Finite Group Databasebeta

← #7646721

Subgroups — #7646721

Order 512.

6558 conjugacy classes of subgroups.

The subgroup lattice has 1261 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3482C211yesmaximal, characteristic, complemented
2C2×#3461C211yesmaximal, characteristic, complemented
3#42992C212yesmaximal, complemented
4#42917C212yesmaximal, complemented
5#42915C212yesmaximal, complemented
6#42911C212yesmaximal, complemented
7#42309C214yesmaximal, complemented
8#42305C214yesmaximal, complemented
9#39727C212yesmaximal, complemented
10#39599C212yesmaximal, complemented
11#38920C212yesmaximal, complemented
12#38911C212yesmaximal, complemented
13#38048C214yesmaximal, complemented
14#38035C214yesmaximal, complemented
15#37553C212yesmaximal, complemented
16#37551C212yesmaximal, complemented
17#36972C218yesmaximal, complemented
18#35637C214yesmaximal, complemented
19#35297C211yesmaximal, characteristic, complemented
20#35248C211yesmaximal, characteristic, complemented
21#35245C212yesmaximal, complemented
22#35179C212yesmaximal, complemented
23#35155C214yesmaximal, complemented
24#34952C211yesmaximal, characteristic, complemented
25#34909C211yesmaximal, characteristic, complemented
26#34193C211yesmaximal, characteristic, complemented
27#3482—216no—
28C2×#557C2211yescharacteristic
29C2×#556C2211yescharacteristic
30C2×#556C2212yes—
31C2×#552C2214yes—
32C2×#552C2212yes—
33C2×D4×Q8C2211yescharacteristic
34C2×#548C2212yes—
35C2×#547C2211yescharacteristic
36C2×#547C2212yes—
37#3461—216no—
38C2×#544C2211yescharacteristic
39C2×#542C2212yes—
40C2×#542C2212yes—
41C2×#541C2212yes—
42C2×#541C2212yes—
43C2×#539C2214yes—
44C2×#537C2211yescharacteristic
45C2×#536C2211yescharacteristic
46C2×#536C2211yescharacteristic
47C2×#533C2212yes—
48C2×#533C2212yes—
49C2×#533C2212yes—
50C2×#533C2211yescharacteristic
51C2×#529C2212yes—
52C2×#529C2214yes—
53C2×#529C2214yes—
54C2×#529C2212yes—
55C2×#529C2212yes—
56C2×C4×#41C2212yes—
57C2×C4×#41C2211yescharacteristic
58C2×C4×#41C2211yescharacteristic
59C2×C4×#41C2211yescharacteristic
60C22×C4×Q8C2212yes—
61C22×C4×Q8C2211yescharacteristic
62#2857C2212yes—
63#2857C2212yes—
64#2855C2218yes—
65#2855C2214yes—
66#2853C2218yes—
67#2821C2214yes—
68#2821C2214yes—
69#2814C2214yes—
70#2813C2214yes—
71#2726C2218yes—
72#2725C2218yes—
73#2724C2218yes—
74#2718C2218yes—
75#2718C2218yes—
76#2710C2218yes—
77#2706C2218yes—
78#2704C2218yes—
79#2702C2218yes—
80#2701C2218yes—
81#2701C2218yes—
82#2700C2218yes—
83#2699C2218yes—
84#2698C2218yes—
85#2689C2218yes—
86#2687C2218yes—
87#2664C2214yes—
88#2663C2214yes—
89#2663C2214yes—
90#2662C2214yes—
91#2638C2218yes—
92#2634C2214yes—
93#2634C2214yes—
94#2632C2214yes—
95#2630C2218yes—
96#2629C2214yes—
97#2627C2214yes—
98#2627C2214yes—
99#2625C2214yes—
100#2625C2212yes—
101#2624C2214yes—
