Finite Group Databasebeta

← #7683747

Subgroups — #7683747

Order 512.

4968 conjugacy classes of subgroups.

The subgroup lattice has 1069 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59951C212yesmaximal, complemented
2#59948C214yesmaximal, complemented
3#59935C212yesmaximal, complemented
4#59908C212yesmaximal, complemented
5#59869C212yesmaximal, complemented
6#59564C214yesmaximal, complemented
7#59427C214yesmaximal, complemented
8#59339C214yesmaximal, complemented
9#45436C212yesmaximal, complemented
10#45410C212yesmaximal, complemented
11#45384C212yesmaximal, complemented
12#45369C212yesmaximal, complemented
13#45170C214yesmaximal, complemented
14#45151C214yesmaximal, complemented
15#43688C214yesmaximal, complemented
16#43621C214yesmaximal, complemented
17#35667C212yesmaximal, complemented
18#35628C212yesmaximal, complemented
19#35621C212yesmaximal
20#34955C211yesmaximal, characteristic
21#34953C211yesmaximal, characteristic, complemented
22C2×#2568C211yesmaximal, characteristic, complemented
23#34276C212yesmaximal, complemented
24#34254C212yesmaximal, complemented
25#34252C212yesmaximal, complemented
26C2×#536C2212yes—
27C2×#536C2212yes—
28C2×#533C2211yescharacteristic
29C2×#532C2211yescharacteristic
30C22×C4⋊Q8C2211yescharacteristic
31C2×#520C2212yes—
32C2×#519C2212yes—
33C22×C4×Q8C2211yescharacteristic
34#2809C2214yes—
35#2809C2214yes—
36#2795C2214yes—
37#2785C2214yes—
38#2784C2214yes—
39#2783C2218yes—
40#2783C2218yes—
41#2781C2218yes—
42#2775C2218yes—
43#2775C2218yes—
44#2769C2214yes—
45#2769C2214yes—
46#2769C2218yes—
47#2744C2218yes—
48#2744C2218yes—
49#2731C2214yes—
50#2612C2214yes—
51#2612C2218yes—
52#2612C2214yes—
53#2609C2214yes—
54#2593C2214yes—
55#2592C2214yes—
56#2592C2212yes—
57#2592C2214yes—
58#2592C2212yes—
59#2591C2212yes—
60#2591C2212yes—
61#2584C2212yes—
62#2584C2212yes—
63#2583C2212yes—
64#2583C2212yes—
65#2574C2218yes—
66#2574C2218yes—
67#2572C2214yes—
68#2571C2214yes—
69#2568C2212yes—
70#2568C2212yes—
71#2568C2212yes—
72#2568C2214yes—
73#2568C2214yes—
74#2568C2212yes—
75#2568C2212yes—
76#2568C2212yes—
77#2568C2212yes—
78#2568C2211yescharacteristic
79#2568C2212yes—
80#2568C2211yescharacteristic
81#2567C2211yescharacteristic
82#2567C2211yescharacteristic
83#2548C2211yescharacteristic
84#2548C2211yescharacteristic
85#2547C2214yes—
86#2546C2214yes—
87#2546C2214yes—
88#2546C2211yescharacteristic
89#2546C2211yescharacteristic
90#2546C2214yes—
91#2545C2214yes—
92#2545C2214yes—
93#2545C2214yes—
94#2544C2214yes—
95#2532C2218yes—
96#2532C2218yes—
97#2529C2218yes—
98#2529C2218yes—
99#2526C2218yes—
100#2518C2218yes—
101#2508C2218yes—
102#2508C2218yes—
103#2504C2212yes—
104#2502C2212yes—
105#2497C2218yes—
106#2495C2218yes—
107#2492C2214yes—
108#2492C2214yes—
109#2489C2214yes—
110#2489C2214yes—
111#2488C2218yes—
112#2488C2218yes—
113#2474C2218yes—
114#2439C2218yes—
115#2436C2212yes—
116#2434C2212yes—
117#2429C2214yes—
