Finite Group Databasebeta

← #7655414

Subgroups — #7655414

Order 512.

7159 conjugacy classes of subgroups.

The subgroup lattice has 1517 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3524C211yesmaximal, characteristic, complemented
2C2×#3480C211yesmaximal, characteristic, complemented
3#42445C213yesmaximal, complemented
4#42444C213yesmaximal, complemented
5#42441C213yesmaximal, complemented
6#42440C213yesmaximal, complemented
7#39963C213yesmaximal, complemented
8#39962C213yesmaximal, complemented
9#39959C213yesmaximal, complemented
10#39958C213yesmaximal, complemented
11#39857C213yesmaximal, complemented
12#39856C213yesmaximal, complemented
13#39853C213yesmaximal, complemented
14#39852C213yesmaximal, complemented
15#37553C213yesmaximal, complemented
16#36455C211yesmaximal, characteristic, complemented
17#36444C211yesmaximal, characteristic, complemented
18#36435C211yesmaximal, characteristic, complemented
19#36434C211yesmaximal, characteristic, complemented
20#36431C211yesmaximal, characteristic, complemented
21#36430C211yesmaximal, characteristic, complemented
22#36430C211yesmaximal, characteristic, complemented
23#36430C211yesmaximal, characteristic, complemented
24#35831C211yesmaximal, characteristic, complemented
25#35816C211yesmaximal, characteristic, complemented
26#35786C211yesmaximal, characteristic, complemented
27#35771C211yesmaximal, characteristic, complemented
28#35189C213yesmaximal, complemented
29#35103C213yesmaximal, complemented
30#34964C213yesmaximal, complemented
31C4⋊C4×#41C211yesmaximal, characteristic, complemented
32#3524—216no—
33#3480—216no—
34C2×#559C2213yes—
35C2×#559C2213yes—
36C2×#557C2211yescharacteristic
37C2×#557C2211yescharacteristic
38C2×#556C2213yes—
39C2×#555C2213yes—
40C2×#553C2213yes—
41C2×#553C2213yes—
42C2×#553C2213yes—
43C2×#552C2213yes—
44C2×#550C2211yescharacteristic
45C2×#550C2211yescharacteristic
46C2×#550C2211yescharacteristic
47C2×D4×Q8C2211yescharacteristic
48C2×#548C2211yescharacteristic
49C2×#548C2211yescharacteristic
50C2×#548C2211yescharacteristic
51C2×#548C2211yescharacteristic
52C2×#548C2211yescharacteristic
53C2×#548C2211yescharacteristic
54C2×#542C2213yes—
55C2×#540C2213yes—
56C2×#532C2213yes—
57C2×#529C2213yes—
58C2×#529C2213yes—
59C2×#529C2213yes—
60C2×#529C2213yes—
61C2×#520C2211yescharacteristic
62C2×#519C2211yescharacteristic
63C2×C4×#41C2211yescharacteristic
64C2×C4×#41C2213yes—
65C2×C4×#41C2211yescharacteristic
66C2×C4×#41C2211yescharacteristic
67C2×C4×#41C2211yescharacteristic
68C22×C4×Q8C2211yescharacteristic
69#2857C2213yes—
70#2856C2213yes—
71#2851C2213yes—
72#2851C2213yes—
73#2850C2213yes—
74#2850C2213yes—
75#2850C2213yes—
76#2850C2213yes—
77#2814C2216yes—
78#2813C2216yes—
79#2722C2216yes—
80#2715C2216yes—
81#2715C2216yes—
82#2712C2216yes—
83#2695C2216yes—
84#2695C2216yes—
85#2693C2216yes—
86#2691C2216yes—
87#2691C2216yes—
88#2676C2216yes—
89#2676C2216yes—
90#2675C2216yes—
91#2672C2216yes—
92#2672C2216yes—
93#2671C2216yes—
94#2671C2216yes—
95#2664C2216yes—
96#2662C2216yes—
97#2630C2216yes—
98#2630C2216yes—
99#2630C2216yes—
100#2630C2216yes—
101#2629C2213yes—
102#2629C2213yes—
103#2620C2213yes—
104#2620C2213yes—
105#2618C2216yes—
106#2618C2216yes—
107#2601C2216yes—
108#2601C2216yes—
109#2601C2213yes—
110#2601C2216yes—
111#2601C2213yes—
112#2601C2211yescharacteristic
113#2601C2213yes—
114#2592C2213yes—
115#2584C2213yes—
116#2582C2213yes—
117#2581C2213yes—
118#2580C2213yes—
119#2566C2213yes—
120#2566C2213yes—
121#2565C2213yes—
122#2565C2213yes—
123#2562C2213yes—
124#2547C2213yes—
125#2545C2213yes—
126#2545C2213yes—
127#2544C2213yes—
128#2544C2213yes—
129#2544C2213yes—
130#2544C2213yes—
131#2541C2213yes—
132#2540C2213yes—
133#2538C2213yes—
134#2538C2213yes—
135#2537C2213yes—
136#2537C2213yes—
137#2537C2213yes—
138#2536C2213yes—
139#2535C2213yes—
