Finite Group Databasebeta

← #8094537

Subgroups — #8094537

Order 512.

4550 conjugacy classes of subgroups.

The subgroup lattice has 1057 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53125C214yesmaximal, complemented
2#53084C214yesmaximal, complemented
3#53039C214yesmaximal, complemented
4#53035C214yesmaximal, complemented
5#52318C218yesmaximal, complemented
6#46075C214yesmaximal, complemented
7#46068C214yesmaximal, complemented
8#46062C214yesmaximal, complemented
9#46056C214yesmaximal, complemented
10#45463C218yesmaximal, complemented
11#35629C211yesmaximal, characteristic, complemented
12#35620C211yesmaximal, characteristic, complemented
13#35576C211yesmaximal, characteristic, complemented
14#35574C211yesmaximal, characteristic, complemented
15#35558C211yesmaximal, characteristic, complemented
16#35531C211yesmaximal, characteristic
17#35339C211yesmaximal, characteristic, complemented
18#35330C211yesmaximal, characteristic, complemented
19#35266C211yesmaximal, characteristic, complemented
20#35264C211yesmaximal, characteristic
21#35174C211yesmaximal, characteristic, complemented
22#35152C211yesmaximal, characteristic
23C2×#2563C211yesmaximal, characteristic, complemented
24#34816C211yesmaximal, characteristic, complemented
25#34815C211yesmaximal, characteristic, complemented
26C2×#544C2211yescharacteristic
27C2×#544C2211yescharacteristic
28C2×#535C2211yescharacteristic
29C22×C4⋊Q8C2211yescharacteristic
30C2×#520C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32#2864C2214yescomplemented
33#2862C2212yescomplemented
34#2861C2212yes—
35#2860C2214yes—
36#2859C2212yescomplemented
37#2858C2212yes—
38#2849C2214yes—
39#2848C2214yes—
40#2841C2218yescomplemented
41#2838C2218yescomplemented
42#2838C2218yescomplemented
43#2832C2218yescomplemented
44#2832C2218yescomplemented
45#2831C2218yescomplemented
46#2830C2218yescomplemented
47#2821C2218yescomplemented
48#2814C2218yescomplemented
49#2814C2218yescomplemented
50#2787C2218yescomplemented
51#2775C2218yescomplemented
52#2770C2218yescomplemented
53#2759C2218yescomplemented
54#2759C2218yescomplemented
55#2745C2218yescomplemented
56#2738C2218yescomplemented
57#2731C2218yescomplemented
58#2723C2218yescomplemented
59#2722C2218yescomplemented
60#2717C2218yescomplemented
61#2716C2218yescomplemented
62#2715C2218yescomplemented
63#2707C2218yescomplemented
64#2702C2218yescomplemented
65#2702C2218yescomplemented
66#2695C2218yescomplemented
67#2695C2218yescomplemented
68#2690C2218yescomplemented
69#2674C2218yescomplemented
70#2660C2212yescomplemented
71#2660C2212yescomplemented
72#2647C2214yescomplemented
73#2644C2214yes—
74#2641C2212yes—
75#2640C2212yes—
76#2626C2214yes—
77#2622C2214yes—
78#2583C2214yes—
79#2579C2214yes—
80#2570C2214yescomplemented
81#2570C2214yescomplemented
82#2569C2218yes—
83#2568C2212yescomplemented
84#2566C2212yescomplemented
85#2565C2212yescomplemented
86#2563C2214yes—
87#2563C2214yes—
88#2563C2214yes—
89#2563C2214yes—
90#2563C2212yescomplemented
91#2551C2214yescomplemented
92#2551C2214yescomplemented
93#2550C2214yescomplemented
94#2550C2214yescomplemented
95#2550C2214yescomplemented
96#2550C2214yescomplemented
97#2549C2218yes—
98#2514C2212yescomplemented
99#2514C2214yescomplemented
100#2513C2214yes—
101#2513C2214yes—
102#2513C2214yes—
103#2513C2212yescomplemented
104#2513C2214yescomplemented
