Finite Group Databasebeta

← #7806320

Subgroups — #7806320

Order 512.

5498 conjugacy classes of subgroups.

The subgroup lattice has 1037 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59676C214yesmaximal, complemented
2#59441C214yesmaximal, complemented
3#59322C211yesmaximal, characteristic, complemented
4#59314C212yesmaximal, complemented
5#59313C211yesmaximal, characteristic, complemented
6#59248C211yesmaximal, characteristic, complemented
7#59234C212yesmaximal, complemented
8#59233C211yesmaximal, characteristic, complemented
9#59136C214yesmaximal, complemented
10#59125C214yesmaximal, complemented
11#47752C214yesmaximal, complemented
12#47750C214yesmaximal, complemented
13#42458C214yesmaximal, complemented
14#42457C214yesmaximal, complemented
15#42021C214yesmaximal, complemented
16#37620C211yesmaximal, characteristic, complemented
17#35747C214yesmaximal, complemented
18#35740C214yesmaximal, complemented
19#35697C214yesmaximal, complemented
20#34964C212yesmaximal, complemented
21C2×#2551C211yesmaximal, characteristic, complemented
22#34243C212yesmaximal, complemented
23#34183C211yesmaximal, characteristic, complemented
24C2×#554C2214yes—
25C2×#548C2214yes—
26C2×#547C2214yes—
27C22×C4⋊Q8C2214yes—
28C2×#529C2212yes—
29C2×#520C2212yes—
30C2×C4×#41C2211yescharacteristic
31#2838C2218yes—
32#2823C2214yes—
33#2801C2218yes—
34#2792C2214yes—
35#2789C2214yes—
36#2785C2214yes—
37#2777C2218yes—
38#2775C2218yes—
39#2765C2218yes—
40#2757C2218yes—
41#2729C2218yes—
42#2729C2218yes—
43#2720C2218yes—
44#2680C2214yes—
45#2674C2218yes—
46#2674C2218yes—
47#2666C2218yes—
48#2663C2218yes—
49#2638C2214yes—
50#2632C2214yes—
51#2629C2214yes—
52#2620C2214yes—
53#2618C2214yes—
54#2610C2214yes—
55#2606C2218yes—
56#2602C2218yes—
57#2601C2214yes—
58#2601C2214yes—
59#2599C2214yes—
60#2592C2212yes—
61#2587C2218yes—
62#2584C2212yes—
63#2583C2214yes—
64#2582C2211yescharacteristic
65#2567C2214yes—
66#2563C2214yes—
67#2562C2212yes—
68#2558C2218yes—
69#2556C2218yes—
70#2551C2211yescharacteristic
71#2551C2212yes—
72#2551C2211yescharacteristic
73#2551C2214yes—
74#2551C2214yes—
75#2551C2214yes—
76#2550C2218yes—
77#2547C2214yes—
78#2543C2214yes—
79#2542C2214yes—
80#2540C2212yes—
81#2538C2212yes—
82#2537C2211yescharacteristic
83#2514C2214yes—
84#2513C2214yes—
85#2510C2218yes—
86#2507C2214yes—
87#2506C2214yes—
88#2498C2214yes—
89#2495C2214yes—
90#2494C2214yes—
91#2492C2214yes—
92#2492C2214yes—
93#2491C2214yes—
94#2491C2214yes—
95#2487C2214yes—
96#2486C2214yes—
97#2474C2218yes—
98#2465C2218yes—
99#2461C2218yes—
100#2452C2218yes—
101#2449C2218yes—
102#2443C2218yes—
103#2443C2218yes—
104#2442C2218yes—
105#2440C2214yes—
106#2440C2214yes—
107#2440C2214yes—
108#2440C2214yes—
109#2432C2218yes—
110#2430C2214yes—
111#2429C2218yes—
112#2423C2214yes—
113#2422C2214yes—
114#2417C2212yes—
115#2417C2214yes—
116#2417C2212yes—
117#2416C2212yes—
118#2416C2214yes—
119#2416C2212yes—
120#2415C2214yes—
121#2414C2214yes—
122#2409C2214yes—
123#2409C2218yes—
124#2406C2214yes—
125#2399C2214yes—
126#2396C2214yes—
127#2392C2214yes—
