Finite Group Databasebeta

← #7711649

Subgroups — #7711649

Order 512.

8482 conjugacy classes of subgroups.

The subgroup lattice has 1199 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3545C211yesmaximal, characteristic, complemented
2C22×#532C211yesmaximal, characteristic, complemented
3#59184C214yesmaximal, complemented
4#59182C214yesmaximal, complemented
5#46228C212yesmaximal, complemented
6#46225C212yesmaximal, complemented
7#46224C214yesmaximal, complemented
8#39460C214yesmaximal, complemented
9#39332C214yesmaximal, complemented
10#37810C218yesmaximal, complemented
11#37808C218yesmaximal, complemented
12#37606C212yesmaximal, complemented
13#37258C212yesmaximal, complemented
14#37232C212yesmaximal, complemented
15#36621C212yesmaximal, complemented
16#36159C214yesmaximal, complemented
17#36099C214yesmaximal, complemented
18#35149C212yesmaximal, complemented
19#35088C212yesmaximal, complemented
20#34366C211yesmaximal, characteristic, complemented
21C23×#41C2211yescharacteristic
22C23×#41C2211yescharacteristic, complemented
23#3545—216no—
24C2×#563C2211yescharacteristic, complemented
25C2×#562C2212yescomplemented
26C2×H(3,𝔽4)C2211yescharacteristic, complemented
27C2×#555C2212yescomplemented
28C2×#551C2214yes—
29C2×#551C2212yescomplemented
30C2×#546C2214yes—
31C2×#542C2214yescomplemented
32C2×#538C2214yescomplemented
33C2×#536C2212yes—
34C2×#535C2212yes—
35C2×#534C2212yes—
36C2×#534C2212yescomplemented
37C2×#532—216no—
38C2×#532C2212yes—
39C2×#532C2212yes—
40C2×#532C2212yescomplemented
41C2×#532C2212yescomplemented
42C2×#532C2218yescomplemented
43C22×C4⋊Q8C2211yescharacteristic, complemented
44C22×#127C2211yescharacteristic
45C2×#529C2212yes—
46C22×#124C2211yescharacteristic
47C22×#124C2211yescharacteristic, complemented
48C2×#525C2212yes—
49C22×#123C2212yescomplemented
50C22×#121C2214yescomplemented
51C22×C4×D4C2214yescomplemented
52C23×C42C2211yescharacteristic, complemented
53#2855C2212yescomplemented
54#2854C2212yes—
55#2853C2214yescomplemented
56#2852C2218yescomplemented
57#2851C2214yescomplemented
58#2850C2214yescomplemented
59#2849C2214yes—
60#2849C2214yescomplemented
61#2849C2214yescomplemented
62#2848C2212yescomplemented
63#2847C2212yes—
64#2820C2214yescomplemented
65#2819C2214yescomplemented
66#2734C2214yescomplemented
67#2734C2214yescomplemented
68#2731C2214yescomplemented
69#2731C2214yescomplemented
70#2729C2218yescomplemented
71#2729C2218yescomplemented
72#2709C2214yescomplemented
73#2709C2214yescomplemented
74#2703C2218yescomplemented
75#2691C2218yescomplemented
76#2681C2218yescomplemented
77#2676C2218yescomplemented
78#2675C2218yescomplemented
79#2673C2218yescomplemented
80#2673C2218yescomplemented
81#2672C2218yescomplemented
82#2671C2218yescomplemented
83#2669C2214yescomplemented
84#2669C2214yescomplemented
85#2669C2218yescomplemented
86#2662C2218yescomplemented
87#2632C2214yescomplemented
88#2631C2214yescomplemented
89#2614C2214yescomplemented
90#2613C2214yes—
91#2613C2214yescomplemented
92#2613C2214yescomplemented
93#2610C2218yescomplemented
94#2561C2214yescomplemented
95#2559C2218yescomplemented
96#2555C2218yescomplemented
