Finite Group Databasebeta

← #7697256

Subgroups — #7697256

Order 512.

5329 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59846C214yesmaximal, complemented
2#59836C212yesmaximal, complemented
3#59827C211yesmaximal, characteristic, complemented
4#59198C212yesmaximal, complemented
5#52304C212yesmaximal, complemented
6#52103C211yesmaximal, characteristic
7#45251C212yesmaximal, complemented
8#45120C214yesmaximal, complemented
9#44862C214yesmaximal, complemented
10#44586C218yesmaximal, complemented
11#40398C218yesmaximal, complemented
12#39493C212yesmaximal, complemented
13#38770C214yesmaximal, complemented
14#37838C214yesmaximal, complemented
15#36534C211yesmaximal, characteristic, complemented
16#36516C212yesmaximal, complemented
17#36089C212yesmaximal, complemented
18#35833C214yesmaximal, complemented
19#34317C212yesmaximal, complemented
20#34202C214yesmaximal, complemented
21C2×#559C2212yes—
22C2×#556C2211yescharacteristic, complemented
23C2×#554C2212yes—
24C2×#554C2211yescharacteristic
25C2×#551C2214yes—
26C2×#525C2214yes—
27C2×#520C2212yes—
28C22×#117C2212yescomplemented
29#2862C2211yescharacteristic, complemented
30#2861C2212yescomplemented
31#2855C2214yescomplemented
32#2848C2212yescomplemented
33#2806C2214yescomplemented
34#2805C2214yescomplemented
35#2804C2214yes—
36#2802C2218yescomplemented
37#2789C2214yescomplemented
38#2787C2218yescomplemented
39#2782C2218yescomplemented
40#2765C2218yescomplemented
41#2760C2214yes—
42#2751C2218yescomplemented
43#2732C2214yes—
44#2724C2212yes—
45#2724C2212yescomplemented
46#2722C2214yescomplemented
47#2717C2214yes—
48#2694C2218yescomplemented
49#2690C2218yescomplemented
50#2687C2218yes—
51#2683C2211yescharacteristic
52#2682C2212yes—
53#2681C2214yes—
54#2680C2212yes—
55#2679C2211yescharacteristic
56#2678C2214yes—
57#2672C2218yes—
58#2669C2212yes—
59#2654C2218yescomplemented
60#2637C2214yescomplemented
61#2628C2214yescomplemented
62#2616C2212yes—
63#2609C2214yes—
64#2607C2214yescomplemented
65#2603C2214yes—
66#2600C2218yes—
67#2589C2218yescomplemented
68#2587C2218yescomplemented
69#2582C2212yescomplemented
70#2570C2214yescomplemented
71#2565C2212yescomplemented
72#2563C2211yescharacteristic, complemented
73#2561C2214yescomplemented
74#2560C2218yescomplemented
75#2557C2218yes—
76#2553C2218yes—
77#2549C2218yescomplemented
78#2547C2211yescharacteristic
79#2547C2214yescomplemented
80#2544C2212yes—
81#2536C2214yes—
82#2536C2214yescomplemented
83#2534C2214yes—
84#2527C2218yescomplemented
85#2521C2218yescomplemented
86#2520C2218yescomplemented
87#2516C2218yescomplemented
88#2503C2212yescomplemented
89#2502C2212yescomplemented
90#2496C2214yescomplemented
91#2494C2214yescomplemented
92#2487C2214yescomplemented
93#2486C2212yes—
94#2486C2214yes—
95#2486C2212yescomplemented
96#2483C2214yescomplemented
97#2477C2218yes—
98#2475C2218yescomplemented
99#2472C2218yescomplemented
