Finite Group Databasebeta

← #7643394

Subgroups — #7643394

Order 512.

5616 conjugacy classes of subgroups.

The subgroup lattice has 1183 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40100C214yesmaximal, complemented
2#40076C214yesmaximal, complemented
3#39659C214yesmaximal, complemented
4#39528C214yesmaximal, complemented
5#38605C218yesmaximal, complemented
6#37909C218yesmaximal, complemented
7#37398C214yesmaximal, complemented
8#37338C214yesmaximal, complemented
9#36626C211yesmaximal, characteristic, complemented
10C2×#2857C211yesmaximal, characteristic, complemented
11#35674C211yesmaximal, characteristic, complemented
12#35666C211yesmaximal, characteristic, complemented
13#35661C211yesmaximal, characteristic, complemented
14#35659C211yesmaximal, characteristic
15#35644C211yesmaximal, characteristic, complemented
16#35633C211yesmaximal, characteristic, complemented
17#35557C211yesmaximal, characteristic, complemented
18#35532C211yesmaximal, characteristic, complemented
19#35313C211yesmaximal, characteristic, complemented
20#35312C211yesmaximal, characteristic, complemented
21#35036C214yesmaximal, complemented
22#35016C214yesmaximal, complemented
23#34268C211yesmaximal, characteristic, complemented
24#34259C211yesmaximal, characteristic, complemented
25C4×#525C211yesmaximal, characteristic, complemented
26C22×2−1+4C2211yescharacteristic
27C2×#544C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C22×C4⋊Q8C2211yescharacteristic
31C2×#525C2211yescharacteristic
32C2×#525C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C22×C22⋊Q8C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×C4×#41C2211yescharacteristic
38C23×C42C2211yescharacteristic
39#2863C2214yescomplemented
40#2862C2212yescomplemented
41#2861C2212yescomplemented
42#2857C2214yes—
43#2857C2214yes—
44#2857C2214yes—
45#2857C2214yes—
46#2855C2212yes—
47#2855C2212yes—
48#2854C2212yes—
49#2854C2212yes—
50#2853C2214yes—
51#2849C2214yes—
52#2805C2218yescomplemented
53#2788C2218yes—
54#2788C2218yescomplemented
55#2787C2218yescomplemented
56#2784C2218yes—
57#2779C2218yescomplemented
58#2778C2218yes—
59#2774C2218yescomplemented
60#2771C2218yescomplemented
61#2765C2218yescomplemented
62#2750C2218yes—
63#2745C2218yes—
64#2743C2218yes—
65#2702C2218yescomplemented
66#2696C2218yes—
67#2695C2218yes—
68#2666C2218yescomplemented
69#2665C2218yes—
70#2649C2218yescomplemented
71#2645C2214yescomplemented
72#2642C2212yescomplemented
73#2640C2212yescomplemented
74#2630C2218yes—
75#2587C2218yescomplemented
76#2586C2218yescomplemented
77#2578C2218yes—
78#2574C2218yes—
79#2567C2212yescomplemented
80#2566C2212yescomplemented
81#2565C2212yescomplemented
82#2561C2214yes—
83#2542C2212yescomplemented
84#2538C2214yes—
85#2536C2214yes—
86#2534C2214yes—
87#2518C2218yescomplemented
88#2514C2214yescomplemented
89#2512C2214yescomplemented
90#2511C2214yescomplemented
91#2511C2214yescomplemented
92#2505C2218yescomplemented
93#2503C2214yes—
94#2497C2214yescomplemented
95#2496C2214yescomplemented
96#2493C2218yes—
97#2492C2214yes—
98#2492C2214yes—
99#2492C2214yescomplemented
100#2489C2214yes—
101#2489C2214yes—
102#2489C2214yescomplemented