140#2535C2213yes—
141#2535C2213yes—
142#2498C2213yes—
143#2498C2213yes—
144#2485C2216yes—
145#2454C2213yes—
146#2454C2213yes—
147#2453C2213yes—
148#2453C2213yes—
149#2452C2213yes—
150#2452C2213yes—
151#2451C2213yes—
152#2451C2213yes—
153#2442C2213yes—
154#2442C2213yes—
155#2441C2213yes—
156#2441C2213yes—
157#2440C2213yes—
158#2440C2213yes—
159#2439C2213yes—
160#2439C2213yes—
161#2430C2213yes—
162#2430C2213yes—
163#2429C2213yes—
164#2429C2213yes—
165#2428C2213yes—
166#2428C2213yes—
167#2428C2213yes—
168#2428C2213yes—
169#2428C2213yes—
170#2428C2213yes—
171#2427C2213yes—
172#2427C2213yes—
173#2427C2213yes—
174#2427C2213yes—
175#2427C2213yes—
176#2427C2213yes—
177#2426C2213yes—
178#2426C2213yes—
179#2417C2213yes—
180#2417C2213yes—
181#2417C2213yes—
182#2417C2213yes—
183#2416C2213yes—
184#2416C2213yes—
185#2416C2213yes—
186#2416C2213yes—
187#2415C2213yes—
188#2415C2213yes—
189#2415C2213yes—
190#2415C2213yes—
191#2415C2213yes—
192#2415C2213yes—
193#2414C2213yes—
194#2414C2213yes—
195#2414C2213yes—
196#2414C2213yes—
197#2414C2213yes—
198#2414C2213yes—
199#2407C2216yes—
200#2396C2213yes—
201#2396C2213yes—
202#2392C2213yes—
203#2392C2213yes—
204#2351C2211yescharacteristic
205#2351C2211yescharacteristic
206#2351C2211yescharacteristic
207#2351C2211yescharacteristic
208Q8×C4⋊C4C2211yescharacteristic
209Q8×C4⋊C4C2211yescharacteristic
210Q8×C4⋊C4C2211yescharacteristic
211Q8×C4⋊C4C2211yescharacteristic
212#2349C2213yes—
213#2349C2213yes—
214D4×C4⋊C4C2213yes—
215D4×C4⋊C4C2213yes—
216#2341C2211yescharacteristic
217#2341C2211yescharacteristic
218#2341C2211yescharacteristic
219#2341C2211yescharacteristic
220Q8×C22⋊C4C2211yescharacteristic
221Q8×C22⋊C4C2211yescharacteristic
222Q8×C22⋊C4C2211yescharacteristic
223Q8×C22⋊C4C2211yescharacteristic
224#2325C2216yes—
225#2325C2216yes—
226#2324C2216yes—
227#2323C2216yes—
228C4×C22⋊Q8C2213yes—
229C4×C22⋊Q8C2213yes—
230C4×#121C2213yes—
231C4×#121C2213yes—
232C4×#121C2213yes—
233C4×#121C2213yes—
234C4×#121C2213yes—
235C4×#121C2213yes—
236#2296C2213yes—
237#2296C2213yes—
238#2285C2213yes—
239C2×C4×C4⋊C4C2213yes—
240C22×#41C2311yescharacteristic
241C22×#41C2311yescharacteristic
242C22×#41C2311yescharacteristic
243C22×#41C2313yes—
244C23×Q8C2311yescharacteristic
245C23×Q8C2311yescharacteristic
246#559—224no—
247#559—224no—
248#557—28no—
249#557—28no—
250#556—224no—
251#555—224no—
252#553—224no—
253#553—224no—
254#553—224no—
255#552—224no—
256#550—28no—
257#550—28no—
258#550—44no—
259D4×Q8—44no—
260#548—28no—
261#548—28no—
262#548—28no—
263#548—28no—
264#548—44no—
265#548—44no—
266#542—224no—
267#540—224no—
268#532—224no—
269C2×C4⋊Q8C2313yes—
270C2×C4⋊Q8C2313yes—
271C2×C4⋊Q8C2313yes—
272C2×#127C2313yes—
273C2×#127C2313yes—
274C2×#127C2313yes—
275#529—224no—
276#529—224no—
277#529—224no—
278#529—224no—
279C2×#126C2311yescharacteristic
280C2×#126C2313yes—
281C2×#126C2316yes—
282C2×#126C2316yes—
283C2×#126C2316yes—
284C2×#125C2313yes—
285C2×#125C2313yes—
286C2×#125C2313yes—
287C2×#125C2313yes—
288C2×#125C2313yes—
289C2×#124C2313yes—
290C2×#124C2313yes—
291C2×#124C2313yes—
292C2×#124C2313yes—
293C2×#124C2316yes—
294C2×#124C2316yes—
295C2×#124C2313yes—
296C2×#124C2313yes—
297C2×#124C2313yes—
298C2×#123C2316yes—
299C2×#123C2316yes—
300C2×#123C2313yes—
301C2×#123C2313yes—
302C2×#123C2316yes—
303C2×#123C2316yes—
304C2×C22⋊Q8C2313yes—
305C2×C22⋊Q8C2313yes—
306C2×C22⋊Q8C2313yes—
307C2×C22⋊Q8C2313yes—
308C2×C22⋊Q8C2313yes—
309C2×C22⋊Q8C2316yes—
310C2×C22⋊Q8C2313yes—
311C2×C22⋊Q8C2313yes—
312C2×C22⋊Q8C2313yes—
313C2×C22⋊Q8C2313yes—
314C2×C22⋊Q8C2313yes—
315C2×C22⋊Q8C2313yes—
316C2×#121C2313yes—
317C2×#121C2313yes—
318C2×#121C2313yes—
319C2×#121C2313yes—
320C2×#121C2316yes—
321C2×#121C2316yes—
322C2×#121C2313yes—
323C2×#121C2313yes—
324C2×#121C2313yes—
325C2×#121C2313yes—
326C2×#121C2313yes—
327C2×#121C2316yes—
