Finite Group Databasebeta

← #8424994

Subgroups — #8424994

Order 512.

5377 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59654C212yesmaximal, complemented
2#59420C211yesmaximal, characteristic, complemented
3#59093C214yesmaximal, complemented
4#53540C218yesmaximal, complemented
5#53025C214yesmaximal, complemented
6#52990C214yesmaximal, complemented
7#52407C214yesmaximal, complemented
8#42979C214yesmaximal, complemented
9#42598C214yesmaximal, complemented
10#40650C214yesmaximal, complemented
11#39362C212yesmaximal, complemented
12#39171C212yesmaximal, complemented
13#39020C214yesmaximal, complemented
14#37748C214yesmaximal, complemented
15#37631C212yesmaximal, complemented
16#37494C214yesmaximal, complemented
17#36609C211yesmaximal, characteristic, complemented
18#36303C212yesmaximal, complemented
19#34925C211yesmaximal, characteristic, complemented
20#34918C212yesmaximal, complemented
21C2×#559C2211yescharacteristic
22C2×D4×Q8C2212yescomplemented
23C2×#548C2214yescomplemented
24C2×#547C2212yes—
25C2×D42C2211yescharacteristic
26C2×#535C2214yes—
27C2×#532C2214yescomplemented
28#2862C2211yescharacteristic, complemented
29#2858C2212yes—
30#2850C2214yes—
31#2841C2214yescomplemented
32#2840C2214yescomplemented
33#2838C2218yescomplemented
34#2832C2218yescomplemented
35#2832C2218yescomplemented
36#2831C2218yescomplemented
37#2824C2218yescomplemented
38#2816C2218yescomplemented
39#2778C2218yescomplemented
40#2760C2214yescomplemented
41#2743C2218yescomplemented
42#2741C2218yescomplemented
43#2736C2218yescomplemented
44#2712C2218yescomplemented
45#2700C2218yescomplemented
46#2697C2214yes—
47#2696C2218yescomplemented
48#2696C2218yescomplemented
49#2688C2218yescomplemented
50#2686C2218yescomplemented
51#2684C2218yescomplemented
52#2684C2218yescomplemented
53#2684C2218yescomplemented
54#2681C2218yescomplemented
55#2678C2218yes—
56#2678C2218yes—
57#2668C2218yescomplemented
58#2668C2214yescomplemented
59#2665C2214yescomplemented
60#2653C2218yescomplemented
61#2650C2218yescomplemented
62#2645C2214yescomplemented
63#2643C2218yescomplemented
64#2640C2214yes—
65#2640C2214yescomplemented
66#2639C2218yescomplemented
67#2635C2218yescomplemented
68#2628C2214yescomplemented
69#2625C2214yescomplemented
70#2620C2214yes—
71#2597C2214yescomplemented
72#2595C2214yescomplemented
73#2592C2212yes—
74#2592C2214yescomplemented
75#2580C2212yescomplemented
76#2580C2212yescomplemented
77#2570C2212yescomplemented
78#2568C2212yescomplemented
79#2563C2214yescomplemented
80#2555C2214yescomplemented
81#2551C2211yescharacteristic, complemented
82#2547C2212yes—
83#2544C2212yes—
84#2544C2214yescomplemented
85#2543C2218yescomplemented
86#2541C2212yes—
87#2538C2212yes—
88#2537C2211yescharacteristic, complemented
89#2536C2214yescomplemented
90#2534C2214yes—
91#2516C2214yescomplemented
92#2513C2212yes—
93#2513C2214yescomplemented
94#2511C2212yescomplemented
95#2503C2214yescomplemented