118#2429C2214yes—
119#2429C2214yes—
120#2429C2214yes—
121#2425C2218yes—
122#2425C2218yes—
123#2417C2214yes—
124#2417C2214yes—
125#2415C2214yes—
126#2415C2214yes—
127#2413C2218yes—
128#2413C2218yes—
129#2399C2212yes—
130#2399C2212yes—
131#2398C2212yes—
132#2398C2212yes—
133C2×#400C2212yes—
134C2×#400C2212yes—
135#2372C2214yes—
136#2369C2214yes—
137#2362C2214yes—
138#2362C2214yes—
139#2360C2214yes—
140#2360C2214yes—
141#2359C2218yes—
142#2359C2218yes—
143#2357C2214yes—
144#2356C2214yes—
145#2356C2214yes—
146#2356C2214yes—
147#2355C2214yes—
148#2355C2214yes—
149#2355C2214yes—
150#2354C2214yes—
151#2347C2214yes—
152#2346C2218yes—
153#2346C2214yes—
154#2345C2214yes—
155#2344C2214yes—
156#2343C2218yes—
157#2343C2218yes—
158#2327C2214yes—
159#2326C2214yes—
160#2320C2214yes—
161#2320C2214yes—
162#2318C2218yes—
163#2317C2212yes—
164#2311C2212yes—
165#2310C2212yes—
166C4×C4⋊Q8C2212yes—
167C4×C4⋊Q8C2212yes—
168C4×C4⋊Q8C2214yes—
169C4×#124C2214yes—
170C4×#124C2212yes—
171C4×#124C2212yes—
172#2297C2212yes—
173#2297C2212yes—
174#2296C2212yes—
175#2296C2212yes—
176#2295C2214yes—
177#2295C2214yes—
178C2×#391C2212yes—
179C2×#391C2212yes—
180C2×#391C2212yes—
181#2290C2218yes—
182C2×#382C2212yes—
183#2274C2212yes—
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2312yes—
188C23×Q8C2312yes—
189C23×Q8C2311yescharacteristic
190#536—216no—
191#536—48no—
192#533—44no—
193#532—44no—
194C2×C4⋊Q8—44no—
195C2×C4⋊Q8C2314yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2311yescharacteristic
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2314yes—
205C2×C4⋊Q8C2311yescharacteristic
206C2×#127C2311yescharacteristic
207C2×#125C2312yes—
208C2×#124C2314yes—
209C2×#124C2312yes—
210C2×#124C2312yes—
211C2×#124C2314yes—
212C2×#124C2312yes—
213C2×#123C2318yes—
214C2×#123C2318yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2312yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2312yes—
221C2×#121C2312yes—
222C2×#121C2312yes—
223#520—216no—
224#519—216no—
225C2×C4×Q8—44no—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2312yes—
241C2×C4×D4C2318yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2312yes—
245C2×#117C2312yes—
246C2×#117C2312yes—
247C2×#117C2318yes—
248C2×#117C2314yes—
249C2×#117C2318yes—
250C2×#117C2312yes—
251C22×C4⋊C4C2312yes—
252C22×C4⋊C4C2314yes—
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2312yes—
258C22×C42C2311yescharacteristic
259C22×C42C2311yescharacteristic
260C22×C42C2311yescharacteristic
261C22×C42C2312yes—
262#400C2314yes—
263#400C2314yes—
264#400C2314yes—
265#400C2314yes—
266#400C2314yes—
267#400C2314yes—
268#400C2314yes—
269#400C2314yes—
270#400C2312yes—
271#400C2318yes—
272#400C2312yes—
273#400C2312yes—
274#400C2312yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#398C2318yes—
279#398C2312yes—
280#398C2312yes—
281#398C2312yes—
282#398C2312yes—
283#398C2314yes—
