Finite Group Databasebeta

← #8726245

Subgroups — #8726245

Order 512.

5479 conjugacy classes of subgroups.

The subgroup lattice has 1562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59817C211yesmaximal, characteristic, complemented
2#59809C212yesmaximal, complemented
3#59481C212yesmaximal, complemented
4#59075C212yesmaximal, complemented
5#59043C212yesmaximal, complemented
6#58943C212yesmaximal, complemented
7#58128C214yesmaximal, complemented
8#57001C214yesmaximal, complemented
9#55126C214yesmaximal, complemented
10#53005C211yesmaximal, characteristic, complemented
11#52956C212yesmaximal, complemented
12#52297C211yesmaximal, characteristic, complemented
13#47814C212yesmaximal, complemented
14#47134C214yesmaximal, complemented
15#45308C211yesmaximal, characteristic, complemented
16#45248C212yesmaximal, complemented
17#44377C212yesmaximal, complemented
18#44260C214yesmaximal, complemented
19#42913C211yesmaximal, characteristic, complemented
20#42855C212yesmaximal, complemented
21#42107C212yesmaximal, complemented
22#41180C214yesmaximal, complemented
23#39858C212yesmaximal, complemented
24#39790C212yesmaximal, complemented
25#39215C212yesmaximal, complemented
26#39169C211yesmaximal, characteristic, complemented
27#39166C212yesmaximal, complemented
28#35757C211yesmaximal, characteristic, complemented
29#35687C212yesmaximal, complemented
30C22×2−1+4C2211yescharacteristic
31C2×#554C2211yescharacteristic
32C2×#550C2211yescharacteristic
33C2×D4×Q8C2212yes—
34C2×D4×Q8C2212yes—
35C2×D4×Q8C2212yes—
36C2×#548C2212yes—
37C2×#548C2212yes—
38C2×#536C2211yescharacteristic
39C2×#529C2212yes—
40#2858C2211yescharacteristic
41#2850C2212yes—
42#2844C2212yes—
43#2838C2214yes—
44#2832C2214yes—
45#2829C2214yes—
46#2829C2214yes—
47#2826C2214yes—
48#2825C2214yes—
49#2824C2212yes—
50#2816C2212yes—
51#2803C2212yes—
52#2803C2214yes—
53#2800C2214yes—
54#2797C2214yes—
55#2795C2211yescharacteristic
56#2792C2211yescharacteristic
57#2789C2212yes—
58#2787C2214yes—
59#2785C2212yes—
60#2784C2214yes—
61#2784C2211yescharacteristic
62#2780C2214yes—
63#2780C2214yes—
64#2780C2214yes—
65#2779C2214yes—
66#2763C2212yes—
67#2759C2214yes—
68#2758C2214yes—
69#2756C2212yes—
70#2753C2214yes—
71#2742C2212yes—
72#2737C2212yes—
73#2731C2214yes—
74#2730C2214yes—
75#2729C2214yes—
76#2728C2214yes—
77#2727C2214yes—
78#2723C2214yes—
79#2722C2214yes—
80#2716C2214yes—
81#2715C2214yes—
82#2714C2212yes—
83#2714C2214yes—
84#2714C2214yes—
85#2714C2214yes—
86#2713C2214yes—
87#2710C2214yes—
88#2709C2214yes—
89#2708C2214yes—
90#2705C2212yes—
91#2705C2214yes—
92#2703C2214yes—
93#2702C2214yes—
94#2699C2211yescharacteristic
95#2696C2214yes—
96#2692C2214yes—
97#2691C2214yes—
98#2689C2214yes—
99#2683C2212yes—
100#2683C2214yes—
101#2683C2212yes—
102#2681C2214yes—
103#2677C2214yes—
104#2676C2214yes—
105#2676C2214yes—
106#2674C2214yes—
107#2673C2212yes—
108#2673C2214yes—
109#2662C2214yes—
110#2652C2214yes—
111#2651C2214yes—
112#2648C2214yes—
113#2641C2212yes—
114#2639C2214yes—
115#2639C2212yes—
116#2638C2212yes—
117#2631C2214yes—
118#2624C2211yescharacteristic
119#2616C2212yes—
120#2616C2214yes—
121#2615C2212yes—
122#2615C2211yescharacteristic
123#2612C2214yes—
124#2612C2212yes—
125#2610C2214yes—
126#2598C2214yes—
127#2597C2214yes—
128#2588C2214yes—
129#2577C2214yes—
130#2576C2214yes—
131#2566C2212yes—
132#2565C2212yes—
133#2564C2212yes—
