Finite Group Databasebeta

← #7672498

Subgroups — #7672498

Order 512.

4848 conjugacy classes of subgroups.

The subgroup lattice has 1023 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59251C214yesmaximal, complemented
2#59250C214yesmaximal, complemented
3#59247C214yesmaximal, complemented
4#59246C214yesmaximal, complemented
5#39151C214yesmaximal, complemented
6#39150C214yesmaximal, complemented
7#37963C214yesmaximal, complemented
8#37962C214yesmaximal, complemented
9#36625C211yesmaximal, characteristic, complemented
10#36531C214yesmaximal, complemented
11#36523C214yesmaximal, complemented
12#36196C214yesmaximal, complemented
13#36175C214yesmaximal, complemented
14#35544C212yesmaximal, complemented
15#35542C212yesmaximal
16#35334C211yesmaximal, characteristic, complemented
17#35330C211yesmaximal, characteristic, complemented
18#35160C212yesmaximal, complemented
19#34271C212yesmaximal, complemented
20#34215C211yesmaximal, characteristic, complemented
21#34189C211yesmaximal, characteristic, complemented
22C4×#525C211yesmaximal, characteristic
23C2×#2283C211yesmaximal, characteristic, complemented
24C2×#544C2212yes—
25C2×#533C2211yescharacteristic
26C2×#525C2211yescharacteristic
27C2×C4×#41C2211yescharacteristic
28C23×C42C2211yescharacteristic
29#2862C2212yescomplemented
30#2859C2212yescomplemented
31#2857C2212yes—
32#2857C2212yes—
33#2855C2212yes—
34#2855C2212yes—
35#2852C2218yes—
36#2851C2212yes—
37#2851C2212yes—
38#2851C2214yescomplemented
39#2848C2212yes—
40#2848C2212yes—
41#2777C2218yescomplemented
42#2762C2218yescomplemented
43#2759C2218yescomplemented
44#2758C2218yescomplemented
45#2745C2218yes—
46#2740C2218yes—
47#2700C2218yes—
48#2689C2218yes—
49#2660C2214yescomplemented
50#2643C2218yes—
51#2628C2212yescomplemented
52#2628C2212yescomplemented
53#2605C2218yescomplemented
54#2604C2218yescomplemented
55#2581C2212yescomplemented
56#2581C2212yescomplemented
57#2580C2212yescomplemented
58#2580C2212yescomplemented
59#2577C2218yes—
60#2573C2218yes—
61#2573C2218yescomplemented
62#2564C2214yes—
63#2564C2214yes—
64#2563C2214yes—
65#2562C2214yes—
66#2562C2214yes—
67#2560C2218yes—
68#2550C2214yescomplemented
69#2550C2214yescomplemented
70#2549C2214yes—
71#2549C2214yes—
72#2547C2214yes—
73#2533C2218yescomplemented
74#2533C2218yescomplemented
75#2532C2218yescomplemented
76#2528C2218yescomplemented
77#2527C2218yes—
78#2527C2218yescomplemented
79#2523C2218yes—
80#2523C2218yescomplemented
81#2521C2218yes—
82#2514C2218yescomplemented
83#2514C2214yescomplemented
84#2513C2214yescomplemented
85#2512C2214yescomplemented
86#2511C2214yescomplemented
87#2497C2214yes—
88#2497C2214yes—
89#2497C2214yescomplemented
90#2496C2214yes—
91#2496C2214yes—
92#2496C2214yescomplemented
93#2495C2214yes—
94#2495C2214yes—
95#2495C2214yescomplemented
96#2494C2214yes—
97#2494C2214yes—
98#2494C2214yescomplemented
