Finite Group Databasebeta

← #7654838

Subgroups — #7654838

Order 512.

7152 conjugacy classes of subgroups.

The subgroup lattice has 1055 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3511C211yesmaximal, characteristic, complemented
2C2×#3482C211yesmaximal, characteristic, complemented
3#42984C214yesmaximal, complemented
4#41948C218yesmaximal, complemented
5#39744C212yesmaximal, complemented
6#39167C212yesmaximal, complemented
7#38922C214yesmaximal, complemented
8#38914C218yesmaximal, complemented
9#38091C214yesmaximal, complemented
10#37680C214yesmaximal, complemented
11#37640C211yesmaximal, characteristic, complemented
12#37619C212yesmaximal, complemented
13#36544C214yesmaximal, complemented
14#36406C212yesmaximal, complemented
15#36127C212yesmaximal, complemented
16#35686C214yesmaximal, complemented
17#35316C211yesmaximal, characteristic, complemented
18#35281C211yesmaximal, characteristic, complemented
19#35200C212yesmaximal, complemented
20#35173C212yesmaximal, complemented
21#34977C211yesmaximal, characteristic, complemented
22#34937C212yesmaximal, complemented
23#34127C211yesmaximal, characteristic, complemented
24#3511—216no—
25#3482—216no—
26C2×#557C2211yescharacteristic
27C2×#556C2211yescharacteristic
28C2×#556C2212yes—
29C2×#556C2212yes—
30C2×#555C2212yes—
31C2×#554C2212yes—
32C2×#553C2214yes—
33C2×#552C2212yes—
34C2×#552C2214yes—
35C2×D4×Q8C2211yescharacteristic
36C2×#548C2214yes—
37C2×#548C2212yes—
38C2×#547C2211yescharacteristic
39C2×#547C2212yes—
40C2×#547C2212yes—
41C2×#542C2214yes—
42C2×#537C2212yes—
43C2×#536C2212yes—
44C2×#533C2211yescharacteristic
45C2×#533C2212yes—
46C2×#533C2212yes—
47C2×#532C2211yescharacteristic
48C2×#532C2212yes—
49C2×#532C2214yes—
50C22×C4⋊Q8C2211yescharacteristic
51C2×#529C2214yes—
52C2×#529C2212yes—
53C2×#520C2212yes—
54C2×C4×#41C2212yes—
55C2×C4×#41C2211yescharacteristic
56C2×C4×#41C2211yescharacteristic
57C22×C4×Q8C2212yes—
58#2868C2212yes—
59#2862C2212yes—
60#2857C2214yes—
61#2857C2214yes—
62#2857C2214yes—
63#2851C2218yes—
64#2820C2214yes—
65#2816C2218yes—
66#2723C22116yes—
67#2721C22116yes—
68#2715C22116yes—
69#2686C22116yes—
70#2672C22116yes—
71#2671C22116yes—
72#2660C2214yes—
73#2659C2218yes—
74#2658C2214yes—
75#2640C2214yes—
76#2638C2218yes—
77#2633C2218yes—
78#2624C2214yes—
79#2624C2218yes—
80#2621C2214yes—
81#2620C2214yes—
82#2616C2214yes—
83#2610C2214yes—
84#2599C2218yes—
85#2584C2218yes—
86#2584C2218yes—
87#2580C2218yes—
88#2567C2212yes—
89#2567C2214yes—
90#2567C2211yescharacteristic
91#2567C2214yes—
92#2563C2211yescharacteristic
93#2553C22116yes—
94#2548C2212yes—
95#2548C2211yescharacteristic
96#2547C2212yes—
97#2547C2212yes—
98#2547C2212yes—
99#2546C2214yes—
100#2546C2212yes—
101#2546C2212yes—
102#2546C2212yes—
103#2546C2212yes—
104#2545C2214yes—
105#2544C2214yes—
106#2543C2218yes—
107#2542C2212yes—
