Finite Group Databasebeta

← #7673861

Subgroups — #7673861

Order 512.

7028 conjugacy classes of subgroups.

The subgroup lattice has 1326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3511C211yesmaximal, characteristic, complemented
2C22×#544C211yesmaximal, characteristic, complemented
3#45109C214yesmaximal, complemented
4#45098C214yesmaximal, complemented
5#44893C214yesmaximal, complemented
6#44878C214yesmaximal, complemented
7#39723C214yesmaximal, complemented
8#39721C214yesmaximal, complemented
9#39717C214yesmaximal, complemented
10#39716C214yesmaximal, complemented
11#39425C214yesmaximal, complemented
12#39424C214yesmaximal, complemented
13#37757C214yesmaximal, complemented
14#37756C214yesmaximal, complemented
15#35649C211yesmaximal, characteristic, complemented
16#35639C211yesmaximal, characteristic, complemented
17#35592C211yesmaximal, characteristic, complemented
18#35574C211yesmaximal, characteristic, complemented
19#35341C211yesmaximal, characteristic, complemented
20#35333C211yesmaximal, characteristic, complemented
21#35223C211yesmaximal, characteristic, complemented
22#35150C211yesmaximal, characteristic, complemented
23#34633C211yesmaximal, characteristic, complemented
24#34216C211yesmaximal, characteristic, complemented
25#34201C211yesmaximal, characteristic, complemented
26#34200C211yesmaximal, characteristic, complemented
27#34065C211yesmaximal, characteristic, complemented
28#3511—216no—
29C2×#556C2212yescomplemented
30C2×#555C2212yescomplemented
31C2×#554C2212yescomplemented
32C2×#553C2214yes—
33C2×#548C2214yes—
34C2×#547C2212yescomplemented
35C2×#544—216no—
36C2×#544C2214yes—
37C2×#544C2214yes—
38C2×#544C2214yes—
39C2×#544C2214yes—
40C2×#542C2212yescomplemented
41C2×#542C2212yescomplemented
42C2×#537C2211yescharacteristic
43C2×#537C2211yescharacteristic
44C2×#533C2212yescomplemented
45C2×#532C2211yescharacteristic
46C2×#532C2212yescomplemented
47C22×C4⋊Q8C2211yescharacteristic
48C22×C4⋊Q8C2212yes—
49C22×C4⋊Q8C2211yescharacteristic
50C22×#125C2211yescharacteristic
51C22×#125C2212yes—
52C22×#125C2211yescharacteristic
53C2×#525C2211yescharacteristic
54C2×#525C2211yescharacteristic
55C2×#525C2211yescharacteristic
56C22×C22⋊Q8C2212yes—
57C22×C22⋊Q8C2212yes—
58C2×#520C2211yescharacteristic
59C2×#520C2211yescharacteristic
60C2×C4×#41C2211yescharacteristic
61C22×#117C2211yescharacteristic
62C22×#117C2211yescharacteristic
63C23×C4⋊C4C2211yescharacteristic
64#2861C2212yescomplemented
65#2861C2212yescomplemented
66#2854C2214yes—
67#2851C2214yescomplemented
68#2847C2214yes—
69#2731C2218yescomplemented
70#2731C2218yescomplemented
71#2730C2218yes—
72#2730C2218yes—
73#2729C2218yescomplemented
74#2729C2218yescomplemented
75#2728C2218yes—
76#2728C2218yes—
77#2725C2218yescomplemented
78#2719C2218yescomplemented
79#2711C2218yescomplemented
80#2707C2218yescomplemented
81#2702C2218yes—
82#2690C2218yes—
83#2681C2218yes—
84#2676C2218yes—
85#2642C2212yescomplemented
86#2641C2212yescomplemented
87#2629C2214yescomplemented
88#2621C2212yes—
89#2620C2212yes—
90#2620C2212yes—
91#2619C2212yes—
92#2618C2212yes—
93#2618C2214yes—
94#2618C2212yes—
95#2617C2212yes—
96#2617C2214yes—
97#2617C2212yes—
98#2591C2214yes—
99#2591C2214yes—
100#2591C2214yes—
101#2591C2214yes—
102#2579C2214yes—
103#2579C2214yes—
104#2579C2214yes—
105#2579C2214yes—
106#2566C2212yescomplemented