97#2539C2214yes—
98#2534C2214yescomplemented
99#2534C2214yescomplemented
100#2484C2214yescomplemented
101#2476C2218yescomplemented
102#2468C2218yescomplemented
103#2466C2218yescomplemented
104#2464C2218yescomplemented
105#2464C2218yescomplemented
106#2464C2218yescomplemented
107#2461C2218yescomplemented
108#2459C2218yescomplemented
109#2457C2218yescomplemented
110#2456C2218yescomplemented
111#2456C2218yescomplemented
112#2455C2218yescomplemented
113#2450C2218yescomplemented
114#2449C2218yescomplemented
115#2432C2214yescomplemented
116#2432C2214yescomplemented
117#2431C2214yescomplemented
118#2431C2214yescomplemented
119#2430C2218yescomplemented
120#2430C2218yescomplemented
121#2428C2218yescomplemented
122#2425C2218yescomplemented
123#2424C2218yescomplemented
124#2424C2218yescomplemented
125#2413C2214yescomplemented
126#2413C2214yescomplemented
127#2410C2214yes—
128#2410C2214yes—
129#2407C2218yescomplemented
130#2407C2218yescomplemented
131#2406C2214yes—
132#2406C2214yescomplemented
133#2406C2214yescomplemented
134#2405C2214yescomplemented
135#2404C2214yescomplemented
136#2404C2214yescomplemented
137#2403C2214yescomplemented
138#2379C2212yescomplemented
139#2379C2212yescomplemented
140#2372C2212yescomplemented
141#2372C2212yescomplemented
142#2364C2218yescomplemented
143#2361C2218yescomplemented
144#2359C2218yescomplemented
145#2358C2218yescomplemented
146#2342C2214yescomplemented
147#2342C2214yescomplemented
148#2337C2218yescomplemented
149#2310C2212yescomplemented
150#2309C2212yescomplemented
151#2308C2212yes—
152#2308C2212yescomplemented
153C4×C22⋊Q8C2214yescomplemented
154C4×#123C2214yescomplemented
155C4×#121C2214yescomplemented
156C4×#120C2214yescomplemented
157#2290C2218yescomplemented
158#2283C2212yescomplemented
159#2280C2212yescomplemented
160C2×#381C2212yescomplemented
161C22×#41—28no—
162C22×#41—28no—
163C22×#41—44no—
164C22×#41—44no—
165C22×#41—44no—
166C22×#41—44no—
167C22×#41C2312yes—
168C22×#41C2314yes—
169C22×#41C2312yes—
170C22×#41C2312yes—
171C22×#41C2314yes—
172C22×#41C2312yes—
173C22×#41C2312yes—
174C23×Q8C2311yescharacteristic
175C23×Q8C2311yescharacteristic
176C23×D4C2312yes—
177C23×D4C2312yes—
178C23×D4C2311yescharacteristic
179C23×D4C2314yes—
180C23×D4C2312yes—
181C23×D4C2311yescharacteristic
182C24×C4C2311yescharacteristic
183C24×C4C2312yes—
184C24×C4C2312yes—
185C24×C4C2312yes—
186#563—28no—
187#562—216no—
188H(3,𝔽4)—28no—
189#555—216no—
190#551—216no—
191#551—232no—
192#546—232no—
193#542—232no—
194#538—232no—
195#536—216no—
196#535—48no—
197#534—216no—
198#534—48no—
199#532—216no—
200#532—216no—
201#532—264no—
202#532—216no—
203#532—216no—
204C2×C4⋊Q8—28no—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×#127—28no—
211C2×#127C2312yes—
212C2×#127C2314yes—
213C2×#127C2312yes—
214C2×#127C2314yes—
215#529—216no—
216C2×#126C2314yes—
217C2×#126C2314yes—
218C2×#126C2314yes—
219C2×#125C2312yes—
220C2×#124—28no—
221C2×#124D4116yescomplemented
222C2×#124C2312yes—
223C2×#124C2312yes—
224C2×#124C2312yes—
225C2×#124C2314yes—
226C2×#124C2314yes—
227C2×#124C2312yes—
228C2×#124C2312yes—
229C2×#124C2314yes—
230C2×#124C2314yes—
