Finite Group Databasebeta

← #7806317

Subgroups — #7806317

Order 512.

7182 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3522C212yesmaximal, complemented
2#59832C211yesmaximal, characteristic, complemented
3#59827C211yesmaximal, characteristic, complemented
4#59660C211yesmaximal, characteristic, complemented
5#59655C212yesmaximal, complemented
6#59419C211yesmaximal, characteristic, complemented
7#59411C212yesmaximal, complemented
8#59112C214yesmaximal, complemented
9#59093C214yesmaximal, complemented
10#59061C214yesmaximal, complemented
11#59031C214yesmaximal, complemented
12#47788C214yesmaximal, complemented
13#47786C214yesmaximal, complemented
14#42442C214yesmaximal, complemented
15#42441C214yesmaximal, complemented
16#42166C214yesmaximal, complemented
17#37620C211yesmaximal, characteristic, complemented
18#36020C214yesmaximal, complemented
19#35806C214yesmaximal, complemented
20#35778C214yesmaximal, complemented
21#34972C212yesmaximal, complemented
22C2×#2582C211yesmaximal, characteristic, complemented
23#34207C211yesmaximal, characteristic, complemented
24#3522—232no—
25C2×#559C2212yes—
26C2×#559C2214yes—
27C2×Q82C2212yes—
28C2×#554C2212yes—
29C2×#554C2214yes—
30C2×#550C2212yes—
31C2×#548C2214yes—
32C2×#547C2214yes—
33C2×#547C2218yes—
34C2×#547C2214yes—
35C2×#542C2218yes—
36C2×#542C2214yes—
37C2×#532C2214yes—
38C2×#532C2211yescharacteristic
39C2×#529C2214yes—
40C2×#529C2212yes—
41C2×#520C2214yes—
42C2×#520C2212yes—
43C22×C4×Q8C2212yes—
44#2823C2214yes—
45#2814C2218yes—
46#2734C2214yes—
47#2729C2218yes—
48#2728C2214yes—
49#2724C2214yes—
50#2715C2218yes—
51#2712C2218yes—
52#2701C2218yes—
53#2700C2218yes—
54#2699C2214yes—
55#2698C2218yes—
56#2695C2218yes—
57#2689C2218yes—
58#2674C2218yes—
59#2672C2218yes—
60#2630C2218yes—
61#2629C2214yes—
62#2627C2218yes—
63#2621C2214yes—
64#2620C2214yes—
65#2618C2214yes—
66#2618C2214yes—
67#2604C2214yes—
68#2604C2214yes—
69#2582C2212yes—
70#2582C2211yescharacteristic
71#2582C2211yescharacteristic
72#2582C2214yes—
73#2582C2214yes—
74#2582C2214yes—
75#2582C2211yescharacteristic
76#2579C2218yes—
77#2565C2212yes—
78#2565C2212yes—
79#2551C2214yes—
80#2550C2214yes—
81#2547C2214yes—
82#2546C2214yes—
83#2545C2212yes—
84#2545C2212yes—
85#2544C2214yes—
86#2543C2214yes—
87#2543C2214yes—
88#2538C2212yes—
89#2537C2211yescharacteristic
90#2536C2214yes—
91#2503C2212yes—
92#2501C2212yes—
93#2492C2214yes—
94#2489C2214yes—
95#2486C2214yes—
96#2486C2214yes—
97#2474C2218yes—
98#2470C2218yes—
99#2459C2218yes—
100#2455C2218yes—
101#2453C2214yes—
102#2452C2214yes—
103#2451C2214yes—
104#2451C2214yes—
105#2450C2218yes—
106#2449C2218yes—
107#2447C2214yes—
108#2447C2214yes—
109#2447C2214yes—
110#2445C2214yes—
111#2444C2218yes—
112#2442C2214yes—
113#2440C2214yes—
114#2438C2218yes—
115#2438C2218yes—
116#2436C2212yes—
117#2434C2212yes—
118#2432C2214yes—
119#2431C2214yes—
120#2430C2218yes—
121#2429C2218yes—
122#2429C2214yes—
123#2428C2214yes—
124#2427C2214yes—
125#2427C2214yes—
126#2425C2218yes—
127#2425C2218yes—
128#2422C2214yes—
129#2420C2214yes—
130#2419C2218yes—
