Finite Group Databasebeta

← #7645779

Subgroups — #7645779

Order 512.

4620 conjugacy classes of subgroups.

The subgroup lattice has 1459 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42329C214yesmaximal, complemented
2#42194C214yesmaximal, complemented
3#42193C214yesmaximal, complemented
4#42161C214yesmaximal, complemented
5#39630C211yesmaximal, characteristic, complemented
6#39629C211yesmaximal, characteristic, complemented
7#39603C212yesmaximal, complemented
8#39374C211yesmaximal, characteristic, complemented
9#39373C211yesmaximal, characteristic, complemented
10#39347C212yesmaximal, complemented
11#39188C211yesmaximal, characteristic, complemented
12#39186C211yesmaximal, characteristic, complemented
13#39143C212yesmaximal, complemented
14#38972C211yesmaximal, characteristic, complemented
15#38970C211yesmaximal, characteristic, complemented
16#38927C212yesmaximal, complemented
17#37503C212yesmaximal, complemented
18#37502C212yesmaximal, complemented
19#36824C214yesmaximal, complemented
20#36823C214yesmaximal, complemented
21#35459C214yesmaximal, complemented
22#35244C212yesmaximal, complemented
23#35243C212yesmaximal, complemented
24#35132C211yesmaximal, characteristic, complemented
25#35130C211yesmaximal, characteristic
26#35098C214yesmaximal, complemented
27#34972C211yesmaximal, characteristic, complemented
28#34971C211yesmaximal, characteristic, complemented
29#34224C211yesmaximal, characteristic, complemented
30C2×#2351C211yesmaximal, characteristic, complemented
31#34060C211yesmaximal, characteristic, complemented
32C2×#542C2212yes—
33C2×#541C2212yes—
34C2×#529C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37C22×C4×Q8C2212yes—
38#2864C2211yescharacteristic
39#2864C2211yescharacteristic
40#2862C2211yescharacteristic
41#2859C2211yescharacteristic
42#2852C2214yes—
43#2852C2214yes—
44#2851C2212yes—
45#2851C2214yes—
46#2850C2214yes—
47#2850C2212yes—
48#2839C2214yes—
49#2838C2214yes—
50#2837C2214yes—
51#2836C2214yes—
52#2807C2214yes—
53#2806C2214yes—
54#2805C2214yes—
55#2803C2214yes—
56#2802C2214yes—
57#2800C2214yes—
58#2792C2214yes—
59#2791C2214yes—
60#2788C2214yes—
61#2788C2214yes—
62#2783C2214yes—
63#2780C2214yes—
64#2779C2214yes—
65#2777C2214yes—
66#2776C2214yes—
67#2775C2214yes—
68#2774C2214yes—
69#2773C2214yes—
70#2770C2214yes—
71#2769C2214yes—
72#2768C2214yes—
73#2768C2214yes—
74#2767C2214yes—
75#2765C2214yes—
76#2727C2214yes—
77#2726C2214yes—
78#2721C2214yes—
79#2720C2214yes—
80#2715C2214yes—
81#2710C2214yes—
82#2695C2214yes—
83#2689C2214yes—
84#2667C2214yes—
85#2666C2214yes—
86#2666C2214yes—
87#2654C2214yes—
88#2649C2214yes—
89#2647C2212yes—
90#2647C2212yes—
91#2645C2212yes—
92#2644C2212yes—
93#2637C2212yes—
94#2637C2214yes—
95#2637C2214yes—
96#2636C2212yes—
97#2634C2214yes—
98#2632C2214yes—
99#2629C2212yes—
100#2628C2212yes—
101#2627C2214yes—
102#2625C2212yes—
103#2624C2212yes—
104#2623C2214yes—
105#2623C2214yes—
106#2618C2214yes—
107#2612C2214yes—
108#2609C2214yes—
109#2604C2214yes—
110#2599C2214yes—
111#2581C2211yescharacteristic
112#2581C2211yescharacteristic
113#2581C2211yescharacteristic
114#2580C2211yescharacteristic
115#2576C2214yes—
116#2575C2214yes—