231C2×#124C2314yes—
232C2×#124C2311yescharacteristic
233C2×#124C2311yescharacteristic
234C2×#124C2311yescharacteristic
235C2×#124C2311yescharacteristic
236#525—48no—
237C2×#123—48no—
238C2×#123C2314yes—
239C2×#123C2314yes—
240C2×#123C2314yes—
241C2×#123C2312yes—
242C2×#123C2312yes—
243C2×#123C2314yes—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×#123C2314yes—
248C2×#123C2318yes—
249C2×#123C2314yes—
250C2×#123C2318yes—
251C2×C22⋊Q8C2312yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×#121—232no—
259C2×#121C2312yes—
260C2×#121C2318yes—
261C2×#121C2318yes—
262C2×#121C2318yes—
263C2×#121C2318yes—
264C2×#121C2314yes—
265C2×#121C2314yes—
266C2×#121C2314yes—
267C2×#121C2314yes—
268C2×#121C2314yes—
269C2×#121C2318yes—
270C2×#121C2318yes—
271C2×#121C2318yes—
272C2×#121C2314yes—
273C2×#121C2318yes—
274C2×#120C2314yes—
275C2×#120C2314yes—
276C2×#120C2312yes—
277C2×#120C2312yes—
278C2×#120C2314yes—
279C2×#120C2314yes—
280C2×#120C2314yes—
281C2×#120C2318yes—
282C2×#120C2314yes—
283C2×C4×Q8C2312yes—
284C2×C4×D4—232no—
285C2×C4×D4C2318yes—
286C2×C4×D4C2318yes—
287C2×C4×D4C2314yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2318yes—
291C2×C4×D4C2318yes—
292C2×C4×D4C2314yes—
293C2×C4×D4C2318yes—
294C2×C4×D4C2318yes—
295C2×#117C2312yes—
296C2×#117C2314yes—
297C2×#117C2314yes—
298C2×#117C2312yes—
299C2×#117C2312yes—
300C22×C4⋊C4C2314yes—
301C22×C4⋊C4C2314yes—
302C22×C22⋊C4C2314yes—
303C22×C22⋊C4C2312yes—
304C22×C22⋊C4C2314yes—
305C22×C22⋊C4C2312yes—
306C22×C22⋊C4C2312yes—
307C22×C22⋊C4C2314yes—
308C22×C22⋊C4C2314yes—
309C22×C42—28no—
310C22×C42C2312yes—
311C22×C42C2314yes—
312C22×C42C2311yescharacteristic
313C22×C42C2312yes—
314C22×C42C2312yes—
315C22×C42C2311yescharacteristic
316#400C2318yes—
317#399C2318yes—
318#398C2318yes—
319#398C2318yes—
320#398C2318yes—
321#397C2318yes—
322#396C2318yes—
323#396C2318yes—
324#396C2318yes—
325#396C2318yes—
326#395C2318yes—
327#395C2318yes—
328#395C2318yes—
329#394C2318yes—
330#394C2318yes—
331#394C2318yes—
332#394C2318yes—
333#394C2318yes—
334#394C2318yes—
335#394C2318yes—
336#394C2318yes—
337#394C2318yes—
338#394C2318yes—
339#394C2318yes—
340#394C2318yes—
341#394C2318yes—
342#393C2318yes—
343#393C2318yes—
344#393C2318yes—
345#392C2318yes—
346#392C2318yes—
347#392C2318yes—
348#392C2318yes—
349#392C2318yes—
350#392C2318yes—
351#392C2318yes—
352#392C2318yes—
353#392C2318yes—
354#392C2318yes—
355#392C2318yes—
356#391C2314yes—
357#391C2314yes—
358#391C2314yes—
359#391C2314yes—
360#391C2314yes—
361#390C2318yes—
362#390C2314yes—
363#390C2314yes—
364#390C2314yes—
365#390C2318yes—
366#390C2318yes—
367#389C2314yes—
368#389C2314yes—
369#389C2318yes—
370#389C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#386C2314yes—
392#386C2314yes—
393#386C2314yes—
394#386C2314yes—
395#386C2314yes—
396#386C2314yes—
397#386C2318yes—
398#386C2318yes—
399#386C2314yes—
400#386C2318yes—
401#386C2318yes—
402#386C2318yes—
403#386C2318yes—
404#386C2318yes—
405#386C2318yes—
406#386C2318yes—
407#386C2314yes—
408#386C2318yes—
409#386C2318yes—
410#386C2318yes—
411#386C2318yes—
412#386C2318yes—
413#386C2318yes—
414#385C2318yes—