284#398C2314yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#397C2314yes—
291#397C2314yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#396C2318yes—
297#396C2318yes—
298#396C2318yes—
299#396C2318yes—
300#396C2318yes—
301#396C2318yes—
302#395C2312yes—
303#395C2312yes—
304#395C2312yes—
305#395C2312yes—
306#395C2314yes—
307#395C2314yes—
308#394C2312yes—
309#394C2312yes—
310#394C2312yes—
311#394C2312yes—
312#394C2318yes—
313#394C2318yes—
314#393C2318yes—
315#393C2314yes—
316#393C2318yes—
317#393C2314yes—
318#391C2312yes—
319#391C2312yes—
320#391C2312yes—
321#391C2314yes—
322#391C2312yes—
323#391C2312yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2314yes—
328#391C2314yes—
329#391C2314yes—
330#391C2312yes—
331#391C2314yes—
332#391C2314yes—
333#391C2314yes—
334#391C2314yes—
335#391C2314yes—
336#391C2314yes—
337#391C2314yes—
338#391C2314yes—
339#391C2314yes—
340#391C2314yes—
341#391C2318yes—
342#391C2312yes—
343#391C2312yes—
344#391C2312yes—
345#391C2312yes—
346#391C2318yes—
347#390C2314yes—
348#390C2312yes—
349#390C2312yes—
350#390C2312yes—
351#390C2312yes—
352#390C2312yes—
353#390C2312yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2318yes—
359#389C2318yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2318yes—
365#389C2318yes—
366#389C2314yes—
367#389C2314yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2318yes—
373#389C2318yes—
374#389C2318yes—
375#389C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2314yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2314yes—
386#388C2314yes—
387#388C2314yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
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#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#386C2318yes—
415#386C2318yes—
416#386C2314yes—
417#386C2314yes—
418#386C2314yes—
419#386C2314yes—
420#386C2318yes—
421#385C2318yes—
422#385C2314yes—
423#385C2318yes—
424#385C2318yes—
425#385C2314yes—
426#385C2314yes—
427#385C2314yes—
428#384C2312yes—
429#384C2312yes—
430#384C2314yes—
431#383C2318yes—
432#383C2318yes—
433#383C2318yes—
434#382C2314yes—
435#382C2314yes—
436#382C2314yes—
437#382C2314yes—
438#382C2318yes—
439#382C2318yes—
440#382C2312yes—
441#382C2312yes—
442#382C2318yes—
443#382C2318yes—
444#382C2314yes—
445#382C2318yes—
446#381C2318yes—
447#381C2318yes—
448#380C2314yes—
449#380C2314yes—
450#380C2318yes—
451#380C2318yes—
452#380C2318yes—
453C4×C4⋊C4C2318yes—
454C4×C4⋊C4C2318yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2318yes—
470C4×C4⋊C4C2318yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2318yes—
476C4×C22⋊C4C2318yes—
477C4×C22⋊C4C2318yes—
478C4×C22⋊C4C2318yes—
479C4×C22⋊C4C2312yes—
480C4×C22⋊C4C2312yes—
481C4×C22⋊C4C2312yes—
482C4×C22⋊C4C2314yes—
483C4×C22⋊C4C2314yes—
484C4×C22⋊C4C2318yes—
485C4×C22⋊C4C2312yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488#376C2312yes—
489#376C2312yes—
490#376C2318yes—
491#376C2318yes—
492#376C2318yes—
