Finite Group Databasebeta

← #7643459

Subgroups — #7643459

Order 512.

6688 conjugacy classes of subgroups.

The subgroup lattice has 1175 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3509C211yesmaximal, characteristic, complemented
2C2×#3511C211yesmaximal, characteristic
3#39613C214yesmaximal, complemented
4#39485C214yesmaximal, complemented
5#39162C214yesmaximal, complemented
6#38946C214yesmaximal, complemented
7#38091C214yesmaximal, complemented
8#38088C214yesmaximal, complemented
9#37871C214yesmaximal, complemented
10#37870C214yesmaximal, complemented
11#37389C214yesmaximal, complemented
12#37388C214yesmaximal, complemented
13#36645C211yesmaximal, characteristic, complemented
14#36639C211yesmaximal, characteristic, complemented
15#35669C214yesmaximal, complemented
16#35622C214yesmaximal, complemented
17#35322C211yesmaximal, characteristic, complemented
18#35322C211yesmaximal, characteristic, complemented
19#35320C211yesmaximal, characteristic, complemented
20#35298C211yesmaximal, characteristic, complemented
21#35298C211yesmaximal, characteristic, complemented
22#35298C211yesmaximal, characteristic, complemented
23#35298C211yesmaximal, characteristic, complemented
24#35289C211yesmaximal, characteristic, complemented
25#35281C211yesmaximal, characteristic, complemented
26#35281C211yesmaximal, characteristic, complemented
27#34026C211yesmaximal, characteristic, complemented
28#3511—216no—
29#3509—216no—
30C2×#557C2212yes—
31C2×#557C2212yes—
32C2×#556C2212yes—
33C2×#556C2212yes—
34C2×#556C2212yes—
35C2×#555C2212yes—
36C2×#554C2212yes—
37C2×#553C2212yes—
38C2×#553C2212yes—
39C2×#552C2212yes—
40C2×#552C2212yes—
41C2×#552C2212yes—
42C2×#552C2212yes—
43C2×#548C2212yes—
44C2×#548C2212yes—
45C2×#547C2212yes—
46C2×#542C2212yes—
47C2×#542C2212yes—
48C2×#541C2212yes—
49C2×#541C2212yes—
50C2×#537C2212yes—
51C2×#536C2212yes—
52C2×#533C2211yescharacteristic
53C2×#533C2211yescharacteristic
54C2×#533C2211yescharacteristic
55C2×#533C2211yescharacteristic
56C2×#533C2211yescharacteristic
57C2×#533C2211yescharacteristic
58C2×#533C2211yescharacteristic
59C2×#532C2211yescharacteristic
60C2×#532C2211yescharacteristic
61C2×#532C2211yescharacteristic
62C22×C4⋊Q8C2211yescharacteristic
63C22×C4⋊Q8C2211yescharacteristic
64C2×#520C2212yes—
65C2×#519C2212yes—
66C2×C4×#41C2211yescharacteristic
67#2868C2211yescharacteristic
68#2868C2211yescharacteristic
69#2868C2211yescharacteristic
70#2868C2211yescharacteristic
71#2862C2211yescharacteristic
72#2862C2211yescharacteristic
73#2862C2211yescharacteristic
74#2862C2211yescharacteristic
75#2862C2211yescharacteristic
76#2862C2211yescharacteristic
77#2862C2211yescharacteristic
78#2862C2211yescharacteristic
79#2861C2214yes—
