Finite Group Databasebeta

← #7695998

Subgroups — #7695998

Order 512.

5597 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60046C212yesmaximal, complemented
2#59827C211yesmaximal, characteristic, complemented
3#59201C212yesmaximal, complemented
4#59173C214yesmaximal, complemented
5#52163C212yesmaximal, complemented
6#52103C211yesmaximal, characteristic, complemented
7#45330C212yesmaximal, complemented
8#44922C214yesmaximal, complemented
9#43805C218yesmaximal, complemented
10#43462C214yesmaximal, complemented
11#40388C218yesmaximal, complemented
12#39493C212yesmaximal, complemented
13#38761C214yesmaximal, complemented
14#37845C214yesmaximal, complemented
15#36415C211yesmaximal, characteristic, complemented
16#36103C212yesmaximal, complemented
17#35774C214yesmaximal, complemented
18#35756C212yesmaximal, complemented
19#34321C212yesmaximal, complemented
20#34200C214yesmaximal, complemented
21C2×#559C2212yes—
22C2×#555C2212yes—
23C2×#555C2211yescharacteristic, complemented
24C2×#547C2211yescharacteristic
25C2×#525C2214yes—
26C2×#525C2214yes—
27C2×#520C2212yes—
28C23×C4⋊C4C2212yescomplemented
29#2862C2211yescharacteristic, complemented
30#2850C2212yescomplemented
31#2849C2214yescomplemented
32#2847C2212yescomplemented
33#2806C2214yescomplemented
34#2805C2214yescomplemented
35#2804C2214yes—
36#2796C2218yescomplemented
37#2780C2218yescomplemented
38#2777C2218yescomplemented
39#2764C2214yescomplemented
40#2757C2218yescomplemented
41#2736C2214yescomplemented
42#2732C2214yes—
43#2728C2214yes—
44#2724C2212yes—
45#2724C2212yescomplemented
46#2708C2218yes—
47#2700C2218yescomplemented
48#2697C2214yes—
49#2688C2218yes—
50#2683C2211yescharacteristic
51#2682C2212yes—
52#2681C2214yes—
53#2680C2212yes—
54#2679C2211yescharacteristic
55#2678C2214yes—
56#2670C2218yescomplemented
57#2669C2212yes—
58#2668C2218yes—
59#2649C2218yescomplemented
60#2631C2214yes—
61#2628C2214yescomplemented
62#2615C2212yes—
63#2602C2218yescomplemented
64#2600C2214yes—
65#2599C2214yescomplemented
66#2598C2218yescomplemented
67#2592C2214yescomplemented
68#2589C2218yescomplemented
69#2588C2218yescomplemented
70#2586C2214yescomplemented
71#2582C2212yescomplemented
72#2573C2218yescomplemented
73#2572C2218yes—
74#2570C2214yescomplemented
75#2563C2211yescharacteristic
76#2557C2218yes—
77#2557C2218yescomplemented
78#2555C2218yes—
79#2547C2211yescharacteristic, complemented
80#2547C2214yescomplemented
81#2535C2214yescomplemented
82#2525C2218yescomplemented
83#2523C2214yescomplemented
84#2523C2218yescomplemented
85#2515C2218yescomplemented
86#2504C2212yescomplemented
87#2501C2212yescomplemented
88#2499C2212yescomplemented
89#2497C2214yescomplemented
90#2495C2214yescomplemented
91#2486C2212yes—
92#2486C2212yescomplemented
93#2485C2214yes—
94#2485C2214yescomplemented
95#2477C2218yescomplemented
96#2474C2218yescomplemented
97#2471C2218yescomplemented
98#2470C2218yescomplemented
99#2465C2218yescomplemented