493C2×#95C2312yes—
494C2×#95C2314yes—
495C2×#95C2314yes—
496C2×#95C2314yes—
497C2×#95C2314yes—
498C43C2312yes—
499C43C2312yes—
500C2×#41—28no—
501C2×#41—28no—
502C2×#41—28no—
503C22×Q8—24no—
504C22×Q8—28no—
505C22×Q8—28no—
506C22×Q8—28no—
507C22×Q8—42no—
508C22×Q8—42no—
509C22×Q8C2414yes—
510C22×Q8C2414yes—
511C22×Q8C2412yes—
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×Q8C2412yes—
516C22×Q8C2412yes—
517C22×Q8C2411yescharacteristic
518C22×D4C2414yes—
519C22×D4C2412yes—
520C22×D4C2412yes—
521C22×D4C2412yes—
522C23×C4C2411yescharacteristic
523C23×C4C2414yes—
524C23×C4C2414yes—
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2418yes—
531C23×C4C2414yes—
532C23×C4C2411yescharacteristic
533C4⋊Q8—28no—
534C4⋊Q8—216no—
535C4⋊Q8—42no—
536C4⋊Q8—42no—
537C4⋊Q8—44no—
538C4⋊Q8—44no—
539C4⋊Q8—44no—
540C4⋊Q8—44no—
541C4⋊Q8—42no—
542C4⋊Q8—48no—
543C4⋊Q8—44no—
544#127—42no—
545#125—44no—
546#124—28no—
547#124—216no—
548#124—44no—
549#124—48no—
550#124—44no—
551#123—232no—
552#123—416no—
553C22⋊Q8—216no—
554C22⋊Q8—216no—
555C22⋊Q8—44no—
556C22⋊Q8—44no—
557C22⋊Q8—48no—
558C22⋊Q8—48no—
559#121—44no—
560#121—44no—
561C4×Q8—216no—
562C4×Q8—216no—
563C4×Q8—216no—
564C4×Q8—216no—
565C4×Q8—216no—
566C4×Q8—42no—
567C4×Q8—42no—
568C4×Q8—42no—
569C4×Q8—42no—
570C4×Q8—42no—
571C4×Q8—42no—
572C4×Q8—42no—
573C4×Q8—42no—
574C4×Q8—44no—
575C4×Q8—44no—
576C4×D4—232no—
577C4×D4—216no—
578C4×D4—44no—
579C4×D4—44no—
580#117—28no—
581#117—28no—
582#117—216no—
583#117—232no—
584#117—416no—
585#117#41116yes—
586C2×C4⋊C4—28no—
587C2×C4⋊C4—216no—
588C2×C4⋊C4—42no—
589C2×C4⋊C4—42no—
590C2×C4⋊C4—42no—
591C2×C4⋊C4—44no—
592C2×C4⋊C4—44no—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C42—24no—
661C2×C42—24no—
662C2×C42—24no—
663C2×C42—44no—
664C2×C42C2414yes—
665C2×C42C2418yes—
666C2×C42C2414yes—
667C2×C42C2414yes—
668C2×C42C2418yes—
669C2×C42C2418yes—
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2418yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2414yes—
688C2×C42C2414yes—
689C2×C42C2418yes—
690C2×C42C2414yes—
691C2×C42C2414yes—
692#95C2418yes—
693#95C2418yes—
694#95C2418yes—
695#95C2418yes—
696#95C2414yes—
697#95C2414yes—
698#95C2418yes—
699#95C2418yes—
700#95C2418yes—
701#95C2418yes—
702#95C2418yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2418yes—
708#95C2412yes—
709#95C2414yes—
710#95C2412yes—
711#95C2412yes—
712#95C2414yes—
713#95C2412yes—
714#95C2418yes—
715#95C2418yes—
716#95C2418yes—
717#95C2414yes—
718#95C2418yes—
719#95C2418yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2418yes—
728#95C2414yes—
729#95C2418yes—
730#95C2418yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734C24C2514yes—
735C24C2511yescharacteristic
736#41—432no—
737C2×Q8—28no—
738C2×Q8—28no—
739C2×Q8—24no—
740C2×Q8—28no—
741C2×Q8—28no—
742C2×Q8—24no—
743C2×Q8—28no—
744C2×Q8—28no—
745C2×Q8—24no—
746C2×Q8—22no—
747C2×Q8—22no—
748C2×Q8—22no—