80#2859C2214yes—
81#2858C2211yescharacteristic
82#2858C2211yescharacteristic
83#2858C2211yescharacteristic
84#2858C2211yescharacteristic
85#2857C2214yes—
86#2857C2214yes—
87#2850C2214yes—
88#2850C2214yes—
89#2729C22116yes—
90#2725C22116yes—
91#2715C22116yes—
92#2708C22116yes—
93#2704C22116yes—
94#2701C22116yes—
95#2695C22116yes—
96#2686C22116yes—
97#2660C2214yes—
98#2660C2214yes—
99#2642C2214yes—
100#2640C2214yes—
101#2621C2214yes—
102#2621C2214yes—
103#2620C2214yes—
104#2620C2214yes—
105#2620C2214yes—
106#2620C2214yes—
107#2568C2214yes—
108#2568C2214yes—
109#2567C2214yes—
110#2567C2214yes—
111#2566C2214yes—
112#2566C2214yes—
113#2566C2214yes—
114#2566C2214yes—
115#2565C2214yes—
116#2565C2214yes—
117#2565C2214yes—
118#2565C2214yes—
119#2563C2214yes—
120#2547C2214yes—
121#2546C2214yes—
122#2546C2214yes—
123#2545C2214yes—
124#2545C2214yes—
125#2545C2214yes—
126#2545C2214yes—
127#2504C2214yes—
128#2503C2214yes—
129#2503C2214yes—
130#2502C2214yes—
131#2502C2214yes—
132#2500C2214yes—
133#2500C2214yes—
134#2500C2214yes—
135#2500C2214yes—
136#2499C2214yes—
137#2499C2214yes—
138#2499C2214yes—
139#2499C2214yes—
140#2475C22116yes—
141#2474C22116yes—
142#2473C22116yes—
143#2470C22116yes—
144#2469C22116yes—
145#2468C22116yes—
146#2466C22116yes—
147#2465C22116yes—
148#2436C2214yes—
149#2434C2214yes—
150#2434C2214yes—
151#2432C2214yes—
152#2432C2214yes—
153#2432C2214yes—
154#2432C2214yes—
155#2327C2214yes—
156#2327C2214yes—
157#2326C2214yes—
158#2326C2214yes—
159#2326C2214yes—
160#2326C2214yes—
161#2317C2214yes—
162#2317C2214yes—
163#2311C2214yes—
164#2310C2214yes—
165C4×C4⋊Q8C2214yes—
166C4×C4⋊Q8C2214yes—
167C4×#124C2214yes—
168C4×#124C2214yes—
169#2298C2212yes—
170#2298C2212yes—
171#2297C2212yes—
172#2297C2214yes—
173#2296C2212yes—
174#2295C2212yes—
175#2295C2212yes—
176#2293C2212yes—
177#2293C2212yes—
178#2290C2212yes—
179#2290C2212yes—
180#2290C2212yes—
181#2290C2212yes—
182#2285C2214yes—
183C4×#117C2211yescharacteristic
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C4×#117C2211yescharacteristic
187C4×#117C2211yescharacteristic
188C2×C43C2211yescharacteristic
189C22×#41C2312yes—
190C22×#41C2312yes—
191C22×#41C2312yes—
192C22×#41C2311yescharacteristic
193C23×Q8C2312yes—
194C23×Q8C2312yes—
195#557—216no—
196#557—216no—
197#556—216no—
198#556—216no—
199#556—216no—
200#555—216no—
201#554—216no—
202#553—216no—
203#553—216no—
204#552—216no—
205#552—216no—
206#552—216no—
207#552—216no—
208#548—216no—
209#548—216no—
210#547—216no—
211#542—216no—
212#542—216no—
213#541—216no—
214#541—216no—
215#537—216no—
216#536—216no—
217#533—28no—
218#533—28no—
219#533—28no—
220#533—28no—
221#533—28no—
222#533—28no—
223#533—28no—
224#532—28no—
225#532—28no—
