Finite Group Databasebeta

← #7715428

Subgroups — #7715428

Order 512.

7036 conjugacy classes of subgroups.

The subgroup lattice has 1295 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3547C211yesmaximal, characteristic, complemented
2C2×#3558C211yesmaximal, characteristic, complemented
3#51070C214yesmaximal, complemented
4#50693C214yesmaximal, complemented
5#47955C218yesmaximal, complemented
6#47686C218yesmaximal, complemented
7#46430C214yesmaximal, complemented
8#46354C214yesmaximal, complemented
9#39171C212yesmaximal, complemented
10#39161C212yesmaximal, complemented
11#38953C212yesmaximal, complemented
12#38948C212yesmaximal, complemented
13#38095C212yesmaximal, complemented
14#38090C212yesmaximal, complemented
15#38082C212yesmaximal, complemented
16#38080C212yesmaximal, complemented
17#37634C211yesmaximal, characteristic, complemented
18#37536C211yesmaximal, characteristic, complemented
19#37423C212yesmaximal, complemented
20#37302C212yesmaximal, complemented
21#35338C211yesmaximal, characteristic, complemented
22#35293C211yesmaximal, characteristic, complemented
23#35276C212yesmaximal, complemented
24#35264C212yesmaximal, complemented
25#34081C211yesmaximal, characteristic, complemented
26#3558—216no—
27#3547—216no—
28C2×#562C2212yes—
29C2×#562C2214yescomplemented
30C2×H(3,𝔽4)C2212yes—
31C2×#559C2212yes—
32C2×#555C2212yescomplemented
33C2×#555C2211yescharacteristic, complemented
34C2×#554C2211yescharacteristic, complemented
35C2×#553C2212yescomplemented
36C2×#552C2212yescomplemented
37C2×D4×Q8C2211yescharacteristic, complemented
38C2×#548C2212yes—
39C2×#548C2212yescomplemented
40C2×#547C2211yescharacteristic, complemented
41C2×#546C2214yes—
42C2×#546C2212yes—
43C2×D42C2212yes—
44C2×#544C2212yescomplemented
45C2×#542C2212yes—
46C2×#542C2214yescomplemented
47C2×#540C2212yescomplemented
48C2×#538C2214yes—
49C2×#538C2212yes—
50C2×#537C2212yes—
51C2×#536C2212yescomplemented
52C2×#535C2212yes—
53C2×#534C2212yes—
54C2×#533C2211yescharacteristic, complemented
55C2×#532C2211yescharacteristic
56C2×#532C2211yescharacteristic, complemented
57C2×#529C2211yescharacteristic
58C22×#124C2211yescharacteristic
59#2867C2211yescharacteristic, complemented
60#2862C2211yescharacteristic, complemented
61#2861C2212yescomplemented
62#2861C2212yescomplemented
63#2861C2212yescomplemented
64#2858C2212yes—
65#2858C2211yescharacteristic, complemented
66#2858C2211yescharacteristic, complemented
67#2856C2212yes—
68#2850C2212yescomplemented
69#2819C2214yescomplemented
70#2816C2214yescomplemented
71#2730C2218yescomplemented
72#2716C2218yescomplemented
73#2714C2218yescomplemented
74#2712C2218yescomplemented
75#2703C2218yescomplemented
76#2702C2218yescomplemented
77#2700C2218yescomplemented
78#2699C2218yescomplemented
79#2696C2218yescomplemented
80#2696C2218yescomplemented
81#2696C2218yescomplemented
82#2690C2218yescomplemented
83#2688C2218yescomplemented
84#2687C2218yescomplemented
85#2681C2218yescomplemented
86#2678C2218yescomplemented
87#2676C2218yescomplemented
88#2673C2218yescomplemented
89#2673C2218yescomplemented