103#2488C2218yes—
104#2486C2214yes—
105#2484C2218yes—
106#2481C2218yes—
107#2467C2218yes—
108#2450C2218yes—
109#2449C2218yes—
110#2446C2214yescomplemented
111#2446C2214yescomplemented
112#2446C2214yescomplemented
113#2446C2214yescomplemented
114#2441C2214yescomplemented
115#2440C2214yescomplemented
116#2434C2214yescomplemented
117#2434C2212yescomplemented
118#2434C2212yescomplemented
119#2432C2212yescomplemented
120#2432C2212yescomplemented
121#2432C2214yescomplemented
122#2429C2214yes—
123#2429C2214yes—
124#2427C2214yes—
125#2426C2214yes—
126#2417C2214yes—
127#2415C2214yes—
128#2413C2214yes—
129#2411C2214yes—
130#2409C2214yes—
131#2409C2214yes—
132#2407C2214yes—
133#2407C2214yes—
134#2406C2218yes—
135#2406C2214yes—
136#2404C2214yes—
137#2367C2214yescomplemented
138#2365C2214yescomplemented
139#2359C2218yes—
140Q8×C22⋊C4C2214yescomplemented
141#2339C2218yes—
142#2339C2214yescomplemented
143#2335C2218yes—
144#2334C2218yescomplemented
145#2329C2218yescomplemented
146#2323C2214yescomplemented
147#2318C2218yes—
148#2317C2211yescharacteristic
149#2316C2211yescharacteristic
150#2311C2211yescharacteristic
151#2311C2211yescharacteristic
152#2311C2211yescharacteristic
153#2311C2212yescomplemented
154#2310C2211yescharacteristic
155#2310C2211yescharacteristic
156#2310C2211yescharacteristic
157#2310C2211yescharacteristic
158#2310C2212yescomplemented
159C4×C22⋊Q8C2212yes—
160C4×C22⋊Q8C2212yes—
161C4×C22⋊Q8C2214yescomplemented
162C4×#123C2214yes—
163C4×#123C2214yes—
164C4×#123C2214yes—
165C4×#121C2212yes—
166C4×#121C2212yes—
167C4×#120C2214yes—
168#2297C2211yescharacteristic
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2297C2212yescomplemented
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2296C2211yescharacteristic
175C2×#391C2211yescharacteristic
176C2×#391C2211yescharacteristic
177C2×#391C2212yescomplemented
178C2×#389C2214yes—
179#2290C2214yes—
180C2×#384C2211yescharacteristic
181#2280C2211yescharacteristic
182#2280C2211yescharacteristic
183C2×#380C2214yes—
184#2274C2211yescharacteristic
185C42×D4C2214yes—
186C4×#117C2211yescharacteristic
187C2×2−1+4—28no—
188C2×2−1+4—44no—
189C2×2−1+4—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2311yescharacteristic
192C22×#41C2312yes—
193C22×#41C2314yes—
194C22×#41C2312yes—
195C23×Q8C2311yescharacteristic
196C23×Q8C2311yescharacteristic
197C23×Q8C2312yes—
198C23×Q8C2312yes—
199C24×C4C2311yescharacteristic
200C24×C4C2312yes—
201#544—44no—
202#536—28no—
203#536—44no—
204C2×C4⋊Q8—44no—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×#126C2318yes—
213C2×#125C2312yes—
214C2×#125C2312yes—
215C2×#124C2312yes—
216C2×#124C2312yes—
217#525—28no—
218#525—44no—
219C2×#123C2314yes—
220C2×#123C2314yes—
221C2×#123C2312yes—
222C2×#123C2314yes—
223C2×#123C2312yes—
224C2×#123C2314yes—
225C2×C22⋊Q8—44no—
226C2×C22⋊Q8—44no—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2318yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2312yes—
238C2×#121C2312yes—
239C2×#121C2312yes—
240C2×#120C2312yes—
241C2×#120C2312yes—
242#520—44no—
243#519—44no—
244C4×#41—44no—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2314yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2312yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2314yes—
