Finite Group Databasebeta

← #7658967

Subgroups — #7658967

Order 512.

6484 conjugacy classes of subgroups.

The subgroup lattice has 1249 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3510C211yesmaximal, characteristic, complemented
2C2×#3518C211yesmaximal, characteristic, complemented
3#42979C212yesmaximal, complemented
4#42912C212yesmaximal, complemented
5#42812C212yesmaximal, complemented
6#42809C212yesmaximal, complemented
7#42441C214yesmaximal, complemented
8#42317C214yesmaximal, complemented
9#42298C218yesmaximal, complemented
10#42156C214yesmaximal, complemented
11#41423C214yesmaximal, complemented
12#41418C214yesmaximal, complemented
13#37641C211yesmaximal, characteristic, complemented
14#37608C212yesmaximal, complemented
15#37555C212yesmaximal, complemented
16#37546C211yesmaximal, characteristic, complemented
17#37541C212yesmaximal, complemented
18#37537C211yesmaximal, characteristic, complemented
19#36699C211yesmaximal, characteristic, complemented
20#36699C212yesmaximal, complemented
21#36075C212yesmaximal, complemented
22#36051C212yesmaximal, complemented
23#36007C212yesmaximal, complemented
24#35959C212yesmaximal, complemented
25#35817C214yesmaximal, complemented
26#34191C211yesmaximal, characteristic, complemented
27#3518—216no—
28#3510—216no—
29C2×#559C2212yes—
30C2×#559C2212yes—
31C2×Q82C2211yescharacteristic, complemented
32C2×#556C2212yes—
33C2×#556C2212yes—
34C2×#556C2212yes—
35C2×#556C2212yes—
36C2×#556C2214yescomplemented
37C2×#556C2211yescharacteristic, complemented
38C2×#555C2212yes—
39C2×#555C2211yescharacteristic, complemented
40C2×#551C2214yes—
41C2×#551C2214yes—
42C2×D4×Q8C2211yescharacteristic, complemented
43C2×#548C2212yes—
44C2×#542C2214yes—
45C2×#542C2212yes—
46C2×#542C2212yes—
47C2×#542C2212yescomplemented
48C2×#536C2211yescharacteristic
49C2×#535C2211yescharacteristic
50C2×#533C2211yescharacteristic
51C2×#533C2211yescharacteristic
52C2×#533C2212yescomplemented
53C2×#529C2211yescharacteristic
54C2×#529C2212yes—
55C2×#529C2212yes—
56C2×#529C2212yescomplemented
57C22×#124C2211yescharacteristic
58C2×#519C2211yescharacteristic
59C2×#519C2212yescomplemented
60C2×#518C2211yescharacteristic
61C2×C4×#41C2211yescharacteristic
62#2822C2212yescomplemented
63#2822C2212yescomplemented
64#2822C2211yescharacteristic, complemented
65#2822C2211yescharacteristic, complemented
66#2821C2214yescomplemented
67#2821C2214yescomplemented
68#2821C2212yescomplemented
69#2821C2212yescomplemented
70#2820C2212yes—
71#2820C2212yes—
72#2820C2212yes—
73#2820C2211yescharacteristic, complemented
74#2820C2211yescharacteristic, complemented
75#2819C2212yes—
76#2817C2212yes—
77#2817C2214yescomplemented
78#2816C2214yes—
79#2816C2212yes—
80#2814C2214yes—
81#2814C2218yescomplemented
82#2723C2218yescomplemented
83#2717C2218yes—
84#2716C2218yescomplemented
85#2715C2218yescomplemented
86#2712C2218yescomplemented
87#2708C2218yes—
88#2695C2218yescomplemented
89#2692C2218yescomplemented
90#2684C2218yes—
91#2677C2218yescomplemented
92#2672C2218yescomplemented
93#2668C2218yes—
94#2663C2214yescomplemented
95#2662C2214yes—
96#2661C2214yescomplemented
97#2659C2214yescomplemented
98#2658C2212yes—
99#2640C2212yes—
100#2639C2214yes—