328C2×#121C2316yes—
329C2×#121C2316yes—
330C2×#121C2313yes—
331C2×#121C2313yes—
332C2×#121C2313yes—
333C2×#121C2313yes—
334C2×#121C2313yes—
335C2×#121C2313yes—
336C2×#121C2313yes—
337C2×#121C2313yes—
338C2×#121C2313yes—
339C2×#121C2313yes—
340#520—28no—
341#519—28no—
342C4×#41—28no—
343C4×#41—224no—
344C4×#41—44no—
345C4×#41—44no—
346C4×#41D4116yescomplemented
347C2×C4×Q8—28no—
348C2×C4×Q8C2313yes—
349C2×C4×Q8C2313yes—
350C2×C4×Q8C2313yes—
351C2×C4×Q8C2313yes—
352C2×C4×Q8C2313yes—
353C2×C4×Q8C2311yescharacteristic
354C2×C4×Q8C2311yescharacteristic
355C2×C4×Q8C2311yescharacteristic
356C2×C4×Q8C2311yescharacteristic
357C2×C4×Q8C2311yescharacteristic
358C2×C4×Q8C2311yescharacteristic
359C2×C4×Q8C2311yescharacteristic
360C2×C4×Q8C2311yescharacteristic
361C2×C4×Q8C2313yes—
362C2×C4×Q8C2313yes—
363C2×C4×Q8C2311yescharacteristic
364C2×C4×Q8C2311yescharacteristic
365C2×C4×D4C2313yes—
366C2×C4×D4C2313yes—
367C2×C4×D4C2313yes—
368C2×C4×D4C2316yes—
369C2×C4×D4C2316yes—
370C2×C4×D4C2313yes—
371C2×C4×D4C2313yes—
372C2×C4×D4C2313yes—
373C2×C4×D4C2313yes—
374C2×C4×D4C2313yes—
375C2×C4×D4C2313yes—
376C2×C4×D4C2313yes—
377C2×C4×D4C2313yes—
378C2×C4×D4C2313yes—
379C2×C4×D4C2313yes—
380C2×C4×D4C2313yes—
381C2×C4×D4C2313yes—
382C2×C4×D4C2313yes—
383C2×C4×D4C2313yes—
384C2×C4×D4C2313yes—
385C2×C4×D4C2313yes—
386C2×C4×D4C2313yes—
387C2×C4×D4C2313yes—
388C2×C4×D4C2313yes—
389C2×C4×D4C2313yes—
390C2×#117C2316yes—
391C2×#117C2311yescharacteristic
392C2×#117C2313yes—
393C2×#117C2313yes—
394C2×#117C2313yes—
395C2×#117C2313yes—
396C2×#117C2313yes—
397C2×#117C2313yes—
398C2×#117C2313yes—
399C2×#117C2313yes—
400C2×#117C2313yes—
401C22×C4⋊C4C2313yes—
402C22×C4⋊C4C2313yes—
403C22×C4⋊C4C2313yes—
404C22×C4⋊C4C2313yes—
405C22×C42C2313yes—
406C22×C42C2313yes—
407C22×C42C2313yes—
408C22×C42C2313yes—
409C22×C42C2313yes—
410#400C2313yes—
411#400C2313yes—
412#400C2316yes—
413#399C2316yes—
414#399C2313yes—
415#399C2313yes—
416#398C2313yes—
417#398C2316yes—
418#398C2316yes—
419#398C2316yes—
420#398C2313yes—
421#398C2313yes—
422#398C2313yes—
423#398C2313yes—
424#398C2311yescharacteristic
425#398C2316yes—
426#398C2316yes—
427#398C2316yes—
428#397C2313yes—
429#397C2313yes—
430#397C2316yes—
431#397C2316yes—
432#397C2316yes—
433#397C2316yes—
434#397C2316yes—
435#396C2313yes—
436#396C2316yes—
437#396C2316yes—
438#396C2316yes—
439#396C2313yes—
440#396C2316yes—
441#396C2316yes—
442#396C2316yes—
443#396C2313yes—
444#396C2313yes—
445#396C2313yes—
446#396C2313yes—
447#396C2311yescharacteristic
448#396C2311yescharacteristic
449#396C2316yes—
450#396C2316yes—
451#396C2316yes—
452#396C2316yes—
453#395C2316yes—
454#395C2313yes—
455#395C2313yes—
456#394C2313yes—
457#394C2313yes—
458#394C2313yes—
459#394C2316yes—
460#394C2316yes—
461#394C2316yes—
462#394C2313yes—
463#394C2313yes—
464#394C2311yescharacteristic
465#394C2316yes—
466#394C2316yes—
467#394C2316yes—
468#394C2316yes—
469#394C2316yes—
470#394C2316yes—
471#394C2316yes—
472#394C2316yes—
473#394C2316yes—
474#394C2316yes—
475#394C2316yes—
476#393C2316yes—
477#393C2313yes—
478#393C2313yes—
479#392C2316yes—
480#392C2316yes—
481#392C2316yes—
482#392C2316yes—
483#392C2313yes—
484#392C2313yes—
485#392C2316yes—
486#391C2313yes—
487#391C2313yes—
488#391C2313yes—
489#391C2313yes—
490#391C2316yes—
491#391C2313yes—
492#391C2313yes—
493#391C2313yes—
494#391C2313yes—
495#391C2313yes—
496#391C2313yes—
497#390C2313yes—
498#390C2313yes—
499#390C2313yes—
500#390C2313yes—
501#390C2313yes—
502#390C2316yes—
503#390C2316yes—
504#390C2313yes—
505#390C2313yes—
506#390C2313yes—
507#390C2313yes—
508#390C2313yes—
509#390C2313yes—
510#390C2313yes—
511#390C2313yes—
512#390C2311yescharacteristic
513#389C2313yes—
514#389C2316yes—
515#389C2316yes—
516#389C2316yes—
517#389C2313yes—
518#389C2313yes—
519#389C2313yes—
520#389C2313yes—
521#389C2313yes—