131#2417C2214yes—
132#2417C2218yes—
133#2416C2214yes—
134#2413C2214yes—
135#2413C2214yes—
136#2413C2218yes—
137#2406C2218yes—
138#2396C2214yes—
139#2396C2214yes—
140#2392C2214yes—
141C2×#398C2214yes—
142C2×#398C2214yes—
143#2367C2214yes—
144#2365C2214yes—
145#2361C2214yes—
146#2361C2214yes—
147#2361C2214yes—
148#2360C2214yes—
149#2354C2214yes—
150#2349C2214yes—
151#2349C2214yes—
152D4×C4⋊C4C2214yes—
153D4×C4⋊C4C2214yes—
154#2339C2214yes—
155#2339C2214yes—
156#2339C2218yes—
157#2326C2212yes—
158#2326C2212yes—
159#2311C2212yes—
160C4×C4⋊Q8C2211yescharacteristic
161C4×C4⋊Q8C2212yes—
162C4×C4⋊Q8C2211yescharacteristic
163C4×C4⋊Q8C2212yes—
164C4×#127C2211yescharacteristic
165C4×#127C2211yescharacteristic
166C4×#124C2212yes—
167C4×#124C2212yes—
168C4×#123C2214yes—
169C4×#123C2214yes—
170C2×#391C2214yes—
171C2×#389C2214yes—
172C2×#384C2211yescharacteristic
173C4×#117C2211yescharacteristic
174C22×#41C2314yes—
175C22×#41C2318yes—
176C22×#41C2312yes—
177C23×Q8C2312yes—
178#559—216no—
179#559—232no—
180Q82—216no—
181#554—216no—
182#554—232no—
183#550—216no—
184#548—232no—
185#547—264no—
186#547—232no—
187#547—416no—
188#542—264no—
189#542—232no—
190#532—232no—
191#532D4116yescomplemented
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2314yes—
194C2×C4⋊Q8C2318yes—
195C2×C4⋊Q8C2314yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2314yes—
198C2×C4⋊Q8C2311yescharacteristic
199C2×#127C2314yes—
200C2×#127C2311yescharacteristic
201#529—232no—
202#529—216no—
203C2×#126C2314yes—
204C2×#126C2318yes—
205C2×#125C2312yes—
206C2×#125C2314yes—
207C2×#124C2312yes—
208C2×#124C2312yes—
209C2×#124C2314yes—
210C2×#124C2318yes—
211C2×#124C2314yes—
212C2×#124C2318yes—
213C2×#124C2312yes—
214C2×#124C2312yes—
215C2×#123C2314yes—
216C2×#123C2318yes—
217C2×#123C2318yes—
218C2×#123C2314yes—
219C2×#123C2318yes—
220C2×#123C2318yes—
221C2×#123C2314yes—
222C2×#123C2318yes—
223C2×C22⋊Q8C2318yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2318yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2318yes—
228C2×C22⋊Q8C2318yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2318yes—
231C2×#121C2312yes—
232C2×#121C2318yes—
233C2×#121C2314yes—
234C2×#121C2318yes—
235C2×#121C2314yes—
236C2×#121C2314yes—
237C2×#121C2314yes—
238C2×#121C2314yes—
239#520—232no—
240#520—48no—
241C2×C4×Q8—216no—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2312yes—
253C2×C4×D4C2318yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2318yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2318yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2312yes—
263C2×C4×D4C2312yes—
264C2×C4×D4C2312yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C2×#117C2314yes—
271C2×#117C2311yescharacteristic
272C2×#117C2318yes—
273C2×#117C2311yescharacteristic
274C2×#117C2314yes—
275C22×C4⋊C4C2318yes—
276C22×C4⋊C4C2314yes—
277C22×C4⋊C4C2314yes—
278C22×C4⋊C4C2312yes—
279C22×C4⋊C4C2312yes—
280C22×C4⋊C4C2314yes—
281C22×C4⋊C4C2314yes—
282C22×C4⋊C4C2314yes—
283C22×C4⋊C4C2314yes—
284C22×C42C2314yes—
285C22×C42C2311yescharacteristic