101#2638C2214yescomplemented
102#2637C2214yescomplemented
103#2637C2218yescomplemented
104#2637C2214yescomplemented
105#2636C2214yes—
106#2636C2214yescomplemented
107#2635C2214yes—
108#2632C2214yes—
109#2630C2218yescomplemented
110#2628C2214yescomplemented
111#2626C2214yes—
112#2626C2212yes—
113#2625C2212yes—
114#2625C2212yes—
115#2625C2214yes—
116#2621C2214yes—
117#2621C2214yescomplemented
118#2620C2214yes—
119#2618C2218yescomplemented
120#2617C2212yes—
121#2609C2218yescomplemented
122#2604C2214yescomplemented
123#2603C2214yes—
124#2601C2218yescomplemented
125#2599C2214yescomplemented
126#2598C2214yescomplemented
127#2592C2212yes—
128#2582C2214yescomplemented
129#2581C2214yescomplemented
130#2568C2212yescomplemented
131#2568C2212yescomplemented
132#2564C2214yescomplemented
133#2564C2214yescomplemented
134#2557C2218yescomplemented
135#2553C2218yescomplemented
136#2547C2214yescomplemented
137#2546C2212yescomplemented
138#2546C2212yescomplemented
139#2545C2214yes—
140#2544C2214yes—
141#2543C2214yes—
142#2543C2214yescomplemented
143#2540C2212yes—
144#2536C2214yes—
145#2521C2218yescomplemented
146#2498C2214yescomplemented
147#2498C2214yescomplemented
148#2491C2218yescomplemented
149#2482C2214yes—
150#2480C2218yes—
151#2479C2218yescomplemented
152#2478C2218yes—
153#2477C2218yescomplemented
154#2474C2218yes—
155#2472C2218yes—
156#2469C2218yescomplemented
157#2465C2218yescomplemented
158#2452C2214yes—
159#2451C2214yescomplemented
160#2448C2214yes—
161#2446C2214yescomplemented
162#2436C2214yes—
163#2435C2212yes—
164#2434C2212yes—
165#2434C2214yescomplemented
166#2429C2214yescomplemented
167#2428C2214yes—
168#2427C2214yes—
169#2427C2214yescomplemented
170#2417C2218yescomplemented
171#2411C2214yes—
172#2409C2212yes—
173#2408C2212yes—
174#2399C2212yescomplemented
175#2399C2214yescomplemented
176#2398C2214yes—
177#2398C2212yescomplemented
178#2396C2218yescomplemented
179#2396C2214yescomplemented
180#2395C2212yes—
181#2395C2212yes—
182#2395C2214yescomplemented
183#2395C2214yescomplemented
184#2367C2214yes—
185#2365C2214yescomplemented
186#2363C2214yes—
187#2362C2214yescomplemented
188#2355C2212yescomplemented
189#2352C2214yes—
190D4×C4⋊C4C2212yescomplemented
191#2346C2212yes—
192#2343C2214yescomplemented
193#2339C2212yes—
194#2320C2212yescomplemented
195#2318C2214yes—
196#2285C2211yescharacteristic
197#2283C2211yescharacteristic
198#2283C2212yescomplemented
199C2×#382C2212yescomplemented
200#2275C2212yescomplemented
201C22×#41C2311yescharacteristic
202C23×Q8C2311yescharacteristic
203C23×Q8C2312yes—
204C23×D4C2311yescharacteristic
205#559—216no—
206#559—216no—
207Q82—28no—
208#556—216no—
209#556—216no—
210#556—216no—
211#556—28no—
212#556—216no—
213#556—232no—
214#555—216no—
215#555—28no—
216#551—232no—
217#551—232no—
218D4×Q8—28no—
219#548—216no—
220#542—232no—
221#542—216no—
222#542—216no—
223#542—216no—
224#536—28no—
225#535—28no—
226#533—28no—
227#533—28no—
228#533—216no—
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2314yes—
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2314yes—
239C2×C4⋊Q8C2314yes—
240C2×#127C2312yes—
241#529—216no—
242#529—216no—
243#529—28no—
244#529—216no—
245C2×#126C2314yes—