105#2512C2214yes—
106#2512C2214yes—
107#2512C2214yes—
108#2512C2212yescomplemented
109#2511C2212yescomplemented
110#2510C2214yes—
111#2510C2218yes—
112#2509C2212yescomplemented
113#2508C2212yescomplemented
114#2507C2212yescomplemented
115#2506C2212yescomplemented
116#2505C2214yes—
117#2504C2212yes—
118#2501C2212yes—
119#2500C2212yes—
120#2500C2212yes—
121#2495C2214yescomplemented
122#2494C2214yescomplemented
123#2491C2214yes—
124#2490C2214yes—
125#2481C2214yes—
126#2480C2218yes—
127#2480C2218yes—
128#2473C2214yes—
129#2472C2218yes—
130#2454C2214yes—
131#2454C2214yes—
132#2452C2214yes—
133#2452C2214yes—
134#2452C2214yescomplemented
135#2451C2214yescomplemented
136#2450C2218yes—
137#2448C2214yes—
138#2447C2214yes—
139#2445C2214yes—
140#2445C2214yes—
141#2442C2214yescomplemented
142#2440C2214yescomplemented
143#2439C2214yescomplemented
144#2439C2214yescomplemented
145#2434C2214yes—
146#2422C2214yes—
147#2420C2214yes—
148#2418C2218yes—
149#2409C2214yes—
150#2402C2214yescomplemented
151#2401C2214yescomplemented
152C2×#393C2214yes—
153#2378C2218yescomplemented
154#2376C2218yescomplemented
155#2317C2211yescharacteristic
156#2317C2211yescharacteristic
157#2317C2211yescharacteristic
158#2317C2211yescharacteristic
159#2316C2211yescharacteristic
160#2316C2211yescharacteristic
161#2311C2211yescharacteristic
162#2311C2211yescharacteristic
163#2309C2211yescharacteristic
164#2309C2211yescharacteristic
165#2309C2211yescharacteristic
166C4×#125C2214yescomplemented
167C4×#126C2214yescomplemented
168#2297C2211yescharacteristic
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2296C2211yescharacteristic
172#2296C2211yescharacteristic
173#2296C2211yescharacteristic
174#2296C2211yescharacteristic
175#2296C2211yescharacteristic
176C2×#390C2211yescharacteristic
177C2×#390C2211yescharacteristic
178#2285C2211yescharacteristic
179#2285C2211yescharacteristic
180C2×#382C2211yescharacteristic
181C2×#382C2211yescharacteristic
182C2×#380C2214yes—
183#2274C2211yescharacteristic
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×Q8C2312yes—
189C23×D4C2311yescharacteristic
190C24×C4C2312yes—
191#544—44no—
192#544—44no—
193#535—44no—
194C2×C4⋊Q8—44no—
195C2×C4⋊Q8C2314yes—
196C2×C4⋊Q8C2314yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2318yes—
202C2×#127C2312yes—
203C2×#126C2314yes—
204C2×#126C2318yes—
205C2×#126C2318yes—
206C2×#125C2314yes—
207C2×#125C2312yes—
208C2×#125C2312yes—
209C2×#125C2312yes—
210C2×#125C2312yes—
211C2×#124C2312yes—
212C2×#124C2318yes—
213C2×#123C2318yes—
214C2×#123C2318yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2318yes—
218C2×C22⋊Q8C2318yes—
219C2×#121C2312yes—
220C2×#121C2312yes—
221C2×#120C2314yes—
222#520—44no—
223C2×C4×Q8C2312yes—
224C2×C4×D4—44no—
225C2×C4×D4C2314yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2312yes—
228C2×C4×D4C2314yes—
229C2×#117C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C2×#117C2311yescharacteristic
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C2×#117C2312yes—
237C22×C4⋊C4C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2312yes—
241C22×C4⋊C4C2312yes—
242C22×C4⋊C4C2312yes—
243C22×C22⋊C4C2312yes—
244C22×C22⋊C4C2314yes—
245C22×C22⋊C4C2314yes—
246C22×C42C2311yescharacteristic
247C22×C42C2311yescharacteristic
248C22×C42C2311yescharacteristic
249#401C2314yes—
250#401C2318yes—
251#400C2314yes—
