Finite Group Databasebeta

← #7720489

Subgroups — #7720489

Order 512.

6574 conjugacy classes of subgroups.

The subgroup lattice has 1215 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3552C211yesmaximal, characteristic, complemented
2C2×#3559C211yesmaximal, characteristic, complemented
3#51753C214yesmaximal, complemented
4#51750C214yesmaximal, complemented
5#50871C218yesmaximal, complemented
6#44513C218yesmaximal, complemented
7#44446C214yesmaximal, complemented
8#43498C214yesmaximal, complemented
9#39173C212yesmaximal, complemented
10#39163C212yesmaximal, complemented
11#38092C212yesmaximal, complemented
12#38085C212yesmaximal, complemented
13#38085C212yesmaximal, complemented
14#38079C212yesmaximal, complemented
15#37422C212yesmaximal, complemented
16#37392C212yesmaximal, complemented
17#36396C212yesmaximal, complemented
18#36303C212yesmaximal, complemented
19#35332C212yesmaximal, complemented
20#35312C212yesmaximal, complemented
21#35303C211yesmaximal, characteristic, complemented
22#35289C211yesmaximal, characteristic, complemented
23#35139C211yesmaximal, characteristic, complemented
24C2×#2642C211yesmaximal, characteristic, complemented
25#34149C211yesmaximal, characteristic, complemented
26#3559—216no—
27#3552—216no—
28C2×#563C2212yes—
29C2×#563C2214yes—
30C2×#562C2212yes—
31C2×#557C2211yescharacteristic
32C2×#556C2211yescharacteristic
33C2×#554C2212yes—
34C2×#554C2212yes—
35C2×#553C2212yes—
36C2×#553C2212yes—
37C2×#553C2212yes—
38C2×D4×Q8C2211yescharacteristic
39C2×D4×Q8C2212yes—
40C2×#548C2212yes—
41C2×#547C2212yes—
42C2×#547C2214yes—
43C2×#547C2211yescharacteristic
44C2×#544C2212yes—
45C2×#544C2212yes—
46C2×#542C2212yes—
47C2×#541C2212yes—
48C2×#540C2212yes—
49C2×#539C2214yes—
50C2×#539C2212yes—
51C2×#539C2214yes—
52C2×#537C2212yes—
53C2×#536C2212yes—
54C2×#532C2211yescharacteristic
55C22×C4⋊Q8C2211yescharacteristic
56C2×#529C2211yescharacteristic
57C2×#529C2211yescharacteristic
58C22×#125C2211yescharacteristic
59#2862C2212yes—
60#2862C2212yes—
61#2861C2212yes—
62#2861C2212yes—
63#2859C2212yes—
64#2858C2212yes—
65#2856C2212yes—
66#2850C2212yes—
67#2850C2212yes—
68#2850C2212yes—
69#2728C2218yes—
70#2719C2218yes—
71#2716C2218yes—
72#2716C2218yes—
73#2713C2218yes—
74#2710C2218yes—
75#2703C2218yes—
76#2703C2218yes—
77#2702C2218yes—
78#2698C2218yes—
79#2696C2218yes—
80#2696C2218yes—
81#2693C2218yes—
82#2692C2218yes—
83#2690C2218yes—
84#2690C2218yes—
85#2689C2218yes—
86#2688C2218yes—
87#2687C2218yes—
88#2687C2218yes—
89#2664C2214yes—
90#2660C2211yescharacteristic
91#2657C2211yescharacteristic
92#2642C2212yes—
93#2642C2212yes—
94#2642C2212yes—
95#2642C2212yes—
96#2642C2214yes—
97#2642C2214yes—
98#2642C2212yes—
99#2641C2211yescharacteristic
100#2640C2214yes—
101#2640C2212yes—