90#2670C2218yescomplemented
91#2670C2218yescomplemented
92#2669C2218yescomplemented
93#2669C2218yescomplemented
94#2668C2218yescomplemented
95#2660C2212yescomplemented
96#2657C2212yescomplemented
97#2641C2212yes—
98#2641C2212yescomplemented
99#2640C2212yescomplemented
100#2640C2212yescomplemented
101#2640C2212yescomplemented
102#2640C2212yescomplemented
103#2632C2214yescomplemented
104#2631C2214yescomplemented
105#2620C2212yescomplemented
106#2619C2212yes—
107#2619C2212yescomplemented
108#2619C2212yescomplemented
109#2617C2214yescomplemented
110#2616C2214yescomplemented
111#2592C2214yescomplemented
112#2592C2214yescomplemented
113#2568C2212yescomplemented
114#2566C2212yescomplemented
115#2565C2212yescomplemented
116#2563C2212yescomplemented
117#2563C2212yescomplemented
118#2561C2214yescomplemented
119#2561C2214yescomplemented
120#2555C2218yescomplemented
121#2554C2218yescomplemented
122#2544C2212yescomplemented
123#2544C2212yescomplemented
124#2544C2214yescomplemented
125#2544C2214yescomplemented
126#2544C2212yescomplemented
127#2544C2212yescomplemented
128#2542C2212yescomplemented
129#2541C2212yes—
130#2541C2212yes—
131#2536C2214yescomplemented
132#2504C2212yes—
133#2503C2212yescomplemented
134#2500C2212yes—
135#2500C2212yescomplemented
136#2500C2212yescomplemented
137#2499C2212yescomplemented
138#2491C2218yescomplemented
139#2490C2218yescomplemented
140#2477C2218yescomplemented
141#2472C2218yescomplemented
142#2472C2218yescomplemented
143#2472C2218yescomplemented
144#2471C2218yescomplemented
145#2464C2218yescomplemented
146#2463C2218yescomplemented
147#2461C2218yescomplemented
148#2459C2218yescomplemented
149#2459C2218yescomplemented
150#2457C2218yescomplemented
151#2443C2218yescomplemented
152#2436C2218yescomplemented
153#2436C2211yescharacteristic, complemented
154#2436C2211yescharacteristic, complemented
155#2433C2211yescharacteristic
156#2433C2211yescharacteristic
157#2433C2212yescomplemented
158#2433C2212yescomplemented
159#2431C2214yescomplemented
160#2431C2212yescomplemented
161#2431C2214yescomplemented
162#2431C2212yescomplemented
163#2427C2218yescomplemented
164#2424C2218yescomplemented
165#2414C2218yescomplemented
166#2412C2218yescomplemented
167#2410C2218yescomplemented
168#2408C2218yescomplemented
169#2404C2218yescomplemented
170#2404C2214yescomplemented
171#2337C2212yescomplemented
172#2336C2212yescomplemented
173#2335C2214yescomplemented
174#2334C2214yescomplemented
175#2333C2212yes—
176#2332C2212yescomplemented
177#2328C2212yescomplemented
178#2328C2212yescomplemented
179#2328C2212yescomplemented
180#2326C2212yescomplemented
181#2311C2212yescomplemented
182#2310C2212yescomplemented
183#2309C2212yes—
184#2309C2212yescomplemented
185C4×#127C2212yescomplemented
186C4×#124C2212yescomplemented
187#2298C2212yescomplemented
188#2297C2212yescomplemented
189#2295C2212yescomplemented
190#2293C2212yescomplemented
191C2×#390C2212yescomplemented
192#2290C2212yescomplemented
193#2290C2212yescomplemented
194#2283C2211yescharacteristic, complemented
195C4×#117C2211yescharacteristic, complemented