252#400C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2314yes—
256#400C2318yes—
257#400C2314yes—
258#400C2314yes—
259#400C2314yes—
260#400C2314yes—
261#400C2314yes—
262#399C2318yes—
263#399C2318yes—
264#398C2318yes—
265#398C2314yes—
266#398C2318yes—
267#398C2318yes—
268#398C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2314yes—
273#398C2314yes—
274#398C2314yes—
275#397C2318yes—
276#397C2318yes—
277#397C2314yes—
278#397C2318yes—
279#397C2318yes—
280#397C2318yes—
281#397C2318yes—
282#397C2318yes—
283#397C2314yes—
284#397C2318yes—
285#397C2318yes—
286#397C2318yes—
287#397C2318yes—
288#397C2318yes—
289#397C2314yes—
290#396C2318yes—
291#396C2318yes—
292#396C2318yes—
293#396C2318yes—
294#396C2318yes—
295#396C2318yes—
296#396C2314yes—
297#395C2318yes—
298#395C2318yes—
299#395C2318yes—
300#395C2318yes—
301#395C2318yes—
302#395C2318yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#394C2318yes—
308#394C2318yes—
309#393C2318yes—
310#393C2318yes—
311#393C2318yes—
312#393C2318yes—
313#393C2318yes—
314#393C2318yes—
315#393C2318yes—
316#393C2318yes—
317#391C2311yescharacteristic
318#391C2312yes—
319#391C2312yes—
320#391C2311yescharacteristic
321#391C2318yes—
322#391C2318yes—
323#391C2318yes—
324#391C2318yes—
325#391C2318yes—
326#391C2312yes—
327#391C2312yes—
328#390C2312yes—
329#390C2312yes—
330#390C2312yes—
331#390C2312yes—
332#390C2314yes—
333#390C2314yes—
334#390C2311yescharacteristic
335#390C2312yes—
336#390C2312yes—
337#390C2314yes—
338#390C2314yes—
339#390C2312yes—
340#390C2314yes—
341#390C2314yes—
342#390C2312yes—
343#390C2312yes—
344#390C2311yescharacteristic
345#390C2312yes—
346#390C2318yes—
347#390C2312yes—
348#390C2312yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2318yes—
360#389C2318yes—
361#389C2318yes—
362#389C2318yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#388C2314yes—
374#388C2314yes—
375#388C2314yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#387C2314yes—
389#387C2314yes—
390#387C2314yes—
391#387C2314yes—
392#387C2314yes—
393#387C2314yes—
394#387C2314yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#386C2314yes—
403#386C2314yes—
404#386C2312yes—
405#386C2318yes—
406#386C2312yes—
407#386C2318yes—
408#386C2314yes—
409#386C2314yes—
410#385C2318yes—
411#385C2314yes—
412#385C2314yes—
413#385C2314yes—
414#385C2314yes—
415#385C2312yes—
416#385C2318yes—
417#385C2312yes—
418#385C2312yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#385C2312yes—
423#385C2312yes—
424#385C2312yes—
425#385C2314yes—
426#385C2314yes—
427#384C2312yes—
428#384C2312yes—
429#384C2312yes—
430#384C2312yes—
431#384C2312yes—
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#383C2314yes—
435#383C2318yes—
436#382C2314yes—
437#382C2312yes—
438#382C2312yes—
439#382C2314yes—
440#382C2312yes—
441#382C2312yes—
442#382C2314yes—
443#382C2312yes—
444#382C2312yes—
445#382C2312yes—
446#382C2312yes—
447#382C2311yescharacteristic
448#382C2311yescharacteristic
449#382C2312yes—
450#381C2318yes—
451#380C2318yes—
452#380C2318yes—
453#380C2318yes—
454#380C2318yes—
455#380C2318yes—
456#380C2314yes—
457#380C2314yes—
458#380C2314yes—
459#380C2314yes—
460#380C2314yes—
461#380C2318yes—
462#380C2314yes—
463#379C2314yes—
464#379C2314yes—
465#379C2314yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2312yes—
484C4×C22⋊C4C2312yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2312yes—
