Finite Group Databasebeta

← #7715426

Subgroups — #7715426

Order 512.

6644 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3546C211yesmaximal, characteristic
2C2×#3563C211yesmaximal, characteristic, complemented
3#51211C214yesmaximal, complemented
4#50897C214yesmaximal, complemented
5#48833C218yesmaximal, complemented
6#47724C218yesmaximal, complemented
7#46429C214yesmaximal, complemented
8#46359C214yesmaximal, complemented
9#39174C212yesmaximal, complemented
10#39162C212yesmaximal, complemented
11#38952C212yesmaximal, complemented
12#38947C212yesmaximal, complemented
13#38093C212yesmaximal, complemented
14#38088C212yesmaximal, complemented
15#38084C212yesmaximal, complemented
16#38078C212yesmaximal, complemented
17#37619C211yesmaximal, characteristic, complemented
18#37539C211yesmaximal, characteristic, complemented
19#37424C212yesmaximal, complemented
20#37303C212yesmaximal, complemented
21#35341C211yesmaximal, characteristic, complemented
22#35318C212yesmaximal, complemented
23#35298C211yesmaximal, characteristic, complemented
24#35264C212yesmaximal, complemented
25#34081C211yesmaximal, characteristic, complemented
26#3563—216no—
27#3546—216no—
28C2×#564C2212yescomplemented
29C2×#563C2212yes—
30C2×#560C2214yes—
31C2×#557C2212yescomplemented
32C2×#556C2211yescharacteristic
33C2×#554C2212yescomplemented
34C2×#553C2212yes—
35C2×#552C2212yes—
36C2×#552C2212yescomplemented
37C2×#552C2214yescomplemented
38C2×#550C2211yescharacteristic
39C2×#550C2212yes—
40C2×#547C2211yescharacteristic
41C2×#546C2212yes—
42C2×#546C2212yes—
43C2×D42C2211yescharacteristic
44C2×#544C2212yescomplemented
45C2×#544C2212yescomplemented
46C2×#542C2212yes—
47C2×#541C2212yescomplemented
48C2×#541C2214yescomplemented
49C2×#539C2212yes—
50C2×#538C2214yes—
51C2×#537C2212yes—
52C2×#535C2212yes—
53C2×#535C2212yes—
54C2×#533C2211yescharacteristic, complemented
55C2×#532C2211yescharacteristic
56C2×#532C2211yescharacteristic
57C2×#529C2211yescharacteristic
58C22×#125C2211yescharacteristic, complemented
59#2868C2211yescharacteristic, complemented
60#2862C2211yescharacteristic, complemented
61#2861C2212yes—
62#2861C2212yescomplemented
63#2861C2212yescomplemented
64#2858C2211yescharacteristic
65#2858C2211yescharacteristic
66#2858C2212yescomplemented
67#2857C2212yescomplemented
68#2850C2212yes—
69#2820C2214yescomplemented
70#2816C2214yescomplemented
71#2729C2218yescomplemented
72#2725C2218yescomplemented
73#2721C2218yescomplemented
74#2711C2218yes—
75#2711C2218yescomplemented
76#2711C2218yescomplemented
77#2711C2218yescomplemented
78#2711C2218yescomplemented
79#2709C2218yescomplemented
80#2708C2218yes—
81#2707C2218yescomplemented
82#2697C2218yescomplemented
83#2695C2218yescomplemented
84#2694C2218yescomplemented
85#2691C2218yescomplemented
86#2685C2218yes—
87#2685C2218yescomplemented
88#2685C2218yescomplemented
89#2681C2218yescomplemented
90#2680C2218yescomplemented
91#2677C2218yescomplemented
92#2674C2218yescomplemented
93#2672C2218yescomplemented
94#2672C2218yescomplemented
95#2660C2212yescomplemented
96#2658C2212yescomplemented
97#2642C2212yescomplemented
98#2641C2212yes—
99#2641C2212yes—
100#2641C2212yescomplemented
101#2640C2212yes—
102#2640C2212yescomplemented
103#2633C2214yescomplemented
104#2633C2214yescomplemented
105#2624C2214yescomplemented
106#2621C2212yescomplemented