102#2620C2214yes—
103#2616C2212yes—
104#2611C2218yes—
105#2604C2218yes—
106#2601C2218yes—
107#2600C2214yes—
108#2599C2212yes—
109#2598C2212yes—
110#2592C2214yes—
111#2591C2214yes—
112#2584C2212yes—
113#2584C2214yes—
114#2583C2214yes—
115#2582C2214yes—
116#2582C2214yes—
117#2582C2212yes—
118#2581C2211yescharacteristic
119#2581C2212yes—
120#2581C2212yes—
121#2581C2212yes—
122#2581C2212yes—
123#2580C2211yescharacteristic
124#2580C2212yes—
125#2579C2214yes—
126#2568C2212yes—
127#2568C2214yes—
128#2567C2214yes—
129#2565C2218yes—
130#2562C2212yes—
131#2560C2218yes—
132#2556C2218yes—
133#2550C2214yes—
134#2546C2212yes—
135#2546C2214yes—
136#2542C2214yes—
137#2538C2212yes—
138#2536C2214yes—
139#2536C2211yescharacteristic
140#2536C2212yes—
141#2535C2211yescharacteristic
142#2519C2218yes—
143#2506C2218yes—
144#2503C2212yes—
145#2492C2214yes—
146#2489C2214yes—
147#2487C2214yes—
148#2487C2212yes—
149#2485C2212yes—
150#2485C2214yes—
151#2484C2214yes—
152#2478C2218yes—
153#2474C2218yes—
154#2466C2218yes—
155#2459C2218yes—
156#2451C2214yes—
157#2447C2214yes—
158#2439C2214yes—
159#2434C2212yes—
160#2432C2214yes—
161#2429C2214yes—
162#2429C2214yes—
163#2429C2214yes—
164#2420C2214yes—
165#2415C2214yes—
166#2415C2214yes—
167#2415C2214yes—
168#2414C2214yes—
169#2409C2212yes—
170#2409C2214yes—
171#2407C2214yes—
172#2407C2212yes—
173#2396C2214yes—
174#2395C2212yes—
175#2388C2212yes—
176#2354C2212yes—
177#2354C2214yes—
178Q8×C4⋊C4C2212yes—
179#2347C2214yes—
180#2347C2212yes—
181#2341C2212yes—
182#2327C2214yes—
183#2323C2214yes—
184#2323C2214yes—
185#2323C2214yes—
186#2319C2212yes—
187#2319C2214yes—
188#2317C2214yes—
189#2310C2214yes—
190C4×C22⋊Q8C2214yes—
191C4×C22⋊Q8C2212yes—
192C4×#121C2212yes—
193#2297C2212yes—
194#2296C2212yes—
195#2290C2214yes—
196#2285C2212yes—
197#2285C2211yescharacteristic
198#2283C2211yescharacteristic
199#2283C2212yes—
200#2276C2212yes—
201C22×#41C2311yescharacteristic
202C22×#41C2311yescharacteristic
203C22×#41C2312yes—
204C22×#41C2311yescharacteristic
205C23×Q8C2312yes—
206C23×Q8C2311yescharacteristic
207#557—28no—
208#556—28no—
209#556—216no—
210#552—216no—
211#552—232no—
212D4×Q8—28no—
213#548—216no—
214#547—216no—
215#547—28no—
216#544—28no—
217#542—216no—
218#542—216no—
219#541—216no—
220#541—216no—
221#539—232no—
222#537—28no—
223#536—28no—
224#536—28no—
225#533—216no—
226#533—216no—
227#533—216no—
228#533—28no—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2314yes—
238#529—232no—
239#529—216no—
240#529—232no—
241#529—216no—
242#529—216no—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#125C2312yes—
251C2×#125C2314yes—
252C2×#125C2312yes—
253C2×#125C2312yes—
254C2×#125C2314yes—
255C2×#125C2312yes—
256C2×#125C2314yes—
257C2×#125C2314yes—
258C2×#125C2314yes—
259C2×#124C2312yes—
260C2×#124C2312yes—
261C2×#124C2312yes—