108#2541C2211yescharacteristic
109#2538C2214yes—
110#2537C2218yes—
111#2502C2214yes—
112#2500C2212yes—
113#2499C2214yes—
114#2486C2214yes—
115#2486C2214yes—
116#2485C2218yes—
117#2466C22116yes—
118#2465C22116yes—
119#2455C22116yes—
120#2449C22116yes—
121#2441C2218yes—
122#2434C2214yes—
123#2432C2214yes—
124#2432C2214yes—
125#2432C2214yes—
126#2431C2212yes—
127#2427C2218yes—
128#2423C2218yes—
129#2422C22116yes—
130#2416C2218yes—
131#2415C2218yes—
132#2414C2214yes—
133#2409C2218yes—
134#2392C2218yes—
135#2388C2214yes—
136#2360C2218yes—
137#2355C2212yes—
138#2352C2214yes—
139D4×C4⋊C4C2212yes—
140D4×C4⋊C4C2218yes—
141#2347C2212yes—
142#2343C2214yes—
143#2339C2212yes—
144#2327C2214yes—
145#2326C2214yes—
146#2317C2214yes—
147#2316C2218yes—
148#2310C2212yes—
149C4×#127C2212yes—
150C4×#124C2212yes—
151C4×#121C2218yes—
152C4×#121C2214yes—
153#2297C2214yes—
154#2295C2212yes—
155#2290C2214yes—
156#2285C2211yescharacteristic
157#2283C2212yes—
158C42×D4C2212yes—
159C4×#117C2211yescharacteristic
160C2×C4×C4⋊C4C2212yes—
161C22×#41C2312yes—
162C22×#41C2311yescharacteristic
163C22×#41C2312yes—
164C22×#41C2314yes—
165C22×#41C2311yescharacteristic
166C23×Q8C2312yes—
167C23×Q8C2312yes—
168#557—28no—
169#556—216no—
170#556—28no—
171#556—216no—
172#555—216no—
173#554—216no—
174#553—232no—
175#552—216no—
176#552—232no—
177D4×Q8—28no—
178#548—216no—
179#548—232no—
180#547—28no—
181#547—216no—
182#547—216no—
183#542—232no—
184#537—216no—
185#536—48no—
186#533—28no—
187#533—216no—
188#533—216no—
189#532—28no—
190#532—216no—
191#532—416no—
192C2×C4⋊Q8—28no—
193C2×C4⋊Q8C2311yescharacteristic
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2311yescharacteristic
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2311yescharacteristic
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2314yes—
203C2×C4⋊Q8C2314yes—
204C2×C4⋊Q8C2314yes—
205C2×#127C2312yes—
206C2×#127C2311yescharacteristic
207#529—232no—
208#529—216no—
209C2×#126C2314yes—
210C2×#126C2314yes—
211C2×#126C2314yes—
212C2×#126C2318yes—
213C2×#125C2312yes—
214C2×#125C2314yes—
215C2×#125C2314yes—
216C2×#125C2312yes—
217C2×#125C2314yes—
218C2×#124C2312yes—
219C2×#124C2314yes—
220C2×#124C2314yes—
221C2×#124C2312yes—
222C2×#124C2314yes—
223C2×#124C2318yes—
224C2×#124C2314yes—
225C2×#124C2312yes—
226C2×#123C2314yes—
227C2×#123C2314yes—
228C2×#123C2314yes—
229C2×#123C2318yes—
230C2×#123C2318yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2312yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2318yes—
242C2×C22⋊Q8C2318yes—
243C2×C22⋊Q8C2318yes—
244C2×#121C2314yes—
245C2×#121C2312yes—
246C2×#121C2312yes—
247C2×#121C2314yes—
248C2×#121C2314yes—
249C2×#121C2314yes—
250C2×#121C2318yes—
251C2×#121C2312yes—
252C2×#121C2314yes—
253C2×#121C23116yes—
254#520—216no—
255C4×#41—28no—
256C4×#41—216no—
257C4×#41D4116yescomplemented
258C2×C4×Q8—216no—