96#2494C2214yescomplemented
97#2492C2214yescomplemented
98#2492C2214yescomplemented
99#2492C2214yescomplemented
100#2491C2214yes—
101#2491C2214yescomplemented
102#2488C2218yescomplemented
103#2488C2218yescomplemented
104#2461C2218yescomplemented
105#2459C2218yescomplemented
106#2458C2214yescomplemented
107#2451C2214yescomplemented
108#2450C2218yescomplemented
109#2448C2214yes—
110#2448C2214yescomplemented
111#2447C2214yescomplemented
112#2447C2212yescomplemented
113#2445C2212yes—
114#2444C2218yescomplemented
115#2444C2218yescomplemented
116#2440C2214yescomplemented
117#2436C2214yes—
118#2436C2214yescomplemented
119#2436C2214yescomplemented
120#2435C2214yes—
121#2435C2214yes—
122#2431C2214yes—
123#2430C2218yescomplemented
124#2428C2214yes—
125#2428C2214yescomplemented
126#2427C2214yes—
127#2427C2214yescomplemented
128#2427C2214yescomplemented
129#2420C2214yes—
130#2418C2218yescomplemented
131#2416C2214yes—
132#2416C2214yes—
133#2409C2214yescomplemented
134#2408C2214yes—
135#2408C2214yes—
136#2407C2214yescomplemented
137#2404C2214yescomplemented
138#2398C2214yescomplemented
139#2395C2214yescomplemented
140#2388C2214yescomplemented
141#2367C2214yescomplemented
142#2361C2214yescomplemented
143#2357C2212yescomplemented
144#2339C2214yescomplemented
145#2339C2214yescomplemented
146#2339C2214yescomplemented
147D4×C22⋊C4C2214yes—
148#2328C2214yescomplemented
149#2312C2214yescomplemented
150C4×C4⋊Q8C2212yescomplemented
151C4×#127C2211yescharacteristic
152C4×#127C2212yes—
153C4×#124C2212yes—
154C4×#124C2212yescomplemented
155C4×#123C2214yescomplemented
156C4×#121C2214yescomplemented
157#2295C2212yescomplemented
158C2×#391C2214yescomplemented
159#2293C2212yes—
160#2290C2214yescomplemented
161C42×Q8C2211yescharacteristic, complemented
162C42×D4C2212yescomplemented
163C22×#41C2314yes—
164C22×#41C2314yes—
165C23×Q8C2314yes—
166C23×D4C2314yes—
167#559—44no—
168D4×Q8—48no—
169#548—416no—
170#547—48no—
171D42—44no—
172#535—416no—
173#532—416no—
174C2×C4⋊Q8C2312yes—
175C2×C4⋊Q8C2314yes—
176C2×C4⋊Q8C2314yes—
177C2×#127C2311yescharacteristic
178C2×#127C2312yes—
179C2×#127C2314yes—
180C2×#124C2312yes—
181C2×#124C2312yes—
182C2×#124C2314yes—
183C2×#124C2314yes—
184C2×#124C2314yes—
185C2×#124C2314yes—
186C2×#124C2318yes—
187C2×#124C2318yes—
188C2×#123C2314yes—
189C2×#123C2318yes—
190C2×#123C2314yes—
191C2×C22⋊Q8C2318yes—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2318yes—
196C2×#121C2314yes—
197C2×#121C2318yes—
198C2×#121C2314yes—
199C2×#121C2314yes—
200C2×#121C2318yes—
201C2×#121C2314yes—
202C2×#121C2314yes—
203C2×#121C2318yes—
204C2×#121C2318yes—
205C2×#120C2318yes—
206C2×#120C2318yes—
207C2×#120C2314yes—
208C2×C4×Q8C2312yes—
209C2×C4×Q8C2314yes—
210C2×C4×Q8C2311yescharacteristic
211C2×C4×Q8C2312yes—
212C2×C4×D4C2312yes—
213C2×C4×D4C2312yes—
214C2×C4×D4C2312yes—
215C2×C4×D4C2312yes—
216C2×C4×D4C2314yes—
217C2×C4×D4C2314yes—
218C2×C4×D4C2314yes—