134#2564C2214yes—
135#2563C2211yescharacteristic
136#2562C2212yes—
137#2559C2214yes—
138#2557C2214yes—
139#2556C2214yes—
140#2554C2214yes—
141#2554C2214yes—
142#2551C2212yes—
143#2549C2214yes—
144#2545C2212yes—
145#2544C2212yes—
146#2543C2214yes—
147#2541C2211yescharacteristic
148#2541C2212yes—
149#2540C2212yes—
150#2538C2212yes—
151#2538C2212yes—
152#2535C2212yes—
153#2531C2214yes—
154#2530C2214yes—
155#2523C2212yes—
156#2520C2214yes—
157#2512C2212yes—
158#2496C2212yes—
159#2494C2212yes—
160#2492C2212yes—
161#2492C2214yes—
162#2490C2212yes—
163#2489C2212yes—
164#2489C2212yes—
165#2488C2214yes—
166#2487C2212yes—
167#2477C2214yes—
168#2474C2214yes—
169#2464C2214yes—
170#2463C2214yes—
171#2461C2214yes—
172#2457C2214yes—
173#2456C2214yes—
174#2453C2212yes—
175#2452C2214yes—
176#2452C2214yes—
177#2452C2214yes—
178#2451C2212yes—
179#2450C2214yes—
180#2450C2214yes—
181#2450C2214yes—
182#2450C2214yes—
183#2448C2212yes—
184#2446C2212yes—
185#2446C2212yes—
186#2439C2214yes—
187#2436C2212yes—
188#2436C2211yescharacteristic
189#2436C2211yescharacteristic
190#2436C2212yes—
191#2434C2214yes—
192#2434C2212yes—
193#2432C2214yes—
194#2432C2212yes—
195#2432C2214yes—
196#2432C2212yes—
197#2431C2214yes—
198#2431C2212yes—
199#2429C2212yes—
200#2427C2212yes—
201#2426C2212yes—
202#2425C2214yes—
203#2422C2212yes—
204#2421C2212yes—
205#2421C2212yes—
206#2417C2212yes—
207#2416C2212yes—
208#2416C2212yes—
209#2409C2211yescharacteristic
210#2409C2212yes—
211#2409C2214yes—
212#2409C2212yes—
213#2409C2212yes—
214#2409C2212yes—
215#2409C2211yescharacteristic
216#2407C2212yes—
217#2407C2212yes—
218#2407C2214yes—
219#2407C2214yes—
220#2407C2212yes—
221#2407C2214yes—
222#2407C2212yes—
223#2395C2211yescharacteristic
224#2392C2212yes—
225#2388C2211yescharacteristic
226#2388C2212yes—
227#2388C2212yes—
228#2388C2214yes—
229#2373C2214yes—
230#2367C2212yes—
231#2366C2212yes—
232#2365C2212yes—
233#2364C2214yes—
234#2364C2214yes—
235#2360C2212yes—
236#2359C2214yes—
237#2356C2212yes—
238#2341C2211yescharacteristic
239#2341C2212yes—
240Q8×C22⋊C4C2212yes—
241Q8×C22⋊C4C2212yes—
242Q8×C22⋊C4C2212yes—
243#2339C2211yescharacteristic
244#2337C2214yes—
245#2334C2214yes—
246#2328C2212yes—
247#2328C2214yes—
248#2325C2214yes—
249#2323C2212yes—
250C4×C4⋊Q8C2212yes—
251C4×#127C2211yescharacteristic
252C4×#126C2212yes—
253C4×C22⋊Q8C2212yes—
254C4×#123C2212yes—
255C4×#121C2212yes—
256C4×#121C2212yes—
257#2295C2211yescharacteristic
258C2×#391C2212yes—
259C2×2−1+4—48no—
260C2×2−1+4—44no—
261C22×#41C2312yes—
262C22×#41C2311yescharacteristic
263C22×#41C2311yescharacteristic
264C22×#41C2311yescharacteristic
265C22×#41C2312yes—
266C22×#41C2314yes—
267C23×Q8C2312yes—
268C23×Q8C2311yescharacteristic
269C23×Q8C2312yes—
270C23×Q8C2312yes—
271C23×Q8C2311yescharacteristic
272#554—44no—
273#550—44no—
274D4×Q8—48no—
275D4×Q8—48no—
276D4×Q8—48no—
277#548—48no—
278#548—48no—
279#536—44no—
280C2×C4⋊Q8C2312yes—
281C2×C4⋊Q8C2312yes—
282C2×C4⋊Q8C2311yescharacteristic
283C2×C4⋊Q8C2314yes—
284C2×C4⋊Q8C2314yes—
285C2×C4⋊Q8C2314yes—
286C2×#127C2311yescharacteristic
287C2×#127C2312yes—
288C2×#127C2311yescharacteristic
289C2×#127C2312yes—
290#529—48no—
291C2×#126C2312yes—
292C2×#126C2314yes—
293C2×#126C2314yes—
294C2×#126C2314yes—
295C2×#125C2312yes—
296C2×#125C2312yes—
297C2×#124C2312yes—
298C2×#124C2314yes—
299C2×#124C2312yes—
300C2×#124C2314yes—
301C2×#124C2314yes—