226#532—28no—
227C2×C4⋊Q8—28no—
228C2×C4⋊Q8—28no—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2311yescharacteristic
236C2×C4⋊Q8C2311yescharacteristic
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2311yescharacteristic
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2312yes—
242C2×C4⋊Q8C2314yes—
243C2×C4⋊Q8C2314yes—
244C2×C4⋊Q8C2314yes—
245C2×C4⋊Q8C2314yes—
246C2×C4⋊Q8C2314yes—
247C2×#127C2311yescharacteristic
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#126C2314yes—
254C2×#125C2312yes—
255C2×#125C2312yes—
256C2×#125C2312yes—
257C2×#125C2312yes—
258C2×#125C2312yes—
259C2×#125C2312yes—
260C2×#125C2312yes—
261C2×#125C2314yes—
262C2×#125C2314yes—
263C2×#125C2314yes—
264C2×#125C2314yes—
265C2×#124C2314yes—
266C2×#124C2312yes—
267C2×#124C2312yes—
268C2×#124C2312yes—
269C2×#124C2314yes—
270C2×#124C2314yes—
271C2×#124C2314yes—
272C2×#124C2314yes—
273C2×#124C2314yes—
274C2×#124C2314yes—
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×#121C2312yes—
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2314yes—
303C2×#121C2314yes—
304C2×#121C2314yes—
305#520—216no—
306#519—216no—
307C4×#41D4116yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2314yes—
323C2×C4×Q8C2314yes—
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2311yescharacteristic
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2311yescharacteristic
335C2×C4×D4C2311yescharacteristic
336C2×C4×D4C2311yescharacteristic
337C2×C4×D4C2311yescharacteristic
338C2×C4×D4C2311yescharacteristic
339C2×C4×D4C2311yescharacteristic
340C2×#117C2312yes—
341C2×#117C2312yes—
342C2×#117C2312yes—
343C2×#117C2312yes—
344C2×#117C2312yes—
345C2×#117C2312yes—
346C2×#117C2314yes—
347C2×#117C2314yes—
348C2×#117C2314yes—
349C2×#117C2312yes—
350C2×#117C2312yes—
351C2×#117C2312yes—
352C2×#117C2312yes—
353C2×#117C2312yes—
354C2×#117C2312yes—
355C2×#117C2311yescharacteristic
356C2×#117C2311yescharacteristic
357C2×#117C2311yescharacteristic
358C22×C4⋊C4C2312yes—
359C22×C4⋊C4C2312yes—
360C22×C4⋊C4C2312yes—
361C22×C4⋊C4C2312yes—
362C22×C4⋊C4C2314yes—
363C22×C42C2312yes—
364C22×C42C2312yes—
365C22×C42C2312yes—
366C22×C42C2311yescharacteristic
367C22×C42C2311yescharacteristic
368C22×C42C2311yescharacteristic
369#400C23116yes—
370#400C23116yes—
371#398C23116yes—
372#398C23116yes—
373#398C23116yes—
374#398C23116yes—
375#397C23116yes—
376#397C23116yes—
377#397C23116yes—
378#396C23116yes—
379#396C23116yes—
380#396C23116yes—
381#396C23116yes—
382#395C23116yes—
383#395C23116yes—
384#394C23116yes—
385#394C23116yes—
386#394C23116yes—
387#394C23116yes—
388#393C23116yes—
389#391C2314yes—
390#391C2314yes—
391#391C2314yes—
392#391C2314yes—
393#391C2314yes—
394#391C2314yes—
395#391C2314yes—
