2470C22semidirect
103. #2466C22semidirect
104. #2460C22semidirect
106. #2447C22semidirect
107. #2446C22semidirect
111. #2370C22semidirect
112. #2370C22semidirect
116. #2367C22semidirect
118. #2365C22semidirect
122. #2356C22semidirect
123. #2355C22semidirect
131. #2330C22semidirect
134. #2323C22semidirect
135. #2320C22semidirect
147. C4×#125C22semidirect
148. C4×#125C22semidirect
149. C4×#125C22semidirect
150. C4×#126C22semidirect
152. C4×C22⋊Q8C22semidirect
153. C4×#123C22semidirect
155. #2298C22semidirect
160. #2295C22semidirect
166. #2290C22semidirect
173. C42×Q8C22semidirect
174. C42×Q8C22semidirect
177. C42×D4C22semidirect
178. C42×D4C22semidirect
182. C4×#117C22semidirect
183. C4×#117C22semidirect
184. C4×#117C22semidirect
186. C2×C43C22semidirect

Maximal subgroups

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

subgroupindex
#366402
#366382
C2×#28612
#365272
#364852
#364212
#363202
#362532
#362482
#353402
#353332
#353272
#353132
#353072
#353002
#352692
#352662
#352542
#342692
#342682
#342552
#342542
#342172
#342112
C42×#412