128#2388C2214yes—
129C2×#395C2214yes—
130#2370C2214yes—
131#2369C2214yes—
132#2367C2214yes—
133#2365C2214yes—
134#2361C2218yes—
135#2361C2214yes—
136#2360C2214yes—
137#2359C2218yes—
138#2355C2212yes—
139#2354C2212yes—
140#2353C2214yes—
141#2352C2214yes—
142Q8×C4⋊C4C2214yes—
143Q8×C4⋊C4C2212yes—
144D4×C4⋊C4C2214yes—
145D4×C4⋊C4C2214yes—
146D4×C4⋊C4C2214yes—
147D4×C4⋊C4C2214yes—
148D4×C4⋊C4C2212yes—
149#2347C2214yes—
150#2346C2214yes—
151#2334C2218yes—
152#2317C2212yes—
153#2317C2212yes—
154#2317C2212yes—
155#2314C2214yes—
156C4×C22⋊Q8C2214yes—
157C4×C22⋊Q8C2212yes—
158C4×C22⋊Q8C2212yes—
159C4×#121C2214yes—
160C4×#121C2214yes—
161C4×#121C2214yes—
162C4×#121C2212yes—
163C4×#121C2212yes—
164C2×#389C2214yes—
165#2285C2211yescharacteristic
166#2285C2211yescharacteristic
167#2285C2211yescharacteristic
168C2×#384C2211yescharacteristic
169C2×#384C2211yescharacteristic
170C2×#384C2211yescharacteristic
171#2274C2214yes—
172C2×C4×C4⋊C4C2212yes—
173C22×#41C2311yescharacteristic
174C22×#41C2314yes—
175C23×Q8C2314yes—
176#554—416no—
177#548—416no—
178#547—416no—
179C2×C4⋊Q8—416no—
180C2×C4⋊Q8C2314yes—
181C2×C4⋊Q8C2314yes—
182C2×C4⋊Q8C2314yes—
183C2×C4⋊Q8C2318yes—
184C2×C4⋊Q8C2318yes—
185C2×C4⋊Q8C2314yes—
186#529—216no—
187C2×#126C2314yes—
188C2×#125C2312yes—
189C2×#125C2318yes—
190C2×#124C2312yes—
191C2×#124C2314yes—
192C2×#124C2318yes—
193C2×#123C2314yes—
194C2×#123C2318yes—
195C2×#123C2318yes—
196C2×C22⋊Q8C2312yes—
197C2×C22⋊Q8C2312yes—
198C2×C22⋊Q8C2312yes—
199C2×C22⋊Q8C2314yes—
200C2×C22⋊Q8C2314yes—
201C2×C22⋊Q8C2318yes—
202C2×C22⋊Q8C2318yes—
203C2×C22⋊Q8C2318yes—
204C2×C22⋊Q8C2318yes—
205C2×#121C2312yes—
206C2×#121C2314yes—
207C2×#121C2312yes—
208C2×#121C2314yes—
209C2×#121C2312yes—
210C2×#121C2314yes—
211C2×#121C2314yes—
212#520—48no—
213C4×#41—28no—
214C2×C4×Q8C2312yes—
215C2×C4×Q8C2312yes—
216C2×C4×Q8C2314yes—
217C2×C4×Q8C2314yes—
218C2×C4×Q8C2314yes—
219C2×C4×D4C2312yes—
220C2×C4×D4C2314yes—
221C2×C4×D4C2312yes—
222C2×C4×D4C2312yes—
223C2×C4×D4C2314yes—
224C2×C4×D4C2312yes—
225C2×C4×D4C2314yes—
226C2×C4×D4C2318yes—
227C2×C4×D4C2314yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2318yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2314yes—
232C2×#117C2314yes—
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C2×#117C2314yes—
237C2×#117C2312yes—
238C2×#117C2312yes—
239C2×#117C2312yes—
240C22×C4⋊C4C2312yes—
241C22×C4⋊C4C2314yes—
242C22×C4⋊C4C2312yes—
243C22×C4⋊C4C2312yes—
244C22×C4⋊C4C2312yes—
245C22×C4⋊C4C2312yes—
246C22×C4⋊C4C2314yes—
247C22×C4⋊C4C2314yes—
248C22×C4⋊C4C2314yes—
249C22×C4⋊C4C2318yes—
250C22×C42C2311yescharacteristic
251C22×C42C2311yescharacteristic
252C22×C42C2314yes—
253C22×C42C2311yescharacteristic
254#401C2318yes—
255#400C2314yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#399C2318yes—
260#399C2318yes—
261#399C2314yes—
262#398C2314yes—
263#398C2318yes—
264#398C2318yes—
265#398C2314yes—
266#398C2314yes—
267#398C2314yes—
268#398C2314yes—
269#398C2318yes—
270#398C2318yes—
271#398C2314yes—
272#398C2318yes—
273#397C2314yes—
274#397C2318yes—