99#2493C2218yes—
100#2492C2214yes—
101#2491C2214yes—
102#2490C2214yes—
103#2489C2214yes—
104#2488C2218yes—
105#2480C2218yes—
106#2472C2218yes—
107#2466C2218yes—
108#2466C2218yes—
109#2465C2218yes—
110#2447C2218yes—
111#2373C2218yes—
112#2373C2218yescomplemented
113#2370C2214yescomplemented
114#2370C2214yescomplemented
115#2370C2214yescomplemented
116#2370C2214yescomplemented
117#2369C2214yescomplemented
118#2369C2214yescomplemented
119#2368C2214yes—
120#2368C2214yes—
121#2367C2218yes—
122#2365C2214yescomplemented
123#2365C2214yescomplemented
124#2357C2212yescomplemented
125#2357C2212yescomplemented
126#2356C2218yescomplemented
127#2356C2212yescomplemented
128#2356C2212yescomplemented
129#2355C2214yescomplemented
130#2355C2214yescomplemented
131#2353C2214yes—
132#2353C2214yes—
133#2331C2212yescomplemented
134#2331C2212yescomplemented
135#2329C2218yes—
136#2317C2212yes—
137#2317C2212yes—
138#2316C2212yes—
139#2314C2214yescomplemented
140#2311C2212yes—
141#2311C2212yes—
142C4×#125C2214yescomplemented
143C4×C22⋊Q8C2214yes—
144C4×C22⋊Q8C2214yes—
145C4×C22⋊Q8C2212yes—
146C4×C22⋊Q8C2212yes—
147C4×C22⋊Q8C2218yes—
148C4×#123C2212yes—
149C4×#123C2212yes—
150C4×#121C2212yes—
151C4×#121C2212yes—
152C4×#120C2212yes—
153C4×#120C2212yes—
154#2297C2211yescharacteristic
155#2296C2212yes—
156#2296C2211yescharacteristic
157#2290C2214yes—
158#2285C2211yescharacteristic
159#2283C2214yes—
160#2283C2214yes—
161#2283C2214yes—
162#2283C2214yes—
163#2283C2212yescomplemented
164#2283C2212yescomplemented
165C2×#383C2212yes—
166C2×#382C2211yescharacteristic
167C2×#382C2211yescharacteristic
168#2280C2212yes—
169#2280C2211yescharacteristic
170C2×#381C2212yes—
171C2×#380C2212yes—
172#2274C2212yes—
173#2274C2212yes—
174C42×D4C2214yes—
175C4×#117C2211yescharacteristic
176C2×C4×C4⋊C4C2212yes—
177C2×C4×C22⋊C4C2212yes—
178C2×#376C2212yes—
179C22×#41C2311yescharacteristic
180C24×C4C2311yescharacteristic
181C24×C4C2311yescharacteristic
182C24×C4C2311yescharacteristic
183#544—216no—
184#533—28no—
185C2×C4⋊Q8C2314yes—
186C2×C4⋊Q8C2311yescharacteristic
187C2×C4⋊Q8C2311yescharacteristic
188C2×C4⋊Q8C2314yes—
189C2×#126C2318yes—
190C2×#126C2318yes—
191C2×#125C2312yes—
192C2×#125C2314yes—
193C2×#125C2314yes—
194C2×#124C2318yes—
195#525—28no—
196C2×#123C2312yes—
197C2×C22⋊Q8C2312yes—
198C2×C22⋊Q8C2312yes—
199C2×C22⋊Q8C2318yes—
200C2×C22⋊Q8C2312yes—
201C2×C22⋊Q8C2314yes—
202C2×C22⋊Q8C2314yes—
203C2×#121C2312yes—
204C2×#120C2312yes—
205C4×#41—28no—
206C2×C4×Q8C2312yes—
207C2×C4×Q8C2312yes—
208C2×C4×Q8C2311yescharacteristic
209C2×C4×Q8C2311yescharacteristic
210C2×C4×Q8C2318yes—
211C2×C4×D4C2314yes—
212C2×C4×D4C2312yes—
213C2×C4×D4C2312yes—
214C2×C4×D4C2311yescharacteristic
215C2×C4×D4C2311yescharacteristic
216C2×C4×D4C2314yes—
217C2×C4×D4C2314yes—
218C2×#117C2312yes—
219C2×#117C2312yes—
220C2×#117C2312yes—
221C2×#117C2311yescharacteristic
