Finite Group Databasebeta

← #7651212

Subgroups — #7651212

Order 512.

4658 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42922C214yesmaximal, complemented
2#42830C214yesmaximal, complemented
3#42721C214yesmaximal, complemented
4#42451C214yesmaximal, complemented
5#40809C218yesmaximal, complemented
6#40215C214yesmaximal, complemented
7#39913C214yesmaximal, complemented
8#39524C214yesmaximal, complemented
9#38929C214yesmaximal, complemented
10#38145C218yesmaximal, complemented
11#35639C211yesmaximal, characteristic, complemented
12#35639C211yesmaximal, characteristic, complemented
13#35629C211yesmaximal, characteristic, complemented
14#35621C211yesmaximal, characteristic
15#35619C211yesmaximal, characteristic, complemented
16#35555C211yesmaximal, characteristic, complemented
17#35313C211yesmaximal, characteristic, complemented
18#35307C211yesmaximal, characteristic, complemented
19#35182C211yesmaximal, characteristic, complemented
20C2×#2565C211yesmaximal, characteristic, complemented
21#34815C211yesmaximal, characteristic, complemented
22#34744C211yesmaximal, characteristic
23#34266C211yesmaximal, characteristic, complemented
24#34207C211yesmaximal, characteristic
25#34184C211yesmaximal, characteristic, complemented
26C2×#536C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#532C2211yescharacteristic
29C22×#125C2211yescharacteristic
30C2×#520C2211yescharacteristic
31C2×#520C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35#2863C2214yes—
36#2855C2214yes—
37#2853C2214yes—
38#2836C2218yes—
39#2834C2218yes—
40#2807C2218yes—
41#2796C2218yes—
42#2787C2218yes—
43#2787C2218yes—
44#2786C2218yes—
45#2776C2218yes—
46#2769C2218yes—
47#2767C2218yes—
48#2765C2218yes—
49#2747C2218yes—
50#2744C2218yes—
51#2740C2218yes—
52#2739C2218yes—
53#2738C2218yes—
54#2726C2218yes—
55#2694C2218yes—
56#2655C2218yes—
57#2654C2218yes—
58#2654C2218yes—
59#2652C2218yes—
60#2646C2218yes—
61#2645C2214yes—
62#2633C2218yes—
63#2625C2214yes—
64#2623C2214yes—
65#2596C2218yes—
66#2590C2218yes—
67#2585C2218yes—
68#2579C2214yes—
69#2579C2214yes—
70#2570C2214yes—
71#2565C2214yes—
72#2565C2214yes—
73#2565C2214yes—
74#2565C2214yes—
75#2552C2214yes—
76#2547C2212yes—
77#2546C2212yes—
78#2545C2212yes—
79#2544C2212yes—
80#2514C2214yes—
81#2514C2214yes—
82#2513C2214yes—
83#2511C2214yes—
84#2510C2218yes—
85#2509C2212yes—
86#2508C2212yes—
87#2507C2214yes—
88#2507C2212yes—
89#2506C2214yes—
90#2506C2212yes—
91#2505C2214yes—
92#2503C2212yes—
93#2502C2212yes—
94#2499C2212yes—
95#2499C2212yes—
96#2495C2214yes—
97#2494C2214yes—
98#2493C2218yes—
99#2493C2218yes—
100#2487C2214yes—
101#2487C2214yes—
102#2473C2218yes—
103#2473C2214yes—
104#2460C2218yes—
105#2454C2214yes—
106#2454C2214yes—
107#2453C2214yes—
108#2453C2214yes—
109#2448C2212yes—
110#2448C2214yes—
111#2447C2214yes—
112#2447C2214yes—
113#2447C2212yes—
114#2446C2212yes—
115#2446C2214yes—
116#2446C2214yes—
117#2446C2214yes—
118#2445C2212yes—
119#2444C2214yes—
120#2443C2214yes—
121#2442C2214yes—
122#2442C2214yes—
123#2441C2214yes—
124#2441C2214yes—
125#2425C2218yes—
126#2423C2214yes—
127#2421C2214yes—
128#2419C2218yes—
129#2419C2218yes—
130#2419C2218yes—
131#2417C2214yes—
132#2415C2214yes—
133#2402C2214yes—
134#2395C2214yes—
135C2×#398C2214yes—
136#2367C2214yes—
137#2365C2214yes—
138#2362C2214yes—
139#2361C2218yes—
140#2360C2214yes—
141#2354C2214yes—
142#2351C2214yes—