286#400C2314yes—
287#400C2314yes—
288#400C2318yes—
289#400C2318yes—
290#399C2314yes—
291#399C2314yes—
292#398C2314yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2314yes—
297#398C2318yes—
298#398C2314yes—
299#398C2314yes—
300#398C2318yes—
301#398C2318yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2318yes—
307#398C2314yes—
308#398C2314yes—
309#398C2318yes—
310#397C2318yes—
311#397C2314yes—
312#397C2314yes—
313#397C2318yes—
314#397C2314yes—
315#397C2318yes—
316#397C2318yes—
317#397C2318yes—
318#396C2318yes—
319#396C2318yes—
320#396C2318yes—
321#396C2314yes—
322#396C2318yes—
323#396C2314yes—
324#396C2318yes—
325#396C2314yes—
326#396C2314yes—
327#395C2314yes—
328#395C2314yes—
329#395C2318yes—
330#395C2318yes—
331#395C2318yes—
332#394C2314yes—
333#394C2318yes—
334#394C2314yes—
335#394C2314yes—
336#394C2318yes—
337#394C2318yes—
338#394C2318yes—
339#394C2318yes—
340#394C2318yes—
341#393C2314yes—
342#393C2314yes—
343#393C2318yes—
344#392C2318yes—
345#392C2314yes—
346#391C2312yes—
347#391C2312yes—
348#391C2312yes—
349#391C2312yes—
350#391C2312yes—
351#391C2312yes—
352#391C2312yes—
353#391C2312yes—
354#391C2314yes—
355#391C2314yes—
356#391C2314yes—
357#391C2314yes—
358#391C2318yes—
359#391C2318yes—
360#391C2314yes—
361#391C2318yes—
362#391C2318yes—
363#390C2312yes—
364#390C2312yes—
365#390C2314yes—
366#390C2314yes—
367#390C2312yes—
368#390C2314yes—
369#390C2312yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2318yes—
379#389C2314yes—
380#389C2314yes—
381#389C2318yes—
382#389C2314yes—
383#389C2314yes—
384#389C2318yes—
385#389C2318yes—
386#389C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2314yes—
390#388C2314yes—
391#388C2314yes—
392#388C2314yes—
393#388C2314yes—
394#388C2314yes—
395#388C2314yes—
396#388C2314yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#387C2314yes—
401#387C2314yes—
402#387C2314yes—
403#387C2314yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#386C2318yes—
408#386C2318yes—
409#386C2318yes—
410#386C2314yes—
411#386C2318yes—
412#386C2318yes—
413#386C2318yes—
414#386C2318yes—
415#386C2318yes—
416#386C2318yes—
417#386C2314yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#385C2318yes—
423#385C2318yes—
424#385C2318yes—
425#385C2314yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2314yes—
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2312yes—
433#384C2312yes—
434#384C2312yes—
435#384C2314yes—
436#382C2312yes—
437#382C2312yes—
438#382C2314yes—
439#381C2314yes—
440#381C2318yes—
441#381C2318yes—
442#381C2318yes—
443#381C2314yes—
444#380C2318yes—
445#380C2314yes—
446#380C2314yes—
447#380C2318yes—
448#380C2318yes—
449#380C2314yes—
450#380C2314yes—
451#380C2318yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2314yes—
461C4×C22⋊C4C2318yes—
462C4×C22⋊C4C2314yes—
463C4×C22⋊C4C2314yes—
464C4×C22⋊C4C2314yes—
465C4×C22⋊C4C2312yes—
466C4×C22⋊C4C2312yes—
467C4×C22⋊C4C2314yes—
468#376C2311yescharacteristic
469#376C2311yescharacteristic
470C2×#95C2318yes—
471C2×#95C2314yes—
472C2×#95C2318yes—
473C2×#95C2314yes—
474C43C2311yescharacteristic