415#385C2314yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#385C2318yes—
423#385C2318yes—
424#385C2318yes—
425#385C2314yes—
426#385C2318yes—
427#385C2318yes—
428#383C2314yes—
429#382C2314yes—
430#381C2314yes—
431#381C2314yes—
432#381C2314yes—
433#381C2314yes—
434#381C2314yes—
435#381C2314yes—
436#381C2314yes—
437#380C2314yes—
438#380C2312yes—
439#380C2314yes—
440#380C2312yes—
441#380C2318yes—
442#379C2314yes—
443#379C2314yes—
444#379C2314yes—
445#379C2314yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2318yes—
448C4×C22⋊C4C2314yes—
449C4×C22⋊C4C2318yes—
450C4×C22⋊C4C2318yes—
451C4×C22⋊C4C2318yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2314yes—
454C4×C22⋊C4C2318yes—
455#376C2314yes—
456C2×#95C2318yes—
457C25C2412yes—
458C25C2412yes—
459C25C2411yescharacteristic
460C25C2412yes—
461C2×#41—28no—
462C2×#41—216no—
463C2×#41—28no—
464C2×#41—28no—
465C2×#41—216no—
466C2×#41—28no—
467C2×#41—28no—
468C2×#41—44no—
469C2×#41—48no—
470C2×#41—44no—
471C2×#41—48no—
472C2×#41—44no—
473C2×#41—44no—
474C2×#41—44no—
475C2×#41—48no—
476C2×#41—44no—
477C2×#41—44no—
478C2×#41—48no—
479C2×#41—44no—
480C2×#41—44no—
481C2×#41—44no—
482C2×#41—464no—
483C2×#41—464no—
484C22×Q8—24no—
485C22×Q8—42no—
486C22×Q8—42no—
487C22×Q8—42no—
488C22×Q8—42no—
489C22×Q8C2×D418yes—
490C22×Q8C2412yes—
491C22×Q8C2412yes—
492C22×Q8C2412yes—
493C22×Q8C2412yes—
494C22×Q8C2411yescharacteristic
495C22×Q8C2412yes—
496C22×Q8C2411yescharacteristic
497C22×D4—216no—
498C22×D4—28no—
499C22×D4—28no—
500C22×D4—28no—
501C22×D4—28no—
502C22×D4—28no—
503C22×D4—24no—
504C22×D4—416no—
505C22×D4—44no—
506C22×D4—42no—
507C22×D4—42no—
508C22×D4—42no—
509C22×D4—42no—
510C22×D4—44no—
511C22×D4—44no—
512C22×D4—44no—
513C22×D4C2×D418yes—
514C22×D4C2414yes—
515C22×D4C2418yes—
516C22×D4C2418yes—
517C22×D4C2414yes—
518C22×D4C2414yes—
519C22×D4C2414yes—
520C22×D4C2414yes—
521C22×D4C2414yes—
522C22×D4C2414yes—
523C22×D4C2412yes—
524C22×D4C2418yes—
525C22×D4C2412yes—
526C22×D4C2414yes—
527C22×D4C2412yes—
528C22×D4C2412yes—
529C22×D4C2418yes—
530C22×D4C2418yes—
531C22×D4C2411yescharacteristic
532C22×D4C2412yes—
533C22×D4C2411yescharacteristic
534C23×C4—24no—
535C23×C4—24no—
536C23×C4—24no—
537C23×C4—28no—
538C23×C4—28no—
539C23×C4—28no—
540C23×C4—28no—
541C23×C4—28no—
542C23×C4—48no—
543C23×C4—44no—
544C23×C4—44no—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2414yes—
550C23×C4C2414yes—
551C23×C4C2414yes—
552C23×C4C2414yes—
553C23×C4C2414yes—
554C23×C4C2414yes—
555C23×C4C2412yes—
556C23×C4C2411yescharacteristic
557C23×C4C2411yescharacteristic
558C23×C4C2414yes—
559C23×C4C2414yes—
560C23×C4C2414yes—
561C23×C4C2412yes—
562C23×C4C2414yes—
563C23×C4C2414yes—
564C23×C4C2412yes—
565C4⋊Q8—28no—
566C4⋊Q8—216no—
567C4⋊Q8—28no—
568C4⋊Q8—28no—
569C4⋊Q8—28no—
570#127—28no—
571#127—216no—
572#127—28no—
573#127—48no—
574#126—216no—
575#126—216no—
576#126—216no—
577#125—28no—
578#124—28no—
579#124—28no—
580#124—216no—
581#124—216no—
582#124—28no—
583#124—216no—
584#124—28no—
585#124—28no—
586#124—48no—
587#124C2×D4132yes—
588#124C2×D418yes—
589#124C2×D418yes—
590#124C2×D418yes—
591#124C2×D418yes—
592#123—28no—