219C2×C4×D4C2314yes—
220C2×C4×D4C2312yes—
221C2×C4×D4C2314yes—
222C2×C4×D4C2318yes—
223C2×C4×D4C2318yes—
224C2×#117C2314yes—
225C22×C4⋊C4C2314yes—
226C22×C22⋊C4C2314yes—
227C22×C42C2314yes—
228#401C2318yes—
229#400C2318yes—
230#400C2318yes—
231#400C2318yes—
232#400C2314yes—
233#400C2314yes—
234#400C2318yes—
235#400C2318yes—
236#400C2314yes—
237#400C2318yes—
238#399C2314yes—
239#399C2318yes—
240#399C2314yes—
241#398C2314yes—
242#398C2318yes—
243#398C2318yes—
244#397C2318yes—
245#397C2318yes—
246#397C2318yes—
247#397C2318yes—
248#397C2318yes—
249#397C2314yes—
250#397C2318yes—
251#397C2318yes—
252#397C2318yes—
253#397C2318yes—
254#397C2314yes—
255#397C2314yes—
256#397C2314yes—
257#397C2314yes—
258#396C2318yes—
259#396C2318yes—
260#396C2318yes—
261#395C2318yes—
262#395C2314yes—
263#395C2318yes—
264#394C2314yes—
265#394C2318yes—
266#394C2318yes—
267#394C2318yes—
268#394C2318yes—
269#394C2318yes—
270#394C2318yes—
271#394C2318yes—
272#394C2318yes—
273#394C2318yes—
274#394C2318yes—
275#394C2314yes—
276#394C2314yes—
277#394C2314yes—
278#394C2318yes—
279#394C2314yes—
280#393C2318yes—
281#393C2318yes—
282#393C2318yes—
283#393C2314yes—
284#393C2314yes—
285#393C2314yes—
286#393C2314yes—
287#393C2318yes—
288#393C2318yes—
289#393C2318yes—
290#393C2318yes—
291#393C2318yes—
292#393C2318yes—
293#392C2318yes—
294#392C2314yes—
295#392C2318yes—
296#392C2318yes—
297#392C2318yes—
298#391C2314yes—
299#391C2314yes—
300#391C2314yes—
301#391C2314yes—
302#391C2318yes—
303#391C2318yes—
304#391C2312yes—
305#391C2312yes—
306#391C2314yes—
307#391C2314yes—
308#391C2314yes—
309#391C2312yes—
310#391C2318yes—
311#391C2312yes—
312#390C2312yes—
313#390C2312yes—
314#390C2314yes—
315#390C2314yes—
316#390C2314yes—
317#390C2312yes—
318#390C2314yes—
319#390C2314yes—
320#390C2312yes—
321#390C2314yes—
322#390C2314yes—
323#390C2312yes—
324#390C2312yes—
325#390C2314yes—
326#390C2314yes—
327#390C2312yes—
328#389C2314yes—
329#389C2314yes—
330#389C2312yes—
331#389C2312yes—
332#389C2312yes—
333#389C2312yes—
334#389C2314yes—
335#389C2314yes—
336#388C2314yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2314yes—
342#388C2318yes—
343#388C2314yes—
344#388C2314yes—
345#388C2318yes—
346#388C2318yes—
347#388C2314yes—
348#388C2314yes—
349#388C2314yes—
350#388C2314yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2314yes—
355#388C2314yes—
356#387C2314yes—
357#387C2314yes—
358#387C2314yes—
359#387C2314yes—
360#387C2318yes—
361#387C2314yes—
362#387C2314yes—
363#386C2318yes—
364#386C2318yes—
365#386C2318yes—
366#386C2318yes—
367#386C2318yes—
368#386C2318yes—
369#386C2318yes—
370#386C2318yes—
371#386C2318yes—
372#386C2318yes—
373#386C2318yes—
374#386C2318yes—
375#386C2314yes—
376#386C2314yes—
377#386C2318yes—
378#386C2318yes—
379#386C2318yes—
380#386C2318yes—
381#386C2318yes—
382#386C2314yes—
383#385C2318yes—
384#385C2314yes—
385#385C2314yes—
386#385C2318yes—
387#385C2318yes—
388#385C2314yes—