222C2×#117C2311yescharacteristic
223C2×#117C2311yescharacteristic
224C22×C4⋊C4C2312yes—
225C22×C4⋊C4C2312yes—
226C22×C22⋊C4C2314yes—
227C22×C42—28no—
228C22×C42C2312yes—
229C22×C42C2312yes—
230C22×C42C2311yescharacteristic
231C22×C42C2311yescharacteristic
232C22×C42C2312yes—
233C22×C42C2311yescharacteristic
234C22×C42C2312yes—
235C22×C42C2312yes—
236C22×C42C2314yes—
237C22×C42C2311yescharacteristic
238#401C2318yes—
239#401C2318yes—
240#400C2318yes—
241#400C2318yes—
242#400C2314yes—
243#400C2314yes—
244#400C2318yes—
245#400C2318yes—
246#400C2318yes—
247#400C2318yes—
248#400C2318yes—
249#400C2318yes—
250#399C2314yes—
251#399C2314yes—
252#398C2318yes—
253#398C2318yes—
254#397C2318yes—
255#397C2318yes—
256#397C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#396C2318yes—
263#396C2318yes—
264#395C2314yes—
265#395C2314yes—
266#395C2318yes—
267#395C2318yes—
268#394C2318yes—
269#394C2318yes—
270#393C2314yes—
271#393C2318yes—
272#393C2318yes—
273#393C2314yes—
274#391C2318yes—
275#391C2314yes—
276#391C2314yes—
277#391C2318yes—
278#391C2318yes—
279#391C2318yes—
280#391C2314yes—
281#391C2314yes—
282#391C2318yes—
283#391C2318yes—
284#391C2318yes—
285#391C2318yes—
286#391C2312yes—
287#390C2318yes—
288#390C2314yes—
289#390C2314yes—
290#390C2312yes—
291#389C2314yes—
292#389C2314yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2318yes—
300#389C2318yes—
301#389C2318yes—
302#389C2318yes—
303#389C2312yes—
304#389C2312yes—
305#389C2312yes—
306#389C2312yes—
307#389C2314yes—
308#389C2314yes—
309#389C2318yes—
310#389C2312yes—
311#389C2312yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2314yes—
324#388C2318yes—
325#388C2314yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2314yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2314yes—
343#387C2314yes—
344#387C2314yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2314yes—
349#387C2318yes—
350#387C2318yes—
351#387C2314yes—
352#386C2314yes—
353#386C2318yes—
354#386C2318yes—
355#386C2312yes—
356#386C2312yes—
357#386C2314yes—
358#385C2318yes—
359#385C2318yes—
360#385C2318yes—
361#385C2318yes—
362#385C2314yes—
363#385C2314yes—
364#385C2312yes—
365#385C2314yes—
366#385C2314yes—
367#385C2314yes—
368#385C2314yes—
369#385C2314yes—
370#385C2314yes—
371#385C2312yes—
372#384C2312yes—
373#384C2314yes—
374#384C2314yes—
375#383C2314yes—
376#383C2318yes—
377#383C2318yes—
378#383C2314yes—
379#383C2318yes—
380#383C2318yes—
381#382C2312yes—
382#382C2318yes—
383#382C2312yes—
384#382C2314yes—
385#382C2314yes—
386#382C2312yes—
387#382C2312yes—
388#382C2311yescharacteristic
389#382C2311yescharacteristic
390#382C2312yes—
391#382C2312yes—
392#382C2312yes—
393#382C2312yes—
394#381C2318yes—
395#381C2314yes—
396#381C2314yes—
397#381C2314yes—
398#381C2318yes—
399#381C2312yes—
400#380C2314yes—
401#380C2312yes—
402#380C2312yes—
403#380C2314yes—
404#380C2314yes—
405#380C2314yes—