396#391C2314yes—
397#391C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C23116yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#390C2314yes—
408#390C2314yes—
409#390C2314yes—
410#390C2314yes—
411#390C2314yes—
412#390C2314yes—
413#390C2314yes—
414#390C2314yes—
415#390C2314yes—
416#389C23116yes—
417#389C23116yes—
418#389C23116yes—
419#389C23116yes—
420#389C2314yes—
421#389C2314yes—
422#388C23116yes—
423#388C23116yes—
424#388C23116yes—
425#388C23116yes—
426#388C23116yes—
427#388C23116yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#387C23116yes—
433#387C23116yes—
434#387C23116yes—
435#387C23116yes—
436#387C2314yes—
437#387C2314yes—
438#387C2314yes—
439#387C2314yes—
440#386C23116yes—
441#386C23116yes—
442#386C2314yes—
443#386C2314yes—
444#385C23116yes—
445#385C23116yes—
446#385C23116yes—
447#385C23116yes—
448#385C23116yes—
449#385C23116yes—
450#385C2314yes—
451#385C2314yes—
452#384C2314yes—
453#384C2314yes—
454#384C2314yes—
455#384C2314yes—
456#384C2314yes—
457#384C2314yes—
458#384C2314yes—
459#384C2314yes—
460#382C2314yes—
461#382C2314yes—
462#382C2314yes—
463#382C2314yes—
464#382C2314yes—
465#382C2314yes—
466#382C2314yes—
467#382C2314yes—
468#381C23116yes—
469#380C23116yes—
470#380C23116yes—
471C4×C4⋊C4C23116yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C22⋊C4C2312yes—
483C4×C22⋊C4C2312yes—
484C4×C22⋊C4C2312yes—
485C4×C22⋊C4C2312yes—
486C4×C22⋊C4C2312yes—
487C4×C22⋊C4C2312yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C23116yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2312yes—
493#376C2312yes—
494#376C2312yes—
495#376C2312yes—
496#376C2312yes—
497#376C2312yes—
498C43C2312yes—
499C43C2312yes—
500C43C2311yescharacteristic
501C43C2311yescharacteristic
502C43C2311yescharacteristic
503C43C2311yescharacteristic
504C43C2312yes—
505C2×#41—28no—
506C2×#41—28no—
507C2×#41—28no—
508C2×#41—44no—
509C2×#41—48no—
510C2×#41—48no—
511C2×#41—48no—
512C2×#41C2×D418yes—
513C22×Q8—28no—
514C22×Q8—28no—
515C22×Q8—48no—
516C22×Q8—48no—
517C22×Q8C2412yes—
518C22×Q8C2412yes—
519C22×Q8C2412yes—
520C22×Q8C2412yes—
521C22×Q8C2412yes—
522C22×Q8C2412yes—
523C22×Q8C2412yes—
524C22×Q8C2414yes—
525C22×Q8C2414yes—
526C22×Q8C2411yescharacteristic
527C22×D4C2412yes—
528C22×D4C2412yes—
529C22×D4C2412yes—
530C22×D4C2414yes—
531C22×D4C2414yes—
532C22×D4C2414yes—
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C23×C4C2411yescharacteristic
538C23×C4C2411yescharacteristic
539C23×C4C2411yescharacteristic
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542C23×C4C2411yescharacteristic
543C23×C4C2411yescharacteristic
544C23×C4C2411yescharacteristic
545C23×C4C2414yes—
546C23×C4C2414yes—
547C23×C4C2414yes—
548C23×C4C2414yes—
549C23×C4C2414yes—