143#2349C2218yes—
144#2349C2214yes—
145D4×C4⋊C4C2214yes—
146#2336C2218yes—
147#2326C2212yes—
148#2326C2212yes—
149#2322C2214yes—
150#2318C2218yes—
151#2317C2211yescharacteristic
152#2317C2211yescharacteristic
153#2317C2211yescharacteristic
154#2317C2212yes—
155#2317C2212yes—
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×#387C2214yes—
179#2285C2211yescharacteristic
180#2285C2212yes—
181C2×#384C2211yescharacteristic
182C2×#382C2212yes—
183C2×#382C2211yescharacteristic
184#2274C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190#536—28no—
191#536—44no—
192#532—28no—
193C2×C4⋊Q8C2311yescharacteristic
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×#127C2311yescharacteristic
197C2×#125—44no—
198C2×#125C2314yes—
199C2×#125C2314yes—
200C2×#125C2314yes—
201C2×#125C2318yes—
202C2×#124C2311yescharacteristic
203C2×#124C2311yescharacteristic
204C2×#124C2312yes—
205C2×#124C2312yes—
206C2×#123C2314yes—
207C2×#123C2314yes—
208C2×#123C2314yes—
209C2×C22⋊Q8C2314yes—
210C2×C22⋊Q8C2312yes—
211C2×C22⋊Q8C2312yes—
212C2×#121C2314yes—
213#520—44no—
214#520—44no—
215#520—44no—
216C4×#41—28no—
217C2×C4×Q8—44no—
218C2×C4×Q8C2312yes—
219C2×C4×Q8C2312yes—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2314yes—
222C2×C4×Q8C2314yes—
223C2×C4×Q8C2312yes—
224C2×C4×D4C2314yes—
225C2×C4×D4C2314yes—
226C2×C4×D4C2312yes—
227C2×C4×D4C2318yes—
228C2×C4×D4C2312yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2312yes—
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2312yes—
240C2×#117C2311yescharacteristic
241C2×#117C2312yes—
242C2×#117C2312yes—
243C2×#117C2312yes—
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2312yes—
248C22×C4⋊C4C2312yes—
249C22×C4⋊C4C2312yes—
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2312yes—
252C22×C4⋊C4C2312yes—
253C22×C4⋊C4C2314yes—
254C22×C4⋊C4C2312yes—
255C22×C42C2312yes—
256C22×C42C2311yescharacteristic
257C22×C42C2311yescharacteristic
258C22×C42C2311yescharacteristic
259C22×C42C2312yes—
260#401C2318yes—
261#401C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#400C2314yes—
266#400C2318yes—
267#400C2314yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2314yes—
274#400C2318yes—
275#400C2314yes—
276#400C2314yes—
277#399C2318yes—
278#399C2314yes—
279#399C2318yes—
280#399C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2314yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2314yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2314yes—
297#398C2314yes—
298#398C2314yes—
299#397C2314yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2314yes—
308#397C2314yes—
309#397C2318yes—
310#396C2318yes—
311#396C2318yes—
312#396C2318yes—
313#394C2314yes—
314#394C2318yes—
315#394C2314yes—
316#391C2312yes—
317#391C2312yes—
318#391C2312yes—
319#391C2312yes—
320#391C2312yes—
321#391C2312yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2312yes—
328#391C2312yes—
329#391C2312yes—
330#391C2312yes—
331#391C2312yes—
332#391C2312yes—
333#390C2312yes—
334#390C2312yes—
335#390C2318yes—
336#390C2312yes—
337#390C2312yes—
338#390C2312yes—
339#390C2312yes—
340#389C2314yes—
341#389C2314yes—
342#389C2318yes—
343#389C2312yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2318yes—
349#389C2314yes—
350#389C2314yes—
351#389C2318yes—
352#389C2314yes—
353#389C2318yes—
354#389C2318yes—
355#389C2318yes—
356#389C2318yes—