107#2566C2212yescomplemented
108#2565C2212yescomplemented
109#2565C2212yescomplemented
110#2562C2214yescomplemented
111#2562C2214yescomplemented
112#2560C2218yes—
113#2558C2218yescomplemented
114#2545C2218yescomplemented
115#2536C2218yes—
116#2519C2218yescomplemented
117#2504C2214yes—
118#2492C2214yescomplemented
119#2492C2214yescomplemented
120#2491C2214yescomplemented
121#2491C2214yescomplemented
122#2490C2214yescomplemented
123#2490C2214yescomplemented
124#2489C2214yescomplemented
125#2489C2214yescomplemented
126#2487C2214yes—
127#2477C2218yes—
128#2475C2218yescomplemented
129#2463C2218yes—
130#2461C2218yes—
131#2460C2218yescomplemented
132#2454C2214yescomplemented
133#2453C2214yescomplemented
134#2452C2214yescomplemented
135#2451C2214yescomplemented
136#2446C2218yescomplemented
137#2442C2214yescomplemented
138#2441C2214yescomplemented
139#2440C2214yescomplemented
140#2439C2214yescomplemented
141#2436C2214yes—
142#2432C2218yescomplemented
143#2429C2218yescomplemented
144#2426C2218yes—
145#2421C2218yes—
146#2417C2214yes—
147#2417C2214yes—
148#2416C2214yes—
149#2416C2214yes—
150#2415C2214yes—
151#2415C2214yes—
152#2414C2214yes—
153#2414C2214yes—
154#2409C2214yes—
155#2407C2218yes—
156#2392C2214yes—
157#2392C2214yes—
158#2369C2214yescomplemented
159#2365C2214yescomplemented
160#2363C2214yes—
161#2362C2214yes—
162#2361C2214yes—
163#2360C2214yes—
164#2354C2214yes—
165#2352C2214yes—
166#2352C2214yes—
167D4×C4⋊C4C2214yes—
168#2345C2214yes—
169Q8×C22⋊C4C2214yes—
170#2331C2214yescomplemented
171#2324C2212yes—
172#2324C2212yes—
173#2323C2212yes—
174#2323C2212yes—
175#2322C2212yes—
176#2322C2212yes—
177#2322C2214yes—
178#2321C2212yes—
179#2321C2212yes—
180#2321C2214yes—
181#2317C2211yescharacteristic
182#2317C2211yescharacteristic
183#2316C2211yescharacteristic
184#2316C2211yescharacteristic
185#2311C2211yescharacteristic
186#2311C2211yescharacteristic
187#2311C2211yescharacteristic
188#2311C2211yescharacteristic
189#2311C2211yescharacteristic
190#2311C2211yescharacteristic
191C4×C4⋊Q8C2214yescomplemented
192C4×#123C2214yes—
193C4×#120C2214yes—
194#2297C2211yescharacteristic
195#2297C2211yescharacteristic
196#2297C2211yescharacteristic
197#2296C2211yescharacteristic
198#2293C2214yes—
199#2290C2214yes—
200#2285C2211yescharacteristic
201#2280C2211yescharacteristic
202#2274C2211yescharacteristic
203#2274C2211yescharacteristic
204C4×#117C2211yescharacteristic
205C22×#41C2311yescharacteristic
206C22×#41C2311yescharacteristic
207C22×#41C2311yescharacteristic
208C22×#41C2314yes—
209C23×Q8C2312yes—
210C23×Q8C2312yes—
211C24×C4C2311yescharacteristic
212C24×C4C2312yes—
213#556—216no—
214#555—216no—
215#554—216no—
216#553—232no—
217#548—232no—
218#547—216no—
219#544—232no—
220#544—232no—
221#544—232no—
222#544—232no—
223#542—216no—
224#542—216no—
225#537—28no—
226#537—28no—
227#533—216no—
228#532—216no—
229#532—28no—
230C2×C4⋊Q8—216no—
231C2×C4⋊Q8—28no—
232C2×C4⋊Q8D4116yescomplemented
233C2×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2318yes—
235C2×C4⋊Q8C2318yes—
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C2314yes—
238C2×C4⋊Q8C2312yes—
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2312yes—
242C2×#127C2311yescharacteristic
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#125—216no—
246C2×#125—28no—
247C2×#125—28no—
248C2×#125C2312yes—