550C23×C4C2414yes—
551C4⋊Q8—216no—
552C4⋊Q8—24no—
553C4⋊Q8—24no—
554C4⋊Q8—24no—
555C4⋊Q8—24no—
556C4⋊Q8—28no—
557C4⋊Q8—28no—
558C4⋊Q8—28no—
559C4⋊Q8—28no—
560C4⋊Q8—28no—
561C4⋊Q8—28no—
562C4⋊Q8—24no—
563C4⋊Q8—24no—
564C4⋊Q8—24no—
565C4⋊Q8—48no—
566C4⋊Q8—48no—
567C4⋊Q8—48no—
568C4⋊Q8—48no—
569#127—24no—
570#126—216no—
571#126—216no—
572#126—216no—
573#126—216no—
574#126—216no—
575#126—216no—
576#125—216no—
577#125—216no—
578#125—216no—
579#125—216no—
580#125—28no—
581#125—28no—
582#125—28no—
583#125—28no—
584#125—28no—
585#125—28no—
586#125—28no—
587#124—216no—
588#124—216no—
589#124—216no—
590#124—28no—
591#124—28no—
592#124—28no—
593#124—216no—
594#124—48no—
595#124—48no—
596#124—48no—
597#123—216no—
598#123—216no—
599#123—216no—
600#123—216no—
601C22⋊Q8—216no—
602C22⋊Q8—28no—
603C22⋊Q8—28no—
604C22⋊Q8—28no—
605C22⋊Q8—28no—
606C22⋊Q8—28no—
607C22⋊Q8—28no—
608C22⋊Q8—28no—
609C22⋊Q8—28no—
610C22⋊Q8—28no—
611C22⋊Q8—28no—
612C22⋊Q8—28no—
613C22⋊Q8—28no—
614C22⋊Q8—28no—
615C22⋊Q8—28no—
616C22⋊Q8—216no—
617C22⋊Q8—216no—
618#121—216no—
619#121—216no—
620#121—216no—
621#121—28no—
622#121—28no—
623#121—28no—
624#121—28no—
625#121—28no—
626#121—28no—
627C4×Q8—216no—
628C4×Q8—216no—
629C4×Q8—28no—
630C4×Q8—28no—
631C4×Q8—28no—
632C4×Q8—28no—
633C4×Q8—28no—
634C4×Q8—28no—
635C4×Q8—28no—
636C4×Q8—28no—
637C4×Q8—28no—
638C4×Q8—28no—
639C4×Q8—28no—
640C4×Q8—28no—
641C4×Q8—28no—
642C4×Q8—28no—
643C4×Q8C2×D418yes—
644C4×Q8C2×D418yes—
645C4×D4—216no—
646C4×D4—216no—
647C4×D4—28no—
648C4×D4—28no—
649C4×D4—28no—
650C4×D4—28no—
651C4×D4—28no—
652C4×D4—28no—
653C4×D4C2×D418yes—
654C4×D4C2×D418yes—
655C4×D4C2×D418yes—
656C4×D4C2×D418yes—
657C4×D4C2×D418yes—
658C4×D4C2×D418yes—
659#117—28no—
660#117—28no—
661#117—28no—
662#117—28no—
663#117—28no—
664#117—28no—
665#117—28no—
666#117—216no—
667#117—216no—
668#117—216no—
669#117—28no—
670#117—28no—
671#117—44no—
672#117—44no—
673#117—44no—
674#117C2×D418yes—
675#117C2×D418yes—
676#117C2×D418yes—
677C2×C4⋊C4—28no—
678C2×C4⋊C4—28no—
679C2×C4⋊C4—28no—
680C2×C4⋊C4—28no—
681C2×C4⋊C4—216no—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2412yes—
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2412yes—
690C2×C4⋊C4C2412yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2412yes—
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2412yes—
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2412yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2412yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C24116yes—
720C2×C4⋊C4C24116yes—
721C2×C4⋊C4C24116yes—
722C2×C4⋊C4C24116yes—
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2411yescharacteristic