262C2×#124C2314yes—
263C2×#124C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×#121C2312yes—
292C2×#121C2312yes—
293C2×#121C2312yes—
294C2×#121C2314yes—
295C2×#121C2314yes—
296C2×#121C2312yes—
297C4×#41—216no—
298C4×#41—28no—
299C4×#41—28no—
300C4×#41D4116yescomplemented
301C2×C4×Q8—28no—
302C2×C4×Q8—216no—
303C2×C4×Q8C2314yes—
304C2×C4×Q8C2314yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2314yes—
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2314yes—
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2311yescharacteristic
322C2×C4×D4C2311yescharacteristic
323C2×C4×D4C2312yes—
324C2×C4×D4C2311yescharacteristic
325C2×C4×D4C2312yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2312yes—
331C2×C4×D4C2311yescharacteristic
332C2×C4×D4C2314yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2311yescharacteristic
336C2×C4×D4C2312yes—
337C2×C4×D4C2311yescharacteristic
338C2×C4×D4C2312yes—
339C2×#117C2314yes—
340C2×#117C2314yes—
341C2×#117C2312yes—
342C2×#117C2312yes—
343C2×#117C2314yes—
344C2×#117C2311yescharacteristic
345C2×#117C2312yes—
346C2×#117C2314yes—
347C2×#117C2311yescharacteristic
348C2×#117C2312yes—
349C2×#117C2314yes—
350C2×#117C2312yes—
351C2×#117C2311yescharacteristic
352C2×#117C2312yes—
353C22×C4⋊C4C2312yes—
354C22×C4⋊C4C2312yes—
355C22×C4⋊C4C2314yes—
356C22×C4⋊C4C2311yescharacteristic
357C22×C42C2314yes—
358C22×C42C2312yes—
359C22×C42C2312yes—
360C22×C42C2312yes—
361C22×C42C2311yescharacteristic
362C22×C42C2312yes—
363#400C2314yes—
364#400C2314yes—
365#400C2318yes—
366#400C2312yes—
367#400C2314yes—
368#400C2314yes—
369#400C2318yes—
370#400C2318yes—
371#399C2312yes—
372#399C2314yes—
373#399C2318yes—
374#399C2318yes—
375#398C2318yes—
376#398C2318yes—
377#398C2318yes—
378#398C2318yes—
379#398C2318yes—
380#398C2318yes—
381#398C2318yes—
382#398C2312yes—
383#398C2314yes—
384#398C2318yes—
385#398C2318yes—
386#398C2318yes—
387#397C2318yes—
388#397C2318yes—
389#397C2312yes—
390#397C2314yes—
391#397C2318yes—
392#397C2318yes—
393#397C2318yes—
394#397C2318yes—
395#396C2318yes—
396#396C2318yes—
397#396C2318yes—
398#396C2318yes—
399#396C2318yes—
400#395C2314yes—
401#395C2314yes—
402#395C2318yes—
403#395C2312yes—
404#395C2314yes—
405#395C2314yes—
406#395C2318yes—
407#394C2318yes—
408#394C2314yes—
409#394C2312yes—
410#394C2314yes—
411#394C2314yes—
412#394C2318yes—
413#394C2318yes—
414#394C2318yes—
415#394C2318yes—
416#394C2318yes—
417#394C2318yes—
418#393C2318yes—
419#393C2312yes—
420#393C2314yes—
421#393C2318yes—
422#392C2312yes—
423#392C2314yes—
424#392C2318yes—
425#391C2318yes—
426#391C2318yes—
427#391C2312yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2318yes—
433#391C2318yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#390C2318yes—
439#390C2314yes—
440#390C2318yes—
441#390C2312yes—
442#390C2314yes—