117#2574C2214yes—
118#2570C2212yes—
119#2565C2211yescharacteristic
120#2565C2211yescharacteristic
121#2553C2214yes—
122#2550C2212yes—
123#2545C2211yescharacteristic
124#2545C2211yescharacteristic
125#2536C2211yescharacteristic
126#2536C2211yescharacteristic
127#2536C2211yescharacteristic
128#2535C2211yescharacteristic
129#2529C2214yes—
130#2528C2214yes—
131#2525C2214yes—
132#2525C2214yes—
133#2524C2214yes—
134#2524C2214yes—
135#2524C2214yes—
136#2522C2214yes—
137#2522C2214yes—
138#2521C2214yes—
139#2521C2214yes—
140#2520C2214yes—
141#2520C2214yes—
142#2520C2214yes—
143#2519C2214yes—
144#2519C2214yes—
145#2519C2214yes—
146#2518C2214yes—
147#2517C2214yes—
148#2516C2214yes—
149#2516C2214yes—
150#2515C2214yes—
151#2515C2214yes—
152#2515C2214yes—
153#2508C2212yes—
154#2508C2214yes—
155#2507C2212yes—
156#2505C2214yes—
157#2503C2211yescharacteristic
158#2501C2211yescharacteristic
159#2498C2212yes—
160#2497C2212yes—
161#2495C2212yes—
162#2493C2214yes—
163#2489C2214yes—
164#2488C2214yes—
165#2488C2214yes—
166#2486C2212yes—
167#2484C2212yes—
168#2481C2214yes—
169#2473C2214yes—
170#2469C2214yes—
171#2465C2214yes—
172#2462C2214yes—
173#2458C2214yes—
174#2454C2212yes—
175#2453C2212yes—
176#2451C2212yes—
177#2451C2212yes—
178#2449C2214yes—
179#2448C2212yes—
180#2446C2212yes—
181#2443C2214yes—
182#2442C2212yes—
183#2440C2212yes—
184#2438C2214yes—
185#2436C2211yescharacteristic
186#2434C2211yescharacteristic
187#2430C2212yes—
188#2429C2212yes—
189#2426C2212yes—
190#2425C2214yes—
191#2423C2212yes—
192#2423C2212yes—
193#2421C2212yes—
194#2420C2212yes—
195#2419C2214yes—
196#2417C2212yes—
197#2416C2212yes—
198#2413C2214yes—
199#2409C2212yes—
200#2406C2212yes—
201#2399C2212yes—
202#2398C2212yes—
203#2396C2214yes—
204#2373C2214yes—
205#2370C2212yes—
206#2367C2212yes—
207#2357C2211yescharacteristic
208#2356C2211yescharacteristic
209#2351C2212yes—
210#2351C2211yescharacteristic
211#2351C2211yescharacteristic
212#2351C2211yescharacteristic
213#2351C2211yescharacteristic
214#2351C2214yes—
215#2351C2212yes—
216#2351C2212yes—
217#2351C2212yes—
218#2351C2211yescharacteristic
219#2349C2211yescharacteristic
220#2347C2212yes—
221#2343C2212yes—
222#2329C2214yes—
223#2327C2212yes—
224#2326C2212yes—
225#2325C2214yes—
226#2323C2212yes—
227#2323C2212yes—
228#2322C2214yes—
229#2320C2212yes—
230#2320C2212yes—
231#2320C2212yes—
232#2319C2212yes—
233#2318C2212yes—
234#2318C2212yes—
235#2318C2212yes—
236#2317C2212yes—
237#2314C2212yes—
238#2314C2212yes—
239#2311C2212yes—
240C4×C4⋊Q8C2211yescharacteristic
241C4×C4⋊Q8C2211yescharacteristic
242C4×#124C2211yescharacteristic
243C4×#124C2211yescharacteristic
244C4×C22⋊Q8C2212yes—
245C4×C22⋊Q8C2212yes—
246C4×C22⋊Q8C2212yes—
247C4×#123C2214yes—
248C4×#123C2214yes—
249C4×#121C2212yes—
250#2295C2211yescharacteristic
251#2295C2211yescharacteristic
252#2293C2211yescharacteristic
253#2293C2211yescharacteristic
254C2×#389C2212yes—
255C2×#389C2214yes—
256#2290C2212yes—
257#2290C2212yes—
258#2285C2212yes—
259#2283C2212yes—
260#2283C2211yescharacteristic
261C2×#382C2211yescharacteristic
262C2×#382C2212yes—
263#2275C2212yes—
264C4×#117C2211yescharacteristic
265C2×C4×C4⋊C4C2211yescharacteristic
