Finite Group Databasebeta

← #7645519

Subgroups — #7645519

Order 512.

7084 conjugacy classes of subgroups.

The subgroup lattice has 1272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#553C211yesmaximal, characteristic, complemented
2C2×#3455C211yesmaximal, characteristic, complemented
3#42393C214yesmaximal, complemented
4#42391C214yesmaximal, complemented
5#41961C214yesmaximal, complemented
6#41959C214yesmaximal, complemented
7#39850C218yesmaximal, complemented
8#39848C218yesmaximal, complemented
9#37548C211yesmaximal, characteristic, complemented
10#37547C211yesmaximal, characteristic, complemented
11#37446C212yesmaximal, complemented
12#37185C212yesmaximal, complemented
13#37120C212yesmaximal, complemented
14#36709C212yesmaximal, complemented
15#36706C212yesmaximal, complemented
16#35395C212yesmaximal, complemented
17#35394C212yesmaximal, complemented
18#35240C211yesmaximal, characteristic, complemented
19#35237C211yesmaximal, characteristic, complemented
20#35143C212yesmaximal, complemented
21#35063C212yesmaximal, complemented
22#34989C212yesmaximal, complemented
23#34987C212yesmaximal, complemented
24#34963C212yesmaximal, complemented
25#34177C211yesmaximal, characteristic, complemented
26C2×#553—216no—
27C2×#553C2214yes—
28C2×#553C2214yes—
29C2×#553C2214yes—
30C2×#553C2214yes—
31#3455—216no—
32C2×#542C2212yescomplemented
33C2×#542C2212yescomplemented
34C2×#541C2212yescomplemented
35C2×#540C2212yescomplemented
36C2×#539C2212yes—
37C2×#539C2212yes—
38C2×#538C2212yes—
39C2×#538C2212yes—
40C2×#533C2211yescharacteristic
41C2×#532C2211yescharacteristic
42C2×#529C2214yescomplemented
43C2×#529C2214yescomplemented
44C22×#126C2211yescharacteristic
45C22×#126C2211yescharacteristic
46C22×#125C2211yescharacteristic
47C2×#525C2212yes—
48C22×#123C2211yescharacteristic
49C22×#123C2211yescharacteristic
50C22×#121C2211yescharacteristic
51C22×#121C2211yescharacteristic
52C22×#121C2211yescharacteristic
53C22×#121C2211yescharacteristic
54C2×C4×#41C2212yes—
55C22×C4×D4C2211yescharacteristic
56C22×C4×D4C2211yescharacteristic
57C22×C4×D4C2211yescharacteristic
58C22×C4×D4C2211yescharacteristic
59C22×#117C2211yescharacteristic
60C23×C4⋊C4C2211yescharacteristic
61#2853C2214yes—
62#2852C2218yescomplemented
63#2849C2214yes—
64#2848C2212yes—
65#2848C2212yes—
66#2847C2212yes—
67#2847C2212yes—
68#2821C2212yescomplemented
69#2821C2212yescomplemented
70#2821C2212yescomplemented
71#2818C2212yescomplemented
72#2816C2214yescomplemented
73#2815C2214yescomplemented
74#2721C2218yescomplemented
75#2719C2218yescomplemented
76#2714C2218yescomplemented
77#2711C2218yescomplemented
78#2695C2218yescomplemented
79#2694C2218yescomplemented
80#2693C2218yescomplemented
81#2691C2218yescomplemented
82#2690C2218yescomplemented
83#2676C2218yescomplemented
84#2676C2218yescomplemented
85#2675C2218yescomplemented
86#2673C2218yescomplemented
87#2672C2218yescomplemented
88#2671C2218yescomplemented
89#2671C2218yescomplemented
90#2664C2214yescomplemented
91#2662C2214yescomplemented
92#2656C2214yescomplemented
93#2639C2214yescomplemented
94#2638C2214yescomplemented
95#2637C2214yescomplemented
96#2637C2214yescomplemented
97#2636C2214yescomplemented
98#2636C2214yescomplemented
99#2635C2218yescomplemented
100#2635C2214yescomplemented
101#2633C2214yescomplemented
102#2631C2214yescomplemented
103#2627C2212yes—
