Finite Group Databasebeta

← #7657584

Subgroups — #7657584

Order 512.

6870 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3506C211yesmaximal, characteristic, complemented
2C2×#3475C211yesmaximal, characteristic, complemented
3#42682C212yesmaximal, complemented
4#42679C212yesmaximal, complemented
5#42432C214yesmaximal, complemented
6#41424C214yesmaximal, complemented
7#41421C214yesmaximal, complemented
8#41376C218yesmaximal, complemented
9#38922C212yesmaximal, complemented
10#38908C212yesmaximal, complemented
11#38051C214yesmaximal, complemented
12#38033C214yesmaximal, complemented
13#37640C211yesmaximal, characteristic, complemented
14#37635C211yesmaximal, characteristic, complemented
15#37445C212yesmaximal, complemented
16#37444C212yesmaximal, complemented
17#36411C212yesmaximal, complemented
18#36404C212yesmaximal, complemented
19#36062C212yesmaximal, complemented
20#35856C212yesmaximal, complemented
21#35758C214yesmaximal, complemented
22#35297C211yesmaximal, characteristic, complemented
23#35263C212yesmaximal, complemented
24#34635C212yesmaximal, complemented
25#34609C211yesmaximal, characteristic, complemented
26#34194C211yesmaximal, characteristic, complemented
27#3506—216no—
28C2×#559C2214yes—
29#3475—216no—
30C2×#556C2211yescharacteristic
31C2×#556C2212yes—
32C2×#555C2211yescharacteristic
33C2×#555C2211yescharacteristic
34C2×#555C2211yescharacteristic
35C2×#554C2211yescharacteristic
36C2×#553C2212yes—
37C2×#553C2212yes—
38C2×#553C2212yes—
39C2×#552C2212yes—
40C2×#552C2212yes—
41C2×#551C2214yes—
42C2×#550C2212yes—
43C2×#547C2211yescharacteristic
44C2×#547C2211yescharacteristic
45C2×#547C2211yescharacteristic
46C2×#546C2212yes—
47C2×#538C2214yes—
48C2×#535C2212yes—
49C2×#533C2211yescharacteristic
50C2×#533C2211yescharacteristic
51C2×#532C2211yescharacteristic
52C2×#529C2212yes—
53C2×#529C2214yes—
54C2×#525C2212yes—
55C2×#525C2212yes—
56C2×#525C2212yes—
57C2×#520C2212yes—
58C2×C4×#41C2211yescharacteristic
59C2×C4×#41C2212yes—
60C22×C4×D4C2211yescharacteristic
61C22×#117C2212yes—
62#2857C2212yescomplemented
63#2857C2212yescomplemented
64#2855C2214yescomplemented
65#2854C2214yescomplemented
66#2820C2214yescomplemented
67#2817C2214yes—
68#2814C2214yescomplemented
69#2813C2214yescomplemented
70#2812C2218yes—
71#2718C2218yescomplemented
72#2717C2218yes—
73#2715C2218yescomplemented
74#2709C2218yes—
75#2703C2218yescomplemented
76#2695C2218yescomplemented
77#2693C2218yescomplemented
78#2689C2218yescomplemented
79#2686C2218yes—
80#2673C2218yes—
81#2672C2218yescomplemented
82#2672C2218yescomplemented
83#2663C2214yescomplemented
84#2661C2214yescomplemented
85#2660C2212yescomplemented
86#2642C2212yescomplemented
87#2638C2214yescomplemented
88#2635C2214yes—
89#2635C2214yescomplemented
90#2634C2214yescomplemented
91#2632C2212yescomplemented
92#2631C2212yescomplemented
93#2630C2218yes—
94#2628C2212yescomplemented
95#2625C2212yes—
96#2625C2212yes—
97#2625C2212yes—
98#2625C2214yescomplemented
99#2624C2212yes—
100#2624C2212yes—
101#2624C2211yescharacteristic
102#2624C2211yescharacteristic
103#2624C2214yescomplemented
104#2623C2214yescomplemented
105#2623C2214yescomplemented
106#2622C2218yes—
107#2620C2214yes—
108#2619C2212yescomplemented
109#2617C2218yes—
110#2616C2214yes—
111#2616C2212yes—
112#2615C2211yescharacteristic
113#2615C2211yescharacteristic