246C2×#126C2312yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#126C2314yes—
254C2×#125C2311yescharacteristic
255C2×#125C2312yes—
256C2×#125C2311yescharacteristic
257C2×#125C2311yescharacteristic
258C2×#124—28no—
259C2×#124C2311yescharacteristic
260C2×#124C2312yes—
261C2×#124C2312yes—
262C2×#124C2312yes—
263C2×#124C2312yes—
264C2×#124C2314yes—
265C2×#124C2312yes—
266C2×#124C2312yes—
267C2×#124C2314yes—
268C2×#124C2314yes—
269C2×#124C2314yes—
270C2×#124C2314yes—
271C2×#124C2314yes—
272C2×#124C2312yes—
273C2×#124C2314yes—
274C2×#123C2314yes—
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×#123C2312yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2311yescharacteristic
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2318yes—
297C2×#121C2311yescharacteristic
298C2×#121C2312yes—
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×#121C2314yes—
302C2×#121C2312yes—
303C2×#121C2314yes—
304C2×#121C2318yes—
305C2×#120C2314yes—
306C2×#120C2314yes—
307#519—216no—
308#519—28no—
309#518—28no—
310C4×#41D4116yescomplemented
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2314yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2314yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2314yes—
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2311yescharacteristic
328C2×C4×D4C2314yes—
329C2×C4×D4C2314yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2311yescharacteristic
337C2×C4×D4C2312yes—
338C2×C4×D4C2314yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2312yes—
342C2×C4×D4C2311yescharacteristic
343C2×#117C2314yes—
344C2×#117C2314yes—
345C2×#117C2314yes—
346C2×#117C2312yes—
347C2×#117C2312yes—
348C2×#117C2311yescharacteristic
349C2×#117C2311yescharacteristic
350C2×#117C2312yes—
351C2×#117C2312yes—
352C2×#117C2312yes—
353C2×#117C2314yes—
354C2×#117C2314yes—
355C2×#117C2312yes—
356C2×#117C2312yes—
357C2×#117C2311yescharacteristic
358C22×C4⋊C4C2314yes—
359C22×C22⋊C4C2312yes—
360C22×C22⋊C4C2312yes—
361C22×C22⋊C4C2314yes—
362C22×C42C2311yescharacteristic
363C22×C42C2312yes—
364#400C2312yes—
365#400C2314yes—
366#400C2312yes—
367#400C2312yes—
368#400C2314yes—
369#400C2318yes—
370#400C2314yes—
371#400C2312yes—
372#400C2314yes—
373#400C2314yes—
374#399C2318yes—
375#399C2314yes—
376#399C2312yes—
377#399C2314yes—
378#399C2314yes—
379#399C2314yes—
380#399C2312yes—
381#399C2318yes—
382#398C2312yes—
383#398C2312yes—
384#398C2312yes—
385#398C2314yes—
386#398C2314yes—
387#398C2312yes—
388#398C2318yes—
389#398C2314yes—
390#398C2318yes—
391#398C2318yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2318yes—
397#398C2318yes—
398#397C2314yes—
399#397C2314yes—
400#397C2318yes—
401#397C2318yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2312yes—
406#397C2312yes—
407#397C2318yes—
408#397C2314yes—
409#397C2318yes—
410#397C2318yes—
411#397C2318yes—
412#397C2318yes—
413#396C2318yes—
414#396C2318yes—
415#396C2318yes—
416#396C2314yes—
417#396C2314yes—
418#396C2318yes—
419#396C2318yes—
420#396C2318yes—
421#395C2312yes—
422#395C2312yes—
423#395C2314yes—
424#395C2314yes—
425#395C2314yes—
426#395C2318yes—
427#395C2314yes—
428#395C2318yes—
429#395C2314yes—
430#395C2318yes—
431#394C2314yes—
432#394C2314yes—
433#394C2312yes—
434#394C2312yes—