102#2640C2211yescharacteristic
103#2620C2212yes—
104#2620C2212yes—
105#2611C2214yes—
106#2610C2214yes—
107#2603C2214yes—
108#2568C2212yes—
109#2567C2212yes—
110#2566C2212yes—
111#2565C2212yes—
112#2565C2212yes—
113#2565C2212yes—
114#2563C2214yes—
115#2560C2218yes—
116#2559C2218yes—
117#2559C2218yes—
118#2558C2218yes—
119#2558C2218yes—
120#2557C2218yes—
121#2547C2212yes—
122#2547C2212yes—
123#2547C2212yes—
124#2547C2212yes—
125#2544C2212yes—
126#2544C2212yes—
127#2543C2218yes—
128#2543C2214yes—
129#2504C2211yescharacteristic
130#2504C2214yes—
131#2503C2212yes—
132#2503C2211yescharacteristic
133#2502C2212yes—
134#2502C2211yescharacteristic
135#2501C2211yescharacteristic
136#2499C2212yes—
137#2499C2212yes—
138#2492C2218yes—
139#2492C2218yes—
140#2489C2218yes—
141#2488C2218yes—
142#2488C2218yes—
143#2488C2218yes—
144#2488C2218yes—
145#2481C2218yes—
146#2481C2218yes—
147#2477C2218yes—
148#2457C2218yes—
149#2450C2218yes—
150#2450C2218yes—
151#2444C2218yes—
152#2444C2218yes—
153#2442C2218yes—
154#2436C2212yes—
155#2436C2212yes—
156#2436C2212yes—
157#2436C2212yes—
158#2431C2212yes—
159#2431C2212yes—
160#2430C2218yes—
161#2430C2214yes—
162#2425C2218yes—
163#2421C2218yes—
164#2413C2214yes—
165C2×#400C2214yes—
166C2×#400C2214yes—
167#2373C2214yes—
168#2372C2212yes—
169#2371C2212yes—
170#2368C2212yes—
171#2364C2218yes—
172#2364C2212yes—
173#2359C2214yes—
174#2339C2218yes—
175#2328C2212yes—
176#2326C2212yes—
177#2326C2212yes—
178#2326C2212yes—
179#2322C2214yes—
180#2311C2212yes—
181#2311C2214yes—
182#2310C2212yes—
183C4×#124C2212yes—
184C4×#124C2212yes—
185#2298C2212yes—
186#2297C2212yes—
187#2295C2212yes—
188C2×#391C2212yes—
189C2×#391C2212yes—
190C2×#391C2212yes—
191#2290C2212yes—
192#2290C2212yes—
193C42×D4C2212yes—
194C4×#117C2212yes—
195C4×#117C2211yescharacteristic
196C2×#376C2211yescharacteristic
197C22×#41C2312yes—
198C22×#41C2312yes—
199C22×#41C2314yes—
200C23×Q8C2312yes—
201C23×Q8C2312yes—
202#563—232no—
203#563—216no—
204#562—216no—
205#557—28no—
206#556—28no—
207#554—216no—
208#554—216no—
209#553—216no—
210#553—216no—
211#553—216no—
212D4×Q8—216no—
213D4×Q8—28no—
214#548—216no—
215#547—232no—
216#547—28no—
217#547—216no—
218#544—216no—
219#544—216no—
220#542—216no—
221#541—216no—
222#540—216no—
223#539—232no—
224#539—232no—
225#539—216no—
226#537—216no—
227#536—216no—
228#532—28no—
229C2×C4⋊Q8—28no—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2311yescharacteristic
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2314yes—
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2314yes—
241C2×#127C2311yescharacteristic
242C2×#127C2312yes—
243#529—28no—
244#529D4116yescomplemented
245C2×#126C2314yes—
246C2×#126C2312yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#126C2312yes—
