Finite Group Databasebeta

← #7695777

Subgroups — #7695777

Order 512.

7345 conjugacy classes of subgroups.

The subgroup lattice has 1472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3503C211yesmaximal, characteristic, complemented
2C2×#3522C211yesmaximal, characteristic, complemented
3#59654C213yesmaximal, complemented
4#59125C213yesmaximal, complemented
5#59080C213yesmaximal, complemented
6#52157C213yesmaximal, complemented
7#45337C213yesmaximal, complemented
8#45271C213yesmaximal, complemented
9#45111C213yesmaximal, complemented
10#45109C213yesmaximal, complemented
11#44883C213yesmaximal, complemented
12#44878C213yesmaximal, complemented
13#39718C213yesmaximal, complemented
14#39424C213yesmaximal, complemented
15#39161C213yesmaximal, complemented
16#39118C213yesmaximal, complemented
17#37756C213yesmaximal, complemented
18#37704C213yesmaximal, complemented
19#36467C211yesmaximal, characteristic, complemented
20#36435C211yesmaximal, characteristic, complemented
21#36430C211yesmaximal, characteristic, complemented
22#36049C211yesmaximal, characteristic, complemented
23#36029C211yesmaximal, characteristic, complemented
24#35948C211yesmaximal, characteristic, complemented
25#35831C211yesmaximal, characteristic, complemented
26#35816C211yesmaximal, characteristic, complemented
27#35748C211yesmaximal, characteristic, complemented
28#34335C211yesmaximal, characteristic, complemented
29#34313C211yesmaximal, characteristic, complemented
30#34295C211yesmaximal, characteristic, complemented
31#34294C211yesmaximal, characteristic, complemented
32#3522—216no—
33#3503—216no—
34C2×#559C2213yes—
35C2×Q82C2211yescharacteristic
36C2×Q82C2211yescharacteristic
37C2×#557C2211yescharacteristic
38C2×#557C2211yescharacteristic
39C2×#554C2213yes—
40C2×#554C2213yes—
41C2×#554C2213yes—
42C2×#550C2211yescharacteristic
43C2×#550C2211yescharacteristic
44C2×#550C2211yescharacteristic
45C2×D4×Q8C2213yes—
46C2×D4×Q8C2213yes—
47C2×#548C2211yescharacteristic
48C2×#548C2211yescharacteristic
49C2×#548C2211yescharacteristic
50C2×#548C2216yes—
51C2×#547C2213yes—
52C2×#547C2213yes—
53C2×#544C2213yes—
54C2×#544C2213yes—
55C2×#542C2213yes—
56C2×#542C2213yes—
57C2×#533C2213yes—
58C2×#532C2213yes—
59C22×C4⋊Q8C2213yes—
60C2×#529C2213yes—
61C2×#520C2211yescharacteristic
62C2×#520C2211yescharacteristic
63C2×#520C2211yescharacteristic
64C2×#520C2211yescharacteristic
65C2×C4×#41C2211yescharacteristic
66C22×C4×Q8C2211yescharacteristic
67#2861C2213yes—
68#2851C2213yes—
69#2850C2213yes—
70#2731C2216yes—
71#2731C2213yes—
72#2730C2216yes—
73#2730C2216yes—
74#2730C2213yes—
75#2729C2216yes—
76#2729C2211yescharacteristic
77#2728C2216yes—
78#2728C2216yes—
79#2728C2216yes—
80#2728C2213yes—
81#2725C2213yes—
82#2723C2213yes—
83#2719C2213yes—
84#2716C2213yes—
85#2711C2213yes—
86#2707C2213yes—
87#2702C2213yes—
88#2696C2216yes—
89#2696C2213yes—
90#2690C2213yes—
91#2690C2216yes—
92#2681C2216yes—
93#2681C2213yes—
94#2681C2216yes—
95#2676C2216yes—
96#2676C2213yes—
97#2674C2216yes—
98#2674C2213yes—
99#2641C2213yes—
100#2640C2213yes—
101#2629C2213yes—
102#2628C2213yes—
103#2620C2213yes—
104#2619C2213yes—
105#2592C2213yes—
106#2592C2213yes—
107#2581C2213yes—
108#2580C2213yes—
109#2566C2213yes—
110#2565C2213yes—
111#2562C2213yes—
112#2562C2213yes—
113#2560C2216yes—
114#2558C2216yes—
115#2548C2213yes—
116#2547C2213yes—
117#2544C2213yes—
118#2544C2213yes—
119#2542C2213yes—
120#2541C2213yes—
121#2538C2213yes—
122#2537C2213yes—
123#2536C2216yes—
124#2535C2213yes—
125#2535C2213yes—
126#2492C2213yes—
127#2492C2213yes—
128#2492C2213yes—
129#2491C2213yes—
130#2491C2213yes—
131#2491C2213yes—
132#2491C2213yes—
133#2491C2213yes—
134#2490C2213yes—
135#2490C2213yes—
136#2490C2213yes—
137#2489C2213yes—