593#123—28no—
594#123—216no—
595#123—216no—
596#123—216no—
597#123—216no—
598#123—216no—
599#123—216no—
600#123—48no—
601#123—416no—
602#123—48no—
603#123—48no—
604#123—416no—
605C22⋊Q8—216no—
606C22⋊Q8—216no—
607C22⋊Q8—28no—
608C22⋊Q8—216no—
609C22⋊Q8—216no—
610C22⋊Q8—48no—
611C22⋊Q8—48no—
612#121—216no—
613#121—216no—
614#121—28no—
615#121—232no—
616#121—232no—
617#121—232no—
618#121—232no—
619#121—216no—
620#121—216no—
621#121—48no—
622#121—48no—
623#121—416no—
624#121—416no—
625#121—416no—
626#121—416no—
627#120—216no—
628#120—216no—
629#120—28no—
630#120—28no—
631#120—216no—
632#120—416no—
633#120—48no—
634#120—48no—
635#120—48no—
636C4×Q8—28no—
637C4×D4—216no—
638C4×D4—232no—
639C4×D4—232no—
640C4×D4—232no—
641C4×D4—232no—
642C4×D4—216no—
643C4×D4—216no—
644C4×D4—28no—
645C4×D4—416no—
646C4×D4—416no—
647#117—28no—
648#117—216no—
649#117—216no—
650#117—44no—
651#117—44no—
652C2×C4⋊C4—216no—
653C2×C4⋊C4—48no—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2418yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C22⋊C4—28no—
675C2×C22⋊C4—216no—
676C2×C22⋊C4—216no—
677C2×C22⋊C4—48no—
678C2×C22⋊C4—44no—
679C2×C22⋊C4—44no—
680C2×C22⋊C4C2×D4132yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2412yes—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2418yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2418yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2418yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2418yes—
713C2×C22⋊C4C2418yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C42—28no—
719C2×C42—24no—
720C2×C42—28no—
721C2×C42—216no—
722C2×C42—28no—
723C2×C42C2×D418yes—
724C2×C42C2412yes—
725C2×C42C2414yes—
726C2×C42C2412yes—
727C2×C42C2414yes—
728C2×C42C2414yes—
729C2×C42C2412yes—
730C2×C42C2412yes—
731C2×C42C2414yes—
732C2×C42C2414yes—
733C2×C42C2418yes—
734C2×C42C2411yescharacteristic
735C2×C42C2412yes—
736C2×C42C2411yescharacteristic
737#95C2418yes—
738#95C2418yes—
739#95C2418yes—
740#95C2418yes—
741#95C2414yes—
742#95C2414yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753#95C2418yes—
754C24—22no—
755C24—22no—
756C24—24no—
757C24—24no—
758C24—24no—
759C24—24no—
760C24—24no—
761C24—24no—
762C24—44no—
763C24—48no—
764C24—48no—
765C24—42no—
766C24—48no—
767C24—42no—
768C24C22×D418yes—
769C24H(5,𝔽2)14yes—
770C24C2514yes—
771C24C2514yes—
772C24C2512yes—
773C24C2512yes—
774C24C2512yes—
775C24C2511yescharacteristic
776#41—432no—
777#41—464no—
778#41—432no—
779#41—432no—
780#41—464no—
781#41—432no—
782#41—816no—
783C2×Q8—24no—
784C2×Q8—24no—
785C2×Q8—24no—
786C2×Q8—24no—
787C2×Q8—416no—
788C2×Q8—41no—
789C2×Q8—42no—
790C2×Q8—41no—
791C2×Q8—42no—
792C2×Q8—41no—
793C2×Q8—41no—
794C2×Q8—42no—
795C2×Q8—42no—
796C2×Q8—42no—
797C2×Q8—42no—
798C2×Q8—42no—
799C2×Q8—44no—
800C2×Q8—42no—
801C2×Q8—416no—
802C2×Q8C22×D414yes—
803C2×Q8C22×D418yes—
804C2×Q8C22×D414yes—
805C2×D4—216no—
806C2×D4—216no—
807C2×D4—28no—
808C2×D4—28no—
809C2×D4—28no—
810C2×D4—28no—
811C2×D4—28no—
812C2×D4—28no—
813C2×D4—28no—
814C2×D4—28no—
815C2×D4—28no—
816C2×D4—28no—
817C2×D4—28no—
818C2×D4—28no—
819C2×D4—216no—
820C2×D4—28no—
821C2×D4—28no—