100#2471C2218yescomplemented
101#2468C2218yes—
102#2468C2218yescomplemented
103#2466C2218yescomplemented
104#2465C2218yescomplemented
105#2461C2218yescomplemented
106#2447C2218yescomplemented
107#2444C2218yes—
108#2440C2214yescomplemented
109#2439C2214yescomplemented
110#2438C2218yescomplemented
111#2419C2218yes—
112#2418C2218yes—
113#2417C2214yescomplemented
114#2415C2214yes—
115#2401C2218yescomplemented
116#2399C2214yescomplemented
117#2392C2214yes—
118#2388C2212yes—
119#2370C2214yescomplemented
120#2369C2212yescomplemented
121#2362C2218yescomplemented
122#2362C2214yescomplemented
123#2359C2218yes—
124#2359C2218yescomplemented
125#2358C2218yes—
126#2358C2218yescomplemented
127#2357C2214yes—
128#2355C2212yescomplemented
129#2354C2212yes—
130#2354C2214yescomplemented
131#2352C2214yes—
132#2352C2214yes—
133#2352C2214yescomplemented
134#2352C2214yescomplemented
135D4×C4⋊C4C2214yes—
136D4×C4⋊C4C2214yescomplemented
137#2346C2212yescomplemented
138#2345C2212yescomplemented
139#2344C2214yescomplemented
140#2332C2218yescomplemented
141#2324C2218yes—
142#2323C2214yescomplemented
143#2323C2218yescomplemented
144#2317C2214yescomplemented
145#2311C2214yes—
146C4×C4⋊Q8C2212yescomplemented
147C4×#127C2211yescharacteristic
148C4×#125C2214yescomplemented
149C4×#124C2212yes—
150C4×C22⋊Q8C2218yescomplemented
151C4×#123C2214yes—
152C4×#121C2218yes—
153C4×#120C2212yes—
154#2293C2212yes—
155#2293C2214yes—
156C2×#380C2214yescomplemented
157#2274C2214yescomplemented
158C42×Q8C2211yescharacteristic, complemented
159C22×#41C2312yes—
160C24×C4C2312yes—
161#559—48no—
162#556—44no—
163#554—216no—
164#554—44no—
165#551—416no—
166C2×C4⋊Q8C2312yes—
167C2×C4⋊Q8C2311yescharacteristic
168C2×C4⋊Q8C2311yescharacteristic
169C2×#127C2311yescharacteristic
170C2×#126C2314yes—
171C2×#126C2318yes—
172C2×#125C2314yes—
173C2×#125C2312yes—
174C2×#124C2312yes—
175C2×#124C2312yes—
176C2×#124C2318yes—
177#525—232no—
178C2×#123C2314yes—
179C2×#123C2314yes—
180C2×#123C2314yes—
181C2×#123C2318yes—
182C2×#123C2314yes—
183C2×C22⋊Q8C2314yes—
184C2×C22⋊Q8C2314yes—
185C2×C22⋊Q8C2318yes—
186C2×C22⋊Q8C2314yes—
187C2×C22⋊Q8C2314yes—
188C2×C22⋊Q8C2312yes—
189C2×C22⋊Q8C2312yes—
190C2×C22⋊Q8C2318yes—
191C2×#121C2314yes—
192C2×#121C2314yes—
193C2×#120C2314yes—
194C2×#120C2314yes—
195C2×#120C2312yes—
196#520—48no—
197C2×C4×Q8C2312yes—
198C2×C4×Q8C2311yescharacteristic
199C2×C4×Q8C2314yes—
200C2×C4×Q8C2312yes—
201C2×C4×Q8C2314yes—
202C2×C4×D4C2314yes—
203C2×C4×D4C2314yes—
204C2×C4×D4C2314yes—
205C2×C4×D4C2314yes—
206C2×C4×D4C2311yescharacteristic
207C2×C4×D4C2311yescharacteristic
208C2×C4×D4C2318yes—
209C2×C4×D4C2318yes—
210C2×C4×D4C2318yes—
211C2×C4×D4C2314yes—
212C2×C4×D4C2312yes—
213C2×C4×D4C2312yes—
214C2×#117—48no—
215C2×#117C2314yes—
216C2×#117C2312yes—
217C2×#117C2314yes—
218C2×#117C2314yes—
219C2×#117C2318yes—
220C2×#117C2318yes—
221C22×C4⋊C4C2314yes—