138#2481C2216yes—
139#2463C2216yes—
140#2463C2216yes—
141#2463C2216yes—
142#2461C2216yes—
143#2461C2216yes—
144#2460C2216yes—
145#2454C2213yes—
146#2453C2213yes—
147#2452C2213yes—
148#2452C2213yes—
149#2452C2213yes—
150#2451C2213yes—
151#2443C2216yes—
152#2443C2216yes—
153#2443C2216yes—
154#2442C2213yes—
155#2442C2213yes—
156#2440C2213yes—
157#2440C2213yes—
158#2440C2213yes—
159#2440C2213yes—
160#2436C2216yes—
161#2432C2216yes—
162#2429C2216yes—
163#2428C2213yes—
164#2428C2213yes—
165#2428C2213yes—
166#2428C2213yes—
167#2427C2213yes—
168#2427C2213yes—
169#2426C2216yes—
170#2417C2213yes—
171#2416C2213yes—
172#2416C2213yes—
173#2416C2213yes—
174#2415C2213yes—
175#2414C2213yes—
176#2409C2216yes—
177#2409C2216yes—
178#2407C2216yes—
179#2407C2216yes—
180#2398C2213yes—
181#2398C2213yes—
182#2396C2213yes—
183#2396C2213yes—
184#2392C2213yes—
185#2392C2213yes—
186#2369C2213yes—
187#2367C2213yes—
188#2366C2213yes—
189#2366C2213yes—
190#2365C2213yes—
191#2365C2213yes—
192#2363C2213yes—
193#2361C2213yes—
194#2361C2213yes—
195#2361C2213yes—
196#2361C2213yes—
197#2360C2213yes—
198#2355C2213yes—
199#2352C2213yes—
200#2351C2211yescharacteristic
201#2351C2211yescharacteristic
202#2351C2211yescharacteristic
203Q8×C4⋊C4C2211yescharacteristic
204Q8×C4⋊C4C2211yescharacteristic
205Q8×C4⋊C4C2211yescharacteristic
206D4×C4⋊C4C2213yes—
207D4×C4⋊C4C2213yes—
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212#2341C2211yescharacteristic
213#2341C2211yescharacteristic
214#2341C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216Q8×C22⋊C4C2211yescharacteristic
217Q8×C22⋊C4C2211yescharacteristic
218#2331C2213yes—
219#2331C2213yes—
220#2328C2213yes—
221#2326C2213yes—
222#2324C2213yes—
223#2324C2213yes—
224#2324C2213yes—
225#2323C2213yes—
226C4×C4⋊Q8C2213yes—
227C4×#127C2213yes—
228C4×#124C2213yes—
229C4×C22⋊Q8C2213yes—
230C4×#121C2213yes—
231C4×#121C2213yes—
232C4×#121C2213yes—
233#2295C2213yes—
234#2293C2213yes—
235#2290C2213yes—
236#2290C2213yes—
237#2276C2211yescharacteristic
238#2276C2211yescharacteristic
239C42×Q8C2211yescharacteristic
240C22×#41C2311yescharacteristic
241C22×#41C2311yescharacteristic
242C22×#41C2311yescharacteristic
243C22×#41C2316yes—
244C23×Q8C2311yescharacteristic
245C23×Q8C2316yes—
246#559—224no—
247Q82—28no—
248Q82D4116yescomplemented
249#557—28no—
250#557—28no—
251#554—224no—
252#554—224no—
253#554—224no—
254#550—28no—
255#550—28no—
256#550—28no—
257D4×Q8—224no—
258D4×Q8—224no—
259#548—28no—
260#548—28no—
261#548—28no—
262#548—424no—
263#547—224no—
264#547—224no—
265#544—224no—
266#544—224no—
267#542—224no—
268#542—224no—
269#533—224no—
270#532—224no—
271C2×C4⋊Q8—224no—
272C2×C4⋊Q8C2313yes—
273C2×C4⋊Q8C2313yes—
274C2×C4⋊Q8C2316yes—
275C2×C4⋊Q8C2313yes—
276C2×C4⋊Q8C2313yes—
277C2×C4⋊Q8C2311yescharacteristic
278C2×C4⋊Q8C2313yes—
279C2×C4⋊Q8C2313yes—
280C2×C4⋊Q8C2313yes—
281C2×C4⋊Q8C2313yes—
282C2×C4⋊Q8C2313yes—
283C2×#127C2313yes—
284C2×#127C2313yes—
285C2×#127C2313yes—
286#529—224no—
287C2×#126C2313yes—
288C2×#126C2313yes—
289C2×#125C2313yes—
290C2×#125C2313yes—
291C2×#125C2313yes—
292C2×#125C2313yes—
293C2×#125C2313yes—
294C2×#125C2313yes—
295C2×#125C2313yes—
296C2×#124C2313yes—
297C2×#124C2313yes—
298C2×#124C2313yes—
299C2×#124C2313yes—
300C2×#124C2313yes—
301C2×#124C2316yes—
302C2×#124C2316yes—
303C2×#124C2316yes—
304C2×#123C2313yes—
305C2×#123C2313yes—
306C2×#123C2316yes—
307C2×#123C2316yes—
308C2×C22⋊Q8C2316yes—
309C2×C22⋊Q8C2313yes—
310C2×C22⋊Q8C2316yes—
311C2×C22⋊Q8C2316yes—
312C2×C22⋊Q8C2316yes—
313C2×C22⋊Q8C2316yes—
314C2×C22⋊Q8C2313yes—
315C2×C22⋊Q8C2311yescharacteristic
316C2×C22⋊Q8C2313yes—
317C2×C22⋊Q8C2313yes—
318C2×C22⋊Q8C2313yes—
319C2×C22⋊Q8C2313yes—
320C2×C22⋊Q8C2313yes—
321C2×C22⋊Q8C2313yes—
322C2×C22⋊Q8C2316yes—