266C2×C4×C4⋊C4C2212yes—
267C22×#41C2311yescharacteristic
268C23×Q8C2311yescharacteristic
269#542—48no—
270#541—48no—
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2312yes—
274#529—28no—
275C2×#126C2312yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#125C2311yescharacteristic
280C2×#125C2314yes—
281C2×#125C2312yes—
282C2×#125C2314yes—
283C2×#124C2311yescharacteristic
284C2×#124C2311yescharacteristic
285C2×#124C2311yescharacteristic
286C2×#124C2314yes—
287C2×#123C2312yes—
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2311yescharacteristic
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2314yes—
297C2×#121C2311yescharacteristic
298C2×#121C2314yes—
299C2×#121C2312yes—
300C4×#41—28no—
301C2×C4×Q8—28no—
302C2×C4×Q8—48no—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2314yes—
318C2×C4×Q8C2314yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2311yescharacteristic
322C2×C4×D4C2311yescharacteristic
323C2×C4×D4C2312yes—
324C2×C4×D4C2311yescharacteristic
325C2×C4×D4C2314yes—
326C2×C4×D4C2312yes—
327C2×#117C2312yes—
328C2×#117C2311yescharacteristic
329C2×#117C2312yes—
330C2×#117C2312yes—
331C2×#117C2312yes—
332C2×#117C2312yes—
333C22×C4⋊C4C2312yes—
334C22×C4⋊C4C2311yescharacteristic
335C22×C4⋊C4C2312yes—
336C22×C4⋊C4C2314yes—
337C22×C4⋊C4C2312yes—
338C22×C4⋊C4C2314yes—
339C22×C42C2312yes—
340C22×C42C2312yes—
341C22×C42C2314yes—
342C22×C42C2312yes—
343C22×C42C2311yescharacteristic
344#401C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2312yes—
351#400C2312yes—
352#400C2312yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#399C2314yes—
367#399C2312yes—
368#399C2314yes—
369#399C2314yes—
370#399C2314yes—
371#399C2314yes—
372#399C2314yes—
373#399C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2312yes—
399#398C2312yes—
400#398C2312yes—
401#398C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2312yes—
413#397C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#395C2314yes—
426#395C2312yes—
427#395C2312yes—
428#395C2312yes—
429#395C2314yes—
430#395C2314yes—
431#395C2314yes—
432#395C2314yes—
433#395C2314yes—
434#395C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2312yes—
441#394C2312yes—
442#394C2312yes—
443#393C2314yes—
444#393C2312yes—
445#393C2314yes—
446#393C2314yes—
447#392C2312yes—
448#391C2311yescharacteristic
449#391C2311yescharacteristic
450#391C2311yescharacteristic
451#391C2311yescharacteristic
452#391C2311yescharacteristic
453#391C2311yescharacteristic
454#391C2312yes—
455#391C2312yes—
456#391C2314yes—
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2314yes—
461#391C2314yes—
462#391C2314yes—
463#391C2312yes—
464#391C2314yes—
465#390C2312yes—
466#390C2312yes—
467#390C2312yes—
468#390C2314yes—
469#390C2312yes—
470#390C2311yescharacteristic
471#390C2311yescharacteristic
472#389C2314yes—
473#389C2314yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2312yes—
482#389C2314yes—
483#389C2314yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2312yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2312yes—
511#389C2314yes—
512#388C2312yes—
513#388C2312yes—
514#388C2312yes—
515#388C2312yes—
516#388C2312yes—