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C2×#117C2312yes—
264C2×#117C2312yes—
265C2×#117C2314yes—
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2312yes—
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2314yes—
271C22×C4⋊C4C2312yes—
272C22×C4⋊C4C2314yes—
273C22×C22⋊C4C2312yes—
274C22×C22⋊C4C2312yes—
275C22×C42—44no—
276C22×C42C2311yescharacteristic
277C22×C42C2311yescharacteristic
278C22×C42C2312yes—
279C22×C42C2312yes—
280C22×C42C2312yes—
281C22×C42C2312yes—
282C22×C42C2312yes—
283C22×C42C2312yes—
284#401C2318yes—
285#400C2318yes—
286#400C2318yes—
287#400C2318yes—
288#400C2318yes—
289#400C2318yes—
290#400C2318yes—
291#400C2318yes—
292#400C2318yes—
293#400C2318yes—
294#400C2318yes—
295#400C2318yes—
296#399C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2318yes—
309#396C2318yes—
310#396C2318yes—
311#395C2318yes—
312#395C2318yes—
313#395C2318yes—
314#395C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2318yes—
318#394C2318yes—
319#394C2318yes—
320#393C2318yes—
321#393C2318yes—
322#393C2318yes—
323#392C2318yes—
324#391C2311yescharacteristic
325#391C2312yes—
326#391C2312yes—
327#391C2312yes—
328#391C2314yes—
329#391C2312yes—
330#391C2312yes—
331#391C2314yes—
332#391C2314yes—
333#391C2314yes—
334#391C2314yes—
335#391C2312yes—
336#391C2312yes—
337#391C2311yescharacteristic
338#391C2312yes—
339#391C2312yes—
340#391C2318yes—
341#391C2312yes—
342#391C2311yescharacteristic
343#391C2318yes—
344#391C2312yes—
345#391C2318yes—
346#391C2318yes—
347#391C2314yes—
348#391C2311yescharacteristic
349#391C2312yes—
350#391C2312yes—
351#391C2312yes—
352#391C2314yes—
353#390C2311yescharacteristic
354#390C2312yes—
355#390C2312yes—
356#390C2312yes—
357#390C2311yescharacteristic
358#390C2318yes—
359#390C2311yescharacteristic
360#390C2312yes—
361#390C2311yescharacteristic
362#389C2318yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2312yes—
367#389C2318yes—
368#389C2318yes—
369#389C2318yes—
370#389C2318yes—
371#389C2318yes—
372#389C2312yes—
373#389C2312yes—
374#389C2312yes—
375#389C2318yes—
376#389C2318yes—
377#389C2312yes—
378#389C2312yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2314yes—
387#388C2318yes—
388#388C2314yes—
389#388C2318yes—
390#388C2318yes—
391#388C2314yes—
392#388C2314yes—
393#388C2314yes—
394#388C2314yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2314yes—
404#387C2318yes—
405#387C2314yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2314yes—
410#387C2314yes—
411#387C2314yes—
412#387C2314yes—
413#386C2314yes—
414#386C2314yes—
415#386C2314yes—
416#386C2318yes—
417#386C2318yes—
418#386C2318yes—
419#386C2314yes—
420#386C2318yes—
421#386C2314yes—
422#386C2314yes—
423#386C2314yes—
424#386C2318yes—
425#386C2314yes—
426#386C2314yes—
427#386C2314yes—
428#385C2318yes—
429#385C2314yes—
430#385C2318yes—
431#385C2314yes—
432#385C2318yes—
433#385C2318yes—
434#385C2318yes—
435#385C2318yes—
436#385C2318yes—
437#385C2314yes—
438#385C2314yes—
439#385C2314yes—
440#385C2318yes—
441#385C2314yes—
442#385C2314yes—
443#385C2314yes—
444#384C2312yes—
445#384C2312yes—
446#384C2312yes—