107#2620C2212yes—
108#2620C2212yes—
109#2620C2212yescomplemented
110#2618C2214yescomplemented
111#2591C2214yescomplemented
112#2591C2214yescomplemented
113#2580C2214yescomplemented
114#2567C2212yescomplemented
115#2566C2212yes—
116#2566C2212yescomplemented
117#2566C2212yescomplemented
118#2566C2214yescomplemented
119#2565C2212yescomplemented
120#2562C2214yescomplemented
121#2562C2214yescomplemented
122#2556C2218yescomplemented
123#2553C2218yescomplemented
124#2548C2212yes—
125#2548C2212yescomplemented
126#2548C2212yescomplemented
127#2546C2212yescomplemented
128#2545C2212yes—
129#2545C2212yes—
130#2545C2214yescomplemented
131#2542C2212yescomplemented
132#2521C2218yescomplemented
133#2519C2218yescomplemented
134#2504C2211yescharacteristic
135#2504C2211yescharacteristic, complemented
136#2502C2212yescomplemented
137#2501C2212yes—
138#2501C2211yescharacteristic
139#2501C2211yescharacteristic, complemented
140#2500C2212yes—
141#2500C2214yescomplemented
142#2499C2212yescomplemented
143#2491C2218yescomplemented
144#2490C2218yescomplemented
145#2480C2218yescomplemented
146#2476C2218yescomplemented
147#2476C2218yescomplemented
148#2475C2218yescomplemented
149#2473C2218yescomplemented
150#2472C2218yescomplemented
151#2472C2218yescomplemented
152#2470C2218yescomplemented
153#2469C2218yescomplemented
154#2460C2218yescomplemented
155#2454C2218yescomplemented
156#2445C2218yescomplemented
157#2437C2218yescomplemented
158#2435C2212yes—
159#2435C2212yes—
160#2432C2218yescomplemented
161#2432C2214yescomplemented
162#2432C2212yescomplemented
163#2432C2212yescomplemented
164#2432C2212yescomplemented
165#2432C2212yescomplemented
166#2426C2218yescomplemented
167#2418C2218yescomplemented
168#2411C2218yes—
169#2406C2214yescomplemented
170#2405C2218yes—
171#2337C2212yes—
172#2336C2212yescomplemented
173#2335C2214yescomplemented
174#2334C2214yescomplemented
175#2333C2212yes—
176#2332C2212yescomplemented
177#2327C2212yescomplemented
178#2326C2212yes—
179#2326C2212yescomplemented
180#2326C2212yescomplemented
181#2311C2212yescomplemented
182#2311C2212yescomplemented
183#2311C2212yescomplemented
184#2309C2212yes—
185C4×C4⋊Q8C2212yescomplemented
186C4×#124C2212yescomplemented
187#2298C2212yescomplemented
188#2297C2212yescomplemented
189#2295C2212yescomplemented
190#2293C2212yescomplemented
191C2×#390C2212yes—
192#2290C2212yes—
193#2290C2212yescomplemented
194#2283C2211yescharacteristic, complemented
195C4×#117C2211yescharacteristic, complemented
196C4×#117C2212yescomplemented
197C22×#41C2312yes—
198C22×#41C2312yes—
199C22×#41C2312yes—
200C22×#41C2312yes—
201C23×D4C2312yes—
202C23×D4C2312yes—
203#564—216no—
204#563—216no—
205#560—232no—
206#557—216no—
207#556—28no—
208#554—216no—
209#553—216no—
210#552—232no—
211#552—216no—
212#552—216no—
213#550—28no—
214#550—216no—
215#547—28no—
216#546—216no—
217#546—216no—
218D42—28no—
219#544—216no—
220#544—216no—
221#542—216no—
222#541—232no—
223#541—216no—
224#539—216no—
225#538—232no—
226#537—216no—
227#535—216no—
228#535—216no—
229#533—28no—
230#532—28no—
231#532—28no—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2311yescharacteristic
236C2×C4⋊Q8C2311yescharacteristic
237C2×C4⋊Q8C2314yes—
238C2×C4⋊Q8C2314yes—
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2314yes—
242C2×#127C2311yescharacteristic
243C2×#127C2312yes—