443#389C2318yes—
444#389C2318yes—
445#389C2312yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2318yes—
451#389C2314yes—
452#389C2318yes—
453#389C2318yes—
454#389C2318yes—
455#389C2314yes—
456#389C2314yes—
457#389C2312yes—
458#389C2314yes—
459#389C2314yes—
460#389C2314yes—
461#389C2318yes—
462#389C2318yes—
463#389C2318yes—
464#388C2318yes—
465#388C2318yes—
466#388C2318yes—
467#388C2318yes—
468#388C2318yes—
469#388C2318yes—
470#388C2318yes—
471#388C2318yes—
472#388C2318yes—
473#388C2318yes—
474#388C2318yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2318yes—
479#388C2318yes—
480#387C2318yes—
481#387C2314yes—
482#387C2318yes—
483#387C2318yes—
484#387C2318yes—
485#387C2318yes—
486#387C2318yes—
487#387C2318yes—
488#387C2318yes—
489#387C2314yes—
490#387C2314yes—
491#386C2314yes—
492#386C2314yes—
493#386C2314yes—
494#386C2318yes—
495#386C2318yes—
496#386C2314yes—
497#386C2314yes—
498#385C2318yes—
499#385C2318yes—
500#385C2318yes—
501#385C2314yes—
502#385C2314yes—
503#385C2314yes—
504#385C2318yes—
505#385C2318yes—
506#385C2314yes—
507#385C2314yes—
508#385C2318yes—
509#384C2318yes—
510#384C2314yes—
511#384C2312yes—
512#383C2314yes—
513#383C2312yes—
514#382C2318yes—
515#382C2314yes—
516#382C2311yescharacteristic
517#382C2312yes—
518#382C2311yescharacteristic
519#381C2318yes—
520#381C2318yes—
521#381C2314yes—
522#381C2312yes—
523#381C2318yes—
524#380C2314yes—
525#380C2314yes—
526#380C2312yes—
527#380C2314yes—
528#380C2312yes—
529#380C2314yes—
530#380C2314yes—
531#380C2312yes—
532#380C2314yes—
533#380C2312yes—
534#380C2314yes—
535#380C2312yes—
536#380C2314yes—
537C4×C4⋊C4C2318yes—
538C4×C4⋊C4C2312yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2312yes—
542C4×C4⋊C4C2312yes—
543C4×C4⋊C4C2314yes—
544C4×C4⋊C4C2314yes—
545C4×C4⋊C4C2314yes—
546C4×C4⋊C4C2318yes—
547C4×C22⋊C4C2318yes—
548C4×C22⋊C4C2314yes—
549C4×C22⋊C4C2312yes—
550C4×C22⋊C4C2314yes—
551C4×C22⋊C4C2314yes—
552#376C2312yes—
553#376C2314yes—
554C2×#41—24no—
555C2×#41—28no—
556C2×#41—24no—
557C2×#41—24no—
558C2×#41—44no—
559C2×#41—42no—
560C2×#41—44no—
561C2×#41—48no—
562C2×#41C2×D418yes—
563C22×Q8—28no—
564C22×Q8—24no—
565C22×Q8—28no—
566C22×Q8—44no—
567C22×Q8—44no—
568C22×Q8C2412yes—
569C22×Q8C2412yes—
570C22×Q8C2412yes—
571C22×Q8C2414yes—
572C22×Q8C2411yescharacteristic
573C22×Q8C2411yescharacteristic
574C22×Q8C2412yes—
575C22×Q8C2411yescharacteristic
576C22×Q8C2414yes—
577C22×D4C2411yescharacteristic
578C22×D4C2412yes—
579C22×D4C2411yescharacteristic
580C22×D4C2412yes—
581C22×D4C2414yes—
582C22×D4C2411yescharacteristic
583C22×D4C2414yes—
584C22×D4C2414yes—
585C22×D4C2412yes—
586C23×C4C2412yes—
587C23×C4C2412yes—
588C23×C4C2412yes—
589C23×C4C2414yes—
590C23×C4C2412yes—
591C23×C4C2412yes—
592C23×C4C2411yescharacteristic
593C23×C4C2411yescharacteristic
594C23×C4C2414yes—