447#384C2314yes—
448#383C2318yes—
449#382C2312yes—
450#382C2318yes—
451#382C2318yes—
452#381C2314yes—
453#381C2314yes—
454#381C2314yes—
455#381C2314yes—
456#381C2318yes—
457#381C2314yes—
458#381C2314yes—
459#381C2312yes—
460#381C2312yes—
461#380C2314yes—
462#380C2314yes—
463#380C2314yes—
464#380C2318yes—
465#380C2314yes—
466#380C2318yes—
467#380C2318yes—
468#380C2318yes—
469#380C2312yes—
470#380C2312yes—
471#380C2318yes—
472#380C2318yes—
473#380C2312yes—
474#380C2312yes—
475#379C2312yes—
476#379C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2318yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2318yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2318yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2314yes—
496C4×C22⋊C4C2314yes—
497C4×C22⋊C4C2314yes—
498C4×C22⋊C4C2312yes—
499C4×C22⋊C4C2312yes—
500C4×C22⋊C4C2314yes—
501C4×C22⋊C4C2314yes—
502#376C2312yes—
503C2×#95C2318yes—
504C2×#95C2314yes—
505C2×#95C2314yes—
506C43C2312yes—
507C25C2411yescharacteristic
5082−1+4—464no—
509C2×#41—216no—
510C2×#41—28no—
511C2×#41—28no—
512C2×#41—24no—
513C2×#41—24no—
514C2×#41—24no—
515C2×#41—24no—
516C2×#41—24no—
517C2×#41—48no—
518C2×#41—48no—
519C2×#41—44no—
520C2×#41—44no—
521C2×#41—44no—
522C2×#41—44no—
523C2×#41#4118yes—
524C22×Q8—28no—
525C22×Q8—24no—
526C22×Q8—28no—
527C22×Q8—24no—
528C22×Q8—24no—
529C22×Q8—24no—
530C22×Q8—24no—
531C22×Q8—24no—
532C22×Q8—44no—
533C22×Q8—44no—
534C22×Q8—44no—
535C22×Q8—44no—
536C22×Q8C2412yes—
537C22×Q8C2412yes—
538C22×Q8C2412yes—
539C22×Q8C2412yes—
540C22×Q8C2411yescharacteristic
541C22×Q8C2411yescharacteristic
542C22×Q8C2414yes—
543C22×Q8C2414yes—
544C22×D4C2412yes—
545C22×D4C2411yescharacteristic
546C22×D4C2414yes—
547C22×D4C2412yes—
548C22×D4C2411yescharacteristic
549C22×D4C2414yes—
550C22×D4C2414yes—
551C23×C4—24no—
552C23×C4—24no—
553C23×C4—24no—
554C23×C4—28no—
555C23×C4—44no—
556C23×C4—44no—
557C23×C4C2412yes—
558C23×C4C2412yes—
559C23×C4C2411yescharacteristic
560C23×C4C2412yes—
561C23×C4C2412yes—
562C23×C4C2412yes—
563C23×C4C2412yes—
564C23×C4C2412yes—
565C23×C4C2412yes—
566C23×C4C2412yes—
567C23×C4C2412yes—
568C23×C4C2412yes—
569C23×C4C2412yes—
570C23×C4C2414yes—
571C23×C4C2412yes—
572C23×C4C2414yes—
573C23×C4C2414yes—
574C23×C4C2414yes—
575C23×C4C2412yes—
576C23×C4C2411yescharacteristic
577C4⋊Q8—28no—
578C4⋊Q8—44no—
579C4⋊Q8—44no—
580C4⋊Q8—48no—
581C4⋊Q8—44no—
582C4⋊Q8—44no—
583C4⋊Q8—44no—
584#126—416no—
585#125—44no—
586#125—44no—
587#124—28no—
588#124—44no—
589#123—28no—
590#123—216no—
591#123—216no—
592#123—48no—
593#123—44no—
594#123—48no—
595C22⋊Q8—28no—
596C22⋊Q8—216no—
597C22⋊Q8—48no—
598C22⋊Q8—416no—
599C22⋊Q8—48no—
600C22⋊Q8—48no—
601C22⋊Q8—48no—
602C22⋊Q8—48no—
603C22⋊Q8—44no—
604C22⋊Q8—44no—
605C22⋊Q8—44no—
606#121—28no—
607#121—44no—
608#120—28no—
609#120—44no—
610C4×Q8—44no—
611C4×Q8—48no—
612C4×Q8—48no—
613C4×Q8—44no—
614C4×D4—216no—
615C4×D4—216no—
616C4×D4—44no—
617C4×D4—44no—
618C4×D4—48no—
619C4×D4—48no—
620C4×D4—48no—
621C4×D4—48no—
622#117—24no—
623#117—24no—
624#117—24no—
625#117—24no—
626#117—24no—
627#117—24no—
628#117—44no—
629#117—48no—
630#117—44no—
631C2×C4⋊C4—24no—
632C2×C4⋊C4—24no—
633C2×C4⋊C4—48no—