275#397C2318yes—
276#397C2314yes—
277#397C2318yes—
278#397C2318yes—
279#396C2318yes—
280#396C2318yes—
281#396C2318yes—
282#396C2318yes—
283#396C2314yes—
284#396C2314yes—
285#396C2314yes—
286#396C2314yes—
287#395C2314yes—
288#395C2318yes—
289#395C2314yes—
290#395C2314yes—
291#395C2314yes—
292#395C2314yes—
293#395C2314yes—
294#395C2318yes—
295#395C2318yes—
296#395C2314yes—
297#395C2318yes—
298#394C2314yes—
299#394C2318yes—
300#394C2314yes—
301#394C2314yes—
302#394C2314yes—
303#394C2314yes—
304#394C2314yes—
305#394C2318yes—
306#394C2318yes—
307#393C2314yes—
308#393C2318yes—
309#393C2314yes—
310#393C2314yes—
311#393C2318yes—
312#392C2314yes—
313#392C2314yes—
314#391C2312yes—
315#391C2314yes—
316#391C2312yes—
317#391C2314yes—
318#391C2318yes—
319#391C2318yes—
320#391C2318yes—
321#390C2318yes—
322#390C2312yes—
323#390C2312yes—
324#390C2314yes—
325#390C2314yes—
326#390C2314yes—
327#390C2314yes—
328#389C2318yes—
329#389C2318yes—
330#389C2318yes—
331#389C2318yes—
332#389C2318yes—
333#389C2314yes—
334#389C2318yes—
335#389C2314yes—
336#389C2314yes—
337#389C2312yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2318yes—
342#389C2318yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2318yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2318yes—
352#388C2314yes—
353#388C2314yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2314yes—
361#388C2314yes—
362#388C2318yes—
363#388C2314yes—
364#388C2314yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2314yes—
377#387C2314yes—
378#387C2318yes—
379#387C2318yes—
380#386C2314yes—
381#386C2314yes—
382#386C2318yes—
383#386C2318yes—
384#386C2314yes—
385#386C2314yes—
386#386C2318yes—
387#386C2314yes—
388#386C2314yes—
389#385C2318yes—
390#385C2318yes—
391#385C2318yes—
392#385C2314yes—
393#385C2318yes—
394#385C2318yes—
395#385C2318yes—
396#385C2318yes—
397#385C2318yes—
398#385C2314yes—
399#385C2318yes—
400#385C2318yes—
401#384C2314yes—
402#384C2314yes—
403#384C2312yes—
404#384C2312yes—
405#384C2312yes—
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#384C2314yes—
409#384C2314yes—
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#383C2314yes—
413#383C2318yes—
414#382C2318yes—
415#382C2314yes—
416#382C2312yes—
417#382C2312yes—
418#382C2312yes—
419#381C2314yes—
420#380C2312yes—
421#380C2312yes—
422#380C2312yes—
423#380C2312yes—
424#380C2314yes—
425#380C2314yes—
426#380C2314yes—
427#380C2314yes—
428#380C2314yes—
429#380C2314yes—
430#380C2314yes—
431#380C2314yes—
432#380C2314yes—
433#380C2314yes—
434C4×C4⋊C4C2312yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2314yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2312yes—
439C4×C4⋊C4C2318yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2318yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2318yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2314yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2318yes—
454C4×C22⋊C4C2314yes—
455C4×C22⋊C4C2314yes—
456C4×C22⋊C4C2318yes—
457C4×C22⋊C4C2318yes—
458C4×C22⋊C4C2314yes—
459C4×C22⋊C4C2314yes—
460#376C2314yes—
461C2×#95C2314yes—