323C2×C22⋊Q8C2316yes—
324C2×C22⋊Q8C2316yes—
325C2×C22⋊Q8C2316yes—
326C2×#121C2313yes—
327C2×#121C2313yes—
328C2×#121C2313yes—
329C2×#121C2313yes—
330C2×#121C2313yes—
331C2×#121C2313yes—
332C2×#121C2313yes—
333C2×#121C2313yes—
334C2×#121C2313yes—
335C2×#121C2313yes—
336C2×#121C2313yes—
337C2×#121C2316yes—
338C2×#121C2316yes—
339C2×#121C2316yes—
340#520—28no—
341#520—28no—
342#520—28no—
343#520—28no—
344C4×#41—28no—
345C2×C4×Q8—28no—
346C2×C4×Q8C2313yes—
347C2×C4×Q8C2313yes—
348C2×C4×Q8C2313yes—
349C2×C4×Q8C2313yes—
350C2×C4×Q8C2311yescharacteristic
351C2×C4×Q8C2311yescharacteristic
352C2×C4×Q8C2311yescharacteristic
353C2×C4×Q8C2311yescharacteristic
354C2×C4×Q8C2311yescharacteristic
355C2×C4×Q8C2311yescharacteristic
356C2×C4×Q8C2311yescharacteristic
357C2×C4×Q8C2311yescharacteristic
358C2×C4×Q8C2313yes—
359C2×C4×Q8C2316yes—
360C2×C4×Q8C2311yescharacteristic
361C2×C4×Q8C2311yescharacteristic
362C2×C4×Q8C2311yescharacteristic
363C2×C4×Q8C2313yes—
364C2×C4×D4C2313yes—
365C2×C4×D4C2313yes—
366C2×C4×D4C2313yes—
367C2×C4×D4C2313yes—
368C2×C4×D4C2313yes—
369C2×C4×D4C2313yes—
370C2×C4×D4C2313yes—
371C2×C4×D4C2313yes—
372C2×C4×D4C2313yes—
373C2×C4×D4C2313yes—
374C2×C4×D4C2313yes—
375C2×C4×D4C2313yes—
376C2×C4×D4C2313yes—
377C2×C4×D4C2313yes—
378C2×C4×D4C2313yes—
379C2×C4×D4C2313yes—
380C2×C4×D4C2316yes—
381C2×C4×D4C2316yes—
382C2×C4×D4C2316yes—
383C2×C4×D4C2316yes—
384C2×C4×D4C2316yes—
385C2×#117C2313yes—
386C2×#117C2313yes—
387C2×#117C2313yes—
388C2×#117C2313yes—
389C2×#117C2313yes—
390C22×C4⋊C4C2313yes—
391C22×C4⋊C4C2313yes—
392C22×C4⋊C4C2313yes—
393C22×C4⋊C4C2313yes—
394C22×C4⋊C4C2313yes—
395C22×C4⋊C4C2316yes—
396C22×C42C2313yes—
397C22×C42C2313yes—
398#400C2313yes—
399#400C2316yes—
400#400C2316yes—
401#400C2313yes—
402#400C2313yes—
403#400C2311yescharacteristic
404#400C2313yes—
405#400C2313yes—
406#399C2316yes—
407#399C2313yes—
408#399C2313yes—
409#398C2313yes—
410#398C2316yes—
411#398C2316yes—
412#398C2316yes—
413#398C2311yescharacteristic
414#398C2313yes—
415#398C2311yescharacteristic
416#398C2313yes—
417#398C2313yes—
418#397C2316yes—
419#397C2316yes—
420#397C2316yes—
421#397C2313yes—
422#397C2313yes—
423#397C2313yes—
424#397C2313yes—
425#397C2313yes—
426#397C2313yes—
427#396C2313yes—
428#396C2316yes—
429#396C2313yes—
430#396C2316yes—
431#396C2316yes—
432#396C2311yescharacteristic
433#396C2313yes—
434#396C2313yes—
435#396C2313yes—
436#396C2313yes—
437#396C2313yes—
438#395C2316yes—
439#395C2316yes—
440#395C2311yescharacteristic
441#395C2313yes—
442#394C2316yes—
443#394C2316yes—
444#394C2316yes—
445#394C2313yes—
446#394C2316yes—
447#394C2316yes—
448#394C2313yes—
449#394C2316yes—
450#394C2316yes—
451#394C2313yes—
452#394C2313yes—
453#394C2313yes—
454#394C2313yes—
455#394C2313yes—
456#394C2313yes—
457#394C2313yes—
458#394C2313yes—
459#394C2316yes—
460#394C2316yes—
461#393C2316yes—
462#393C2313yes—
463#393C2313yes—
464#393C2316yes—
465#393C2316yes—
466#393C2316yes—
467#393C2313yes—
468#393C2311yescharacteristic
469#393C2313yes—
470#393C2313yes—
471#392C2316yes—
472#392C2316yes—
473#392C2313yes—
474#392C2313yes—
475#392C2316yes—
476#391C2316yes—
477#391C2316yes—
478#391C2313yes—
479#391C2313yes—
480#391C2313yes—
481#391C2313yes—
482#391C2313yes—
483#391C2313yes—
484#391C2316yes—
485#391C2316yes—
486#391C2313yes—
487#391C2313yes—
488#391C2313yes—
489#391C2311yescharacteristic
490#390C2316yes—
491#390C2313yes—
492#390C2316yes—
493#390C2313yes—
494#390C2313yes—
495#390C2313yes—
496#390C2313yes—
497#390C2313yes—
498#390C2313yes—
499#390C2313yes—
500#390C2313yes—
501#390C2313yes—
502#390C2313yes—
503#390C2313yes—
504#390C2313yes—
505#390C2313yes—
506#390C2313yes—
507#390C2313yes—
508#390C2313yes—
509#390C2316yes—
510#390C2313yes—
511#389C2313yes—