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2314yes—
261C2×C4×Q8C2312yes—
262C2×C4×Q8C2311yescharacteristic
263C2×C4×Q8C2314yes—
264C2×C4×Q8C2312yes—
265C2×C4×Q8C2314yes—
266C2×C4×Q8C2312yes—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2314yes—
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×D4C2311yescharacteristic
273C2×C4×D4C2312yes—
274C2×C4×D4C2311yescharacteristic
275C2×C4×D4C2314yes—
276C2×C4×D4C2312yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2318yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2318yes—
285C2×C4×D4C2314yes—
286C2×C4×D4C23116yes—
287C2×C4×D4C2311yescharacteristic
288C2×C4×D4C2312yes—
289C2×C4×D4C2311yescharacteristic
290C2×C4×D4C2312yes—
291C2×#117C2311yescharacteristic
292C2×#117C2314yes—
293C2×#117C2314yes—
294C2×#117C2312yes—
295C2×#117C2312yes—
296C2×#117C2314yes—
297C2×#117C2312yes—
298C2×#117C2312yes—
299C2×#117C2314yes—
300C2×#117C2312yes—
301C2×#117C2312yes—
302C2×#117C2311yescharacteristic
303C22×C4⋊C4C2314yes—
304C22×C4⋊C4C2312yes—
305C22×C4⋊C4C2312yes—
306C22×C4⋊C4C2314yes—
307C22×C4⋊C4C2314yes—
308C22×C4⋊C4C2312yes—
309C22×C42C2314yes—
310C22×C42C2312yes—
311C22×C42C2314yes—
312C22×C42C2311yescharacteristic
313C22×C42C2312yes—
314#399C23116yes—
315#399C2318yes—
316#399C23116yes—
317#398C2318yes—
318#398C2318yes—
319#398C2318yes—
320#398C23116yes—
321#398C2318yes—
322#397C2318yes—
323#397C2318yes—
324#397C2318yes—
325#397C23116yes—
326#397C23116yes—
327#396C23116yes—
328#396C23116yes—
329#395C2318yes—
330#395C2314yes—
331#395C23116yes—
332#395C23116yes—
333#394C2314yes—
334#394C2318yes—
335#394C23116yes—
336#394C23116yes—
337#394C23116yes—
338#394C23116yes—
339#394C2318yes—
340#394C23116yes—
341#393C23116yes—
342#393C2314yes—
343#392C2314yes—
344#392C2318yes—
345#391C2314yes—
346#391C2314yes—
347#391C2318yes—
348#391C2314yes—
349#391C2312yes—
350#391C2314yes—
351#391C2318yes—
352#391C2314yes—
353#391C2314yes—
354#390C2312yes—
355#390C2318yes—
356#390C2312yes—
357#390C2314yes—
358#390C2318yes—
359#390C2314yes—
360#390C2312yes—
361#389C2314yes—
362#389C2318yes—
363#389C2318yes—
364#389C23116yes—
365#389C2318yes—
366#389C2318yes—
367#389C23116yes—
368#389C23116yes—
369#389C23116yes—
370#389C2318yes—
371#389C2314yes—
372#388C23116yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C23116yes—
377#387C23116yes—
378#387C23116yes—
379#387C23116yes—
380#387C2318yes—
381#387C2318yes—
382#386C2318yes—
383#386C2318yes—
384#386C23116yes—
385#386C23116yes—
386#385C23116yes—
387#385C23116yes—
388#385C23116yes—
389#385C23116yes—
390#385C23116yes—
391#385C2318yes—
392#384C2312yes—
393#384C2314yes—
394#384C2318yes—
395#384C2318yes—
396#384C2312yes—
397#383C2314yes—
398#382C2312yes—
399#382C2312yes—
400#382C2318yes—
401#382C2314yes—
402#381C2314yes—
403#381C2318yes—
404#380C2314yes—
405#380C23116yes—
406#380C23116yes—