389#384C2311yescharacteristic
390#384C2312yes—
391#382C2312yes—
392#382C2314yes—
393#382C2312yes—
394#382C2312yes—
395#382C2312yes—
396#381C2318yes—
397#381C2314yes—
398#381C2314yes—
399#381C2318yes—
400#381C2314yes—
401#380C2318yes—
402#380C2318yes—
403#380C2314yes—
404#380C2314yes—
405#380C2314yes—
406#380C2314yes—
407#380C2314yes—
408#379C2318yes—
409#379C2318yes—
410#379C2314yes—
411#379C2318yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2312yes—
416C4×C4⋊C4C2312yes—
417C4×C4⋊C4C2312yes—
418C4×C4⋊C4C2312yes—
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2312yes—
421C4×C4⋊C4C2312yes—
422C4×C4⋊C4C2312yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2314yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2314yes—
433#376C2314yes—
434C2×#95C2318yes—
435C2×#95C2318yes—
436C43C2312yes—
437C43C2311yescharacteristic
438C25C2414yes—
439C2×#41—216no—
440C2×#41—48no—
441C2×#41—416no—
442C2×#41—48no—
443C2×#41—48no—
444C22×Q8—48no—
445C22×Q8—48no—
446C22×Q8—48no—
447C22×Q8C2412yes—
448C22×Q8C2414yes—
449C22×Q8C2411yescharacteristic
450C22×Q8C2418yes—
451C22×Q8C2414yes—
452C22×D4—48no—
453C22×D4—48no—
454C22×D4—48no—
455C22×D4C2414yes—
456C22×D4C2412yes—
457C22×D4C2414yes—
458C22×D4C2412yes—
459C22×D4C2414yes—
460C22×D4C2414yes—
461C22×D4C2412yes—
462C22×D4C2418yes—
463C22×D4C2418yes—
464C22×D4C2418yes—
465C22×D4C2418yes—
466C23×C4C2414yes—
467C23×C4C2414yes—
468C23×C4C2414yes—
469C23×C4C2414yes—
470C23×C4C2418yes—
471C23×C4C2414yes—
472C23×C4C2418yes—
473C23×C4C2414yes—
474C4⋊Q8—28no—
475C4⋊Q8—48no—
476C4⋊Q8—48no—
477#127—216no—
478#127—28no—
479#127—24no—
480#124—28no—
481#124—44no—
482#124—48no—
483#124—48no—
484#124—48no—
485#124—48no—
486#124—416no—
487#124—416no—
488#123—416no—
489#123—48no—
490#123—48no—
491C22⋊Q8—416no—
492C22⋊Q8—416no—
493C22⋊Q8—48no—
494C22⋊Q8—48no—
495C22⋊Q8—48no—
496#121—216no—
497#121—416no—
498#121—416no—
499#121—48no—
500#121—48no—
501#121—48no—
502#121—48no—
503#121—416no—
504#121—416no—
505#120—48no—
506#120—416no—
507#120—416no—
508C4×Q8—28no—
509C4×Q8—44no—
510C4×Q8—42no—
511C4×Q8—48no—
512C4×D4—28no—
513C4×D4—28no—
514C4×D4—28no—
515C4×D4—44no—
516C4×D4—48no—
517C4×D4—48no—
518C4×D4—48no—
519C4×D4—48no—
520C4×D4—44no—
521C4×D4—48no—
522C4×D4—416no—
523C4×D4—416no—
524#117—48no—
525C2×C4⋊C4—48no—
526C2×C4⋊C4C2412yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2412yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2411yescharacteristic
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C22⋊C4—48no—
553C2×C22⋊C4C2414yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2418yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2414yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C2418yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2414yes—
591C2×C42—48no—
592C2×C42C2412yes—
593C2×C42C2414yes—
594C2×C42C2412yes—
595C2×C42C2412yes—
596C2×C42C2414yes—
597C2×C42C2412yes—