244C2×#127C2311yescharacteristic
245C2×#127C2314yes—
246#529D4116yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#126C2312yes—
254C2×#125—28no—
255C2×#125C2312yes—
256C2×#125C2312yes—
257C2×#125C2312yes—
258C2×#125C2312yes—
259C2×#125C2312yes—
260C2×#125C2312yes—
261C2×#125C2314yes—
262C2×#125C2314yes—
263C2×#125C2314yes—
264C2×#125C2314yes—
265C2×#125C2314yes—
266C2×#125C2314yes—
267C2×#125C2314yes—
268C2×#125C2314yes—
269C2×#125C2311yescharacteristic
270C2×#124C2312yes—
271C2×#124C2312yes—
272C2×#124C2312yes—
273C2×#124C2314yes—
274C2×#124C2312yes—
275C2×#124C2312yes—
276C2×#124C2312yes—
277C2×#124C2312yes—
278C2×#124C2314yes—
279C2×#124C2318yes—
280C2×#124C2311yescharacteristic
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2318yes—
289C2×#123C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2318yes—
302C2×C22⋊Q8C2311yescharacteristic
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#121C2312yes—
306C2×#121C2312yes—
307C2×#121C2311yescharacteristic
308C2×#121C2311yescharacteristic
309C2×#121C2314yes—
310C2×#121C2314yes—
311C2×#121C2314yes—
312C2×#121C2312yes—
313C2×#121C2312yes—
314C2×#121C2314yes—
315C2×#121C2314yes—
316C2×#121C2312yes—
317C2×#121C2314yes—
318C2×#121C2311yescharacteristic
319C2×#120C2314yes—
320C2×#120C2314yes—
321C2×#120C2314yes—
322C2×#120C2314yes—
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2314yes—
329C2×C4×Q8C2311yescharacteristic
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2311yescharacteristic
333C2×C4×D4C2311yescharacteristic
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2311yescharacteristic
339C2×C4×D4C2312yes—
340C2×#117C2312yes—
341C2×#117C2312yes—
342C2×#117C2314yes—
343C2×#117C2312yes—
344C2×#117C2314yes—
345C2×#117C2312yes—
346C2×#117C2312yes—
347C2×#117C2312yes—
348C22×C4⋊C4C2311yescharacteristic
349C22×C4⋊C4C2311yescharacteristic
350C22×C4⋊C4C2312yes—
351C22×C4⋊C4C2312yes—
352C22×C4⋊C4C2312yes—
353C22×C4⋊C4C2312yes—
354C22×C22⋊C4C2314yes—
355C22×C22⋊C4C2318yes—
356C22×C42C2312yes—
357C22×C42C2311yescharacteristic
358#400C2318yes—
359#400C2318yes—
360#399C2318yes—
361#399C2314yes—
362#399C2314yes—
363#399C2318yes—
364#399C2318yes—
365#399C2318yes—
366#398C2318yes—
367#398C2318yes—
368#398C2318yes—
369#398C2318yes—
370#398C2318yes—
371#397C2314yes—
372#397C2314yes—
373#397C2318yes—
374#397C2318yes—
375#397C2318yes—
376#397C2318yes—
377#396C2318yes—
378#396C2318yes—
379#396C2318yes—
380#396C2318yes—
381#396C2318yes—
382#396C2318yes—
383#396C2318yes—
384#396C2318yes—
385#395C2318yes—
386#395C2318yes—
387#394C2318yes—
388#394C2318yes—
389#394C2318yes—
390#394C2318yes—
391#394C2318yes—
392#394C2318yes—
393#394C2318yes—
394#394C2318yes—
395#394C2318yes—
396#394C2318yes—
397#394C2318yes—
398#394C2318yes—
399#394C2318yes—
400#394C2318yes—
401#394C2318yes—
402#394C2318yes—
403#394C2318yes—
404#394C2318yes—
405#394C2318yes—
406#393C2318yes—
407#393C2318yes—
408#391C2312yes—
409#391C2312yes—
410#391C2312yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#391C2314yes—
417#391C2314yes—
418#390C2312yes—
419#390C2312yes—
420#390C2312yes—
421#390C2312yes—
422#390C2318yes—
423#390C2312yes—
424#390C2312yes—
425#390C2312yes—
426#390C2314yes—
427#390C2314yes—
428#390C2312yes—
429#390C2312yes—
430#390C2312yes—
431#390C2312yes—
432#390C2318yes—
433#390C2314yes—
434#390C2314yes—
435#390C2318yes—