512#389C2313yes—
513#389C2313yes—
514#389C2313yes—
515#389C2316yes—
516#389C2313yes—
517#389C2313yes—
518#389C2313yes—
519#389C2313yes—
520#389C2313yes—
521#389C2313yes—
522#389C2313yes—
523#389C2313yes—
524#389C2313yes—
525#389C2313yes—
526#389C2313yes—
527#389C2313yes—
528#389C2313yes—
529#389C2311yescharacteristic
530#388C2313yes—
531#388C2316yes—
532#388C2316yes—
533#388C2313yes—
534#388C2316yes—
535#388C2316yes—
536#388C2316yes—
537#388C2313yes—
538#388C2316yes—
539#388C2313yes—
540#388C2313yes—
541#388C2316yes—
542#388C2316yes—
543#388C2313yes—
544#388C2316yes—
545#388C2313yes—
546#388C2316yes—
547#388C2316yes—
548#388C2313yes—
549#388C2313yes—
550#388C2313yes—
551#388C2313yes—
552#388C2311yescharacteristic
553#388C2313yes—
554#388C2311yescharacteristic
555#387C2316yes—
556#387C2313yes—
557#387C2316yes—
558#387C2313yes—
559#387C2313yes—
560#387C2313yes—
561#387C2313yes—
562#387C2316yes—
563#387C2316yes—
564#387C2313yes—
565#387C2313yes—
566#387C2313yes—
567#387C2313yes—
568#387C2311yescharacteristic
569#386C2316yes—
570#386C2316yes—
571#386C2316yes—
572#386C2316yes—
573#386C2313yes—
574#386C2316yes—
575#386C2316yes—
576#386C2316yes—
577#386C2316yes—
578#386C2313yes—
579#386C2313yes—
580#386C2316yes—
581#386C2316yes—
582#386C2316yes—
583#386C2313yes—
584#386C2313yes—
585#386C2313yes—
586#385C2316yes—
587#385C2316yes—
588#385C2313yes—
589#385C2316yes—
590#385C2316yes—
591#385C2316yes—
592#385C2316yes—
593#385C2316yes—
594#385C2316yes—
595#385C2313yes—
596#385C2316yes—
597#385C2313yes—
598#385C2313yes—
599#385C2311yescharacteristic
600#385C2311yescharacteristic
601#384C2313yes—
602#384C2313yes—
603#384C2313yes—
604#382C2313yes—
605#382C2313yes—
606#382C2313yes—
607#382C2313yes—
608#380C2313yes—
609#380C2313yes—
610#380C2313yes—
611#380C2313yes—
612#380C2313yes—
613#380C2313yes—
614#380C2313yes—
615#380C2313yes—
616#380C2313yes—
617#380C2313yes—
618#380C2313yes—
619#380C2316yes—
620#380C2313yes—
621#380C2316yes—
622C4×C4⋊C4C2316yes—
623C4×C4⋊C4C2313yes—
624C4×C4⋊C4C2313yes—
625C4×C4⋊C4C2313yes—
626C4×C4⋊C4C2313yes—
627C4×C4⋊C4C2313yes—
628C4×C4⋊C4C2313yes—
629C4×C4⋊C4C2313yes—
630C4×C4⋊C4C2313yes—
631C4×C4⋊C4C2313yes—
632C4×C4⋊C4C2313yes—
633C4×C4⋊C4C2313yes—
634C4×C4⋊C4C2313yes—
635C4×C4⋊C4C2313yes—
636C4×C4⋊C4C2313yes—
637C4×C4⋊C4C2313yes—
638C4×C22⋊C4C2316yes—
639C4×C22⋊C4C2313yes—
640C4×C22⋊C4C2313yes—
641C4×C22⋊C4C2313yes—
642C4×C22⋊C4C2313yes—
643C4×C22⋊C4C2313yes—
644C4×C22⋊C4C2313yes—
645C4×C22⋊C4C2313yes—
646C4×C22⋊C4C2313yes—
647C4×C22⋊C4C2313yes—
648C4×C22⋊C4C2313yes—
649C4×C22⋊C4C2316yes—
650#376C2313yes—
651#376C2313yes—
652C43C2313yes—
653C2×#41—24no—
654C2×#41—24no—
655C2×#41—24no—
656C2×#41—224no—
657C2×#41—24no—
658C2×#41—24no—
659C2×#41—24no—
660C2×#41—24no—
661C2×#41—24no—
662C2×#41—412no—
663C2×#41—86no—
664C2×#41#4118yescomplemented
665C22×Q8—24no—
666C22×Q8—24no—
667C22×Q8—24no—
668C22×Q8—224no—
669C22×Q8—412no—
670C22×Q8—86no—
671C22×Q8C2413yes—
672C22×Q8C2413yes—
673C22×Q8C2413yes—
674C22×Q8C2411yescharacteristic
675C22×Q8C2416yes—
676C22×Q8C2411yescharacteristic
677C22×Q8C2416yes—
678C22×Q8C2411yescharacteristic
679C22×D4C2413yes—
680C22×D4C2413yes—
681C22×D4C2413yes—
682C22×D4C2413yes—
683C22×D4C2413yes—
684C22×D4C2413yes—
685C22×D4C2413yes—
686C22×D4C2413yes—
687C22×D4C2416yes—
688C22×D4C2416yes—
689C22×D4C2413yes—
690C22×D4C2416yes—
691C23×C4C2413yes—
692C23×C4C2413yes—
693C23×C4C2413yes—
694C23×C4C2413yes—
695C23×C4C2413yes—
696C23×C4C2413yes—
697C23×C4C2416yes—
698C23×C4C2416yes—
699C23×C4C2413yes—
700C23×C4C2416yes—
701C23×C4C2416yes—
702C23×C4C2411yescharacteristic
703C4⋊Q8—224no—
704C4⋊Q8—24no—
705C4⋊Q8—212no—
706C4⋊Q8—212no—
707C4⋊Q8—212no—
708C4⋊Q8—212no—
709C4⋊Q8—212no—
710C4⋊Q8—212no—