406#380C2314yes—
407#380C2312yes—
408#380C2314yes—
409#380C2318yes—
410#380C2314yes—
411#380C2312yes—
412#380C2312yes—
413#380C2314yes—
414#380C2312yes—
415#380C2314yes—
416#380C2314yes—
417#380C2312yes—
418#380C2312yes—
419#379C2314yes—
420#379C2312yes—
421C4×C4⋊C4C2318yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2318yes—
425C4×C4⋊C4C2318yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2318yes—
429C4×C4⋊C4C2318yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2312yes—
433C4×C4⋊C4C2312yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2314yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2312yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2314yes—
447C4×C22⋊C4C2318yes—
448C4×C22⋊C4C2314yes—
449C4×C22⋊C4C2314yes—
450C4×C22⋊C4C2318yes—
451C4×C22⋊C4C2318yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2314yes—
454C4×C22⋊C4C2318yes—
455C4×C22⋊C4C2312yes—
456C4×C22⋊C4C2312yes—
457C4×C22⋊C4C2314yes—
458C4×C22⋊C4C2314yes—
459C4×C22⋊C4C2314yes—
460C4×C22⋊C4C2314yes—
461C4×C22⋊C4C2314yes—
462C4×C22⋊C4C2314yes—
463#376C2312yes—
464#376C2318yes—
465#376C2314yes—
466#376C2314yes—
467#376C2318yes—
468C2×#95C2312yes—
469C2×#95C2312yes—
470C2×#95C2314yes—
471C2×#95C2312yes—
472C2×#95C2312yes—
473C2×#95C2314yes—
474C43C2312yes—
475C25C2411yescharacteristic
476C2×#41—24no—
477C2×#41—24no—
478C2×#41—24no—
479C22×Q8C2411yescharacteristic
480C22×Q8C2412yes—
481C22×Q8C2412yes—
482C22×Q8C2418yes—
483C22×D4C2412yes—
484C22×D4C2411yescharacteristic
485C22×D4C2414yes—
486C23×C4—24no—
487C23×C4—24no—
488C23×C4—24no—
489C23×C4—24no—
490C23×C4—24no—
491C23×C4—44no—
492C23×C4—44no—
493C23×C4C2412yes—
494C23×C4C2412yes—
495C23×C4C2412yes—
496C23×C4C2411yescharacteristic
497C23×C4C2411yescharacteristic
498C23×C4C2412yes—
499C23×C4C2412yes—
500C23×C4C2412yes—
501C23×C4C2412yes—
502C23×C4C2414yes—
503C23×C4C2414yes—
504C23×C4C2412yes—
505C23×C4C2412yes—
506C23×C4C2411yescharacteristic
507C23×C4C2411yescharacteristic
508C23×C4C2411yescharacteristic
509C23×C4C2411yescharacteristic
510C4⋊Q8—216no—
511C4⋊Q8—24no—
512C4⋊Q8—24no—
513C4⋊Q8—216no—
514#126—416no—
515#126—416no—
516#125—216no—
517#125—28no—
518#125—216no—
519#124—416no—
520#123—28no—
521C22⋊Q8—28no—
522C22⋊Q8—28no—
523C22⋊Q8—28no—
524C22⋊Q8—232no—
525C22⋊Q8—48no—
526C22⋊Q8—48no—
527#121—28no—
528#120—28no—
529C4×Q8—24no—
530C4×Q8—24no—
531C4×Q8—28no—
532C4×Q8—28no—
533C4×Q8—416no—
534C4×D4—28no—
535C4×D4—28no—
536C4×D4—24no—
537C4×D4—24no—
538C4×D4—216no—
539C4×D4—48no—
540C4×D4—48no—
541#117—24no—
542#117—28no—
543#117—28no—
544#117—24no—
545#117—28no—
546#117#4118yes—
547C2×C4⋊C4—28no—
548C2×C4⋊C4—28no—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2411yescharacteristic
554C2×C4⋊C4C2411yescharacteristic
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2418yes—
580C2×C4⋊C4C2418yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2412yes—