104#2626C2212yes—
105#2623C2214yes—
106#2618C2212yes—
107#2617C2212yes—
108#2613C2214yes—
109#2604C2214yescomplemented
110#2604C2214yescomplemented
111#2603C2214yescomplemented
112#2603C2214yescomplemented
113#2601C2218yescomplemented
114#2600C2218yescomplemented
115#2598C2218yescomplemented
116#2591C2212yes—
117#2583C2212yes—
118#2580C2214yescomplemented
119#2579C2214yes—
120#2564C2214yescomplemented
121#2563C2212yescomplemented
122#2561C2212yes—
123#2559C2218yescomplemented
124#2557C2218yescomplemented
125#2555C2218yescomplemented
126#2553C2218yescomplemented
127#2547C2212yescomplemented
128#2543C2218yescomplemented
129#2543C2214yescomplemented
130#2542C2212yescomplemented
131#2541C2212yescomplemented
132#2539C2212yes—
133#2536C2214yescomplemented
134#2535C2214yescomplemented
135#2535C2214yescomplemented
136#2534C2214yes—
137#2504C2212yes—
138#2502C2212yes—
139#2487C2214yes—
140#2484C2212yes—
141#2482C2212yes—
142#2482C2212yes—
143#2482C2212yes—
144#2481C2218yescomplemented
145#2473C2218yescomplemented
146#2467C2218yescomplemented
147#2464C2218yescomplemented
148#2464C2218yescomplemented
149#2463C2218yescomplemented
150#2460C2218yescomplemented
151#2456C2218yescomplemented
152#2449C2218yescomplemented
153#2443C2218yescomplemented
154#2435C2212yes—
155#2433C2212yes—
156#2428C2218yescomplemented
157#2422C2218yescomplemented
158#2412C2214yes—
159#2410C2214yes—
160#2410C2214yes—
161#2410C2214yes—
162#2408C2214yes—
163#2406C2212yes—
164#2404C2212yes—
165#2404C2212yes—
166#2404C2212yes—
167#2398C2214yescomplemented
168#2397C2214yescomplemented
169#2343C2214yescomplemented
170#2343C2214yescomplemented
171#2343C2214yescomplemented
172#2343C2214yescomplemented
173#2328C2214yescomplemented
174#2326C2214yescomplemented
175#2325C2218yescomplemented
176#2322C2214yes—
177#2321C2214yes—
178#2315C2212yes—
179#2313C2212yes—
180#2313C2212yes—
181C4×#121C2218yescomplemented
182C4×#120C2214yes—
183C4×#120C2214yes—
184#2283C2212yes—
185#2283C2211yescharacteristic
186#2283C2211yescharacteristic
187C2×#381C2212yes—
188#2273C2212yes—
189C22×#41C2312yes—
190C23×D4C2311yescharacteristic
191C23×D4C2311yescharacteristic
192C23×D4C2311yescharacteristic
193C23×D4C2311yescharacteristic
194C23×D4C2311yescharacteristic
195C23×D4C2311yescharacteristic
196C24×C4C2311yescharacteristic
197C24×C4C2311yescharacteristic
198C24×C4C2311yescharacteristic
199C24×C4C2311yescharacteristic
200C24×C4C2311yescharacteristic
201C24×C4C2311yescharacteristic
202#553—232no—
203#553—232no—
204#553—232no—
205#553—232no—
206#542—216no—
207#542—216no—
208#541—216no—
209#540—216no—
210#539—216no—
211#539—216no—
212#538—216no—
213#538—216no—
214#533—28no—
215#532—28no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#127C2314yes—
221#529—232no—
222#529—232no—
223C2×#126—28no—
224C2×#126—28no—
225C2×#126C2312yes—
226C2×#126C2312yes—
227C2×#126C2314yes—
228C2×#126C2312yes—
229C2×#126C2314yes—
230C2×#126C2312yes—
231C2×#126C2314yes—
232C2×#126C2314yes—
233C2×#126C2314yes—
234C2×#126C2314yes—
235C2×#125—28no—
236C2×#125C2312yes—
237C2×#125C2314yes—
238C2×#125C2314yes—
239C2×#125C2314yes—
240C2×#125C2314yes—
241C2×#124C2312yes—
242C2×#124C2314yes—
243C2×#124C2314yes—
244C2×#124C2314yes—
245#525—216no—
246C2×#123—28no—
247C2×#123—28no—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×#123C2314yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×#121—28no—