517#388C2312yes—
518#388C2312yes—
519#388C2312yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2312yes—
551#387C2312yes—
552#387C2312yes—
553#387C2312yes—
554#387C2312yes—
555#387C2312yes—
556#387C2312yes—
557#387C2312yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#386C2312yes—
597#386C2312yes—
598#386C2312yes—
599#386C2312yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#385C2312yes—
610#385C2312yes—
611#385C2312yes—
612#385C2312yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#384C2311yescharacteristic
629#384C2311yescharacteristic
630#384C2312yes—
631#384C2312yes—
632#384C2312yes—
633#383C2312yes—
634#383C2312yes—
635#383C2312yes—
636#383C2314yes—
637#383C2314yes—
638#383C2312yes—
639#383C2314yes—
640#382C2311yescharacteristic
641#382C2311yescharacteristic
642#382C2312yes—
643#382C2312yes—
644#382C2312yes—
645#382C2312yes—
646#382C2312yes—
647#382C2312yes—
648#382C2312yes—
649#382C2314yes—
650#382C2314yes—
651#382C2314yes—
652#382C2314yes—
653#382C2311yescharacteristic
654#382C2311yescharacteristic
655#382C2311yescharacteristic
656#382C2311yescharacteristic
657#382C2312yes—
658#382C2312yes—
659#382C2312yes—
660#382C2312yes—
661#382C2312yes—
662#382C2312yes—
663#382C2314yes—
664#381C2312yes—
665#381C2312yes—
666#381C2312yes—
667#381C2312yes—
668#381C2314yes—
669#381C2314yes—
670#381C2314yes—
671#380C2312yes—
672#380C2312yes—
673#380C2312yes—
674#380C2312yes—
675#380C2312yes—
676#380C2312yes—
677#380C2312yes—
678#380C2312yes—
679#380C2312yes—
680#380C2314yes—
681#380C2314yes—
682#380C2312yes—
683#380C2312yes—
684#380C2312yes—
685#380C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2311yescharacteristic
701C4×C4⋊C4C2311yescharacteristic
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2314yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2314yes—
707C4×C4⋊C4C2312yes—
708C4×C4⋊C4C2312yes—
709C4×C4⋊C4C2314yes—
710C4×C4⋊C4C2314yes—
711C4×C4⋊C4C2312yes—
712C4×C4⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2314yes—
716C4×C22⋊C4C2314yes—
717C4×C22⋊C4C2314yes—
718C4×C22⋊C4C2314yes—
719C4×C22⋊C4C2314yes—
720C4×C22⋊C4C2312yes—
721C4×C22⋊C4C2314yes—
722C4×C22⋊C4C2314yes—
723C4×C22⋊C4C2312yes—
724C4×C22⋊C4C2312yes—
725C4×C22⋊C4C2311yescharacteristic
726C4×C22⋊C4C2311yescharacteristic
727#376C2312yes—
728#376C2312yes—
729#376C2312yes—
730#376C2312yes—
731#376C2312yes—
732C2×#95C2311yescharacteristic
733C2×#95C2311yescharacteristic
734C2×#95C2312yes—
735C2×#95C2312yes—
736C2×#95C2314yes—
737C2×#95C2312yes—
738C43C2311yescharacteristic
739C43C2311yescharacteristic
740C2×#41—24no—
741C2×#41—44no—
742C22×Q8—24no—
743C22×Q8—24no—
744C22×Q8—24no—
745C22×Q8C2412yes—
746C22×Q8C2411yescharacteristic
747C22×Q8C2411yescharacteristic
748C22×Q8C2411yescharacteristic
749C22×Q8C2411yescharacteristic
750C22×Q8C2414yes—
751C22×D4C2412yes—
752C22×D4C2411yescharacteristic
753C22×D4C2412yes—
754C22×D4C2411yescharacteristic
755C22×D4C2414yes—
756C23×C4C2412yes—
757C23×C4C2412yes—
758C23×C4C2412yes—
759C23×C4C2411yescharacteristic
760C23×C4C2411yescharacteristic
761C23×C4C2412yes—
762C23×C4C2414yes—
763C23×C4C2412yes—
764C23×C4C2412yes—
765C23×C4C2412yes—
766C23×C4C2412yes—