435#394C2314yes—
436#394C2314yes—
437#394C2318yes—
438#394C2318yes—
439#394C2318yes—
440#394C2314yes—
441#394C2318yes—
442#394C2318yes—
443#394C2318yes—
444#394C2318yes—
445#393C2318yes—
446#393C2314yes—
447#393C2314yes—
448#393C2314yes—
449#393C2318yes—
450#393C2314yes—
451#393C2318yes—
452#393C2318yes—
453#392C2314yes—
454#392C2314yes—
455#392C2318yes—
456#391C2314yes—
457#391C2314yes—
458#391C2318yes—
459#391C2314yes—
460#391C2314yes—
461#391C2314yes—
462#391C2318yes—
463#391C2314yes—
464#391C2314yes—
465#390C2314yes—
466#390C2318yes—
467#390C2314yes—
468#390C2318yes—
469#389C2314yes—
470#389C2318yes—
471#389C2314yes—
472#389C2314yes—
473#389C2318yes—
474#389C2318yes—
475#388C2318yes—
476#388C2318yes—
477#388C2318yes—
478#388C2318yes—
479#388C2318yes—
480#388C2318yes—
481#388C2318yes—
482#388C2318yes—
483#388C2318yes—
484#388C2318yes—
485#388C2318yes—
486#388C2318yes—
487#387C2318yes—
488#387C2318yes—
489#387C2318yes—
490#387C2318yes—
491#387C2318yes—
492#387C2318yes—
493#387C2318yes—
494#387C2318yes—
495#386C2318yes—
496#386C2318yes—
497#386C2318yes—
498#386C2318yes—
499#386C2318yes—
500#386C2318yes—
501#386C2318yes—
502#386C2314yes—
503#386C2318yes—
504#386C2318yes—
505#385C2318yes—
506#385C2318yes—
507#385C2318yes—
508#385C2318yes—
509#385C2318yes—
510#385C2314yes—
511#385C2318yes—
512#384C2312yes—
513#383C2314yes—
514#383C2312yes—
515#382C2312yes—
516#382C2311yescharacteristic
517#382C2311yescharacteristic
518#382C2314yes—
519#382C2314yes—
520#382C2314yes—
521#382C2314yes—
522#381C2312yes—
523#381C2314yes—
524#380C2318yes—
525#380C2312yes—
526#380C2312yes—
527#380C2314yes—
528#380C2312yes—
529#380C2318yes—
530#380C2318yes—
531#380C2318yes—
532#379C2314yes—
533#379C2318yes—
534C4×C4⋊C4C2312yes—
535C4×C4⋊C4C2312yes—
536C4×C4⋊C4C2314yes—
537C4×C4⋊C4C2314yes—
538C4×C4⋊C4C2312yes—
539C4×C4⋊C4C2318yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2318yes—
542C4×C4⋊C4C2314yes—
543C4×C22⋊C4C2314yes—
544C4×C22⋊C4C2312yes—
545C4×C22⋊C4C2318yes—
546C4×C22⋊C4C2314yes—
547C4×C22⋊C4C2314yes—
548C4×C22⋊C4C2318yes—
549C4×C22⋊C4C2318yes—
550#376C2312yes—
551#376C2314yes—
552C2×#95C2314yes—
553C2×#95C2314yes—
554C25C2412yes—
555C2×#41—44no—
556C2×#41C2×D418yes—
557C22×Q8—28no—
558C22×Q8—24no—
559C22×Q8—44no—
560C22×Q8—48no—
561C22×Q8C2412yes—
562C22×Q8C2412yes—
563C22×Q8C2411yescharacteristic
564C22×Q8C2411yescharacteristic
565C22×Q8C2412yes—
566C22×Q8C2414yes—
567C22×Q8C2414yes—
568C22×Q8C2412yes—
569C22×Q8C2412yes—
570C22×Q8C2412yes—
571C22×D4—24no—
572C22×D4—44no—
573C22×D4C2412yes—
574C22×D4C2411yescharacteristic
575C22×D4C2411yescharacteristic
576C22×D4C2412yes—
577C22×D4C2412yes—
578C22×D4C2414yes—
579C22×D4C2414yes—
580C22×D4C2414yes—
581C22×D4C2418yes—
582C22×D4C2412yes—
583C23×C4C2412yes—
584C23×C4C2411yescharacteristic
585C23×C4C2412yes—
586C23×C4C2414yes—
587C23×C4C2414yes—
588C23×C4C2414yes—
589C23×C4C2418yes—
590C23×C4C2411yescharacteristic
591C23×C4C2411yescharacteristic
592C23×C4C2412yes—
593C23×C4C2412yes—
594C23×C4C2412yes—
595C4⋊Q8—28no—
596C4⋊Q8—28no—
597C4⋊Q8—216no—
598C4⋊Q8—24no—
599C4⋊Q8—24no—
600C4⋊Q8—28no—
601C4⋊Q8—24no—
602C4⋊Q8—28no—
603C4⋊Q8—24no—
604C4⋊Q8—48no—
605C4⋊Q8—84no—
606#127—28no—
607#126—216no—