267C2×#121—28no—
268C2×#121—28no—
269C2×#121—28no—
270C2×#121C2314yes—
271C2×#121C2312yes—
272C2×#121C2312yes—
273C2×#121C2312yes—
274C2×#121C2314yes—
275C2×#121C2314yes—
276C2×#121C2314yes—
277C2×#121C2314yes—
278C2×#121C2314yes—
279C2×#121C2314yes—
280C2×#121C2314yes—
281C2×#121C2312yes—
282C2×#121C2314yes—
283C2×#121C2314yes—
284C2×#121C2318yes—
285C2×#121C2318yes—
286C2×#121C2314yes—
287C2×#121C2314yes—
288C2×#121C2318yes—
289C2×#121C2318yes—
290C2×#120C2314yes—
291C2×#120C2314yes—
292C2×#120C2314yes—
293C2×#120C2314yes—
294C4×#41—216no—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×D4—28no—
300C2×C4×D4—28no—
301C2×C4×D4—28no—
302C2×C4×D4—28no—
303C2×C4×D4C2312yes—
304C2×C4×D4C2314yes—
305C2×C4×D4C2314yes—
306C2×C4×D4C2314yes—
307C2×C4×D4C2314yes—
308C2×C4×D4C2314yes—
309C2×C4×D4C2314yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2314yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2314yes—
321C2×C4×D4C2318yes—
322C2×C4×D4C2318yes—
323C2×#117D4116yescomplemented
324C2×#117C2314yes—
325C2×#117C2312yes—
326C2×#117C2312yes—
327C2×#117C2312yes—
328C2×#117C2312yes—
329C2×#117C2312yes—
330C22×C4⋊C4—28no—
331C22×C4⋊C4C2311yescharacteristic
332C22×C4⋊C4C2311yescharacteristic
333C22×C4⋊C4C2311yescharacteristic
334C22×C4⋊C4C2311yescharacteristic
335C22×C4⋊C4C2311yescharacteristic
336C22×C4⋊C4C2314yes—
337C22×C4⋊C4C2314yes—
338C22×C4⋊C4C2311yescharacteristic
339C22×C4⋊C4C2311yescharacteristic
340C22×C4⋊C4C2311yescharacteristic
341C22×C4⋊C4C2311yescharacteristic
342C22×C4⋊C4C2311yescharacteristic
343C22×C22⋊C4C2311yescharacteristic
344C22×C22⋊C4C2311yescharacteristic
345C22×C22⋊C4C2311yescharacteristic
346C22×C22⋊C4C2311yescharacteristic
347C22×C22⋊C4C2311yescharacteristic
348C22×C22⋊C4C2311yescharacteristic
349C22×C22⋊C4C2311yescharacteristic
350C22×C22⋊C4C2311yescharacteristic
351C22×C22⋊C4C2314yes—
352C22×C22⋊C4C2311yescharacteristic
353C22×C22⋊C4C2311yescharacteristic
354C22×C42C2314yes—
355C22×C42C2311yescharacteristic
356C22×C42C2311yescharacteristic
357C22×C42C2311yescharacteristic
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2318yes—
362#400C2318yes—
363#399C2314yes—
364#399C2314yes—
365#399C2314yes—
366#399C2314yes—
367#399C2314yes—
368#399C2318yes—
369#399C2318yes—
370#398C2318yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2318yes—
375#398C2318yes—
376#398C2318yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2318yes—
381#397C2314yes—
382#397C2318yes—
383#397C2318yes—
384#397C2314yes—
385#396C2318yes—
386#396C2318yes—
387#396C2318yes—
388#396C2318yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#394C2318yes—
393#394C2318yes—
394#394C2318yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2318yes—
399#394C2318yes—
400#394C2318yes—
401#394C2318yes—
402#394C2318yes—
403#394C2318yes—
404#394C2318yes—
405#393C2314yes—
406#393C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2314yes—
410#392C2314yes—
411#392C2314yes—
412#392C2314yes—
413#392C2318yes—
414#392C2318yes—
415#392C2314yes—
416#392C2318yes—
417#392C2318yes—
418#392C2314yes—
419#392C2318yes—
420#392C2318yes—
421#392C2318yes—
422#391C2314yes—
423#390C2314yes—
424#390C2318yes—
425#390C2318yes—
426#390C2314yes—
427#390C2314yes—
428#390C2318yes—
429#389C2318yes—
430#389C2318yes—
431#389C2318yes—
432#388C2318yes—