407#380C2312yes—
408#380C2318yes—
409#380C2318yes—
410#380C2314yes—
411#380C2318yes—
412#380C2312yes—
413C4×C4⋊C4C2311yescharacteristic
414C4×C4⋊C4C2312yes—
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2312yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2312yes—
422C4×C22⋊C4C2312yes—
423C4×C22⋊C4C2318yes—
424C4×C22⋊C4C2318yes—
425C4×C22⋊C4C23116yes—
426C4×C22⋊C4C2312yes—
427C4×C22⋊C4C2314yes—
428#376C2314yes—
429#376C2312yes—
430C2×#95C2314yes—
431C43C2312yes—
432C2×#41—28no—
433C2×#41—24no—
434C2×#41—24no—
435C2×#41—28no—
436C2×#41—28no—
437C2×#41—216no—
438C2×#41—48no—
439C2×#41—42no—
440C2×#41—44no—
441C2×#41—44no—
442C2×#41—48no—
443C2×#41—48no—
444C2×#41C2×D418yes—
445C22×Q8—28no—
446C22×Q8—28no—
447C22×Q8—48no—
448C22×Q8—44no—
449C22×Q8—44no—
450C22×Q8C2412yes—
451C22×Q8C2412yes—
452C22×Q8C2411yescharacteristic
453C22×Q8C2414yes—
454C22×Q8C2411yescharacteristic
455C22×Q8C2414yes—
456C22×Q8C2412yes—
457C22×Q8C2414yes—
458C22×D4C2412yes—
459C22×D4C2412yes—
460C22×D4C2418yes—
461C22×D4C2414yes—
462C22×D4C2412yes—
463C22×D4C2411yescharacteristic
464C22×D4C2411yescharacteristic
465C22×D4C2414yes—
466C22×D4C2412yes—
467C22×D4C2418yes—
468C22×D4C2412yes—
469C23×C4C2414yes—
470C23×C4C2412yes—
471C23×C4C2412yes—
472C23×C4C2414yes—
473C23×C4C2412yes—
474C23×C4C2412yes—
475C23×C4C2411yescharacteristic
476C23×C4C2411yescharacteristic
477C23×C4C2411yescharacteristic
478C23×C4C2412yes—
479C23×C4C2414yes—
480C23×C4C2418yes—
481C23×C4C2414yes—
482C23×C4C2418yes—
483C23×C4C2412yes—
484C4⋊Q8—28no—
485C4⋊Q8—28no—
486C4⋊Q8—28no—
487C4⋊Q8—28no—
488C4⋊Q8—24no—
489C4⋊Q8—24no—
490C4⋊Q8—28no—
491C4⋊Q8—24no—
492C4⋊Q8—28no—
493C4⋊Q8—48no—
494C4⋊Q8—48no—
495C4⋊Q8—48no—
496#127—28no—
497#127—24no—
498#126—232no—
499#126—216no—
500#126—216no—
501#126—216no—
502#125—28no—
503#125—216no—
504#125—216no—
505#125—28no—
506#125—216no—
507#124—28no—
508#124—216no—
509#124—216no—
510#124—232no—
511#124—28no—
512#124—216no—
513#124—44no—
514#124—48no—
515#123—216no—
516#123—216no—
517#123—216no—
518#123—232no—
519#123—416no—
520C22⋊Q8—216no—
521C22⋊Q8—216no—
522C22⋊Q8—216no—
523C22⋊Q8—28no—
524C22⋊Q8—28no—
525C22⋊Q8—28no—
526C22⋊Q8—28no—
527C22⋊Q8—216no—
528C22⋊Q8—28no—
529C22⋊Q8—216no—
530C22⋊Q8—232no—
531C22⋊Q8—416no—
532C22⋊Q8—416no—
533#121—28no—
534#121—216no—
535#121—216no—
536#121—232no—
537#121—216no—
538#121—28no—
539#121—28no—
540#121—216no—
541#121—216no—
542#121—432no—
543C4×Q8—28no—
544C4×Q8—28no—
545C4×Q8—216no—
546C4×Q8—216no—
547C4×Q8—28no—
548C4×Q8—28no—
549C4×Q8—24no—
550C4×Q8—24no—
551C4×Q8—28no—
552C4×Q8—216no—
553C4×Q8—216no—
554C4×Q8C2×D418yes—
555C4×Q8C2×D418yes—
556C4×D4—28no—
557C4×D4—216no—
558C4×D4—28no—
559C4×D4—216no—
560C4×D4—232no—
561C4×D4—24no—
562C4×D4—24no—
563C4×D4—28no—
564C4×D4—216no—
565C4×D4—28no—
566C4×D4—216no—
567C4×D4—28no—
568C4×D4—48no—