114#2602C2218yes—
115#2584C2212yescomplemented
116#2581C2214yescomplemented
117#2581C2212yescomplemented
118#2568C2212yescomplemented
119#2567C2212yescomplemented
120#2567C2212yescomplemented
121#2564C2214yescomplemented
122#2562C2212yescomplemented
123#2559C2218yescomplemented
124#2555C2218yescomplemented
125#2548C2212yescomplemented
126#2547C2212yescomplemented
127#2543C2214yescomplemented
128#2542C2212yescomplemented
129#2538C2212yescomplemented
130#2538C2212yescomplemented
131#2537C2214yes—
132#2536C2212yescomplemented
133#2535C2214yes—
134#2521C2218yescomplemented
135#2499C2214yes—
136#2498C2214yescomplemented
137#2498C2214yescomplemented
138#2496C2218yescomplemented
139#2487C2214yescomplemented
140#2486C2214yescomplemented
141#2485C2218yes—
142#2485C2214yes—
143#2485C2214yescomplemented
144#2485C2214yescomplemented
145#2474C2218yescomplemented
146#2470C2218yescomplemented
147#2469C2218yescomplemented
148#2467C2218yescomplemented
149#2462C2218yescomplemented
150#2461C2218yescomplemented
151#2460C2218yescomplemented
152#2457C2218yescomplemented
153#2442C2214yescomplemented
154#2441C2214yescomplemented
155#2427C2214yes—
156#2427C2214yes—
157#2422C2214yes—
158#2420C2214yes—
159#2417C2214yescomplemented
160#2417C2214yescomplemented
161#2416C2214yescomplemented
162#2415C2214yes—
163#2415C2214yescomplemented
164#2415C2214yescomplemented
165#2414C2214yescomplemented
166#2412C2218yes—
167#2407C2214yes—
168#2407C2214yes—
169#2407C2214yescomplemented
170#2407C2214yescomplemented
171#2398C2212yescomplemented
172#2397C2212yescomplemented
173#2395C2218yes—
174#2395C2214yescomplemented
175#2395C2214yescomplemented
176#2388C2214yes—
177#2362C2214yescomplemented
178#2360C2214yescomplemented
179#2354C2212yes—
180#2354C2214yescomplemented
181#2352C2214yes—
182#2352C2214yescomplemented
183D4×C4⋊C4C2212yes—
184#2345C2212yes—
185#2342C2214yes—
186D4×C22⋊C4C2212yes—
187#2323C2214yescomplemented
188#2319C2212yes—
189#2318C2214yes—
190#2316C2214yescomplemented
191#2311C2214yescomplemented
192C4×#121C2212yescomplemented
193C4×#121C2212yescomplemented
194#2297C2214yescomplemented
195#2296C2214yescomplemented
196#2285C2211yescharacteristic
197#2283C2211yescharacteristic
198#2280C2212yes—
199C2×#380C2212yes—
200#2275C2212yes—
201C22×#41C2312yes—
202C22×#41C2311yescharacteristic
203C22×#41C2312yes—
204C22×#41C2312yes—
205C22×#41C2312yes—
206C23×D4C2311yescharacteristic
207C24×C4C2312yes—
208#559—232no—
209#556—28no—
210#556—216no—
211#555—28no—
212#555—28no—
213#555—28no—
214#554—28no—
215#553—216no—
216#553—216no—
217#553—216no—
218#552—216no—
219#552—216no—
220#551—232no—
221#550—216no—
222#547—28no—
223#547—28no—
224#547—28no—
225#546—216no—
226#538—232no—
227#535—216no—
228#533—28no—
229#533—28no—
230#532—28no—
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2311yescharacteristic
236C2×#127C2311yescharacteristic
237C2×#127C2314yes—
238#529—232no—
239#529—216no—
240C2×#126C2314yes—
241C2×#126C2314yes—
242C2×#126C2314yes—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#125C2312yes—
246C2×#125C2312yes—
247C2×#125C2312yes—
248C2×#125C2314yes—
249C2×#124C2312yes—
250C2×#124C2312yes—
251C2×#124C2314yes—
252C2×#124C2314yes—
253C2×#124C2314yes—
254C2×#124C2314yes—
255C2×#124C2314yes—
256#525—216no—
257#525—216no—
258#525—216no—