433#388C2318yes—
434#388C2318yes—
435#388C2318yes—
436#388C2318yes—
437#388C2318yes—
438#388C2318yes—
439#388C2318yes—
440#388C2318yes—
441#388C2318yes—
442#388C2318yes—
443#387C2318yes—
444#387C2318yes—
445#387C2318yes—
446#387C2318yes—
447#387C2318yes—
448#387C2318yes—
449#387C2318yes—
450#387C2318yes—
451#387C2318yes—
452#386C2318yes—
453#386C2314yes—
454#386C2318yes—
455#386C2314yes—
456#386C2318yes—
457#386C2318yes—
458#386C2318yes—
459#386C2318yes—
460#386C2318yes—
461#386C2318yes—
462#386C2314yes—
463#386C2314yes—
464#386C2318yes—
465#386C2318yes—
466#386C2318yes—
467#386C2318yes—
468#386C2318yes—
469#386C2318yes—
470#386C2318yes—
471#385C2318yes—
472#385C2318yes—
473#385C2318yes—
474#385C2314yes—
475#385C2314yes—
476#385C2318yes—
477#385C2318yes—
478#385C2318yes—
479#385C2318yes—
480#385C2318yes—
481#385C2318yes—
482#385C2318yes—
483#385C2318yes—
484#385C2314yes—
485#385C2314yes—
486#384C2314yes—
487#383C2312yes—
488#383C2312yes—
489#383C2314yes—
490#382C2314yes—
491#382C2314yes—
492#382C2312yes—
493#382C2312yes—
494#381C2314yes—
495#381C2314yes—
496#381C2314yes—
497#381C2314yes—
498#381C2312yes—
499#381C2312yes—
500#380C2314yes—
501#380C2314yes—
502#380C2318yes—
503#380C2314yes—
504#380C2312yes—
505#380C2312yes—
506#380C2314yes—
507#380C2314yes—
508#380C2318yes—
509#379C2314yes—
510#379C2314yes—
511#379C2314yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2314yes—
514C4×C4⋊C4C2312yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2318yes—
519C4×C22⋊C4C2318yes—
520C4×C22⋊C4C2318yes—
521C4×C22⋊C4C2318yes—
522#376C2312yes—
523#376C2312yes—
524#376C2314yes—
525C2×#95C2314yes—
526C2×#95C2314yes—
527C25C2411yescharacteristic
528C25C2411yescharacteristic
529C25C2411yescharacteristic
530C25C2411yescharacteristic
531C2×#41—28no—
532C2×#41—48no—
533C22×Q8C2412yes—
534C22×Q8C2412yes—
535C22×Q8C2412yes—
536C22×D4—24no—
537C22×D4—24no—
538C22×D4—24no—
539C22×D4—24no—
540C22×D4—24no—
541C22×D4—24no—
542C22×D4—44no—
543C22×D4—44no—
544C22×D4—44no—
545C22×D4—44no—
546C22×D4—82no—
547C22×D4—82no—
548C22×D4C2414yes—
549C22×D4C2414yes—
550C22×D4C2414yes—
551C22×D4C2412yes—
552C22×D4C2412yes—
553C22×D4C2414yes—
554C22×D4C2412yes—
555C22×D4C2414yes—
556C22×D4C2414yes—
557C22×D4C2418yes—
558C22×D4C2412yes—
559C22×D4C2412yes—
560C22×D4C2414yes—
561C22×D4C2414yes—
562C22×D4C2418yes—
563C22×D4C2418yes—
564C23×C4—24no—
565C23×C4—24no—
566C23×C4—24no—
567C23×C4—24no—
568C23×C4—24no—
569C23×C4—44no—
570C23×C4—44no—
571C23×C4—82no—
572C23×C4—82no—
573C23×C4—82no—
574C23×C4—82no—
575C23×C4C2×D418yes—
576C23×C4C2411yescharacteristic
577C23×C4C2411yescharacteristic
578C23×C4C2411yescharacteristic
579C23×C4C2411yescharacteristic
580C23×C4C2411yescharacteristic
581C23×C4C2411yescharacteristic
582C23×C4C2411yescharacteristic
583C23×C4C2414yes—
584C23×C4C2412yes—
585C23×C4C2412yes—
586C23×C4C2414yes—
587C23×C4C2414yes—
588C23×C4C2414yes—
589C23×C4C2414yes—
590C23×C4C2412yes—
591C23×C4C2412yes—
592C23×C4C2414yes—
593C23×C4C2418yes—
594C23×C4C2411yescharacteristic
595C23×C4C2411yescharacteristic
596C23×C4C2411yescharacteristic
597C23×C4C2411yescharacteristic
598C23×C4C2412yes—
599C23×C4C2412yes—
600C4⋊Q8—24no—
601C4⋊Q8—24no—
602C4⋊Q8—24no—
603#127—24no—
604#127—48no—
605#126—216no—
606#126—216no—
607#126—216no—
608#126—216no—
609#126—216no—
610#126—28no—
611#126—216no—
612#126—28no—