302C2×#124C2312yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×#123C2312yes—
306C2×#123C2314yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2312yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2312yes—
314C2×C22⋊Q8C2312yes—
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2314yes—
317C2×C22⋊Q8C2314yes—
318C2×C22⋊Q8C2314yes—
319C2×C22⋊Q8C2312yes—
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2314yes—
322C2×C22⋊Q8C2314yes—
323C2×C22⋊Q8C2314yes—
324C2×C22⋊Q8C2314yes—
325C2×#121C2312yes—
326C2×#121C2312yes—
327C2×#121C2314yes—
328C2×#121C2312yes—
329C2×#121C2311yescharacteristic
330C2×#121C2312yes—
331C2×#121C2312yes—
332C2×#121C2314yes—
333C2×#121C2314yes—
334C2×#121C2311yescharacteristic
335C2×#121C2314yes—
336C2×#121C2312yes—
337C2×#121C2312yes—
338C2×C4×Q8C2312yes—
339C2×C4×Q8C2311yescharacteristic
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2312yes—
342C2×C4×Q8C2312yes—
343C2×C4×Q8C2312yes—
344C2×C4×D4C2311yescharacteristic
345C2×C4×D4C2312yes—
346C2×C4×D4C2312yes—
347C2×C4×D4C2311yescharacteristic
348C2×C4×D4C2312yes—
349C2×C4×D4C2312yes—
350C2×C4×D4C2314yes—
351C2×C4×D4C2314yes—
352C2×C4×D4C2312yes—
353C2×C4×D4C2314yes—
354C2×C4×D4C2312yes—
355C2×C4×D4C2314yes—
356C2×C4×D4C2314yes—
357C2×C4×D4C2314yes—
358C2×C4×D4C2312yes—
359C2×C4×D4C2312yes—
360C2×#117C2311yescharacteristic
361C2×#117C2314yes—
362C22×C4⋊C4C2312yes—
363C22×C42C2312yes—
364#401C2314yes—
365#400C2314yes—
366#400C2311yescharacteristic
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2314yes—
377#399C2311yescharacteristic
378#399C2312yes—
379#399C2314yes—
380#399C2314yes—
381#399C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2311yescharacteristic
389#398C2312yes—
390#398C2314yes—
391#398C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2312yes—
404#397C2311yescharacteristic
405#397C2312yes—
406#397C2312yes—
407#397C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2312yes—
417#396C2312yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#395C2314yes—
423#395C2312yes—
424#395C2312yes—
425#395C2314yes—
426#395C2314yes—
427#395C2311yescharacteristic
428#395C2314yes—
429#395C2312yes—
430#395C2314yes—
431#395C2314yes—
432#395C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2312yes—
441#394C2314yes—
442#394C2314yes—
443#394C2312yes—
444#394C2312yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2312yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2311yescharacteristic
458#394C2312yes—
459#394C2314yes—
460#394C2312yes—
461#394C2312yes—
462#394C2312yes—
463#393C2312yes—
464#393C2312yes—
465#393C2312yes—
466#393C2312yes—
467#393C2312yes—
468#393C2314yes—
469#393C2314yes—
470#393C2312yes—
471#393C2314yes—
472#393C2312yes—
473#393C2312yes—
474#393C2314yes—
475#393C2314yes—
476#393C2314yes—
477#393C2312yes—
478#393C2312yes—
479#393C2311yescharacteristic
480#392C2311yescharacteristic
481#392C2312yes—
482#392C2312yes—
483#392C2314yes—
484#392C2314yes—
485#392C2314yes—
486#392C2314yes—
487#392C2314yes—
488#392C2314yes—
489#392C2314yes—
490#392C2314yes—
491#392C2312yes—
492#392C2312yes—
493#392C2314yes—
494#392C2312yes—
495#392C2312yes—
496#392C2314yes—
497#391C2312yes—
498#391C2312yes—
499#391C2312yes—
500#391C2312yes—
501#391C2314yes—
502#391C2312yes—
503#391C2314yes—
504#391C2314yes—
505#391C2314yes—
506#391C2312yes—
507#391C2314yes—
508#391C2314yes—
509#391C2314yes—