357#389C2318yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2314yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2314yes—
377#388C2318yes—
378#387C2314yes—
379#387C2314yes—
380#387C2314yes—
381#387C2314yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2314yes—
396#387C2318yes—
397#387C2318yes—
398#387C2314yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#386C2314yes—
405#386C2314yes—
406#386C2314yes—
407#386C2314yes—
408#386C2318yes—
409#386C2312yes—
410#386C2312yes—
411#386C2312yes—
412#386C2312yes—
413#386C2314yes—
414#385C2318yes—
415#385C2314yes—
416#385C2314yes—
417#385C2314yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2312yes—
422#385C2318yes—
423#385C2318yes—
424#385C2312yes—
425#385C2318yes—
426#385C2318yes—
427#385C2312yes—
428#385C2318yes—
429#385C2314yes—
430#385C2314yes—
431#385C2314yes—
432#385C2314yes—
433#385C2312yes—
434#384C2312yes—
435#384C2314yes—
436#384C2312yes—
437#384C2312yes—
438#384C2312yes—
439#384C2311yescharacteristic
440#384C2311yescharacteristic
441#384C2312yes—
442#383C2318yes—
443#383C2318yes—
444#382C2314yes—
445#382C2312yes—
446#382C2314yes—
447#382C2312yes—
448#382C2312yes—
449#382C2312yes—
450#382C2312yes—
451#382C2318yes—
452#382C2311yescharacteristic
453#382C2311yescharacteristic
454#381C2314yes—
455#381C2314yes—
456#381C2318yes—
457#381C2318yes—
458#381C2314yes—
459#380C2314yes—
460#380C2314yes—
461#380C2314yes—
462#380C2314yes—
463#380C2314yes—
464#380C2318yes—
465#380C2314yes—
466#380C2318yes—
467#380C2318yes—
468#380C2318yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2318yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2318yes—
482C4×C4⋊C4C2318yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C22⋊C4C2318yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2312yes—
494#376C2312yes—
495C2×#95C2318yes—
496C2×#95C2314yes—
497C2×#95C2314yes—
498C2×#95C2314yes—
499C2×#95C2312yes—
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×Q8C2412yes—
511C22×Q8C2412yes—
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×D4C2412yes—
515C22×D4C2411yescharacteristic
516C22×D4C2414yes—
517C22×D4C2412yes—
518C22×D4C2411yescharacteristic
519C23×C4C2412yes—
520C23×C4C2412yes—
521C23×C4C2412yes—
522C23×C4C2412yes—
523C23×C4C2411yescharacteristic
524C23×C4C2412yes—
525C23×C4C2412yes—
526C23×C4C2412yes—
527C23×C4C2411yescharacteristic
528C23×C4C2412yes—
529C23×C4C2414yes—
530C23×C4C2414yes—
531C23×C4C2414yes—
532C23×C4C2414yes—
533C23×C4C2411yescharacteristic
534C4⋊Q8—24no—
535C4⋊Q8—28no—
536C4⋊Q8—44no—
537#127—24no—
538#125—48no—
539#125—48no—
540#125—48no—
541#125—416no—
542#124—24no—
543#124—24no—
544#124—28no—
545#124—44no—
546#123—216no—
547#123—48no—
548#123—48no—
549C22⋊Q8—216no—
550C22⋊Q8—44no—
551C22⋊Q8—44no—
552#121—216no—
553C4×Q8—28no—
554C4×Q8—48no—
555C4×Q8—48no—
556C4×Q8—44no—
557C4×Q8—44no—
558C4×Q8—44no—
559C4×D4—216no—
560C4×D4—28no—
561C4×D4—216no—
562C4×D4—416no—
563C4×D4—44no—
564C4×D4—44no—
565C4×D4—44no—
566C4×D4—48no—
567C4×D4—48no—
568C4×D4—48no—
569#117—28no—
570#117—24no—
571#117—24no—
572#117—24no—
573#117—24no—
574#117—24no—
575#117—24no—
576#117—44no—
577#117—44no—
578#117—44no—
579C2×C4⋊C4—24no—
580C2×C4⋊C4—24no—
581C2×C4⋊C4—24no—
582C2×C4⋊C4—48no—
583C2×C4⋊C4—44no—
584C2×C4⋊C4—44no—
585C2×C4⋊C4—44no—
586C2×C4⋊C4—44no—
587C2×C4⋊C4—44no—
588C2×C4⋊C4—44no—
589C2×C4⋊C4—44no—
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2418yes—
