Finite Group Databasebeta

← #7652080

Subgroups — #7652080

Order 512.

4822 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42924C214yesmaximal, complemented
2#42837C214yesmaximal, complemented
3#42639C214yesmaximal, complemented
4#42452C214yesmaximal, complemented
5#40836C218yesmaximal, complemented
6#40165C214yesmaximal, complemented
7#39939C214yesmaximal, complemented
8#39655C214yesmaximal, complemented
9#39604C214yesmaximal, complemented
10#38573C218yesmaximal, complemented
11#35621C211yesmaximal, characteristic
12#35619C211yesmaximal, characteristic, complemented
13#35574C211yesmaximal, characteristic, complemented
14#35574C211yesmaximal, characteristic, complemented
15#35557C211yesmaximal, characteristic, complemented
16#35555C211yesmaximal, characteristic, complemented
17#35313C211yesmaximal, characteristic, complemented
18#35307C211yesmaximal, characteristic, complemented
19#35182C211yesmaximal, characteristic, complemented
20C2×#2567C211yesmaximal, characteristic, complemented
21#34815C211yesmaximal, characteristic, complemented
22#34744C211yesmaximal, characteristic
23#34266C211yesmaximal, characteristic, complemented
24#34207C211yesmaximal, characteristic
25#34183C211yesmaximal, characteristic, complemented
26C2×#536C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#532C2211yescharacteristic
29C22×C4⋊Q8C2211yescharacteristic
30C2×#520C2211yescharacteristic
31C2×#520C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35#2863C2214yes—
36#2855C2214yes—
37#2853C2214yes—
38#2838C2218yes—
39#2835C2218yes—
40#2805C2218yes—
41#2802C2218yes—
42#2792C2218yes—
43#2791C2218yes—
44#2790C2218yes—
45#2787C2218yes—
46#2771C2218yes—
47#2757C2218yes—
48#2745C2218yes—
49#2739C2218yes—
50#2737C2218yes—
51#2723C2218yes—
52#2720C2218yes—
53#2707C2218yes—
54#2690C2218yes—
55#2689C2218yes—
56#2666C2218yes—
57#2664C2218yes—
58#2652C2218yes—
59#2650C2218yes—
60#2645C2214yes—
61#2638C2218yes—
62#2627C2218yes—
63#2625C2214yes—
64#2623C2214yes—
65#2594C2218yes—
66#2588C2218yes—
67#2585C2218yes—
68#2579C2214yes—
69#2579C2214yes—
70#2570C2214yes—
71#2567C2214yes—
72#2567C2214yes—
73#2567C2214yes—
74#2567C2214yes—
75#2552C2214yes—
76#2547C2212yes—
77#2546C2212yes—
78#2545C2212yes—
79#2544C2212yes—
80#2514C2214yes—
81#2512C2214yes—
82#2511C2214yes—
83#2511C2214yes—
84#2509C2212yes—
85#2508C2212yes—
86#2507C2212yes—
87#2507C2214yes—
88#2506C2212yes—
89#2506C2214yes—
90#2505C2214yes—
91#2503C2212yes—
92#2502C2212yes—
93#2499C2212yes—
94#2499C2212yes—
95#2497C2214yes—
96#2496C2214yes—
97#2493C2218yes—
98#2481C2218yes—
99#2473C2218yes—
100#2473C2218yes—
101#2473C2214yes—
102#2466C2218yes—
103#2452C2214yes—
104#2452C2214yes—
105#2451C2214yes—
106#2451C2214yes—
107#2449C2218yes—
108#2448C2212yes—
109#2448C2214yes—
110#2447C2214yes—
111#2447C2212yes—
112#2447C2214yes—
113#2446C2214yes—
114#2446C2214yes—
115#2446C2214yes—
116#2446C2212yes—
117#2445C2212yes—
118#2444C2214yes—
119#2443C2214yes—
120#2440C2214yes—
121#2440C2214yes—
122#2439C2214yes—
123#2439C2214yes—
124#2425C2218yes—
