Finite Group Databasebeta

← #7643419

Subgroups — #7643419

Order 512.

4708 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40097C214yesmaximal, complemented
2#40074C214yesmaximal, complemented
3#39660C214yesmaximal, complemented
4#39535C214yesmaximal, complemented
5#38598C218yesmaximal, complemented
6#37907C218yesmaximal, complemented
7#37401C214yesmaximal, complemented
8#37352C214yesmaximal, complemented
9#36641C211yesmaximal, characteristic
10C2×#2862C211yesmaximal, characteristic, complemented
11#35674C211yesmaximal, characteristic, complemented
12#35668C211yesmaximal, characteristic, complemented
13#35667C211yesmaximal, characteristic
14#35662C211yesmaximal, characteristic, complemented
15#35628C211yesmaximal, characteristic
16#35619C211yesmaximal, characteristic
17#35576C211yesmaximal, characteristic, complemented
18#35574C211yesmaximal, characteristic
19#35313C211yesmaximal, characteristic, complemented
20#35312C211yesmaximal, characteristic
21#35199C214yesmaximal, complemented
22#35117C214yesmaximal, complemented
23#34276C211yesmaximal, characteristic
24#34254C211yesmaximal, characteristic, complemented
25C4×#533C211yesmaximal, characteristic, complemented
26C2×#544C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#533C2211yescharacteristic
30C22×C4⋊Q8C2211yescharacteristic
31C22×C4⋊Q8C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×#519C2211yescharacteristic
34C2×#519C2211yescharacteristic
35#2863C2212yes—
36#2863C2212yes—
37#2863C2214yes—
38#2862C2214yes—
39#2862C2214yes—
40#2862C2214yes—
41#2862C2214yes—
42#2862C2212yes—
43#2861C2212yes—
44#2860C2212yes—
45#2860C2212yes—
46#2852C2214yes—
47#2852C2214yes—
48#2799C2218yes—
49#2775C2218yes—
50#2774C2218yes—
51#2772C2218yes—
52#2767C2218yes—
53#2767C2218yes—
54#2766C2218yes—
55#2765C2218yes—
56#2763C2218yes—
57#2762C2218yes—
58#2759C2218yes—
59#2758C2218yes—
60#2755C2218yes—
61#2729C2218yes—
62#2716C2218yes—
63#2698C2218yes—
64#2666C2218yes—
65#2666C2218yes—
66#2650C2218yes—
67#2645C2214yes—
68#2642C2212yes—
69#2640C2212yes—
70#2637C2218yes—
71#2592C2214yes—
72#2583C2214yes—
73#2582C2214yes—
74#2581C2214yes—
75#2579C2214yes—
76#2568C2214yes—
77#2568C2212yes—
78#2567C2212yes—
79#2565C2212yes—
80#2565C2212yes—
81#2551C2214yes—
82#2551C2214yes—
83#2550C2214yes—
84#2550C2214yes—
85#2546C2214yes—
86#2545C2214yes—
87#2532C2218yes—
88#2529C2218yes—
89#2520C2218yes—
90#2520C2218yes—
91#2515C2218yes—
92#2514C2214yes—
93#2511C2214yes—
94#2508C2218yes—
95#2503C2212yes—
96#2502C2212yes—
97#2499C2212yes—
98#2499C2212yes—
99#2493C2218yes—
100#2492C2214yes—
101#2492C2214yes—
102#2489C2214yes—
103#2489C2214yes—
104#2488C2218yes—
105#2488C2218yes—
106#2484C2214yes—
107#2484C2214yes—
108#2465C2218yes—
109#2453C2214yes—
110#2453C2214yes—
111#2452C2214yes—
112#2451C2214yes—
113#2451C2214yes—
114#2451C2214yes—
115#2451C2218yes—
116#2447C2214yes—
117#2446C2214yes—
118#2446C2214yes—
119#2446C2214yes—
120#2446C2214yes—
121#2446C2214yes—
122#2440C2214yes—
123#2439C2214yes—
124#2438C2218yes—
125#2438C2218yes—
126#2434C2214yes—
127#2429C2214yes—
128#2429C2214yes—
129#2419C2218yes—
130#2413C2214yes—
131#2413C2214yes—
132#2409C2214yes—
133#2362C2214yes—
134#2360C2214yes—
135#2359C2218yes—
136#2356C2214yes—
137#2355C2214yes—
138#2343C2218yes—
139#2334C2218yes—
140#2332C2218yes—
141#2331C2218yes—
142#2327C2212yes—
143#2326C2212yes—
144#2320C2218yes—