585C2×C22⋊C4—48no—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2412yes—
588C2×C22⋊C4C2412yes—
589C2×C22⋊C4C2412yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2412yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2412yes—
609C2×C42—24no—
610C2×C42—24no—
611C2×C42—24no—
612C2×C42—28no—
613C2×C42—28no—
614C2×C42—28no—
615C2×C42—28no—
616C2×C42—28no—
617C2×C42—48no—
618C2×C42#4118yes—
619C2×C42C2412yes—
620C2×C42C2414yes—
621C2×C42C2414yes—
622C2×C42C2412yes—
623C2×C42C2412yes—
624C2×C42C2412yes—
625C2×C42C2418yes—
626C2×C42C2412yes—
627C2×C42C2412yes—
628C2×C42C2412yes—
629C2×C42C2412yes—
630C2×C42C2412yes—
631C2×C42C2412yes—
632C2×C42C2414yes—
633C2×C42C2414yes—
634C2×C42C2418yes—
635C2×C42C2418yes—
636C2×C42C2418yes—
637C2×C42C2418yes—
638C2×C42C2418yes—
639C2×C42C2411yescharacteristic
640C2×C42C2412yes—
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644#95C2414yes—
645#95C2418yes—
646#95C2418yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2414yes—
651#95C2414yes—
652#95C2414yes—
653#95C2414yes—
654#95C2418yes—
655#95C2418yes—
656#95C2412yes—
657#95C2412yes—
658#95C2414yes—
659#95C2414yes—
660#95C2418yes—
661#95C2418yes—
662#95C2414yes—
663#95C2414yes—
664#95C2414yes—
665#95C2412yes—
666#95C2412yes—
667#95C2414yes—
668#95C2414yes—
669#95C2414yes—
670#95C2418yes—
671#95C2418yes—
672#95C2418yes—
673#95C2418yes—
674#95C2414yes—
675#95C2414yes—
676#95C2414yes—
677#95C2414yes—
678#95C2414yes—
679#95C2414yes—
680#95C2418yes—
681#95C2414yes—
682#95C2414yes—
683#95C2418yes—
684#95C2418yes—
685#95C2418yes—
686#95C2418yes—
687#95C2418yes—
688#95C2418yes—
689#95C2418yes—
690C24—22no—
691C24—24no—
692C24—22no—
693C24—22no—
694C24—42no—
695C24C2512yes—
696C24C2512yes—
697C24C2511yescharacteristic
698#41—416no—
699C2×Q8—22no—
700C2×Q8—22no—
701C2×Q8—24no—
702C2×Q8—24no—
703C2×Q8—216no—
704C2×Q8—22no—
705C2×Q8—48no—
706C2×Q8—44no—
707C2×Q8—44no—
708C2×Q8—48no—
709C2×D4—24no—
710C2×D4—24no—
711C2×D4—24no—
712C2×D4—28no—
713C2×D4—22no—
714C2×D4—28no—
715C2×D4—22no—
716C2×D4—22no—
717C2×D4—44no—
718C22×C4—22no—
719C22×C4—24no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—24no—
725C22×C4—24no—
726C22×C4—28no—
727C22×C4—28no—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—24no—
731C22×C4—24no—
732C22×C4—24no—
733C22×C4—24no—
734C22×C4—24no—
735C22×C4—24no—
736C22×C4—24no—
737C22×C4—24no—
738C22×C4—24no—
739C22×C4—24no—
740C22×C4—24no—
741C22×C4—24no—
742C22×C4—24no—
743C22×C4—24no—
744C22×C4—24no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—416no—
759C22×C4—416no—
760C22×C4—416no—
761C22×C4C2×#4114yes—
762C22×C4C2×#4114yes—
763C22×C4C2×#4114yes—
764C22×C4C2×#4114yes—
765C22×C42−1+414yes—
766C22×C4C2512yes—
767C22×C4C2512yes—
768C22×C4C2518yes—
769C22×C4C2512yes—
770C22×C4C2514yes—
771C22×C4C2514yes—
772C22×C4C2518yes—
773C22×C4C2512yes—