475C43C2311yescharacteristic
476C2×#41—216no—
477C2×#41—216no—
478C2×#41—232no—
479C2×#41—44no—
480C2×#41—44no—
481C2×#41—416no—
482C2×#41—416no—
483C2×#41—48no—
484C2×#41C2×D4116yes—
485C22×Q8—28no—
486C22×Q8—28no—
487C22×Q8—44no—
488C22×Q8C2412yes—
489C22×Q8C2412yes—
490C22×Q8C2414yes—
491C22×Q8C2412yes—
492C22×Q8C2418yes—
493C22×Q8C2412yes—
494C22×D4C2412yes—
495C22×D4C2414yes—
496C22×D4C2418yes—
497C22×D4C2414yes—
498C22×D4C2414yes—
499C22×D4C2418yes—
500C22×D4C2414yes—
501C22×D4C2412yes—
502C23×C4C2414yes—
503C23×C4C2414yes—
504C23×C4C2418yes—
505C23×C4C2414yes—
506C23×C4C2411yescharacteristic
507C23×C4C2412yes—
508C23×C4C2414yes—
509C23×C4C2414yes—
510C23×C4C2418yes—
511C23×C4C2418yes—
512C23×C4C2414yes—
513C23×C4C2414yes—
514C4⋊Q8—232no—
515C4⋊Q8—28no—
516C4⋊Q8—216no—
517C4⋊Q8—216no—
518C4⋊Q8—48no—
519C4⋊Q8—44no—
520C4⋊Q8C2×D418yes—
521#127—216no—
522#127C2×D418yes—
523#126—232no—
524#126—216no—
525#125—216no—
526#125—28no—
527#124—28no—
528#124—216no—
529#124—216no—
530#124—232no—
531#124—232no—
532#124—28no—
533#124—44no—
534#124C2×D4116yes—
535#123—232no—
536#123—232no—
537#123—216no—
538#123—232no—
539#123—232no—
540#123—216no—
541#123—416no—
542#123—48no—
543C22⋊Q8—232no—
544C22⋊Q8—28no—
545C22⋊Q8—232no—
546C22⋊Q8—216no—
547C22⋊Q8—232no—
548C22⋊Q8—232no—
549C22⋊Q8—416no—
550C22⋊Q8—48no—
551#121—232no—
552#121—216no—
553#121—232no—
554#121—28no—
555#121—48no—
556#121—48no—
557#121—48no—
558#121C2×D4132yes—
559C4×Q8—216no—
560C4×Q8—216no—
561C4×Q8—28no—
562C4×Q8—216no—
563C4×Q8—28no—
564C4×Q8—28no—
565C4×Q8—28no—
566C4×Q8—216no—
567C4×Q8—28no—
568C4×Q8—44no—
569C4×Q8—44no—
570C4×D4—216no—
571C4×D4—232no—
572C4×D4—216no—
573C4×D4—216no—
574C4×D4—232no—
575C4×D4—216no—
576C4×D4—216no—
577C4×D4—232no—
578C4×D4—216no—
579C4×D4—28no—
580C4×D4—44no—
581C4×D4—48no—
582C4×D4—48no—
583C4×D4—48no—
584C4×D4—44no—
585C4×D4—48no—
586C4×D4C2×D4132yes—
587#117—232no—
588#117—24no—
589#117—216no—
590#117—48no—
591#117—42no—
592C2×C4⋊C4—28no—
593C2×C4⋊C4—216no—
594C2×C4⋊C4—232no—
595C2×C4⋊C4—216no—
596C2×C4⋊C4—48no—
597C2×C4⋊C4—48no—
598C2×C4⋊C4—48no—
599C2×C4⋊C4—44no—
600C2×C4⋊C4—48no—
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C22⋊C4C2411yescharacteristic
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2418yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2411yescharacteristic
672C2×C42—216no—
673C2×C42C2×D418yes—
674C2×C42C2414yes—
675C2×C42C2418yes—
676C2×C42C2414yes—
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2414yes—
680C2×C42C2414yes—
681C2×C42C2412yes—
682C2×C42C2412yes—
683C2×C42C2414yes—
684C2×C42C2414yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2414yes—
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2412yes—
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693#95C2414yes—
694#95C2418yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2418yes—
700#95C2418yes—
701#95C2414yes—
702#95C2418yes—
703#95C2418yes—
704#95C2418yes—
705#95C2412yes—
706#95C2412yes—
707#95C2412yes—
708#95C2412yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2418yes—