595C23×C4C2412yes—
596C23×C4C2412yes—
597C23×C4C2412yes—
598C23×C4C2412yes—
599C23×C4C2411yescharacteristic
600C23×C4C2412yes—
601C23×C4C2412yes—
602C4⋊Q8—28no—
603C4⋊Q8—28no—
604C4⋊Q8—28no—
605C4⋊Q8—28no—
606C4⋊Q8—28no—
607C4⋊Q8—28no—
608C4⋊Q8—24no—
609C4⋊Q8—24no—
610C4⋊Q8—48no—
611#126—216no—
612#126—216no—
613#126—216no—
614#126—216no—
615#126—216no—
616#126—216no—
617#126—216no—
618#125—216no—
619#125—28no—
620#125—216no—
621#125—216no—
622#125—216no—
623#125—28no—
624#125—28no—
625#125—216no—
626#125—28no—
627#124—28no—
628#124—216no—
629#124—216no—
630#124—28no—
631#124—28no—
632#123—216no—
633#123—216no—
634#123—216no—
635#123—216no—
636#123—216no—
637#123—216no—
638#123—216no—
639C22⋊Q8—28no—
640C22⋊Q8—28no—
641C22⋊Q8—28no—
642C22⋊Q8—28no—
643C22⋊Q8—28no—
644C22⋊Q8—28no—
645C22⋊Q8—28no—
646C22⋊Q8—216no—
647C22⋊Q8—28no—
648C22⋊Q8—28no—
649C22⋊Q8—28no—
650C22⋊Q8—28no—
651C22⋊Q8—216no—
652C22⋊Q8—28no—
653C22⋊Q8—216no—
654C22⋊Q8—216no—
655C22⋊Q8—216no—
656C22⋊Q8—48no—
657C22⋊Q8—48no—
658C22⋊Q8—48no—
659#121—216no—
660#121—28no—
661#121—216no—
662#121—28no—
663#121—28no—
664#121—44no—
665C4×Q8—28no—
666C4×Q8—24no—
667C4×Q8—216no—
668C4×Q8—28no—
669C4×Q8—28no—
670C4×Q8—28no—
671C4×Q8—28no—
672C4×Q8—28no—
673C4×Q8—28no—
674C4×Q8—28no—
675C4×Q8—216no—
676C4×Q8—28no—
677C4×Q8—24no—
678C4×Q8—24no—
679C4×Q8—24no—
680C4×Q8—216no—
681C4×Q8—48no—
682C4×Q8C2×D418yes—
683C4×Q8C2×D418yes—
684C4×D4—28no—
685C4×D4—28no—
686C4×D4—28no—
687C4×D4—216no—
688C4×D4—28no—
689C4×D4—28no—
690C4×D4—216no—
691C4×D4—216no—
692C4×D4—24no—
693C4×D4—24no—
694C4×D4—24no—
695C4×D4—24no—
696C4×D4—48no—
697C4×D4C2×D418yes—
698C4×D4C2×D4116yes—
699C4×D4C2×D418yes—
700C4×D4C2×D4116yes—
701#117—24no—
702#117—24no—
703#117—216no—
704#117—28no—
705#117—28no—
706#117—216no—
707#117—28no—
708#117—28no—
709#117—216no—
710#117—216no—
711#117—48no—
712#117—44no—
713#117C2×D418yes—
714#117C2×D4116yes—
715C2×C4⋊C4—24no—
716C2×C4⋊C4—28no—
717C2×C4⋊C4—28no—
718C2×C4⋊C4—216no—
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2418yes—
758C2×C4⋊C4C2418yes—
759C2×C4⋊C4C2418yes—
760C2×C4⋊C4C2418yes—
761C2×C4⋊C4C2418yes—
762C2×C4⋊C4C2418yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2418yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2418yes—
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C22⋊C4C2412yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2412yes—
774C2×C22⋊C4C2412yes—
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2412yes—
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2418yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2418yes—
795C2×C22⋊C4C2418yes—
796C2×C22⋊C4C2418yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2418yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2418yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2412yes—