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C24116yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C24116yes—
749C2×C22⋊C4C24116yes—
750C2×C22⋊C4C24116yes—
751C2×C22⋊C4C2411yescharacteristic
752C2×C22⋊C4C2411yescharacteristic
753C2×C22⋊C4C2411yescharacteristic
754C2×C22⋊C4C2411yescharacteristic
755C2×C22⋊C4C2411yescharacteristic
756C2×C22⋊C4C2411yescharacteristic
757C2×C42—28no—
758C2×C42—44no—
759C2×C42—44no—
760C2×C42C2×D418yes—
761C2×C42C2×D418yes—
762C2×C42C2×D418yes—
763C2×C42C2414yes—
764C2×C42C2414yes—
765C2×C42C2414yes—
766C2×C42C2414yes—
767C2×C42C2414yes—
768C2×C42C2414yes—
769C2×C42C2412yes—
770C2×C42C2414yes—
771C2×C42C2412yes—
772C2×C42C2412yes—
773C2×C42C2412yes—
774C2×C42C2412yes—
775C2×C42C2412yes—
776C2×C42C2412yes—
777C2×C42C2412yes—
778C2×C42C2412yes—
779C2×C42C2412yes—
780C2×C42C2412yes—
781C2×C42C2414yes—
782C2×C42C2414yes—
783C2×C42C2414yes—
784C2×C42C2411yescharacteristic
785C2×C42C2411yescharacteristic
786C2×C42C2411yescharacteristic
787C2×C42C2411yescharacteristic
788C2×C42C2411yescharacteristic
789C2×C42C2411yescharacteristic
790C2×C42C2411yescharacteristic
791C2×C42C2411yescharacteristic
792C2×C42C2411yescharacteristic
793C2×C42C2411yescharacteristic
794C2×C42C2412yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C24116yes—
806#95C24116yes—
807#95C24116yes—
808#95C24116yes—
809#95C24116yes—
810#95C24116yes—
811#95C24116yes—
812#95C24116yes—
813C24C2514yes—
814C24C2511yescharacteristic
815C24C2511yescharacteristic
816C24C2511yescharacteristic
817#41—416no—
818#41—432no—
819#41—816no—
820#41—816no—
821C2×Q8—24no—
822C2×Q8—24no—
823C2×Q8—24no—
824C2×Q8—24no—
825C2×Q8—24no—
826C2×Q8—28no—
827C2×Q8—24no—
828C2×Q8—24no—
829C2×Q8—28no—
830C2×Q8—28no—
831C2×Q8—28no—
832C2×Q8—28no—
833C2×Q8—28no—
834C2×Q8—28no—
835C2×Q8—28no—
836C2×Q8—28no—
837C2×Q8—48no—
838C2×Q8—42no—
839C2×Q8—48no—
840C2×Q8—432no—
841C2×Q8—816no—
842C2×Q8C22×D414yes—
843C2×D4—28no—
844C2×D4—28no—
845C2×D4—28no—
846C2×D4—24no—
847C2×D4—24no—
848C2×D4—24no—
849C2×D4—28no—
850C2×D4—28no—
851C2×D4—28no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—48no—
856C2×D4—48no—
857C2×D4—48no—
858C2×D4C22×D414yes—
859C2×D4C22×D414yes—
860C2×D4C22×D414yes—
861C22×C4—24no—
862C22×C4—24no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—24no—
867C22×C4—24no—
868C22×C4—24no—
869C22×C4—24no—
870C22×C4—28no—
871C22×C4—28no—
872C22×C4—28no—
873C22×C4—28no—
874C22×C4—28no—
875C22×C4—28no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—48no—
879C22×C4—48no—
880C22×C4—48no—
881C22×C4—48no—
882C22×C4—48no—
883C22×C4C22×D414yes—
884C22×C4C22×D414yes—
885C22×C4C22×D414yes—
886C22×C4C22×D414yes—
887C22×C4C22×D414yes—
888C22×C4C22×D414yes—
889C22×C4C22×D414yes—
890C22×C4C22×D414yes—
891C22×C4C22×D414yes—