719#95C2418yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2418yes—
726C24C2514yes—
727C24C2514yes—
728C24C2511yescharacteristic
729#41—432no—
730#41—464no—
731#41—864no—
732C2×Q8—24no—
733C2×Q8—24no—
734C2×Q8—28no—
735C2×Q8—24no—
736C2×Q8—216no—
737C2×Q8—24no—
738C2×Q8—28no—
739C2×Q8—24no—
740C2×Q8—24no—
741C2×Q8—24no—
742C2×Q8—24no—
743C2×Q8—42no—
744C2×Q8—44no—
745C2×Q8—42no—
746C2×Q8—48no—
747C2×Q8—48no—
748C2×Q8—432no—
749C2×Q8C22×D418yes—
750C2×Q82−1+418yes—
751C2×D4—28no—
752C2×D4—28no—
753C2×D4—216no—
754C2×D4—28no—
755C2×D4—28no—
756C2×D4—28no—
757C2×D4—216no—
758C2×D4—24no—
759C2×D4—28no—
760C2×D4—24no—
761C2×D4—216no—
762C2×D4—28no—
763C2×D4—24no—
764C2×D4—42no—
765C2×D4—42no—
766C2×D4—48no—
767C2×D4—44no—
768C2×D4—48no—
769C2×D4—48no—
770C2×D4—48no—
771C2×D4C22×D4116yes—
772C2×D4C22×D4116yes—
773C2×D4C22×D418yes—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—28no—
779C22×C4—28no—
780C22×C4—216no—
781C22×C4—28no—
782C22×C4—28no—
783C22×C4—216no—
784C22×C4—28no—
785C22×C4—28no—
786C22×C4—28no—
787C22×C4—216no—
788C22×C4—28no—
789C22×C4—28no—
790C22×C4—216no—
791C22×C4—28no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—48no—
796C22×C4—48no—
797C22×C4—48no—
798C22×C4—48no—
799C22×C4—48no—
800C22×C4—48no—
801C22×C4—48no—
802C22×C4—44no—
803C22×C4—48no—
804C22×C4C22×D418yes—
805C22×C4C22×D414yes—
806C22×C4C22×D4116yes—
807C22×C4C2511yescharacteristic
808C22×C4C2512yes—
809C22×C4C2512yes—
810C22×C4C2511yescharacteristic
811C22×C4C2514yes—
812C22×C4C2514yes—
813C22×C4C2514yes—
814C22×C4C2514yes—
815C22×C4C2514yes—
816C22×C4C2514yes—
817C22×C4C2514yes—
818C22×C4C2514yes—
819C22×C4C2512yes—
820C22×C4C2514yes—
821C22×C4C2511yescharacteristic
822C22×C4C2511yescharacteristic
823C22×C4C2511yescharacteristic
824C22×C4C2511yescharacteristic
825C22×C4C2514yes—
826C22×C4C2512yes—
827C4⋊C4—28no—
828C4⋊C4—24no—
829C4⋊C4—216no—
830C4⋊C4—28no—
831C4⋊C4—216no—
832C4⋊C4—28no—
833C4⋊C4—24no—
834C4⋊C4—28no—
835C4⋊C4—28no—
836C4⋊C4—28no—
837C4⋊C4—28no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—216no—
841C4⋊C4—28no—
842C4⋊C4—216no—
843C4⋊C4—28no—
844C4⋊C4—22no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—22no—
848C4⋊C4—28no—
849C4⋊C4—28no—
850C4⋊C4—28no—
851C4⋊C4—28no—
852C4⋊C4—28no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4—48no—
856C4⋊C4—42no—
857C4⋊C4—42no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—48no—
862C4⋊C4—42no—
863C4⋊C4—48no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4C22×D4116yes—
869C22⋊C4—216no—
870C22⋊C4—28no—
871C22⋊C4—216no—
872C22⋊C4—216no—
873C22⋊C4—216no—
874C22⋊C4—22no—
875C22⋊C4—24no—
876C22⋊C4—28no—
877C22⋊C4—28no—
878C22⋊C4—28no—
879C22⋊C4—216no—
880C22⋊C4—28no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—28no—
885C22⋊C4—28no—
886C22⋊C4—44no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—48no—
890C22⋊C4—48no—
891C22⋊C4—48no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4C22×D4132yes—
897C22⋊C4H(5,𝔽2)14yes—
898C42—28no—
899C42—28no—
900C42—28no—