222C22×C4⋊C4C2312yes—
223C22×C4⋊C4C2314yes—
224C22×C4⋊C4C2312yes—
225C22×C4⋊C4C2312yes—
226C22×C22⋊C4C2314yes—
227C22×C22⋊C4C2318yes—
228C22×C42C2314yes—
229#401C2318yes—
230#400C2318yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#400C2318yes—
235#399C2318yes—
236#399C2318yes—
237#398C2318yes—
238#398C2318yes—
239#398C2314yes—
240#398C2314yes—
241#398C2318yes—
242#398C2314yes—
243#398C2314yes—
244#398C2314yes—
245#398C2318yes—
246#398C2318yes—
247#397C2314yes—
248#397C2318yes—
249#397C2318yes—
250#397C2314yes—
251#397C2314yes—
252#397C2318yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#397C2314yes—
257#396C2314yes—
258#396C2318yes—
259#396C2318yes—
260#396C2314yes—
261#395C2314yes—
262#395C2318yes—
263#395C2312yes—
264#395C2318yes—
265#394C2318yes—
266#394C2318yes—
267#394C2314yes—
268#394C2312yes—
269#394C2318yes—
270#394C2314yes—
271#394C2314yes—
272#394C2314yes—
273#394C2314yes—
274#393C2314yes—
275#393C2318yes—
276#393C2312yes—
277#393C2318yes—
278#392C2314yes—
279#392C2312yes—
280#392C2314yes—
281#391C2314yes—
282#391C2314yes—
283#391C2312yes—
284#391C2312yes—
285#391C2318yes—
286#391C2314yes—
287#391C2318yes—
288#391C2318yes—
289#391C2318yes—
290#391C2312yes—
291#390C2314yes—
292#390C2311yescharacteristic
293#390C2311yescharacteristic
294#390C2312yes—
295#390C2318yes—
296#390C2314yes—
297#390C2318yes—
298#390C2312yes—
299#390C2312yes—
300#389C2312yes—
301#389C2314yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2318yes—
306#389C2318yes—
307#389C2318yes—
308#389C2318yes—
309#389C2314yes—
310#389C2318yes—
311#389C2318yes—
312#389C2314yes—
313#389C2312yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2314yes—
327#388C2318yes—
328#388C2318yes—
329#388C2314yes—
330#388C2318yes—
331#388C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#386C2318yes—
348#386C2318yes—
349#386C2318yes—
350#386C2318yes—
351#386C2318yes—
352#386C2318yes—
353#386C2318yes—
354#386C2312yes—
355#386C2314yes—
356#386C2318yes—
357#385C2318yes—
358#385C2318yes—
359#385C2318yes—
360#385C2318yes—
361#385C2318yes—
362#385C2318yes—
363#385C2314yes—
364#385C2318yes—
365#385C2312yes—
366#385C2318yes—
367#385C2318yes—
368#385C2318yes—
369#385C2314yes—
370#384C2311yescharacteristic
371#384C2312yes—
372#384C2314yes—
373#382C2314yes—
374#382C2312yes—
375#382C2314yes—
376#382C2314yes—
377#382C2314yes—
378#381C2314yes—
379#381C2314yes—
380#381C2318yes—
381#381C2314yes—
382#381C2314yes—
383#381C2318yes—
384#380C2314yes—
385#380C2314yes—
386#380C2314yes—
387#380C2314yes—
388#380C2318yes—
389#380C2312yes—
390#380C2314yes—
391#380C2312yes—
392#380C2314yes—
393#380C2314yes—
394#380C2314yes—
395#380C2318yes—
396#380C2318yes—
397#379C2312yes—
398#379C2314yes—
399C4×C4⋊C4C2314yes—
400C4×C4⋊C4C2318yes—
401C4×C4⋊C4C2314yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2318yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2311yescharacteristic