805C2×C42—216no—
806C2×C42—28no—
807C2×C42—28no—
808C2×C42—28no—
809C2×C42C2×D418yes—
810C2×C42C2×D4116yes—
811C2×C42C2412yes—
812C2×C42C2414yes—
813C2×C42C2412yes—
814C2×C42C2414yes—
815C2×C42C2414yes—
816C2×C42C2412yes—
817C2×C42C2412yes—
818C2×C42C2414yes—
819C2×C42C2412yes—
820C2×C42C2412yes—
821C2×C42C2414yes—
822C2×C42C2414yes—
823C2×C42C2414yes—
824C2×C42C2418yes—
825C2×C42C2418yes—
826C2×C42C2411yescharacteristic
827C2×C42C2412yes—
828C2×C42C2411yescharacteristic
829C2×C42C2412yes—
830C2×C42C2412yes—
831C2×C42C2411yescharacteristic
832C2×C42C2411yescharacteristic
833#95C2412yes—
834#95C2414yes—
835#95C2412yes—
836#95C2414yes—
837#95C2418yes—
838#95C2412yes—
839#95C2412yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2418yes—
844#95C2418yes—
845#95C2414yes—
846#95C2414yes—
847#95C2418yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2418yes—
852#95C2418yes—
853#95C2418yes—
854#95C2418yes—
855#95C2418yes—
856#95C2418yes—
857#95C2418yes—
858#95C2418yes—
859#95C2418yes—
860#95C2418yes—
861#95C2418yes—
862#95C2418yes—
863C24C2512yes—
864C24C2512yes—
865C24C2512yes—
866C24C2511yescharacteristic
867#41—416no—
868#41—416no—
869#41—416no—
870#41—432no—
871C2×Q8—22no—
872C2×Q8—28no—
873C2×Q8—24no—
874C2×Q8—24no—
875C2×Q8—24no—
876C2×Q8—22no—
877C2×Q8—24no—
878C2×Q8—28no—
879C2×Q8—28no—
880C2×Q8—24no—
881C2×Q8—24no—
882C2×Q8—22no—
883C2×Q8—24no—
884C2×Q8—24no—
885C2×Q8—28no—
886C2×Q8—24no—
887C2×Q8—44no—
888C2×Q8—44no—
889C2×Q8—42no—
890C2×Q8—44no—
891C2×Q8—44no—
892C2×Q8—432no—
893C2×Q8—416no—
894C2×Q8C22×D414yes—
895C2×Q82−1+414yes—
896C2×D4—24no—
897C2×D4—28no—
898C2×D4—24no—
899C2×D4—28no—
900C2×D4—22no—
901C2×D4—22no—
902C2×D4—24no—
903C2×D4—22no—
904C2×D4—24no—
905C2×D4—22no—
906C2×D4—44no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—42no—
910C2×D4—48no—
911C2×D4—42no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4C22×D414yes—
918C2×D4C22×D418yes—
919C22×C4—24no—
920C22×C4—22no—
921C22×C4—24no—
922C22×C4—22no—
923C22×C4—24no—
924C22×C4—28no—
925C22×C4—28no—
926C22×C4—24no—
927C22×C4—24no—
928C22×C4—24no—
929C22×C4—24no—
930C22×C4—24no—
931C22×C4—24no—
932C22×C4—24no—
933C22×C4—24no—
934C22×C4—28no—
935C22×C4—24no—
936C22×C4—24no—
937C22×C4—28no—
938C22×C4—24no—
939C22×C4—24no—
940C22×C4—24no—
941C22×C4—42no—
942C22×C4—44no—
943C22×C4—44no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4—42no—
947C22×C4—44no—
948C22×C4—48no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—44no—
952C22×C4C22×D414yes—
953C22×C4C22×D418yes—
954C22×C4C22×D414yes—
955C22×C4C22×D418yes—
956C22×C4C22×D414yes—
957C22×C4C22×D418yes—
958C22×C4C2514yes—
959C22×C4C2514yes—
960C22×C4C2518yes—
961C22×C4C2514yes—
962C22×C4C2512yes—
963C22×C4C2514yes—
964C22×C4C2512yes—
965C22×C4C2512yes—
966C22×C4C2512yes—
967C22×C4C2514yes—