490C4×C22⋊C4C2314yes—
491#376C2312yes—
492#376C2312yes—
493C2×#95C2314yes—
494C2×#95C2312yes—
495C2×#95C2314yes—
496C43C2312yes—
497C43C2312yes—
498C25C2412yes—
499C2×#41—24no—
500C2×#41—24no—
501C2×#41—24no—
502C22×Q8—44no—
503C22×Q8—84no—
504C22×Q8C2411yescharacteristic
505C22×Q8C2414yes—
506C22×Q8C2414yes—
507C22×Q8C2418yes—
508C22×D4—24no—
509C22×D4—24no—
510C22×D4—24no—
511C22×D4C2412yes—
512C22×D4C2412yes—
513C22×D4C2412yes—
514C22×D4C2411yescharacteristic
515C22×D4C2414yes—
516C22×D4C2414yes—
517C23×C4—48no—
518C23×C4—44no—
519C23×C4C2411yescharacteristic
520C23×C4C2412yes—
521C23×C4C2412yes—
522C23×C4C2412yes—
523C23×C4C2412yes—
524C23×C4C2412yes—
525C23×C4C2411yescharacteristic
526C23×C4C2412yes—
527C23×C4C2418yes—
528C23×C4C2414yes—
529C23×C4C2411yescharacteristic
530C4⋊Q8—48no—
531C4⋊Q8—48no—
532C4⋊Q8—44no—
533C4⋊Q8—44no—
534C4⋊Q8—44no—
535C4⋊Q8—44no—
536C4⋊Q8—88no—
537#127—44no—
538#126—48no—
539#126—88no—
540#126—88no—
541#125—44no—
542#125—44no—
543#125—44no—
544#125—44no—
545#125—48no—
546#124—44no—
547#124—88no—
548#123—416no—
549#123—88no—
550C22⋊Q8—48no—
551C22⋊Q8—48no—
552C22⋊Q8—416no—
553C22⋊Q8—88no—
554#121—44no—
555#121—44no—
556#120—48no—
557C4×Q8—44no—
558C4×D4—48no—
559C4×D4—48no—
560C4×D4—44no—
561C4×D4—48no—
562#117—24no—
563#117—24no—
564#117—24no—
565#117—24no—
566#117—24no—
567#117—24no—
568#117—24no—
569#117—44no—
570C2×C4⋊C4—24no—
571C2×C4⋊C4—24no—
572C2×C4⋊C4—24no—
573C2×C4⋊C4—44no—
574C2×C4⋊C4—44no—
575C2×C4⋊C4—44no—
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
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⋊C4C2418yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C22⋊C4—44no—
625C2×C22⋊C4—84no—
626C2×C22⋊C4—84no—
627C2×C22⋊C4C2412yes—
628C2×C22⋊C4C2412yes—
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2412yes—
631C2×C22⋊C4C2412yes—
632C2×C22⋊C4C2412yes—
633C2×C22⋊C4C2412yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C42—24no—
657C2×C42—24no—
658C2×C42—24no—
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2412yes—
665C2×C42C2412yes—
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2412yes—
673C2×C42C2412yes—
674C2×C42C2414yes—
675C2×C42C2414yes—
676C2×C42C2414yes—
677C2×C42C2414yes—
678C2×C42C2418yes—
679C2×C42C2414yes—
680#95C2412yes—
681#95C2412yes—
682#95C2412yes—
683#95C2412yes—
684#95C2418yes—
685#95C2418yes—
686#95C2418yes—
687#95C2418yes—
688#95C2414yes—
689#95C2414yes—
690#95C2414yes—
691#95C2414yes—
692#95C2418yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2418yes—
714#95C2418yes—
715#95C2418yes—
716#95C2418yes—
717#95C2418yes—
718#95C2418yes—
719#95C2418yes—
720#95C2418yes—
721C24—24no—
722C24—24no—
723C24—24no—
724C24—44no—
725C24—44no—
726C24C2514yes—
727C24C2512yes—
728C24C2511yescharacteristic
729#41—416no—
730C2×Q8—22no—
731C2×Q8—22no—
732C2×Q8—22no—
733C2×Q8—48no—
734C2×Q8—48no—
735C2×Q8—48no—
736C2×Q8—44no—
737C2×Q8—44no—
738C2×Q8—48no—
739C2×Q8—48no—
740C2×Q8—816no—
741C2×D4—24no—
742C2×D4—24no—
743C2×D4—24no—
744C2×D4—24no—
745C2×D4—24no—
746C2×D4—22no—
747C2×D4—24no—
748C2×D4—24no—
749C2×D4—24no—
750C2×D4—24no—
751C2×D4—22no—
752C2×D4—22no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—416no—
758C22×C4—22no—
759C22×C4—24no—
760C22×C4—22no—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—216no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—48no—