125#2423C2214yes—
126#2421C2214yes—
127#2419C2218yes—
128#2419C2218yes—
129#2417C2214yes—
130#2415C2214yes—
131#2409C2214yes—
132#2409C2214yes—
133#2402C2214yes—
134#2395C2214yes—
135C2×#395C2214yes—
136#2367C2214yes—
137#2365C2214yes—
138#2362C2214yes—
139#2361C2218yes—
140#2360C2214yes—
141#2354C2214yes—
142Q8×C4⋊C4C2214yes—
143D4×C4⋊C4C2218yes—
144D4×C4⋊C4C2214yes—
145D4×C4⋊C4C2214yes—
146#2336C2218yes—
147#2326C2212yes—
148#2326C2212yes—
149#2322C2214yes—
150#2322C2218yes—
151#2317C2211yescharacteristic
152#2317C2211yescharacteristic
153#2317C2212yes—
154#2317C2212yes—
155#2317C2211yescharacteristic
156#2316C2211yescharacteristic
157#2316C2211yescharacteristic
158#2311C2211yescharacteristic
159#2311C2211yescharacteristic
160#2311C2211yescharacteristic
161#2310C2211yescharacteristic
162#2310C2211yescharacteristic
163C4×C4⋊Q8C2212yes—
164C4×#127C2212yes—
165C4×#125C2214yes—
166C4×#123C2214yes—
167C4×#123C2214yes—
168#2297C2211yescharacteristic
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2296C2211yescharacteristic
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2296C2211yescharacteristic
175#2296C2211yescharacteristic
176C2×#391C2211yescharacteristic
177C2×#391C2211yescharacteristic
178C2×#389C2214yes—
179#2285C2212yes—
180#2285C2211yescharacteristic
181C2×#384C2211yescharacteristic
182C2×#384C2211yescharacteristic
183C2×#384C2212yes—
184#2274C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C23×Q8C2312yes—
191#536—28no—
192#536—44no—
193#532—28no—
194C2×C4⋊Q8—44no—
195C2×C4⋊Q8C2311yescharacteristic
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2314yes—
198C2×C4⋊Q8C2314yes—
199C2×C4⋊Q8C2312yes—
200C2×#127C2311yescharacteristic
201C2×#126C2318yes—
202C2×#125C2314yes—
203C2×#125C2318yes—
204C2×#124C2311yescharacteristic
205C2×#124C2311yescharacteristic
206C2×#124C2312yes—
207C2×#124C2312yes—
208C2×#123C2314yes—
209C2×#123C2314yes—
210C2×#123C2314yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2312yes—
213C2×C22⋊Q8C2312yes—
214C2×C22⋊Q8C2318yes—
215C2×C22⋊Q8C2318yes—
216C2×#121C2314yes—
217#520—44no—
218#520—44no—
219#520—44no—
220C4×#41—28no—
221C2×C4×Q8—44no—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2312yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2312yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2318yes—
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2312yes—
244C2×#117C2311yescharacteristic
245C2×#117C2312yes—
246C2×#117C2312yes—
247C2×#117C2312yes—
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2312yes—
252C22×C4⋊C4C2312yes—
253C22×C4⋊C4C2312yes—
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2312yes—
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2318yes—
258C22×C4⋊C4C2314yes—
259C22×C4⋊C4C2314yes—
260C22×C42C2312yes—
261C22×C42C2311yescharacteristic
262C22×C42C2311yescharacteristic
263C22×C42C2311yescharacteristic
264C22×C42C2312yes—
265#401C2318yes—
266#400C2318yes—
267#400C2314yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2314yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#399C2318yes—