613#126—28no—
614#126—28no—
615#125—216no—
616#125—216no—
617#125—216no—
618#125—216no—
619#125—28no—
620#124—216no—
621#124—216no—
622#124—28no—
623#124—48no—
624#123—216no—
625#123—216no—
626#123—216no—
627#123—216no—
628#123—216no—
629#123—216no—
630#123—216no—
631#123—216no—
632#123—216no—
633#123—48no—
634C22⋊Q8—28no—
635C22⋊Q8—28no—
636C22⋊Q8—28no—
637C22⋊Q8—28no—
638C22⋊Q8—216no—
639C22⋊Q8—216no—
640C22⋊Q8—84no—
641C22⋊Q8—84no—
642#121—216no—
643#121—216no—
644#121—28no—
645#121—28no—
646#121—28no—
647#121—28no—
648#121—216no—
649#121—216no—
650#121—216no—
651#121—216no—
652#121—216no—
653#121—216no—
654#121—216no—
655#121—216no—
656#121—416no—
657#121—416no—
658#121—84no—
659#121—88no—
660#121—88no—
661#121—84no—
662#120—216no—
663#120—48no—
664#120—48no—
665#120—48no—
666C4×Q8—28no—
667C4×Q8—28no—
668C4×Q8—28no—
669C4×Q8—28no—
670C4×D4—216no—
671C4×D4—216no—
672C4×D4—216no—
673C4×D4—216no—
674C4×D4—216no—
675C4×D4—216no—
676C4×D4—216no—
677C4×D4—216no—
678C4×D4—216no—
679C4×D4—216no—
680C4×D4—28no—
681C4×D4—28no—
682C4×D4—28no—
683C4×D4—28no—
684C4×D4—28no—
685C4×D4—28no—
686C4×D4—28no—
687C4×D4—28no—
688C4×D4—88no—
689C4×D4—88no—
690#117—28no—
691#117—216no—
692#117C2×D4116yes—
693#117C2×D4116yes—
694#117C2×D4116yes—
695#117C2×D4116yes—
696C2×C4⋊C4—24no—
697C2×C4⋊C4—24no—
698C2×C4⋊C4—24no—
699C2×C4⋊C4—24no—
700C2×C4⋊C4—24no—
701C2×C4⋊C4—24no—
702C2×C4⋊C4—24no—
703C2×C4⋊C4—24no—
704C2×C4⋊C4—216no—
705C2×C4⋊C4—216no—
706C2×C4⋊C4C2×D418yes—
707C2×C4⋊C4C2×D418yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2412yes—
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2418yes—
733C2×C4⋊C4C2418yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2418yes—
736C2×C4⋊C4C2418yes—
737C2×C4⋊C4C2418yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2418yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C22⋊C4—24no—
745C2×C22⋊C4—24no—
746C2×C22⋊C4—24no—
747C2×C22⋊C4—24no—
748C2×C22⋊C4—24no—
749C2×C22⋊C4—24no—
750C2×C22⋊C4—24no—
751C2×C22⋊C4—24no—
752C2×C22⋊C4—48no—
753C2×C22⋊C4C2×D418yes—
754C2×C22⋊C4C2×D418yes—
755C2×C22⋊C4C2412yes—
756C2×C22⋊C4C2412yes—
757C2×C22⋊C4C2412yes—
758C2×C22⋊C4C2412yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2412yes—
761C2×C22⋊C4C2412yes—
762C2×C22⋊C4C2412yes—
763C2×C22⋊C4C2412yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2412yes—
769C2×C22⋊C4C2412yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2418yes—
780C2×C22⋊C4C2418yes—
781C2×C22⋊C4C2418yes—
782C2×C22⋊C4C2418yes—
783C2×C22⋊C4C2418yes—
784C2×C22⋊C4C2418yes—
785C2×C22⋊C4C2418yes—
786C2×C22⋊C4C2418yes—
787C2×C22⋊C4C2418yes—
788C2×C22⋊C4C2418yes—
789C2×C22⋊C4C2418yes—
790C2×C22⋊C4C2418yes—
791C2×C22⋊C4C2418yes—
792C2×C22⋊C4C2418yes—
793C2×C22⋊C4C2418yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2412yes—
798C2×C42—24no—
799C2×C42—216no—
800C2×C42C2×D418yes—
801C2×C42C2×D418yes—
802C2×C42C2414yes—
803C2×C42C2414yes—
804C2×C42C2414yes—
805C2×C42C2414yes—
806C2×C42C2418yes—
807C2×C42C2414yes—
808C2×C42C2414yes—
809C2×C42C2412yes—
810C2×C42C2411yescharacteristic
811C2×C42C2411yescharacteristic
812C2×C42C2412yes—
813C2×C42C2411yescharacteristic
814C2×C42C2411yescharacteristic
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2418yes—
820#95C2418yes—
821#95C2414yes—
822#95C2418yes—
823#95C2414yes—
824#95C2418yes—
825#95C2414yes—
826#95C2414yes—