608#126—216no—
609#126—216no—
610#126—216no—
611#126—216no—
612#126—216no—
613#126—216no—
614#126—216no—
615#126—28no—
616#125—24no—
617#125—24no—
618#125—24no—
619#125—28no—
620#124—28no—
621#124—28no—
622#124—28no—
623#124—216no—
624#124—216no—
625#124—216no—
626#124—216no—
627#124—216no—
628#124—216no—
629#124—28no—
630#124—28no—
631#124—28no—
632#124—28no—
633#124—24no—
634#124—48no—
635#123—216no—
636#123—28no—
637#123—216no—
638#123—216no—
639#123—216no—
640#123—216no—
641#123—216no—
642C22⋊Q8—28no—
643C22⋊Q8—28no—
644C22⋊Q8—24no—
645C22⋊Q8—28no—
646C22⋊Q8—28no—
647C22⋊Q8—216no—
648C22⋊Q8—28no—
649C22⋊Q8—216no—
650C22⋊Q8—28no—
651C22⋊Q8—28no—
652C22⋊Q8—28no—
653C22⋊Q8—216no—
654C22⋊Q8—216no—
655C22⋊Q8—216no—
656C22⋊Q8—48no—
657C22⋊Q8—88no—
658#121—28no—
659#121—216no—
660#121—28no—
661#121—28no—
662#121—24no—
663#121—28no—
664#121—48no—
665#121—88no—
666#120—216no—
667#120—84no—
668C4×Q8—28no—
669C4×Q8—28no—
670C4×Q8—216no—
671C4×Q8—28no—
672C4×Q8—28no—
673C4×Q8—28no—
674C4×Q8—28no—
675C4×Q8—216no—
676C4×Q8—28no—
677C4×Q8—28no—
678C4×Q8—24no—
679C4×Q8—216no—
680C4×Q8—28no—
681C4×Q8—28no—
682C4×Q8—28no—
683C4×Q8C2×D418yes—
684C4×Q8C2×D418yes—
685C4×D4—28no—
686C4×D4—216no—
687C4×D4—216no—
688C4×D4—216no—
689C4×D4—28no—
690C4×D4—28no—
691C4×D4—28no—
692C4×D4—28no—
693C4×D4—28no—
694C4×D4—24no—
695C4×D4—48no—
696C4×D4C2×D4116yes—
697C4×D4C2×D418yes—
698C4×D4C2×D4116yes—
699C4×D4C2×D418yes—
700#117—24no—
701#117—24no—
702#117—28no—
703#117—28no—
704#117—28no—
705#117—28no—
706#117—216no—
707#117—216no—
708#117—216no—
709#117—28no—
710#117—216no—
711#117—216no—
712#117—82no—
713#117C2×D418yes—
714#117C2×D4116yes—
715C2×C4⋊C4—84no—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2411yescharacteristic
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2418yes—
750C2×C4⋊C4C2418yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2418yes—
753C2×C4⋊C4C2418yes—
754C2×C4⋊C4C2418yes—
755C2×C4⋊C4C2418yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2411yescharacteristic
764C2×C4⋊C4C2412yes—
765C2×C22⋊C4—28no—
766C2×C22⋊C4—28no—
767C2×C22⋊C4—216no—
768C2×C22⋊C4C2412yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2412yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2412yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2418yes—
793C2×C22⋊C4C2418yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2418yes—
796C2×C22⋊C4C2418yes—
797C2×C22⋊C4C2418yes—
798C2×C22⋊C4C2418yes—
799C2×C22⋊C4C2418yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2418yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2418yes—
806C2×C22⋊C4C2412yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2412yes—
809C2×C42C2×D418yes—
810C2×C42C2×D4116yes—
811C2×C42C2414yes—
812C2×C42C2414yes—
813C2×C42C2414yes—
814C2×C42C2414yes—
815C2×C42C2414yes—
816C2×C42C2412yes—
817C2×C42C2412yes—
818C2×C42C2414yes—
819C2×C42C2412yes—
820C2×C42C2414yes—
821C2×C42C2414yes—
822C2×C42C2418yes—
823C2×C42C2412yes—
824C2×C42C2412yes—
825C2×C42C2412yes—
826C2×C42C2411yescharacteristic
827C2×C42C2411yescharacteristic
828C2×C42C2411yescharacteristic
829C2×C42C2411yescharacteristic
830#95C2412yes—
831#95C2412yes—
832#95C2414yes—
833#95C2414yes—
834#95C2418yes—