249C2×#125C2312yes—
250C2×#125C2312yes—
251C2×#125C2312yes—
252C2×#125C2314yes—
253C2×#125C2318yes—
254C2×#125C2314yes—
255C2×#125C2318yes—
256C2×#125C2314yes—
257C2×#124C2311yescharacteristic
258C2×#124C2311yescharacteristic
259C2×#124C2314yes—
260C2×#124C2314yes—
261C2×#124C2314yes—
262C2×#124C2318yes—
263#525—28no—
264#525—28no—
265#525—28no—
266C2×#123C2312yes—
267C2×#123C2312yes—
268C2×#123C2312yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×C22⋊Q8—216no—
272C2×C22⋊Q8—216no—
273C2×C22⋊Q8C2318yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2318yes—
278C2×C22⋊Q8C2318yes—
279C2×C22⋊Q8C2318yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2318yes—
288C2×#121C2312yes—
289C2×#121C2312yes—
290C2×#121C2312yes—
291C2×#121C2314yes—
292C2×#121C2314yes—
293C2×#121C2312yes—
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#121C2312yes—
297C2×#121C2312yes—
298C2×#121C2312yes—
299C2×#121C2314yes—
300C2×#121C2318yes—
301C2×#120C2312yes—
302C2×#120C2312yes—
303C2×#120C2312yes—
304#520—28no—
305#520—28no—
306C4×#41—28no—
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2314yes—
312C2×C4×Q8C2318yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2311yescharacteristic
316C2×C4×D4C2311yescharacteristic
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2314yes—
321C2×C4×D4C2314yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2318yes—
328C2×#117—28no—
329C2×#117—28no—
330C2×#117C2311yescharacteristic
331C2×#117C2311yescharacteristic
332C2×#117C2311yescharacteristic
333C2×#117C2311yescharacteristic
334C2×#117C2311yescharacteristic
335C2×#117C2312yes—
336C2×#117C2312yes—
337C2×#117C2312yes—
338C2×#117C2314yes—
339C2×#117C2312yes—
340C2×#117C2314yes—
341C2×#117C2312yes—
342C2×#117C2312yes—
343C2×#117C2312yes—
344C2×#117C2314yes—
345C22×C4⋊C4—28no—
346C22×C4⋊C4C2311yescharacteristic
347C22×C4⋊C4C2311yescharacteristic
348C22×C4⋊C4C2312yes—
349C22×C4⋊C4C2311yescharacteristic
350C22×C4⋊C4C2311yescharacteristic
351C22×C4⋊C4C2312yes—
352C22×C4⋊C4C2312yes—
353C22×C4⋊C4C2312yes—
354C22×C4⋊C4C2312yes—
355C22×C4⋊C4C2312yes—
356C22×C4⋊C4C2314yes—
357C22×C4⋊C4C2312yes—
358C22×C4⋊C4C2314yes—
359C22×C4⋊C4C2312yes—
360C22×C4⋊C4C2311yescharacteristic
361C22×C4⋊C4C2311yescharacteristic
362C22×C4⋊C4C2312yes—
363C22×C22⋊C4C2311yescharacteristic
364C22×C22⋊C4C2311yescharacteristic
365C22×C22⋊C4C2312yes—
366C22×C42C2312yes—
367C22×C42C2312yes—
368C22×C42C2311yescharacteristic
369C22×C42C2311yescharacteristic
370#400C2318yes—
371#400C2318yes—
372#400C2318yes—
373#400C2318yes—
374#400C2318yes—
375#399C2318yes—
376#398C2318yes—
377#398C2318yes—
378#398C2318yes—
379#398C2318yes—
380#398C2314yes—
381#398C2314yes—
382#398C2318yes—
383#397C2318yes—
384#397C2314yes—
385#397C2314yes—
386#397C2318yes—
387#397C2318yes—
388#396C2318yes—
389#396C2318yes—
390#396C2318yes—
391#396C2318yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2318yes—
397#396C2318yes—
398#395C2318yes—
399#394C2314yes—
400#394C2318yes—
401#394C2318yes—
402#394C2318yes—
403#394C2318yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2318yes—
408#394C2318yes—
409#394C2314yes—
410#394C2314yes—
411#394C2318yes—
412#393C2318yes—
413#393C2318yes—
414#393C2318yes—
415#392C2314yes—
416#392C2314yes—
417#392C2318yes—
418#391C2318yes—
419#391C2318yes—
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2318yes—