827#95C2418yes—
828#95C2418yes—
829#95C2418yes—
830#95C2418yes—
831#95C2418yes—
832#95C2418yes—
833#95C2418yes—
834#95C2418yes—
835#95C2418yes—
836#95C2418yes—
837C24—22no—
838C24—24no—
839C24—24no—
840C24—22no—
841C24—22no—
842C24—24no—
843C24—24no—
844C24—24no—
845C24—42no—
846C24—42no—
847C24—42no—
848C24—42no—
849C24—42no—
850C24—42no—
851C24—42no—
852C24C22×D414yes—
853C24C2512yes—
854C24C2512yes—
855C24C2514yes—
856C24C2512yes—
857C24C2512yes—
858C24C2511yescharacteristic
859#41—432no—
860C2×Q8—24no—
861C2×Q8—24no—
862C2×Q8—24no—
863C2×Q8—44no—
864C2×Q8—44no—
865C2×Q8—44no—
866C2×D4—28no—
867C2×D4—28no—
868C2×D4—28no—
869C2×D4—28no—
870C2×D4—28no—
871C2×D4—28no—
872C2×D4—24no—
873C2×D4—24no—
874C2×D4—28no—
875C2×D4—28no—
876C2×D4—28no—
877C2×D4—28no—
878C2×D4—216no—
879C2×D4—28no—
880C2×D4—28no—
881C2×D4—24no—
882C2×D4—24no—
883C2×D4—24no—
884C2×D4—24no—
885C2×D4—24no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—44no—
889C2×D4—48no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—416no—
893C2×D4—48no—
894C2×D4—48no—
895C2×D4—48no—
896C2×D4—48no—
897C2×D4—48no—
898C2×D4—48no—
899C2×D4—44no—
900C2×D4—48no—
901C2×D4—48no—
902C2×D4—48no—
903C2×D4—44no—
904C2×D4—48no—
905C2×D4—48no—
906C2×D4—48no—
907C2×D4—416no—
908C2×D4—416no—
909C2×D4—416no—
910C2×D4—88no—
911C2×D4—88no—
912C22×C4—24no—
913C22×C4—24no—
914C22×C4—22no—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—22no—
919C22×C4—24no—
920C22×C4—28no—
921C22×C4—28no—
922C22×C4—28no—
923C22×C4—28no—
924C22×C4—28no—
925C22×C4—24no—
926C22×C4—24no—
927C22×C4—28no—
928C22×C4—24no—
929C22×C4—24no—
930C22×C4—416no—
931C22×C4—44no—
932C22×C4—44no—
933C22×C4—48no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—44no—
943C22×C4—44no—
944C22×C4—48no—
945C22×C4—48no—
946C22×C4—48no—
947C22×C4—48no—
948C22×C4—44no—
949C22×C4—44no—
950C22×C4—44no—
951C22×C4—44no—
952C22×C4—48no—
953C22×C4—48no—
954C22×C4—48no—
955C22×C4—416no—
956C22×C4—88no—
957C22×C4—88no—
958C22×C4—88no—
959C22×C4—88no—
960C22×C4C22×D414yes—
961C22×C4C22×D414yes—
962C22×C4C22×D414yes—
963C22×C4C22×D414yes—
964C22×C4C22×D414yes—
965C22×C4C22×D414yes—
966C22×C4C22×D418yes—
967C22×C4C22×D418yes—
968C22×C4C2518yes—
969C22×C4C2518yes—
970C22×C4C2514yes—
971C22×C4C2514yes—
972C22×C4C2512yes—
973C22×C4C2512yes—
974C22×C4C2512yes—
975C22×C4C2512yes—
976C22×C4C2512yes—
977C22×C4C2514yes—
978C22×C4C2511yescharacteristic
979C22×C4C2511yescharacteristic
980C22×C4C2512yes—
981C22×C4C2512yes—
982C22×C4C2511yescharacteristic
983C22×C4C2511yescharacteristic
984C22×C4C2512yes—
985C22×C4C2511yescharacteristic
986C22×C4C2511yescharacteristic
987C4⋊C4—28no—
988C4⋊C4—28no—
989C4⋊C4—24no—
990C4⋊C4—24no—
991C4⋊C4—28no—
992C4⋊C4—24no—
993C4⋊C4—24no—
994C4⋊C4—24no—
995C4⋊C4—24no—
996C4⋊C4—28no—
997C4⋊C4—24no—
998C4⋊C4—24no—
999C4⋊C4—24no—
1000C4⋊C4—24no—
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—24no—
1004C4⋊C4—24no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—28no—
1008C4⋊C4—28no—
1009C4⋊C4—24no—
1010C4⋊C4—24no—
1011C4⋊C4—48no—
1012C4⋊C4—48no—
1013C4⋊C4—48no—
1014C4⋊C4—48no—
1015C4⋊C4—44no—
1016C4⋊C4—48no—
1017C4⋊C4—44no—
1018C4⋊C4—48no—
1019C4⋊C4C22×D418yes—
1020C4⋊C4C22×D418yes—
1021C4⋊C4C22×D418yes—
1022C4⋊C4C22×D418yes—
1023C22⋊C4—28no—
1024C22⋊C4—28no—
1025C22⋊C4—28no—
1026C22⋊C4—28no—
1027C22⋊C4—28no—
1028C22⋊C4—28no—