100#2461C2218yescomplemented
101#2459C2218yes—
102#2459C2218yescomplemented
103#2456C2218yes—
104#2456C2218yescomplemented
105#2449C2218yescomplemented
106#2447C2218yescomplemented
107#2443C2218yes—
108#2440C2214yescomplemented
109#2439C2214yescomplemented
110#2431C2212yes—
111#2416C2214yes—
112#2414C2214yescomplemented
113#2413C2214yescomplemented
114#2406C2214yes—
115#2395C2218yes—
116#2392C2214yes—
117#2392C2214yes—
118#2388C2212yes—
119#2374C2214yes—
120#2369C2212yescomplemented
121#2367C2218yescomplemented
122#2363C2214yes—
123#2361C2218yes—
124#2361C2218yes—
125#2361C2214yescomplemented
126#2360C2218yescomplemented
127#2360C2218yescomplemented
128#2354C2212yescomplemented
129#2352C2214yes—
130#2352C2214yes—
131#2352C2214yescomplemented
132#2352C2214yescomplemented
133D4×C4⋊C4C2214yes—
134D4×C4⋊C4C2212yes—
135D4×C4⋊C4C2214yescomplemented
136D4×C4⋊C4C2214yescomplemented
137#2347C2214yescomplemented
138#2347C2214yescomplemented
139#2347C2212yescomplemented
140#2344C2212yescomplemented
141#2337C2218yescomplemented
142#2324C2214yescomplemented
143#2322C2218yes—
144#2322C2218yescomplemented
145#2317C2214yescomplemented
146#2311C2214yes—
147C4×C4⋊Q8C2212yescomplemented
148C4×#127C2211yescharacteristic
149C4×#121C2214yes—
150C4×#120C2212yes—
151C4×#120C2218yes—
152C4×#120C2218yescomplemented
153#2297C2212yes—
154#2296C2214yescomplemented
155#2293C2212yes—
156#2280C2214yescomplemented
157#2274C2214yescomplemented
158C42×D4C2211yescharacteristic, complemented
159C22×#41C2312yes—
160C22×#41C2312yes—
161C24×C4C2312yes—
162C24×C4C2314yes—
163#559—48no—
164#555—216no—
165#555—44no—
166#547—44no—
167C2×C4⋊Q8C2312yes—
168C2×C4⋊Q8C2311yescharacteristic
169C2×C4⋊Q8C2311yescharacteristic
170C2×#127C2311yescharacteristic
171C2×#124C2318yes—
172C2×#124C2314yes—
173C2×#124C2318yes—
174C2×#124C2312yes—
175#525—232no—
176#525—416no—
177C2×#123C2314yes—
178C2×#123C2314yes—
179C2×#123C2314yes—
180C2×#123C2314yes—
181C2×#123C2314yes—
182C2×#123C2314yes—
183C2×#123C2314yes—
184C2×C22⋊Q8C2314yes—
185C2×C22⋊Q8C2314yes—
186C2×C22⋊Q8C2312yes—
187C2×C22⋊Q8C2318yes—
188C2×#121C2314yes—
189C2×#121C2314yes—
190C2×#121C2314yes—
191C2×#121C2314yes—
192C2×#121C2312yes—
193C2×#121C2312yes—
194C2×#121C2312yes—
195C2×#121C2318yes—
196C2×#120C2312yes—
197C2×#120C2314yes—
198C2×#120C2314yes—
199C2×#120C2314yes—
200#520—48no—
201C2×C4×Q8C2314yes—
202C2×C4×Q8C2314yes—
203C2×C4×D4C2314yes—
204C2×C4×D4C2312yes—
205C2×C4×D4C2314yes—
206C2×C4×D4C2314yes—
207C2×C4×D4C2311yescharacteristic
208C2×C4×D4C2311yescharacteristic
209C2×C4×D4C2311yescharacteristic
210C2×C4×D4C2314yes—
211C2×C4×D4C2318yes—
212C2×C4×D4C2318yes—
213C2×C4×D4C2318yes—
214C2×C4×D4C2318yes—
215C2×C4×D4C2318yes—
216C2×C4×D4C2314yes—
217C2×C4×D4C2312yes—
218C2×#117C2314yes—
219C2×#117C2314yes—
220C2×#117C2312yes—
221C2×#117C2314yes—
222C2×#117C2314yes—
223C2×#117C2312yes—
224C2×#117C2314yes—
225C2×#117C2314yes—