281#399C2314yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2314yes—
287#398C2318yes—
288#398C2314yes—
289#398C2318yes—
290#398C2318yes—
291#398C2314yes—
292#398C2318yes—
293#398C2314yes—
294#398C2314yes—
295#398C2318yes—
296#397C2314yes—
297#397C2318yes—
298#397C2318yes—
299#397C2314yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2314yes—
306#396C2318yes—
307#396C2318yes—
308#396C2318yes—
309#396C2318yes—
310#395C2318yes—
311#395C2318yes—
312#395C2318yes—
313#395C2318yes—
314#395C2318yes—
315#395C2318yes—
316#394C2314yes—
317#394C2318yes—
318#394C2314yes—
319#393C2318yes—
320#393C2318yes—
321#391C2312yes—
322#391C2312yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2312yes—
327#391C2312yes—
328#391C2312yes—
329#391C2312yes—
330#391C2312yes—
331#391C2312yes—
332#391C2312yes—
333#391C2314yes—
334#391C2314yes—
335#391C2318yes—
336#391C2318yes—
337#391C2312yes—
338#391C2312yes—
339#391C2312yes—
340#390C2312yes—
341#390C2312yes—
342#390C2318yes—
343#390C2312yes—
344#390C2312yes—
345#390C2312yes—
346#390C2312yes—
347#389C2314yes—
348#389C2314yes—
349#389C2318yes—
350#389C2318yes—
351#389C2318yes—
352#389C2318yes—
353#389C2318yes—
354#389C2312yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2318yes—
360#389C2314yes—
361#389C2318yes—
362#389C2314yes—
363#389C2314yes—
364#389C2318yes—
365#389C2318yes—
366#389C2318yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2312yes—
375#389C2312yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2314yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2314yes—
386#387C2314yes—
387#387C2314yes—
388#387C2314yes—
389#387C2314yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2314yes—
401#387C2318yes—
402#387C2318yes—
403#387C2314yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#386C2314yes—
410#386C2314yes—
411#386C2314yes—
412#386C2312yes—
413#386C2318yes—
414#386C2312yes—
415#386C2312yes—
416#386C2312yes—
417#386C2314yes—
418#386C2314yes—
419#385C2314yes—
420#385C2314yes—
421#385C2318yes—
422#385C2314yes—
423#385C2318yes—
424#385C2312yes—
425#385C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2312yes—
430#385C2312yes—
431#385C2318yes—
432#385C2318yes—
433#385C2318yes—
434#385C2312yes—
435#385C2314yes—
436#385C2314yes—
437#385C2314yes—
438#385C2314yes—
439#384C2312yes—
440#384C2314yes—
441#384C2312yes—
442#384C2312yes—
443#384C2314yes—
444#384C2312yes—
445#384C2312yes—
446#384C2312yes—
447#384C2312yes—
448#384C2318yes—
449#384C2311yescharacteristic
450#384C2311yescharacteristic
451#383C2318yes—
452#382C2314yes—
453#382C2312yes—
454#382C2312yes—
455#382C2312yes—
456#382C2311yescharacteristic
457#382C2311yescharacteristic
458#381C2314yes—
459#381C2314yes—
460#381C2318yes—
461#381C2314yes—
462#381C2318yes—
463#380C2314yes—
464#380C2314yes—
465#380C2314yes—
466#380C2314yes—
467#380C2314yes—
468#380C2314yes—
469#380C2318yes—
470#380C2318yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2318yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2318yes—