510#391C2312yes—
511#391C2312yes—
512#391C2314yes—
513#391C2312yes—
514#391C2312yes—
515#391C2314yes—
516#391C2314yes—
517#390C2311yescharacteristic
518#390C2311yescharacteristic
519#390C2312yes—
520#390C2312yes—
521#390C2312yes—
522#390C2312yes—
523#390C2312yes—
524#390C2314yes—
525#390C2314yes—
526#390C2312yes—
527#390C2314yes—
528#390C2314yes—
529#390C2312yes—
530#390C2312yes—
531#390C2312yes—
532#390C2314yes—
533#390C2314yes—
534#390C2312yes—
535#390C2314yes—
536#390C2314yes—
537#390C2314yes—
538#390C2312yes—
539#390C2312yes—
540#389C2314yes—
541#389C2314yes—
542#389C2314yes—
543#389C2312yes—
544#389C2314yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2312yes—
550#389C2314yes—
551#389C2312yes—
552#389C2312yes—
553#389C2312yes—
554#389C2312yes—
555#388C2312yes—
556#388C2312yes—
557#388C2312yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2312yes—
578#388C2312yes—
579#388C2314yes—
580#388C2312yes—
581#388C2314yes—
582#388C2314yes—
583#388C2312yes—
584#388C2312yes—
585#388C2312yes—
586#387C2312yes—
587#387C2312yes—
588#387C2312yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2312yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2312yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2312yes—
623#386C2314yes—
624#386C2314yes—
625#386C2312yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2312yes—
637#386C2314yes—
638#386C2314yes—
639#386C2312yes—
640#386C2312yes—
641#386C2312yes—
642#386C2312yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2312yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2312yes—
661#385C2314yes—
662#385C2312yes—
663#385C2314yes—
664#384C2311yescharacteristic
665#384C2312yes—
666#383C2312yes—
667#383C2314yes—
668#382C2312yes—
669#382C2312yes—
670#382C2314yes—
671#382C2314yes—
672#381C2312yes—
673#381C2312yes—
674#380C2311yescharacteristic
675#380C2312yes—
676#380C2312yes—
677#380C2312yes—
678#380C2312yes—
679#380C2312yes—
680#380C2314yes—
681#380C2314yes—
682#380C2314yes—
683#380C2312yes—
684#380C2314yes—
685#380C2314yes—
686#380C2311yescharacteristic
687#380C2312yes—
688#380C2314yes—
689#380C2312yes—
690#380C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2311yescharacteristic
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2314yes—
701C4×C4⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2311yescharacteristic
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2311yescharacteristic
715C4×C22⋊C4C2314yes—
716C4×C22⋊C4C2312yes—
717#376C2314yes—
718#376C2312yes—
719C2×#95C2312yes—
720C2×#95C2314yes—
721C2×#95C2314yes—
722C43C2311yescharacteristic
7232−1+4—464no—
724C2×#41—28no—
725C2×#41—24no—
726C2×#41—24no—
727C2×#41—44no—
728C2×#41—48no—
729C2×#41—42no—
730C2×#41—44no—
731C2×#41—44no—
732C2×#41—48no—
733C2×#41—44no—
734C2×#41—48no—
735C2×#41—44no—
736C2×#41—48no—
737C2×#41—44no—
738C22×Q8—28no—
739C22×Q8—28no—
740C22×Q8—28no—
741C22×Q8—28no—
742C22×Q8—42no—
743C22×Q8—44no—
744C22×Q8—44no—
745C22×Q8—48no—
746C22×Q8—42no—
747C22×Q8—44no—
748C22×Q8—44no—
749C22×Q8—44no—
750C22×Q8C2412yes—
751C22×Q8C2414yes—
752C22×Q8C2412yes—
753C22×Q8C2412yes—
754C22×Q8C2411yescharacteristic
755C22×Q8C2414yes—
756C22×Q8C2412yes—
757C22×Q8C2412yes—
758C22×Q8C2411yescharacteristic
759C22×D4C2411yescharacteristic
760C22×D4C2411yescharacteristic
761C22×D4C2412yes—
762C22×D4C2412yes—
763C22×D4C2412yes—
764C22×D4C2412yes—
765C22×D4C2414yes—