1029C22⋊C4—216no—
1030C22⋊C4—24no—
1031C22⋊C4—24no—
1032C22⋊C4—28no—
1033C22⋊C4—24no—
1034C22⋊C4—24no—
1035C22⋊C4—24no—
1036C22⋊C4—24no—
1037C22⋊C4—24no—
1038C22⋊C4—24no—
1039C22⋊C4—28no—
1040C22⋊C4—24no—
1041C22⋊C4—24no—
1042C22⋊C4—28no—
1043C22⋊C4—28no—
1044C22⋊C4—28no—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—28no—
1048C22⋊C4—48no—
1049C22⋊C4—48no—
1050C22⋊C4—48no—
1051C22⋊C4—48no—
1052C22⋊C4—48no—
1053C22⋊C4—48no—
1054C22⋊C4—48no—
1055C22⋊C4—48no—
1056C22⋊C4—48no—
1057C22⋊C4—48no—
1058C22⋊C4—48no—
1059C22⋊C4—48no—
1060C22⋊C4—48no—
1061C22⋊C4—48no—
1062C22⋊C4C22×D418yes—
1063C22⋊C4C22×D418yes—
1064C22⋊C4C22×D418yes—
1065C22⋊C4C22×D418yes—
1066C42—28no—
1067C42—28no—
1068C42—28no—
1069C42—28no—
1070C42—48no—
1071C42—44no—
1072C42—44no—
1073C42C22×D418yes—
1074C42C22×D414yes—
1075C42C22×D414yes—
1076C42C22×D418yes—
1077C42C22×D414yes—
1078C42C22×D414yes—
1079C23—22no—
1080C23—22no—
1081C23—28no—
1082C23—22no—
1083C23—24no—
1084C23—24no—
1085C23—24no—
1086C23—22no—
1087C23—24no—
1088C23—24no—
1089C23—28no—
1090C23—24no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—24no—
1095C23—24no—
1096C23—24no—
1097C23—24no—
1098C23—28no—
1099C23—24no—
1100C23—22no—
1101C23—28no—
1102C23—24no—
1103C23—24no—
1104C23—44no—
1105C23—44no—
1106C23—416no—
1107C23—44no—
1108C23—44no—
1109C23—44no—
1110C23—44no—
1111C23—44no—
1112C23—44no—
1113C23—44no—
1114C23—44no—
1115C23—88no—
1116C23—88no—
1117C23—88no—
1118C23C23×D414yes—
1119C23C23×D412yes—
1120C23#58514yes—
1121C23#58514yes—
1122C23C2611yescharacteristic
1123Q8—48no—
1124Q8—84no—
1125Q8—84no—
1126D4—416no—
1127D4—48no—
1128D4—48no—
1129D4—416no—
1130D4—48no—
1131D4—416no—
1132D4—416no—
1133D4—84no—
1134D4—84no—
1135D4—88no—
1136D4—88no—
1137D4—816no—
1138D4—88no—
1139D4—88no—
1140D4—816no—
1141D4—168no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—22no—
1146C2×C4—24no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—28no—
1152C2×C4—28no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—28no—
1162C2×C4—28no—
1163C2×C4—28no—
1164C2×C4—28no—
1165C2×C4—28no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—28no—
1171C2×C4—28no—
1172C2×C4—28no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—48no—
1177C2×C4—48no—
1178C2×C4—44no—
1179C2×C4—44no—
1180C2×C4—44no—
1181C2×C4—44no—
1182C2×C4—416no—
1183C2×C4—416no—
1184C2×C4—44no—
1185C2×C4—44no—
1186C2×C4—44no—
1187C2×C4—44no—
1188C2×C4—44no—
1189C2×C4—88no—
1190C2×C4—88no—
1191C2×C4—88no—
1192C2×C4—88no—
1193C2×C4—84no—
1194C2×C4—84no—
1195C2×C4—84no—
1196C2×C4—84no—
1197C2×C4—168no—
1198C2×C4C23×D412yes—
1199C2×C4C23×D414yes—
1200C2×C4C23×D414yes—
1201C2×C4C23×D414yes—
1202C2×C4C23×D412yes—
1203C2×C4C23×D412yes—
1204C2×C4C23×D412yes—
1205C2×C4C23×D412yes—
1206C2×C4C23×D412yes—
1207C22—22no—
1208C22—22no—
1209C22—28no—
1210C22—24no—
1211C22—24no—
1212C22—24no—
1213C22—24no—
1214C22—28no—
1215C22—416no—
1216C22—42no—
1217C22—42no—
1218C22—48no—
1219C22—44no—
1220C22—44no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—44no—
1226C22—44no—
1227C22—42no—
1228C22—42no—
1229C22—48no—
1230C22—48no—
1231C22—44no—
1232C22—48no—
1233C22—44no—
1234C22—88no—
1235C22—88no—
1236C22—88no—
1237C22#344914yes—
1238C22C24×D411yescharacteristic
1239C22C2×#58512yes—
1240C22C2×#58512yes—
1241C22H(7,𝔽2)12yes—
1242C4—24no—
1243C4—22no—
1244C4—22no—
1245C4—24no—