598C2×C42C2411yescharacteristic
599C2×C42C2412yes—
600C2×C42C2412yes—
601C2×C42C2414yes—
602C2×C42C2418yes—
603C2×C42C2412yes—
604C2×C42C2414yes—
605C2×C42C2411yescharacteristic
606C2×C42C2412yes—
607C2×C42C2411yescharacteristic
608#95C2414yes—
609#95C2414yes—
610#95C2414yes—
611#95C2418yes—
612#95C2418yes—
613#95C2418yes—
614#95C2418yes—
615#95C2418yes—
616#95C2414yes—
617#95C2414yes—
618#95C2414yes—
619#95C2414yes—
620#95C2411yescharacteristic
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2414yes—
625#95C2414yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2414yes—
634#95C2411yescharacteristic
635#95C2412yes—
636#95C2412yes—
637#95C2418yes—
638#95C2414yes—
639#95C2418yes—
640#95C2414yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644#95C2414yes—
645C24—44no—
646C24—48no—
647C24—44no—
648C24—48no—
649C24—44no—
650C24C2514yes—
651C24C2514yes—
652C24C2514yes—
653#41—832no—
654#41—832no—
655C2×Q8—24no—
656C2×Q8—28no—
657C2×Q8—24no—
658C2×Q8—28no—
659C2×Q8—24no—
660C2×Q8—28no—
661C2×Q8—42no—
662C2×Q8—41no—
663C2×Q8—48no—
664C2×Q8—48no—
665C2×Q8—48no—
666C2×Q8—48no—
667C2×Q8—44no—
668C2×Q8—832no—
669C2×D4—216no—
670C2×D4—216no—
671C2×D4—28no—
672C2×D4—28no—
673C2×D4—216no—
674C2×D4—216no—
675C2×D4—24no—
676C2×D4—24no—
677C2×D4—28no—
678C2×D4—28no—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—24no—
682C2×D4—28no—
683C2×D4—24no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—42no—
687C2×D4—44no—
688C2×D4—48no—
689C2×D4—48no—
690C2×D4—48no—
691C2×D4—48no—
692C2×D4—48no—
693C2×D4—44no—
694C2×D4—48no—
695C2×D4—42no—
696C2×D4—44no—
697C2×D4—48no—
698C2×D4—48no—
699C2×D4—48no—
700C2×D4—832no—
701C2×D4H(5,𝔽2)18yes—
702C22×C4—28no—
703C22×C4—216no—
704C22×C4—28no—
705C22×C4—28no—
706C22×C4—28no—
707C22×C4—28no—
708C22×C4—28no—
709C22×C4—28no—
710C22×C4—28no—
711C22×C4—28no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—48no—
715C22×C4—48no—
716C22×C4—48no—
717C22×C4—48no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—48no—
721C22×C4—48no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4C2514yes—
726C22×C4C2512yes—
727C22×C4C2511yescharacteristic
728C22×C4C2512yes—
729C22×C4C2512yes—
730C22×C4C2514yes—
731C22×C4C2514yes—
732C22×C4C2514yes—
733C22×C4C2518yes—
734C22×C4C2514yes—
735C22×C4C2512yes—
736C22×C4C2514yes—
737C22×C4C2514yes—
738C22×C4C2512yes—
739C22×C4C2511yescharacteristic
740C22×C4C2511yescharacteristic
741C22×C4C2512yes—
742C4⋊C4—24no—
743C4⋊C4—28no—
744C4⋊C4—24no—
745C4⋊C4—24no—
746C4⋊C4—24no—
747C4⋊C4—28no—
748C4⋊C4—28no—
749C4⋊C4—28no—
750C4⋊C4—24no—
751C4⋊C4—24no—
752C4⋊C4—48no—
753C4⋊C4—44no—
754C4⋊C4—44no—
755C4⋊C4—44no—
756C4⋊C4—42no—
757C4⋊C4—44no—
758C4⋊C4—48no—
759C4⋊C4—44no—
760C4⋊C4—48no—
761C4⋊C4—42no—
762C4⋊C4—42no—
763C4⋊C4—42no—
764C4⋊C4—41no—
765C4⋊C4—48no—
766C4⋊C4—48no—
767C4⋊C4—44no—
768C22⋊C4—28no—
769C22⋊C4—28no—
770C22⋊C4—216no—
771C22⋊C4—28no—
772C22⋊C4—28no—