778C22×C4—48no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4—48no—
782C22×C4—816no—
783C22×C4H(5,𝔽2)14yes—
784C22×C42−1+414yes—
785C22×C42−1+414yes—
786C22×C4C2512yes—
787C22×C4C2512yes—
788C22×C4C2512yes—
789C22×C4C2512yes—
790C22×C4C2512yes—
791C22×C4C2514yes—
792C22×C4C2514yes—
793C22×C4C2514yes—
794C22×C4C2514yes—
795C22×C4C2514yes—
796C22×C4C2512yes—
797C22×C4C2512yes—
798C22×C4C2512yes—
799C22×C4C2512yes—
800C22×C4C2512yes—
801C22×C4C2514yes—
802C22×C4C2514yes—
803C22×C4C2512yes—
804C22×C4C2512yes—
805C22×C4C2512yes—
806C22×C4C2511yescharacteristic
807C22×C4C2511yescharacteristic
808C4⋊C4—24no—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—22no—
815C4⋊C4—22no—
816C4⋊C4—22no—
817C4⋊C4—22no—
818C4⋊C4—22no—
819C4⋊C4—22no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—24no—
826C4⋊C4—28no—
827C4⋊C4—28no—
828C4⋊C4—28no—
829C4⋊C4—42no—
830C4⋊C4—42no—
831C4⋊C4—44no—
832C4⋊C4—48no—
833C4⋊C4—48no—
834C4⋊C4—44no—
835C4⋊C4—44no—
836C4⋊C4—44no—
837C4⋊C4—44no—
838C4⋊C4—44no—
839C4⋊C4—44no—
840C4⋊C4—44no—
841C4⋊C4—48no—
842C4⋊C4—48no—
843C4⋊C4—48no—
844C4⋊C4—44no—
845C4⋊C4—48no—
846C4⋊C4—44no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—44no—
852C4⋊C4—44no—
853C4⋊C4—48no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C22⋊C4—24no—
857C22⋊C4—24no—
858C22⋊C4—24no—
859C22⋊C4—24no—
860C22⋊C4—24no—
861C22⋊C4—24no—
862C22⋊C4—24no—
863C22⋊C4—28no—
864C22⋊C4—48no—
865C22⋊C4—48no—
866C22⋊C4—48no—
867C22⋊C4—48no—
868C22⋊C4—48no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—48no—
873C22⋊C4—48no—
874C22⋊C4—44no—
875C22⋊C4—48no—
876C22⋊C4—48no—
877C22⋊C4—48no—
878C22⋊C4—44no—
879C22⋊C4—48no—
880C22⋊C4—44no—
881C22⋊C4—48no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—48no—
885C42—24no—
886C42—24no—
887C42—24no—
888C42—24no—
889C42—24no—
890C42—22no—
891C42—22no—
892C42—24no—
893C42—22no—
894C42—22no—
895C42—24no—
896C42—24no—
897C42—24no—
898C42—24no—
899C42—24no—
900C42—44no—
901C42—44no—
902C42—44no—
903C42—44no—
904C42—44no—
905C42—48no—
906C23—22no—
907C23—22no—
908C23—24no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—24no—
913C23—24no—
914C23—24no—
915C23—28no—
916C23—28no—
917C23—24no—
918C23—416no—
919C23—48no—
920C23—84no—
921C23—84no—
922C23—88no—
923C23C2×H(5,𝔽2)12yes—
924C23C2×2−1+412yes—
925C23C2×2−1+412yes—
926C23C2611yescharacteristic
927Q8—44no—
928Q8—816no—
929Q8—164no—
930Q8—164no—
931D4—48no—
932D4—48no—
933D4—48no—
934D4—44no—
935D4—164no—
936D4—164no—
937C2×C4—28no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
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—24no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—22no—
970C2×C4—24no—
971C2×C4—28no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—28no—
981C2×C4—24no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—24no—
985C2×C4—28no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—44no—
989C2×C4—48no—
990C2×C4—816no—
991C2×C4—84no—
992C2×C4—84no—
993C2×C4—84no—
994C2×C4—84no—
995C2×C4—84no—
996C2×C4—164no—
997C2×C4#563116yes—
998C2×C4C2×H(5,𝔽2)12yes—
999C2×C4C2×H(5,𝔽2)12yes—
1000C2×C4C2×2−1+412yes—
1001C2×C4C2×2−1+412yes—
1002C2×C4C2×2−1+412yes—
1003C2×C4C2×2−1+412yes—
1004C2×C4#58514yes—
1005C22—22no—
1006C22—22no—
1007C22—24no—
1008C22—24no—
1009C22—44no—
1010C22—42no—
1011C22—42no—
1012C22—44no—