522#389C2313yes—
523#389C2311yescharacteristic
524#389C2313yes—
525#389C2313yes—
526#389C2313yes—
527#389C2313yes—
528#389C2313yes—
529#389C2313yes—
530#389C2313yes—
531#389C2313yes—
532#389C2313yes—
533#389C2313yes—
534#389C2313yes—
535#389C2313yes—
536#389C2313yes—
537#389C2313yes—
538#389C2313yes—
539#389C2313yes—
540#388C2311yescharacteristic
541#388C2313yes—
542#388C2313yes—
543#388C2313yes—
544#388C2313yes—
545#388C2316yes—
546#388C2316yes—
547#388C2316yes—
548#388C2316yes—
549#388C2313yes—
550#388C2316yes—
551#388C2316yes—
552#388C2316yes—
553#388C2311yescharacteristic
554#388C2313yes—
555#388C2313yes—
556#388C2313yes—
557#388C2313yes—
558#388C2311yescharacteristic
559#387C2313yes—
560#387C2316yes—
561#387C2316yes—
562#387C2316yes—
563#387C2316yes—
564#387C2316yes—
565#387C2313yes—
566#387C2313yes—
567#387C2311yescharacteristic
568#386C2316yes—
569#386C2316yes—
570#386C2313yes—
571#386C2316yes—
572#386C2316yes—
573#386C2316yes—
574#386C2316yes—
575#386C2316yes—
576#386C2316yes—
577#386C2316yes—
578#386C2313yes—
579#386C2313yes—
580#386C2311yescharacteristic
581#386C2313yes—
582#386C2313yes—
583#386C2313yes—
584#386C2313yes—
585#386C2313yes—
586#386C2313yes—
587#386C2313yes—
588#386C2313yes—
589#385C2313yes—
590#385C2316yes—
591#385C2316yes—
592#385C2316yes—
593#385C2316yes—
594#385C2316yes—
595#385C2313yes—
596#385C2313yes—
597#385C2311yescharacteristic
598#385C2316yes—
599#385C2316yes—
600#385C2316yes—
601#385C2316yes—
602#384C2313yes—
603#384C2313yes—
604#384C2313yes—
605#384C2313yes—
606#382C2313yes—
607#382C2313yes—
608#382C2313yes—
609#382C2313yes—
610#380C2313yes—
611#380C2313yes—
612#380C2313yes—
613#380C2313yes—
614#380C2316yes—
615#380C2316yes—
616#380C2316yes—
617#380C2316yes—
618#380C2313yes—
619#380C2313yes—
620#380C2313yes—
621#380C2313yes—
622#380C2313yes—
623#380C2313yes—
624#380C2313yes—
625#380C2313yes—
626#380C2316yes—
627#380C2316yes—
628#380C2313yes—
629#380C2313yes—
630#380C2313yes—
631#380C2313yes—
632C4×C4⋊C4C2313yes—
633C4×C4⋊C4C2313yes—
634C4×C4⋊C4C2313yes—
635C4×C4⋊C4C2313yes—
636C4×C4⋊C4C2313yes—
637C4×C4⋊C4C2316yes—
638C4×C4⋊C4C2313yes—
639C4×C4⋊C4C2311yescharacteristic
640C4×C4⋊C4C2313yes—
641C4×C4⋊C4C2313yes—
642C4×C4⋊C4C2313yes—
643C4×C4⋊C4C2313yes—
644C4×C4⋊C4C2313yes—
645C4×C22⋊C4C2313yes—
646C4×C22⋊C4C2313yes—
647C4×C22⋊C4C2313yes—
648C4×C22⋊C4C2313yes—
649C4×C22⋊C4C2313yes—
650C4×C22⋊C4C2313yes—
651C4×C22⋊C4C2313yes—
652C4×C22⋊C4C2313yes—
653C2×#95C2313yes—
654C2×#95C2313yes—
655C2×#41—24no—
656C2×#41—24no—
657C2×#41—24no—
658C2×#41—24no—
659C2×#41—24no—
660C2×#41—24no—
661C2×#41—24no—
662C2×#41—24no—
663C2×#41—212no—
664C2×#41—46no—
665C2×#41—46no—
666C2×#41C2×D418yes—
667C22×Q8—24no—
668C22×Q8—24no—
669C22×Q8—24no—
670C22×Q8—24no—
671C22×Q8—24no—
672C22×Q8—24no—
673C22×Q8C2413yes—
674C22×Q8C2413yes—
675C22×Q8C2413yes—
676C22×Q8C2413yes—
677C22×Q8C2411yescharacteristic
678C22×D4C2413yes—
679C22×D4C2413yes—
680C22×D4C2411yescharacteristic
681C22×D4C2413yes—
682C22×D4C2413yes—
683C22×D4C2413yes—
684C22×D4C2413yes—
685C22×D4C2413yes—
686C22×D4C2413yes—
687C22×D4C2413yes—
688C22×D4C2416yes—
689C22×D4C2416yes—
690C22×D4C2413yes—
691C22×D4C2413yes—
692C22×D4C2413yes—
693C22×D4C2416yes—
694C23×C4C2413yes—
695C23×C4C2413yes—
696C23×C4C2413yes—
697C23×C4C2413yes—
698C23×C4C2411yescharacteristic
699C23×C4C2413yes—
700C23×C4C2413yes—
701C23×C4C2416yes—
702C23×C4C2413yes—
703C23×C4C2413yes—
704C23×C4C2413yes—
705C23×C4C2413yes—
706C23×C4C2413yes—
707C23×C4C2413yes—
708C23×C4C2413yes—
709C23×C4C2413yes—
710C4⋊Q8—212no—
711C4⋊Q8—212no—
712C4⋊Q8—46no—
713#127—212no—
714#127—212no—
715#127—46no—
716#126—224no—
717#126—224no—
718#126—24no—
719#126—212no—
720#126—224no—
721#125—212no—
722#125—212no—
723#125—212no—
724#125—212no—
725#125—212no—
726#124—212no—
727#124—212no—
728#124—224no—