226C22×C4⋊C4—48no—
227C22×C4⋊C4C2312yes—
228C22×C4⋊C4C2314yes—
229C22×C4⋊C4C2314yes—
230C22×C4⋊C4C2318yes—
231C22×C4⋊C4C2312yes—
232C22×C4⋊C4C2312yes—
233C22×C4⋊C4C2314yes—
234C22×C42C2312yes—
235#400C2318yes—
236#400C2318yes—
237#400C2318yes—
238#400C2318yes—
239#399C2318yes—
240#399C2318yes—
241#398C2318yes—
242#398C2314yes—
243#398C2314yes—
244#398C2314yes—
245#398C2318yes—
246#397C2318yes—
247#397C2314yes—
248#397C2314yes—
249#397C2314yes—
250#397C2314yes—
251#397C2318yes—
252#397C2314yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#397C2314yes—
257#397C2318yes—
258#396C2314yes—
259#396C2314yes—
260#396C2318yes—
261#396C2318yes—
262#396C2318yes—
263#395C2312yes—
264#395C2318yes—
265#395C2318yes—
266#394C2318yes—
267#394C2314yes—
268#394C2318yes—
269#394C2314yes—
270#394C2318yes—
271#394C2312yes—
272#394C2314yes—
273#394C2314yes—
274#394C2318yes—
275#393C2314yes—
276#393C2318yes—
277#393C2312yes—
278#393C2314yes—
279#393C2318yes—
280#392C2318yes—
281#392C2312yes—
282#392C2318yes—
283#392C2314yes—
284#392C2318yes—
285#392C2314yes—
286#392C2314yes—
287#391C2314yes—
288#391C2318yes—
289#391C2318yes—
290#391C2318yes—
291#391C2312yes—
292#391C2318yes—
293#391C2314yes—
294#391C2312yes—
295#391C2312yes—
296#390C2311yescharacteristic
297#390C2314yes—
298#390C2311yescharacteristic
299#390C2312yes—
300#390C2318yes—
301#390C2314yes—
302#390C2318yes—
303#390C2318yes—
304#390C2312yes—
305#390C2312yes—
306#389C2314yes—
307#389C2314yes—
308#389C2314yes—
309#389C2314yes—
310#389C2318yes—
311#389C2318yes—
312#389C2314yes—
313#389C2318yes—
314#389C2318yes—
315#389C2314yes—
316#389C2318yes—
317#389C2314yes—
318#389C2312yes—
319#389C2312yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C2314yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2314yes—
336#388C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#386C2318yes—
349#386C2318yes—
350#386C2314yes—
351#386C2318yes—
352#386C2318yes—
353#386C2314yes—
354#386C2318yes—
355#386C2318yes—
356#386C2318yes—
357#386C2318yes—
358#386C2318yes—
359#386C2318yes—
360#386C2318yes—
361#386C2318yes—
362#386C2312yes—
363#386C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2318yes—
367#385C2318yes—
368#385C2318yes—
369#385C2318yes—
370#385C2318yes—
371#385C2318yes—
372#385C2318yes—
373#385C2318yes—
374#385C2318yes—
375#385C2318yes—
376#385C2312yes—
377#385C2314yes—
378#384C2311yescharacteristic
379#384C2312yes—
380#384C2314yes—
381#383C2318yes—
382#383C2318yes—
383#383C2314yes—
384#382C2312yes—
385#382C2314yes—
386#382C2314yes—
387#381C2314yes—
388#381C2318yes—
389#381C2314yes—
390#381C2314yes—
391#380C2314yes—
392#380C2314yes—
393#380C2314yes—
394#380C2314yes—
395#380C2314yes—
396#380C2312yes—
397#380C2314yes—
398#380C2312yes—
399#380C2314yes—
400#380C2314yes—
401#379C2312yes—
402#379C2318yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2311yescharacteristic
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2318yes—