196C4×#117C2212yescomplemented
197C22×#41C2312yes—
198C22×#41C2312yes—
199C22×#41C2312yes—
200C22×#41C2312yes—
201C23×Q8C2311yescharacteristic
202C23×Q8C2312yes—
203C23×D4C2311yescharacteristic
204C23×D4C2312yes—
205C23×D4C2314yes—
206#562—216no—
207#562—232no—
208H(3,𝔽4)—216no—
209#559—216no—
210#555—216no—
211#555—28no—
212#554—28no—
213#553—216no—
214#552—216no—
215D4×Q8—28no—
216#548—216no—
217#548—216no—
218#547—28no—
219#546—232no—
220#546—216no—
221D42—216no—
222#544—216no—
223#542—232no—
224#542—216no—
225#540—216no—
226#538—232no—
227#538—216no—
228#537—216no—
229#536—216no—
230#535—216no—
231#534—216no—
232#533—28no—
233#532—28no—
234#532—28no—
235C2×C4⋊Q8C2311yescharacteristic
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2311yescharacteristic
240C2×C4⋊Q8C2314yes—
241C2×#127C2312yes—
242C2×#127C2311yescharacteristic
243C2×#127C2311yescharacteristic
244C2×#127C2312yes—
245C2×#127C2312yes—
246C2×#127C2312yes—
247C2×#127C2312yes—
248C2×#127C2314yes—
249C2×#127C2314yes—
250#529D4116yescomplemented
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#126C2312yes—
254C2×#125C2312yes—
255C2×#125C2312yes—
256C2×#125C2314yes—
257C2×#125C2311yescharacteristic
258C2×#124—28no—
259C2×#124C2312yes—
260C2×#124C2312yes—
261C2×#124C2312yes—
262C2×#124C2312yes—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2312yes—
266C2×#124C2314yes—
267C2×#124C2314yes—
268C2×#124C2314yes—
269C2×#124C2314yes—
270C2×#124C2314yes—
271C2×#124C2314yes—
272C2×#124C2312yes—
273C2×#124C2312yes—
274C2×#124C2318yes—
275C2×#124C2314yes—
276C2×#124C2314yes—
277C2×#124C2311yescharacteristic
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×#123C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2318yes—
300C2×C22⋊Q8C2311yescharacteristic
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#121C2312yes—
306C2×#121C2312yes—
307C2×#121C2311yescharacteristic
308C2×#121C2311yescharacteristic
309C2×#121C2314yes—
310C2×#121C2314yes—
311C2×#121C2312yes—
312C2×#121C2314yes—
313C2×#121C2314yes—
314C2×#121C2314yes—
315C2×#121C2314yes—
316C2×#121C2314yes—
317C2×#121C2314yes—
318C2×#121C2314yes—
319C2×#121C2318yes—
320C2×#121C2318yes—
321C2×#121C2318yes—
322C2×#121C2311yescharacteristic
323C2×#120C2314yes—
324C2×#120C2314yes—
325C2×#120C2314yes—
326C2×#120C2314yes—
327C2×#120C2314yes—
328C2×#120C2314yes—
329C2×#120C2314yes—
330C2×#120C2318yes—
331C2×#120C2318yes—
332C2×C4×Q8C2312yes—
333C2×C4×Q8C2312yes—
334C2×C4×Q8C2312yes—
335C2×C4×Q8C2311yescharacteristic
336C2×C4×D4C2312yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2311yescharacteristic
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2312yes—
342C2×C4×D4C2312yes—
343C2×C4×D4C2312yes—
344C2×C4×D4C2314yes—
345C2×C4×D4C2314yes—
346C2×C4×D4C2314yes—
347C2×C4×D4C2318yes—
348C2×C4×D4C2312yes—
349C2×C4×D4C2311yescharacteristic
350C2×#117C2312yes—
351C2×#117C2312yes—
352C2×#117C2314yes—
353C2×#117C2312yes—
354C2×#117C2312yes—
355C2×#117C2312yes—
356C2×#117C2312yes—
357C22×C4⋊C4C2312yes—
358C22×C4⋊C4C2312yes—
359C22×C22⋊C4C2312yes—
360C22×C22⋊C4C2312yes—