428#391C2318yes—
429#391C2312yes—
430#391C2312yes—
431#391C2318yes—
432#390C2318yes—
433#390C2312yes—
434#390C2312yes—
435#390C2312yes—
436#390C2312yes—
437#390C2312yes—
438#390C2312yes—
439#390C2314yes—
440#390C2314yes—
441#390C2312yes—
442#390C2318yes—
443#390C2312yes—
444#390C2312yes—
445#390C2318yes—
446#389C2314yes—
447#389C2314yes—
448#389C2318yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2318yes—
456#389C2312yes—
457#389C2312yes—
458#389C2318yes—
459#389C2318yes—
460#388C2314yes—
461#388C2318yes—
462#388C2318yes—
463#388C2318yes—
464#388C2318yes—
465#388C2318yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2318yes—
470#388C2318yes—
471#388C2314yes—
472#388C2314yes—
473#388C2318yes—
474#388C2318yes—
475#388C2318yes—
476#388C2318yes—
477#388C2318yes—
478#388C2318yes—
479#388C2318yes—
480#387C2318yes—
481#387C2318yes—
482#387C2318yes—
483#387C2314yes—
484#387C2314yes—
485#387C2318yes—
486#387C2318yes—
487#387C2318yes—
488#387C2318yes—
489#387C2318yes—
490#386C2318yes—
491#386C2314yes—
492#386C2314yes—
493#386C2314yes—
494#386C2314yes—
495#386C2314yes—
496#386C2314yes—
497#386C2312yes—
498#386C2312yes—
499#386C2314yes—
500#386C2314yes—
501#386C2318yes—
502#386C2312yes—
503#386C2312yes—
504#386C2312yes—
505#386C2312yes—
506#386C2318yes—
507#386C2318yes—
508#385C2318yes—
509#385C2318yes—
510#385C2314yes—
511#385C2314yes—
512#385C2312yes—
513#385C2312yes—
514#385C2314yes—
515#385C2314yes—
516#385C2318yes—
517#385C2318yes—
518#385C2318yes—
519#385C2318yes—
520#384C2312yes—
521#384C2312yes—
522#384C2312yes—
523#382C2312yes—
524#382C2312yes—
525#382C2312yes—
526#382C2318yes—
527#381C2312yes—
528#380C2314yes—
529#380C2314yes—
530#380C2314yes—
531#380C2314yes—
532#380C2314yes—
533#380C2314yes—
534#380C2314yes—
535#380C2314yes—
536#380C2312yes—
537#380C2312yes—
538#380C2312yes—
539#380C2312yes—
540#380C2318yes—
541#380C2318yes—
542#379C2312yes—
543C4×C4⋊C4C2318yes—
544C4×C4⋊C4C2312yes—
545C4×C4⋊C4C2312yes—
546C4×C4⋊C4C2314yes—
547C4×C4⋊C4C2314yes—
548C4×C4⋊C4C2312yes—
549C4×C4⋊C4C2312yes—
550C4×C4⋊C4C2314yes—
551C4×C4⋊C4C2314yes—
552C4×C4⋊C4C2318yes—
553C4×C4⋊C4C2314yes—
554C4×C22⋊C4C2318yes—
555C4×C22⋊C4C2312yes—
556C4×C22⋊C4C2312yes—
557C4×C22⋊C4C2314yes—
558C4×C22⋊C4C2314yes—
559C4×C22⋊C4C2318yes—
560C4×C22⋊C4C2314yes—
561C4×C22⋊C4C2314yes—
562C4×C22⋊C4C2314yes—
563C4×C22⋊C4C2314yes—
564#376C2312yes—
565C43C2312yes—
566C25C2411yescharacteristic
567C2×#41—216no—
568C2×#41—24no—
569C2×#41—24no—
570C2×#41—24no—
571C2×#41—24no—
572C2×#41—24no—
573C2×#41—24no—
574C2×#41—24no—
575C2×#41—24no—
576C2×#41—24no—
577C2×#41—88no—
578C22×Q8—28no—
579C22×Q8—84no—
580C22×Q8—84no—
581C22×Q8C2×D4116yes—
582C22×Q8C2411yescharacteristic
583C22×Q8C2411yescharacteristic
584C22×Q8C2411yescharacteristic
585C22×Q8C2418yes—
586C22×Q8C2414yes—
587C22×Q8C2414yes—
588C22×D4C2412yes—
589C22×D4C2412yes—
590C22×D4C2412yes—
591C22×D4C2411yescharacteristic
592C22×D4C2411yescharacteristic
593C22×D4C2411yescharacteristic
594C22×D4C2414yes—
595C22×D4C2412yes—
596C22×D4C2414yes—
597C22×D4C2414yes—
598C22×D4C2412yes—
599C22×D4C2414yes—
600C22×D4C2414yes—
601C23×C4—24no—
602C23×C4—24no—
603C23×C4—28no—
604C23×C4—84no—
605C23×C4#4118yescomplemented
606C23×C4C2412yes—
607C23×C4C2412yes—
608C23×C4C2412yes—
609C23×C4C2411yescharacteristic
610C23×C4C2412yes—
611C23×C4C2412yes—
612C23×C4C2412yes—