252C2×#125—28no—
253C2×#125C2312yes—
254C2×#125C2312yes—
255C2×#125C2311yescharacteristic
256C2×#125C2312yes—
257C2×#125C2312yes—
258C2×#125C2312yes—
259C2×#125C2314yes—
260C2×#125C2314yes—
261C2×#125C2314yes—
262C2×#125C2314yes—
263C2×#125C2312yes—
264C2×#125C2311yescharacteristic
265C2×#124C2311yescharacteristic
266C2×#124C2312yes—
267C2×#124C2312yes—
268C2×#124C2314yes—
269C2×#124C2312yes—
270C2×#124C2312yes—
271C2×#124C2312yes—
272C2×#124C2312yes—
273C2×#124C2312yes—
274C2×#124C2311yescharacteristic
275C2×#123C2312yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×#123C2312yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2311yescharacteristic
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2311yescharacteristic
304C2×#121C2312yes—
305C2×#121C2312yes—
306C2×#121C2312yes—
307C2×#121C2311yescharacteristic
308C2×#121C2312yes—
309C2×#121C2314yes—
310C2×#121C2314yes—
311C2×#121C2314yes—
312C2×#121C2314yes—
313C2×#121C2314yes—
314C2×#121C2312yes—
315C2×#121C2318yes—
316C2×#121C2311yescharacteristic
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2311yescharacteristic
322C2×C4×D4C2312yes—
323C2×C4×D4C2311yescharacteristic
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2314yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2311yescharacteristic
336C2×#117C2312yes—
337C2×#117C2312yes—
338C2×#117C2312yes—
339C2×#117C2312yes—
340C2×#117C2312yes—
341C2×#117C2312yes—
342C22×C4⋊C4C2312yes—
343C22×C4⋊C4C2312yes—
344C22×C4⋊C4C2312yes—
345C22×C4⋊C4C2312yes—
346C22×C4⋊C4C2312yes—
347C22×C4⋊C4C2311yescharacteristic
348C22×C4⋊C4C2311yescharacteristic
349C22×C4⋊C4C2314yes—
350C22×C4⋊C4C2312yes—
351C22×C42C2312yes—
352C22×C42C2312yes—
353C22×C42C2311yescharacteristic
354#400C2318yes—
355#400C2314yes—
356#400C2318yes—
357#400C2318yes—
358#400C2318yes—
359#400C2318yes—
360#400C2318yes—
361#400C2318yes—
362#400C2318yes—
363#400C2318yes—
364#400C2318yes—
365#400C2318yes—
366#400C2318yes—
367#399C2314yes—
368#398C2318yes—
369#398C2318yes—
370#398C2318yes—
371#398C2314yes—
372#398C2314yes—
373#398C2318yes—
374#397C2314yes—
375#397C2314yes—
376#397C2318yes—
377#397C2318yes—
378#397C2318yes—
379#397C2318yes—
380#397C2318yes—
381#397C2318yes—
382#397C2318yes—
383#396C2318yes—
384#396C2318yes—
385#396C2318yes—
386#395C2318yes—
387#395C2314yes—
388#394C2318yes—
389#394C2314yes—
390#394C2314yes—
391#394C2318yes—
392#394C2318yes—
393#394C2318yes—
394#393C2318yes—
395#393C2318yes—
396#393C2314yes—
397#393C2318yes—
398#393C2318yes—
399#393C2318yes—
400#392C2314yes—
401#392C2314yes—
402#392C2318yes—
403#392C2318yes—
404#391C2318yes—
405#391C2312yes—
406#391C2312yes—
407#391C2312yes—
408#391C2312yes—
409#391C2312yes—
410#391C2312yes—
411#391C2312yes—
412#391C2312yes—
413#391C2318yes—
414#391C2312yes—