361C22×C22⋊C4C2314yes—
362C22×C22⋊C4C2318yes—
363C22×C42C2312yes—
364C22×C42C2311yescharacteristic
365#400C2318yes—
366#400C2318yes—
367#399C2318yes—
368#398C2318yes—
369#398C2318yes—
370#397C2318yes—
371#397C2318yes—
372#397C2318yes—
373#397C2318yes—
374#397C2318yes—
375#397C2318yes—
376#396C2318yes—
377#396C2318yes—
378#395C2318yes—
379#394C2318yes—
380#394C2318yes—
381#394C2318yes—
382#394C2318yes—
383#394C2318yes—
384#394C2318yes—
385#394C2318yes—
386#394C2318yes—
387#394C2318yes—
388#394C2318yes—
389#394C2318yes—
390#394C2318yes—
391#394C2318yes—
392#394C2318yes—
393#394C2318yes—
394#393C2318yes—
395#393C2318yes—
396#393C2318yes—
397#393C2318yes—
398#393C2314yes—
399#393C2314yes—
400#393C2318yes—
401#393C2318yes—
402#392C2314yes—
403#392C2314yes—
404#392C2318yes—
405#392C2318yes—
406#392C2318yes—
407#392C2318yes—
408#392C2318yes—
409#392C2318yes—
410#392C2318yes—
411#392C2318yes—
412#392C2318yes—
413#392C2318yes—
414#392C2318yes—
415#391C2312yes—
416#391C2312yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2318yes—
421#391C2312yes—
422#391C2318yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#390C2312yes—
427#390C2312yes—
428#390C2318yes—
429#390C2312yes—
430#390C2312yes—
431#390C2312yes—
432#390C2312yes—
433#390C2312yes—
434#390C2312yes—
435#390C2318yes—
436#390C2312yes—
437#390C2312yes—
438#390C2318yes—
439#390C2312yes—
440#390C2312yes—
441#390C2312yes—
442#390C2314yes—
443#390C2318yes—
444#390C2318yes—
445#390C2314yes—
446#390C2314yes—
447#390C2312yes—
448#390C2318yes—
449#389C2314yes—
450#389C2314yes—
451#388C2318yes—
452#388C2318yes—
453#388C2318yes—
454#388C2318yes—
455#388C2318yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2318yes—
463#388C2318yes—
464#388C2318yes—
465#388C2318yes—
466#388C2318yes—
467#388C2318yes—
468#388C2318yes—
469#387C2318yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2318yes—
477#386C2318yes—
478#386C2318yes—
479#386C2318yes—
480#386C2318yes—
481#386C2318yes—
482#386C2318yes—
483#386C2318yes—
484#386C2314yes—
485#386C2314yes—
486#386C2318yes—
487#386C2314yes—
488#386C2314yes—
489#386C2318yes—
490#386C2318yes—
491#386C2318yes—
492#386C2318yes—
493#386C2318yes—
494#386C2318yes—
495#386C2318yes—
496#386C2318yes—
497#385C2318yes—
498#385C2318yes—
499#385C2314yes—
500#385C2314yes—
501#384C2312yes—
502#384C2312yes—
503#383C2312yes—
504#382C2312yes—
505#382C2312yes—
506#382C2312yes—
507#382C2312yes—
508#382C2312yes—
509#381C2312yes—
510#381C2318yes—
511#381C2318yes—
512#380C2318yes—
513#380C2318yes—
514#380C2318yes—
515#380C2312yes—
516#379C2318yes—
517#379C2318yes—
518C4×C4⋊C4C2312yes—
519C4×C4⋊C4C2312yes—
520C4×C4⋊C4C2312yes—
521C4×C4⋊C4C2314yes—
522C4×C4⋊C4C2312yes—
523C4×C4⋊C4C2314yes—
524C4×C4⋊C4C2312yes—
525C4×C22⋊C4C2312yes—
526C4×C22⋊C4C2312yes—
527C4×C22⋊C4C2314yes—
528C4×C22⋊C4C2314yes—
529C4×C22⋊C4C2318yes—
530C4×C22⋊C4C2312yes—
531C4×C22⋊C4C2312yes—
532C4×C22⋊C4C2311yescharacteristic
533C4×C22⋊C4C2311yescharacteristic
534C4×C22⋊C4C2318yes—
535#376C2312yes—
536#376C2312yes—
537#376C2312yes—
538C43C2312yes—
539C43C2311yescharacteristic