892C22×C4C2514yes—
893C22×C4C2514yes—
894C22×C4C2514yes—
895C22×C4C2514yes—
896C22×C4C2514yes—
897C22×C4C2514yes—
898C22×C4C2514yes—
899C22×C4C2514yes—
900C22×C4C2514yes—
901C22×C4C2514yes—
902C22×C4C2511yescharacteristic
903C22×C4C2511yescharacteristic
904C22×C4C2511yescharacteristic
905C22×C4C2511yescharacteristic
906C22×C4C2511yescharacteristic
907C22×C4C2511yescharacteristic
908C22×C4C2511yescharacteristic
909C22×C4C2511yescharacteristic
910C22×C4C2511yescharacteristic
911C22×C4C2514yes—
912C22×C4C2511yescharacteristic
913C22×C4C2511yescharacteristic
914C22×C4C2511yescharacteristic
915C4⋊C4—28no—
916C4⋊C4—24no—
917C4⋊C4—24no—
918C4⋊C4—24no—
919C4⋊C4—24no—
920C4⋊C4—24no—
921C4⋊C4—24no—
922C4⋊C4—24no—
923C4⋊C4—24no—
924C4⋊C4—28no—
925C4⋊C4—28no—
926C4⋊C4—28no—
927C4⋊C4—28no—
928C4⋊C4—28no—
929C4⋊C4—24no—
930C4⋊C4—24no—
931C4⋊C4—24no—
932C4⋊C4—24no—
933C4⋊C4—24no—
934C4⋊C4—28no—
935C4⋊C4—28no—
936C4⋊C4—28no—
937C4⋊C4—28no—
938C4⋊C4—24no—
939C4⋊C4—28no—
940C4⋊C4—28no—
941C4⋊C4—28no—
942C4⋊C4—28no—
943C4⋊C4—28no—
944C4⋊C4—28no—
945C4⋊C4—28no—
946C4⋊C4—28no—
947C4⋊C4—28no—
948C4⋊C4—28no—
949C4⋊C4—44no—
950C4⋊C4—44no—
951C4⋊C4—44no—
952C4⋊C4—416no—
953C4⋊C4—416no—
954C4⋊C4—416no—
955C4⋊C4—416no—
956C4⋊C4C22×D414yes—
957C4⋊C4C22×D414yes—
958C4⋊C4C22×D414yes—
959C4⋊C4C22×D414yes—
960C4⋊C4C22×D414yes—
961C4⋊C4C22×D414yes—
962C22⋊C4—28no—
963C22⋊C4—28no—
964C22⋊C4—28no—
965C22⋊C4—28no—
966C22⋊C4—28no—
967C22⋊C4—28no—
968C22⋊C4—28no—
969C22⋊C4—28no—
970C22⋊C4—28no—
971C22⋊C4—28no—
972C22⋊C4—28no—
973C22⋊C4—28no—
974C22⋊C4—28no—
975C22⋊C4—28no—
976C22⋊C4—28no—
977C22⋊C4—232no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—416no—
982C22⋊C4—416no—
983C22⋊C4—416no—
984C22⋊C4C22×D414yes—
985C22⋊C4C22×D414yes—
986C22⋊C4C22×D414yes—
987C22⋊C4C22×D414yes—
988C22⋊C4C22×D414yes—
989C22⋊C4C22×D414yes—
990C42—28no—
991C42—28no—
992C42—28no—
993C42—28no—
994C42—28no—
995C42—28no—
996C42—28no—
997C42—28no—
998C42—24no—
999C42—24no—
1000C42—24no—
1001C42—24no—
1002C42—24no—
1003C42—24no—
1004C42—24no—
1005C42—24no—
1006C42—24no—
1007C42—24no—
1008C42—24no—
1009C42—44no—
1010C42—44no—
1011C42C22×D414yes—
1012C42C22×D414yes—
1013C42C22×D414yes—
1014C42C22×D414yes—
1015C42C22×D414yes—
1016C42C22×D414yes—
1017C42C22×D414yes—
1018C42C22×D414yes—
1019C42C22×D414yes—
1020C42C22×D414yes—
1021C422−1+418yes—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—24no—
1032C23—28no—
1033C23—28no—
1034C23—28no—
1035C23C23×D412yes—
1036C23C23×D412yes—
1037C23C23×D412yes—
1038C23C2611yescharacteristic
1039Q8—44no—
1040Q8—416no—
1041Q8—48no—
1042Q8—48no—
1043Q8—48no—
1044Q8—48no—
1045Q8—48no—
1046Q8—48no—
1047Q8—48no—
1048Q8—88no—
1049D4—44no—
1050D4—44no—
1051D4—44no—