766C22×D4C2414yes—
767C22×D4C2411yescharacteristic
768C22×D4C2412yes—
769C22×D4C2412yes—
770C22×D4C2414yes—
771C22×D4C2412yes—
772C22×D4C2412yes—
773C22×D4C2414yes—
774C22×D4C2412yes—
775C22×D4C2412yes—
776C22×D4C2412yes—
777C22×D4C2411yescharacteristic
778C22×D4C2412yes—
779C22×D4C2411yescharacteristic
780C23×C4C2412yes—
781C23×C4C2411yescharacteristic
782C23×C4C2412yes—
783C23×C4C2411yescharacteristic
784C23×C4C2414yes—
785C23×C4C2412yes—
786C23×C4C2414yes—
787C23×C4C2412yes—
788C23×C4C2412yes—
789C23×C4C2414yes—
790C23×C4C2412yes—
791C23×C4C2414yes—
792C23×C4C2414yes—
793C23×C4C2412yes—
794C23×C4C2412yes—
795C4⋊Q8—28no—
796C4⋊Q8—28no—
797C4⋊Q8—42no—
798C4⋊Q8—48no—
799C4⋊Q8—48no—
800C4⋊Q8—48no—
801#127—24no—
802#127—28no—
803#127—44no—
804#127—42no—
805#126—44no—
806#126—48no—
807#126—48no—
808#126—48no—
809#125—44no—
810#125—44no—
811#124—28no—
812#124—48no—
813#124—44no—
814#124—44no—
815#124—48no—
816#124—48no—
817#123—48no—
818#123—48no—
819#123—44no—
820#123—48no—
821C22⋊Q8—28no—
822C22⋊Q8—28no—
823C22⋊Q8—28no—
824C22⋊Q8—48no—
825C22⋊Q8—48no—
826C22⋊Q8—48no—
827C22⋊Q8—48no—
828C22⋊Q8—48no—
829C22⋊Q8—44no—
830C22⋊Q8—44no—
831C22⋊Q8—48no—
832C22⋊Q8—48no—
833C22⋊Q8—48no—
834C22⋊Q8—44no—
835C22⋊Q8—48no—
836C22⋊Q8—44no—
837C22⋊Q8—44no—
838C22⋊Q8—44no—
839#121—28no—
840#121—48no—
841#121—44no—
842#121—48no—
843#121—48no—
844#121—44no—
845#121—44no—
846#121—48no—
847#121—44no—
848#121—42no—
849#121—42no—
850#121—44no—
851#121—44no—
852C4×Q8—28no—
853C4×Q8—24no—
854C4×Q8—44no—
855C4×Q8—44no—
856C4×Q8—44no—
857C4×Q8—44no—
858C4×D4—48no—
859C4×D4—44no—
860C4×D4—44no—
861C4×D4—44no—
862C4×D4—44no—
863C4×D4—48no—
864C4×D4—44no—
865C4×D4—44no—
866C4×D4—44no—
867C4×D4—44no—
868C4×D4—42no—
869C4×D4—42no—
870C4×D4—48no—
871C4×D4—48no—
872C4×D4—48no—
873C4×D4—48no—
874#117—42no—
875#117—48no—
876C2×C4⋊C4—44no—
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2411yescharacteristic
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2411yescharacteristic
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2414yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2412yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2414yes—
922C2×C4⋊C4C2412yes—
923C2×C4⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2411yescharacteristic
942C2×C22⋊C4C2411yescharacteristic
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2412yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2412yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2412yes—
956C2×C22⋊C4C2412yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2412yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2414yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2414yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2412yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2414yes—
977C2×C22⋊C4C2414yes—
978C2×C22⋊C4C2412yes—
979C2×C22⋊C4C2414yes—
980C2×C22⋊C4C2414yes—
981C2×C22⋊C4C2412yes—
982C2×C22⋊C4C2412yes—
983C2×C22⋊C4C2414yes—
984C2×C22⋊C4C2412yes—
985C2×C42—44no—
986C2×C42C2414yes—
987C2×C42C2412yes—
988C2×C42C2412yes—
989C2×C42C2412yes—
990C2×C42C2412yes—
991C2×C42C2411yescharacteristic
992C2×C42C2412yes—
993C2×C42C2412yes—
994C2×C42C2411yescharacteristic
995C2×C42C2412yes—
996C2×C42C2412yes—
997C2×C42C2414yes—
998C2×C42C2414yes—
999C2×C42C2414yes—
1000C2×C42C2414yes—
1001C2×C42C2412yes—
1002C2×C42C2414yes—
1003C2×C42C2414yes—