540C43C2311yescharacteristic
541C25C2414yes—
542C25C2412yes—
543C2×#41—28no—
544C2×#41—28no—
545C2×#41—28no—
546C2×#41—28no—
547C2×#41—44no—
548C2×#41—44no—
549C2×#41—84no—
550C2×#41—84no—
551C2×#41—84no—
552C22×Q8—28no—
553C22×Q8—24no—
554C22×Q8—44no—
555C22×Q8—84no—
556C22×Q8C2412yes—
557C22×Q8C2412yes—
558C22×Q8C2412yes—
559C22×Q8C2412yes—
560C22×Q8C2414yes—
561C22×Q8C2412yes—
562C22×Q8C2412yes—
563C22×Q8C2411yescharacteristic
564C22×D4—216no—
565C22×D4—24no—
566C22×D4—28no—
567C22×D4—44no—
568C22×D4—44no—
569C22×D4—44no—
570C22×D4—88no—
571C22×D4C2411yescharacteristic
572C22×D4C2411yescharacteristic
573C22×D4C2412yes—
574C22×D4C2412yes—
575C22×D4C2414yes—
576C22×D4C2414yes—
577C22×D4C2412yes—
578C22×D4C2414yes—
579C22×D4C2412yes—
580C22×D4C2414yes—
581C22×D4C2412yes—
582C22×D4C2414yes—
583C22×D4C2414yes—
584C22×D4C2412yes—
585C22×D4C2412yes—
586C22×D4C2412yes—
587C22×D4C2414yes—
588C22×D4C2414yes—
589C22×D4C2412yes—
590C22×D4C2418yes—
591C22×D4C2418yes—
592C22×D4C2418yes—
593C22×D4C2418yes—
594C22×D4C2411yescharacteristic
595C22×D4C2412yes—
596C23×C4C2412yes—
597C23×C4C2411yescharacteristic
598C23×C4C2414yes—
599C23×C4C2412yes—
600C23×C4C2414yes—
601C23×C4C2414yes—
602C23×C4C2414yes—
603C23×C4C2412yes—
604C23×C4C2412yes—
605C23×C4C2414yes—
606C23×C4C2414yes—
607C23×C4C2414yes—
608C23×C4C2411yescharacteristic
609C23×C4C2411yescharacteristic
610C4⋊Q8—216no—
611C4⋊Q8—24no—
612C4⋊Q8—24no—
613C4⋊Q8—24no—
614C4⋊Q8—24no—
615C4⋊Q8—28no—
616#127—24no—
617#127—24no—
618#127—28no—
619#127—44no—
620#127—44no—
621#127—44no—
622#127—44no—
623#127—84no—
624#127—84no—
625#126—216no—
626#126—216no—
627#126C2×D4116yes—
628#125—216no—
629#125—28no—
630#125—28no—
631#125C2×D418yes—
632#124—216no—
633#124—216no—
634#124—216no—
635#124—216no—
636#124—216no—
637#124—216no—
638#124—28no—
639#124—28no—
640#124—28no—
641#124—28no—
642#124—28no—
643#124—28no—
644#124—28no—
645#124—44no—
646#124—44no—
647#124—84no—
648#124—88no—
649#124—84no—
650#124C2×D418yes—
651#123—216no—
652#123—216no—
653#123—216no—
654#123—216no—
655#123—216no—
656#123—216no—
657#123—216no—
658#123—216no—
659#123C2×D4116yes—
660C22⋊Q8—28no—
661C22⋊Q8—28no—
662C22⋊Q8—28no—
663C22⋊Q8—28no—
664C22⋊Q8—28no—
665C22⋊Q8—28no—
666C22⋊Q8—216no—
667C22⋊Q8—216no—
668C22⋊Q8—216no—
669C22⋊Q8—216no—
670C22⋊Q8—216no—
671C22⋊Q8—216no—
672C22⋊Q8—88no—
673C22⋊Q8C2×D418yes—
674#121—216no—
675#121—28no—
676#121—216no—
677#121—216no—
678#121—28no—
679#121—28no—
680#121—24no—
681#121—24no—
682#121—28no—
683#121—28no—
684#121—28no—
685#121—28no—
686#121—216no—
687#121—216no—
688#121—216no—
689#121—216no—
690#121—216no—
691#121—216no—
692#121—88no—
693#121—88no—
694#121—88no—
695#121C2×D418yes—
696#120—216no—
697#120—216no—
698#120—216no—
699#120—216no—
700#120—216no—
701#120—84no—
702#120—88no—
703#120—88no—
704#120—84no—
705C4×Q8—28no—
706C4×Q8—28no—
707C4×Q8—28no—
708C4×Q8C2×D418yes—
709C4×D4—216no—
710C4×D4—216no—
711C4×D4—216no—
712C4×D4—28no—
713C4×D4—28no—
714C4×D4—24no—
715C4×D4—28no—
716C4×D4—24no—
717C4×D4—28no—
718C4×D4—28no—
719C4×D4—28no—
720C4×D4—88no—
721C4×D4C2×D4116yes—