1013C22—44no—
1014C22—48no—
1015C22—44no—
1016C22—48no—
1017C22—42no—
1018C22—44no—
1019C22—816no—
1020C22C2×#56314yes—
1021C22C22×H(5,𝔽2)11yescharacteristic
1022C22C22×2−1+411yescharacteristic
1023C22C22×2−1+411yescharacteristic
1024C22C2×#58512yes—
1025C22H(7,𝔽2)12yes—
1026C4—24no—
1027C4—44no—
1028C4—42no—
1029C4—42no—
1030C4—42no—
1031C4—42no—
1032C4—44no—
1033C4—44no—
1034C4—42no—
1035C4—42no—
1036C4—42no—
1037C4—44no—
1038C4—44no—
1039C4—44no—
1040C4—44no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—42no—
1046C4C2×#56314yes—
1047C4C2×#56314yes—
1048C2—24no—
1049C2—82no—
1050C2—84no—
1051C2C22×#56311yescharacteristic
1052C2#6282411yescharacteristic
1053C2#6287611yescharacteristic
1054C2#6292612yes—
1055C2#6292912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#535C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53125C2semidirect
2. #53084C2semidirect
3. #53039C2semidirect
4. #53035C2semidirect
5. #52318C2semidirect
6. #46075C2semidirect
7. #46068C2semidirect
8. #46062C2semidirect
9. #46056C2semidirect
10. #45463C2semidirect
11. #35629C2semidirect
12. #35620C2semidirect
13. #35576C2semidirect
14. #35574C2semidirect
15. #35558C2semidirect
17. #35339C2semidirect
18. #35330C2semidirect
19. #35266C2semidirect
21. #35174C2semidirect
23. C2×#2563C2semidirect
24. #34816C2semidirect
25. #34815C2semidirect
32. #2864C22semidirect
33. #2862C22semidirect
36. #2859C22semidirect
40. #2841C22semidirect
41. #2838C22semidirect
42. #2838C22semidirect
43. #2832C22semidirect
44. #2832C22semidirect
45. #2831C22semidirect
46. #2830C22semidirect
47. #2821C22semidirect
48. #2814C22semidirect
49. #2814C22semidirect
50. #2787C22semidirect
51. #2775C22semidirect
52. #2770C22semidirect
53. #2759C22semidirect
54. #2759C22semidirect
55. #2745C22semidirect
56. #2738C22semidirect
57. #2731C22semidirect
58. #2723C22semidirect
59. #2722C22semidirect
60. #2717C22semidirect
61. #2716C22semidirect
62. #2715C22semidirect
63. #2707C22semidirect
64. #2702C22semidirect
65. #2702C22semidirect
66. #2695C22semidirect
67. #2695C22semidirect
68. #2690C22semidirect
69. #2674C22semidirect
70. #2660C22semidirect
71. #2660C22semidirect
72. #2647C22semidirect
80. #2570C22semidirect
81. #2570C22semidirect
83. #2568C22semidirect
84. #2566C22semidirect
85. #2565C22semidirect
90. #2563C22semidirect
91. #2551C22semidirect
92. #2551C22semidirect
93. #2550C22semidirect
94. #2550C22semidirect
95. #2550C22semidirect
96. #2550C22semidirect
98. #2514C22semidirect
99. #2514C22semidirect
103. #2513C22semidirect
104. #2513C22semidirect
108. #2512C22semidirect
109. #2511C22semidirect
112. #2509C22semidirect
113. #2508C22semidirect
114. #2507C22semidirect
115. #2506C22semidirect
121. #2495C22semidirect
122. #2494C22semidirect
134. #2452C22semidirect
135. #2451C22semidirect
141. #2442C22semidirect
142. #2440C22semidirect
143. #2439C22semidirect
144. #2439C22semidirect
150. #2402C22semidirect
151. #2401C22semidirect
153. #2378C22semidirect
154. #2376C22semidirect
166. C4×#125C22semidirect
167. C4×#126C22semidirect

Maximal subgroups

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

subgroupindex
#531252
#530842
#530392
#530352
#523182
#460752
#460682
#460622
#460562
#454632
#356292
#356202
#355762
#355742
#355582
#355312
#353392
#353302
#352662
#352642
#351742
#351522
C2×#25632
#348162
#348152