407C4×C4⋊C4C2312yes—
408C4×C4⋊C4C2312yes—
409C4×C4⋊C4C2318yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2312yes—
414C4×C4⋊C4C2318yes—
415C4×C22⋊C4C2318yes—
416C4×C22⋊C4C2314yes—
417C4×C22⋊C4C2318yes—
418C4×C22⋊C4C2318yes—
419C4×C22⋊C4C2318yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2312yes—
422C4×C22⋊C4C2312yes—
423C4×C22⋊C4C2318yes—
424C4×C22⋊C4C2318yes—
425#376C2314yes—
426C2×#95C2318yes—
427C43C2312yes—
428C43C2311yescharacteristic
429C25C2412yes—
430C2×#41—216no—
431C2×#41—44no—
432C22×Q8C2411yescharacteristic
433C22×Q8C2412yes—
434C22×Q8C2412yes—
435C22×Q8C2414yes—
436C22×Q8C2412yes—
437C22×D4C2414yes—
438C22×D4C2414yes—
439C22×D4C2412yes—
440C22×D4C2414yes—
441C22×D4C2414yes—
442C22×D4C2411yescharacteristic
443C22×D4C2412yes—
444C22×D4C2411yescharacteristic
445C23×C4—216no—
446C23×C4—44no—
447C23×C4C2412yes—
448C23×C4C2412yes—
449C23×C4C2414yes—
450C23×C4C2412yes—
451C23×C4C2414yes—
452C23×C4C2418yes—
453C23×C4C2414yes—
454C23×C4C2414yes—
455C23×C4C2418yes—
456C23×C4C2414yes—
457C4⋊Q8—28no—
458C4⋊Q8—42no—
459C4⋊Q8—42no—
460#127—24no—
461#126—48no—
462#126—416no—
463#125—216no—
464#125—44no—
465#124—28no—
466#124—44no—
467#124—416no—
468#123—216no—
469#123—216no—
470#123—216no—
471#123—416no—
472#123—48no—
473C22⋊Q8—216no—
474C22⋊Q8—216no—
475C22⋊Q8—216no—
476C22⋊Q8—232no—
477C22⋊Q8—416no—
478C22⋊Q8—48no—
479C22⋊Q8—44no—
480C22⋊Q8—44no—
481#121—216no—
482#121—216no—
483#120—216no—
484#120—28no—
485#120—216no—
486C4×Q8—24no—
487C4×Q8—28no—
488C4×Q8—48no—
489C4×Q8—44no—
490C4×Q8—48no—
491C4×D4—216no—
492C4×D4—216no—
493C4×D4—216no—
494C4×D4—216no—
495C4×D4—416no—
496C4×D4—48no—
497C4×D4—42no—
498C4×D4—44no—
499C4×D4—42no—
500C4×D4—416no—
501C4×D4—416no—
502C4×D4#41116yes—
503#117—216no—
504#117—28no—
505#117—216no—
506#117—416no—
507#117—416no—
508#117—48no—
509C2×C4⋊C4—216no—
510C2×C4⋊C4—28no—
511C2×C4⋊C4—44no—
512C2×C4⋊C4—44no—
513C2×C4⋊C4—48no—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2412yes—
516C2×C4⋊C4C2412yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2412yes—
519C2×C4⋊C4C2418yes—
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2418yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2412yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2418yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2411yescharacteristic
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2411yescharacteristic
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2411yescharacteristic
551C2×C22⋊C4—48no—
552C2×C22⋊C4—416no—
553C2×C22⋊C4C2418yes—
554C2×C22⋊C4C2418yes—
555C2×C22⋊C4C2418yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2414yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2414yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C2412yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2418yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2412yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2412yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2412yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C42—48no—