415#391C2312yes—
416#391C2318yes—
417#391C2312yes—
418#391C2318yes—
419#391C2312yes—
420#391C2312yes—
421#391C2318yes—
422#391C2312yes—
423#391C2312yes—
424#391C2314yes—
425#391C2318yes—
426#391C2318yes—
427#390C2318yes—
428#390C2318yes—
429#390C2312yes—
430#390C2312yes—
431#390C2312yes—
432#390C2318yes—
433#390C2312yes—
434#390C2312yes—
435#389C2318yes—
436#389C2318yes—
437#389C2318yes—
438#389C2314yes—
439#388C2318yes—
440#388C2318yes—
441#388C2318yes—
442#388C2318yes—
443#388C2318yes—
444#388C2318yes—
445#388C2318yes—
446#388C2318yes—
447#388C2318yes—
448#388C2318yes—
449#388C2318yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2318yes—
455#387C2318yes—
456#387C2318yes—
457#387C2318yes—
458#387C2318yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2318yes—
466#386C2318yes—
467#386C2318yes—
468#386C2318yes—
469#386C2318yes—
470#386C2314yes—
471#386C2318yes—
472#386C2318yes—
473#386C2318yes—
474#386C2318yes—
475#386C2318yes—
476#386C2318yes—
477#386C2314yes—
478#386C2314yes—
479#386C2318yes—
480#386C2318yes—
481#386C2318yes—
482#386C2318yes—
483#386C2318yes—
484#385C2318yes—
485#385C2314yes—
486#385C2318yes—
487#385C2318yes—
488#385C2318yes—
489#385C2314yes—
490#385C2314yes—
491#385C2318yes—
492#384C2312yes—
493#384C2312yes—
494#384C2312yes—
495#382C2318yes—
496#382C2312yes—
497#382C2312yes—
498#382C2312yes—
499#382C2318yes—
500#381C2318yes—
501#381C2314yes—
502#381C2318yes—
503#380C2318yes—
504#380C2318yes—
505#380C2318yes—
506#380C2318yes—
507#380C2318yes—
508C4×C4⋊C4C2314yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2314yes—
514C4×C4⋊C4C2314yes—
515C4×C22⋊C4C2318yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2318yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2318yes—
522C4×C22⋊C4C2314yes—
523C4×C22⋊C4C2312yes—
524C4×C22⋊C4C2312yes—
525C4×C22⋊C4C2311yescharacteristic
526C4×C22⋊C4C2311yescharacteristic
527#376C2312yes—
528#376C2312yes—
529#376C2312yes—
530#376C2312yes—
531#376C2312yes—
532#376C2311yescharacteristic
533#376C2311yescharacteristic
534C2×#95C2318yes—
535C2×#95C2318yes—
536C2×#95C2312yes—
537C2×#95C2312yes—
538C2×#95C2318yes—
539C43C2312yes—
540C43C2312yes—
541C2×#41—216no—
542C2×#41—28no—
543C2×#41—28no—
544C2×#41—48no—
545C2×#41—416no—
546C2×#41—44no—
547C2×#41—44no—
548C22×Q8—28no—
549C22×Q8—28no—
550C22×Q8—44no—
551C22×Q8—44no—
552C22×Q8—44no—
553C22×Q8—44no—
554C22×Q8C2411yescharacteristic
555C22×Q8C2412yes—
556C22×Q8C2412yes—
557C22×Q8C2414yes—
558C22×Q8C2414yes—
559C22×Q8C2414yes—
560C22×Q8C2412yes—
561C22×Q8C2411yescharacteristic
562C22×D4C2412yes—
563C22×D4C2412yes—
564C22×D4C2414yes—
565C22×D4C2411yescharacteristic
566C22×D4C2412yes—
567C22×D4C2414yes—
568C22×D4C2412yes—
569C22×D4C2414yes—
570C22×D4C2414yes—
571C22×D4C2412yes—