613C23×C4C2411yescharacteristic
614C23×C4C2411yescharacteristic
615C23×C4C2412yes—
616C23×C4C2418yes—
617C23×C4C2414yes—
618C23×C4C2414yes—
619C23×C4C2412yes—
620C23×C4C2412yes—
621C23×C4C2411yescharacteristic
622C23×C4C2412yes—
623C23×C4C2411yescharacteristic
624C23×C4C2412yes—
625C23×C4C2411yescharacteristic
626C4⋊Q8—232no—
627C4⋊Q8—232no—
628C4⋊Q8—216no—
629C4⋊Q8—216no—
630C4⋊Q8—24no—
631C4⋊Q8C2×D4116yes—
632C4⋊Q8C2×D4116yes—
633C4⋊Q8C2×D4116yes—
634C4⋊Q8C2×D4116yes—
635#127—24no—
636#126—216no—
637#126—216no—
638#125—232no—
639#125—232no—
640#125—216no—
641#125—216no—
642#125—216no—
643#125—28no—
644#125—28no—
645#125—28no—
646#125—28no—
647#124—216no—
648#124—216no—
649#124—216no—
650#124—24no—
651#124—24no—
652#124—88no—
653#123—28no—
654#123—28no—
655#123—28no—
656#123—216no—
657#123—216no—
658C22⋊Q8—232no—
659C22⋊Q8—232no—
660C22⋊Q8—216no—
661C22⋊Q8—216no—
662C22⋊Q8—216no—
663C22⋊Q8—28no—
664C22⋊Q8—28no—
665C22⋊Q8—28no—
666C22⋊Q8—232no—
667C22⋊Q8—232no—
668C22⋊Q8—28no—
669C22⋊Q8—28no—
670C22⋊Q8—28no—
671C22⋊Q8—28no—
672C22⋊Q8—88no—
673#121—28no—
674#121—28no—
675#121—216no—
676#121—216no—
677#121—28no—
678#121—28no—
679#121—28no—
680#121—28no—
681#121—28no—
682#121—216no—
683#121—28no—
684#121—28no—
685#121—88no—
686#120—28no—
687#120—28no—
688#120—28no—
689C4×Q8—216no—
690C4×Q8—28no—
691C4×Q8—28no—
692C4×Q8—24no—
693C4×Q8—24no—
694C4×Q8—88no—
695C4×D4—28no—
696C4×D4—28no—
697C4×D4—216no—
698C4×D4—216no—
699C4×D4—216no—
700C4×D4—216no—
701C4×D4—216no—
702C4×D4—28no—
703C4×D4—28no—
704C4×D4—216no—
705C4×D4—24no—
706C4×D4—24no—
707C4×D4—28no—
708C4×D4—28no—
709C4×D4—88no—
710#117—24no—
711#117—24no—
712#117—24no—
713#117—24no—
714#117—24no—
715#117—216no—
716#117—216no—
717#117—28no—
718#117—28no—
719#117—216no—
720#117—28no—
721#117—28no—
722#117—28no—
723#117—28no—
724#117—28no—
725C2×C4⋊C4—28no—
726C2×C4⋊C4—24no—
727C2×C4⋊C4—24no—
728C2×C4⋊C4—24no—
729C2×C4⋊C4—24no—
730C2×C4⋊C4—28no—
731C2×C4⋊C4—28no—
732C2×C4⋊C4—28no—
733C2×C4⋊C4—28no—
734C2×C4⋊C4—28no—
735C2×C4⋊C4—216no—
736C2×C4⋊C4—216no—
737C2×C4⋊C4—28no—
738C2×C4⋊C4—28no—
739C2×C4⋊C4C2×D418yes—
740C2×C4⋊C4C2×D418yes—
741C2×C4⋊C4C2×D4116yes—
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2418yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2418yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2418yes—
759C2×C4⋊C4C2418yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2418yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2418yes—
778C2×C4⋊C4C2418yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2418yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C22⋊C4—28no—
790C2×C22⋊C4—24no—
791C2×C22⋊C4—24no—
792C2×C22⋊C4C2412yes—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2418yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2412yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2412yes—
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2418yes—
822C2×C22⋊C4C2418yes—
823C2×C22⋊C4C2418yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2418yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2418yes—
833C2×C22⋊C4C2418yes—
834C2×C42—28no—
835C2×C42—24no—
836C2×C42—28no—
837C2×C42C2×D418yes—
838C2×C42C2412yes—
839C2×C42C2414yes—
840C2×C42C2414yes—
841C2×C42C2412yes—
842C2×C42C2412yes—
843C2×C42C2418yes—
844C2×C42C2412yes—
845C2×C42C2412yes—