585C2×C42C2412yes—
586C2×C42C2418yes—
587C2×C42C2414yes—
588C2×C42C2414yes—
589C2×C42C2411yescharacteristic
590C2×C42C2412yes—
591C2×C42C2414yes—
592C2×C42C2411yescharacteristic
593C2×C42C2418yes—
594C2×C42C2418yes—
595C2×C42C2418yes—
596C2×C42C2411yescharacteristic
597C2×C42C2414yes—
598C2×C42C2412yes—
599C2×C42C2418yes—
600C2×C42C2412yes—
601#95C2418yes—
602#95C2418yes—
603#95C2418yes—
604#95C2418yes—
605#95C2412yes—
606#95C2414yes—
607#95C2418yes—
608#95C2414yes—
609#95C2418yes—
610#95C2418yes—
611#95C2418yes—
612#95C2414yes—
613#95C2418yes—
614#95C2418yes—
615#95C2418yes—
616#95C2418yes—
617#95C2412yes—
618#95C2418yes—
619#95C2418yes—
620#95C2414yes—
621#95C2414yes—
622#95C2418yes—
623#95C2412yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C2414yes—
630#95C2414yes—
631C24—28no—
632C24—24no—
633C24—42no—
634C24—44no—
635C24—42no—
636C24C2512yes—
637C24C2514yes—
638C24C2512yes—
639#41—432no—
640C2×Q8—24no—
641C2×Q8—28no—
642C2×Q8—28no—
643C2×Q8—22no—
644C2×Q8—24no—
645C2×Q8—42no—
646C2×Q8—44no—
647C2×Q8—42no—
648C2×Q8—44no—
649C2×Q8—42no—
650C2×Q8—42no—
651C2×Q8—44no—
652C2×D4—28no—
653C2×D4—28no—
654C2×D4—28no—
655C2×D4—28no—
656C2×D4—28no—
657C2×D4—28no—
658C2×D4—28no—
659C2×D4—28no—
660C2×D4—22no—
661C2×D4—41no—
662C2×D4—44no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4—41no—
667C2×D4—44no—
668C2×D4—44no—
669C2×D4—41no—
670C2×D4—41no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4C2×#4118yes—
674C2×D4H(5,𝔽2)14yes—
675C22×C4—28no—
676C22×C4—28no—
677C22×C4—28no—
678C22×C4—216no—
679C22×C4—28no—
680C22×C4—28no—
681C22×C4—28no—
682C22×C4—28no—
683C22×C4—28no—
684C22×C4—24no—
685C22×C4—24no—
686C22×C4—28no—
687C22×C4—42no—
688C22×C4—44no—
689C22×C4—432no—
690C22×C4—44no—
691C22×C4—48no—
692C22×C4—48no—
693C22×C4—48no—
694C22×C4—44no—
695C22×C4—48no—
696C22×C4—44no—
697C22×C4—48no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—48no—
701C22×C4C2×#41116yes—
702C22×C4C2514yes—
703C22×C4C2511yescharacteristic
704C22×C4C2514yes—
705C22×C4C2514yes—
706C22×C4C2518yes—
707C22×C4C2512yes—
708C22×C4C2512yes—
709C22×C4C2518yes—
710C22×C4C2514yes—
711C22×C4C2514yes—
712C22×C4C2512yes—
713C22×C4C2512yes—
714C22×C4C2512yes—
715C22×C4C2514yes—
716C22×C4C2512yes—
717C22×C4C2511yescharacteristic
718C22×C4C2511yescharacteristic
719C4⋊C4—24no—
720C4⋊C4—216no—
721C4⋊C4—28no—
722C4⋊C4—28no—
723C4⋊C4—28no—
724C4⋊C4—28no—
725C4⋊C4—28no—
726C4⋊C4—28no—
727C4⋊C4—28no—
728C4⋊C4—28no—
729C4⋊C4—216no—
730C4⋊C4—28no—
731C4⋊C4—24no—
732C4⋊C4—28no—
733C4⋊C4—24no—
734C4⋊C4—216no—
735C4⋊C4—24no—
736C4⋊C4—44no—
737C4⋊C4—48no—
738C4⋊C4—44no—
739C4⋊C4—42no—
740C4⋊C4—42no—
741C4⋊C4—44no—
742C4⋊C4—48no—