711C4⋊Q8C2×D4124yes—
712C4⋊Q8C2×D4124yes—
713C4⋊Q8C2×D4124yes—
714#127—212no—
715#127—212no—
716#127—212no—
717#126—212no—
718#126—212no—
719#125—212no—
720#125—212no—
721#125—212no—
722#125—212no—
723#125—212no—
724#125—212no—
725#125—212no—
726#124—212no—
727#124—224no—
728#124—212no—
729#124—212no—
730#124—212no—
731#124—212no—
732#124—412no—
733#124—412no—
734#123—212no—
735#123—212no—
736#123—224no—
737#123—224no—
738C22⋊Q8—24no—
739C22⋊Q8—212no—
740C22⋊Q8—224no—
741C22⋊Q8—224no—
742C22⋊Q8—224no—
743C22⋊Q8—224no—
744C22⋊Q8—212no—
745C22⋊Q8—212no—
746C22⋊Q8—212no—
747C22⋊Q8—212no—
748C22⋊Q8—212no—
749C22⋊Q8—212no—
750C22⋊Q8—224no—
751C22⋊Q8—224no—
752C22⋊Q8—212no—
753C22⋊Q8—412no—
754C22⋊Q8—412no—
755C22⋊Q8—86no—
756#121—212no—
757#121—212no—
758#121—212no—
759#121—212no—
760#121—212no—
761#121—212no—
762#121—212no—
763#121—212no—
764#121—212no—
765#121—212no—
766#121—212no—
767#121—412no—
768#121—412no—
769#121—86no—
770C4×Q8—24no—
771C4×Q8—24no—
772C4×Q8—24no—
773C4×Q8—24no—
774C4×Q8—24no—
775C4×Q8—24no—
776C4×Q8—24no—
777C4×Q8—24no—
778C4×Q8—212no—
779C4×Q8—212no—
780C4×Q8—212no—
781C4×Q8—212no—
782C4×Q8—212no—
783C4×Q8—412no—
784C4×Q8C2×D418yes—
785C4×Q8C2×D418yes—
786C4×Q8C2×D418yes—
787C4×Q8C2×D4124yes—
788C4×D4—212no—
789C4×D4—212no—
790C4×D4—212no—
791C4×D4—212no—
792C4×D4—212no—
793C4×D4—212no—
794C4×D4—212no—
795C4×D4—212no—
796C4×D4—224no—
797C4×D4—212no—
798C4×D4—212no—
799C4×D4—212no—
800C4×D4—212no—
801C4×D4—212no—
802C4×D4—212no—
803C4×D4—212no—
804C4×D4—212no—
805C4×D4—412no—
806C4×D4—412no—
807C4×D4—412no—
808C4×D4—86no—
809#117—212no—
810#117—212no—
811#117—212no—
812#117—212no—
813#117—212no—
814C2×C4⋊C4—212no—
815C2×C4⋊C4—212no—
816C2×C4⋊C4—212no—
817C2×C4⋊C4—212no—
818C2×C4⋊C4—212no—
819C2×C4⋊C4—224no—
820C2×C4⋊C4C2413yes—
821C2×C4⋊C4C2413yes—
822C2×C4⋊C4C2413yes—
823C2×C4⋊C4C2413yes—
824C2×C4⋊C4C2413yes—
825C2×C4⋊C4C2413yes—
826C2×C4⋊C4C2413yes—
827C2×C4⋊C4C2413yes—
828C2×C4⋊C4C2416yes—
829C2×C4⋊C4C2416yes—
830C2×C4⋊C4C2416yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2413yes—
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2413yes—
840C2×C4⋊C4C2413yes—
841C2×C4⋊C4C2413yes—
842C2×C4⋊C4C2413yes—
843C2×C4⋊C4C2413yes—
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2413yes—
847C2×C4⋊C4C2413yes—
848C2×C4⋊C4C2413yes—
849C2×C4⋊C4C2413yes—
850C2×C4⋊C4C2413yes—
851C2×C4⋊C4C2413yes—
852C2×C4⋊C4C2413yes—
853C2×C4⋊C4C2413yes—
854C2×C4⋊C4C2413yes—
855C2×C4⋊C4C2413yes—
856C2×C4⋊C4C2413yes—
857C2×C4⋊C4C2413yes—
858C2×C4⋊C4C2416yes—
859C2×C4⋊C4C2416yes—
860C2×C4⋊C4C2416yes—
861C2×C4⋊C4C2413yes—
862C2×C4⋊C4C2413yes—
863C2×C4⋊C4C2413yes—
864C2×C4⋊C4C2413yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2413yes—
869C2×C4⋊C4C2413yes—
870C2×C4⋊C4C2413yes—
871C2×C4⋊C4C2413yes—
872C2×C4⋊C4C2413yes—
873C2×C4⋊C4C2413yes—
874C2×C4⋊C4C2413yes—
875C2×C22⋊C4C2413yes—
876C2×C22⋊C4C2413yes—
877C2×C22⋊C4C2413yes—
878C2×C22⋊C4C2416yes—
879C2×C22⋊C4C2413yes—
880C2×C22⋊C4C2413yes—
881C2×C22⋊C4C2413yes—
882C2×C22⋊C4C2413yes—
883C2×C22⋊C4C2413yes—
884C2×C22⋊C4C2411yescharacteristic
885C2×C22⋊C4C2411yescharacteristic
886C2×C22⋊C4C2411yescharacteristic
887C2×C22⋊C4C2413yes—
888C2×C22⋊C4C2413yes—
889C2×C22⋊C4C2413yes—
890C2×C22⋊C4C2413yes—
891C2×C22⋊C4C2413yes—
892C2×C22⋊C4C2413yes—
893C2×C22⋊C4C2413yes—
894C2×C22⋊C4C2413yes—
895C2×C22⋊C4C2416yes—
896C2×C22⋊C4C2416yes—
897C2×C22⋊C4C2413yes—
898C2×C22⋊C4C2413yes—
899C2×C22⋊C4C2413yes—
900C2×C22⋊C4C2413yes—
901C2×C22⋊C4C2413yes—
902C2×C22⋊C4C2413yes—
903C2×C22⋊C4C2416yes—
904C2×C22⋊C4C2416yes—
905C2×C22⋊C4C2413yes—
906C2×C22⋊C4C2413yes—
907C2×C22⋊C4C2416yes—
908C2×C22⋊C4C2413yes—
909C2×C22⋊C4C2416yes—
910C2×C22⋊C4C2416yes—
911C2×C22⋊C4C2416yes—
912C2×C22⋊C4C2413yes—
913C2×C22⋊C4C2411yescharacteristic