729#124—224no—
730#124—212no—
731#124—212no—
732#124—212no—
733#124—46no—
734#124—46no—
735#123—224no—
736#123—212no—
737#123—224no—
738#123—212no—
739#123—224no—
740#123—224no—
741C22⋊Q8—212no—
742C22⋊Q8—212no—
743C22⋊Q8—212no—
744C22⋊Q8—212no—
745C22⋊Q8—212no—
746C22⋊Q8—46no—
747C22⋊Q8—46no—
748C22⋊Q8—412no—
749C22⋊Q8—46no—
750C22⋊Q8—46no—
751C22⋊Q8—46no—
752C22⋊Q8—46no—
753#121—212no—
754#121—212no—
755#121—212no—
756#121—212no—
757#121—212no—
758#121—212no—
759#121—212no—
760#121—212no—
761#121—212no—
762#121—224no—
763#121—224no—
764#121—412no—
765#121—46no—
766#121—46no—
767#121—46no—
768#121—46no—
769#121—46no—
770#121—46no—
771#121—412no—
772#121—412no—
773#121—46no—
774#121—46no—
775#121—46no—
776#121—46no—
777C4×Q8—24no—
778C4×Q8—24no—
779C4×Q8—24no—
780C4×Q8—24no—
781C4×Q8—24no—
782C4×Q8—24no—
783C4×Q8—24no—
784C4×Q8—24no—
785C4×Q8—212no—
786C4×Q8—212no—
787C4×Q8—212no—
788C4×Q8—212no—
789C4×Q8—212no—
790C4×Q8—212no—
791C4×Q8—212no—
792C4×Q8C2×D418yes—
793C4×Q8C2×D418yes—
794C4×D4—212no—
795C4×D4—212no—
796C4×D4—212no—
797C4×D4—212no—
798C4×D4—224no—
799C4×D4—212no—
800C4×D4—212no—
801C4×D4—224no—
802C4×D4—212no—
803C4×D4—212no—
804C4×D4—212no—
805C4×D4—212no—
806C4×D4—212no—
807C4×D4—212no—
808C4×D4—212no—
809C4×D4—46no—
810C4×D4—46no—
811C4×D4—46no—
812C4×D4—46no—
813C4×D4—46no—
814C4×D4—46no—
815C4×D4—46no—
816C4×D4—46no—
817C4×D4C2×D4124yes—
818C4×D4C2×D4124yes—
819#117—212no—
820#117—212no—
821#117—212no—
822#117—24no—
823#117—212no—
824#117—212no—
825#117—212no—
826#117—224no—
827#117—46no—
828#117—46no—
829#117C2×D4124yes—
830C2×C4⋊C4—212no—
831C2×C4⋊C4—212no—
832C2×C4⋊C4—46no—
833C2×C4⋊C4—46no—
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2413yes—
837C2×C4⋊C4C2413yes—
838C2×C4⋊C4C2413yes—
839C2×C4⋊C4C2416yes—
840C2×C4⋊C4C2413yes—
841C2×C4⋊C4C2413yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2413yes—
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2413yes—
847C2×C4⋊C4C2413yes—
848C2×C4⋊C4C2413yes—
849C2×C4⋊C4C2413yes—
850C2×C4⋊C4C2413yes—
851C2×C4⋊C4C2413yes—
852C2×C4⋊C4C2413yes—
853C2×C4⋊C4C2413yes—
854C2×C4⋊C4C2413yes—
855C2×C4⋊C4C2413yes—
856C2×C4⋊C4C2413yes—
857C2×C4⋊C4C2413yes—
858C2×C4⋊C4C2416yes—
859C2×C4⋊C4C2411yescharacteristic
860C2×C4⋊C4C2413yes—
861C2×C4⋊C4C2416yes—
862C2×C4⋊C4C2413yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2413yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2413yes—
867C2×C4⋊C4C2413yes—
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2413yes—
870C2×C4⋊C4C2413yes—
871C2×C4⋊C4C2413yes—
872C2×C4⋊C4C2413yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2413yes—
875C2×C4⋊C4C2413yes—
876C2×C4⋊C4C2413yes—
877C2×C4⋊C4C2413yes—
878C2×C4⋊C4C2416yes—
879C2×C4⋊C4C2413yes—
880C2×C4⋊C4C2416yes—
881C2×C4⋊C4C2416yes—
882C2×C4⋊C4C2416yes—
883C2×C4⋊C4C2413yes—
884C2×C4⋊C4C2413yes—
885C2×C4⋊C4C2416yes—
886C2×C4⋊C4C2413yes—
887C2×C4⋊C4C2413yes—
888C2×C22⋊C4C2411yescharacteristic
889C2×C22⋊C4C2413yes—
890C2×C22⋊C4C2413yes—
891C2×C22⋊C4C2411yescharacteristic
892C2×C22⋊C4C2411yescharacteristic
893C2×C22⋊C4C2413yes—
894C2×C22⋊C4C2413yes—
895C2×C22⋊C4C2413yes—
896C2×C22⋊C4C2416yes—
897C2×C22⋊C4C2413yes—
898C2×C22⋊C4C2413yes—
899C2×C22⋊C4C2413yes—
900C2×C22⋊C4C2416yes—
901C2×C22⋊C4C2411yescharacteristic
902C2×C22⋊C4C2413yes—
903C2×C22⋊C4C2411yescharacteristic
904C2×C22⋊C4C2413yes—
905C2×C22⋊C4C2416yes—
906C2×C22⋊C4C2416yes—
907C2×C22⋊C4C2416yes—
908C2×C22⋊C4C2413yes—
909C2×C22⋊C4C2411yescharacteristic
910C2×C22⋊C4C2411yescharacteristic
911C2×C22⋊C4C2411yescharacteristic
912C2×C22⋊C4C2413yes—
913C2×C22⋊C4C2413yes—
914C2×C22⋊C4C2413yes—
915C2×C22⋊C4C2413yes—
916C2×C22⋊C4C2411yescharacteristic
917C2×C22⋊C4C2416yes—
918C2×C22⋊C4C2416yes—
919C2×C22⋊C4C2411yescharacteristic
920C2×C22⋊C4C2411yescharacteristic
921C2×C22⋊C4C2413yes—
922C2×C22⋊C4C2413yes—