901C42—28no—
902C42—216no—
903C42—28no—
904C42—22no—
905C42—22no—
906C42—28no—
907C42—24no—
908C42—24no—
909C42—24no—
910C42—24no—
911C42—41no—
912C42—41no—
913C42—44no—
914C42C22×D418yes—
915C42C22×D414yes—
916C42C22×D414yes—
917C23—22no—
918C23—22no—
919C23—24no—
920C23—28no—
921C23—28no—
922C23—24no—
923C23—24no—
924C23—24no—
925C23—24no—
926C23—24no—
927C23—24no—
928C23—24no—
929C23—24no—
930C23C23×D418yes—
931C23C23×D412yes—
932C23C2×H(5,𝔽2)12yes—
933C23#58512yes—
934C23C2611yescharacteristic
935Q8—216no—
936Q8—48no—
937Q8—416no—
938Q8—48no—
939Q8—48no—
940Q8—816no—
941D4—232no—
942D4—232no—
943D4—48no—
944D4—432no—
945D4—416no—
946D4—48no—
947D4—816no—
948D4—88no—
949C2×C4—24no—
950C2×C4—21no—
951C2×C4—24no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—21no—
957C2×C4—22no—
958C2×C4—21no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—28no—
962C2×C4—216no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—28no—
988C2×C4—28no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—416no—
996C2×C4—416no—
997C2×C4—432no—
998C2×C4—416no—
999C2×C4—416no—
1000C2×C4—88no—
1001C2×C4—816no—
1002C2×C4—88no—
1003C2×C4—816no—
1004C2×C4—164no—
1005C2×C4C23×D414yes—
1006C2×C4C23×D418yes—
1007C2×C4C23×D412yes—
1008C2×C4C23×D412yes—
1009C2×C4C23×D414yes—
1010C2×C4C2×H(5,𝔽2)12yes—
1011C2×C4C2×H(5,𝔽2)12yes—
1012C2×C4C2×2−1+418yes—
1013C2×C4C2×2−1+414yes—
1014C2×C4#58514yes—
1015C22—22no—
1016C22—24no—
1017C22—22no—
1018C22—24no—
1019C22—28no—
1020C22—216no—
1021C22—44no—
1022C22—48no—
1023C22—44no—
1024C22—44no—
1025C22—44no—
1026C22—44no—
1027C22—44no—
1028C22—44no—
1029C22—44no—
1030C22—44no—
1031C22#349614yes—
1032C22C24×D411yescharacteristic
1033C22C22×H(5,𝔽2)11yescharacteristic
1034C22C22×2−1+412yes—
1035C22C2×#58511yescharacteristic
1036C22C2×#58512yes—
1037C4—22no—
1038C4—22no—
1039C4—28no—
1040C4—22no—
1041C4—22no—
1042C4—24no—
1043C4—28no—
1044C4—44no—
1045C4—44no—
1046C4—44no—
1047C4—44no—
1048C4—44no—
1049C4—41no—
1050C4—42no—
1051C4—42no—
1052C4—41no—
1053C4—44no—
1054C4—44no—
1055C4—44no—
1056C4#348918yes—
1057C2—24no—
1058C2—48no—
1059C2—84no—
1060C2C2×#349611yescharacteristic
1061C2C2×#348912yes—
1062C2#6302111yescharacteristic
1063C2#6303312yes—
1064C2#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. C2×#3522C2semidirect
2. #59832C2semidirect
3. #59827C2semidirect
4. #59660C2semidirect
5. #59655C2semidirect
6. #59419C2semidirect
7. #59411C2semidirect
8. #59112C2semidirect
9. #59093C2semidirect
10. #59061C2semidirect
11. #59031C2semidirect
12. #47788C2semidirect
13. #47786C2semidirect
14. #42442C2semidirect
15. #42441C2semidirect
16. #42166C2semidirect
17. #37620C2semidirect
18. #36020C2semidirect
19. #35806C2semidirect
20. #35778C2semidirect
21. #34972C2semidirect
22. C2×#2582C2semidirect
23. #34207C2semidirect
191. #532D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35222
#598322
#598272
#596602
#596552
#594192
#594112
#591122
#590932
#590612
#590312
#477882
#477862
#424422
#424412
#421662
#376202
#360202
#358062
#357782
#349722
C2×#25822
#342072