408C4×C4⋊C4C2318yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2318yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2312yes—
415C4×C22⋊C4C2318yes—
416C4×C22⋊C4C2318yes—
417C4×C22⋊C4C2318yes—
418C4×C22⋊C4C2318yes—
419C4×C22⋊C4C2318yes—
420C4×C22⋊C4C2318yes—
421C4×C22⋊C4C2314yes—
422C4×C22⋊C4C2312yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2312yes—
425C4×C22⋊C4C2318yes—
426C4×C22⋊C4C2318yes—
427C4×C22⋊C4C2312yes—
428C43C2311yescharacteristic
429C25C2412yes—
430C2×#41—28no—
431C2×#41—216no—
432C2×#41—44no—
433C2×#41—44no—
434C2×#41—82no—
435C22×Q8C2412yes—
436C22×Q8C2414yes—
437C22×Q8C2412yes—
438C22×Q8C2412yes—
439C22×D4C2411yescharacteristic
440C22×D4C2414yes—
441C22×D4C2414yes—
442C22×D4C2412yes—
443C22×D4C2414yes—
444C22×D4C2414yes—
445C22×D4C2418yes—
446C22×D4C2411yescharacteristic
447C22×D4C2414yes—
448C22×D4C2414yes—
449C22×D4C2412yes—
450C22×D4C2411yescharacteristic
451C23×C4—216no—
452C23×C4—44no—
453C23×C4—48no—
454C23×C4—48no—
455C23×C4—84no—
456C23×C4C2412yes—
457C23×C4C2412yes—
458C23×C4C2414yes—
459C23×C4C2412yes—
460C23×C4C2414yes—
461C23×C4C2412yes—
462C23×C4C2414yes—
463C23×C4C2418yes—
464C23×C4C2414yes—
465C23×C4C2414yes—
466C23×C4C2418yes—
467C23×C4C2414yes—
468C4⋊Q8—28no—
469C4⋊Q8—42no—
470C4⋊Q8—42no—
471#127—24no—
472#124—232no—
473#124—48no—
474#124—416no—
475#124—82no—
476#123—216no—
477#123—216no—
478#123—216no—
479#123—48no—
480#123—48no—
481#123—48no—
482#123—84no—
483C22⋊Q8—216no—
484C22⋊Q8—216no—
485C22⋊Q8—416no—
486C22⋊Q8—44no—
487#121—216no—
488#121—216no—
489#121—216no—
490#121—216no—
491#121—44no—
492#121—416no—
493#121—44no—
494#121—44no—
495#120—216no—
496#120—28no—
497#120—216no—
498#120—48no—
499C4×Q8—48no—
500C4×Q8—48no—
501C4×D4—216no—
502C4×D4—216no—
503C4×D4—24no—
504C4×D4—216no—
505C4×D4—28no—
506C4×D4—48no—
507C4×D4—42no—
508C4×D4—42no—
509C4×D4—416no—
510C4×D4—416no—
511C4×D4—416no—
512C4×D4—416no—
513C4×D4—84no—
514C4×D4—88no—
515C4×D4#41116yescomplemented
516#117—216no—
517#117—216no—
518#117—28no—
519#117—216no—
520#117—44no—
521#117—48no—
522#117—48no—
523#117—84no—
524C2×C4⋊C4—216no—
525C2×C4⋊C4—28no—
526C2×C4⋊C4—44no—
527C2×C4⋊C4—48no—
528C2×C4⋊C4—48no—
529C2×C4⋊C4—416no—
530C2×C4⋊C4—44no—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2412yes—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2411yescharacteristic
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2411yescharacteristic
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2411yescharacteristic
563C2×C22⋊C4C2412yes—
564C2×C22⋊C4C2414yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2418yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2412yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2412yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2412yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2412yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2414yes—
598C2×C42—82no—