1246C4—22no—
1247C4—22no—
1248C4—22no—
1249C4—24no—
1250C4—22no—
1251C4—42no—
1252C4—44no—
1253C4—42no—
1254C4—42no—
1255C4—42no—
1256C4—44no—
1257C4—42no—
1258C4—44no—
1259C4—48no—
1260C4—48no—
1261C2—24no—
1262C2—44no—
1263C2—44no—
1264C2—84no—
1265C2—82no—
1266C2—82no—
1267C2C2×#344911yescharacteristic
1268C2#6281111yescharacteristic
1269C2#6285211yescharacteristic
1270C2#6296314yes—
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. C22×#553C2semidirect
2. C2×#3455C2semidirect
3. #42393C2semidirect
4. #42391C2semidirect
5. #41961C2semidirect
6. #41959C2semidirect
7. #39850C2semidirect
8. #39848C2semidirect
9. #37548C2semidirect
10. #37547C2semidirect
11. #37446C2semidirect
12. #37185C2semidirect
13. #37120C2semidirect
14. #36709C2semidirect
15. #36706C2semidirect
16. #35395C2semidirect
17. #35394C2semidirect
18. #35240C2semidirect
19. #35237C2semidirect
20. #35143C2semidirect
21. #35063C2semidirect
22. #34989C2semidirect
23. #34987C2semidirect
24. #34963C2semidirect
25. #34177C2semidirect
32. C2×#542C22semidirect
33. C2×#542C22semidirect
34. C2×#541C22semidirect
35. C2×#540C22semidirect
42. C2×#529C22semidirect
43. C2×#529C22semidirect
62. #2852C22semidirect
68. #2821C22semidirect
69. #2821C22semidirect
70. #2821C22semidirect
71. #2818C22semidirect
72. #2816C22semidirect
73. #2815C22semidirect
74. #2721C22semidirect
75. #2719C22semidirect
76. #2714C22semidirect
77. #2711C22semidirect
78. #2695C22semidirect
79. #2694C22semidirect
80. #2693C22semidirect
81. #2691C22semidirect
82. #2690C22semidirect
83. #2676C22semidirect
84. #2676C22semidirect
85. #2675C22semidirect
86. #2673C22semidirect
87. #2672C22semidirect
88. #2671C22semidirect
89. #2671C22semidirect
90. #2664C22semidirect
91. #2662C22semidirect
92. #2656C22semidirect
93. #2639C22semidirect
94. #2638C22semidirect
95. #2637C22semidirect
96. #2637C22semidirect
97. #2636C22semidirect
98. #2636C22semidirect
99. #2635C22semidirect
100. #2635C22semidirect
101. #2633C22semidirect
102. #2631C22semidirect
109. #2604C22semidirect
110. #2604C22semidirect
111. #2603C22semidirect
112. #2603C22semidirect
113. #2601C22semidirect
114. #2600C22semidirect
115. #2598C22semidirect
118. #2580C22semidirect
120. #2564C22semidirect
121. #2563C22semidirect
123. #2559C22semidirect
124. #2557C22semidirect
125. #2555C22semidirect
126. #2553C22semidirect
127. #2547C22semidirect
128. #2543C22semidirect
129. #2543C22semidirect
130. #2542C22semidirect
131. #2541C22semidirect
133. #2536C22semidirect
134. #2535C22semidirect
135. #2535C22semidirect
144. #2481C22semidirect
145. #2473C22semidirect
146. #2467C22semidirect
147. #2464C22semidirect
148. #2464C22semidirect
149. #2463C22semidirect
150. #2460C22semidirect
151. #2456C22semidirect
152. #2449C22semidirect
153. #2443C22semidirect
156. #2428C22semidirect
157. #2422C22semidirect
167. #2398C22semidirect
168. #2397C22semidirect
169. #2343C22semidirect
170. #2343C22semidirect
171. #2343C22semidirect
172. #2343C22semidirect
173. #2328C22semidirect
174. #2326C22semidirect
175. #2325C22semidirect
181. C4×#121C22semidirect
323. C2×#117D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5532
C2×#34552
#423932
#423912
#419612
#419592
#398502
#398482
#375482
#375472
#374462
#371852
#371202
#367092
#367062
#353952
#353942
#352402
#352372
#351432
#350632
#349892
#349872
#349632
#341772