773C22⋊C4—28no—
774C22⋊C4—28no—
775C22⋊C4—48no—
776C22⋊C4—44no—
777C22⋊C4—44no—
778C22⋊C4—44no—
779C22⋊C4—44no—
780C22⋊C4—44no—
781C22⋊C4—44no—
782C22⋊C4—44no—
783C22⋊C4—44no—
784C22⋊C4—44no—
785C22⋊C4—44no—
786C22⋊C4—48no—
787C22⋊C4—48no—
788C22⋊C4—48no—
789C22⋊C4—48no—
790C22⋊C4—44no—
791C22⋊C4—44no—
792C22⋊C4—48no—
793C22⋊C4—48no—
794C22⋊C4—48no—
795C22⋊C4—48no—
796C22⋊C4—48no—
797C22⋊C4—48no—
798C22⋊C4—48no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4—44no—
802C22⋊C4—48no—
803C22⋊C4—48no—
804C22⋊C4—44no—
805C22⋊C4—44no—
806C42—24no—
807C42—28no—
808C42—24no—
809C42—28no—
810C42—24no—
811C42—22no—
812C42—24no—
813C42—24no—
814C42—24no—
815C42—44no—
816C42—44no—
817C42—42no—
818C42—41no—
819C42—48no—
820C42—42no—
821C42H(5,𝔽2)14yes—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—28no—
832C23—24no—
833C23—24no—
834C23—28no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—24no—
839C23—24no—
840C23—816no—
841C23—88no—
842C23—164no—
843C23—168no—
844C23—164no—
845C23C2×H(5,𝔽2)18yes—
846C23C2611yescharacteristic
847Q8—44no—
848Q8—48no—
849Q8—416no—
850Q8—816no—
851Q8—88no—
852D4—216no—
853D4—416no—
854D4—416no—
855D4—48no—
856D4—84no—
857D4—88no—
858D4—816no—
859D4—88no—
860D4—816no—
861D4—816no—
862D4—816no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—28no—
877C2×C4—28no—
878C2×C4—24no—
879C2×C4—24no—
880C2×C4—24no—
881C2×C4—24no—
882C2×C4—28no—
883C2×C4—24no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—28no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—24no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—24no—
905C2×C4—24no—
906C2×C4—416no—
907C2×C4—416no—
908C2×C4—416no—
909C2×C4—88no—
910C2×C4—816no—
911C2×C4—88no—
912C2×C4—816no—
913C2×C4—164no—
914C2×C4C2×H(5,𝔽2)12yes—
915C2×C4C2×H(5,𝔽2)14yes—
916C2×C4C2×H(5,𝔽2)14yes—
917C2×C4#58512yes—
918C2×C4#58514yes—
919C22—28no—
920C22—28no—
921C22—28no—
922C22—44no—
923C22—44no—
924C22—44no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—48no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—44no—
933C22—48no—
934C22—44no—
935C22—44no—
936C22—44no—
937C22—44no—
938C22—1616no—
939C22C22×H(5,𝔽2)11yescharacteristic
940C22C22×H(5,𝔽2)12yes—
941C22C2×#58512yes—
942C22C2×#58511yescharacteristic
943C222−1+611yescharacteristic
944C4—22no—
945C4—22no—
946C4—44no—
947C4—44no—
948C4—48no—
949C4—44no—
950C4—44no—
951C4—44no—
952C4—42no—
953C4—41no—
954C4—42no—
955C4—42no—
956C4—42no—
957C4—44no—
958C4—42no—
959C4—44no—
960C4#355818yes—
961C2—48no—
962C2—84no—
963C2—84no—
964C2C2×#355812yes—
965C2#6276211yescharacteristic
966C2#6292112yes—
967C2#6293111yescharacteristic
968C2#6301211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59654C2semidirect
2. #59420C2semidirect
3. #59093C2semidirect
4. #53540C2semidirect
5. #53025C2semidirect
6. #52990C2semidirect
7. #52407C2semidirect
8. #42979C2semidirect
9. #42598C2semidirect
10. #40650C2semidirect
11. #39362C2semidirect