436#390C2312yes—
437#390C2318yes—
438#390C2318yes—
439#390C2318yes—
440#389C2318yes—
441#389C2318yes—
442#389C2318yes—
443#389C2314yes—
444#389C2314yes—
445#389C2318yes—
446#388C2318yes—
447#388C2318yes—
448#388C2318yes—
449#388C2318yes—
450#388C2318yes—
451#388C2318yes—
452#388C2318yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2318yes—
460#388C2318yes—
461#388C2318yes—
462#388C2318yes—
463#388C2318yes—
464#388C2318yes—
465#388C2318yes—
466#387C2318yes—
467#387C2318yes—
468#387C2318yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2318yes—
476#386C2318yes—
477#386C2318yes—
478#386C2318yes—
479#386C2314yes—
480#386C2314yes—
481#386C2318yes—
482#386C2314yes—
483#386C2314yes—
484#386C2318yes—
485#385C2318yes—
486#385C2318yes—
487#385C2318yes—
488#385C2318yes—
489#385C2318yes—
490#385C2318yes—
491#385C2318yes—
492#385C2318yes—
493#385C2314yes—
494#385C2314yes—
495#385C2318yes—
496#385C2318yes—
497#385C2318yes—
498#384C2312yes—
499#384C2312yes—
500#384C2312yes—
501#384C2312yes—
502#384C2314yes—
503#383C2312yes—
504#382C2312yes—
505#382C2312yes—
506#382C2312yes—
507#382C2314yes—
508#381C2312yes—
509#380C2318yes—
510#380C2318yes—
511#380C2318yes—
512#380C2312yes—
513#380C2318yes—
514#379C2318yes—
515#379C2318yes—
516#379C2318yes—
517C4×C4⋊C4C2312yes—
518C4×C4⋊C4C2312yes—
519C4×C4⋊C4C2318yes—
520C4×C4⋊C4C2312yes—
521C4×C4⋊C4C2312yes—
522C4×C4⋊C4C2312yes—
523C4×C4⋊C4C2314yes—
524C4×C4⋊C4C2314yes—
525C4×C22⋊C4C2312yes—
526C4×C22⋊C4C2314yes—
527C4×C22⋊C4C2312yes—
528C4×C22⋊C4C2314yes—
529C4×C22⋊C4C2318yes—
530C4×C22⋊C4C2311yescharacteristic
531C4×C22⋊C4C2311yescharacteristic
532C4×C22⋊C4C2312yes—
533C4×C22⋊C4C2312yes—
534C4×C22⋊C4C2318yes—
535#376C2312yes—
536#376C2312yes—
537#376C2312yes—
538C43C2312yes—
539C43C2311yescharacteristic
540C43C2311yescharacteristic
541C25C2414yes—
542C2×#41—28no—
543C2×#41—28no—
544C2×#41—28no—
545C2×#41—28no—
546C2×#41—44no—
547C2×#41—44no—
548C2×#41—44no—
549C2×#41—44no—
550C2×#41—84no—
551C2×#41—84no—
552C22×Q8C2412yes—
553C22×Q8C2412yes—
554C22×Q8C2414yes—
555C22×Q8C2412yes—
556C22×Q8C2412yes—
557C22×Q8C2411yescharacteristic
558C22×D4—28no—
559C22×D4—28no—
560C22×D4—44no—
561C22×D4—44no—
562C22×D4—84no—
563C22×D4C2411yescharacteristic
564C22×D4C2412yes—
565C22×D4C2411yescharacteristic
566C22×D4C2412yes—
567C22×D4C2412yes—
568C22×D4C2414yes—
569C22×D4C2412yes—
570C22×D4C2412yes—
571C22×D4C2414yes—
572C22×D4C2412yes—
573C22×D4C2414yes—
574C22×D4C2414yes—
575C22×D4C2414yes—
576C22×D4C2414yes—
577C22×D4C2412yes—
578C22×D4C2412yes—
579C22×D4C2411yescharacteristic
580C23×C4C2411yescharacteristic
581C23×C4C2412yes—
582C23×C4C2414yes—
583C23×C4C2414yes—
584C23×C4C2414yes—
585C23×C4C2412yes—
586C23×C4C2412yes—
587C23×C4C2412yes—
588C23×C4C2414yes—
589C23×C4C2412yes—
590C23×C4C2414yes—
591C23×C4C2411yescharacteristic
592C23×C4C2411yescharacteristic
593C4⋊Q8—216no—
594C4⋊Q8—216no—
595C4⋊Q8—24no—
596C4⋊Q8—24no—
597C4⋊Q8—24no—
598C4⋊Q8—24no—
599C4⋊Q8—28no—
600C4⋊Q8—44no—
601C4⋊Q8—44no—
602C4⋊Q8—84no—
603#127—216no—
604#127—24no—
605#127—24no—
606#127—28no—
607#126—216no—
608#126—216no—
609#126—216no—
610#126—216no—
611#126—216no—
612#126—216no—
613#126C2×D4116yes—
614#125—216no—
615#125—216no—
616#125—216no—
617#125—216no—
618#125—216no—
619#125—216no—
620#125—216no—
621#125—216no—
622#125—28no—
623#125—28no—
624#125—28no—