572C22×D4C2418yes—
573C22×D4C2411yescharacteristic
574C23×C4C2412yes—
575C23×C4C2411yescharacteristic
576C23×C4C2411yescharacteristic
577C23×C4C2412yes—
578C23×C4C2412yes—
579C23×C4C2414yes—
580C23×C4C2412yes—
581C23×C4C2414yes—
582C23×C4C2414yes—
583C23×C4C2414yes—
584C23×C4C2414yes—
585C23×C4C2414yes—
586C23×C4C2414yes—
587C23×C4C2414yes—
588C23×C4C2414yes—
589C23×C4C2411yescharacteristic
590C4⋊Q8—216no—
591C4⋊Q8—28no—
592C4⋊Q8—216no—
593C4⋊Q8—28no—
594C4⋊Q8—28no—
595C4⋊Q8—24no—
596C4⋊Q8—24no—
597C4⋊Q8—28no—
598C4⋊Q8—24no—
599C4⋊Q8—28no—
600C4⋊Q8—28no—
601#127—24no—
602#127—44no—
603#126—216no—
604#126—216no—
605#126—216no—
606#126—216no—
607#126—216no—
608#126—28no—
609#126C2×D4116yes—
610#125—216no—
611#125—216no—
612#125—216no—
613#125—216no—
614#125—28no—
615#125—28no—
616#125—28no—
617#125—28no—
618#125—28no—
619#125—24no—
620#125—28no—
621#125C2×D418yes—
622#124—216no—
623#124—24no—
624#124—28no—
625#124—28no—
626#124—44no—
627#124—44no—
628#124—44no—
629#124—44no—
630#124—44no—
631#124C2×D418yes—
632#123—28no—
633#123—216no—
634#123—216no—
635#123—216no—
636#123—216no—
637#123—216no—
638#123—216no—
639#123—216no—
640#123—216no—
641#123—216no—
642#123—48no—
643#123C2×D4116yes—
644C22⋊Q8—216no—
645C22⋊Q8—28no—
646C22⋊Q8—24no—
647C22⋊Q8—28no—
648C22⋊Q8—28no—
649C22⋊Q8—216no—
650C22⋊Q8—216no—
651C22⋊Q8—216no—
652C22⋊Q8—216no—
653C22⋊Q8—216no—
654C22⋊Q8—216no—
655C22⋊Q8—216no—
656C22⋊Q8—216no—
657C22⋊Q8—216no—
658C22⋊Q8—216no—
659C22⋊Q8—216no—
660C22⋊Q8C2×D418yes—
661#121—216no—
662#121—216no—
663#121—216no—
664#121—28no—
665#121—24no—
666#121—28no—
667#121—28no—
668#121—28no—
669#121—28no—
670#121—216no—
671#121—216no—
672#121—416no—
673#121C2×D418yes—
674C4×Q8—28no—
675C4×Q8—24no—
676C4×Q8—28no—
677C4×Q8—28no—
678C4×Q8C2×D418yes—
679C4×D4—216no—
680C4×D4—28no—
681C4×D4—28no—
682C4×D4—216no—
683C4×D4—216no—
684C4×D4—216no—
685C4×D4—24no—
686C4×D4—28no—
687C4×D4—28no—
688C4×D4—28no—
689C4×D4—28no—
690C4×D4—48no—
691C4×D4C2×D4116yes—
692C4×D4C2×D418yes—
693#117—28no—
694#117—28no—
695#117—28no—
696#117—44no—
697#117—44no—
698#117C2×D4116yes—
699C2×C4⋊C4—28no—
700C2×C4⋊C4—24no—
701C2×C4⋊C4—28no—
702C2×C4⋊C4—24no—
703C2×C4⋊C4—28no—
704C2×C4⋊C4—28no—
705C2×C4⋊C4—28no—
706C2×C4⋊C4—216no—
707C2×C4⋊C4—28no—
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2412yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2418yes—
744C2×C4⋊C4C2418yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2418yes—
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2411yescharacteristic
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C22⋊C4C2412yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2412yes—
757C2×C22⋊C4C2412yes—
758C2×C22⋊C4C2412yes—