259C2×#123C2314yes—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×#123C2314yes—
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×#123C2318yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×#121C2312yes—
283C2×#121C2311yescharacteristic
284C2×#121C2311yescharacteristic
285C2×#121C2312yes—
286C2×#121C2312yes—
287C2×#121C2312yes—
288C2×#121C2312yes—
289C2×#121C2312yes—
290C2×#121C2312yes—
291C2×#121C2314yes—
292C2×#121C2312yes—
293C2×#121C2314yes—
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#121C2314yes—
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×#121C2318yes—
300C2×#120C2314yes—
301C2×#120C2314yes—
302C2×#120C2314yes—
303#520—216no—
304C4×#41—216no—
305C4×#41—28no—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2314yes—
314C2×C4×D4D4116yescomplemented
315C2×C4×D4C2311yescharacteristic
316C2×C4×D4C2314yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2312yes—
321C2×C4×D4C2314yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2314yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2311yescharacteristic
331C2×C4×D4C2314yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2311yescharacteristic
336C2×C4×D4C2311yescharacteristic
337C2×C4×D4C2312yes—
338C2×C4×D4C2311yescharacteristic
339C2×C4×D4C2311yescharacteristic
340C2×#117—216no—
341C2×#117C2314yes—
342C2×#117C2312yes—
343C2×#117C2312yes—
344C2×#117C2312yes—
345C2×#117C2312yes—
346C2×#117C2311yescharacteristic
347C2×#117C2312yes—
348C2×#117C2314yes—
349C2×#117C2312yes—
350C2×#117C2312yes—
351C2×#117C2314yes—
352C2×#117C2312yes—
353C2×#117C2312yes—
354C2×#117C2312yes—
355C2×#117C2314yes—
356C2×#117C2312yes—
357C22×C4⋊C4C2312yes—
358C22×C4⋊C4C2312yes—
359C22×C4⋊C4C2312yes—
360C22×C4⋊C4C2312yes—
361C22×C4⋊C4C2314yes—
362C22×C4⋊C4C2311yescharacteristic
363C22×C22⋊C4C2314yes—
364C22×C22⋊C4C2314yes—
365C22×C22⋊C4C2312yes—
366C22×C42C2314yes—
367C22×C42C2312yes—
368C22×C42C2311yescharacteristic
369#400C2318yes—
370#400C2318yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2318yes—
375#400C2314yes—
376#399C2314yes—
377#399C2314yes—
378#399C2312yes—
379#399C2318yes—
380#399C2312yes—
381#399C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2318yes—
385#398C2314yes—
386#398C2318yes—
387#397C2318yes—
388#397C2318yes—
389#397C2314yes—
390#397C2314yes—
391#397C2318yes—
392#397C2318yes—
393#397C2318yes—
394#397C2318yes—
395#397C2312yes—
396#397C2318yes—
397#397C2312yes—
398#397C2318yes—
399#397C2318yes—
400#396C2318yes—
401#396C2318yes—
402#396C2318yes—
403#396C2318yes—
404#395C2318yes—
405#395C2318yes—
406#395C2314yes—
407#395C2318yes—
408#395C2314yes—
409#394C2314yes—
410#394C2318yes—
411#394C2318yes—
412#394C2318yes—
413#394C2318yes—
414#394C2318yes—
415#394C2318yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2318yes—
420#394C2318yes—
421#394C2314yes—
422#394C2318yes—
423#394C2318yes—
424#394C2318yes—
425#394C2318yes—
426#394C2318yes—
427#393C2312yes—
428#393C2312yes—
429#393C2314yes—
430#392C2314yes—
431#392C2314yes—
432#392C2312yes—
433#392C2312yes—
434#392C2318yes—
435#392C2314yes—
436#392C2314yes—
437#392C2318yes—
438#392C2318yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#390C2312yes—
447#390C2314yes—
448#390C2314yes—
449#390C2318yes—
450#390C2312yes—
451#390C2314yes—
452#390C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2312yes—