846C2×C42C2412yes—
847C2×C42C2412yes—
848C2×C42C2412yes—
849C2×C42C2412yes—
850C2×C42C2418yes—
851C2×C42C2414yes—
852C2×C42C2418yes—
853C2×C42C2414yes—
854C2×C42C2411yescharacteristic
855C2×C42C2411yescharacteristic
856C2×C42C2411yescharacteristic
857C2×C42C2411yescharacteristic
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2418yes—
863#95C2418yes—
864#95C2418yes—
865#95C2418yes—
866#95C2414yes—
867#95C2414yes—
868#95C2418yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2418yes—
877#95C2418yes—
878#95C2418yes—
879#95C2414yes—
880#95C2418yes—
881#95C2418yes—
882#95C2418yes—
883#95C2418yes—
884C24—22no—
885C24—22no—
886C24—42no—
887C24—42no—
888C24C2×#4114yes—
889C24C2512yes—
890C24C2512yes—
891C24C2512yes—
892C24C2512yes—
893C24C2511yescharacteristic
894#41—416no—
895#41—416no—
896#41—416no—
897#41—832no—
898C2×Q8—22no—
899C2×Q8—22no—
900C2×Q8—22no—
901C2×Q8—216no—
902C2×Q8—22no—
903C2×Q8—22no—
904C2×Q8—22no—
905C2×Q8—22no—
906C2×Q8—22no—
907C2×Q8—22no—
908C2×Q8—48no—
909C2×Q8—48no—
910C2×Q8—48no—
911C2×Q8—48no—
912C2×Q8—816no—
913C2×Q8—816no—
914C2×Q8C22×D4116yes—
915C2×Q8C22×D4116yes—
916C2×D4—24no—
917C2×D4—24no—
918C2×D4—24no—
919C2×D4—28no—
920C2×D4—24no—
921C2×D4—24no—
922C2×D4—24no—
923C2×D4—24no—
924C2×D4—24no—
925C2×D4—24no—
926C2×D4—28no—
927C2×D4—28no—
928C2×D4—24no—
929C2×D4—22no—
930C2×D4—22no—
931C2×D4—22no—
932C2×D4—24no—
933C2×D4—28no—
934C2×D4—28no—
935C2×D4—22no—
936C2×D4—22no—
937C2×D4—22no—
938C2×D4—22no—
939C2×D4—22no—
940C2×D4—22no—
941C2×D4—44no—
942C2×D4—44no—
943C2×D4—44no—
944C2×D4—44no—
945C2×D4—44no—
946C2×D4—44no—
947C2×D4—48no—
948C2×D4—48no—
949C2×D4—44no—
950C2×D4—44no—
951C22×C4—22no—
952C22×C4—22no—
953C22×C4—232no—
954C22×C4—24no—
955C22×C4—24no—
956C22×C4—24no—
957C22×C4—24no—
958C22×C4—24no—
959C22×C4—22no—
960C22×C4—22no—
961C22×C4—24no—
962C22×C4—24no—
963C22×C4—24no—
964C22×C4—24no—
965C22×C4—24no—
966C22×C4—24no—
967C22×C4—24no—
968C22×C4—24no—
969C22×C4—24no—
970C22×C4—24no—
971C22×C4—24no—
972C22×C4—24no—
973C22×C4—216no—
974C22×C4—28no—
975C22×C4—28no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—42no—
979C22×C4—44no—
980C22×C4—42no—
981C22×C4—44no—
982C22×C4—42no—
983C22×C4—44no—
984C22×C4—42no—
985C22×C4—44no—
986C22×C4—48no—
987C22×C4—48no—
988C22×C4—48no—
989C22×C4—48no—
990C22×C4—816no—
991C22×C4C22×D418yes—
992C22×C4C22×D414yes—
993C22×C4C22×D414yes—
994C22×C4C22×D418yes—
995C22×C4C22×D414yes—
996C22×C4C2×#4118yes—
997C22×C4C2×#4118yes—
998C22×C4C2×#4114yes—
999C22×C4C2×#4114yes—
1000C22×C42−1+414yes—
1001C22×C4C2514yes—
1002C22×C4C2514yes—
1003C22×C4C2514yes—
1004C22×C4C2514yes—
1005C22×C4C2512yes—
1006C22×C4C2512yes—
1007C22×C4C2512yes—
1008C22×C4C2512yes—
1009C22×C4C2512yes—
1010C22×C4C2514yes—
1011C22×C4C2512yes—
1012C22×C4C2512yes—
1013C22×C4C2514yes—
1014C22×C4C2511yescharacteristic
1015C22×C4C2511yescharacteristic
1016C22×C4C2514yes—
1017C22×C4C2514yes—
1018C22×C4C2511yescharacteristic
1019C22×C4C2511yescharacteristic
1020C22×C4C2512yes—
1021C22×C4C2511yescharacteristic
1022C22×C4C2511yescharacteristic
1023C4⋊C4—22no—
1024C4⋊C4—216no—
1025C4⋊C4—24no—
1026C4⋊C4—24no—
1027C4⋊C4—24no—
1028C4⋊C4—24no—
1029C4⋊C4—24no—
1030C4⋊C4—24no—
1031C4⋊C4—24no—
1032C4⋊C4—24no—
1033C4⋊C4—28no—
1034C4⋊C4—28no—
1035C4⋊C4—216no—
1036C4⋊C4—28no—
1037C4⋊C4—28no—
1038C4⋊C4—216no—
1039C4⋊C4—216no—
1040C4⋊C4—28no—