749C2×Q8—24no—
750C2×Q8—22no—
751C2×Q8—22no—
752C2×Q8—41no—
753C2×Q8—41no—
754C2×Q8—41no—
755C2×Q8—41no—
756C2×Q8—41no—
757C2×Q8—41no—
758C2×Q8—42no—
759C2×Q8—42no—
760C2×Q8—42no—
761C2×Q8—44no—
762C2×Q8—416no—
763C2×Q8—432no—
764C2×Q82−1+414yes—
765C2×D4—28no—
766C2×D4—28no—
767C2×D4—28no—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—24no—
771C2×D4—24no—
772C2×D4—42no—
773C2×D4—42no—
774C2×D4—42no—
775C2×D4—44no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—28no—
780C22×C4—28no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—28no—
785C22×C4—28no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—28no—
789C22×C4—28no—
790C22×C4—28no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—216no—
794C22×C4—42no—
795C22×C4—41no—
796C22×C4—41no—
797C22×C4—44no—
798C22×C4—48no—
799C22×C4—48no—
800C22×C4—42no—
801C22×C4—42no—
802C22×C4—44no—
803C22×C4C2×#4118yes—
804C22×C4H(5,𝔽2)14yes—
805C22×C4C2514yes—
806C22×C4C2518yes—
807C22×C4C2511yescharacteristic
808C22×C4C2511yescharacteristic
809C22×C4C2511yescharacteristic
810C22×C4C2511yescharacteristic
811C22×C4C2514yes—
812C22×C4C2511yescharacteristic
813C22×C4C2511yescharacteristic
814C22×C4C2514yes—
815C22×C4C2514yes—
816C22×C4C2511yescharacteristic
817C22×C4C2511yescharacteristic
818C22×C4C2518yes—
819C22×C4C2514yes—
820C22×C4C2514yes—
821C22×C4C2514yes—
822C22×C4C2511yescharacteristic
823C22×C4C2511yescharacteristic
824C22×C4C2511yescharacteristic
825C22×C4C2511yescharacteristic
826C22×C4C2511yescharacteristic
827C22×C4C2511yescharacteristic
828C4⋊C4—28no—
829C4⋊C4—216no—
830C4⋊C4—28no—
831C4⋊C4—24no—
832C4⋊C4—24no—
833C4⋊C4—216no—
834C4⋊C4—216no—
835C4⋊C4—216no—
836C4⋊C4—216no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—28no—
840C4⋊C4—28no—
841C4⋊C4—28no—
842C4⋊C4—41no—
843C4⋊C4—41no—
844C4⋊C4—41no—
845C4⋊C4—41no—
846C4⋊C4—41no—
847C4⋊C4—41no—
848C4⋊C4—41no—
849C4⋊C4—41no—
850C4⋊C4—41no—
851C4⋊C4—41no—
852C4⋊C4—41no—
853C4⋊C4—41no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—48no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4—44no—
863C4⋊C4—48no—
864C4⋊C4—42no—
865C4⋊C4—42no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—42no—
869C4⋊C4—42no—
870C4⋊C4—48no—
871C4⋊C4—48no—
872C4⋊C4—44no—
873C4⋊C4C2×#4118yes—
874C4⋊C4C2×#4118yes—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—216no—
878C22⋊C4—216no—
879C22⋊C4—216no—
880C22⋊C4—28no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C22⋊C4—44no—
894C22⋊C4C2×#41116yes—
895C42—216no—
896C42—28no—
897C42—216no—
898C42—216no—
899C42—22no—
900C42—22no—
901C42—22no—
902C42—22no—
903C42—22no—
904C42—22no—
905C42—22no—
906C42—22no—
907C42—22no—
908C42—22no—
909C42—22no—
910C42—22no—
911C42—28no—
912C42—24no—
913C42—24no—
914C42—28no—
915C42—44no—
916C42—44no—
917C42—44no—
918C42—48no—
919C42—48no—
920C42—42no—
921C42—42no—
922C42C2×#41116yes—
923C23—21no—
924C23—21no—
925C23—22no—
926C23—24no—