968C22×C4C2512yes—
969C22×C4C2514yes—
970C22×C4C2511yescharacteristic
971C22×C4C2511yescharacteristic
972C22×C4C2511yescharacteristic
973C22×C4C2512yes—
974C22×C4C2512yes—
975C22×C4C2511yescharacteristic
976C22×C4C2512yes—
977C22×C4C2512yes—
978C22×C4C2511yescharacteristic
979C22×C4C2511yescharacteristic
980C4⋊C4—24no—
981C4⋊C4—22no—
982C4⋊C4—28no—
983C4⋊C4—24no—
984C4⋊C4—24no—
985C4⋊C4—24no—
986C4⋊C4—28no—
987C4⋊C4—28no—
988C4⋊C4—28no—
989C4⋊C4—28no—
990C4⋊C4—28no—
991C4⋊C4—24no—
992C4⋊C4—22no—
993C4⋊C4—22no—
994C4⋊C4—24no—
995C4⋊C4—28no—
996C4⋊C4—22no—
997C4⋊C4—24no—
998C4⋊C4—24no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—24no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—24no—
1008C4⋊C4—28no—
1009C4⋊C4—28no—
1010C4⋊C4—28no—
1011C4⋊C4—28no—
1012C4⋊C4—24no—
1013C4⋊C4—28no—
1014C4⋊C4—24no—
1015C4⋊C4—28no—
1016C4⋊C4—28no—
1017C4⋊C4—44no—
1018C4⋊C4—48no—
1019C4⋊C4—44no—
1020C4⋊C4—48no—
1021C4⋊C4—44no—
1022C4⋊C4—48no—
1023C4⋊C4—48no—
1024C4⋊C4—48no—
1025C4⋊C4—48no—
1026C4⋊C4—48no—
1027C4⋊C4—48no—
1028C4⋊C4C22×D414yes—
1029C4⋊C4C22×D414yes—
1030C4⋊C4C22×D418yes—
1031C4⋊C4C22×D418yes—
1032C22⋊C4—24no—
1033C22⋊C4—28no—
1034C22⋊C4—24no—
1035C22⋊C4—28no—
1036C22⋊C4—28no—
1037C22⋊C4—28no—
1038C22⋊C4—28no—
1039C22⋊C4—24no—
1040C22⋊C4—24no—
1041C22⋊C4—24no—
1042C22⋊C4—24no—
1043C22⋊C4—28no—
1044C22⋊C4—28no—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—28no—
1048C22⋊C4—28no—
1049C22⋊C4—28no—
1050C22⋊C4—48no—
1051C22⋊C4—44no—
1052C22⋊C4—44no—
1053C22⋊C4—48no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—48no—
1057C22⋊C4—44no—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—48no—
1061C22⋊C4—48no—
1062C22⋊C4—48no—
1063C22⋊C4C22×D418yes—
1064C22⋊C4C22×D418yes—
1065C22⋊C4C22×D418yes—
1066C42—24no—
1067C42—24no—
1068C42—28no—
1069C42—28no—
1070C42—24no—
1071C42—28no—
1072C42—24no—
1073C42—24no—
1074C42—28no—
1075C42—24no—
1076C42—28no—
1077C42—28no—
1078C42—44no—
1079C42—48no—
1080C42—48no—
1081C42C22×D414yes—
1082C42C22×D414yes—
1083C42C22×D414yes—
1084C42C22×D414yes—
1085C42C22×D418yes—
1086C42C22×D418yes—
1087C42C22×D418yes—
1088C23—22no—
1089C23—21no—
1090C23—22no—
1091C23—21no—
1092C23—22no—
1093C23—24no—
1094C23—22no—
1095C23—24no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—24no—
1103C23—22no—
1104C23—22no—
1105C23—24no—
1106C23—22no—
1107C23—22no—
1108C23C23×D414yes—
1109C23C23×D412yes—
1110C23C2611yescharacteristic
1111Q8—28no—
1112Q8—28no—
1113Q8—416no—
1114Q8—48no—
1115Q8—44no—
1116Q8—48no—
1117Q8—48no—
1118Q8—48no—
1119Q8—88no—
1120D4—28no—
1121D4—48no—
1122D4—48no—
1123D4—44no—
1124D4—48no—
1125D4—416no—
1126D4—44no—
1127D4—88no—
1128D4—88no—
1129C2×C4—22no—
1130C2×C4—21no—
1131C2×C4—22no—
1132C2×C4—21no—
1133C2×C4—22no—
1134C2×C4—24no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—24no—