634C2×C4⋊C4—44no—
635C2×C4⋊C4—44no—
636C2×C4⋊C4—44no—
637C2×C4⋊C4—48no—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2418yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2418yes—
675C2×C22⋊C4—44no—
676C2×C22⋊C4—44no—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2412yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2418yes—
706C2×C22⋊C4C2418yes—
707C2×C42—24no—
708C2×C42—24no—
709C2×C42—44no—
710C2×C42—44no—
711C2×C42—44no—
712C2×C42—44no—
713C2×C42—44no—
714C2×C42—44no—
715C2×C42C2412yes—
716C2×C42C2411yescharacteristic
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2414yes—
724C2×C42C2411yescharacteristic
725C2×C42C2412yes—
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2414yes—
729C2×C42C2418yes—
730C2×C42C2414yes—
731C2×C42C2414yes—
732C2×C42C2418yes—
733C2×C42C2412yes—
734C2×C42C2412yes—
735C2×C42C2412yes—
736C2×C42C2412yes—
737#95C2418yes—
738#95C2414yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2418yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2418yes—
758#95C2414yes—
759#95C2414yes—
760#95C2418yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2418yes—
765#95C2418yes—
766#95C2418yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771#95C2418yes—
772#95C2418yes—
773C24—22no—
774C24—24no—
775C24—22no—
776C24—22no—
777C24—42no—
778C24C2512yes—
779C24C2512yes—
780C24C2512yes—
781C24C2511yescharacteristic
782#41—232no—
783#41—432no—
784#41—464no—
785#41—432no—
786#41—416no—
787C2×Q8—24no—
788C2×Q8—24no—
789C2×Q8—28no—
790C2×Q8—24no—
791C2×Q8—24no—
792C2×Q8—22no—
793C2×Q8—22no—
794C2×Q8—22no—
795C2×Q8—24no—
796C2×Q8—24no—
797C2×Q8—24no—
798C2×Q8—24no—
799C2×Q8—24no—
800C2×Q8—24no—
801C2×Q8—22no—
802C2×Q8—24no—
803C2×Q8—24no—
804C2×Q8—22no—
805C2×Q8—44no—
806C2×Q8—44no—
807C2×Q8—44no—
808C2×Q8—48no—
809C2×Q8—432no—
810C2×Q8—432no—
811C2×Q8—416no—
812C2×Q8—416no—
813C2×Q8C2×#4114yes—
814C2×D4—24no—
815C2×D4—24no—
816C2×D4—28no—
817C2×D4—28no—
818C2×D4—24no—
819C2×D4—24no—
820C2×D4—24no—
821C2×D4—28no—
822C2×D4—28no—
823C2×D4—22no—
824C2×D4—22no—
825C2×D4—22no—
826C2×D4—22no—
827C2×D4—22no—
828C2×D4—44no—
829C2×D4—44no—
830C2×D4—44no—
831C2×D4—44no—
832C2×D4—44no—
833C2×D4C2×#4118yes—
834C2×D4C2×#4114yes—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—22no—
841C22×C4—24no—
842C22×C4—28no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—22no—
846C22×C4—24no—
847C22×C4—24no—
848C22×C4—22no—
849C22×C4—24no—
850C22×C4—24no—
851C22×C4—24no—
852C22×C4—24no—
853C22×C4—24no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—28no—
857C22×C4—24no—
858C22×C4—24no—
859C22×C4—24no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—24no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—24no—
867C22×C4—24no—
868C22×C4—24no—
869C22×C4—28no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—48no—
887C22×C4—432no—
888C22×C4—416no—
889C22×C4C2×#4118yes—
890C22×C4C2×#4114yes—
891C22×C4H(5,𝔽2)14yes—
892C22×C4H(5,𝔽2)14yes—
893C22×C42−1+418yescomplemented
894C22×C4C2512yes—
895C22×C4C2514yes—
896C22×C4C2512yes—
897C22×C4C2514yes—
898C22×C4C2514yes—
899C22×C4C2512yes—
900C22×C4C2512yes—
901C22×C4C2512yes—
902C22×C4C2514yes—
903C22×C4C2514yes—