774C22×C4C2512yes—
775C22×C4C2514yes—
776C22×C4C2514yes—
777C22×C4C2514yes—
778C22×C4C2511yescharacteristic
779C22×C4C2511yescharacteristic
780C22×C4C2511yescharacteristic
781C22×C4C2511yescharacteristic
782C22×C4C2514yes—
783C22×C4C2512yes—
784C22×C4C2511yescharacteristic
785C22×C4C2511yescharacteristic
786C4⋊C4—28no—
787C4⋊C4—28no—
788C4⋊C4—22no—
789C4⋊C4—22no—
790C4⋊C4—24no—
791C4⋊C4—24no—
792C4⋊C4—24no—
793C4⋊C4—24no—
794C4⋊C4—24no—
795C4⋊C4—24no—
796C4⋊C4—28no—
797C4⋊C4—28no—
798C4⋊C4—28no—
799C4⋊C4—24no—
800C4⋊C4—24no—
801C4⋊C4—216no—
802C4⋊C4—216no—
803C4⋊C4—216no—
804C4⋊C4—28no—
805C4⋊C4—28no—
806C4⋊C4—24no—
807C4⋊C4—28no—
808C4⋊C4—28no—
809C4⋊C4—28no—
810C4⋊C4—44no—
811C4⋊C4—48no—
812C4⋊C4—44no—
813C4⋊C4—44no—
814C4⋊C4—44no—
815C4⋊C4—44no—
816C4⋊C4—48no—
817C4⋊C4—48no—
818C4⋊C4—48no—
819C4⋊C4—48no—
820C4⋊C4—48no—
821C4⋊C4C2×#4118yes—
822C22⋊C4—24no—
823C22⋊C4—28no—
824C22⋊C4—28no—
825C22⋊C4—24no—
826C22⋊C4—216no—
827C22⋊C4—28no—
828C22⋊C4—28no—
829C22⋊C4—28no—
830C22⋊C4—24no—
831C22⋊C4—24no—
832C22⋊C4—28no—
833C22⋊C4—28no—
834C22⋊C4—28no—
835C22⋊C4—48no—
836C22⋊C4—44no—
837C22⋊C4—44no—
838C22⋊C4—44no—
839C22⋊C4—44no—
840C22⋊C4—48no—
841C22⋊C4—48no—
842C22⋊C4—48no—
843C22⋊C4—48no—
844C22⋊C4C2×#4118yes—
845C42—24no—
846C42—24no—
847C42—24no—
848C42—24no—
849C42—24no—
850C42—24no—
851C42—24no—
852C42—24no—
853C42—24no—
854C42—28no—
855C42—28no—
856C42—24no—
857C42—216no—
858C42—48no—
859C42—44no—
860C42—44no—
861C42—48no—
862C42—48no—
863C42—48no—
864C42—48no—
865C42C2×#4114yes—
866C42C2×#4114yes—
867C42C2×#4114yes—
868C42C2×#4114yes—
869C42C2×#4118yes—
870C23—22no—
871C23—22no—
872C23—28no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—24no—
883C23—24no—
884C23—48no—
885C23—48no—
886C23—44no—
887C23—44no—
888C23C22×#4112yes—
889C23C22×#4112yes—
890C23C2×2−1+412yes—
891C23#58514yes—
892C23C2611yescharacteristic
893Q8—44no—
894Q8—816no—
895Q8—84no—
896Q8—84no—
897D4—416no—
898D4—48no—
899D4—44no—
900C2×C4—28no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—28no—
921C2×C4—24no—
922C2×C4—28no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—28no—
926C2×C4—28no—
927C2×C4—28no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—28no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—44no—
944C2×C4—44no—
945C2×C4—48no—
946C2×C4—48no—
947C2×C4—48no—
948C2×C4—48no—
949C2×C4—44no—
950C2×C4—44no—
951C2×C4—48no—
952C2×C4—48no—
953C2×C4—48no—
954C2×C4—84no—
955C2×C4—84no—
956C2×C4—88no—
957C2×C4—88no—
958C2×C4#556116yes—
959C2×C4C22×#4112yes—
960C2×C4C22×#4112yes—
961C2×C4C22×#4112yes—
962C2×C4C22×#4112yes—
963C2×C4C22×#4118yes—
964C2×C4C22×#4112yes—
965C2×C4C22×#4112yes—
966C2×C4C22×#4112yes—
967C2×C4C22×#4112yes—
968C2×C4C2×2−1+412yes—
969C2×C4C2×2−1+412yes—
970C2×C4#58514yes—
971C22—24no—
972C22—22no—
973C22—22no—
974C22—24no—
975C22—24no—
976C22—24no—
977C22—24no—