12. #39171C2semidirect
13. #39020C2semidirect
14. #37748C2semidirect
15. #37631C2semidirect
16. #37494C2semidirect
17. #36609C2semidirect
18. #36303C2semidirect
19. #34925C2semidirect
20. #34918C2semidirect
22. C2×D4×Q8C22semidirect
23. C2×#548C22semidirect
27. C2×#532C22semidirect
28. #2862C22semidirect
31. #2841C22semidirect
32. #2840C22semidirect
33. #2838C22semidirect
34. #2832C22semidirect
35. #2832C22semidirect
36. #2831C22semidirect
37. #2824C22semidirect
38. #2816C22semidirect
39. #2778C22semidirect
40. #2760C22semidirect
41. #2743C22semidirect
42. #2741C22semidirect
43. #2736C22semidirect
44. #2712C22semidirect
45. #2700C22semidirect
47. #2696C22semidirect
48. #2696C22semidirect
49. #2688C22semidirect
50. #2686C22semidirect
51. #2684C22semidirect
52. #2684C22semidirect
53. #2684C22semidirect
54. #2681C22semidirect
57. #2668C22semidirect
58. #2668C22semidirect
59. #2665C22semidirect
60. #2653C22semidirect
61. #2650C22semidirect
62. #2645C22semidirect
63. #2643C22semidirect
65. #2640C22semidirect
66. #2639C22semidirect
67. #2635C22semidirect
68. #2628C22semidirect
69. #2625C22semidirect
71. #2597C22semidirect
72. #2595C22semidirect
74. #2592C22semidirect
75. #2580C22semidirect
76. #2580C22semidirect
77. #2570C22semidirect
78. #2568C22semidirect
79. #2563C22semidirect
80. #2555C22semidirect
81. #2551C22semidirect
84. #2544C22semidirect
85. #2543C22semidirect
88. #2537C22semidirect
89. #2536C22semidirect
91. #2516C22semidirect
93. #2513C22semidirect
94. #2511C22semidirect
95. #2503C22semidirect
96. #2494C22semidirect
97. #2492C22semidirect
98. #2492C22semidirect
99. #2492C22semidirect
101. #2491C22semidirect
102. #2488C22semidirect
103. #2488C22semidirect
104. #2461C22semidirect
105. #2459C22semidirect
106. #2458C22semidirect
107. #2451C22semidirect
108. #2450C22semidirect
110. #2448C22semidirect
111. #2447C22semidirect
112. #2447C22semidirect
114. #2444C22semidirect
115. #2444C22semidirect
116. #2440C22semidirect
118. #2436C22semidirect
119. #2436C22semidirect
123. #2430C22semidirect
125. #2428C22semidirect
127. #2427C22semidirect
128. #2427C22semidirect
130. #2418C22semidirect
133. #2409C22semidirect
136. #2407C22semidirect
137. #2404C22semidirect
138. #2398C22semidirect
139. #2395C22semidirect
140. #2388C22semidirect
141. #2367C22semidirect
142. #2361C22semidirect
143. #2357C22semidirect
144. #2339C22semidirect
145. #2339C22semidirect
146. #2339C22semidirect
148. #2328C22semidirect
149. #2312C22semidirect
150. C4×C4⋊Q8C22semidirect
154. C4×#124C22semidirect
155. C4×#123C22semidirect
156. C4×#121C22semidirect
157. #2295C22semidirect
158. C2×#391C22semidirect
160. #2290C22semidirect
161. C42×Q8C22semidirect
162. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#596542
#594202
#590932
#535402
#530252
#529902
#524072
#429792
#425982
#406502
#393622
#391712
#390202
#377482
#376312
#374942
#366092
#363032
#349252
#349182