462C2×#95C2314yes—
463C2×#41—24no—
464C2×#41—24no—
465C2×#41—24no—
466C2×#41—48no—
467C2×#41—416no—
468C22×Q8—48no—
469C22×Q8—416no—
470C22×Q8C2411yescharacteristic
471C22×Q8C2412yes—
472C22×Q8C2414yes—
473C22×Q8C2418yes—
474C22×Q8C2414yes—
475C22×D4C2411yescharacteristic
476C22×D4C2414yes—
477C22×D4C2412yes—
478C22×D4C2414yes—
479C22×D4C2414yes—
480C22×D4C2411yescharacteristic
481C22×D4C2411yescharacteristic
482C22×D4C2414yes—
483C23×C4C2411yescharacteristic
484C23×C4C2411yescharacteristic
485C23×C4C2412yes—
486C23×C4C2412yes—
487C23×C4C2414yes—
488C23×C4C2414yes—
489C23×C4C2414yes—
490C23×C4C2412yes—
491C23×C4C2411yescharacteristic
492C23×C4C2414yes—
493C23×C4C2414yes—
494C23×C4C2418yes—
495C23×C4C2414yes—
496C4⋊Q8—216no—
497C4⋊Q8—216no—
498C4⋊Q8—48no—
499C4⋊Q8—48no—
500C4⋊Q8—416no—
501C4⋊Q8—416no—
502#126—216no—
503#125—28no—
504#125—416no—
505#124—28no—
506#124—48no—
507#124—416no—
508#123—216no—
509#123—416no—
510#123—416no—
511C22⋊Q8—28no—
512C22⋊Q8—28no—
513C22⋊Q8—28no—
514C22⋊Q8—48no—
515C22⋊Q8—416no—
516C22⋊Q8—416no—
517C22⋊Q8—416no—
518C22⋊Q8—48no—
519C22⋊Q8—416no—
520#121—216no—
521#121—216no—
522#121—28no—
523#121—28no—
524#121—28no—
525#121—48no—
526#121—48no—
527C4×Q8—28no—
528C4×Q8—28no—
529C4×Q8—48no—
530C4×Q8—48no—
531C4×Q8—48no—
532C4×D4—216no—
533C4×D4—28no—
534C4×D4—28no—
535C4×D4—216no—
536C4×D4—28no—
537C4×D4—28no—
538C4×D4—48no—
539C4×D4—48no—
540C4×D4—48no—
541C4×D4—416no—
542C4×D4—48no—
543C4×D4—48no—
544C4×D4—416no—
545#117—24no—
546#117—216no—
547#117—24no—
548#117—24no—
549#117—216no—
550#117—44no—
551#117—44no—
552#117—44no—
553C2×C4⋊C4—28no—
554C2×C4⋊C4—216no—
555C2×C4⋊C4—28no—
556C2×C4⋊C4—44no—
557C2×C4⋊C4—48no—
558C2×C4⋊C4—416no—
559C2×C4⋊C4—48no—
560C2×C4⋊C4—48no—
561C2×C4⋊C4—44no—
562C2×C4⋊C4—44no—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2412yes—
610C2×C22⋊C4C2412yes—
611C2×C22⋊C4C2412yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2418yes—
636C2×C42—24no—
637C2×C42—24no—
638C2×C42—48no—
639C2×C42#4118yescomplemented
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2414yes—
643C2×C42C2414yes—
644C2×C42C2418yes—
645C2×C42C2414yes—
646C2×C42C2414yes—
647C2×C42C2412yes—
648C2×C42C2412yes—
649C2×C42C2414yes—
650C2×C42C2414yes—
651C2×C42C2418yes—
652C2×C42C2418yes—
653C2×C42C2414yes—
654C2×C42C2414yes—
655C2×C42C2412yes—
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658#95C2414yes—
659#95C2414yes—
660#95C2414yes—
661#95C2414yes—
662#95C2414yes—
663#95C2414yes—
664#95C2418yes—
665#95C2414yes—
666#95C2414yes—
667#95C2418yes—
668#95C2418yes—
669#95C2414yes—
670#95C2418yes—
671#95C2414yes—
672#95C2414yes—
673#95C2418yes—
674#95C2414yes—
675#95C2414yes—
676#95C2414yes—
677#95C2418yes—
678#95C2414yes—
679#95C2414yes—
680#95C2418yes—
681#95C2418yes—
682#95C2418yes—
683#95C2418yes—
684#95C2414yes—
685#95C2414yes—
686#95C2418yes—
687#95C2414yes—
688#95C2414yes—
689#95C2418yes—
690C24C2514yes—
691C24C2511yescharacteristic
692C24C2511yescharacteristic
693C24C2511yescharacteristic
694#41—232no—
695#41—832no—
696C2×Q8—22no—