569C4×D4—416no—
570C4×D4—432no—
571C4×D4C2×D4116yes—
572C4×D4C2×D418yes—
573C4×D4C2×D418yes—
574C4×D4C2×D4116yes—
575#117—24no—
576#117—28no—
577#117—28no—
578#117—216no—
579#117—216no—
580#117—216no—
581#117—28no—
582#117—216no—
583#117—28no—
584#117—44no—
585#117C2×D418yes—
586#117C2×D4116yes—
587C2×C4⋊C4—28no—
588C2×C4⋊C4—28no—
589C2×C4⋊C4—28no—
590C2×C4⋊C4—216no—
591C2×C4⋊C4—216no—
592C2×C4⋊C4—216no—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C24116yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C24116yes—
625C2×C4⋊C4C24116yes—
626C2×C4⋊C4C24116yes—
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C22⋊C4C2412yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2412yes—
636C2×C22⋊C4C2412yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C24116yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C24116yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C24116yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2412yes—
658C2×C42—216no—
659C2×C42—28no—
660C2×C42—48no—
661C2×C42C2×D418yes—
662C2×C42C2×D4116yes—
663C2×C42C2412yes—
664C2×C42C2414yes—
665C2×C42C2418yes—
666C2×C42C2414yes—
667C2×C42C2412yes—
668C2×C42C2414yes—
669C2×C42C2414yes—
670C2×C42C2414yes—
671C2×C42C2412yes—
672C2×C42C2414yes—
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2418yes—
676C2×C42C2412yes—
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2412yes—
680C2×C42C2411yescharacteristic
681C2×C42C2412yes—
682C2×C42C2411yescharacteristic
683#95C2412yes—
684#95C2414yes—
685#95C2418yes—
686#95C2412yes—
687#95C2414yes—
688#95C2418yes—
689#95C2418yes—
690#95C2414yes—
691#95C2418yes—
692#95C2418yes—
693#95C24116yes—
694#95C24116yes—
695#95C2418yes—
696#95C24116yes—
697#95C24116yes—
698#95C24116yes—
699C24C2514yes—
700C24C2511yescharacteristic
701C24C2512yes—
702C24C2512yes—
703#41—416no—
704#41—416no—
705#41—432no—
706#41—432no—
707#41—832no—
708C2×Q8—28no—
709C2×Q8—24no—
710C2×Q8—24no—
711C2×Q8—24no—
712C2×Q8—22no—
713C2×Q8—28no—
714C2×Q8—28no—
715C2×Q8—28no—
716C2×Q8—24no—
717C2×Q8—22no—
718C2×Q8—24no—
719C2×Q8—28no—
720C2×Q8—22no—
721C2×Q8—24no—
722C2×Q8—28no—
723C2×Q8—48no—
724C2×Q8—44no—
725C2×Q8—44no—
726C2×Q8—44no—
727C2×Q8—432no—
728C2×Q8—816no—
729C2×Q8C22×D414yes—
730C2×D4—28no—
731C2×D4—28no—
732C2×D4—24no—
733C2×D4—216no—
734C2×D4—28no—
735C2×D4—24no—
736C2×D4—216no—
737C2×D4—22no—
738C2×D4—24no—
739C2×D4—24no—
740C2×D4—24no—
741C2×D4—24no—
742C2×D4—216no—
743C2×D4—28no—
744C2×D4—24no—
745C2×D4—22no—
746C2×D4—24no—
747C2×D4—48no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—42no—
751C2×D4—48no—
752C2×D4—44no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4C22×D414yes—
756C2×D4C22×D418yes—
757C2×D4H(5,𝔽2)14yes—
758C22×C4—24no—
759C22×C4—22no—
760C22×C4—28no—
761C22×C4—24no—
762C22×C4—22no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—28no—