458#389C2314yes—
459#389C2318yes—
460#389C2318yes—
461#389C2314yes—
462#389C2318yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2318yes—
467#389C2312yes—
468#388C2318yes—
469#388C2318yes—
470#388C2318yes—
471#388C2318yes—
472#388C2318yes—
473#388C2318yes—
474#388C2318yes—
475#388C2318yes—
476#388C2318yes—
477#388C2318yes—
478#388C2314yes—
479#388C2314yes—
480#387C2318yes—
481#387C2318yes—
482#387C2318yes—
483#387C2318yes—
484#387C2318yes—
485#387C2318yes—
486#387C2318yes—
487#387C2318yes—
488#386C2318yes—
489#386C2318yes—
490#386C2318yes—
491#386C2318yes—
492#386C2318yes—
493#386C2318yes—
494#386C2318yes—
495#386C2318yes—
496#386C2318yes—
497#386C2318yes—
498#386C2314yes—
499#386C2314yes—
500#385C2318yes—
501#385C2318yes—
502#385C2318yes—
503#385C2318yes—
504#385C2318yes—
505#385C2318yes—
506#384C2314yes—
507#384C2314yes—
508#384C2312yes—
509#383C2312yes—
510#382C2312yes—
511#382C2314yes—
512#382C2312yes—
513#381C2312yes—
514#381C2314yes—
515#381C2318yes—
516#380C2314yes—
517#380C2314yes—
518#380C2318yes—
519#380C2318yes—
520#380C2318yes—
521#380C2318yes—
522#380C2318yes—
523#380C2314yes—
524#380C2314yes—
525#380C2312yes—
526#380C2314yes—
527#380C2314yes—
528#380C2314yes—
529#380C2314yes—
530#380C2314yes—
531#380C2314yes—
532#380C2311yescharacteristic
533#380C2311yescharacteristic
534#380C2312yes—
535#380C2312yes—
536#380C2312yes—
537#379C2314yes—
538C4×C4⋊C4C2312yes—
539C4×C4⋊C4C2312yes—
540C4×C4⋊C4C2312yes—
541C4×C4⋊C4C2314yes—
542C4×C4⋊C4C2318yes—
543C4×C4⋊C4C2318yes—
544C4×C22⋊C4C2314yes—
545C4×C22⋊C4C2312yes—
546C4×C22⋊C4C2314yes—
547C4×C22⋊C4C2318yes—
548C4×C22⋊C4C2318yes—
549C4×C22⋊C4C2314yes—
550C4×C22⋊C4C2318yes—
551C4×C22⋊C4C2314yes—
552#376C2312yes—
553C2×#95C2314yes—
554C25C2412yes—
555C2×#41—28no—
556C2×#41—24no—
557C2×#41—28no—
558C2×#41—28no—
559C2×#41—28no—
560C2×#41—44no—
561C2×#41—48no—
562C2×#41—44no—
563C2×#41—44no—
564C2×#41—48no—
565C2×#41—48no—
566C22×Q8C2412yes—
567C22×Q8C2412yes—
568C22×Q8C2411yescharacteristic
569C22×Q8C2412yes—
570C22×Q8C2412yes—
571C22×Q8C2412yes—
572C22×D4—44no—
573C22×D4C2×D418yes—
574C22×D4C2411yescharacteristic
575C22×D4C2411yescharacteristic
576C22×D4C2411yescharacteristic
577C22×D4C2411yescharacteristic
578C22×D4C2412yes—
579C22×D4C2412yes—
580C22×D4C2412yes—
581C22×D4C2414yes—
582C22×D4C2411yescharacteristic
583C22×D4C2412yes—
584C22×D4C2414yes—
585C22×D4C2414yes—
586C22×D4C2414yes—
587C22×D4C2412yes—
588C22×D4C2414yes—
589C22×D4C2414yes—
590C22×D4C2414yes—
591C22×D4C2414yes—
592C22×D4C2412yes—
593C23×C4—48no—
594C23×C4C2×D4116yes—
595C23×C4C2412yes—
596C23×C4C2412yes—
597C23×C4C2412yes—
598C23×C4C2412yes—
599C23×C4C2412yes—
600C23×C4C2411yescharacteristic
601C23×C4C2412yes—
602C23×C4C2411yescharacteristic
603C23×C4C2414yes—
604C23×C4C2414yes—
605C23×C4C2414yes—
606C23×C4C2414yes—
607C23×C4C2412yes—
608C23×C4C2418yes—
609C23×C4C2411yescharacteristic
610C23×C4C2412yes—
611C23×C4C2412yes—
612C23×C4C2412yes—
613C4⋊Q8—24no—
614C4⋊Q8—24no—
615C4⋊Q8—24no—
616C4⋊Q8—24no—
617C4⋊Q8—24no—
618#127—216no—
619#127—24no—
620#126—216no—
621#126—216no—
622#126—216no—
623#126—216no—
624#126—216no—
625#125—216no—
626#125—28no—
627#125—28no—
628#125—28no—
629#124—28no—
630#124—216no—
631#124—216no—
632#124—216no—
633#124—216no—
634#124—28no—
635#124—84no—
636#123—216no—
637#123—216no—
638#123—216no—