697C2×Q8—24no—
698C2×Q8—22no—
699C2×Q8—24no—
700C2×Q8—216no—
701C2×Q8—216no—
702C2×Q8—22no—
703C2×Q8—24no—
704C2×Q8—44no—
705C2×Q8—48no—
706C2×Q8—44no—
707C2×Q8—48no—
708C2×Q8—48no—
709C2×Q8—832no—
710C2×D4—22no—
711C2×D4—22no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—22no—
716C2×D4—28no—
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—22no—
722C2×D4—24no—
723C2×D4—24no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—24no—
727C2×D4—44no—
728C2×D4—44no—
729C2×D4—48no—
730C2×D4—44no—
731C2×D4H(5,𝔽2)14yes—
732C2×D42−1+414yes—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—24no—
740C22×C4—22no—
741C22×C4—24no—
742C22×C4—22no—
743C22×C4—28no—
744C22×C4—28no—
745C22×C4—28no—
746C22×C4—28no—
747C22×C4—24no—
748C22×C4—24no—
749C22×C4—28no—
750C22×C4—28no—
751C22×C4—28no—
752C22×C4—24no—
753C22×C4—24no—
754C22×C4—28no—
755C22×C4—28no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—216no—
759C22×C4—44no—
760C22×C4—44no—
761C22×C4—48no—
762C22×C4—48no—
763C22×C4—48no—
764C22×C4—48no—
765C22×C4—44no—
766C22×C4—48no—
767C22×C4C2×#4114yes—
768C22×C4C2×#4118yes—
769C22×C4C2514yes—
770C22×C4C2514yes—
771C22×C4C2514yes—
772C22×C4C2514yes—
773C22×C4C2512yes—
774C22×C4C2512yes—
775C22×C4C2514yes—
776C22×C4C2514yes—
777C22×C4C2514yes—
778C22×C4C2514yes—
779C22×C4C2514yes—
780C22×C4C2511yescharacteristic
781C22×C4C2511yescharacteristic
782C22×C4C2512yes—
783C22×C4C2511yescharacteristic
784C22×C4C2514yes—
785C22×C4C2514yes—
786C22×C4C2511yescharacteristic
787C22×C4C2512yes—
788C4⋊C4—24no—
789C4⋊C4—24no—
790C4⋊C4—24no—
791C4⋊C4—28no—
792C4⋊C4—28no—
793C4⋊C4—24no—
794C4⋊C4—28no—
795C4⋊C4—24no—
796C4⋊C4—28no—
797C4⋊C4—28no—
798C4⋊C4—216no—
799C4⋊C4—28no—
800C4⋊C4—24no—
801C4⋊C4—28no—
802C4⋊C4—28no—
803C4⋊C4—28no—
804C4⋊C4—216no—
805C4⋊C4—216no—
806C4⋊C4—28no—
807C4⋊C4—28no—
808C4⋊C4—28no—
809C4⋊C4—24no—
810C4⋊C4—28no—
811C4⋊C4—28no—
812C4⋊C4—28no—
813C4⋊C4—42no—
814C4⋊C4—42no—
815C4⋊C4—42no—
816C4⋊C4—44no—
817C4⋊C4—44no—
818C4⋊C4—48no—
819C4⋊C4—48no—
820C4⋊C4—48no—
821C4⋊C4—48no—
822C4⋊C4—48no—
823C4⋊C4—42no—
824C4⋊C4—44no—
825C4⋊C4—48no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—48no—
829C4⋊C4—48no—
830C4⋊C4H(5,𝔽2)18yes—
831C4⋊C42−1+418yes—
832C22⋊C4—24no—
833C22⋊C4—28no—
834C22⋊C4—28no—
835C22⋊C4—28no—
836C22⋊C4—28no—
837C22⋊C4—28no—
838C22⋊C4—24no—
839C22⋊C4—24no—
840C22⋊C4—28no—
841C22⋊C4—28no—
842C22⋊C4—28no—
843C22⋊C4—28no—
844C22⋊C4—28no—
845C22⋊C4—28no—
846C22⋊C4—28no—
847C22⋊C4—216no—
848C22⋊C4—28no—
849C22⋊C4—28no—
850C22⋊C4—28no—
851C22⋊C4—44no—
852C22⋊C4—44no—
853C22⋊C4—44no—
854C22⋊C4—48no—
855C22⋊C4—48no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—48no—
859C22⋊C4—48no—
860C22⋊C4—48no—
861C42—22no—
862C42—22no—
863C42—24no—
864C42—24no—
865C42—28no—
866C42—28no—
867C42—28no—
868C42—28no—
869C42—216no—
870C42—44no—
871C42—44no—
872C42—44no—
873C42—44no—
874C42—48no—
875C42—48no—
876C42C2×#4114yes—
877C42C2×#4118yes—
878C42C2×#4114yes—
879C23—22no—
880C23—22no—
881C23—21no—
882C23—21no—
883C23—22no—
884C23—21no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—21no—