599C2×C42C2414yes—
600C2×C42C2418yes—
601C2×C42C2414yes—
602C2×C42C2411yescharacteristic
603C2×C42C2411yescharacteristic
604C2×C42C2418yes—
605C2×C42C2418yes—
606C2×C42C2418yes—
607C2×C42C2418yes—
608C2×C42C2414yes—
609C2×C42C2412yes—
610C2×C42C2412yes—
611C2×C42C2411yescharacteristic
612C2×C42C2412yes—
613#95C2414yes—
614#95C2418yes—
615#95C2412yes—
616#95C2418yes—
617#95C2418yes—
618#95C2418yes—
619#95C2414yes—
620#95C2412yes—
621#95C2418yes—
622#95C2418yes—
623#95C2418yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C2418yes—
630#95C2418yes—
631#95C2414yes—
632#95C2414yes—
633#95C2412yes—
634#95C2414yes—
635#95C2418yes—
636#95C2418yes—
637#95C2414yes—
638#95C2414yes—
639#95C2418yes—
640#95C2418yes—
641C24—28no—
642C24—24no—
643C24—42no—
644C24—42no—
645C24—44no—
646C24C2512yes—
647C24C2512yes—
648C24C2514yes—
649C24C2512yes—
650#41—432no—
651#41—816no—
652C2×Q8—28no—
653C2×Q8—28no—
654C2×Q8—24no—
655C2×Q8—42no—
656C2×Q8—44no—
657C2×Q8—42no—
658C2×Q8—42no—
659C2×Q8—44no—
660C2×Q8—42no—
661C2×Q8—44no—
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—28no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—216no—
669C2×D4—28no—
670C2×D4—28no—
671C2×D4—24no—
672C2×D4—28no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—44no—
676C2×D4—42no—
677C2×D4—41no—
678C2×D4—42no—
679C2×D4—44no—
680C2×D4—42no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—41no—
685C2×D4—48no—
686C2×D4—41no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—41no—
690C2×D4—48no—
691C2×D4—44no—
692C2×D4—48no—
693C2×D4C2×#4118yes—
694C2×D4H(5,𝔽2)14yes—
695C22×C4—28no—
696C22×C4—28no—
697C22×C4—28no—
698C22×C4—28no—
699C22×C4—28no—
700C22×C4—28no—
701C22×C4—28no—
702C22×C4—28no—
703C22×C4—28no—
704C22×C4—28no—
705C22×C4—24no—
706C22×C4—28no—
707C22×C4—24no—
708C22×C4—24no—
709C22×C4—24no—
710C22×C4—216no—
711C22×C4—44no—
712C22×C4—42no—
713C22×C4—42no—
714C22×C4—44no—
715C22×C4—44no—
716C22×C4—44no—
717C22×C4—432no—
718C22×C4—44no—
719C22×C4—48no—
720C22×C4—48no—
721C22×C4—48no—
722C22×C4—48no—
723C22×C4—48no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—44no—
728C22×C4—832no—
729C22×C4C2×#41116yes—
730C22×C4C2511yescharacteristic
731C22×C4C2514yes—
732C22×C4C2514yes—
733C22×C4C2514yes—
734C22×C4C2518yes—
735C22×C4C2512yes—
736C22×C4C2512yes—
737C22×C4C2514yes—
738C22×C4C2514yes—
739C22×C4C2518yes—
740C22×C4C2512yes—
741C22×C4C2512yes—
742C22×C4C2514yes—
743C22×C4C2512yes—
744C22×C4C2511yescharacteristic
745C22×C4C2511yescharacteristic
746C4⋊C4—24no—
747C4⋊C4—28no—
748C4⋊C4—28no—
749C4⋊C4—28no—
750C4⋊C4—28no—
751C4⋊C4—28no—
752C4⋊C4—28no—
753C4⋊C4—28no—
754C4⋊C4—28no—
755C4⋊C4—216no—
756C4⋊C4—24no—
757C4⋊C4—28no—
758C4⋊C4—24no—
759C4⋊C4—216no—
760C4⋊C4—48no—
761C4⋊C4—44no—
762C4⋊C4—44no—
763C4⋊C4—42no—
764C4⋊C4—48no—
765C4⋊C4—48no—
766C4⋊C4—41no—
767C4⋊C4—48no—
768C4⋊C4—42no—
769C4⋊C4—42no—
770C4⋊C4—44no—
771C4⋊C4—44no—
772C4⋊C4—41no—
773C4⋊C4—48no—