1052D4—416no—
1053D4—48no—
1054D4—48no—
1055D4—48no—
1056D4—88no—
1057D4—88no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—28no—
1070C2×C4—28no—
1071C2×C4—28no—
1072C2×C4—28no—
1073C2×C4—28no—
1074C2×C4—28no—
1075C2×C4—28no—
1076C2×C4—28no—
1077C2×C4—28no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—28no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—28no—
1096C2×C4—28no—
1097C2×C4—28no—
1098C2×C4—28no—
1099C2×C4—28no—
1100C2×C4—28no—
1101C2×C4—416no—
1102C2×C4—416no—
1103C2×C4—416no—
1104C2×C4—88no—
1105C2×C4—88no—
1106C2×C4—88no—
1107C2×C4C23×D412yes—
1108C2×C4C23×D412yes—
1109C2×C4C23×D412yes—
1110C2×C4C23×D412yes—
1111C2×C4C23×D412yes—
1112C2×C4C23×D412yes—
1113C2×C4C23×D412yes—
1114C2×C4C23×D412yes—
1115C2×C4C23×D412yes—
1116C2×C4C23×D412yes—
1117C2×C4C23×D412yes—
1118C2×C4C23×D412yes—
1119C2×C4C2×2−1+418yes—
1120C2×C4C2×2−1+414yes—
1121C2×C4#58514yes—
1122C2×C4#58514yes—
1123C22—22no—
1124C22—22no—
1125C22—22no—
1126C22—22no—
1127C22—22no—
1128C22—22no—
1129C22—22no—
1130C22—22no—
1131C22—22no—
1132C22—44no—
1133C22—44no—
1134C22—44no—
1135C22—44no—
1136C22—44no—
1137C22—416no—
1138C22—44no—
1139C22C24×D411yescharacteristic
1140C22C22×2−1+412yes—
1141C22C2×#58512yes—
1142C22C2×#58512yes—
1143C4—22no—
1144C4—22no—
1145C4—22no—
1146C4—22no—
1147C4—22no—
1148C4—22no—
1149C4—28no—
1150C4—22no—
1151C4—22no—
1152C4—22no—
1153C4—44no—
1154C4—44no—
1155C4—44no—
1156C4—44no—
1157C4—44no—
1158C4—44no—
1159C4—44no—
1160C4—44no—
1161C4—44no—
1162C4—44no—
1163C4#344914yes—
1164C4#349914yes—
1165C4#350014yes—
1166C2—42no—
1167C2—42no—
1168C2—42no—
1169C2—84no—
1170C2C2×#344911yescharacteristic
1171C2C2×#349911yescharacteristic
1172C2C2×#350011yescharacteristic
1173C2#6283814yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3511C2
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×#3509C2semidirect
3. #39613C2semidirect
4. #39485C2semidirect
5. #39162C2semidirect
6. #38946C2semidirect
7. #38091C2semidirect
8. #38088C2semidirect
9. #37871C2semidirect
10. #37870C2semidirect
11. #37389C2semidirect
12. #37388C2semidirect
13. #36645C2semidirect
14. #36639C2semidirect
15. #35669C2semidirect
16. #35622C2semidirect
17. #35322C2semidirect
18. #35322C2semidirect
19. #35320C2semidirect
20. #35298C2semidirect
21. #35298C2semidirect
22. #35298C2semidirect
23. #35298C2semidirect
24. #35289C2semidirect
25. #35281C2semidirect
26. #35281C2semidirect
27. #34026C2semidirect

Maximal subgroups

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

subgroupindex
C2×#35092
C2×#35112
#396132
#394852
#391622
#389462
#380912
#380882
#378712
#378702
#373892
#373882
#366452
#366392
#356692
#356222
#353222
#353202
#352982
#352892
#352812
#340262