1004C2×C42C2411yescharacteristic
1005#95C2411yescharacteristic
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2411yescharacteristic
1023#95C2412yes—
1024#95C2412yes—
1025#95C2414yes—
1026#95C2412yes—
1027#95C2411yescharacteristic
1028#95C2414yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2414yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2411yescharacteristic
1036#95C2412yes—
1037#95C2412yes—
1038#95C2414yes—
1039#95C2412yes—
1040#95C2414yes—
1041#95C2412yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2412yes—
1046#95C2412yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2412yes—
1050#95C2412yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2412yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2414yes—
1058#95C2414yes—
1059#95C2414yes—
1060#95C2414yes—
1061#95C2414yes—
1062C24C2512yes—
1063C24C2511yescharacteristic
1064C24C2511yescharacteristic
1065C24C2512yes—
1066C24C2512yes—
1067C24C2512yes—
1068#41—432no—
1069#41—416no—
1070#41—432no—
1071#41—464no—
1072#41—416no—
1073#41—88no—
1074C2×Q8—24no—
1075C2×Q8—24no—
1076C2×Q8—24no—
1077C2×Q8—24no—
1078C2×Q8—24no—
1079C2×Q8—24no—
1080C2×Q8—28no—
1081C2×Q8—28no—
1082C2×Q8—28no—
1083C2×Q8—28no—
1084C2×Q8—44no—
1085C2×Q8—42no—
1086C2×Q8—41no—
1087C2×Q8—42no—
1088C2×Q8—42no—
1089C2×Q8—44no—
1090C2×Q8—44no—
1091C2×Q8—44no—
1092C2×Q8—42no—
1093C2×Q8—44no—
1094C2×Q8—416no—
1095C2×Q8—432no—
1096C2×Q8—432no—
1097C2×Q8—816no—
1098C2×Q8—88no—
1099C2×Q8H(5,𝔽2)18yes—
1100C2×Q8H(5,𝔽2)14yes—
1101C2×D4—24no—
1102C2×D4—24no—
1103C2×D4—24no—
1104C2×D4—24no—
1105C2×D4—28no—
1106C2×D4—28no—
1107C2×D4—24no—
1108C2×D4—22no—
1109C2×D4—28no—
1110C2×D4—24no—
1111C2×D4—24no—
1112C2×D4—22no—
1113C2×D4—24no—
1114C2×D4—22no—
1115C2×D4—24no—
1116C2×D4—24no—
1117C2×D4—24no—
1118C2×D4—41no—
1119C2×D4—42no—
1120C2×D4—42no—
1121C2×D4—42no—
1122C2×D4—41no—
1123C2×D4—42no—
1124C2×D4—44no—
1125C2×D4—44no—
1126C2×D4—44no—
1127C2×D4—41no—
1128C2×D4—42no—
1129C2×D4—42no—
1130C2×D4—42no—
1131C2×D4—42no—
1132C2×D4—42no—
1133C2×D4—42no—
1134C2×D4—44no—
1135C2×D4—44no—
1136C2×D4—44no—
1137C2×D4—42no—
1138C2×D4—41no—
1139C2×D4—44no—
1140C2×D4—44no—
1141C2×D4—44no—
1142C2×D4—42no—
1143C2×D4—42no—
1144C2×D4—44no—
1145C2×D4—41no—
1146C2×D4—42no—
1147C2×D4—44no—
1148C2×D4—42no—
1149C2×D4—42no—
1150C2×D4—42no—
1151C2×D4—42no—
1152C2×D4—44no—
1153C2×D4—44no—
1154C2×D4—44no—
1155C2×D42−1+414yescomplemented
1156C22×C4—24no—
1157C22×C4—24no—
1158C22×C4—24no—
1159C22×C4—22no—
1160C22×C4—24no—
1161C22×C4—24no—
1162C22×C4—28no—
1163C22×C4—24no—
1164C22×C4—24no—
1165C22×C4—22no—
1166C22×C4—28no—
1167C22×C4—28no—
1168C22×C4—24no—
1169C22×C4—24no—
1170C22×C4—28no—
1171C22×C4—24no—
1172C22×C4—28no—
1173C22×C4—24no—
1174C22×C4—44no—
1175C22×C4—44no—
1176C22×C4—42no—
1177C22×C4—44no—
1178C22×C4—44no—
1179C22×C4—42no—
1180C22×C4—42no—
1181C22×C4—44no—
1182C22×C4—44no—
1183C22×C4—44no—
1184C22×C4—44no—
1185C22×C4—44no—
1186C22×C4—42no—
1187C22×C4—42no—
1188C22×C4—42no—
1189C22×C4—44no—
1190C22×C4—44no—
1191C22×C4—42no—
1192C22×C4—44no—
1193C22×C4—44no—
1194C22×C4—44no—
1195C22×C4C2512yes—
1196C22×C4C2512yes—
1197C22×C4C2514yes—
1198C22×C4C2511yescharacteristic
1199C22×C4C2512yes—
1200C22×C4C2512yes—
1201C22×C4C2512yes—
1202C22×C4C2512yes—
1203C22×C4C2511yescharacteristic
1204C22×C4C2512yes—
1205C22×C4C2514yes—
1206C22×C4C2514yes—
1207C22×C4C2514yes—