923C2×C22⋊C4C2413yes—
924C2×C22⋊C4C2413yes—
925C2×C22⋊C4C2413yes—
926C2×C22⋊C4C2413yes—
927C2×C22⋊C4C2416yes—
928C2×C22⋊C4C2416yes—
929C2×C22⋊C4C2413yes—
930C2×C22⋊C4C2413yes—
931C2×C22⋊C4C2413yes—
932C2×C22⋊C4C2413yes—
933C2×C22⋊C4C2413yes—
934C2×C22⋊C4C2413yes—
935C2×C22⋊C4C2416yes—
936C2×C22⋊C4C2416yes—
937C2×C22⋊C4C2416yes—
938C2×C22⋊C4C2413yes—
939C2×C22⋊C4C2413yes—
940C2×C22⋊C4C2416yes—
941C2×C22⋊C4C2416yes—
942C2×C42—212no—
943C2×C42—212no—
944C2×C42—46no—
945C2×C42—46no—
946C2×C42C2×D4124yes—
947C2×C42C2411yescharacteristic
948C2×C42C2413yes—
949C2×C42C2416yes—
950C2×C42C2413yes—
951C2×C42C2413yes—
952C2×C42C2413yes—
953C2×C42C2413yes—
954C2×C42C2413yes—
955C2×C42C2413yes—
956C2×C42C2413yes—
957C2×C42C2413yes—
958C2×C42C2413yes—
959C2×C42C2413yes—
960C2×C42C2413yes—
961C2×C42C2413yes—
962C2×C42C2411yescharacteristic
963C2×C42C2411yescharacteristic
964C2×C42C2413yes—
965C2×C42C2411yescharacteristic
966C2×C42C2413yes—
967C2×C42C2413yes—
968#95C2411yescharacteristic
969#95C2411yescharacteristic
970#95C2413yes—
971#95C2413yes—
972#95C2413yes—
973#95C2413yes—
974#95C2413yes—
975#95C2413yes—
976#95C2411yescharacteristic
977#95C2411yescharacteristic
978#95C2411yescharacteristic
979#95C2411yescharacteristic
980#95C2413yes—
981#95C2413yes—
982#95C2413yes—
983#95C2413yes—
984#95C2413yes—
985#95C2413yes—
986#95C2413yes—
987#95C2413yes—
988#95C2413yes—
989#95C2413yes—
990#95C2413yes—
991#95C2413yes—
992#95C2411yescharacteristic
993#95C2411yescharacteristic
994#95C2413yes—
995#95C2413yes—
996#95C2416yes—
997#95C2416yes—
998#95C2413yes—
999#95C2413yes—
1000#95C2413yes—
1001#95C2413yes—
1002#95C2416yes—
1003#95C2416yes—
1004#95C2416yes—
1005#95C2416yes—
1006#95C2416yes—
1007#95C2416yes—
1008C24C2511yescharacteristic
1009C24C2513yes—
1010C24C2513yes—
1011C24C2513yes—
1012C24C2511yescharacteristic
1013#41—232no—
1014#41—448no—
1015#41—416no—
1016#41—416no—
1017C2×Q8—26no—
1018C2×Q8—26no—
1019C2×Q8—26no—
1020C2×Q8—26no—
1021C2×Q8—26no—
1022C2×Q8—26no—
1023C2×Q8—26no—
1024C2×Q8—26no—
1025C2×Q8—26no—
1026C2×Q8—43no—
1027C2×Q8—43no—
1028C2×Q8—43no—
1029C2×Q8—416no—
1030C2×Q8—416no—
1031C2×Q8C22×D414yes—
1032C2×Q8H(5,𝔽2)14yes—
1033C2×Q82−1+414yes—
1034C2×D4—26no—
1035C2×D4—26no—
1036C2×D4—22no—
1037C2×D4—26no—
1038C2×D4—26no—
1039C2×D4—26no—
1040C2×D4—212no—
1041C2×D4—212no—
1042C2×D4—26no—
1043C2×D4—26no—
1044C2×D4—26no—
1045C2×D4—26no—
1046C2×D4—26no—
1047C2×D4—26no—
1048C2×D4—26no—
1049C2×D4—26no—
1050C2×D4—26no—
1051C2×D4—26no—
1052C2×D4—26no—
1053C2×D4—26no—
1054C2×D4—22no—
1055C2×D4—26no—
1056C2×D4—26no—
1057C2×D4—41no—
1058C2×D4—43no—
1059C2×D4—43no—
1060C2×D4—43no—
1061C2×D4—43no—
1062C2×D4—43no—
1063C2×D4—43no—
1064C2×D4—43no—
1065C2×D4—43no—
1066C2×D4—43no—
1067C2×D4—43no—
1068C2×D4—46no—
1069C2×D4—43no—
1070C2×D4—46no—
1071C2×D4—43no—
1072C2×D4—46no—
1073C2×D4—43no—
1074C2×D4—43no—
1075C2×D4—43no—
1076C2×D4—46no—
1077C2×D4—43no—
1078C2×D4—46no—
1079C2×D4—46no—
1080C2×D4—46no—
1081C2×D4C22×D4112yes—
1082C22×C4—22no—
1083C22×C4—22no—
1084C22×C4—26no—
1085C22×C4—26no—
1086C22×C4—22no—
1087C22×C4—26no—
1088C22×C4—26no—
1089C22×C4—26no—
1090C22×C4—26no—
1091C22×C4—26no—
1092C22×C4—26no—
1093C22×C4—26no—
1094C22×C4—26no—
1095C22×C4—26no—
1096C22×C4—26no—
1097C22×C4—26no—
1098C22×C4—26no—
1099C22×C4—26no—
1100C22×C4—26no—
1101C22×C4—26no—
1102C22×C4—212no—
1103C22×C4—26no—
1104C22×C4—26no—
1105C22×C4—43no—
1106C22×C4—43no—
1107C22×C4—43no—
1108C22×C4—43no—
1109C22×C4—43no—
1110C22×C4—43no—
1111C22×C4—43no—
1112C22×C4—43no—
1113C22×C4—43no—
1114C22×C4—43no—
1115C22×C4—43no—
1116C22×C4—43no—
1117C22×C4—43no—
1118C22×C4—43no—
1119C22×C4—43no—
1120C22×C4—43no—
1121C22×C4—46no—
1122C22×C4—43no—
1123C22×C4—43no—
1124C22×C4—43no—
1125C22×C4—43no—
1126C22×C4—46no—
1127C22×C4C22×D4112yes—
1128C22×C4C22×D4112yes—
1129C22×C4C22×D4112yes—