1041C4⋊C4—28no—
1042C4⋊C4—22no—
1043C4⋊C4—24no—
1044C4⋊C4—24no—
1045C4⋊C4—24no—
1046C4⋊C4—24no—
1047C4⋊C4—28no—
1048C4⋊C4—28no—
1049C4⋊C4—24no—
1050C4⋊C4—24no—
1051C4⋊C4—24no—
1052C4⋊C4—28no—
1053C4⋊C4—28no—
1054C4⋊C4—28no—
1055C4⋊C4—24no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—48no—
1059C4⋊C4—48no—
1060C4⋊C4—44no—
1061C4⋊C4—48no—
1062C4⋊C4—48no—
1063C4⋊C4—44no—
1064C4⋊C4C22×D418yes—
1065C4⋊C4C22×D418yes—
1066C4⋊C4C22×D418yes—
1067C4⋊C4C22×D418yes—
1068C4⋊C4C22×D4116yes—
1069C4⋊C4C22×D4116yes—
1070C22⋊C4—24no—
1071C22⋊C4—24no—
1072C22⋊C4—24no—
1073C22⋊C4—24no—
1074C22⋊C4—28no—
1075C22⋊C4—28no—
1076C22⋊C4—28no—
1077C22⋊C4—24no—
1078C22⋊C4—216no—
1079C22⋊C4—24no—
1080C22⋊C4—24no—
1081C22⋊C4—24no—
1082C22⋊C4—24no—
1083C22⋊C4—28no—
1084C22⋊C4—28no—
1085C22⋊C4—24no—
1086C22⋊C4—24no—
1087C22⋊C4—28no—
1088C22⋊C4—28no—
1089C22⋊C4—28no—
1090C22⋊C4—28no—
1091C22⋊C4—24no—
1092C22⋊C4—24no—
1093C22⋊C4—24no—
1094C22⋊C4—24no—
1095C22⋊C4—28no—
1096C22⋊C4—28no—
1097C22⋊C4—28no—
1098C22⋊C4—44no—
1099C22⋊C4—48no—
1100C22⋊C4—44no—
1101C22⋊C4—48no—
1102C22⋊C4—44no—
1103C22⋊C4—48no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—48no—
1107C22⋊C4—48no—
1108C22⋊C4—48no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C42—24no—
1113C42—216no—
1114C42—24no—
1115C42—24no—
1116C42—24no—
1117C42—24no—
1118C42—28no—
1119C42—28no—
1120C42—24no—
1121C42—24no—
1122C42—24no—
1123C42—24no—
1124C42—44no—
1125C42—48no—
1126C42—44no—
1127C42—48no—
1128C42C22×D414yes—
1129C42C22×D414yes—
1130C42C22×D414yes—
1131C42C22×D414yes—
1132C23—22no—
1133C23—22no—
1134C23—22no—
1135C23—22no—
1136C23—22no—
1137C23—22no—
1138C23—22no—
1139C23—22no—
1140C23—28no—
1141C23—22no—
1142C23—22no—
1143C23—22no—
1144C23—22no—
1145C23—22no—
1146C23—22no—
1147C23—22no—
1148C23—22no—
1149C23—22no—
1150C23—24no—
1151C23—24no—
1152C23—24no—
1153C23—24no—
1154C23—24no—
1155C23—24no—
1156C23—48no—
1157C23—44no—
1158C23—44no—
1159C23—48no—
1160C23C23×D412yes—
1161C23C22×#4114yes—
1162C23C22×#4112yes—
1163C23C2×2−1+412yes—
1164C23C2611yescharacteristic
1165Q8—416no—
1166Q8—416no—
1167Q8—44no—
1168Q8—44no—
1169Q8—44no—
1170Q8—816no—
1171D4—48no—
1172D4—48no—
1173D4—416no—
1174D4—48no—
1175D4—48no—
1176D4—48no—
1177D4—44no—
1178D4—44no—
1179D4—44no—
1180D4—88no—
1181D4—88no—
1182D4—88no—
1183D4—88no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—28no—
1188C2×C4—28no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—28no—
1193C2×C4—216no—
1194C2×C4—216no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—24no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—28no—
1220C2×C4—22no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—22no—
1225C2×C4—28no—
1226C2×C4—24no—
1227C2×C4—22no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—48no—
1231C2×C4—44no—
1232C2×C4—44no—
1233C2×C4—48no—
1234C2×C4—48no—
1235C2×C4—48no—
1236C2×C4—44no—
1237C2×C4—48no—
1238C2×C4—48no—
1239C2×C4—44no—
1240C2×C4—48no—
1241C2×C4—48no—
1242C2×C4—48no—
1243C2×C4—816no—
1244C2×C4—88no—
1245C2×C4—88no—
1246C2×C4#548116yes—
1247C2×C4C23×D418yes—
1248C2×C4C23×D412yes—
1249C2×C4C23×D412yes—
1250C2×C4C23×D418yes—
1251C2×C4C23×D412yes—
1252C2×C4C23×D412yes—
1253C2×C4C23×D412yes—
1254C2×C4C23×D412yes—
1255C2×C4C22×#4114yes—
1256C2×C4C22×#4112yes—
1257C2×C4C22×#4112yes—
1258C2×C4C2×2−1+412yes—
1259C2×C4C2×2−1+412yes—
1260C22—22no—