1139C2×C4—22no—
1140C2×C4—28no—
1141C2×C4—216no—
1142C2×C4—28no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—24no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—22no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—28no—
1158C2×C4—24no—
1159C2×C4—28no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—28no—
1166C2×C4—22no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—28no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—22no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—22no—
1176C2×C4—44no—
1177C2×C4—48no—
1178C2×C4—48no—
1179C2×C4—48no—
1180C2×C4—416no—
1181C2×C4—48no—
1182C2×C4—48no—
1183C2×C4—416no—
1184C2×C4—48no—
1185C2×C4—48no—
1186C2×C4—48no—
1187C2×C4—84no—
1188C2×C4—84no—
1189C2×C4C23×D412yes—
1190C2×C4C23×D412yes—
1191C2×C4C23×D414yes—
1192C2×C4C23×D412yes—
1193C2×C4C23×D412yes—
1194C2×C4C23×D414yes—
1195C2×C4C23×D414yes—
1196C2×C4C23×D412yes—
1197C2×C4C23×D412yes—
1198C2×C4C2×2−1+414yes—
1199C2×C4C2×2−1+412yes—
1200C2×C4#58514yes—
1201C2×C4#58512yes—
1202C22—24no—
1203C22—22no—
1204C22—22no—
1205C22—24no—
1206C22—22no—
1207C22—24no—
1208C22—44no—
1209C22—42no—
1210C22—44no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—44no—
1221C22—42no—
1222C22—44no—
1223C22—42no—
1224C22C24×D411yescharacteristic
1225C22C22×2−1+411yescharacteristic
1226C22C2×#58511yescharacteristic
1227C22C2×#58512yes—
1228C222−1+612yes—
1229C4—22no—
1230C4—24no—
1231C4—24no—
1232C4—22no—
1233C4—22no—
1234C4—24no—
1235C4—22no—
1236C4—24no—
1237C4—42no—
1238C4—44no—
1239C4—42no—
1240C4—44no—
1241C4—42no—
1242C4—42no—
1243C4—42no—
1244C4—44no—
1245C4—44no—
1246C4—44no—
1247C4—48no—
1248C4—44no—
1249C4#344914yes—
1250C4#348914yes—
1251C2—44no—
1252C2—42no—
1253C2—82no—
1254C2—82no—
1255C2C2×#344911yescharacteristic
1256C2C2×#348911yescharacteristic
1257C2#6285911yescharacteristic
1258C2#6295312yes—
1259C2#6296712yes—
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×#3482C2semidirect
2. C2×#3461C2semidirect
3. #42992C2semidirect
4. #42917C2semidirect
5. #42915C2semidirect
6. #42911C2semidirect
7. #42309C2semidirect
8. #42305C2semidirect
9. #39727C2semidirect
10. #39599C2semidirect
11. #38920C2semidirect
12. #38911C2semidirect
13. #38048C2semidirect
14. #38035C2semidirect
15. #37553C2semidirect
16. #37551C2semidirect
17. #36972C2semidirect
18. #35637C2semidirect
19. #35297C2semidirect
20. #35248C2semidirect
21. #35245C2semidirect
22. #35179C2semidirect
23. #35155C2semidirect
24. #34952C2semidirect
25. #34909C2semidirect
26. #34193C2semidirect
300. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34822
C2×#34612
#429922
#429172
#429152
#429112
#423092
#423052
#397272
#395992
#389202
#389112
#380482
#380352
#375532
#375512
#369722
#356372
#352972
#352482
#352452
#351792
#351552
#349522
#349092
#341932