978C22—416no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—44no—
984C22—42no—
985C22—42no—
986C22—44no—
987C22—42no—
988C22C2×#55614yes—
989C22C23×#4111yescharacteristic
990C22C23×#4111yescharacteristic
991C22C22×2−1+411yescharacteristic
992C22C2×#58512yes—
993C22C2×#58512yes—
994C4—28no—
995C4—24no—
996C4—22no—
997C4—22no—
998C4—22no—
999C4—22no—
1000C4—44no—
1001C4—48no—
1002C4—44no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—44no—
1007C4—44no—
1008C4—44no—
1009C4—48no—
1010C4—42no—
1011C4—42no—
1012C4C2×#55614yes—
1013C4C2×#55614yes—
1014C2—24no—
1015C2—44no—
1016C2—82no—
1017C2C22×#55611yescharacteristic
1018C2#6281012yes—
1019C2#6281411yescharacteristic
1020C2#6281411yescharacteristic
1021C2#6283112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59251C2semidirect
2. #59250C2semidirect
3. #59247C2semidirect
4. #59246C2semidirect
5. #39151C2semidirect
6. #39150C2semidirect
7. #37963C2semidirect
8. #37962C2semidirect
9. #36625C2semidirect
10. #36531C2semidirect
11. #36523C2semidirect
12. #36196C2semidirect
13. #36175C2semidirect
14. #35544C2semidirect
16. #35334C2semidirect
17. #35330C2semidirect
18. #35160C2semidirect
19. #34271C2semidirect
20. #34215C2semidirect
21. #34189C2semidirect
23. C2×#2283C2semidirect
29. #2862C22semidirect
30. #2859C22semidirect
38. #2851C22semidirect
41. #2777C22semidirect
42. #2762C22semidirect
43. #2759C22semidirect
44. #2758C22semidirect
49. #2660C22semidirect
51. #2628C22semidirect
52. #2628C22semidirect
53. #2605C22semidirect
54. #2604C22semidirect
55. #2581C22semidirect
56. #2581C22semidirect
57. #2580C22semidirect
58. #2580C22semidirect
61. #2573C22semidirect
68. #2550C22semidirect
69. #2550C22semidirect
73. #2533C22semidirect
74. #2533C22semidirect
75. #2532C22semidirect
76. #2528C22semidirect
78. #2527C22semidirect
80. #2523C22semidirect
82. #2514C22semidirect
83. #2514C22semidirect
84. #2513C22semidirect
85. #2512C22semidirect
86. #2511C22semidirect
89. #2497C22semidirect
92. #2496C22semidirect
95. #2495C22semidirect
98. #2494C22semidirect
112. #2373C22semidirect
113. #2370C22semidirect
114. #2370C22semidirect
115. #2370C22semidirect
116. #2370C22semidirect
117. #2369C22semidirect
118. #2369C22semidirect
122. #2365C22semidirect
123. #2365C22semidirect
124. #2357C22semidirect
125. #2357C22semidirect
126. #2356C22semidirect
127. #2356C22semidirect
128. #2356C22semidirect
129. #2355C22semidirect
130. #2355C22semidirect
133. #2331C22semidirect
134. #2331C22semidirect
139. #2314C22semidirect
142. C4×#125C22semidirect
163. #2283C22semidirect
164. #2283C22semidirect

Maximal subgroups

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

subgroupindex
#592512
#592502
#592472
#592462
#391512
#391502
#379632
#379622
#366252
#365312
#365232
#361962
#361752
#355442
#355422
#353342
#353302
#351602
#342712
#342152
#341892
C4×#5252
C2×#22832