774C4⋊C4—48no—
775C4⋊C4—42no—
776C4⋊C4C2×#4118yes—
777C4⋊C4H(5,𝔽2)14yes—
778C22⋊C4—216no—
779C22⋊C4—28no—
780C22⋊C4—28no—
781C22⋊C4—24no—
782C22⋊C4—28no—
783C22⋊C4—216no—
784C22⋊C4—28no—
785C22⋊C4—28no—
786C22⋊C4—216no—
787C22⋊C4—28no—
788C22⋊C4—28no—
789C22⋊C4—28no—
790C22⋊C4—28no—
791C22⋊C4—28no—
792C22⋊C4—28no—
793C22⋊C4—24no—
794C22⋊C4—28no—
795C22⋊C4—44no—
796C22⋊C4—48no—
797C22⋊C4—44no—
798C22⋊C4—48no—
799C22⋊C4—48no—
800C22⋊C4—44no—
801C22⋊C4—48no—
802C22⋊C4—48no—
803C22⋊C4—48no—
804C22⋊C4—42no—
805C22⋊C4—48no—
806C22⋊C4—42no—
807C22⋊C4—48no—
808C22⋊C4—48no—
809C22⋊C4—44no—
810C22⋊C4—44no—
811C22⋊C4—42no—
812C22⋊C4C2×#41116yes—
813C42—216no—
814C42—28no—
815C42—28no—
816C42—22no—
817C42—22no—
818C42—41no—
819C42—44no—
820C42—42no—
821C42—42no—
822C42—48no—
823C42—48no—
824C42—48no—
825C42—48no—
826C42C2×#4118yes—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—22no—
832C23—24no—
833C23—22no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—24no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—24no—
846C23—24no—
847C23—48no—
848C23—416no—
849C23—48no—
850C23—416no—
851C23—48no—
852C23C22×#4118yes—
853C23C2×H(5,𝔽2)14yes—
854C23C2611yescharacteristic
855Q8—48no—
856Q8—88no—
857Q8—84no—
858Q8—162no—
859D4—48no—
860D4—44no—
861D4—416no—
862D4—416no—
863D4—416no—
864D4—48no—
865D4—416no—
866D4—44no—
867D4—82no—
868D4—816no—
869D4—88no—
870D4—164no—
871C2×C4—24no—
872C2×C4—22no—
873C2×C4—21no—
874C2×C4—22no—
875C2×C4—24no—
876C2×C4—22no—
877C2×C4—21no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—232no—
882C2×C4—24no—
883C2×C4—24no—
884C2×C4—24no—
885C2×C4—28no—
886C2×C4—24no—
887C2×C4—24no—
888C2×C4—22no—
889C2×C4—24no—
890C2×C4—21no—
891C2×C4—28no—
892C2×C4—24no—
893C2×C4—28no—
894C2×C4—28no—
895C2×C4—22no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—28no—
901C2×C4—24no—
902C2×C4—22no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—28no—
906C2×C4—24no—
907C2×C4—28no—
908C2×C4—48no—
909C2×C4—48no—
910C2×C4—416no—
911C2×C4—416no—
912C2×C4—416no—
913C2×C4—48no—
914C2×C4—48no—
915C2×C4—816no—
916C2×C4—88no—
917C2×C4—816no—
918C2×C4—164no—
919C2×C4C22×#4118yes—
920C2×C4C22×#4114yes—
921C2×C4C22×#4114yes—
922C2×C4C22×#4114yes—
923C2×C4C2×H(5,𝔽2)14yes—
924C2×C4C2×H(5,𝔽2)12yes—
925C2×C4C2×H(5,𝔽2)12yes—
926C22—28no—
927C22—28no—
928C22—28no—
929C22—24no—
930C22—28no—
931C22—432no—
932C22—44no—
933C22—44no—
934C22—42no—
935C22—44no—
936C22—44no—
937C22—44no—
938C22—42no—
939C22—44no—
940C22—44no—
941C22—42no—
942C22—42no—
943C22—44no—
944C22—44no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22C23×#4112yes—
950C22C22×H(5,𝔽2)11yescharacteristic
951C22C22×H(5,𝔽2)11yescharacteristic
952C22H(7,𝔽2)11yescharacteristic
953C222−1+612yes—
954C4—24no—
955C4—24no—
956C4—24no—
957C4—22no—
958C4—28no—
959C4—44no—
960C4—48no—
961C4—44no—
962C4—41no—
963C4—44no—
964C4—44no—
965C4—44no—
966C4—48no—
967C4—42no—
968C4—42no—
969C4#348114yes—