639#123—216no—
640#123—216no—
641#123—216no—
642#123—216no—
643#123—216no—
644#123—88no—
645C22⋊Q8—28no—
646C22⋊Q8—28no—
647C22⋊Q8—28no—
648C22⋊Q8—28no—
649C22⋊Q8—28no—
650C22⋊Q8—28no—
651C22⋊Q8—28no—
652C22⋊Q8—28no—
653C22⋊Q8—28no—
654C22⋊Q8—216no—
655C22⋊Q8—48no—
656C22⋊Q8—48no—
657C22⋊Q8—48no—
658C22⋊Q8—84no—
659#121—216no—
660#121—28no—
661#121—28no—
662#121—28no—
663#121—28no—
664#121—28no—
665#121—24no—
666#121—24no—
667#121—28no—
668#121—28no—
669#121—28no—
670#121—28no—
671#121—28no—
672#121—216no—
673#121—216no—
674#121—44no—
675#121—44no—
676#121—88no—
677#120—216no—
678#120—216no—
679#120—216no—
680C4×Q8—28no—
681C4×Q8—216no—
682C4×Q8—28no—
683C4×Q8—24no—
684C4×Q8—24no—
685C4×Q8—28no—
686C4×Q8—28no—
687C4×Q8—28no—
688C4×D4—28no—
689C4×D4—216no—
690C4×D4—28no—
691C4×D4—28no—
692C4×D4—216no—
693C4×D4—216no—
694C4×D4—216no—
695C4×D4—216no—
696C4×D4—216no—
697C4×D4—216no—
698C4×D4—216no—
699C4×D4—24no—
700C4×D4—24no—
701C4×D4—24no—
702C4×D4—24no—
703C4×D4—28no—
704C4×D4—48no—
705C4×D4—48no—
706C4×D4—48no—
707C4×D4C2×D418yes—
708C4×D4C2×D418yes—
709C4×D4C2×D4116yes—
710C4×D4C2×D418yes—
711C4×D4C2×D4116yes—
712C4×D4C2×D418yes—
713#117—24no—
714#117—28no—
715#117—216no—
716#117—216no—
717#117—28no—
718#117—28no—
719#117—28no—
720#117—28no—
721#117—28no—
722#117—28no—
723#117—28no—
724#117—28no—
725#117—216no—
726#117—28no—
727#117—48no—
728#117—82no—
729C2×C4⋊C4—28no—
730C2×C4⋊C4—28no—
731C2×C4⋊C4—28no—
732C2×C4⋊C4—28no—
733C2×C4⋊C4—48no—
734C2×C4⋊C4C2×D418yes—
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2411yescharacteristic
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2418yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2418yes—
769C2×C4⋊C4C2418yes—
770C2×C4⋊C4C2418yes—
771C2×C4⋊C4C2418yes—
772C2×C4⋊C4C2418yes—
773C2×C4⋊C4C2418yes—
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2411yescharacteristic
776C2×C4⋊C4C2412yes—
777C2×C22⋊C4—216no—
778C2×C22⋊C4—84no—
779C2×C22⋊C4C2×D4116yes—
780C2×C22⋊C4C2412yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2412yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2412yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2418yes—
804C2×C22⋊C4C2418yes—
805C2×C22⋊C4C2418yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2418yes—
811C2×C22⋊C4C2418yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2418yes—
815C2×C22⋊C4C2418yes—
816C2×C22⋊C4C2418yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2418yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
825C2×C42—216no—
826C2×C42—28no—
827C2×C42C2×D418yes—
828C2×C42C2414yes—
829C2×C42C2412yes—
830C2×C42C2414yes—
831C2×C42C2414yes—
832C2×C42C2414yes—
833C2×C42C2414yes—
834C2×C42C2412yes—
835C2×C42C2414yes—
836C2×C42C2414yes—
837C2×C42C2412yes—
838C2×C42C2414yes—
839C2×C42C2418yes—
840C2×C42C2411yescharacteristic
841C2×C42C2411yescharacteristic
842C2×C42C2411yescharacteristic
843C2×C42C2411yescharacteristic
844#95C2412yes—
845#95C2414yes—
846#95C2418yes—
847#95C2412yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2418yes—
853#95C2418yes—
854#95C2418yes—
855#95C2414yes—
856#95C2414yes—
857#95C2418yes—
858#95C2418yes—
859#95C2418yes—
860#95C2414yes—
861#95C2418yes—
862#95C2414yes—
863#95C2418yes—
864#95C2418yes—
865#95C2418yes—
866#95C2418yes—
867#95C2418yes—
868#95C2418yes—
869C24—42no—
870C24—44no—