766C22×C4—24no—
767C22×C4—28no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—28no—
771C22×C4—28no—
772C22×C4—24no—
773C22×C4—28no—
774C22×C4—28no—
775C22×C4—28no—
776C22×C4—216no—
777C22×C4—216no—
778C22×C4—216no—
779C22×C4—48no—
780C22×C4—44no—
781C22×C4—44no—
782C22×C4—42no—
783C22×C4—48no—
784C22×C4—48no—
785C22×C4—48no—
786C22×C4—44no—
787C22×C4—44no—
788C22×C4—48no—
789C22×C4C22×D414yes—
790C22×C4C22×D414yes—
791C22×C4C22×D418yes—
792C22×C4C22×D414yes—
793C22×C4C22×D418yes—
794C22×C4C22×D418yes—
795C22×C4C2514yes—
796C22×C4C2512yes—
797C22×C4C2518yes—
798C22×C4C2512yes—
799C22×C4C2514yes—
800C22×C4C2514yes—
801C22×C4C2518yes—
802C22×C4C2514yes—
803C22×C4C2512yes—
804C22×C4C2512yes—
805C22×C4C2511yescharacteristic
806C22×C4C2512yes—
807C22×C4C2511yescharacteristic
808C22×C4C2512yes—
809C22×C4C2511yescharacteristic
810C22×C4C2514yes—
811C22×C4C2511yescharacteristic
812C22×C4C2511yescharacteristic
813C22×C4C2511yescharacteristic
814C4⋊C4—28no—
815C4⋊C4—28no—
816C4⋊C4—28no—
817C4⋊C4—216no—
818C4⋊C4—28no—
819C4⋊C4—24no—
820C4⋊C4—28no—
821C4⋊C4—28no—
822C4⋊C4—28no—
823C4⋊C4—28no—
824C4⋊C4—22no—
825C4⋊C4—24no—
826C4⋊C4—28no—
827C4⋊C4—24no—
828C4⋊C4—22no—
829C4⋊C4—24no—
830C4⋊C4—28no—
831C4⋊C4—24no—
832C4⋊C4—28no—
833C4⋊C4—24no—
834C4⋊C4—28no—
835C4⋊C4—24no—
836C4⋊C4—24no—
837C4⋊C4—216no—
838C4⋊C4—216no—
839C4⋊C4—28no—
840C4⋊C4—24no—
841C4⋊C4—28no—
842C4⋊C4—44no—
843C4⋊C4—48no—
844C4⋊C4—416no—
845C4⋊C4—416no—
846C4⋊C4—416no—
847C4⋊C4—416no—
848C4⋊C4C22×D414yes—
849C4⋊C4C22×D418yes—
850C4⋊C4C22×D414yes—
851C4⋊C4C22×D418yes—
852C4⋊C42−1+418yes—
853C22⋊C4—28no—
854C22⋊C4—24no—
855C22⋊C4—216no—
856C22⋊C4—28no—
857C22⋊C4—28no—
858C22⋊C4—28no—
859C22⋊C4—232no—
860C22⋊C4—24no—
861C22⋊C4—216no—
862C22⋊C4—28no—
863C22⋊C4—24no—
864C22⋊C4—216no—
865C22⋊C4—28no—
866C22⋊C4—28no—
867C22⋊C4—28no—
868C22⋊C4—216no—
869C22⋊C4—44no—
870C22⋊C4—48no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4—416no—
874C22⋊C4—416no—
875C22⋊C4—48no—
876C22⋊C4C22×D418yes—
877C22⋊C4C22×D418yes—
878C22⋊C4C22×D418yes—
879C42—28no—
880C42—24no—
881C42—24no—
882C42—28no—
883C42—28no—
884C42—24no—
885C42—216no—
886C42—24no—
887C42—28no—
888C42—28no—
889C42—28no—
890C42—24no—
891C42—48no—
892C42C22×D418yes—
893C42C22×D414yes—
894C42C22×D414yes—
895C42C22×D418yes—
896C42C22×D414yes—
897C42C22×D414yes—
898C42C22×D418yes—
899C23—22no—
900C23—21no—
901C23—22no—
902C23—22no—
903C23—24no—
904C23—24no—
905C23—24no—
906C23—24no—
907C23—21no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—24no—
912C23—24no—
913C23—28no—
914C23—28no—
915C23—24no—
916C23C23×D414yes—
917C23C23×D412yes—
918C23C2×H(5,𝔽2)14yes—
919C23C2611yescharacteristic
920Q8—28no—
921Q8—416no—
922Q8—48no—
923Q8—48no—
924Q8—416no—
925Q8—48no—
926Q8—44no—
927Q8—88no—
928D4—28no—
929D4—28no—
930D4—48no—
931D4—432no—
932D4—48no—
933D4—48no—