1208C22×C4C2512yes—
1209C22×C4C2514yes—
1210C22×C4C2511yescharacteristic
1211C22×C4C2512yes—
1212C22×C4C2512yes—
1213C22×C4C2514yes—
1214C22×C4C2512yes—
1215C22×C4C2511yescharacteristic
1216C22×C4C2512yes—
1217C22×C4C2511yescharacteristic
1218C4⋊C4—22no—
1219C4⋊C4—24no—
1220C4⋊C4—28no—
1221C4⋊C4—28no—
1222C4⋊C4—24no—
1223C4⋊C4—28no—
1224C4⋊C4—28no—
1225C4⋊C4—24no—
1226C4⋊C4—24no—
1227C4⋊C4—28no—
1228C4⋊C4—24no—
1229C4⋊C4—28no—
1230C4⋊C4—28no—
1231C4⋊C4—28no—
1232C4⋊C4—24no—
1233C4⋊C4—28no—
1234C4⋊C4—24no—
1235C4⋊C4—24no—
1236C4⋊C4—28no—
1237C4⋊C4—44no—
1238C4⋊C4—44no—
1239C4⋊C4—42no—
1240C4⋊C4—41no—
1241C4⋊C4—41no—
1242C4⋊C4—44no—
1243C4⋊C4—41no—
1244C4⋊C4—42no—
1245C4⋊C4—42no—
1246C4⋊C4—44no—
1247C4⋊C4—41no—
1248C4⋊C4—44no—
1249C4⋊C4—42no—
1250C4⋊C4—42no—
1251C4⋊C4—42no—
1252C4⋊C4—42no—
1253C4⋊C4—44no—
1254C4⋊C4—44no—
1255C4⋊C4—44no—
1256C4⋊C4—44no—
1257C4⋊C4—44no—
1258C4⋊C4—44no—
1259C4⋊C4—44no—
1260C4⋊C4—44no—
1261C4⋊C4—42no—
1262C4⋊C4—42no—
1263C4⋊C4—44no—
1264C4⋊C4—44no—
1265C22⋊C4—24no—
1266C22⋊C4—28no—
1267C22⋊C4—28no—
1268C22⋊C4—28no—
1269C22⋊C4—28no—
1270C22⋊C4—28no—
1271C22⋊C4—24no—
1272C22⋊C4—24no—
1273C22⋊C4—28no—
1274C22⋊C4—28no—
1275C22⋊C4—24no—
1276C22⋊C4—42no—
1277C22⋊C4—44no—
1278C22⋊C4—42no—
1279C22⋊C4—42no—
1280C22⋊C4—44no—
1281C22⋊C4—42no—
1282C22⋊C4—44no—
1283C22⋊C4—44no—
1284C22⋊C4—42no—
1285C22⋊C4—42no—
1286C22⋊C4—42no—
1287C22⋊C4—41no—
1288C22⋊C4—41no—
1289C22⋊C4—42no—
1290C22⋊C4—42no—
1291C22⋊C4—42no—
1292C22⋊C4—42no—
1293C22⋊C4—42no—
1294C22⋊C4—42no—
1295C22⋊C4—42no—
1296C22⋊C4—42no—
1297C22⋊C4—42no—
1298C22⋊C4—44no—
1299C22⋊C4—44no—
1300C22⋊C4—44no—
1301C22⋊C4—44no—
1302C22⋊C4—44no—
1303C22⋊C4—42no—
1304C22⋊C4—42no—
1305C22⋊C4—44no—
1306C22⋊C4—44no—
1307C22⋊C4—42no—
1308C22⋊C4—44no—
1309C22⋊C4—44no—
1310C22⋊C4—44no—
1311C22⋊C4—44no—
1312C22⋊C4—44no—
1313C22⋊C4—44no—
1314C22⋊C4—42no—
1315C22⋊C4—44no—
1316C22⋊C4—42no—
1317C22⋊C4—42no—
1318C22⋊C4—44no—
1319C22⋊C4—44no—
1320C22⋊C4—42no—
1321C22⋊C4—42no—
1322C22⋊C4—44no—
1323C22⋊C4—44no—
1324C22⋊C4—44no—
1325C22⋊C4—44no—
1326C42—24no—
1327C42—24no—
1328C42—28no—
1329C42—24no—
1330C42—24no—
1331C42—22no—
1332C42—24no—
1333C42—22no—
1334C42—24no—
1335C42—24no—
1336C42—42no—
1337C42—42no—
1338C42—41no—
1339C42—44no—
1340C42—44no—
1341C42—44no—
1342C42—44no—
1343C42—44no—
1344C42—44no—
1345C23—22no—
1346C23—22no—
1347C23—22no—
1348C23—22no—
1349C23—22no—
1350C23—22no—
1351C23—24no—
1352C23—22no—
1353C23—22no—
1354C23—22no—
1355C23—22no—
1356C23—22no—
1357C23—24no—
1358C23—21no—
1359C23—22no—
1360C23—22no—
1361C23—21no—
1362C23—22no—
1363C23—21no—
1364C23—21no—
1365C23—22no—
1366C23—22no—
1367C23—22no—
1368C23—24no—
1369C23—22no—
1370C23—24no—
1371C23—22no—
1372C23—22no—
1373C23—21no—
1374C23—22no—
1375C23—21no—
1376C23—22no—
1377C23—22no—
1378C23C2×2−1+414yes—
1379C23C2611yescharacteristic
1380Q8—216no—
1381Q8—28no—
1382Q8—416no—
1383Q8—48no—
1384Q8—44no—
1385Q8—48no—
1386Q8—88no—
1387Q8—84no—
1388Q8—162no—
1389D4—44no—
1390D4—48no—
1391D4—48no—
1392D4—48no—
1393D4—416no—
1394D4—48no—
1395D4—44no—
1396D4—48no—
1397D4—44no—
1398D4—44no—
1399D4—84no—
1400D4—82no—
1401D4—84no—
1402D4—84no—
1403D4—88no—
1404D4—88no—
1405D4—84no—
1406D4—88no—
1407D4—162no—
1408D4—162no—
1409D4—162no—
1410C2×C4—21no—
1411C2×C4—22no—
1412C2×C4—24no—
1413C2×C4—24no—
1414C2×C4—24no—
1415C2×C4—22no—
1416C2×C4—21no—
1417C2×C4—22no—