871C24—44no—
872C24—42no—
873C24C22×D418yes—
874C24C2512yes—
875C24C2512yes—
876C24C2512yes—
877C24C2511yescharacteristic
878C24C2512yes—
879C24C2512yes—
880#41—432no—
881#41—416no—
882#41—432no—
883#41—816no—
884#41—816no—
885C2×Q8—22no—
886C2×Q8—24no—
887C2×Q8—24no—
888C2×Q8—24no—
889C2×Q8—24no—
890C2×Q8—24no—
891C2×Q8—24no—
892C2×Q8—24no—
893C2×Q8—28no—
894C2×Q8—42no—
895C2×Q8—44no—
896C2×Q8—42no—
897C2×Q8—42no—
898C2×Q8—42no—
899C2×Q8—42no—
900C2×D4—24no—
901C2×D4—24no—
902C2×D4—24no—
903C2×D4—28no—
904C2×D4—28no—
905C2×D4—28no—
906C2×D4—28no—
907C2×D4—28no—
908C2×D4—28no—
909C2×D4—22no—
910C2×D4—24no—
911C2×D4—22no—
912C2×D4—22no—
913C2×D4—24no—
914C2×D4—24no—
915C2×D4—24no—
916C2×D4—24no—
917C2×D4—24no—
918C2×D4—416no—
919C2×D4—44no—
920C2×D4—42no—
921C2×D4—44no—
922C2×D4—42no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—44no—
926C2×D4—44no—
927C2×D4—42no—
928C2×D4—44no—
929C2×D4—44no—
930C2×D4—44no—
931C2×D4—44no—
932C2×D4—44no—
933C2×D4—44no—
934C2×D4—44no—
935C2×D4—44no—
936C2×D4—42no—
937C2×D4—42no—
938C2×D4—44no—
939C2×D4—44no—
940C2×D4—44no—
941C2×D4—44no—
942C2×D4—48no—
943C2×D4—48no—
944C2×D4C22×D414yes—
945C2×D4C22×D414yes—
946C2×D4C22×D418yes—
947C22×C4—28no—
948C22×C4—28no—
949C22×C4—24no—
950C22×C4—24no—
951C22×C4—28no—
952C22×C4—28no—
953C22×C4—24no—
954C22×C4—24no—
955C22×C4—24no—
956C22×C4—24no—
957C22×C4—24no—
958C22×C4—24no—
959C22×C4—28no—
960C22×C4—28no—
961C22×C4—24no—
962C22×C4—24no—
963C22×C4—24no—
964C22×C4—28no—
965C22×C4—28no—
966C22×C4—432no—
967C22×C4—41no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—41no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4—42no—
975C22×C4—44no—
976C22×C4—42no—
977C22×C4—44no—
978C22×C4—48no—
979C22×C4—48no—
980C22×C4—48no—
981C22×C4—48no—
982C22×C4—48no—
983C22×C4C22×D418yes—
984C22×C4C22×D414yes—
985C22×C4C22×D414yes—
986C22×C4C22×D418yes—
987C22×C4C22×D414yes—
988C22×C4C22×D418yes—
989C22×C4C22×D418yes—
990C22×C4C22×D418yes—
991C22×C4C2514yes—
992C22×C4C2514yes—
993C22×C4C2514yes—
994C22×C4C2518yes—
995C22×C4C2512yes—
996C22×C4C2512yes—
997C22×C4C2514yes—
998C22×C4C2512yes—
999C22×C4C2512yes—
1000C22×C4C2512yes—
1001C22×C4C2514yes—
1002C22×C4C2514yes—
1003C22×C4C2511yescharacteristic
1004C22×C4C2511yescharacteristic
1005C22×C4C2512yes—
1006C22×C4C2511yescharacteristic
1007C22×C4C2511yescharacteristic
1008C22×C4C2512yes—
1009C22×C4C2511yescharacteristic
1010C22×C4C2511yescharacteristic
1011C4⋊C4—22no—
1012C4⋊C4—22no—
1013C4⋊C4—24no—
1014C4⋊C4—24no—
1015C4⋊C4—24no—
1016C4⋊C4—28no—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—28no—
1020C4⋊C4—24no—
1021C4⋊C4—22no—
1022C4⋊C4—22no—
1023C4⋊C4—24no—
1024C4⋊C4—24no—
1025C4⋊C4—24no—
1026C4⋊C4—28no—
1027C4⋊C4—28no—
1028C4⋊C4—24no—
1029C4⋊C4—28no—
1030C4⋊C4—24no—
1031C4⋊C4—28no—
1032C4⋊C4—28no—
1033C4⋊C4—28no—
1034C4⋊C4—24no—
1035C4⋊C4—24no—
1036C4⋊C4—24no—
1037C4⋊C4—28no—
1038C4⋊C4—24no—
1039C4⋊C4—28no—
1040C4⋊C4—48no—
1041C4⋊C4—48no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—48no—
1046C4⋊C4—48no—
1047C4⋊C4—48no—
1048C4⋊C4—48no—
1049C4⋊C4—48no—
1050C4⋊C4C22×D414yes—
1051C4⋊C4C22×D414yes—
1052C4⋊C4C22×D418yes—
1053C22⋊C4—24no—
1054C22⋊C4—28no—
1055C22⋊C4—28no—
1056C22⋊C4—28no—
1057C22⋊C4—28no—
1058C22⋊C4—28no—
1059C22⋊C4—28no—
1060C22⋊C4—28no—
1061C22⋊C4—28no—