145#2320C2214yes—
146#2317C2211yescharacteristic
147#2317C2211yescharacteristic
148#2317C2211yescharacteristic
149#2316C2211yescharacteristic
150#2311C2211yescharacteristic
151#2310C2211yescharacteristic
152#2310C2211yescharacteristic
153#2310C2211yescharacteristic
154#2310C2211yescharacteristic
155C4×C4⋊Q8C2212yes—
156C4×C4⋊Q8C2212yes—
157C4×C4⋊Q8C2212yes—
158C4×#125C2212yes—
159C4×#125C2212yes—
160C4×#126C2214yes—
161C4×#126C2214yes—
162C4×#124C2212yes—
163C4×C22⋊Q8C2214yes—
164C4×C22⋊Q8C2214yes—
165#2297C2211yescharacteristic
166#2297C2211yescharacteristic
167#2297C2211yescharacteristic
168#2296C2211yescharacteristic
169#2296C2211yescharacteristic
170#2296C2211yescharacteristic
171#2296C2211yescharacteristic
172#2296C2211yescharacteristic
173#2295C2214yes—
174#2295C2214yes—
175C2×#391C2211yescharacteristic
176C2×#391C2211yescharacteristic
177C2×#391C2214yes—
178C2×#391C2211yescharacteristic
179C2×#391C2211yescharacteristic
180#2285C2211yescharacteristic
181C2×#382C2214yes—
182#2274C2211yescharacteristic
183C42×Q8C2214yes—
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C43C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C23×Q8C2312yes—
191#544—44no—
192#536—28no—
193#536—44no—
194#533—28no—
195C2×C4⋊Q8—44no—
196C2×C4⋊Q8—44no—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2318yes—
201C2×C4⋊Q8C2314yes—
202C2×C4⋊Q8C2314yes—
203C2×C4⋊Q8C2314yes—
204C2×C4⋊Q8C2314yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×#126C2314yes—
208C2×#126C2314yes—
209C2×#125C2312yes—
210C2×#125C2312yes—
211C2×#125C2312yes—
212C2×#124C2312yes—
213C2×#124C2312yes—
214C2×#123C2314yes—
215C2×#123C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2318yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2312yes—
222#520—44no—
223#519—28no—
224#519—44no—
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2312yes—
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2314yes—
244C2×#117C2314yes—
245C2×#117C2312yes—
246C2×#117C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2312yes—
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2312yes—
252C22×C4⋊C4C2312yes—
253C22×C42C2312yes—
254C22×C42C2311yescharacteristic
255C22×C42C2311yescharacteristic
256C22×C42C2311yescharacteristic
257C22×C42C2312yes—
258#401C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#398C2318yes—
272#398C2318yes—
273#398C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#397C2318yes—
283#397C2318yes—
284#397C2318yes—
285#397C2318yes—
286#396C2318yes—
287#396C2318yes—
288#396C2318yes—
289#395C2318yes—
290#395C2318yes—
291#395C2318yes—
292#395C2318yes—
293#395C2318yes—
294#395C2318yes—
295#393C2318yes—
296#393C2318yes—
297#393C2318yes—
298#391C2311yescharacteristic
299#391C2312yes—
300#391C2314yes—
301#391C2314yes—
302#391C2312yes—
303#391C2312yes—
304#391C2312yes—
305#391C2312yes—
306#391C2314yes—
307#391C2314yes—
308#391C2312yes—
309#391C2312yes—
310#391C2314yes—
311#391C2312yes—
312#391C2312yes—
313#391C2314yes—
314#391C2314yes—
315#391C2312yes—
316#391C2312yes—
317#391C2318yes—
318#391C2318yes—
319#391C2314yes—
320#391C2312yes—
321#391C2318yes—
322#391C2314yes—
323#391C2312yes—
324#391C2311yescharacteristic
325#391C2318yes—
326#391C2318yes—
327#391C2318yes—
328#391C2318yes—
329#391C2312yes—
330#391C2314yes—
331#391C2314yes—
332#391C2318yes—
333#391C2312yes—
334#391C2318yes—
335#391C2312yes—
336#391C2318yes—