927C23—24no—
928C23—24no—
929C23—24no—
930C23—24no—
931C23—24no—
932C23—24no—
933C23C22×#4114yes—
934C23C2×H(5,𝔽2)12yes—
935C23C2611yescharacteristic
936Q8—44no—
937Q8—44no—
938Q8—44no—
939Q8—44no—
940Q8—416no—
941Q8—416no—
942Q8—48no—
943Q8—84no—
944Q8—84no—
945D4—416no—
946D4—48no—
947D4—84no—
948D4—84no—
949C2×C4—28no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—24no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—28no—
966C2×C4—28no—
967C2×C4—28no—
968C2×C4—24no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—28no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—28no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—24no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—28no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—24no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—44no—
1002C2×C4—44no—
1003C2×C4—44no—
1004C2×C4—416no—
1005C2×C4—416no—
1006C2×C4—816no—
1007C2×C4—88no—
1008C2×C4—82no—
1009C2×C4—82no—
1010C2×C4#555116yes—
1011C2×C4C22×#4118yes—
1012C2×C4C22×#4118yes—
1013C2×C4C22×#4114yes—
1014C2×C4C22×#4114yes—
1015C2×C4C2×H(5,𝔽2)12yes—
1016C2×C4C2×H(5,𝔽2)12yes—
1017C2×C4C2×2−1+412yes—
1018C2×C4C2×2−1+412yes—
1019C2×C4C2×2−1+412yes—
1020C2×C4#58512yes—
1021C22—24no—
1022C22—24no—
1023C22—22no—
1024C22—22no—
1025C22—44no—
1026C22—44no—
1027C22—44no—
1028C22—44no—
1029C22—44no—
1030C22—44no—
1031C22—44no—
1032C22C2×#55514yes—
1033C22C23×#4112yes—
1034C22C22×H(5,𝔽2)11yescharacteristic
1035C22C22×2−1+411yescharacteristic
1036C22C2×#58511yescharacteristic
1037C222−1+612yes—
1038C4—28no—
1039C4—28no—
1040C4—22no—
1041C4—22no—
1042C4—22no—
1043C4—22no—
1044C4—44no—
1045C4—48no—
1046C4—44no—
1047C4—41no—
1048C4—41no—
1049C4—44no—
1050C4—41no—
1051C4—41no—
1052C4—41no—
1053C4—41no—
1054C4—41no—
1055C4—41no—
1056C4—44no—
1057C4—44no—
1058C4—48no—
1059C4C2×#55514yes—
1060C4C2×#55514yes—
1061C2—24no—
1062C2—84no—
1063C2C22×#55511yescharacteristic
1064C2#6281911yescharacteristic
1065C2#6288611yescharacteristic
1066C2#6299512yes—
1067C2#6300112yes—
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. #59951C2semidirect
2. #59948C2semidirect
3. #59935C2semidirect
4. #59908C2semidirect
5. #59869C2semidirect
6. #59564C2semidirect
7. #59427C2semidirect
8. #59339C2semidirect
9. #45436C2semidirect
10. #45410C2semidirect
11. #45384C2semidirect
12. #45369C2semidirect
13. #45170C2semidirect
14. #45151C2semidirect
15. #43688C2semidirect
16. #43621C2semidirect
17. #35667C2semidirect
18. #35628C2semidirect
21. #34953C2semidirect
22. C2×#2568C2semidirect
23. #34276C2semidirect
24. #34254C2semidirect
25. #34252C2semidirect

Maximal subgroups

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

subgroupindex
#599512
#599482
#599352
#599082
#598692
#595642
#594272
#593392
#454362
#454102
#453842
#453692
#451702
#451512
#436882
#436212
#356672
#356282
#356212
#349552
#349532
C2×#25682
#342762
#342542
#342522