1062C22⋊C4—28no—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—24no—
1067C22⋊C4—28no—
1068C22⋊C4—24no—
1069C22⋊C4—24no—
1070C22⋊C4—24no—
1071C22⋊C4—28no—
1072C22⋊C4—24no—
1073C22⋊C4—24no—
1074C22⋊C4—42no—
1075C22⋊C4—44no—
1076C22⋊C4—48no—
1077C22⋊C4—42no—
1078C22⋊C4—44no—
1079C22⋊C4—48no—
1080C22⋊C4—48no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—48no—
1088C22⋊C4—48no—
1089C22⋊C4—48no—
1090C22⋊C4—48no—
1091C22⋊C4—48no—
1092C22⋊C4—44no—
1093C22⋊C4—48no—
1094C22⋊C4C22×D418yes—
1095C22⋊C4C22×D418yes—
1096C22⋊C4C22×D418yes—
1097C22⋊C4C22×D418yes—
1098C42—24no—
1099C42—28no—
1100C42—28no—
1101C42—28no—
1102C42—24no—
1103C42—24no—
1104C42—28no—
1105C42—28no—
1106C42—28no—
1107C42—28no—
1108C42—48no—
1109C42—44no—
1110C42C22×D414yes—
1111C42C22×D414yes—
1112C42C22×D414yes—
1113C42C22×D414yes—
1114C23—24no—
1115C23—24no—
1116C23—24no—
1117C23—22no—
1118C23—22no—
1119C23—24no—
1120C23—21no—
1121C23—22no—
1122C23—22no—
1123C23—21no—
1124C23—22no—
1125C23—22no—
1126C23—22no—
1127C23—22no—
1128C23—22no—
1129C23—22no—
1130C23—24no—
1131C23—24no—
1132C23—22no—
1133C23—22no—
1134C23—24no—
1135C23—24no—
1136C23—22no—
1137C23—22no—
1138C23—22no—
1139C23—22no—
1140C23—22no—
1141C23—22no—
1142C23—22no—
1143C23—48no—
1144C23—48no—
1145C23—48no—
1146C23—88no—
1147C23—88no—
1148C23C23×D414yes—
1149C23C23×D412yes—
1150C23C23×D414yes—
1151C23C2611yescharacteristic
1152Q8—44no—
1153Q8—48no—
1154Q8—48no—
1155Q8—48no—
1156Q8—84no—
1157Q8—84no—
1158D4—28no—
1159D4—28no—
1160D4—48no—
1161D4—44no—
1162D4—48no—
1163D4—48no—
1164D4—48no—
1165D4—48no—
1166D4—416no—
1167D4—44no—
1168D4—44no—
1169D4—84no—
1170D4—88no—
1171D4—88no—
1172D4—88no—
1173D4—88no—
1174D4—88no—
1175D4—88no—
1176D4—88no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—28no—
1186C2×C4—28no—
1187C2×C4—216no—
1188C2×C4—216no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—24no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—28no—
1202C2×C4—22no—
1203C2×C4—28no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—28no—
1212C2×C4—22no—
1213C2×C4—28no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—22no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—48no—
1223C2×C4—48no—
1224C2×C4—48no—
1225C2×C4—44no—
1226C2×C4—416no—
1227C2×C4—48no—
1228C2×C4—48no—
1229C2×C4—48no—
1230C2×C4—48no—
1231C2×C4—84no—
1232C2×C4—88no—
1233C2×C4—88no—
1234C2×C4—88no—
1235C2×C4—168no—
1236C2×C4C23×D414yes—
1237C2×C4C23×D412yes—
1238C2×C4C23×D412yes—
1239C2×C4C23×D414yes—
1240C2×C4C23×D412yes—
1241C2×C4C23×D412yes—
1242C2×C4C23×D412yes—
1243C2×C4C23×D412yes—
1244C2×C4#58514yes—
1245C2×C4#58514yes—
1246C22—22no—
1247C22—24no—
1248C22—24no—
1249C22—22no—
1250C22—24no—
1251C22—24no—
1252C22—22no—
1253C22—24no—
1254C22—24no—
1255C22—44no—
1256C22—44no—
1257C22—42no—
1258C22—44no—
1259C22—44no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—44no—
1269C22—42no—
1270C22—44no—
1271C22—42no—
1272C22—44no—
1273C22—42no—
1274C22—44no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—816no—
1279C22C24×D411yescharacteristic
1280C22C2×#58512yes—
1281C22C2×#58512yes—
1282C22H(7,𝔽2)11yescharacteristic
1283C222−1+611yescharacteristic
1284C4—22no—
1285C4—24no—
1286C4—24no—
1287C4—22no—
1288C4—22no—
1289C4—22no—
1290C4—42no—
1291C4—44no—
1292C4—42no—
1293C4—44no—
1294C4—44no—
1295C4—44no—
1296C4—48no—
1297C4—44no—
1298C4—42no—