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⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2418yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2418yes—
662C2×C42—28no—
663C2×C42—24no—
664C2×C42—24no—
665C2×C42—24no—
666C2×C42—44no—
667C2×C42C2412yes—
668C2×C42C2411yescharacteristic
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2412yes—
673C2×C42C2412yes—
674C2×C42C2414yes—
675C2×C42C2412yes—
676C2×C42C2412yes—
677C2×C42C2414yes—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2414yes—
684C2×C42C2414yes—
685C2×C42C2414yes—
686C2×C42C2418yes—
687C2×C42C2418yes—
688C2×C42C2414yes—
689#95C2414yes—
690#95C2418yes—
691#95C2412yes—
692#95C2412yes—
693#95C2412yes—
694#95C2412yes—
695#95C2418yes—
696#95C2418yes—
697#95C2418yes—
698#95C2418yes—
699#95C2418yes—
700#95C2418yes—
701#95C2418yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2418yes—
706#95C2414yes—
707#95C2418yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2418yes—
716#95C2418yes—
717#95C2414yes—
718#95C2414yes—
719#95C2418yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732C24C2512yes—
733C24C2512yes—
734C24C2511yescharacteristic
735#41—232no—
736#41—416no—
737C2×Q8—24no—
738C2×Q8—24no—
739C2×Q8—22no—
740C2×Q8—22no—
741C2×Q8—24no—
742C2×Q8—24no—
743C2×Q8—22no—
744C2×Q8—22no—
745C2×Q8—24no—
746C2×Q8—24no—
747C2×Q8—22no—
748C2×Q8—416no—
749C2×Q8C2×#4114yes—
750C2×D4—24no—
751C2×D4—24no—
752C2×D4—28no—
753C2×D4—24no—
754C2×D4—24no—
755C2×D4—24no—
756C2×D4—22no—
757C2×D4—22no—
758C2×D4—22no—
759C2×D4—22no—
760C2×D4—22no—
761C2×D4—28no—
762C2×D4—44no—
763C2×D4C2×#4118yes—
764C2×D4C2×#4114yes—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—28no—
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—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—44no—
786C22×C4—42no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—42no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—48no—
796C22×C4—48no—
797C22×C4—48no—
798C22×C4C2×#4118yes—
799C22×C4C2×#4114yes—
800C22×C4H(5,𝔽2)14yes—
801C22×C42−1+414yes—
802C22×C4C2512yes—
803C22×C4C2514yes—
804C22×C4C2514yes—
805C22×C4C2514yes—
806C22×C4C2512yes—
807C22×C4C2512yes—
808C22×C4C2512yes—
809C22×C4C2514yes—
810C22×C4C2512yes—
811C22×C4C2512yes—
812C22×C4C2514yes—
813C22×C4C2512yes—
814C22×C4C2514yes—
815C22×C4C2512yes—
816C22×C4C2514yes—
817C22×C4C2514yes—
818C22×C4C2512yes—
819C22×C4C2512yes—
820C22×C4C2512yes—
821C22×C4C2512yes—
822C22×C4C2511yescharacteristic
823C22×C4C2511yescharacteristic
824C4⋊C4—28no—
825C4⋊C4—24no—
826C4⋊C4—24no—
827C4⋊C4—28no—
828C4⋊C4—216no—
829C4⋊C4—24no—
830C4⋊C4—24no—
831C4⋊C4—24no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—24no—
835C4⋊C4—22no—
836C4⋊C4—22no—
837C4⋊C4—22no—
838C4⋊C4—22no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—216no—
842C4⋊C4—24no—
843C4⋊C4—24no—
844C4⋊C4—28no—
845C4⋊C4—28no—
846C4⋊C4—48no—
847C4⋊C4—42no—
848C4⋊C4—42no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—44no—
852C4⋊C4—48no—
853C4⋊C4—48no—
854C4⋊C4—48no—
855C4⋊C4—44no—
856C4⋊C4—48no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—48no—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—48no—
870C4⋊C4—48no—
871C4⋊C4—48no—
872C22⋊C4—28no—
873C22⋊C4—24no—
874C22⋊C4—24no—
875C22⋊C4—28no—
876C22⋊C4—216no—
877C22⋊C4—24no—
878C22⋊C4—24no—
879C22⋊C4—24no—
880C22⋊C4—24no—