822C2×D4—24no—
823C2×D4—24no—
824C2×D4—24no—
825C2×D4—24no—
826C2×D4—216no—
827C2×D4—216no—
828C2×D4—416no—
829C2×D4—48no—
830C2×D4—48no—
831C2×D4—44no—
832C2×D4—44no—
833C2×D4—41no—
834C2×D4—42no—
835C2×D4—41no—
836C2×D4—42no—
837C2×D4—41no—
838C2×D4—41no—
839C2×D4—42no—
840C2×D4—42no—
841C2×D4—42no—
842C2×D4—42no—
843C2×D4—44no—
844C2×D4—44no—
845C2×D4—432no—
846C2×D4—464no—
847C2×D4—416no—
848C2×D4—48no—
849C2×D4—48no—
850C2×D4—48no—
851C2×D4—44no—
852C2×D4—42no—
853C2×D4—44no—
854C2×D4—48no—
855C2×D4—48no—
856C2×D4—48no—
857C2×D4—48no—
858C2×D4—44no—
859C2×D4—42no—
860C2×D4—48no—
861C2×D4—48no—
862C2×D4—48no—
863C2×D4—432no—
864C2×D4—816no—
865C2×D4C22×D414yes—
866C2×D4C22×D418yes—
867C2×D4C22×D414yes—
868C22×C4—232no—
869C22×C4—24no—
870C22×C4—22no—
871C22×C4—24no—
872C22×C4—24no—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—24no—
877C22×C4—24no—
878C22×C4—24no—
879C22×C4—24no—
880C22×C4—24no—
881C22×C4—24no—
882C22×C4—28no—
883C22×C4—24no—
884C22×C4—28no—
885C22×C4—28no—
886C22×C4—24no—
887C22×C4—24no—
888C22×C4—28no—
889C22×C4—24no—
890C22×C4—28no—
891C22×C4—28no—
892C22×C4—28no—
893C22×C4—28no—
894C22×C4—28no—
895C22×C4—28no—
896C22×C4—28no—
897C22×C4—28no—
898C22×C4—28no—
899C22×C4—28no—
900C22×C4—28no—
901C22×C4—28no—
902C22×C4—44no—
903C22×C4—44no—
904C22×C4—44no—
905C22×C4—44no—
906C22×C4—44no—
907C22×C4—44no—
908C22×C4—44no—
909C22×C4—432no—
910C22×C4—44no—
911C22×C4—42no—
912C22×C4—44no—
913C22×C4—48no—
914C22×C4—44no—
915C22×C4—48no—
916C22×C4—42no—
917C22×C4—48no—
918C22×C4—44no—
919C22×C4—48no—
920C22×C4—432no—
921C22×C4—432no—
922C22×C4C22×D414yes—
923C22×C4C22×D418yes—
924C22×C4C22×D418yes—
925C22×C4H(5,𝔽2)14yes—
926C22×C4C2518yes—
927C22×C4C2518yes—
928C22×C4C2514yes—
929C22×C4C2514yes—
930C22×C4C2514yes—
931C22×C4C2514yes—
932C22×C4C2511yescharacteristic
933C22×C4C2511yescharacteristic
934C22×C4C2512yes—
935C22×C4C2512yes—
936C22×C4C2512yes—
937C22×C4C2512yes—
938C22×C4C2512yes—
939C22×C4C2514yes—
940C4⋊C4—216no—
941C4⋊C4—216no—
942C4⋊C4—28no—
943C4⋊C4—28no—
944C4⋊C4—28no—
945C4⋊C4—28no—
946C4⋊C4—28no—
947C4⋊C4—28no—
948C4⋊C4—24no—
949C4⋊C4—24no—
950C4⋊C4—28no—
951C4⋊C4—216no—
952C4⋊C4—216no—
953C4⋊C4—216no—
954C4⋊C4—48no—
955C4⋊C4—44no—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C4⋊C4—48no—
959C4⋊C4—44no—
960C22⋊C4—28no—
961C22⋊C4—28no—
962C22⋊C4—24no—
963C22⋊C4—24no—
964C22⋊C4—28no—
965C22⋊C4—28no—
966C22⋊C4—28no—
967C22⋊C4—216no—
968C22⋊C4—28no—
969C22⋊C4—216no—
970C22⋊C4—216no—
971C22⋊C4—28no—
972C22⋊C4—28no—
973C22⋊C4—28no—
974C22⋊C4—28no—
975C22⋊C4—28no—
976C22⋊C4—216no—
977C22⋊C4—216no—
978C22⋊C4—216no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—48no—
982C22⋊C4—48no—
983C22⋊C4—48no—
984C22⋊C4—48no—
985C22⋊C4—48no—
986C22⋊C4—48no—
987C22⋊C4—48no—
988C22⋊C4—48no—
989C22⋊C4—48no—
990C22⋊C4—48no—
991C22⋊C4—48no—
992C22⋊C4—48no—
993C22⋊C4C22×D4116yes—
994C22⋊C4C22×D4116yes—
995C22⋊C4C22×D4116yes—
996C22⋊C4C22×D4116yes—
997C42—28no—
998C42—28no—
999C42—24no—
1000C42—24no—
1001C42—24no—
1002C42—28no—
1003C42—24no—
1004C42—44no—
1005C42—44no—
1006C42—48no—
1007C42C22×D414yes—
1008C42C22×D418yes—