1418C2×C4—22no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—22no—
1424C2×C4—21no—
1425C2×C4—24no—
1426C2×C4—22no—
1427C2×C4—24no—
1428C2×C4—22no—
1429C2×C4—24no—
1430C2×C4—24no—
1431C2×C4—24no—
1432C2×C4—22no—
1433C2×C4—24no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—22no—
1437C2×C4—22no—
1438C2×C4—22no—
1439C2×C4—24no—
1440C2×C4—22no—
1441C2×C4—22no—
1442C2×C4—22no—
1443C2×C4—24no—
1444C2×C4—22no—
1445C2×C4—22no—
1446C2×C4—22no—
1447C2×C4—22no—
1448C2×C4—22no—
1449C2×C4—22no—
1450C2×C4—22no—
1451C2×C4—24no—
1452C2×C4—24no—
1453C2×C4—24no—
1454C2×C4—24no—
1455C2×C4—24no—
1456C2×C4—22no—
1457C2×C4—22no—
1458C2×C4—22no—
1459C2×C4—22no—
1460C2×C4—24no—
1461C2×C4—22no—
1462C2×C4—22no—
1463C2×C4—24no—
1464C2×C4—24no—
1465C2×C4—22no—
1466C2×C4—22no—
1467C2×C4—416no—
1468C2×C4—48no—
1469C2×C4—48no—
1470C2×C4—416no—
1471C2×C4—48no—
1472C2×C4—44no—
1473C2×C4—48no—
1474C2×C4—44no—
1475C2×C4—88no—
1476C2×C4—84no—
1477C2×C4—84no—
1478C2×C4—88no—
1479C2×C4—84no—
1480C2×C4—84no—
1481C2×C4—164no—
1482C2×C4C2×H(5,𝔽2)18yes—
1483C2×C4C2×H(5,𝔽2)14yes—
1484C2×C4C2×H(5,𝔽2)14yes—
1485C2×C4C2×H(5,𝔽2)12yes—
1486C2×C4C2×2−1+412yes—
1487C2×C4#58514yes—
1488C22—24no—
1489C22—24no—
1490C22—24no—
1491C22—42no—
1492C22—42no—
1493C22—42no—
1494C22—42no—
1495C22—42no—
1496C22—42no—
1497C22—44no—
1498C22—42no—
1499C22—44no—
1500C22—42no—
1501C22—42no—
1502C22—41no—
1503C22—42no—
1504C22—41no—
1505C22—42no—
1506C22—42no—
1507C22—42no—
1508C22—41no—
1509C22—41no—
1510C22—42no—
1511C22—44no—
1512C22—42no—
1513C22—42no—
1514C22—42no—
1515C22—42no—
1516C22—44no—
1517C22—41no—
1518C22—42no—
1519C22—42no—
1520C22—41no—
1521C22—42no—
1522C22C22×H(5,𝔽2)12yes—
1523C22C22×H(5,𝔽2)11yescharacteristic
1524C22C22×2−1+411yescharacteristic
1525C22C2×#58512yes—
1526C222−1+611yescharacteristic
1527C4—24no—
1528C4—22no—
1529C4—24no—
1530C4—28no—
1531C4—42no—
1532C4—42no—
1533C4—44no—
1534C4—42no—
1535C4—42no—
1536C4—44no—
1537C4—41no—
1538C4—42no—
1539C4—42no—
1540C4—44no—
1541C4—42no—
1542C4—42no—
1543C4—44no—
1544C4—41no—
1545C4—42no—
1546C4—41no—
1547C4—42no—
1548C4—44no—
1549C4#353214yes—
1550C2—44no—
1551C2—81no—
1552C2—81no—
1553C2—82no—
1554C2—82no—
1555C2—82no—
1556C2C2×#353211yescharacteristic
1557C2#6289311yescharacteristic
1558C2#6292212yes—
1559C2#6301512yes—
1560C2#6303511yescharacteristic
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. #59817C2semidirect
2. #59809C2semidirect
3. #59481C2semidirect
4. #59075C2semidirect
5. #59043C2semidirect
6. #58943C2semidirect
7. #58128C2semidirect
8. #57001C2semidirect
9. #55126C2semidirect
10. #53005C2semidirect
11. #52956C2semidirect
12. #52297C2semidirect
13. #47814C2semidirect
14. #47134C2semidirect
15. #45308C2semidirect
16. #45248C2semidirect
17. #44377C2semidirect
18. #44260C2semidirect
19. #42913C2semidirect
20. #42855C2semidirect
21. #42107C2semidirect
22. #41180C2semidirect
23. #39858C2semidirect
24. #39790C2semidirect
25. #39215C2semidirect
26. #39169C2semidirect
27. #39166C2semidirect
28. #35757C2semidirect
29. #35687C2semidirect
1155. C2×D42−1+4semidirect

Maximal subgroups

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

subgroupindex
#598172
#598092
#594812
#590752
#590432
#589432
#581282
#570012
#551262
#530052
#529562
#522972
#478142
#471342
#453082
#452482
#443772
#442602
#429132
#428552
#421072
#411802
#398582
#397902
#392152
#391692
#391662
#357572
#356872