904C22×C4C2512yes—
905C22×C4C2514yes—
906C22×C4C2514yes—
907C22×C4C2512yes—
908C22×C4C2514yes—
909C22×C4C2512yes—
910C22×C4C2512yes—
911C22×C4C2512yes—
912C22×C4C2512yes—
913C22×C4C2511yescharacteristic
914C22×C4C2511yescharacteristic
915C4⋊C4—24no—
916C4⋊C4—24no—
917C4⋊C4—28no—
918C4⋊C4—216no—
919C4⋊C4—24no—
920C4⋊C4—24no—
921C4⋊C4—24no—
922C4⋊C4—24no—
923C4⋊C4—22no—
924C4⋊C4—22no—
925C4⋊C4—24no—
926C4⋊C4—24no—
927C4⋊C4—22no—
928C4⋊C4—22no—
929C4⋊C4—28no—
930C4⋊C4—28no—
931C4⋊C4—28no—
932C4⋊C4—216no—
933C4⋊C4—28no—
934C4⋊C4—28no—
935C4⋊C4—48no—
936C4⋊C4—44no—
937C4⋊C4—48no—
938C4⋊C4—48no—
939C4⋊C4—48no—
940C4⋊C4—48no—
941C4⋊C4—44no—
942C4⋊C4—48no—
943C4⋊C4—44no—
944C4⋊C4—48no—
945C4⋊C4—44no—
946C4⋊C4—44no—
947C4⋊C4—44no—
948C4⋊C4—44no—
949C4⋊C4—44no—
950C4⋊C4—44no—
951C4⋊C4—48no—
952C22⋊C4—24no—
953C22⋊C4—24no—
954C22⋊C4—28no—
955C22⋊C4—216no—
956C22⋊C4—24no—
957C22⋊C4—24no—
958C22⋊C4—24no—
959C22⋊C4—24no—
960C22⋊C4—28no—
961C22⋊C4—28no—
962C22⋊C4—28no—
963C22⋊C4—28no—
964C22⋊C4—28no—
965C22⋊C4—28no—
966C22⋊C4—28no—
967C22⋊C4—28no—
968C22⋊C4—48no—
969C22⋊C4—48no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—48no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—48no—
981C22⋊C4—48no—
982C42—24no—
983C42—24no—
984C42—22no—
985C42—22no—
986C42—24no—
987C42—22no—
988C42—24no—
989C42—22no—
990C42—24no—
991C42—24no—
992C42—24no—
993C42—24no—
994C42—28no—
995C42—42no—
996C42—42no—
997C42—42no—
998C42—42no—
999C42—44no—
1000C42—44no—
1001C42—48no—
1002C42—44no—
1003C42—48no—
1004C23—22no—
1005C23—22no—
1006C23—28no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—24no—
1013C23—22no—
1014C23—24no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—24no—
1021C23—24no—
1022C23—48no—
1023C23—48no—
1024C23—44no—
1025C23—44no—
1026C23C22×#4114yes—
1027C23C22×#4112yes—
1028C23C2×H(5,𝔽2)12yes—
1029C23C2×H(5,𝔽2)12yes—
1030C23C2×2−1+414yes—
1031C23C2611yescharacteristic
1032Q8—28no—
1033Q8—416no—
1034Q8—48no—
1035Q8—48no—
1036Q8—48no—
1037Q8—44no—
1038Q8—48no—
1039Q8—164no—
1040D4—216no—
1041D4—28no—
1042D4—416no—
1043D4—416no—
1044D4—48no—
1045D4—44no—
1046D4—88no—
1047C2×C4—216no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—216no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—24no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—22no—
1076C2×C4—24no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—22no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—28no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—22no—
1095C2×C4—28no—
1096C2×C4—48no—
1097C2×C4—48no—
1098C2×C4—48no—
1099C2×C4—48no—
1100C2×C4—48no—
1101C2×C4—416no—
1102C2×C4—416no—
1103C2×C4—44no—
1104C2×C4—48no—
1105C2×C4—48no—
1106C2×C4—48no—
1107C2×C4—48no—
1108C2×C4—48no—
1109C2×C4—88no—
1110C2×C4—84no—
1111C2×C4—84no—
1112C2×C4—164no—
1113C2×C4#538116yes—
1114C2×C4C22×#4114yes—
1115C2×C4C22×#4112yes—
1116C2×C4C22×#4112yes—
1117C2×C4C2×H(5,𝔽2)12yes—
1118C2×C4C2×H(5,𝔽2)12yes—
1119C2×C4C2×H(5,𝔽2)12yes—
1120C2×C4C2×H(5,𝔽2)12yes—
1121C2×C4C2×2−1+414yes—
1122C2×C4C2×2−1+414yes—
1123C2×C4#58514yes—
1124C22—24no—
1125C22—24no—
1126C22—22no—
1127C22—22no—
1128C22—24no—
1129C22—28no—
1130C22—24no—