767C23×C4C2414yes—
768C23×C4C2411yescharacteristic
769C4⋊Q8—24no—
770C4⋊Q8—24no—
771C4⋊Q8—44no—
772#126—28no—
773#126—48no—
774#126—48no—
775#126—48no—
776#125—24no—
777#125—48no—
778#125—44no—
779#125—48no—
780#124—24no—
781#124—24no—
782#124—24no—
783#124—48no—
784#123—28no—
785#123—48no—
786#123—48no—
787#123—48no—
788C22⋊Q8—28no—
789C22⋊Q8—28no—
790C22⋊Q8—24no—
791C22⋊Q8—48no—
792C22⋊Q8—48no—
793C22⋊Q8—44no—
794#121—24no—
795#121—44no—
796#121—48no—
797C4×Q8—28no—
798C4×Q8—28no—
799C4×Q8—24no—
800C4×Q8—24no—
801C4×Q8—28no—
802C4×Q8—24no—
803C4×Q8—24no—
804C4×Q8—28no—
805C4×Q8—24no—
806C4×Q8—24no—
807C4×Q8—24no—
808C4×Q8—44no—
809C4×Q8—44no—
810C4×Q8—48no—
811C4×Q8—48no—
812C4×Q8—44no—
813C4×D4—28no—
814C4×D4—28no—
815C4×D4—28no—
816C4×D4—24no—
817C4×D4—24no—
818C4×D4—24no—
819C4×D4—44no—
820C4×D4—48no—
821#117—24no—
822#117—28no—
823#117—28no—
824#117—44no—
825#117—44no—
826#117—44no—
827C2×C4⋊C4—28no—
828C2×C4⋊C4—24no—
829C2×C4⋊C4—44no—
830C2×C4⋊C4—48no—
831C2×C4⋊C4—44no—
832C2×C4⋊C4—48no—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C42—28no—
937C2×C42—28no—
938C2×C42—44no—
939C2×C42—48no—
940C2×C42#4118yes—
941C2×C42C2411yescharacteristic
942C2×C42C2411yescharacteristic
943C2×C42C2412yes—
944C2×C42C2412yes—
945C2×C42C2412yes—
946C2×C42C2412yes—
947C2×C42C2412yes—
948C2×C42C2412yes—
949C2×C42C2414yes—
950C2×C42C2414yes—
951C2×C42C2412yes—
952C2×C42C2412yes—
953C2×C42C2412yes—
954C2×C42C2412yes—
955C2×C42C2411yescharacteristic
956C2×C42C2411yescharacteristic
957C2×C42C2412yes—
958C2×C42C2412yes—
959C2×C42C2414yes—
960C2×C42C2412yes—
961C2×C42C2412yes—
962C2×C42C2414yes—
963C2×C42C2414yes—
964C2×C42C2414yes—
965C2×C42C2412yes—
966C2×C42C2412yes—
967C2×C42C2414yes—
968C2×C42C2414yes—
969C2×C42C2411yescharacteristic
970C2×C42C2411yescharacteristic
971C2×C42C2411yescharacteristic
972C2×C42C2411yescharacteristic
973#95C2411yescharacteristic
974#95C2412yes—
975#95C2411yescharacteristic
976#95C2412yes—
977#95C2414yes—
978#95C2411yescharacteristic
979#95C2412yes—
980#95C2411yescharacteristic
981#95C2412yes—
982#95C2414yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2414yes—
993#95C2412yes—
994#95C2414yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2412yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2412yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049C24C2512yes—
1050C24C2512yes—
1051C24C2511yescharacteristic
1052#41—416no—
1053C2×Q8—232no—
1054C2×Q8—24no—
1055C2×Q8—22no—
1056C2×Q8—22no—
1057C2×Q8—22no—
1058C2×Q8—22no—
1059C2×Q8—24no—
1060C2×Q8—22no—
1061C2×Q8—22no—
1062C2×Q8—24no—
1063C2×Q8—22no—
1064C2×Q8—22no—
1065C2×Q8—42no—
1066C2×Q8—44no—
1067C2×Q8—44no—
1068C2×Q8—44no—
1069C2×Q8H(5,𝔽2)14yes—
1070C2×Q82−1+414yes—
1071C2×D4—24no—
1072C2×D4—24no—
1073C2×D4—28no—
1074C2×D4—24no—
1075C2×D4—24no—
1076C2×D4—22no—
1077C2×D4—22no—
1078C2×D4—22no—
1079C2×D4—22no—
1080C2×D4—42no—
1081C2×D4—44no—
1082C2×D4—44no—
1083C2×D4—44no—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—22no—
1088C22×C4—24no—
1089C22×C4—22no—
1090C22×C4—24no—
1091C22×C4—24no—
1092C22×C4—28no—
1093C22×C4—24no—
1094C22×C4—28no—
1095C22×C4—24no—
1096C22×C4—24no—
1097C22×C4—24no—