337#391C2312yes—
338#390C2312yes—
339#390C2311yescharacteristic
340#390C2312yes—
341#390C2311yescharacteristic
342#390C2312yes—
343#389C2312yes—
344#389C2312yes—
345#389C2312yes—
346#389C2312yes—
347#389C2318yes—
348#389C2314yes—
349#389C2314yes—
350#389C2318yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2312yes—
357#389C2318yes—
358#389C2318yes—
359#389C2312yes—
360#389C2312yes—
361#389C2318yes—
362#389C2318yes—
363#389C2318yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#388C2314yes—
368#388C2314yes—
369#388C2314yes—
370#388C2314yes—
371#388C2314yes—
372#388C2314yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#387C2314yes—
382#387C2314yes—
383#387C2314yes—
384#387C2314yes—
385#387C2314yes—
386#387C2314yes—
387#387C2314yes—
388#387C2314yes—
389#387C2314yes—
390#387C2314yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#386C2314yes—
412#386C2312yes—
413#386C2314yes—
414#386C2312yes—
415#386C2314yes—
416#385C2314yes—
417#385C2314yes—
418#385C2314yes—
419#385C2312yes—
420#385C2318yes—
421#385C2318yes—
422#385C2312yes—
423#385C2312yes—
424#385C2318yes—
425#385C2314yes—
426#385C2312yes—
427#385C2314yes—
428#385C2312yes—
429#385C2312yes—
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2312yes—
433#384C2312yes—
434#384C2312yes—
435#383C2314yes—
436#383C2314yes—
437#383C2318yes—
438#383C2318yes—
439#382C2311yescharacteristic
440#382C2311yescharacteristic
441#382C2312yes—
442#382C2318yes—
443#382C2312yes—
444#382C2312yes—
445#382C2318yes—
446#382C2318yes—
447#382C2318yes—
448#382C2318yes—
449#382C2318yes—
450#382C2318yes—
451#381C2314yes—
452#381C2314yes—
453#381C2314yes—
454#381C2314yes—
455#381C2318yes—
456#380C2314yes—
457#380C2314yes—
458#380C2314yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2318yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2318yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C22⋊C4C2314yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2312yes—
483C4×C22⋊C4C2312yes—
484C4×C22⋊C4C2314yes—
485C4×C22⋊C4C2318yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488#376C2312yes—
489#376C2318yes—
490#376C2312yes—
491C2×#95C2314yes—
492C2×#95C2314yes—
493C2×#95C2314yes—
494C2×#95C2314yes—
495C43C2312yes—
496C43C2312yes—
497C43C2312yes—
498C43C2312yes—
499C43C2312yes—
500C43C2312yes—
501C2×#41—24no—
502C2×#41—24no—
503C2×#41—24no—
504C22×Q8—24no—
505C22×Q8—24no—
506C22×Q8—24no—
507C22×Q8—24no—
508C22×Q8—24no—
509C22×Q8—24no—
510C22×Q8—44no—
511C22×Q8—48no—
512C22×Q8C2412yes—
513C22×Q8C2412yes—
514C22×Q8C2412yes—
515C22×Q8C2412yes—
516C22×Q8C2411yescharacteristic
517C22×Q8C2414yes—
518C22×Q8C2418yes—
519C22×Q8C2414yes—
520C22×D4C2412yes—
521C22×D4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C23×C4C2412yes—
524C23×C4C2412yes—
525C23×C4C2411yescharacteristic
526C23×C4C2412yes—
527C23×C4C2412yes—
528C23×C4C2412yes—
529C23×C4C2412yes—
530C23×C4C2412yes—
531C23×C4C2414yes—
532C23×C4C2411yescharacteristic
533C4⋊Q8—28no—
534C4⋊Q8—28no—
535C4⋊Q8—48no—
536C4⋊Q8—48no—
537C4⋊Q8—44no—
538C4⋊Q8—44no—
539C4⋊Q8—48no—
540C4⋊Q8—48no—
541C4⋊Q8—44no—
542C4⋊Q8—416no—
543#126—216no—
544#126—48no—
545#125—28no—
546#125—44no—
547#125—44no—
548#124—28no—
549#124—44no—
550#123—216no—
551#123—48no—
552C22⋊Q8—216no—
553C22⋊Q8—216no—
554C22⋊Q8—48no—
555C22⋊Q8—416no—
556C22⋊Q8—44no—
557C22⋊Q8—44no—
558C4×Q8—216no—
559C4×Q8—216no—
560C4×Q8—216no—
561C4×Q8—216no—