914C2×C22⋊C4C2413yes—
915C2×C22⋊C4C2411yescharacteristic
916C2×C22⋊C4C2413yes—
917C2×C22⋊C4C2413yes—
918C2×C22⋊C4C2416yes—
919C2×C22⋊C4C2413yes—
920C2×C22⋊C4C2413yes—
921C2×C22⋊C4C2413yes—
922C2×C22⋊C4C2413yes—
923C2×C22⋊C4C2413yes—
924C2×C22⋊C4C2416yes—
925C2×C22⋊C4C2411yescharacteristic
926C2×C42—212no—
927C2×C42—212no—
928C2×C42C2413yes—
929C2×C42C2413yes—
930C2×C42C2413yes—
931C2×C42C2413yes—
932C2×C42C2413yes—
933C2×C42C2413yes—
934C2×C42C2413yes—
935C2×C42C2413yes—
936C2×C42C2413yes—
937C2×C42C2413yes—
938C2×C42C2413yes—
939C2×C42C2413yes—
940C2×C42C2411yescharacteristic
941C2×C42C2413yes—
942C2×C42C2416yes—
943C2×C42C2416yes—
944C2×C42C2411yescharacteristic
945C2×C42C2413yes—
946C2×C42C2413yes—
947C2×C42C2413yes—
948C2×C42C2413yes—
949#95C2411yescharacteristic
950#95C2411yescharacteristic
951#95C2413yes—
952#95C2413yes—
953#95C2413yes—
954#95C2413yes—
955#95C2413yes—
956#95C2413yes—
957#95C2411yescharacteristic
958#95C2413yes—
959#95C2411yescharacteristic
960#95C2411yescharacteristic
961#95C2411yescharacteristic
962#95C2411yescharacteristic
963#95C2411yescharacteristic
964#95C2411yescharacteristic
965#95C2413yes—
966#95C2413yes—
967#95C2413yes—
968#95C2413yes—
969#95C2413yes—
970#95C2413yes—
971#95C2413yes—
972#95C2416yes—
973#95C2416yes—
974#95C2413yes—
975#95C2413yes—
976#95C2413yes—
977#95C2413yes—
978#95C2413yes—
979#95C2413yes—
980#95C2416yes—
981#95C2411yescharacteristic
982#95C2411yescharacteristic
983#95C2411yescharacteristic
984#95C2413yes—
985#95C2413yes—
986#95C2413yes—
987#95C2413yes—
988#95C2413yes—
989#95C2416yes—
990#95C2416yes—
991#95C2413yes—
992#95C2413yes—
993#95C2413yes—
994#95C2416yes—
995#95C2416yes—
996C24C2513yes—
997C24C2513yes—
998C24C2513yes—
999C24C2511yescharacteristic
1000#41—232no—
1001#41—416no—
1002#41—416no—
1003#41—848no—
1004C2×Q8—22no—
1005C2×Q8—26no—
1006C2×Q8—26no—
1007C2×Q8—26no—
1008C2×Q8—212no—
1009C2×Q8—26no—
1010C2×Q8—26no—
1011C2×Q8—26no—
1012C2×Q8—26no—
1013C2×Q8—46no—
1014C2×Q8—43no—
1015C2×Q8—43no—
1016C2×Q8—46no—
1017C2×Q8—41no—
1018C2×Q8—41no—
1019C2×Q8—41no—
1020C2×Q8—41no—
1021C2×Q8—46no—
1022C2×Q8—46no—
1023C2×Q8—416no—
1024C2×Q8—848no—
1025C2×Q8C22×D414yes—
1026C2×Q8C22×D4124yes—
1027C2×Q8C22×D414yes—
1028C2×Q8C2×#4114yes—
1029C2×Q82−1+414yes—
1030C2×D4—26no—
1031C2×D4—26no—
1032C2×D4—26no—
1033C2×D4—26no—
1034C2×D4—26no—
1035C2×D4—26no—
1036C2×D4—212no—
1037C2×D4—212no—
1038C2×D4—26no—
1039C2×D4—26no—
1040C2×D4—26no—
1041C2×D4—26no—
1042C2×D4—26no—
1043C2×D4—26no—
1044C2×D4—212no—
1045C2×D4—26no—
1046C2×D4—26no—
1047C2×D4—26no—
1048C2×D4—26no—
1049C2×D4—26no—
1050C2×D4—26no—
1051C2×D4—43no—
1052C2×D4—43no—
1053C2×D4—43no—
1054C2×D4—43no—
1055C2×D4—43no—
1056C2×D4—43no—
1057C2×D4—46no—
1058C2×D4—46no—
1059C2×D4—46no—
1060C2×D4—43no—
1061C2×D4—46no—
1062C2×D4—46no—
1063C2×D4—46no—
1064C2×D4—43no—
1065C2×D4C2×#41112yes—
1066C22×C4—26no—
1067C22×C4—26no—
1068C22×C4—26no—
1069C22×C4—22no—
1070C22×C4—26no—
1071C22×C4—26no—
1072C22×C4—26no—
1073C22×C4—26no—
1074C22×C4—26no—
1075C22×C4—26no—
1076C22×C4—26no—
1077C22×C4—26no—
1078C22×C4—26no—
1079C22×C4—26no—
1080C22×C4—26no—
1081C22×C4—26no—
1082C22×C4—26no—
1083C22×C4—212no—
1084C22×C4—212no—
1085C22×C4—212no—
1086C22×C4—212no—
1087C22×C4—43no—
1088C22×C4—43no—
1089C22×C4—41no—
1090C22×C4—41no—
1091C22×C4—43no—
1092C22×C4—43no—
1093C22×C4—46no—
1094C22×C4—46no—
1095C22×C4—46no—
1096C22×C4—46no—
1097C22×C4—46no—
1098C22×C4—46no—
1099C22×C4—46no—
1100C22×C4—46no—
1101C22×C4C2×#41112yes—
1102C22×C4C2511yescharacteristic
1103C22×C4C2511yescharacteristic
1104C22×C4C2513yes—
1105C22×C4C2513yes—
1106C22×C4C2513yes—
1107C22×C4C2513yes—
1108C22×C4C2511yescharacteristic
1109C22×C4C2511yescharacteristic
1110C22×C4C2511yescharacteristic