1130C22×C4C2511yescharacteristic
1131C22×C4C2511yescharacteristic
1132C22×C4C2513yes—
1133C22×C4C2513yes—
1134C22×C4C2513yes—
1135C22×C4C2511yescharacteristic
1136C22×C4C2511yescharacteristic
1137C22×C4C2511yescharacteristic
1138C22×C4C2513yes—
1139C22×C4C2511yescharacteristic
1140C22×C4C2513yes—
1141C22×C4C2513yes—
1142C22×C4C2513yes—
1143C22×C4C2513yes—
1144C22×C4C2513yes—
1145C22×C4C2513yes—
1146C22×C4C2511yescharacteristic
1147C22×C4C2511yescharacteristic
1148C22×C4C2513yes—
1149C22×C4C2513yes—
1150C22×C4C2511yescharacteristic
1151C22×C4C2511yescharacteristic
1152C22×C4C2511yescharacteristic
1153C22×C4C2511yescharacteristic
1154C22×C4C2511yescharacteristic
1155C22×C4C2513yes—
1156C4⋊C4—26no—
1157C4⋊C4—26no—
1158C4⋊C4—26no—
1159C4⋊C4—212no—
1160C4⋊C4—22no—
1161C4⋊C4—26no—
1162C4⋊C4—22no—
1163C4⋊C4—22no—
1164C4⋊C4—26no—
1165C4⋊C4—26no—
1166C4⋊C4—26no—
1167C4⋊C4—26no—
1168C4⋊C4—26no—
1169C4⋊C4—26no—
1170C4⋊C4—26no—
1171C4⋊C4—26no—
1172C4⋊C4—212no—
1173C4⋊C4—22no—
1174C4⋊C4—26no—
1175C4⋊C4—212no—
1176C4⋊C4—26no—
1177C4⋊C4—22no—
1178C4⋊C4—26no—
1179C4⋊C4—26no—
1180C4⋊C4—26no—
1181C4⋊C4—26no—
1182C4⋊C4—26no—
1183C4⋊C4—22no—
1184C4⋊C4—22no—
1185C4⋊C4—26no—
1186C4⋊C4—26no—
1187C4⋊C4—22no—
1188C4⋊C4—26no—
1189C4⋊C4—26no—
1190C4⋊C4—22no—
1191C4⋊C4—43no—
1192C4⋊C4—43no—
1193C4⋊C4—43no—
1194C4⋊C4—43no—
1195C4⋊C4—41no—
1196C4⋊C4—43no—
1197C4⋊C4—43no—
1198C4⋊C4—43no—
1199C4⋊C4—43no—
1200C4⋊C4—46no—
1201C4⋊C4—46no—
1202C4⋊C4—43no—
1203C4⋊C4—46no—
1204C4⋊C4—46no—
1205C4⋊C4—43no—
1206C4⋊C4—43no—
1207C4⋊C4—46no—
1208C4⋊C4C22×D4112yes—
1209C4⋊C4C22×D4112yes—
1210C22⋊C4—26no—
1211C22⋊C4—26no—
1212C22⋊C4—26no—
1213C22⋊C4—212no—
1214C22⋊C4—212no—
1215C22⋊C4—26no—
1216C22⋊C4—22no—
1217C22⋊C4—26no—
1218C22⋊C4—22no—
1219C22⋊C4—26no—
1220C22⋊C4—26no—
1221C22⋊C4—22no—
1222C22⋊C4—22no—
1223C22⋊C4—26no—
1224C22⋊C4—26no—
1225C22⋊C4—212no—
1226C22⋊C4—26no—
1227C22⋊C4—26no—
1228C22⋊C4—212no—
1229C22⋊C4—22no—
1230C22⋊C4—26no—
1231C22⋊C4—22no—
1232C22⋊C4—212no—
1233C22⋊C4—22no—
1234C22⋊C4—22no—
1235C22⋊C4—26no—
1236C22⋊C4—26no—
1237C22⋊C4—26no—
1238C22⋊C4—22no—
1239C22⋊C4—46no—
1240C22⋊C4—46no—
1241C22⋊C4—41no—
1242C22⋊C4—41no—
1243C22⋊C4—43no—
1244C22⋊C4—43no—
1245C22⋊C4—43no—
1246C22⋊C4—43no—
1247C22⋊C4—43no—
1248C22⋊C4—43no—
1249C22⋊C4—43no—
1250C22⋊C4—43no—
1251C22⋊C4—43no—
1252C22⋊C4—46no—
1253C22⋊C4—43no—
1254C22⋊C4—43no—
1255C22⋊C4—43no—
1256C22⋊C4—46no—
1257C22⋊C4—46no—
1258C22⋊C4—46no—
1259C22⋊C4—46no—
1260C22⋊C4—43no—
1261C22⋊C4—43no—
1262C22⋊C4—46no—
1263C22⋊C4C22×D4124yes—
1264C42—22no—
1265C42—26no—
1266C42—26no—
1267C42—26no—
1268C42—26no—
1269C42—26no—
1270C42—212no—
1271C42—26no—
1272C42—26no—
1273C42—26no—
1274C42—26no—
1275C42—26no—
1276C42—26no—
1277C42—41no—
1278C42—41no—
1279C42—43no—
1280C42—43no—
1281C42C22×D4112yes—
1282C42C22×D414yes—
1283C42C22×D4112yes—
1284C42C22×D4112yes—
1285C23—21no—
1286C23—21no—
1287C23—23no—
1288C23—21no—
1289C23—23no—
1290C23—21no—
1291C23—23no—
1292C23—23no—
1293C23—21no—
1294C23—21no—
1295C23—23no—
1296C23—23no—
1297C23—23no—
1298C23—23no—
1299C23—21no—
1300C23—21no—
1301C23—23no—
1302C23—23no—
1303C23—21no—
1304C23—23no—
1305C23—23no—
1306C23—23no—
1307C23—23no—
1308C23—21no—
1309C23—21no—
1310C23—23no—
1311C23—23no—
1312C23—21no—
1313C23—21no—
1314C23—23no—
1315C23—23no—
1316C23—23no—
1317C23—23no—
1318C23C23×D416yes—
1319C23#58512yes—
1320C23C2611yescharacteristic
1321Q8—412no—
1322Q8—412no—
1323Q8—412no—
1324Q8—86no—
1325Q8#537116yes—
1326D4—224no—
1327D4—44no—
1328D4—412no—
1329D4—412no—
1330D4—412no—
1331D4—412no—
1332D4—412no—
1333D4—86no—
1334D4—86no—
1335D4—86no—
1336D4—86no—
1337D4—86no—
1338D4—812no—
1339D4—812no—
1340D4—86no—
1341D4—166no—
1342C2×C4—28no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—23no—
1351C2×C4—23no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—23no—