759C2×C22⋊C4C2412yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2412yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2412yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2418yes—
774C2×C22⋊C4C2418yes—
775C2×C22⋊C4C2418yes—
776C2×C22⋊C4C2418yes—
777C2×C22⋊C4C2418yes—
778C2×C22⋊C4C2418yes—
779C2×C22⋊C4C2418yes—
780C2×C22⋊C4C2418yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2418yes—
783C2×C22⋊C4C2418yes—
784C2×C22⋊C4C2412yes—
785C2×C22⋊C4C2412yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2412yes—
788C2×C22⋊C4C2412yes—
789C2×C42—44no—
790C2×C42—44no—
791C2×C42C2×D418yes—
792C2×C42C2412yes—
793C2×C42C2414yes—
794C2×C42C2414yes—
795C2×C42C2412yes—
796C2×C42C2412yes—
797C2×C42C2414yes—
798C2×C42C2412yes—
799C2×C42C2412yes—
800C2×C42C2414yes—
801C2×C42C2414yes—
802C2×C42C2414yes—
803C2×C42C2414yes—
804C2×C42C2414yes—
805C2×C42C2414yes—
806C2×C42C2411yescharacteristic
807C2×C42C2411yescharacteristic
808C2×C42C2412yes—
809C2×C42C2411yescharacteristic
810C2×C42C2411yescharacteristic
811#95C2418yes—
812#95C2412yes—
813#95C2412yes—
814#95C2414yes—
815#95C2414yes—
816#95C2412yes—
817#95C2412yes—
818#95C2418yes—
819#95C2418yes—
820#95C2418yes—
821#95C2418yes—
822#95C2418yes—
823#95C2418yes—
824#95C2418yes—
825#95C2418yes—
826#95C2418yes—
827#95C2418yes—
828#95C2412yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2412yes—
833#95C2414yes—
834#95C2414yes—
835#95C2418yes—
836#95C2418yes—
837#95C2418yes—
838#95C2414yes—
839#95C2414yes—
840#95C2418yes—
841#95C2418yes—
842#95C2418yes—
843#95C2418yes—
844C24C2512yes—
845C24C2514yes—
846C24C2512yes—
847C24C2511yescharacteristic
848#41—816no—
849#41—816no—
850#41—832no—
851C2×Q8—22no—
852C2×Q8—24no—
853C2×Q8—24no—
854C2×Q8—28no—
855C2×Q8—28no—
856C2×Q8—28no—
857C2×Q8—24no—
858C2×Q8—24no—
859C2×Q8—24no—
860C2×Q8—24no—
861C2×Q8—24no—
862C2×Q8—24no—
863C2×Q8—42no—
864C2×Q8—44no—
865C2×Q8—44no—
866C2×Q8—44no—
867C2×Q8—44no—
868C2×Q8—44no—
869C2×Q8—48no—
870C2×Q8—816no—
871C2×Q8—816no—
872C2×Q8C22×D414yes—
873C2×D4—28no—
874C2×D4—24no—
875C2×D4—28no—
876C2×D4—28no—
877C2×D4—216no—
878C2×D4—28no—
879C2×D4—28no—
880C2×D4—28no—
881C2×D4—24no—
882C2×D4—22no—
883C2×D4—24no—
884C2×D4—24no—
885C2×D4—24no—
886C2×D4—24no—
887C2×D4—24no—
888C2×D4—42no—
889C2×D4—44no—
890C2×D4—48no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—48no—
895C2×D4—48no—
896C2×D4—48no—
897C2×D4—48no—
898C2×D4C22×D418yes—
899C2×D4C22×D414yes—
900C22×C4—24no—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—24no—
904C22×C4—24no—
905C22×C4—28no—
906C22×C4—24no—
907C22×C4—28no—
908C22×C4—28no—
909C22×C4—28no—
910C22×C4—28no—
911C22×C4—24no—
912C22×C4—28no—
913C22×C4—28no—
914C22×C4—28no—
915C22×C4—28no—
916C22×C4—42no—
917C22×C4—44no—
918C22×C4—44no—
919C22×C4—44no—
920C22×C4—44no—
921C22×C4—48no—
922C22×C4—44no—