1098C22×C4—24no—
1099C22×C4—24no—
1100C22×C4—24no—
1101C22×C4—42no—
1102C22×C4—42no—
1103C22×C4—42no—
1104C22×C4—42no—
1105C22×C4—42no—
1106C22×C4—42no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—42no—
1110C22×C4—42no—
1111C22×C4—42no—
1112C22×C4—44no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4—44no—
1116C22×C4C2×#4114yes—
1117C22×C4C2×#4114yes—
1118C22×C4C2×#4114yes—
1119C22×C4C2512yes—
1120C22×C4C2512yes—
1121C22×C4C2514yes—
1122C22×C4C2512yes—
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2512yes—
1126C22×C4C2514yes—
1127C22×C4C2512yes—
1128C22×C4C2512yes—
1129C22×C4C2512yes—
1130C22×C4C2512yes—
1131C22×C4C2512yes—
1132C22×C4C2512yes—
1133C22×C4C2514yes—
1134C22×C4C2512yes—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2514yes—
1138C22×C4C2512yes—
1139C22×C4C2511yescharacteristic
1140C22×C4C2511yescharacteristic
1141C22×C4C2511yescharacteristic
1142C22×C4C2511yescharacteristic
1143C22×C4C2511yescharacteristic
1144C22×C4C2512yes—
1145C22×C4C2512yes—
1146C22×C4C2511yescharacteristic
1147C4⋊C4—24no—
1148C4⋊C4—24no—
1149C4⋊C4—24no—
1150C4⋊C4—24no—
1151C4⋊C4—24no—
1152C4⋊C4—22no—
1153C4⋊C4—22no—
1154C4⋊C4—22no—
1155C4⋊C4—22no—
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—24no—
1160C4⋊C4—22no—
1161C4⋊C4—24no—
1162C4⋊C4—22no—
1163C4⋊C4—24no—
1164C4⋊C4—24no—
1165C4⋊C4—28no—
1166C4⋊C4—24no—
1167C4⋊C4—28no—
1168C4⋊C4—24no—
1169C4⋊C4—28no—
1170C4⋊C4—28no—
1171C4⋊C4—24no—
1172C4⋊C4—28no—
1173C4⋊C4—28no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—42no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—42no—
1192C4⋊C4—42no—
1193C4⋊C4—42no—
1194C4⋊C4—42no—
1195C4⋊C4—42no—
1196C4⋊C4—42no—
1197C4⋊C4—42no—
1198C4⋊C4—42no—
1199C4⋊C4—42no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—44no—
1210C4⋊C4—44no—
1211C4⋊C4—44no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C22⋊C4—24no—
1215C22⋊C4—24no—
1216C22⋊C4—24no—
1217C22⋊C4—24no—
1218C22⋊C4—28no—
1219C22⋊C4—24no—
1220C22⋊C4—24no—
1221C22⋊C4—24no—
1222C22⋊C4—24no—
1223C22⋊C4—24no—
1224C22⋊C4—24no—
1225C22⋊C4—28no—
1226C22⋊C4—28no—
1227C22⋊C4—28no—
1228C22⋊C4—28no—
1229C22⋊C4—44no—
1230C22⋊C4—42no—
1231C22⋊C4—42no—
1232C22⋊C4—42no—
1233C22⋊C4—42no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—42no—
1237C22⋊C4—42no—
1238C22⋊C4—42no—
1239C22⋊C4—42no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C42—24no—
1251C42—24no—
1252C42—24no—
1253C42—24no—
1254C42—24no—
1255C42—24no—
1256C42—24no—
1257C42—24no—
1258C42—24no—
1259C42—24no—
1260C42—28no—
1261C42—28no—
1262C42—22no—
1263C42—22no—
1264C42—22no—
1265C42—22no—
1266C42—42no—
1267C42—44no—
1268C42—42no—
1269C42—44no—
1270C42—44no—
1271C42—42no—
1272C42—42no—
1273C42—44no—
1274C42—42no—
1275C42—42no—
1276C42—44no—
1277C42—44no—
1278C42C2×#4114yes—
1279C42C2×#4114yes—
1280C42C2×#4114yes—
1281C42C2×#4114yes—
1282C23—21no—
1283C23—21no—
1284C23—22no—
1285C23—22no—
1286C23—22no—
1287C23—22no—
1288C23—22no—
1289C23—22no—
1290C23—22no—
1291C23—24no—
1292C23—22no—
1293C23—22no—
1294C23—22no—
1295C23—24no—
1296C23—22no—
1297C23C22×#4112yes—
1298C23#58514yes—
1299C23C2611yescharacteristic
1300Q8—216no—
1301Q8—28no—
1302Q8—28no—