1261C22—22no—
1262C22—24no—
1263C22—24no—
1264C22—24no—
1265C22—24no—
1266C22—24no—
1267C22—416no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—44no—
1279C22—44no—
1280C22—44no—
1281C22—44no—
1282C22—44no—
1283C22—44no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22C2×#54814yes—
1288C22C24×D411yescharacteristic
1289C22C23×#4111yescharacteristic
1290C22C22×2−1+411yescharacteristic
1291C22H(7,𝔽2)12yes—
1292C222−1+612yes—
1293C4—22no—
1294C4—28no—
1295C4—28no—
1296C4—22no—
1297C4—22no—
1298C4—22no—
1299C4—24no—
1300C4—42no—
1301C4—44no—
1302C4—42no—
1303C4—42no—
1304C4—42no—
1305C4—44no—
1306C4—44no—
1307C4—44no—
1308C4—44no—
1309C4—44no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4C2×#54814yes—
1314C4C2×#54814yes—
1315C2—24no—
1316C2—44no—
1317C2—82no—
1318C2—82no—
1319C2—82no—
1320C2C22×#54811yescharacteristic
1321C2#6284211yescharacteristic
1322C2#6284811yescharacteristic
1323C2#6285612yes—
1324C2#6287712yes—
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×#3511C2semidirect
2. C22×#544C2semidirect
3. #45109C2semidirect
4. #45098C2semidirect
5. #44893C2semidirect
6. #44878C2semidirect
7. #39723C2semidirect
8. #39721C2semidirect
9. #39717C2semidirect
10. #39716C2semidirect
11. #39425C2semidirect
12. #39424C2semidirect
13. #37757C2semidirect
14. #37756C2semidirect
15. #35649C2semidirect
16. #35639C2semidirect
17. #35592C2semidirect
18. #35574C2semidirect
19. #35341C2semidirect
20. #35333C2semidirect
21. #35223C2semidirect
22. #35150C2semidirect
23. #34633C2semidirect
24. #34216C2semidirect
25. #34201C2semidirect
26. #34200C2semidirect
27. #34065C2semidirect
29. C2×#556C22semidirect
30. C2×#555C22semidirect
31. C2×#554C22semidirect
34. C2×#547C22semidirect
40. C2×#542C22semidirect
41. C2×#542C22semidirect
44. C2×#533C22semidirect
46. C2×#532C22semidirect
64. #2861C22semidirect
65. #2861C22semidirect
67. #2851C22semidirect
69. #2731C22semidirect
70. #2731C22semidirect
73. #2729C22semidirect
74. #2729C22semidirect
77. #2725C22semidirect
78. #2719C22semidirect
79. #2711C22semidirect
80. #2707C22semidirect
85. #2642C22semidirect
86. #2641C22semidirect
87. #2629C22semidirect
106. #2566C22semidirect
107. #2566C22semidirect
108. #2565C22semidirect
109. #2565C22semidirect
110. #2562C22semidirect
111. #2562C22semidirect
113. #2558C22semidirect
114. #2545C22semidirect
116. #2519C22semidirect
118. #2492C22semidirect
119. #2492C22semidirect
120. #2491C22semidirect
121. #2491C22semidirect
122. #2490C22semidirect
123. #2490C22semidirect
124. #2489C22semidirect
125. #2489C22semidirect
128. #2475C22semidirect
131. #2460C22semidirect
132. #2454C22semidirect
133. #2453C22semidirect
134. #2452C22semidirect
135. #2451C22semidirect
136. #2446C22semidirect
137. #2442C22semidirect
138. #2441C22semidirect
139. #2440C22semidirect
140. #2439C22semidirect
142. #2432C22semidirect
143. #2429C22semidirect
158. #2369C22semidirect
159. #2365C22semidirect
170. #2331C22semidirect
191. C4×C4⋊Q8C22semidirect
232. C2×C4⋊Q8D4semidirect
605. C23×C4#41semidirect

Maximal subgroups

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

subgroupindex
C2×#35112
C22×#5442
#451092
#450982
#448932
#448782
#397232
#397212
#397172
#397162
#394252
#394242
#377572
#377562
#356492
#356392
#355922
#355742
#353412
#353332
#352232
#351502
#346332
#342162
#342012
#342002
#340652