923C22×C4—44no—
924C22×C4—44no—
925C22×C4—44no—
926C22×C4—44no—
927C22×C4—44no—
928C22×C4—44no—
929C22×C4—44no—
930C22×C4—48no—
931C22×C4—48no—
932C22×C4—44no—
933C22×C4—48no—
934C22×C4C22×D414yes—
935C22×C4C22×D414yes—
936C22×C4C22×D418yes—
937C22×C4C22×D414yes—
938C22×C4C2514yes—
939C22×C4C2514yes—
940C22×C4C2514yes—
941C22×C4C2514yes—
942C22×C4C2514yes—
943C22×C4C2512yes—
944C22×C4C2514yes—
945C22×C4C2514yes—
946C22×C4C2514yes—
947C22×C4C2514yes—
948C22×C4C2512yes—
949C22×C4C2512yes—
950C22×C4C2511yescharacteristic
951C22×C4C2511yescharacteristic
952C22×C4C2511yescharacteristic
953C22×C4C2511yescharacteristic
954C22×C4C2512yes—
955C22×C4C2512yes—
956C22×C4C2512yes—
957C22×C4C2511yescharacteristic
958C22×C4C2511yescharacteristic
959C4⋊C4—24no—
960C4⋊C4—28no—
961C4⋊C4—24no—
962C4⋊C4—24no—
963C4⋊C4—24no—
964C4⋊C4—24no—
965C4⋊C4—28no—
966C4⋊C4—28no—
967C4⋊C4—28no—
968C4⋊C4—28no—
969C4⋊C4—24no—
970C4⋊C4—28no—
971C4⋊C4—28no—
972C4⋊C4—24no—
973C4⋊C4—28no—
974C4⋊C4—28no—
975C4⋊C4—28no—
976C4⋊C4—24no—
977C4⋊C4—24no—
978C4⋊C4—24no—
979C4⋊C4—24no—
980C4⋊C4—22no—
981C4⋊C4—24no—
982C4⋊C4—28no—
983C4⋊C4—28no—
984C4⋊C4—28no—
985C4⋊C4—24no—
986C4⋊C4—22no—
987C4⋊C4—28no—
988C4⋊C4—28no—
989C4⋊C4—28no—
990C4⋊C4—24no—
991C4⋊C4—44no—
992C4⋊C4—48no—
993C4⋊C4—44no—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—48no—
997C4⋊C4—48no—
998C4⋊C4C22×D414yes—
999C4⋊C4C22×D418yes—
1000C4⋊C4C22×D414yes—
1001C4⋊C4C22×D418yes—
1002C4⋊C4C22×D418yes—
1003C4⋊C4C22×D418yes—
1004C22⋊C4—28no—
1005C22⋊C4—24no—
1006C22⋊C4—28no—
1007C22⋊C4—28no—
1008C22⋊C4—24no—
1009C22⋊C4—24no—
1010C22⋊C4—28no—
1011C22⋊C4—24no—
1012C22⋊C4—24no—
1013C22⋊C4—28no—
1014C22⋊C4—28no—
1015C22⋊C4—28no—
1016C22⋊C4—28no—
1017C22⋊C4—28no—
1018C22⋊C4—28no—
1019C22⋊C4—24no—
1020C22⋊C4—28no—
1021C22⋊C4—24no—
1022C22⋊C4—48no—
1023C22⋊C4—48no—
1024C22⋊C4—44no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—48no—
1028C22⋊C4—48no—
1029C22⋊C4—48no—
1030C22⋊C4—48no—
1031C22⋊C4—48no—
1032C22⋊C4—48no—
1033C22⋊C4—48no—
1034C22⋊C4—48no—
1035C22⋊C4C22×D418yes—
1036C22⋊C4C22×D418yes—
1037C22⋊C4C22×D418yes—
1038C22⋊C4C22×D418yes—
1039C22⋊C4C22×D418yes—
1040C42—24no—
1041C42—28no—
1042C42—28no—
1043C42—28no—
1044C42—24no—
1045C42—24no—
1046C42—24no—
1047C42—24no—
1048C42—44no—
1049C42—44no—
1050C42—44no—
1051C42—44no—
1052C42—44no—
1053C42—44no—
1054C42C22×D414yes—
1055C42C22×D414yes—
1056C42C22×D414yes—
1057C42C22×D414yes—
1058C42C22×D418yes—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—24no—
1063C23—22no—
1064C23—24no—
1065C23—22no—
1066C23—24no—
1067C23—24no—
1068C23—24no—
1069C23—24no—
1070C23—28no—
1071C23—24no—
1072C23—24no—
1073C23—28no—
1074C23C23×D414yes—
1075C23C23×D412yes—
1076C23#58514yes—
1077C23C2611yescharacteristic
1078Q8—44no—