1009C42C22×D414yes—
1010C23—24no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—24no—
1018C23—24no—
1019C23—28no—
1020C23—28no—
1021C23—28no—
1022C23—216no—
1023C23—24no—
1024C23—24no—
1025C23—24no—
1026C23—24no—
1027C23—24no—
1028C23—24no—
1029C23—28no—
1030C23—28no—
1031C23—28no—
1032C23—28no—
1033C23—48no—
1034C23—416no—
1035C23—48no—
1036C23—48no—
1037C23—416no—
1038C23—48no—
1039C23—88no—
1040C23—88no—
1041C23—88no—
1042C23—88no—
1043C23—84no—
1044C23—88no—
1045C23—88no—
1046C23—164no—
1047C23C23×D414yes—
1048C23C23×D414yes—
1049C23C23×D412yes—
1050C23C2×H(5,𝔽2)14yes—
1051C23C2×H(5,𝔽2)12yes—
1052C23C2×H(5,𝔽2)12yes—
1053C23C2611yescharacteristic
1054Q8—44no—
1055Q8—48no—
1056Q8—44no—
1057Q8—48no—
1058Q8—48no—
1059Q8—84no—
1060Q8—84no—
1061D4—44no—
1062D4—48no—
1063D4—44no—
1064D4—432no—
1065D4—432no—
1066D4—416no—
1067D4—416no—
1068D4—48no—
1069D4—48no—
1070D4—416no—
1071D4—416no—
1072D4—416no—
1073D4—84no—
1074D4—84no—
1075D4—88no—
1076D4—88no—
1077D4—816no—
1078D4—88no—
1079D4—816no—
1080D4—168no—
1081C2×C4—216no—
1082C2×C4—216no—
1083C2×C4—216no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—28no—
1099C2×C4—28no—
1100C2×C4—216no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—28no—
1106C2×C4—28no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—28no—
1112C2×C4—28no—
1113C2×C4—28no—
1114C2×C4—28no—
1115C2×C4—28no—
1116C2×C4—28no—
1117C2×C4—48no—
1118C2×C4—416no—
1119C2×C4—416no—
1120C2×C4—416no—
1121C2×C4—416no—
1122C2×C4—416no—
1123C2×C4—416no—
1124C2×C4—48no—
1125C2×C4—88no—
1126C2×C4—88no—
1127C2×C4—88no—
1128C2×C4—84no—
1129C2×C4—88no—
1130C2×C4—164no—
1131C2×C4C23×D414yes—
1132C2×C4C23×D414yes—
1133C2×C4C23×D412yes—
1134C2×C4C23×D412yes—
1135C2×C4C23×D414yes—
1136C2×C4C23×D414yes—
1137C2×C4C2×H(5,𝔽2)14yes—
1138C2×C4#58518yes—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—28no—
1146C22—28no—
1147C22—28no—
1148C22—416no—
1149C22—44no—
1150C22—42no—
1151C22—42no—
1152C22—44no—
1153C22—44no—
1154C22—44no—
1155C22—44no—
1156C22—44no—
1157C22—48no—
1158C22—44no—
1159C22—44no—
1160C22—44no—
1161C22—44no—
1162C22—48no—
1163C22—44no—
1164C22—48no—
1165C22—48no—
1166C22—816no—
1167C22—816no—
1168C22—168no—
1169C22#348414yes—
1170C22C24×D411yescharacteristic
1171C22C22×H(5,𝔽2)11yescharacteristic
1172C22C22×H(5,𝔽2)11yescharacteristic
1173C22C2×#58514yes—
1174C4—24no—
1175C4—22no—
1176C4—22no—
1177C4—24no—
1178C4—24no—
1179C4—28no—
1180C4—24no—
1181C4—24no—
1182C4—48no—
1183C4—44no—
1184C4—44no—
1185C4—44no—
1186C4—44no—
1187C4—48no—
1188C2—24no—
1189C2—44no—
1190C2—44no—
1191C2—44no—
1192C2—84no—
1193C2—84no—
1194C2#6275912yes—
1195C2C2×#348411yescharacteristic
1196C2#6281112yes—
1197C2#6282212yes—
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×#3545C2semidirect
2. C22×#532C2semidirect
3. #59184C2semidirect
4. #59182C2semidirect
5. #46228C2semidirect
6. #46225C2semidirect
7. #46224C2semidirect
8. #39460C2semidirect
9. #39332C2semidirect
10. #37810C2semidirect
11. #37808C2semidirect
12. #37606C2semidirect
13. #37258C2semidirect
14. #37232C2semidirect
15. #36621C2semidirect
16. #36159C2semidirect
17. #36099C2semidirect