934D4—416no—
935D4—416no—
936D4—48no—
937D4—48no—
938D4—816no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—21no—
942C2×C4—22no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—21no—
948C2×C4—24no—
949C2×C4—28no—
950C2×C4—28no—
951C2×C4—216no—
952C2×C4—216no—
953C2×C4—28no—
954C2×C4—22no—
955C2×C4—24no—
956C2×C4—22no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—22no—
960C2×C4—28no—
961C2×C4—28no—
962C2×C4—28no—
963C2×C4—24no—
964C2×C4—22no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—28no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—22no—
971C2×C4—28no—
972C2×C4—24no—
973C2×C4—28no—
974C2×C4—28no—
975C2×C4—24no—
976C2×C4—28no—
977C2×C4—48no—
978C2×C4—416no—
979C2×C4—48no—
980C2×C4—416no—
981C2×C4—48no—
982C2×C4—416no—
983C2×C4—48no—
984C2×C4—816no—
985C2×C4—816no—
986C2×C4—88no—
987C2×C4C23×D414yes—
988C2×C4C23×D412yes—
989C2×C4C23×D414yes—
990C2×C4C23×D414yes—
991C2×C4C23×D412yes—
992C2×C4C23×D412yes—
993C2×C4C23×D412yes—
994C2×C4C23×D412yes—
995C2×C4C23×D412yes—
996C2×C4C2×H(5,𝔽2)12yes—
997C2×C4C2×2−1+418yes—
998C2×C4C2×2−1+414yes—
999C2×C4#58514yes—
1000C2×C4#58512yes—
1001C22—28no—
1002C22—22no—
1003C22—24no—
1004C22—24no—
1005C22—22no—
1006C22—24no—
1007C22—22no—
1008C22—24no—
1009C22—44no—
1010C22—42no—
1011C22—42no—
1012C22—44no—
1013C22—44no—
1014C22—42no—
1015C22—42no—
1016C22—48no—
1017C22—48no—
1018C22—44no—
1019C22—44no—
1020C22—44no—
1021C22C24×D411yescharacteristic
1022C22C22×H(5,𝔽2)11yescharacteristic
1023C22C22×2−1+412yes—
1024C22C2×#58512yes—
1025C22C2×#58511yescharacteristic
1026C4—28no—
1027C4—24no—
1028C4—22no—
1029C4—22no—
1030C4—24no—
1031C4—22no—
1032C4—24no—
1033C4—48no—
1034C4—44no—
1035C4—44no—
1036C4—42no—
1037C4—48no—
1038C4—42no—
1039C4—44no—
1040C4—42no—
1041C4—44no—
1042C4#344914yes—
1043C4#348814yes—
1044C4#349914yes—
1045C2—44no—
1046C2—42no—
1047C2—44no—
1048C2—84no—
1049C2C2×#344911yescharacteristic
1050C2C2×#348811yescharacteristic
1051C2C2×#349911yescharacteristic
1052C2#6301312yes—
1053C2#6303412yes—
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×#3511C2semidirect
2. C2×#3482C2semidirect
3. #42984C2semidirect
4. #41948C2semidirect
5. #39744C2semidirect
6. #39167C2semidirect
7. #38922C2semidirect
8. #38914C2semidirect
9. #38091C2semidirect
10. #37680C2semidirect
11. #37640C2semidirect
12. #37619C2semidirect
13. #36544C2semidirect
14. #36406C2semidirect
15. #36127C2semidirect
16. #35686C2semidirect
17. #35316C2semidirect
18. #35281C2semidirect
19. #35200C2semidirect
20. #35173C2semidirect
21. #34977C2semidirect
22. #34937C2semidirect
23. #34127C2semidirect
257. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35112
C2×#34822
#429842
#419482
#397442
#391672
#389222
#389142
#380912
#376802
#376402
#376192
#365442
#364062
#361272
#356862
#353162
#352812
#352002
#351732
#349772
#349372
#341272