1299C4—42no—
1300C4—42no—
1301C4—44no—
1302C4#344914yes—
1303C4#348514yes—
1304C2—44no—
1305C2—44no—
1306C2—42no—
1307C2—82no—
1308C2—82no—
1309C2—82no—
1310C2C2×#344911yescharacteristic
1311C2C2×#348511yescharacteristic
1312C2#6285311yescharacteristic
1313C2#6293612yes—
1314C2#6293712yes—
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×#3506C2semidirect
2. C2×#3475C2semidirect
3. #42682C2semidirect
4. #42679C2semidirect
5. #42432C2semidirect
6. #41424C2semidirect
7. #41421C2semidirect
8. #41376C2semidirect
9. #38922C2semidirect
10. #38908C2semidirect
11. #38051C2semidirect
12. #38033C2semidirect
13. #37640C2semidirect
14. #37635C2semidirect
15. #37445C2semidirect
16. #37444C2semidirect
17. #36411C2semidirect
18. #36404C2semidirect
19. #36062C2semidirect
20. #35856C2semidirect
21. #35758C2semidirect
22. #35297C2semidirect
23. #35263C2semidirect
24. #34635C2semidirect
25. #34609C2semidirect
26. #34194C2semidirect
62. #2857C22semidirect
63. #2857C22semidirect
64. #2855C22semidirect
65. #2854C22semidirect
66. #2820C22semidirect
68. #2814C22semidirect
69. #2813C22semidirect
71. #2718C22semidirect
73. #2715C22semidirect
75. #2703C22semidirect
76. #2695C22semidirect
77. #2693C22semidirect
78. #2689C22semidirect
81. #2672C22semidirect
82. #2672C22semidirect
83. #2663C22semidirect
84. #2661C22semidirect
85. #2660C22semidirect
86. #2642C22semidirect
87. #2638C22semidirect
89. #2635C22semidirect
90. #2634C22semidirect
91. #2632C22semidirect
92. #2631C22semidirect
94. #2628C22semidirect
98. #2625C22semidirect
103. #2624C22semidirect
104. #2623C22semidirect
105. #2623C22semidirect
108. #2619C22semidirect
115. #2584C22semidirect
116. #2581C22semidirect
117. #2581C22semidirect
118. #2568C22semidirect
119. #2567C22semidirect
120. #2567C22semidirect
121. #2564C22semidirect
122. #2562C22semidirect
123. #2559C22semidirect
124. #2555C22semidirect
125. #2548C22semidirect
126. #2547C22semidirect
127. #2543C22semidirect
128. #2542C22semidirect
129. #2538C22semidirect
130. #2538C22semidirect
132. #2536C22semidirect
134. #2521C22semidirect
136. #2498C22semidirect
137. #2498C22semidirect
138. #2496C22semidirect
139. #2487C22semidirect
140. #2486C22semidirect
143. #2485C22semidirect
144. #2485C22semidirect
145. #2474C22semidirect
146. #2470C22semidirect
147. #2469C22semidirect
148. #2467C22semidirect
149. #2462C22semidirect
150. #2461C22semidirect
151. #2460C22semidirect
152. #2457C22semidirect
153. #2442C22semidirect
154. #2441C22semidirect
159. #2417C22semidirect
160. #2417C22semidirect
161. #2416C22semidirect
163. #2415C22semidirect
164. #2415C22semidirect
165. #2414C22semidirect
169. #2407C22semidirect
170. #2407C22semidirect
171. #2398C22semidirect
172. #2397C22semidirect
174. #2395C22semidirect
175. #2395C22semidirect
177. #2362C22semidirect
178. #2360C22semidirect
180. #2354C22semidirect
182. #2352C22semidirect
187. #2323C22semidirect
190. #2316C22semidirect
191. #2311C22semidirect
192. C4×#121C22semidirect
193. C4×#121C22semidirect
194. #2297C22semidirect
195. #2296C22semidirect
314. C2×C4×D4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35062
C2×#34752
#426822
#426792
#424322
#414242
#414212
#413762
#389222
#389082
#380512
#380332
#376402
#376352
#374452
#374442
#364112
#364042
#360622
#358562
#357582
#352972
#352632
#346352
#346092
#341942