835#95C2418yes—
836#95C2412yes—
837#95C2414yes—
838#95C2412yes—
839#95C2418yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2418yes—
845#95C2414yes—
846#95C2418yes—
847#95C2418yes—
848#95C2414yes—
849#95C2418yes—
850#95C2414yes—
851#95C2418yes—
852#95C2414yes—
853#95C2414yes—
854#95C2418yes—
855#95C2418yes—
856#95C2418yes—
857#95C2418yes—
858#95C2418yes—
859#95C2418yes—
860C24—24no—
861C24—44no—
862C24—42no—
863C24—44no—
864C24—42no—
865C24C2514yes—
866C24C2512yes—
867C24C2511yescharacteristic
868C24C2512yes—
869#41—416no—
870C2×Q8—22no—
871C2×Q8—24no—
872C2×Q8—28no—
873C2×Q8—24no—
874C2×Q8—24no—
875C2×Q8—24no—
876C2×Q8—24no—
877C2×Q8—28no—
878C2×Q8—24no—
879C2×Q8—24no—
880C2×Q8—28no—
881C2×Q8—28no—
882C2×Q8—44no—
883C2×Q8—48no—
884C2×Q8—42no—
885C2×Q8—44no—
886C2×Q8—42no—
887C2×Q8—42no—
888C2×Q8—44no—
889C2×Q8—44no—
890C2×Q8—42no—
891C2×Q8—42no—
892C2×Q8—416no—
893C2×Q8—432no—
894C2×Q8C22×D414yes—
895C2×D4—28no—
896C2×D4—28no—
897C2×D4—24no—
898C2×D4—28no—
899C2×D4—22no—
900C2×D4—24no—
901C2×D4—24no—
902C2×D4—24no—
903C2×D4—28no—
904C2×D4—44no—
905C2×D4—42no—
906C2×D4—44no—
907C2×D4—416no—
908C2×D4—42no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—48no—
913C2×D4—44no—
914C2×D4—42no—
915C2×D4—48no—
916C2×D4—48no—
917C2×D4—48no—
918C2×D4C22×D414yes—
919C2×D4C22×D418yes—
920C22×C4—24no—
921C22×C4—24no—
922C22×C4—28no—
923C22×C4—24no—
924C22×C4—28no—
925C22×C4—28no—
926C22×C4—28no—
927C22×C4—42no—
928C22×C4—41no—
929C22×C4—44no—
930C22×C4—42no—
931C22×C4—41no—
932C22×C4—42no—
933C22×C4—48no—
934C22×C4—44no—
935C22×C4—44no—
936C22×C4—44no—
937C22×C4—48no—
938C22×C4—44no—
939C22×C4—48no—
940C22×C4—48no—
941C22×C4—48no—
942C22×C4C22×D414yes—
943C22×C4C22×D414yes—
944C22×C4C22×D414yes—
945C22×C4C22×D418yes—
946C22×C4C22×D418yes—
947C22×C4C22×D418yes—
948C22×C4C2514yes—
949C22×C4C2518yes—
950C22×C4C2514yes—
951C22×C4C2512yes—
952C22×C4C2512yes—
953C22×C4C2512yes—
954C22×C4C2512yes—
955C22×C4C2514yes—
956C22×C4C2512yes—
957C22×C4C2514yes—
958C22×C4C2512yes—
959C22×C4C2514yes—
960C22×C4C2512yes—
961C22×C4C2511yescharacteristic
962C22×C4C2512yes—
963C22×C4C2511yescharacteristic
964C22×C4C2512yes—
965C22×C4C2511yescharacteristic
966C22×C4C2511yescharacteristic
967C22×C4C2512yes—
968C22×C4C2511yescharacteristic
969C22×C4C2511yescharacteristic
970C4⋊C4—24no—
971C4⋊C4—22no—
972C4⋊C4—24no—
973C4⋊C4—22no—
974C4⋊C4—24no—
975C4⋊C4—24no—
976C4⋊C4—22no—
977C4⋊C4—22no—
978C4⋊C4—22no—
979C4⋊C4—22no—
980C4⋊C4—28no—
981C4⋊C4—24no—
982C4⋊C4—28no—
983C4⋊C4—24no—
984C4⋊C4—28no—
985C4⋊C4—28no—
986C4⋊C4—28no—
987C4⋊C4—24no—
988C4⋊C4—28no—
989C4⋊C4—28no—
990C4⋊C4—24no—
991C4⋊C4—24no—
992C4⋊C4—28no—
993C4⋊C4—24no—
994C4⋊C4—28no—
995C4⋊C4—24no—
996C4⋊C4—24no—
997C4⋊C4—24no—
998C4⋊C4—28no—
999C4⋊C4—24no—
1000C4⋊C4—28no—
1001C4⋊C4—42no—
1002C4⋊C4—44no—
1003C4⋊C4—48no—
1004C4⋊C4—42no—
1005C4⋊C4—44no—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C4⋊C4—48no—
1010C4⋊C4—48no—
1011C4⋊C4—44no—
1012C4⋊C4—48no—
1013C4⋊C4—48no—
1014C4⋊C4—48no—
1015C4⋊C4C22×D414yes—
1016C4⋊C4C22×D418yes—
1017C4⋊C4C22×D414yes—
1018C4⋊C4C22×D418yes—
1019C22⋊C4—24no—
1020C22⋊C4—24no—
1021C22⋊C4—28no—
1022C22⋊C4—28no—
1023C22⋊C4—28no—
1024C22⋊C4—28no—
1025C22⋊C4—28no—