484C4×C4⋊C4C2318yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2312yes—
489C4×C22⋊C4C2318yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2312yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2312yes—
496#376C2312yes—
497C2×#95C2312yes—
498C2×#95C2314yes—
499C2×#95C2314yes—
500C43C2312yes—
501C2×#41—24no—
502C2×#41—24no—
503C2×#41—24no—
504C2×#41—24no—
505C2×#41—24no—
506C2×#41#4118yes—
507C22×Q8—24no—
508C22×Q8—24no—
509C22×Q8—24no—
510C22×Q8—44no—
511C22×Q8—84no—
512C22×Q8C2412yes—
513C22×Q8C2412yes—
514C22×Q8C2411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×Q8C2418yes—
517C22×D4C2412yes—
518C22×D4C2411yescharacteristic
519C22×D4C2414yes—
520C22×D4C2412yes—
521C22×D4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C23×C4C2412yes—
524C23×C4C2412yes—
525C23×C4C2412yes—
526C23×C4C2412yes—
527C23×C4C2414yes—
528C23×C4C2412yes—
529C23×C4C2412yes—
530C23×C4C2412yes—
531C23×C4C2412yes—
532C23×C4C2411yescharacteristic
533C23×C4C2414yes—
534C23×C4C2414yes—
535C23×C4C2414yes—
536C23×C4C2411yescharacteristic
537C4⋊Q8—24no—
538C4⋊Q8—28no—
539C4⋊Q8—48no—
540C4⋊Q8—48no—
541C4⋊Q8—44no—
542#127—24no—
543#126—88no—
544#125—216no—
545#125—88no—
546#124—24no—
547#124—24no—
548#124—28no—
549#124—44no—
550#123—216no—
551#123—216no—
552#123—48no—
553C22⋊Q8—216no—
554C22⋊Q8—44no—
555C22⋊Q8—44no—
556C22⋊Q8—88no—
557C22⋊Q8—88no—
558#121—216no—
559C4×Q8—28no—
560C4×Q8—48no—
561C4×Q8—48no—
562C4×Q8—44no—
563C4×Q8—44no—
564C4×Q8—44no—
565C4×D4—216no—
566C4×D4—28no—
567C4×D4—216no—
568C4×D4—44no—
569C4×D4—44no—
570C4×D4—44no—
571C4×D4—48no—
572C4×D4—48no—
573C4×D4—48no—
574C4×D4—88no—
575#117—28no—
576#117—24no—
577#117—24no—
578#117—24no—
579#117—24no—
580#117—24no—
581#117—24no—
582#117—44no—
583#117—44no—
584#117—44no—
585C2×C4⋊C4—24no—
586C2×C4⋊C4—24no—
587C2×C4⋊C4—24no—
588C2×C4⋊C4—28no—
589C2×C4⋊C4—44no—
590C2×C4⋊C4—44no—
591C2×C4⋊C4—44no—
592C2×C4⋊C4—44no—
593C2×C4⋊C4—44no—
594C2×C4⋊C4—88no—
595C2×C4⋊C4—84no—
596C2×C4⋊C4—84no—
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⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2414yes—
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⋊C4C2418yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2412yes—
646C2×C22⋊C4C2412yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2412yes—
651C2×C22⋊C4C2412yes—
652C2×C22⋊C4C2412yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2414yes—
670C2×C42—28no—
671C2×C42—24no—
672C2×C42—24no—
673C2×C42—24no—
674C2×C42—44no—
675C2×C42C2412yes—
676C2×C42C2411yescharacteristic
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2414yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2411yescharacteristic
688C2×C42C2414yes—
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2414yes—
692C2×C42C2414yes—
693C2×C42C2414yes—
694C2×C42C2414yes—
695C2×C42C2418yes—
696C2×C42C2418yes—
697#95C2412yes—
698#95C2412yes—
699#95C2412yes—
700#95C2412yes—
701#95C2418yes—
702#95C2418yes—
703#95C2418yes—
704#95C2418yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2418yes—
709#95C2414yes—