18. #35149C2semidirect
19. #35088C2semidirect
20. #34366C2semidirect
22. C23×#41C22semidirect
24. C2×#563C22semidirect
25. C2×#562C22semidirect
26. C2×H(3,𝔽4)C22semidirect
27. C2×#555C22semidirect
29. C2×#551C22semidirect
31. C2×#542C22semidirect
32. C2×#538C22semidirect
36. C2×#534C22semidirect
40. C2×#532C22semidirect
41. C2×#532C22semidirect
42. C2×#532C22semidirect
43. C22×C4⋊Q8C22semidirect
47. C22×#124C22semidirect
49. C22×#123C22semidirect
50. C22×#121C22semidirect
51. C22×C4×D4C22semidirect
52. C23×C42C22semidirect
53. #2855C22semidirect
55. #2853C22semidirect
56. #2852C22semidirect
57. #2851C22semidirect
58. #2850C22semidirect
60. #2849C22semidirect
61. #2849C22semidirect
62. #2848C22semidirect
64. #2820C22semidirect
65. #2819C22semidirect
66. #2734C22semidirect
67. #2734C22semidirect
68. #2731C22semidirect
69. #2731C22semidirect
70. #2729C22semidirect
71. #2729C22semidirect
72. #2709C22semidirect
73. #2709C22semidirect
74. #2703C22semidirect
75. #2691C22semidirect
76. #2681C22semidirect
77. #2676C22semidirect
78. #2675C22semidirect
79. #2673C22semidirect
80. #2673C22semidirect
81. #2672C22semidirect
82. #2671C22semidirect
83. #2669C22semidirect
84. #2669C22semidirect
85. #2669C22semidirect
86. #2662C22semidirect
87. #2632C22semidirect
88. #2631C22semidirect
89. #2614C22semidirect
91. #2613C22semidirect
92. #2613C22semidirect
93. #2610C22semidirect
94. #2561C22semidirect
95. #2559C22semidirect
96. #2555C22semidirect
98. #2534C22semidirect
99. #2534C22semidirect
100. #2484C22semidirect
101. #2476C22semidirect
102. #2468C22semidirect
103. #2466C22semidirect
104. #2464C22semidirect
105. #2464C22semidirect
106. #2464C22semidirect
107. #2461C22semidirect
108. #2459C22semidirect
109. #2457C22semidirect
110. #2456C22semidirect
111. #2456C22semidirect
112. #2455C22semidirect
113. #2450C22semidirect
114. #2449C22semidirect
115. #2432C22semidirect
116. #2432C22semidirect
117. #2431C22semidirect
118. #2431C22semidirect
119. #2430C22semidirect
120. #2430C22semidirect
121. #2428C22semidirect
122. #2425C22semidirect
123. #2424C22semidirect
124. #2424C22semidirect
125. #2413C22semidirect
126. #2413C22semidirect
129. #2407C22semidirect
130. #2407C22semidirect
132. #2406C22semidirect
133. #2406C22semidirect
134. #2405C22semidirect
135. #2404C22semidirect
136. #2404C22semidirect
137. #2403C22semidirect
138. #2379C22semidirect
139. #2379C22semidirect
140. #2372C22semidirect
141. #2372C22semidirect
142. #2364C22semidirect
143. #2361C22semidirect
144. #2359C22semidirect
145. #2358C22semidirect
146. #2342C22semidirect
147. #2342C22semidirect
148. #2337C22semidirect
149. #2310C22semidirect
150. #2309C22semidirect
152. #2308C22semidirect
153. C4×C22⋊Q8C22semidirect
154. C4×#123C22semidirect
155. C4×#121C22semidirect
156. C4×#120C22semidirect
157. #2290C22semidirect
158. #2283C22semidirect
159. #2280C22semidirect
160. C2×#381C22semidirect
221. C2×#124D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35452
C22×#5322
#591842
#591822
#462282
#462252
#462242
#394602
#393322
#378102
#378082
#376062
#372582
#372322
#366212
#361592
#360992
#351492
#350882
#343662