562C4×Q8—48no—
563C4×Q8—44no—
564C4×Q8—44no—
565C4×Q8—44no—
566C4×Q8—44no—
567C4×Q8—44no—
568C4×D4—44no—
569C4×D4—48no—
570#117—24no—
571#117—24no—
572#117—24no—
573#117—24no—
574#117—24no—
575#117—24no—
576#117—216no—
577#117—48no—
578#117—44no—
579#117#4118yes—
580C2×C4⋊C4—24no—
581C2×C4⋊C4—24no—
582C2×C4⋊C4—44no—
583C2×C4⋊C4—44no—
584C2×C4⋊C4—44no—
585C2×C4⋊C4—44no—
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2412yes—
632C2×C22⋊C4C2412yes—
633C2×C22⋊C4C2412yes—
634C2×C22⋊C4C2412yes—
635C2×C22⋊C4C2412yes—
636C2×C22⋊C4C2412yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2412yes—
650C2×C42—24no—
651C2×C42—24no—
652C2×C42—24no—
653C2×C42—28no—
654C2×C42—44no—
655C2×C42C2412yes—
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2418yes—
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2414yes—
665C2×C42C2414yes—
666C2×C42C2411yescharacteristic
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2414yes—
678C2×C42C2414yes—
679C2×C42C2414yes—
680C2×C42C2414yes—
681C2×C42C2414yes—
682C2×C42C2418yes—
683C2×C42C2412yes—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687#95C2418yes—
688#95C2418yes—
689#95C2418yes—
690#95C2418yes—
691#95C2418yes—
692#95C2418yes—
693#95C2418yes—
694#95C2418yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2418yes—
701#95C2418yes—
702#95C2414yes—
703#95C2418yes—
704#95C2414yes—
705#95C2418yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2418yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2418yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729#95C2418yes—
730#95C2418yes—
731C24C2512yes—
732C24C2511yescharacteristic
733#41—416no—
734C2×Q8—24no—
735C2×Q8—24no—
736C2×Q8—28no—
737C2×Q8—24no—
738C2×Q8—24no—
739C2×Q8—22no—
740C2×Q8—24no—
741C2×Q8—24no—
742C2×Q8—22no—
743C2×Q8—24no—
744C2×Q8—24no—
745C2×Q8—28no—
746C2×Q8—24no—
747C2×Q8—24no—
748C2×Q8—24no—
749C2×Q8—24no—
750C2×Q8—22no—
751C2×Q8—216no—
752C2×Q8—44no—
753C2×Q8—48no—
754C2×Q8—48no—
755C2×Q8—44no—
756C2×Q8—48no—
757C2×Q8—416no—
758C2×Q8—416no—
759C2×Q8—816no—
760C2×D4—24no—
761C2×D4—24no—
762C2×D4—24no—
763C2×D4—22no—
764C2×D4—22no—
765C2×D4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—42no—
786C22×C4—42no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—44no—
790C22×C4—48no—
791C22×C4C2×#4114yes—
792C22×C4H(5,𝔽2)14yes—
793C22×C42−1+414yes—
794C22×C4C2512yes—
795C22×C4C2514yes—
796C22×C4C2512yes—
797C22×C4C2514yes—
798C22×C4C2514yes—
799C22×C4C2514yes—
800C22×C4C2512yes—
801C22×C4C2512yes—
802C22×C4C2514yes—
803C22×C4C2512yes—
804C22×C4C2512yes—
805C22×C4C2514yes—
806C22×C4C2514yes—
807C22×C4C2512yes—
808C22×C4C2512yes—
809C22×C4C2512yes—
810C22×C4C2514yes—
811C22×C4C2512yes—
812C22×C4C2512yes—
813C22×C4C2512yes—
814C22×C4C2512yes—
815C22×C4C2511yescharacteristic
816C22×C4C2511yescharacteristic
817C4⋊C4—24no—
818C4⋊C4—216no—
819C4⋊C4—24no—
820C4⋊C4—28no—
821C4⋊C4—28no—
822C4⋊C4—28no—
823C4⋊C4—216no—
824C4⋊C4—24no—
825C4⋊C4—24no—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—22no—
829C4⋊C4—22no—
830C4⋊C4—22no—
831C4⋊C4—22no—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—24no—
835C4⋊C4—28no—
836C4⋊C4—28no—
837C4⋊C4—28no—
838C4⋊C4—28no—
839C4⋊C4—28no—
840C4⋊C4—28no—
841C4⋊C4—28no—
842C4⋊C4—28no—
843C4⋊C4—28no—
844C4⋊C4—44no—
845C4⋊C4—48no—
846C4⋊C4—48no—
847C4⋊C4—48no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—48no—