625#125—28no—
626#125—28no—
627#125—28no—
628#125C2×D418yes—
629#124—216no—
630#124—28no—
631#124—28no—
632#124—28no—
633#124—44no—
634#124—44no—
635#124—44no—
636#124—44no—
637#124—84no—
638#124—88no—
639#124C2×D418yes—
640#123—216no—
641#123—216no—
642#123—216no—
643#123—216no—
644#123—216no—
645#123—84no—
646#123—88no—
647#123—84no—
648#123C2×D4116yes—
649C22⋊Q8—28no—
650C22⋊Q8—28no—
651C22⋊Q8—28no—
652C22⋊Q8—28no—
653C22⋊Q8—28no—
654C22⋊Q8—28no—
655C22⋊Q8—216no—
656C22⋊Q8—216no—
657C22⋊Q8—216no—
658C22⋊Q8—216no—
659C22⋊Q8—216no—
660C22⋊Q8—88no—
661C22⋊Q8C2×D418yes—
662#121—28no—
663#121—28no—
664#121—24no—
665#121—24no—
666#121—28no—
667#121—28no—
668#121—28no—
669#121—216no—
670#121—28no—
671#121—216no—
672#121—28no—
673#121—216no—
674#121—216no—
675#121—216no—
676#121—216no—
677#121C2×D418yes—
678#120—216no—
679#120—216no—
680#120—216no—
681#120—216no—
682C4×Q8—216no—
683C4×Q8—28no—
684C4×Q8—28no—
685C4×Q8—28no—
686C4×Q8—28no—
687C4×Q8—28no—
688C4×Q8C2×D418yes—
689C4×D4—216no—
690C4×D4—216no—
691C4×D4—28no—
692C4×D4—24no—
693C4×D4—28no—
694C4×D4—28no—
695C4×D4—24no—
696C4×D4—28no—
697C4×D4C2×D418yes—
698C4×D4C2×D4116yes—
699#117—28no—
700#117—28no—
701#117—28no—
702#117—216no—
703#117—216no—
704#117—44no—
705#117—44no—
706#117C2×D4116yes—
707C2×C4⋊C4—28no—
708C2×C4⋊C4—24no—
709C2×C4⋊C4—28no—
710C2×C4⋊C4—24no—
711C2×C4⋊C4—28no—
712C2×C4⋊C4—28no—
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2412yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2411yescharacteristic
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2418yes—
746C2×C4⋊C4C2418yes—
747C2×C4⋊C4C2418yes—
748C2×C4⋊C4C2418yes—
749C2×C4⋊C4C2418yes—
750C2×C4⋊C4C2418yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2411yescharacteristic
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C22⋊C4—216no—
760C2×C22⋊C4—88no—
761C2×C22⋊C4C2412yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2412yes—
769C2×C22⋊C4C2412yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2412yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2418yes—
777C2×C22⋊C4C2418yes—
778C2×C22⋊C4C2418yes—
779C2×C22⋊C4C2418yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2418yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2412yes—
785C2×C22⋊C4C2412yes—
786C2×C22⋊C4C2418yes—
787C2×C22⋊C4C2418yes—
788C2×C22⋊C4C2418yes—
789C2×C22⋊C4C2418yes—
790C2×C22⋊C4C2418yes—
791C2×C22⋊C4C2418yes—
792C2×C22⋊C4C2418yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2418yes—
795C2×C22⋊C4C2418yes—
796C2×C22⋊C4C2418yes—
797C2×C22⋊C4C2418yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2412yes—
803C2×C42—44no—
804C2×C42C2×D418yes—
805C2×C42C2414yes—
806C2×C42C2414yes—
807C2×C42C2412yes—
808C2×C42C2414yes—
809C2×C42C2414yes—
810C2×C42C2412yes—
811C2×C42C2412yes—
812C2×C42C2414yes—
813C2×C42C2412yes—
814C2×C42C2412yes—
815C2×C42C2414yes—
816C2×C42C2412yes—
817C2×C42C2412yes—
818C2×C42C2414yes—
819C2×C42C2412yes—
820C2×C42C2414yes—
821C2×C42C2411yescharacteristic
822C2×C42C2412yes—
823C2×C42C2411yescharacteristic
824C2×C42C2411yescharacteristic
825C2×C42C2411yescharacteristic
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2418yes—
833#95C2418yes—
834#95C2412yes—
835#95C2412yes—
836#95C2418yes—
837#95C2414yes—
838#95C2418yes—
839#95C2414yes—
840#95C2418yes—
841#95C2414yes—
842#95C2418yes—
843#95C2414yes—