710#95C2418yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2418yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722#95C2414yes—
723#95C2418yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2418yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737#95C2418yes—
738C24C2512yes—
739C24C2512yes—
740C24C2511yescharacteristic
741#41—232no—
742#41—416no—
743C2×Q8—24no—
744C2×Q8—24no—
745C2×Q8—22no—
746C2×Q8—22no—
747C2×Q8—24no—
748C2×Q8—24no—
749C2×Q8—22no—
750C2×Q8—22no—
751C2×Q8—24no—
752C2×Q8—24no—
753C2×Q8—22no—
754C2×Q8—48no—
755C2×Q8—48no—
756C2×Q8—48no—
757C2×Q8—416no—
758C2×Q8—816no—
759C2×Q8C2×#4114yes—
760C2×D4—24no—
761C2×D4—24no—
762C2×D4—28no—
763C2×D4—24no—
764C2×D4—24no—
765C2×D4—24no—
766C2×D4—22no—
767C2×D4—22no—
768C2×D4—22no—
769C2×D4—22no—
770C2×D4—28no—
771C2×D4—22no—
772C2×D4—44no—
773C2×D4C2×#4118yes—
774C2×D4C2×#4114yes—
775C22×C4—22no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—28no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—22no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—24no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—28no—
794C22×C4—24no—
795C22×C4—42no—
796C22×C4—42no—
797C22×C4—44no—
798C22×C4—42no—
799C22×C4—44no—
800C22×C4—44no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—44no—
805C22×C4—48no—
806C22×C4—48no—
807C22×C4—48no—
808C22×C4C2×#4118yes—
809C22×C4C2×#4114yes—
810C22×C4H(5,𝔽2)14yes—
811C22×C42−1+414yes—
812C22×C4C2514yes—
813C22×C4C2514yes—
814C22×C4C2514yes—
815C22×C4C2512yes—
816C22×C4C2512yes—
817C22×C4C2512yes—
818C22×C4C2512yes—
819C22×C4C2514yes—
820C22×C4C2512yes—
821C22×C4C2514yes—
822C22×C4C2512yes—
823C22×C4C2512yes—
824C22×C4C2514yes—
825C22×C4C2514yes—
826C22×C4C2514yes—
827C22×C4C2512yes—
828C22×C4C2512yes—
829C22×C4C2512yes—
830C22×C4C2512yes—
831C22×C4C2512yes—
832C22×C4C2511yescharacteristic
833C22×C4C2511yescharacteristic
834C4⋊C4—28no—
835C4⋊C4—24no—
836C4⋊C4—24no—
837C4⋊C4—28no—
838C4⋊C4—216no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—24no—
844C4⋊C4—24no—
845C4⋊C4—22no—
846C4⋊C4—22no—
847C4⋊C4—22no—
848C4⋊C4—22no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—28no—
855C4⋊C4—28no—
856C4⋊C4—28no—
857C4⋊C4—28no—
858C4⋊C4—28no—
859C4⋊C4—28no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C4⋊C4—48no—
864C4⋊C4—48no—
865C4⋊C4—48no—
866C4⋊C4—44no—
867C4⋊C4—48no—
868C4⋊C4—48no—
869C4⋊C4—48no—
870C4⋊C4—48no—
871C4⋊C4—48no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C4⋊C4—44no—
876C4⋊C4—48no—
877C4⋊C4—48no—
878C4⋊C4—48no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C42−1+418yes—
883C22⋊C4—28no—
884C22⋊C4—24no—
885C22⋊C4—24no—
886C22⋊C4—28no—
887C22⋊C4—216no—
888C22⋊C4—24no—
889C22⋊C4—24no—
890C22⋊C4—24no—
891C22⋊C4—24no—
892C22⋊C4—28no—
893C22⋊C4—28no—
894C22⋊C4—28no—
895C22⋊C4—28no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—48no—
906C22⋊C4—44no—
907C42—22no—
908C42—24no—
909C42—22no—
910C42—24no—
911C42—28no—
912C42—24no—
913C42—22no—
914C42—22no—
915C42—24no—
916C42—24no—
917C42—24no—
918C42—24no—
919C42—24no—