1079Q8—44no—
1080Q8—48no—
1081Q8—48no—
1082Q8—88no—
1083Q8—88no—
1084Q8—84no—
1085Q8—88no—
1086D4—216no—
1087D4—44no—
1088D4—48no—
1089D4—416no—
1090D4—48no—
1091D4—44no—
1092D4—84no—
1093D4—84no—
1094D4—88no—
1095D4—88no—
1096D4—88no—
1097D4—168no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—24no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—24no—
1106C2×C4—22no—
1107C2×C4—28no—
1108C2×C4—28no—
1109C2×C4—216no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—22no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—28no—
1133C2×C4—28no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—28no—
1139C2×C4—24no—
1140C2×C4—44no—
1141C2×C4—48no—
1142C2×C4—48no—
1143C2×C4—88no—
1144C2×C4—88no—
1145C2×C4—88no—
1146C2×C4—88no—
1147C2×C4—84no—
1148C2×C4—88no—
1149C2×C4—88no—
1150C2×C4—88no—
1151C2×C4—88no—
1152C2×C4—88no—
1153C2×C4C23×D412yes—
1154C2×C4C23×D414yes—
1155C2×C4C23×D414yes—
1156C2×C4C23×D414yes—
1157C2×C4C23×D412yes—
1158C2×C4C23×D412yes—
1159C2×C4C23×D412yes—
1160C2×C4C23×D412yes—
1161C2×C4C23×D412yes—
1162C2×C4#58514yes—
1163C22—22no—
1164C22—22no—
1165C22—28no—
1166C22—24no—
1167C22—24no—
1168C22—24no—
1169C22—44no—
1170C22—44no—
1171C22—44no—
1172C22—42no—
1173C22—42no—
1174C22—44no—
1175C22—42no—
1176C22—44no—
1177C22—48no—
1178C22—48no—
1179C22—48no—
1180C22#350014yes—
1181C22C24×D411yescharacteristic
1182C22C2×#58512yes—
1183C22C2×#58512yes—
1184C222−1+612yes—
1185C4—22no—
1186C4—24no—
1187C4—22no—
1188C4—22no—
1189C4—24no—
1190C4—22no—
1191C4—22no—
1192C4—24no—
1193C4—44no—
1194C4—44no—
1195C4—44no—
1196C4—42no—
1197C4—44no—
1198C4—42no—
1199C4—42no—
1200C4—44no—
1201C4—44no—
1202C4—44no—
1203C4—44no—
1204C4—44no—
1205C4#350014yes—
1206C2—24no—
1207C2—44no—
1208C2—82no—
1209C2—84no—
1210C2C2×#350011yescharacteristic
1211C2C2×#350011yescharacteristic
1212C2#6285911yescharacteristic
1213C2#6297114yes—
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×#3552C2semidirect
2. C2×#3559C2semidirect
3. #51753C2semidirect
4. #51750C2semidirect
5. #50871C2semidirect
6. #44513C2semidirect
7. #44446C2semidirect
8. #43498C2semidirect
9. #39173C2semidirect
10. #39163C2semidirect
11. #38092C2semidirect
12. #38085C2semidirect
13. #38085C2semidirect
14. #38079C2semidirect
15. #37422C2semidirect
16. #37392C2semidirect
17. #36396C2semidirect
18. #36303C2semidirect
19. #35332C2semidirect
20. #35312C2semidirect
21. #35303C2semidirect
22. #35289C2semidirect
23. #35139C2semidirect
24. C2×#2642C2semidirect
25. #34149C2semidirect
244. #529D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35522
C2×#35592
#517532
#517502
#508712
#445132
#444462
#434982
#391732
#391632
#380922
#380852
#380792
#374222
#373922
#363962
#363032
#353322
#353122
#353032
#352892
#351392
C2×#26422
#341492