743C4⋊C4—48no—
744C4⋊C4—48no—
745C4⋊C4—44no—
746C4⋊C4—41no—
747C4⋊C4—48no—
748C4⋊C4—41no—
749C4⋊C4—42no—
750C4⋊C4—44no—
751C4⋊C4—44no—
752C4⋊C4—48no—
753C4⋊C4—42no—
754C4⋊C4C2×#4118yes—
755C4⋊C4H(5,𝔽2)14yes—
756C22⋊C4—28no—
757C22⋊C4—28no—
758C22⋊C4—216no—
759C22⋊C4—216no—
760C22⋊C4—216no—
761C22⋊C4—24no—
762C22⋊C4—28no—
763C22⋊C4—28no—
764C22⋊C4—28no—
765C22⋊C4—28no—
766C22⋊C4—28no—
767C22⋊C4—28no—
768C22⋊C4—28no—
769C22⋊C4—216no—
770C22⋊C4—28no—
771C22⋊C4—28no—
772C22⋊C4—48no—
773C22⋊C4—48no—
774C22⋊C4—48no—
775C22⋊C4—44no—
776C22⋊C4—44no—
777C22⋊C4—48no—
778C22⋊C4—48no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—44no—
782C22⋊C4—48no—
783C22⋊C4—42no—
784C22⋊C4—44no—
785C22⋊C4—44no—
786C22⋊C4C2×#41116yes—
787C42—28no—
788C42—28no—
789C42—216no—
790C42—28no—
791C42—24no—
792C42—22no—
793C42—24no—
794C42—22no—
795C42—48no—
796C42—44no—
797C42—42no—
798C42—48no—
799C42—41no—
800C42—48no—
801C42—48no—
802C42C2×#4118yes—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—22no—
808C23—24no—
809C23—24no—
810C23—22no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—22no—
815C23—22no—
816C23—24no—
817C23—22no—
818C23—48no—
819C23—416no—
820C23—88no—
821C23—84no—
822C23—84no—
823C23C22×#4118yes—
824C23C2×H(5,𝔽2)14yes—
825C23C2611yescharacteristic
826Q8—48no—
827Q8—44no—
828Q8—88no—
829Q8—84no—
830Q8—162no—
831D4—48no—
832D4—44no—
833D4—416no—
834D4—416no—
835D4—416no—
836D4—48no—
837D4—82no—
838D4—88no—
839C2×C4—24no—
840C2×C4—21no—
841C2×C4—24no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—24no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—21no—
848C2×C4—232no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—28no—
856C2×C4—22no—
857C2×C4—24no—
858C2×C4—28no—
859C2×C4—24no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—24no—
863C2×C4—28no—
864C2×C4—24no—
865C2×C4—28no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—22no—
871C2×C4—28no—
872C2×C4—28no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—28no—
876C2×C4—24no—
877C2×C4—48no—
878C2×C4—416no—
879C2×C4—48no—
880C2×C4—48no—
881C2×C4—88no—
882C2×C4—816no—
883C2×C4—88no—
884C2×C4—164no—
885C2×C4—168no—
886C2×C4C22×#4114yes—
887C2×C4C22×#4114yes—
888C2×C4C22×#4118yes—
889C2×C4C22×#4114yes—
890C2×C4C2×H(5,𝔽2)14yes—
891C2×C4C2×H(5,𝔽2)12yes—
892C2×C4C2×H(5,𝔽2)12yes—
893C22—28no—
894C22—28no—
895C22—28no—
896C22—24no—
897C22—28no—
898C22—44no—
899C22—42no—
900C22—44no—
901C22—44no—
902C22—44no—
903C22—44no—
904C22—42no—
905C22—44no—
906C22—42no—
907C22—44no—
908C22—42no—
909C22—42no—
910C22—816no—
911C22C23×#4112yes—
912C22C22×H(5,𝔽2)11yescharacteristic
913C22C22×H(5,𝔽2)11yescharacteristic
914C222−1+612yes—
915C222−1+611yescharacteristic
916C4—24no—
917C4—24no—
918C4—24no—
919C4—22no—
920C4—28no—
921C4—44no—
922C4—48no—
923C4—44no—
924C4—44no—
925C4—41no—
926C4—44no—
927C4—48no—
928C4—44no—
929C4—42no—
930C4—42no—