1111C22×C4C2513yes—
1112C22×C4C2511yescharacteristic
1113C22×C4C2511yescharacteristic
1114C22×C4C2511yescharacteristic
1115C22×C4C2513yes—
1116C22×C4C2513yes—
1117C22×C4C2513yes—
1118C22×C4C2513yes—
1119C22×C4C2511yescharacteristic
1120C22×C4C2511yescharacteristic
1121C22×C4C2513yes—
1122C22×C4C2513yes—
1123C22×C4C2513yes—
1124C22×C4C2511yescharacteristic
1125C22×C4C2511yescharacteristic
1126C22×C4C2511yescharacteristic
1127C22×C4C2511yescharacteristic
1128C22×C4C2513yes—
1129C4⋊C4—26no—
1130C4⋊C4—26no—
1131C4⋊C4—26no—
1132C4⋊C4—26no—
1133C4⋊C4—26no—
1134C4⋊C4—26no—
1135C4⋊C4—26no—
1136C4⋊C4—26no—
1137C4⋊C4—212no—
1138C4⋊C4—212no—
1139C4⋊C4—212no—
1140C4⋊C4—22no—
1141C4⋊C4—22no—
1142C4⋊C4—22no—
1143C4⋊C4—22no—
1144C4⋊C4—26no—
1145C4⋊C4—22no—
1146C4⋊C4—26no—
1147C4⋊C4—26no—
1148C4⋊C4—22no—
1149C4⋊C4—22no—
1150C4⋊C4—26no—
1151C4⋊C4—26no—
1152C4⋊C4—26no—
1153C4⋊C4—26no—
1154C4⋊C4—26no—
1155C4⋊C4—26no—
1156C4⋊C4—22no—
1157C4⋊C4—22no—
1158C4⋊C4—26no—
1159C4⋊C4—26no—
1160C4⋊C4—26no—
1161C4⋊C4—26no—
1162C4⋊C4—26no—
1163C4⋊C4—26no—
1164C4⋊C4—26no—
1165C4⋊C4—26no—
1166C4⋊C4—26no—
1167C4⋊C4—41no—
1168C4⋊C4—43no—
1169C4⋊C4—41no—
1170C4⋊C4—41no—
1171C4⋊C4—43no—
1172C4⋊C4—46no—
1173C4⋊C4—46no—
1174C4⋊C4—46no—
1175C4⋊C4—43no—
1176C4⋊C4—43no—
1177C4⋊C4—43no—
1178C4⋊C4C22×D4112yes—
1179C4⋊C4C22×D4112yes—
1180C4⋊C4C22×D4112yes—
1181C4⋊C4C22×D4112yes—
1182C4⋊C4C22×D4112yes—
1183C4⋊C4C22×D4112yes—
1184C22⋊C4—26no—
1185C22⋊C4—26no—
1186C22⋊C4—26no—
1187C22⋊C4—212no—
1188C22⋊C4—26no—
1189C22⋊C4—26no—
1190C22⋊C4—26no—
1191C22⋊C4—26no—
1192C22⋊C4—26no—
1193C22⋊C4—26no—
1194C22⋊C4—212no—
1195C22⋊C4—26no—
1196C22⋊C4—26no—
1197C22⋊C4—26no—
1198C22⋊C4—26no—
1199C22⋊C4—22no—
1200C22⋊C4—22no—
1201C22⋊C4—26no—
1202C22⋊C4—26no—
1203C22⋊C4—212no—
1204C22⋊C4—212no—
1205C22⋊C4—26no—
1206C22⋊C4—26no—
1207C22⋊C4—22no—
1208C22⋊C4—26no—
1209C22⋊C4—26no—
1210C22⋊C4—26no—
1211C22⋊C4—26no—
1212C22⋊C4—26no—
1213C22⋊C4—46no—
1214C22⋊C4—41no—
1215C22⋊C4—43no—
1216C22⋊C4—43no—
1217C22⋊C4—43no—
1218C22⋊C4—43no—
1219C22⋊C4—43no—
1220C22⋊C4—43no—
1221C22⋊C4—43no—
1222C22⋊C4—41no—
1223C22⋊C4—46no—
1224C22⋊C4—43no—
1225C22⋊C4—46no—
1226C22⋊C4—46no—
1227C22⋊C4—43no—
1228C22⋊C4—43no—
1229C22⋊C4—46no—
1230C22⋊C4—46no—
1231C22⋊C4—43no—
1232C22⋊C4—46no—
1233C22⋊C4—43no—
1234C22⋊C4H(5,𝔽2)14yes—
1235C42—22no—
1236C42—26no—
1237C42—26no—
1238C42—26no—
1239C42—26no—
1240C42—26no—
1241C42—26no—
1242C42—26no—
1243C42—26no—
1244C42—26no—
1245C42—26no—
1246C42—26no—
1247C42—26no—
1248C42—43no—
1249C42—41no—
1250C42—46no—
1251C42—46no—
1252C42—43no—
1253C42C22×D4112yes—
1254C42C22×D4112yes—
1255C42C22×D4112yes—
1256C23—23no—
1257C23—21no—
1258C23—21no—
1259C23—23no—
1260C23—21no—
1261C23—23no—
1262C23—23no—
1263C23—21no—
1264C23—21no—
1265C23—21no—
1266C23—23no—
1267C23—23no—
1268C23—23no—
1269C23—23no—
1270C23—23no—
1271C23—23no—
1272C23—23no—
1273C23—23no—
1274C23—23no—
1275C23—23no—
1276C23—23no—
1277C23—23no—
1278C23—23no—
1279C23—23no—
1280C23—23no—
1281C23—23no—
1282C23C22×#4116yes—
1283C23C2×H(5,𝔽2)12yes—
1284C23C2611yescharacteristic
1285Q8—424no—
1286Q8—44no—
1287Q8—412no—
1288Q8—412no—
1289Q8—44no—
1290Q8—412no—
1291Q8—812no—
1292Q8#548116yescomplemented
1293D4—224no—
1294D4—412no—
1295D4—412no—
1296D4—412no—
1297D4—412no—
1298D4—412no—
1299D4—412no—
1300D4—412no—
1301D4—812no—
1302D4—812no—
1303D4—812no—
1304D4—86no—
1305C2×C4—21no—
1306C2×C4—21no—
1307C2×C4—21no—
1308C2×C4—23no—
1309C2×C4—23no—
1310C2×C4—23no—
1311C2×C4—21no—
1312C2×C4—23no—
1313C2×C4—23no—
1314C2×C4—23no—
1315C2×C4—21no—
1316C2×C4—21no—
1317C2×C4—21no—
1318C2×C4—21no—
1319C2×C4—21no—
1320C2×C4—21no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—224no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—23no—