970C2—44no—
971C2—48no—
972C2—82no—
973C2—82no—
974C2C2×#348111yescharacteristic
975C2#6284512yes—
976C2#6289211yescharacteristic
977C2#6298512yes—
978C2#6304811yescharacteristic
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. #60046C2semidirect
2. #59827C2semidirect
3. #59201C2semidirect
4. #59173C2semidirect
5. #52163C2semidirect
6. #52103C2semidirect
7. #45330C2semidirect
8. #44922C2semidirect
9. #43805C2semidirect
10. #43462C2semidirect
11. #40388C2semidirect
12. #39493C2semidirect
13. #38761C2semidirect
14. #37845C2semidirect
15. #36415C2semidirect
16. #36103C2semidirect
17. #35774C2semidirect
18. #35756C2semidirect
19. #34321C2semidirect
20. #34200C2semidirect
23. C2×#555C22semidirect
28. C23×C4⋊C4C22semidirect
29. #2862C22semidirect
30. #2850C22semidirect
31. #2849C22semidirect
32. #2847C22semidirect
33. #2806C22semidirect
34. #2805C22semidirect
36. #2796C22semidirect
37. #2780C22semidirect
38. #2777C22semidirect
39. #2764C22semidirect
40. #2757C22semidirect
41. #2736C22semidirect
45. #2724C22semidirect
47. #2700C22semidirect
56. #2670C22semidirect
59. #2649C22semidirect
61. #2628C22semidirect
63. #2602C22semidirect
65. #2599C22semidirect
66. #2598C22semidirect
67. #2592C22semidirect
68. #2589C22semidirect
69. #2588C22semidirect
70. #2586C22semidirect
71. #2582C22semidirect
72. #2573C22semidirect
74. #2570C22semidirect
77. #2557C22semidirect
79. #2547C22semidirect
80. #2547C22semidirect
81. #2535C22semidirect
82. #2525C22semidirect
83. #2523C22semidirect
84. #2523C22semidirect
85. #2515C22semidirect
86. #2504C22semidirect
87. #2501C22semidirect
88. #2499C22semidirect
89. #2497C22semidirect
90. #2495C22semidirect
92. #2486C22semidirect
94. #2485C22semidirect
95. #2477C22semidirect
96. #2474C22semidirect
97. #2471C22semidirect
98. #2470C22semidirect
99. #2465C22semidirect
100. #2461C22semidirect
102. #2459C22semidirect
104. #2456C22semidirect
105. #2449C22semidirect
106. #2447C22semidirect
108. #2440C22semidirect
109. #2439C22semidirect
112. #2414C22semidirect
113. #2413C22semidirect
120. #2369C22semidirect
121. #2367C22semidirect
125. #2361C22semidirect
126. #2360C22semidirect
127. #2360C22semidirect
128. #2354C22semidirect
131. #2352C22semidirect
132. #2352C22semidirect
135. D4×C4⋊C4C22semidirect
136. D4×C4⋊C4C22semidirect
137. #2347C22semidirect
138. #2347C22semidirect
139. #2347C22semidirect
140. #2344C22semidirect
141. #2337C22semidirect
142. #2324C22semidirect
144. #2322C22semidirect
145. #2317C22semidirect
147. C4×C4⋊Q8C22semidirect
152. C4×#120C22semidirect
154. #2296C22semidirect
156. #2280C22semidirect
157. #2274C22semidirect
158. C42×D4C22semidirect
515. C4×D4#41semidirect

Maximal subgroups

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

subgroupindex
#600462
#598272
#592012
#591732
#521632
#521032
#453302
#449222
#438052
#434622
#403882
#394932
#387612
#378452
#364152
#361032
#357742
#357562
#343212
#342002