881C22⋊C4—28no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—48no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—48no—
890C22⋊C4—48no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C42—22no—
897C42—24no—
898C42—22no—
899C42—24no—
900C42—28no—
901C42—24no—
902C42—22no—
903C42—22no—
904C42—24no—
905C42—24no—
906C42—24no—
907C42—24no—
908C42—24no—
909C42—24no—
910C42—24no—
911C42—28no—
912C42—48no—
913C42—44no—
914C42—44no—
915C42—44no—
916C42—44no—
917C42—48no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—24no—
923C23—24no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—24no—
928C23—24no—
929C23C22×#4114yes—
930C23C22×#4112yes—
931C23C2×H(5,𝔽2)12yes—
932C23C2×2−1+412yes—
933C23C2611yescharacteristic
934Q8—28no—
935Q8—48no—
936Q8—48no—
937Q8—44no—
938D4—216no—
939D4—28no—
940D4—416no—
941D4—48no—
942D4—44no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—216no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—24no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—22no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—28no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—24no—
978C2×C4—28no—
979C2×C4—24no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—24no—
991C2×C4—28no—
992C2×C4—22no—
993C2×C4—24no—
994C2×C4—22no—
995C2×C4—48no—
996C2×C4—44no—
997C2×C4—44no—
998C2×C4—48no—
999C2×C4—48no—
1000C2×C4—84no—
1001C2×C4—88no—
1002C2×C4—84no—
1003C2×C4—84no—
1004C2×C4—84no—
1005C2×C4—164no—
1006C2×C4—164no—
1007C2×C4—164no—
1008C2×C4#539116yes—
1009C2×C4C22×#4114yes—
1010C2×C4C22×#4112yes—
1011C2×C4C22×#4112yes—
1012C2×C4C2×H(5,𝔽2)12yes—
1013C2×C4C2×H(5,𝔽2)12yes—
1014C2×C4C2×2−1+412yes—
1015C2×C4C2×2−1+412yes—
1016C2×C4#58514yes—
1017C22—24no—
1018C22—22no—
1019C22—22no—
1020C22—24no—
1021C22—28no—
1022C22—24no—
1023C22—42no—
1024C22—42no—
1025C22—44no—
1026C22—44no—
1027C22—42no—
1028C22—42no—
1029C22—42no—
1030C22—44no—
1031C22C2×#53914yes—
1032C22C23×#4111yescharacteristic
1033C22C22×H(5,𝔽2)11yescharacteristic
1034C22C22×2−1+411yescharacteristic
1035C22C2×#58512yes—
1036C222−1+612yes—
1037C4—24no—
1038C4—24no—
1039C4—44no—
1040C4—42no—
1041C4—44no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—42no—
1046C4—44no—
1047C4—44no—
1048C4—42no—
1049C4—42no—
1050C4—42no—
1051C4—44no—
1052C4—42no—
1053C4—42no—
1054C4—44no—
1055C4—44no—
1056C4—44no—
1057C4C2×#53914yes—
1058C4C2×#53914yes—
1059C2—24no—
1060C2—44no—
1061C2—82no—
1062C2C22×#53911yescharacteristic
1063C2#6283611yescharacteristic
1064C2#6288711yescharacteristic
1065C2#6295612yes—
1066C2#6299312yes—
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. #42922C2semidirect
2. #42830C2semidirect
3. #42721C2semidirect
4. #42451C2semidirect
5. #40809C2semidirect
6. #40215C2semidirect
7. #39913C2semidirect
8. #39524C2semidirect
9. #38929C2semidirect
10. #38145C2semidirect
11. #35639C2semidirect
12. #35639C2semidirect
13. #35629C2semidirect
15. #35619C2semidirect
16. #35555C2semidirect
17. #35313C2semidirect
18. #35307C2semidirect
19. #35182C2semidirect
20. C2×#2565C2semidirect
21. #34815C2semidirect
23. #34266C2semidirect
25. #34184C2semidirect

Maximal subgroups

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

subgroupindex
#429222
#428302
#427212
#424512
#408092
#402152
#399132
#395242
#389292
#381452
#356392
#356292
#356212
#356192
#355552
#353132
#353072
#351822
C2×#25652
#348152
#347442
#342662
#342072
#341842