1303Q8—44no—
1304Q8—44no—
1305Q8—164no—
1306D4—44no—
1307D4—48no—
1308D4—48no—
1309D4—44no—
1310D4—164no—
1311C2×C4—216no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—21no—
1315C2×C4—22no—
1316C2×C4—21no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—28no—
1323C2×C4—28no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—24no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—24no—
1355C2×C4—24no—
1356C2×C4—22no—
1357C2×C4—24no—
1358C2×C4—24no—
1359C2×C4—24no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—24no—
1370C2×C4—22no—
1371C2×C4—24no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—24no—
1377C2×C4—22no—
1378C2×C4—24no—
1379C2×C4—22no—
1380C2×C4—44no—
1381C2×C4—48no—
1382C2×C4—48no—
1383C2×C4—48no—
1384C2×C4—48no—
1385C2×C4—84no—
1386C2×C4—84no—
1387C2×C4—84no—
1388C2×C4—88no—
1389C2×C4—164no—
1390C2×C4C22×#4112yes—
1391C2×C4C22×#4112yes—
1392C2×C4C22×#4112yes—
1393C2×C4C22×#4112yes—
1394C2×C4C22×#4112yes—
1395C2×C4C22×#4112yes—
1396C2×C4C2×H(5,𝔽2)14yes—
1397C2×C4C2×H(5,𝔽2)12yes—
1398C2×C4C2×2−1+414yes—
1399C2×C4C2×2−1+412yes—
1400C22—22no—
1401C22—22no—
1402C22—24no—
1403C22—24no—
1404C22—42no—
1405C22—42no—
1406C22—42no—
1407C22—42no—
1408C22—44no—
1409C22—42no—
1410C22—42no—
1411C22—42no—
1412C22—42no—
1413C22—42no—
1414C22—42no—
1415C22—44no—
1416C22#345514yes—
1417C22C23×#4111yescharacteristic
1418C22C22×H(5,𝔽2)11yescharacteristic
1419C22C22×2−1+411yescharacteristic
1420C22C2×#58512yes—
1421C222−1+612yes—
1422C4—22no—
1423C4—24no—
1424C4—24no—
1425C4—22no—
1426C4—22no—
1427C4—22no—
1428C4—22no—
1429C4—42no—
1430C4—42no—
1431C4—42no—
1432C4—42no—
1433C4—42no—
1434C4—42no—
1435C4—42no—
1436C4—42no—
1437C4—44no—
1438C4—42no—
1439C4—44no—
1440C4—44no—
1441C4—42no—
1442C4—42no—
1443C4—42no—
1444C4—42no—
1445C4—42no—
1446C4—42no—
1447C4—42no—
1448C4—44no—
1449C4#349214yes—
1450C2—24no—
1451C2—82no—
1452C2—82no—
1453C2C2×#345511yescharacteristic
1454C2C2×#349211yescharacteristic
1455C2#6286011yescharacteristic
1456C2#6291912yes—
1457C2#6294912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35130C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #42329C2semidirect
2. #42194C2semidirect
3. #42193C2semidirect
4. #42161C2semidirect
5. #39630C2semidirect
6. #39629C2semidirect
7. #39603C2semidirect
8. #39374C2semidirect
9. #39373C2semidirect
10. #39347C2semidirect
11. #39188C2semidirect
12. #39186C2semidirect
13. #39143C2semidirect
14. #38972C2semidirect
15. #38970C2semidirect
16. #38927C2semidirect
17. #37503C2semidirect
18. #37502C2semidirect
19. #36824C2semidirect
20. #36823C2semidirect
21. #35459C2semidirect
22. #35244C2semidirect
23. #35243C2semidirect
24. #35132C2semidirect
26. #35098C2semidirect
27. #34972C2semidirect
28. #34971C2semidirect
29. #34224C2semidirect
30. C2×#2351C2semidirect
31. #34060C2semidirect

Maximal subgroups

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

subgroupindex
#423292
#421942
#421932
#421612
#396302
#396292
#396032
#393742
#393732
#393472
#391882
#391862
#391432
#389722
#389702
#389272
#375032
#375022
#368242
#368232
#354592
#352442
#352432
#351322
#351302
#350982
#349722
#349712
#342242
C2×#23512
#340602