852C4⋊C4—48no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—48no—
861C4⋊C4—48no—
862C4⋊C4C2×#4118yes—
863C22⋊C4—24no—
864C22⋊C4—24no—
865C22⋊C4—24no—
866C22⋊C4—24no—
867C22⋊C4—24no—
868C22⋊C4—24no—
869C22⋊C4—216no—
870C22⋊C4—28no—
871C22⋊C4—28no—
872C22⋊C4—28no—
873C22⋊C4—28no—
874C22⋊C4—44no—
875C22⋊C4—48no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4C2×#4118yes—
881C42—24no—
882C42—22no—
883C42—22no—
884C42—24no—
885C42—216no—
886C42—24no—
887C42—24no—
888C42—24no—
889C42—24no—
890C42—24no—
891C42—24no—
892C42—22no—
893C42—24no—
894C42—24no—
895C42—24no—
896C42—24no—
897C42—22no—
898C42—24no—
899C42—28no—
900C42—28no—
901C42—24no—
902C42—24no—
903C42—42no—
904C42—42no—
905C42—44no—
906C42—44no—
907C42—44no—
908C42—44no—
909C42—44no—
910C42—48no—
911C42C2×#4118yes—
912C422−1+418yes—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—24no—
918C23—22no—
919C23—24no—
920C23C22×#4112yes—
921C23C2×H(5,𝔽2)12yes—
922C23C2×2−1+412yes—
923C23C2611yescharacteristic
924Q8—416no—
925Q8—48no—
926Q8—48no—
927Q8—48no—
928Q8—48no—
929Q8—44no—
930Q8—816no—
931Q8—164no—
932D4—48no—
933D4—44no—
934C2×C4—28no—
935C2×C4—28no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—24no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—24no—
945C2×C4—22no—
946C2×C4—24no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—22no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—28no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—28no—
986C2×C4—48no—
987C2×C4—48no—
988C2×C4—48no—
989C2×C4—48no—
990C2×C4—48no—
991C2×C4—84no—
992C2×C4—84no—
993C2×C4—164no—
994C2×C4#542116yes—
995C2×C4C22×#4118yes—
996C2×C4C22×#4112yes—
997C2×C4C22×#4112yes—
998C2×C4C2×H(5,𝔽2)12yes—
999C2×C4C2×H(5,𝔽2)12yes—
1000C2×C4C2×2−1+414yes—
1001C2×C4C2×2−1+414yes—
1002C2×C4C2×2−1+414yes—
1003C2×C4C2×2−1+412yes—
1004C2×C4C2×2−1+412yes—
1005C2×C4#58514yes—
1006C22—24no—
1007C22—22no—
1008C22—22no—
1009C22—24no—
1010C22—44no—
1011C22—42no—
1012C22—42no—
1013C22—44no—
1014C22—42no—
1015C22C2×#54214yes—
1016C22C23×#4111yescharacteristic
1017C22C22×H(5,𝔽2)11yescharacteristic
1018C22C22×2−1+412yes—
1019C22C22×2−1+411yescharacteristic
1020C22C2×#58512yes—
1021C4—24no—
1022C4—28no—
1023C4—24no—
1024C4—24no—
1025C4—24no—
1026C4—44no—
1027C4—42no—
1028C4—44no—
1029C4—44no—
1030C4—44no—
1031C4—42no—
1032C4—42no—
1033C4—42no—
1034C4—42no—
1035C4—42no—
1036C4—42no—
1037C4—44no—
1038C4—42no—
1039C4—42no—
1040C4—44no—
1041C4—44no—
1042C4C2×#54214yes—
1043C4C2×#54214yes—
1044C2—24no—
1045C2—82no—
1046C2C22×#54211yescharacteristic
1047C2#6280512yes—
1048C2#6282411yescharacteristic
1049C2#6283311yescharacteristic
1050C2#6283712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40097C2semidirect
2. #40074C2semidirect
3. #39660C2semidirect
4. #39535C2semidirect
5. #38598C2semidirect
6. #37907C2semidirect
7. #37401C2semidirect
8. #37352C2semidirect
10. C2×#2862C2semidirect
11. #35674C2semidirect
12. #35668C2semidirect
14. #35662C2semidirect
17. #35576C2semidirect
19. #35313C2semidirect
21. #35199C2semidirect
22. #35117C2semidirect
24. #34254C2semidirect
25. C4×#533C2semidirect

Maximal subgroups

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

subgroupindex
#400972
#400742
#396602
#395352
#385982
#379072
#374012
#373522
#366412
C2×#28622
#356742
#356682
#356672
#356622
#356282
#356192
#355762
#355742
#353132
#353122
#351992
#351172
#342762
#342542
C4×#5332