1026C22⋊C4—24no—
1027C22⋊C4—28no—
1028C22⋊C4—28no—
1029C22⋊C4—28no—
1030C22⋊C4—28no—
1031C22⋊C4—28no—
1032C22⋊C4—28no—
1033C22⋊C4—28no—
1034C22⋊C4—28no—
1035C22⋊C4—24no—
1036C22⋊C4—24no—
1037C22⋊C4—28no—
1038C22⋊C4—28no—
1039C22⋊C4—24no—
1040C22⋊C4—28no—
1041C22⋊C4—24no—
1042C22⋊C4—44no—
1043C22⋊C4—44no—
1044C22⋊C4—48no—
1045C22⋊C4—44no—
1046C22⋊C4—48no—
1047C22⋊C4—44no—
1048C22⋊C4—44no—
1049C22⋊C4—48no—
1050C22⋊C4—48no—
1051C22⋊C4—48no—
1052C22⋊C4—44no—
1053C22⋊C4—48no—
1054C22⋊C4—48no—
1055C22⋊C4—48no—
1056C22⋊C4—48no—
1057C22⋊C4C22×D418yes—
1058C22⋊C4C22×D418yes—
1059C22⋊C4C22×D418yes—
1060C42—28no—
1061C42—28no—
1062C42—28no—
1063C42—28no—
1064C42—28no—
1065C42—24no—
1066C42—28no—
1067C42—24no—
1068C42—24no—
1069C42—28no—
1070C42—48no—
1071C42—44no—
1072C42C22×D414yes—
1073C42C22×D418yes—
1074C42C22×D418yes—
1075C42C22×D414yes—
1076C42C22×D418yes—
1077C42C22×D414yes—
1078C42C22×D414yes—
1079C23—24no—
1080C23—22no—
1081C23—21no—
1082C23—22no—
1083C23—22no—
1084C23—24no—
1085C23—22no—
1086C23—21no—
1087C23—22no—
1088C23—24no—
1089C23—28no—
1090C23—24no—
1091C23—24no—
1092C23—22no—
1093C23—24no—
1094C23—22no—
1095C23—24no—
1096C23—28no—
1097C23—48no—
1098C23—84no—
1099C23—84no—
1100C23—164no—
1101C23—164no—
1102C23C23×D412yes—
1103C23C23×D414yes—
1104C23C2611yescharacteristic
1105Q8—28no—
1106Q8—44no—
1107Q8—48no—
1108Q8—416no—
1109Q8—48no—
1110Q8—48no—
1111Q8—88no—
1112Q8—84no—
1113Q8—84no—
1114Q8—84no—
1115D4—28no—
1116D4—48no—
1117D4—44no—
1118D4—48no—
1119D4—48no—
1120D4—88no—
1121D4—88no—
1122D4—84no—
1123D4—88no—
1124D4—168no—
1125C2×C4—22no—
1126C2×C4—24no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—22no—
1130C2×C4—24no—
1131C2×C4—21no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—21no—
1136C2×C4—28no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—28no—
1150C2×C4—24no—
1151C2×C4—28no—
1152C2×C4—28no—
1153C2×C4—28no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—24no—
1160C2×C4—28no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—22no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—48no—
1171C2×C4—44no—
1172C2×C4—48no—
1173C2×C4—44no—
1174C2×C4—48no—
1175C2×C4—416no—
1176C2×C4—48no—
1177C2×C4—48no—
1178C2×C4—88no—
1179C2×C4—88no—
1180C2×C4—168no—
1181C2×C4C23×D414yes—
1182C2×C4C23×D412yes—
1183C2×C4C23×D414yes—
1184C2×C4C23×D414yes—
1185C2×C4C23×D412yes—
1186C2×C4C23×D412yes—
1187C2×C4C23×D412yes—
1188C2×C4C23×D412yes—
1189C2×C4C23×D412yes—
1190C2×C4#58514yes—
1191C22—24no—
1192C22—22no—
1193C22—24no—
1194C22—22no—
1195C22—22no—
1196C22—24no—
1197C22—44no—
1198C22—42no—
1199C22—44no—
1200C22—42no—
1201C22—44no—
1202C22—48no—
1203C22—44no—
1204C22—48no—
1205C22—44no—
1206C22—42no—
1207C22—44no—
1208C22—42no—
1209C22—42no—
1210C22—44no—
1211C22—168no—
1212C22C24×D411yescharacteristic
1213C22C2×#58512yes—
1214C22H(7,𝔽2)11yescharacteristic
1215C222−1+611yescharacteristic
1216C222−1+612yes—
1217C4—22no—
1218C4—24no—
1219C4—22no—
1220C4—22no—
1221C4—24no—
1222C4—22no—
1223C4—22no—
1224C4—24no—
1225C4—44no—
1226C4—44no—
1227C4—48no—
1228C4—42no—
1229C4—42no—
1230C4—42no—
1231C4—44no—
1232C4—42no—
1233C4—42no—
1234C4—42no—
1235C4—44no—
1236C4—42no—
1237C4—44no—
1238C4#344914yes—
1239C2—44no—