889C23—24no—
890C23—24no—
891C23—24no—
892C23—24no—
893C23—24no—
894C23—24no—
895C23—24no—
896C23C22×#4112yes—
897C23C2×H(5,𝔽2)12yes—
898C23C2×H(5,𝔽2)12yes—
899C23C2×2−1+412yes—
900C23C2×2−1+412yes—
901C23C2611yescharacteristic
902Q8—28no—
903Q8—416no—
904Q8—48no—
905Q8—816no—
906Q8—88no—
907D4—28no—
908D4—28no—
909D4—28no—
910D4—416no—
911D4—416no—
912D4—416no—
913D4—48no—
914D4—88no—
915C2×C4—28no—
916C2×C4—28no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—22no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—24no—
925C2×C4—21no—
926C2×C4—22no—
927C2×C4—24no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—28no—
932C2×C4—216no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—28no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—22no—
951C2×C4—28no—
952C2×C4—28no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—28no—
956C2×C4—24no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—416no—
963C2×C4—416no—
964C2×C4—48no—
965C2×C4—48no—
966C2×C4—416no—
967C2×C4—816no—
968C2×C4—88no—
969C2×C4—88no—
970C2×C4—164no—
971C2×C4C22×#4112yes—
972C2×C4C22×#4114yes—
973C2×C4C22×#4112yes—
974C2×C4C22×#4114yes—
975C2×C4C2×H(5,𝔽2)12yes—
976C2×C4C2×H(5,𝔽2)18yes—
977C2×C4C2×H(5,𝔽2)14yes—
978C2×C4C2×2−1+418yes—
979C2×C4C2×2−1+412yes—
980C2×C4C2×2−1+414yes—
981C22—22no—
982C22—24no—
983C22—22no—
984C22—24no—
985C22—22no—
986C22—24no—
987C22—22no—
988C22—22no—
989C22—22no—
990C22—41no—
991C22—42no—
992C22—41no—
993C22—42no—
994C22—42no—
995C22—44no—
996C22—44no—
997C22—44no—
998C22—44no—
999C22—44no—
1000C22—44no—
1001C22—44no—
1002C22#349214yes—
1003C22C23×#4111yescharacteristic
1004C22C22×H(5,𝔽2)12yes—
1005C22C22×H(5,𝔽2)11yescharacteristic
1006C22C22×2−1+411yescharacteristic
1007C22C22×2−1+412yes—
1008C4—28no—
1009C4—28no—
1010C4—22no—
1011C4—22no—
1012C4—22no—
1013C4—22no—
1014C4—24no—
1015C4—44no—
1016C4—44no—
1017C4—44no—
1018C4—44no—
1019C4—44no—
1020C4—44no—
1021C4—44no—
1022C4—42no—
1023C4—42no—
1024C4—44no—
1025C4—44no—
1026C4#351118yes—
1027C2—24no—
1028C2—42no—
1029C2—42no—
1030C2—84no—
1031C2C2×#349211yescharacteristic
1032C2C2×#351112yes—
1033C2#6301111yescharacteristic
1034C2#6301612yes—
1035C2#6303711yescharacteristic
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. #59676C2semidirect
2. #59441C2semidirect
3. #59322C2semidirect
4. #59314C2semidirect
5. #59313C2semidirect
6. #59248C2semidirect
7. #59234C2semidirect
8. #59233C2semidirect
9. #59136C2semidirect
10. #59125C2semidirect
11. #47752C2semidirect
12. #47750C2semidirect
13. #42458C2semidirect
14. #42457C2semidirect
15. #42021C2semidirect
16. #37620C2semidirect
17. #35747C2semidirect
18. #35740C2semidirect
19. #35697C2semidirect
20. #34964C2semidirect
21. C2×#2551C2semidirect
22. #34243C2semidirect
23. #34183C2semidirect
639. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#596762
#594412
#593222
#593142
#593132
#592482
#592342
#592332
#591362
#591252
#477522
#477502
#424582
#424572
#420212
#376202
#357472
#357402
#356972
#349642
C2×#25512
#342432
#341832