844#95C2414yes—
845#95C2418yes—
846#95C2418yes—
847#95C2418yes—
848#95C2418yes—
849C24—28no—
850C24—44no—
851C24—48no—
852C24—48no—
853C24—44no—
854C24C2512yes—
855C24C2514yes—
856C24C2512yes—
857C24C2512yes—
858C24C2511yescharacteristic
859#41—816no—
860#41—816no—
861#41—816no—
862#41—816no—
863C2×Q8—24no—
864C2×Q8—24no—
865C2×Q8—24no—
866C2×Q8—28no—
867C2×Q8—24no—
868C2×Q8—24no—
869C2×Q8—24no—
870C2×Q8—24no—
871C2×Q8—24no—
872C2×Q8—42no—
873C2×Q8—48no—
874C2×Q8—44no—
875C2×Q8—44no—
876C2×Q8C22×D414yes—
877C2×D4—24no—
878C2×D4—28no—
879C2×D4—28no—
880C2×D4—28no—
881C2×D4—24no—
882C2×D4—24no—
883C2×D4—22no—
884C2×D4—24no—
885C2×D4—22no—
886C2×D4—24no—
887C2×D4—24no—
888C2×D4—28no—
889C2×D4—24no—
890C2×D4—28no—
891C2×D4—28no—
892C2×D4—24no—
893C2×D4—24no—
894C2×D4—24no—
895C2×D4—24no—
896C2×D4—42no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—48no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—48no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—48no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—816no—
914C2×D4—816no—
915C2×D4C22×D418yes—
916C2×D4C22×D414yes—
917C22×C4—24no—
918C22×C4—24no—
919C22×C4—24no—
920C22×C4—24no—
921C22×C4—24no—
922C22×C4—28no—
923C22×C4—24no—
924C22×C4—24no—
925C22×C4—28no—
926C22×C4—28no—
927C22×C4—28no—
928C22×C4—42no—
929C22×C4—44no—
930C22×C4—44no—
931C22×C4—42no—
932C22×C4—44no—
933C22×C4—44no—
934C22×C4—44no—
935C22×C4—48no—
936C22×C4—48no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—44no—
940C22×C4—44no—
941C22×C4—44no—
942C22×C4—44no—
943C22×C4C22×D414yes—
944C22×C4C22×D418yes—
945C22×C4C22×D414yes—
946C22×C4C22×D414yes—
947C22×C4C2514yes—
948C22×C4C2514yes—
949C22×C4C2514yes—
950C22×C4C2514yes—
951C22×C4C2514yes—
952C22×C4C2514yes—
953C22×C4C2512yes—
954C22×C4C2512yes—
955C22×C4C2514yes—
956C22×C4C2514yes—
957C22×C4C2514yes—
958C22×C4C2511yescharacteristic
959C22×C4C2512yes—
960C22×C4C2511yescharacteristic
961C22×C4C2511yescharacteristic
962C22×C4C2511yescharacteristic
963C22×C4C2512yes—
964C22×C4C2512yes—
965C22×C4C2511yescharacteristic
966C22×C4C2511yescharacteristic
967C4⋊C4—24no—
968C4⋊C4—24no—
969C4⋊C4—24no—
970C4⋊C4—24no—
971C4⋊C4—28no—
972C4⋊C4—28no—
973C4⋊C4—24no—
974C4⋊C4—28no—
975C4⋊C4—28no—
976C4⋊C4—28no—
977C4⋊C4—28no—
978C4⋊C4—24no—
979C4⋊C4—28no—
980C4⋊C4—24no—
981C4⋊C4—28no—
982C4⋊C4—28no—
983C4⋊C4—24no—
984C4⋊C4—22no—
985C4⋊C4—22no—
986C4⋊C4—24no—
987C4⋊C4—24no—
988C4⋊C4—28no—
989C4⋊C4—28no—
990C4⋊C4—28no—
991C4⋊C4—28no—
992C4⋊C4—28no—
993C4⋊C4—28no—
994C4⋊C4—24no—
995C4⋊C4—28no—
996C4⋊C4—44no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C4⋊C4—44no—
1001C4⋊C4—48no—
1002C4⋊C4—48no—
1003C4⋊C4—48no—
1004C4⋊C4—48no—
1005C4⋊C4—48no—
1006C4⋊C4—48no—
1007C4⋊C4C22×D414yes—
1008C4⋊C4C22×D414yes—
1009C4⋊C4C22×D418yes—
1010C4⋊C4C22×D418yes—
1011C4⋊C4C22×D418yes—
1012C4⋊C4C22×D418yes—
1013C22⋊C4—28no—
1014C22⋊C4—28no—
1015C22⋊C4—28no—
1016C22⋊C4—28no—
1017C22⋊C4—28no—
1018C22⋊C4—24no—
1019C22⋊C4—28no—
1020C22⋊C4—28no—
1021C22⋊C4—24no—
1022C22⋊C4—24no—
1023C22⋊C4—28no—
1024C22⋊C4—28no—
1025C22⋊C4—28no—
1026C22⋊C4—28no—
1027C22⋊C4—24no—
1028C22⋊C4—48no—
1029C22⋊C4—48no—
1030C22⋊C4—48no—
1031C22⋊C4—48no—
1032C22⋊C4—48no—
1033C22⋊C4—48no—
1034C22⋊C4—44no—
1035C22⋊C4—48no—
1036C22⋊C4—48no—
1037C22⋊C4—44no—
1038C22⋊C4—44no—
1039C22⋊C4—48no—
1040C22⋊C4—42no—
1041C22⋊C4—44no—