1240C2—42no—
1241C2—82no—
1242C2—84no—
1243C2C2×#344911yescharacteristic
1244C2#6285311yescharacteristic
1245C2#6285911yescharacteristic
1246C2#6306212yes—
1247C2#6306912yes—
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×#3510C2semidirect
2. C2×#3518C2semidirect
3. #42979C2semidirect
4. #42912C2semidirect
5. #42812C2semidirect
6. #42809C2semidirect
7. #42441C2semidirect
8. #42317C2semidirect
9. #42298C2semidirect
10. #42156C2semidirect
11. #41423C2semidirect
12. #41418C2semidirect
13. #37641C2semidirect
14. #37608C2semidirect
15. #37555C2semidirect
16. #37546C2semidirect
17. #37541C2semidirect
18. #37537C2semidirect
19. #36699C2semidirect
20. #36699C2semidirect
21. #36075C2semidirect
22. #36051C2semidirect
23. #36007C2semidirect
24. #35959C2semidirect
25. #35817C2semidirect
26. #34191C2semidirect
31. C2×Q82C22semidirect
36. C2×#556C22semidirect
37. C2×#556C22semidirect
39. C2×#555C22semidirect
42. C2×D4×Q8C22semidirect
47. C2×#542C22semidirect
52. C2×#533C22semidirect
56. C2×#529C22semidirect
59. C2×#519C22semidirect
62. #2822C22semidirect
63. #2822C22semidirect
64. #2822C22semidirect
65. #2822C22semidirect
66. #2821C22semidirect
67. #2821C22semidirect
68. #2821C22semidirect
69. #2821C22semidirect
73. #2820C22semidirect
74. #2820C22semidirect
77. #2817C22semidirect
81. #2814C22semidirect
82. #2723C22semidirect
84. #2716C22semidirect
85. #2715C22semidirect
86. #2712C22semidirect
88. #2695C22semidirect
89. #2692C22semidirect
91. #2677C22semidirect
92. #2672C22semidirect
94. #2663C22semidirect
96. #2661C22semidirect
97. #2659C22semidirect
101. #2638C22semidirect
102. #2637C22semidirect
103. #2637C22semidirect
104. #2637C22semidirect
106. #2636C22semidirect
109. #2630C22semidirect
110. #2628C22semidirect
117. #2621C22semidirect
119. #2618C22semidirect
121. #2609C22semidirect
122. #2604C22semidirect
124. #2601C22semidirect
125. #2599C22semidirect
126. #2598C22semidirect
128. #2582C22semidirect
129. #2581C22semidirect
130. #2568C22semidirect
131. #2568C22semidirect
132. #2564C22semidirect
133. #2564C22semidirect
134. #2557C22semidirect
135. #2553C22semidirect
136. #2547C22semidirect
137. #2546C22semidirect
138. #2546C22semidirect
142. #2543C22semidirect
145. #2521C22semidirect
146. #2498C22semidirect
147. #2498C22semidirect
148. #2491C22semidirect
151. #2479C22semidirect
153. #2477C22semidirect
156. #2469C22semidirect
157. #2465C22semidirect
159. #2451C22semidirect
161. #2446C22semidirect
165. #2434C22semidirect
166. #2429C22semidirect
169. #2427C22semidirect
170. #2417C22semidirect
174. #2399C22semidirect
175. #2399C22semidirect
177. #2398C22semidirect
178. #2396C22semidirect
179. #2396C22semidirect
182. #2395C22semidirect
183. #2395C22semidirect
185. #2365C22semidirect
187. #2362C22semidirect
188. #2355C22semidirect
190. D4×C4⋊C4C22semidirect
192. #2343C22semidirect
194. #2320C22semidirect
198. #2283C22semidirect
199. C2×#382C22semidirect
200. #2275C22semidirect
310. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35102
C2×#35182
#429792
#429122
#428122
#428092
#424412
#423172
#422982
#421562
#414232
#414182
#376412
#376082
#375552
#375462
#375412
#375372
#366992
#360752
#360512
#360072
#359592
#358172
#341912