931C4—42no—
932C4#348114yes—
933C2—48no—
934C2—44no—
935C2—82no—
936C2C2×#348111yescharacteristic
937C2#6286012yes—
938C2#6289511yescharacteristic
939C2#6298512yes—
940C2#6306311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#52103C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59846C2semidirect
2. #59836C2semidirect
3. #59827C2semidirect
4. #59198C2semidirect
5. #52304C2semidirect
7. #45251C2semidirect
8. #45120C2semidirect
9. #44862C2semidirect
10. #44586C2semidirect
11. #40398C2semidirect
12. #39493C2semidirect
13. #38770C2semidirect
14. #37838C2semidirect
15. #36534C2semidirect
16. #36516C2semidirect
17. #36089C2semidirect
18. #35833C2semidirect
19. #34317C2semidirect
20. #34202C2semidirect
22. C2×#556C22semidirect
28. C22×#117C22semidirect
29. #2862C22semidirect
30. #2861C22semidirect
31. #2855C22semidirect
32. #2848C22semidirect
33. #2806C22semidirect
34. #2805C22semidirect
36. #2802C22semidirect
37. #2789C22semidirect
38. #2787C22semidirect
39. #2782C22semidirect
40. #2765C22semidirect
42. #2751C22semidirect
45. #2724C22semidirect
46. #2722C22semidirect
48. #2694C22semidirect
49. #2690C22semidirect
59. #2654C22semidirect
60. #2637C22semidirect
61. #2628C22semidirect
64. #2607C22semidirect
67. #2589C22semidirect
68. #2587C22semidirect
69. #2582C22semidirect
70. #2570C22semidirect
71. #2565C22semidirect
72. #2563C22semidirect
73. #2561C22semidirect
74. #2560C22semidirect
77. #2549C22semidirect
79. #2547C22semidirect
82. #2536C22semidirect
84. #2527C22semidirect
85. #2521C22semidirect
86. #2520C22semidirect
87. #2516C22semidirect
88. #2503C22semidirect
89. #2502C22semidirect
90. #2496C22semidirect
91. #2494C22semidirect
92. #2487C22semidirect
95. #2486C22semidirect
96. #2483C22semidirect
98. #2475C22semidirect
99. #2472C22semidirect
100. #2471C22semidirect
102. #2468C22semidirect
103. #2466C22semidirect
104. #2465C22semidirect
105. #2461C22semidirect
106. #2447C22semidirect
108. #2440C22semidirect
109. #2439C22semidirect
110. #2438C22semidirect
113. #2417C22semidirect
115. #2401C22semidirect
116. #2399C22semidirect
119. #2370C22semidirect
120. #2369C22semidirect
121. #2362C22semidirect
122. #2362C22semidirect
124. #2359C22semidirect
126. #2358C22semidirect
128. #2355C22semidirect
130. #2354C22semidirect
133. #2352C22semidirect
134. #2352C22semidirect
136. D4×C4⋊C4C22semidirect
137. #2346C22semidirect
138. #2345C22semidirect
139. #2344C22semidirect
140. #2332C22semidirect
142. #2323C22semidirect
143. #2323C22semidirect
144. #2317C22semidirect
146. C4×C4⋊Q8C22semidirect
148. C4×#125C22semidirect
150. C4×C22⋊Q8C22semidirect
156. C2×#380C22semidirect
157. #2274C22semidirect
158. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#598462
#598362
#598272
#591982
#523042
#521032
#452512
#451202
#448622
#445862
#403982
#394932
#387702
#378382
#365342
#365162
#360892
#358332
#343172
#342022