1042C22⋊C4—42no—
1043C22⋊C4—48no—
1044C22⋊C4—48no—
1045C22⋊C4—48no—
1046C22⋊C4—48no—
1047C22⋊C4—48no—
1048C22⋊C4—48no—
1049C22⋊C4—48no—
1050C22⋊C4C22×D418yes—
1051C22⋊C4C22×D418yes—
1052C22⋊C4C22×D418yes—
1053C22⋊C4C22×D418yes—
1054C22⋊C4C22×D418yes—
1055C42—28no—
1056C42—28no—
1057C42—28no—
1058C42—28no—
1059C42—28no—
1060C42—24no—
1061C42—24no—
1062C42—24no—
1063C42—24no—
1064C42—44no—
1065C42—42no—
1066C42—42no—
1067C42—44no—
1068C42—42no—
1069C42—44no—
1070C42—42no—
1071C42C22×D414yes—
1072C42C22×D414yes—
1073C42C22×D414yes—
1074C42C22×D414yes—
1075C42C22×D418yes—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—24no—
1081C23—24no—
1082C23—22no—
1083C23—22no—
1084C23—24no—
1085C23—22no—
1086C23—24no—
1087C23—24no—
1088C23—24no—
1089C23—24no—
1090C23—24no—
1091C23—28no—
1092C23—24no—
1093C23—24no—
1094C23—28no—
1095C23—24no—
1096C23—88no—
1097C23—88no—
1098C23—88no—
1099C23—816no—
1100C23—168no—
1101C23C23×D414yes—
1102C23C23×D412yes—
1103C23C2611yescharacteristic
1104Q8—44no—
1105Q8—48no—
1106Q8—48no—
1107Q8—84no—
1108Q8—88no—
1109Q8—84no—
1110D4—44no—
1111D4—48no—
1112D4—48no—
1113D4—44no—
1114D4—48no—
1115D4—44no—
1116D4—84no—
1117D4—84no—
1118D4—88no—
1119D4—88no—
1120D4—84no—
1121D4—88no—
1122D4—88no—
1123D4—88no—
1124D4—88no—
1125D4—84no—
1126D4—84no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—24no—
1135C2×C4—22no—
1136C2×C4—216no—
1137C2×C4—28no—
1138C2×C4—24no—
1139C2×C4—22no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—22no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—28no—
1158C2×C4—28no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—28no—
1165C2×C4—24no—
1166C2×C4—44no—
1167C2×C4—44no—
1168C2×C4—48no—
1169C2×C4—48no—
1170C2×C4—48no—
1171C2×C4—88no—
1172C2×C4—88no—
1173C2×C4—88no—
1174C2×C4—84no—
1175C2×C4—88no—
1176C2×C4—88no—
1177C2×C4C23×D412yes—
1178C2×C4C23×D414yes—
1179C2×C4C23×D414yes—
1180C2×C4C23×D414yes—
1181C2×C4C23×D412yes—
1182C2×C4C23×D412yes—
1183C2×C4C23×D412yes—
1184C2×C4C23×D412yes—
1185C2×C4C23×D412yes—
1186C2×C4#58514yes—
1187C22—22no—
1188C22—24no—
1189C22—22no—
1190C22—24no—
1191C22—22no—
1192C22—24no—
1193C22—44no—
1194C22—44no—
1195C22—44no—
1196C22—42no—
1197C22—44no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—44no—
1202C22—42no—
1203C22—44no—
1204C22—42no—
1205C22—48no—
1206C22—48no—
1207C22—48no—
1208C22—48no—
1209C22—1616no—
1210C22C24×D411yescharacteristic
1211C22C2×#58512yes—
1212C22H(7,𝔽2)12yes—
1213C222−1+612yes—
1214C4—22no—
1215C4—24no—
1216C4—22no—
1217C4—22no—
1218C4—24no—
1219C4—22no—
1220C4—22no—
1221C4—24no—
1222C4—44no—
1223C4—44no—
1224C4—42no—
1225C4—42no—
1226C4—44no—
1227C4—44no—
1228C4—44no—
1229C4—44no—
1230C4—44no—
1231C4—44no—
1232C4—44no—
1233C4#350014yes—
1234C2—42no—
1235C2—44no—
1236C2—82no—
1237C2—84no—
1238C2—82no—
1239C2C2×#350011yescharacteristic
1240C2#6285211yescharacteristic
1241C2#6285911yescharacteristic
1242C2#6288414yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3546C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3563C2semidirect
3. #51211C2semidirect
4. #50897C2semidirect
5. #48833C2semidirect
6. #47724C2semidirect
7. #46429C2semidirect
8. #46359C2semidirect
9. #39174C2semidirect
10. #39162C2semidirect
11. #38952C2semidirect
12. #38947C2semidirect
13. #38093C2semidirect
14. #38088C2semidirect
15. #38084C2semidirect