1355C2×C4—23no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—224no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—23no—
1364C2×C4—21no—
1365C2×C4—23no—
1366C2×C4—23no—
1367C2×C4—23no—
1368C2×C4—23no—
1369C2×C4—23no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—23no—
1374C2×C4—23no—
1375C2×C4—23no—
1376C2×C4—23no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—23no—
1380C2×C4—23no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—23no—
1384C2×C4—23no—
1385C2×C4—21no—
1386C2×C4—21no—
1387C2×C4—21no—
1388C2×C4—23no—
1389C2×C4—23no—
1390C2×C4—23no—
1391C2×C4—23no—
1392C2×C4—21no—
1393C2×C4—23no—
1394C2×C4—21no—
1395C2×C4—23no—
1396C2×C4—21no—
1397C2×C4—23no—
1398C2×C4—21no—
1399C2×C4—23no—
1400C2×C4—23no—
1401C2×C4—23no—
1402C2×C4—23no—
1403C2×C4—23no—
1404C2×C4—23no—
1405C2×C4—23no—
1406C2×C4—23no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—23no—
1411C2×C4—412no—
1412C2×C4—412no—
1413C2×C4—412no—
1414C2×C4—412no—
1415C2×C4—412no—
1416C2×C4—412no—
1417C2×C4—412no—
1418C2×C4—86no—
1419C2×C4—86no—
1420C2×C4—812no—
1421C2×C4—86no—
1422C2×C4—86no—
1423C2×C4—86no—
1424C2×C4—86no—
1425C2×C4C23×D412yes—
1426C2×C4C23×D416yes—
1427C2×C4C23×D416yes—
1428C2×C4C23×D412yes—
1429C2×C4C23×D412yes—
1430C2×C4C23×D416yes—
1431C2×C4C2×H(5,𝔽2)16yes—
1432C2×C4C2×2−1+416yes—
1433C2×C4#58512yes—
1434C2×C4#58512yes—
1435C2×C4#58512yes—
1436C22—22no—
1437C22—22no—
1438C22—22no—
1439C22—26no—
1440C22—26no—
1441C22—26no—
1442C22—43no—
1443C22—41no—
1444C22—43no—
1445C22—43no—
1446C22—41no—
1447C22—43no—
1448C22—41no—
1449C22—41no—
1450C22—41no—
1451C22—43no—
1452C22—43no—
1453C22—41no—
1454C22—43no—
1455C22—43no—
1456C22—41no—
1457C22—43no—
1458C22—43no—
1459C22—41no—
1460C22—43no—
1461C22—43no—
1462C22—43no—
1463C22—43no—
1464C22—41no—
1465C22—43no—
1466C22—41no—
1467C22—43no—
1468C22—41no—
1469C22—43no—
1470C22—43no—
1471C22C24×D411yescharacteristic
1472C22C22×H(5,𝔽2)11yescharacteristic
1473C22C22×2−1+411yescharacteristic
1474C22C2×#58511yescharacteristic
1475C22C2×#58511yescharacteristic
1476C22C2×#58511yescharacteristic
1477C22C2×#58511yescharacteristic
1478C4—22no—
1479C4—22no—
1480C4—22no—
1481C4—22no—
1482C4—26no—
1483C4—22no—
1484C4—26no—
1485C4—22no—
1486C4—43no—
1487C4—41no—
1488C4—43no—
1489C4—41no—
1490C4—43no—
1491C4—43no—
1492C4—43no—
1493C4—43no—
1494C4—41no—
1495C4—41no—
1496C4—43no—
1497C4—43no—
1498C4—41no—
1499C4—41no—
1500C4—41no—
1501C4—43no—
1502C4—43no—
1503C4C2×#537112yes—
1504C2—42no—
1505C2—46no—
1506C2—81no—
1507C2—83no—
1508C2—83no—
1509C2C22×#53711yescharacteristic
1510C2#6281111yescharacteristic
1511C2#6281211yescharacteristic
1512C2#6301911yescharacteristic
1513C2#6302011yescharacteristic
1514C2#6303311yescharacteristic
1515C2#6303411yescharacteristic
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×#3524C2semidirect
2. C2×#3480C2semidirect
3. #42445C2semidirect
4. #42444C2semidirect
5. #42441C2semidirect
6. #42440C2semidirect
7. #39963C2semidirect
8. #39962C2semidirect
9. #39959C2semidirect
10. #39958C2semidirect
11. #39857C2semidirect
12. #39856C2semidirect
13. #39853C2semidirect
14. #39852C2semidirect
15. #37553C2semidirect
16. #36455C2semidirect
17. #36444C2semidirect
18. #36435C2semidirect
19. #36434C2semidirect
20. #36431C2semidirect
21. #36430C2semidirect
22. #36430C2semidirect
23. #36430C2semidirect
24. #35831C2semidirect
25. #35816C2semidirect
26. #35786C2semidirect
27. #35771C2semidirect
28. #35189C2semidirect
29. #35103C2semidirect
30. #34964C2semidirect
31. C4⋊C4×#41C2semidirect
346. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35242
C2×#34802
#424452
#424442
#424412
#424402
#399632
#399622
#399592
#399582
#398572
#398562
#398532
#398522
#375532
#364552
#364442
#364352
#364342
#364312
#364302
#358312
#358162
#357862
#357712
#351892
#351032
#349642
C4⋊C4×#412