1328C2×C4—23no—
1329C2×C4—23no—
1330C2×C4—23no—
1331C2×C4—23no—
1332C2×C4—21no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—23no—
1337C2×C4—23no—
1338C2×C4—23no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—23no—
1342C2×C4—23no—
1343C2×C4—23no—
1344C2×C4—23no—
1345C2×C4—23no—
1346C2×C4—23no—
1347C2×C4—23no—
1348C2×C4—21no—
1349C2×C4—23no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—23no—
1353C2×C4—21no—
1354C2×C4—23no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—23no—
1358C2×C4—23no—
1359C2×C4—23no—
1360C2×C4—21no—
1361C2×C4—23no—
1362C2×C4—23no—
1363C2×C4—23no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—23no—
1368C2×C4—21no—
1369C2×C4—23no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—23no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—412no—
1376C2×C4—412no—
1377C2×C4—412no—
1378C2×C4—44no—
1379C2×C4—412no—
1380C2×C4—412no—
1381C2×C4—412no—
1382C2×C4—812no—
1383C2×C4—812no—
1384C2×C4—812no—
1385C2×C4—812no—
1386C2×C4C23×D412yes—
1387C2×C4C23×D412yes—
1388C2×C4C23×D416yes—
1389C2×C4C23×D416yes—
1390C2×C4C23×D412yes—
1391C2×C4C23×D416yes—
1392C2×C4C23×D416yes—
1393C2×C4C22×#4112yes—
1394C2×C4C22×#4116yes—
1395C2×C4C2×H(5,𝔽2)12yes—
1396C2×C4C2×H(5,𝔽2)12yes—
1397C2×C4C2×2−1+416yes—
1398C22—22no—
1399C22—22no—
1400C22—26no—
1401C22—26no—
1402C22—22no—
1403C22—26no—
1404C22—43no—
1405C22—41no—
1406C22—43no—
1407C22—43no—
1408C22—41no—
1409C22—41no—
1410C22—43no—
1411C22—41no—
1412C22—43no—
1413C22—43no—
1414C22—43no—
1415C22—43no—
1416C22—43no—
1417C22—43no—
1418C22—43no—
1419C22—43no—
1420C22—43no—
1421C22—43no—
1422C22—43no—
1423C22—43no—
1424C22—43no—
1425C22—43no—
1426C22C24×D411yescharacteristic
1427C22C23×#4111yescharacteristic
1428C22C22×H(5,𝔽2)11yescharacteristic
1429C22C22×2−1+411yescharacteristic
1430C22H(7,𝔽2)11yescharacteristic
1431C222−1+611yescharacteristic
1432C222−1+611yescharacteristic
1433C4—22no—
1434C4—26no—
1435C4—26no—
1436C4—26no—
1437C4—22no—
1438C4—22no—
1439C4—22no—
1440C4—22no—
1441C4—22no—
1442C4—43no—
1443C4—43no—
1444C4—43no—
1445C4—43no—
1446C4—43no—
1447C4—41no—
1448C4—41no—
1449C4—43no—
1450C4—41no—
1451C4—41no—
1452C4—41no—
1453C4—43no—
1454C4—41no—
1455C4—43no—
1456C4—41no—
1457C4—41no—
1458C4—43no—
1459C4C2×#548112yes—
1460C2—42no—
1461C2—46no—
1462C2—83no—
1463C2—83no—
1464C2C22×#54811yescharacteristic
1465C2#6284811yescharacteristic
1466C2#6285711yescharacteristic
1467C2#6294611yescharacteristic
1468C2D4×H(5,𝔽2)11yescharacteristic
1469C2#6298511yescharacteristic
1470C2#6306111yescharacteristic
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×#3503C2semidirect
2. C2×#3522C2semidirect
3. #59654C2semidirect
4. #59125C2semidirect
5. #59080C2semidirect
6. #52157C2semidirect
7. #45337C2semidirect
8. #45271C2semidirect
9. #45111C2semidirect
10. #45109C2semidirect
11. #44883C2semidirect
12. #44878C2semidirect
13. #39718C2semidirect
14. #39424C2semidirect
15. #39161C2semidirect
16. #39118C2semidirect
17. #37756C2semidirect
18. #37704C2semidirect
19. #36467C2semidirect
20. #36435C2semidirect
21. #36430C2semidirect
22. #36049C2semidirect
23. #36029C2semidirect
24. #35948C2semidirect
25. #35831C2semidirect
26. #35816C2semidirect
27. #35748C2semidirect
28. #34335C2semidirect
29. #34313C2semidirect
30. #34295C2semidirect
31. #34294C2semidirect
248. Q82D4semidirect
664. C2×#41#41semidirect
1292. Q8#548semidirect

Maximal subgroups

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

subgroupindex
C2×#35032
C2×#35222
#596542
#591252
#590802
#521572
#453372
#452712
#451112
#451092
#448832
#448782
#397182
#394242
#391612
#391182
#377562
#377042
#364672
#364352
#364302
#360492
#360292
#359482
#358312
#358162
#357482
#343352
#343132
#342952
#342942