16. #38078C2semidirect
17. #37619C2semidirect
18. #37539C2semidirect
19. #37424C2semidirect
20. #37303C2semidirect
21. #35341C2semidirect
22. #35318C2semidirect
23. #35298C2semidirect
24. #35264C2semidirect
25. #34081C2semidirect
28. C2×#564C22semidirect
31. C2×#557C22semidirect
33. C2×#554C22semidirect
36. C2×#552C22semidirect
37. C2×#552C22semidirect
44. C2×#544C22semidirect
45. C2×#544C22semidirect
47. C2×#541C22semidirect
48. C2×#541C22semidirect
54. C2×#533C22semidirect
58. C22×#125C22semidirect
59. #2868C22semidirect
60. #2862C22semidirect
62. #2861C22semidirect
63. #2861C22semidirect
66. #2858C22semidirect
67. #2857C22semidirect
69. #2820C22semidirect
70. #2816C22semidirect
71. #2729C22semidirect
72. #2725C22semidirect
73. #2721C22semidirect
75. #2711C22semidirect
76. #2711C22semidirect
77. #2711C22semidirect
78. #2711C22semidirect
79. #2709C22semidirect
81. #2707C22semidirect
82. #2697C22semidirect
83. #2695C22semidirect
84. #2694C22semidirect
85. #2691C22semidirect
87. #2685C22semidirect
88. #2685C22semidirect
89. #2681C22semidirect
90. #2680C22semidirect
91. #2677C22semidirect
92. #2674C22semidirect
93. #2672C22semidirect
94. #2672C22semidirect
95. #2660C22semidirect
96. #2658C22semidirect
97. #2642C22semidirect
100. #2641C22semidirect
102. #2640C22semidirect
103. #2633C22semidirect
104. #2633C22semidirect
105. #2624C22semidirect
106. #2621C22semidirect
109. #2620C22semidirect
110. #2618C22semidirect
111. #2591C22semidirect
112. #2591C22semidirect
113. #2580C22semidirect
114. #2567C22semidirect
116. #2566C22semidirect
117. #2566C22semidirect
118. #2566C22semidirect
119. #2565C22semidirect
120. #2562C22semidirect
121. #2562C22semidirect
122. #2556C22semidirect
123. #2553C22semidirect
125. #2548C22semidirect
126. #2548C22semidirect
127. #2546C22semidirect
130. #2545C22semidirect
131. #2542C22semidirect
132. #2521C22semidirect
133. #2519C22semidirect
135. #2504C22semidirect
136. #2502C22semidirect
139. #2501C22semidirect
141. #2500C22semidirect
142. #2499C22semidirect
143. #2491C22semidirect
144. #2490C22semidirect
145. #2480C22semidirect
146. #2476C22semidirect
147. #2476C22semidirect
148. #2475C22semidirect
149. #2473C22semidirect
150. #2472C22semidirect
151. #2472C22semidirect
152. #2470C22semidirect
153. #2469C22semidirect
154. #2460C22semidirect
155. #2454C22semidirect
156. #2445C22semidirect
157. #2437C22semidirect
160. #2432C22semidirect
161. #2432C22semidirect
162. #2432C22semidirect
163. #2432C22semidirect
164. #2432C22semidirect
165. #2432C22semidirect
166. #2426C22semidirect
167. #2418C22semidirect
169. #2406C22semidirect
172. #2336C22semidirect
173. #2335C22semidirect
174. #2334C22semidirect
176. #2332C22semidirect
177. #2327C22semidirect
179. #2326C22semidirect
180. #2326C22semidirect
181. #2311C22semidirect
182. #2311C22semidirect
183. #2311C22semidirect
185. C4×C4⋊Q8C22semidirect
186. C4×#124C22semidirect
187. #2298C22semidirect
188. #2297C22semidirect
189. #2295C22semidirect
190. #2293C22semidirect
193. #2290C22semidirect
194. #2283C22semidirect
195. C4×#117C22semidirect
196. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35462
C2×#35632
#512112
#508972
#488332
#477242
#464292
#463592
#391742
#391622
#389522
#389472
#380932
#380882
#380842
#380782
#376192
#375392
#374242
#373032
#353412
#353182
#352982
#352642
#340812