920C42—24no—
921C42—24no—
922C42—28no—
923C42—48no—
924C42—44no—
925C42—44no—
926C42—44no—
927C42—44no—
928C42—48no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—24no—
933C23—22no—
934C23—24no—
935C23—22no—
936C23—22no—
937C23—24no—
938C23—22no—
939C23—24no—
940C23C22×#4114yes—
941C23C22×#4112yes—
942C23C2×H(5,𝔽2)12yes—
943C23C2×2−1+412yes—
944C23C2611yescharacteristic
945Q8—28no—
946Q8—48no—
947Q8—48no—
948Q8—44no—
949Q8—816no—
950D4—216no—
951D4—28no—
952D4—416no—
953D4—48no—
954D4—44no—
955C2×C4—28no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—216no—
965C2×C4—22no—
966C2×C4—24no—
967C2×C4—22no—
968C2×C4—24no—
969C2×C4—22no—
970C2×C4—24no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—22no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—28no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—28no—
1003C2×C4—28no—
1004C2×C4—22no—
1005C2×C4—24no—
1006C2×C4—48no—
1007C2×C4—416no—
1008C2×C4—48no—
1009C2×C4—44no—
1010C2×C4—48no—
1011C2×C4—48no—
1012C2×C4—84no—
1013C2×C4—84no—
1014C2×C4—84no—
1015C2×C4—164no—
1016C2×C4—164no—
1017C2×C4—164no—
1018C2×C4#539116yes—
1019C2×C4C22×#4114yes—
1020C2×C4C22×#4112yes—
1021C2×C4C22×#4112yes—
1022C2×C4C2×H(5,𝔽2)12yes—
1023C2×C4C2×H(5,𝔽2)12yes—
1024C2×C4C2×2−1+414yes—
1025C2×C4C2×2−1+414yes—
1026C2×C4C2×2−1+414yes—
1027C2×C4C2×2−1+412yes—
1028C2×C4C2×2−1+412yes—
1029C22—24no—
1030C22—22no—
1031C22—22no—
1032C22—24no—
1033C22—28no—
1034C22—24no—
1035C22—42no—
1036C22—42no—
1037C22—44no—
1038C22—44no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—44no—
1043C22C2×#53914yes—
1044C22C23×#4111yescharacteristic
1045C22C22×H(5,𝔽2)11yescharacteristic
1046C22C22×2−1+412yes—
1047C22C22×2−1+411yescharacteristic
1048C22H(7,𝔽2)12yes—
1049C4—24no—
1050C4—24no—
1051C4—24no—
1052C4—24no—
1053C4—44no—
1054C4—42no—
1055C4—44no—
1056C4—42no—
1057C4—42no—
1058C4—42no—
1059C4—42no—
1060C4—44no—
1061C4—44no—
1062C4—44no—
1063C4—42no—
1064C4—42no—
1065C4—42no—
1066C4—44no—
1067C4—44no—
1068C4—44no—
1069C4C2×#53914yes—
1070C4C2×#53914yes—
1071C2—24no—
1072C2—44no—
1073C2—82no—
1074C2C22×#53911yescharacteristic
1075C2#6283311yescharacteristic
1076C2#6287611yescharacteristic
1077C2#6294312yes—
1078C2#6300012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42924C2semidirect
2. #42837C2semidirect
3. #42639C2semidirect
4. #42452C2semidirect
5. #40836C2semidirect
6. #40165C2semidirect
7. #39939C2semidirect
8. #39655C2semidirect
9. #39604C2semidirect
10. #38573C2semidirect
12. #35619C2semidirect
13. #35574C2semidirect
14. #35574C2semidirect
15. #35557C2semidirect
16. #35555C2semidirect
17. #35313C2semidirect
18. #35307C2semidirect
19. #35182C2semidirect
20. C2×#2567C2semidirect
21. #34815C2semidirect
23. #34266C2semidirect
25. #34183C2semidirect

Maximal subgroups

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

subgroupindex
#429242
#428372
#426392
#424522
#408362
#401652
#399392
#396552
#396042
#385732
#356212
#356192
#355742
#355572
#355552
#353132
#353072
#351822
C2×#25672
#348152
#347442
#342662
#342072
#341832