1131C22—24no—
1132C22—24no—
1133C22—416no—
1134C22—42no—
1135C22—42no—
1136C22—44no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—44no—
1142C22—44no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22C2×#53814yes—
1147C22C23×#4111yescharacteristic
1148C22C22×H(5,𝔽2)11yescharacteristic
1149C22C22×H(5,𝔽2)11yescharacteristic
1150C22C22×2−1+412yes—
1151C22C2×#58512yes—
1152C4—24no—
1153C4—24no—
1154C4—24no—
1155C4—24no—
1156C4—44no—
1157C4—44no—
1158C4—42no—
1159C4—44no—
1160C4—44no—
1161C4—42no—
1162C4—42no—
1163C4—44no—
1164C4—44no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—42no—
1169C4—44no—
1170C4—44no—
1171C4C2×#53814yes—
1172C4C2×#53814yes—
1173C2—24no—
1174C2—44no—
1175C2—44no—
1176C2—82no—
1177C2C22×#53811yescharacteristic
1178C2#6280512yes—
1179C2#6281912yes—
1180C2#6283311yescharacteristic
1181C2#6283611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35659C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40100C2semidirect
2. #40076C2semidirect
3. #39659C2semidirect
4. #39528C2semidirect
5. #38605C2semidirect
6. #37909C2semidirect
7. #37398C2semidirect
8. #37338C2semidirect
9. #36626C2semidirect
10. C2×#2857C2semidirect
11. #35674C2semidirect
12. #35666C2semidirect
13. #35661C2semidirect
15. #35644C2semidirect
16. #35633C2semidirect
17. #35557C2semidirect
18. #35532C2semidirect
19. #35313C2semidirect
20. #35312C2semidirect
21. #35036C2semidirect
22. #35016C2semidirect
23. #34268C2semidirect
24. #34259C2semidirect
25. C4×#525C2semidirect
39. #2863C22semidirect
40. #2862C22semidirect
41. #2861C22semidirect
52. #2805C22semidirect
54. #2788C22semidirect
55. #2787C22semidirect
57. #2779C22semidirect
59. #2774C22semidirect
60. #2771C22semidirect
61. #2765C22semidirect
65. #2702C22semidirect
68. #2666C22semidirect
70. #2649C22semidirect
71. #2645C22semidirect
72. #2642C22semidirect
73. #2640C22semidirect
75. #2587C22semidirect
76. #2586C22semidirect
79. #2567C22semidirect
80. #2566C22semidirect
81. #2565C22semidirect
83. #2542C22semidirect
87. #2518C22semidirect
88. #2514C22semidirect
89. #2512C22semidirect
90. #2511C22semidirect
91. #2511C22semidirect
92. #2505C22semidirect
94. #2497C22semidirect
95. #2496C22semidirect
99. #2492C22semidirect
102. #2489C22semidirect
110. #2446C22semidirect
111. #2446C22semidirect
112. #2446C22semidirect
113. #2446C22semidirect
114. #2441C22semidirect
115. #2440C22semidirect
116. #2434C22semidirect
117. #2434C22semidirect
118. #2434C22semidirect
119. #2432C22semidirect
120. #2432C22semidirect
121. #2432C22semidirect
137. #2367C22semidirect
138. #2365C22semidirect
140. Q8×C22⋊C4C22semidirect
142. #2339C22semidirect
144. #2334C22semidirect
145. #2329C22semidirect
146. #2323C22semidirect
153. #2311C22semidirect
158. #2310C22semidirect
161. C4×C22⋊Q8C22semidirect
171. #2297C22semidirect
177. C2×#391C22semidirect
893. C22×C42−1+4semidirect

Maximal subgroups

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

subgroupindex
#401002
#400762
#396592
#395282
#386052
#379092
#373982
#373382
#366262
C2×#28572
#356742
#356662
#356612
#356592
#356442
#356332
#355572
#355322
#353132
#353122
#350362
#350162
#342682
#342592
C4×#5252