722C4×D4C2×D418yes—
723#117—28no—
724#117—28no—
725#117—28no—
726#117—216no—
727#117—44no—
728#117—44no—
729#117C2×D4116yes—
730C2×C4⋊C4—28no—
731C2×C4⋊C4—28no—
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2412yes—
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2412yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2412yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2418yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2418yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2411yescharacteristic
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C22⋊C4—28no—
763C2×C22⋊C4—28no—
764C2×C22⋊C4—216no—
765C2×C22⋊C4—88no—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C22⋊C4C2412yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2414yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2414yes—
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⋊C4C2418yes—
788C2×C22⋊C4C2418yes—
789C2×C22⋊C4C2418yes—
790C2×C22⋊C4C2418yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2418yes—
794C2×C22⋊C4C2418yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2418yes—
800C2×C22⋊C4C2418yes—
801C2×C22⋊C4C2418yes—
802C2×C22⋊C4C2418yes—
803C2×C22⋊C4C2418yes—
804C2×C22⋊C4C2418yes—
805C2×C22⋊C4C2418yes—
806C2×C22⋊C4C2418yes—
807C2×C22⋊C4C2418yes—
808C2×C22⋊C4C2418yes—
809C2×C22⋊C4C2412yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2412yes—
813C2×C22⋊C4C2412yes—
814C2×C42—44no—
815C2×C42C2×D418yes—
816C2×C42C2414yes—
817C2×C42C2414yes—
818C2×C42C2412yes—
819C2×C42C2412yes—
820C2×C42C2412yes—
821C2×C42C2414yes—
822C2×C42C2412yes—
823C2×C42C2414yes—
824C2×C42C2412yes—
825C2×C42C2412yes—
826C2×C42C2414yes—
827C2×C42C2412yes—
828C2×C42C2412yes—
829C2×C42C2414yes—
830C2×C42C2411yescharacteristic
831C2×C42C2412yes—
832C2×C42C2411yescharacteristic
833C2×C42C2411yescharacteristic
834C2×C42C2411yescharacteristic
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840#95C2414yes—
841#95C2418yes—
842#95C2418yes—
843#95C2418yes—
844#95C2412yes—
845#95C2412yes—
846#95C2414yes—
847#95C2418yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2418yes—
853#95C2418yes—
854#95C2418yes—
855#95C2418yes—
856#95C2418yes—
857#95C2418yes—
858C24—24no—
859C24—28no—
860C24—44no—
861C24—44no—
862C24—48no—
863C24—48no—
864C24—44no—
865C24—44no—
866C24—44no—
867C24C2514yes—
868C24C2514yes—
869C24C2512yes—
870C24C2512yes—
871C24C2511yescharacteristic
872C24C2512yes—
873#41—816no—
874#41—816no—
875#41—816no—
876#41—816no—
877C2×Q8—24no—
878C2×Q8—24no—
879C2×Q8—24no—
880C2×Q8—24no—
881C2×Q8—24no—
882C2×Q8—28no—
883C2×Q8—24no—
884C2×Q8—24no—
885C2×Q8—24no—
886C2×Q8—42no—
887C2×Q8—44no—
888C2×Q8—44no—
889C2×Q8—48no—
890C2×Q8—44no—
891C2×Q8—44no—
892C2×Q8—44no—
893C2×Q8—88no—
894C2×Q8—816no—
895C2×Q8C22×D414yes—
896C2×D4—28no—
897C2×D4—28no—
898C2×D4—28no—
899C2×D4—28no—
900C2×D4—24no—
901C2×D4—28no—
902C2×D4—24no—
903C2×D4—22no—
904C2×D4—22no—
905C2×D4—24no—
906C2×D4—24no—
907C2×D4—28no—
908C2×D4—24no—
909C2×D4—24no—
910C2×D4—24no—
911C2×D4—24no—
912C2×D4—28no—
913C2×D4—28no—
914C2×D4—24no—
915C2×D4—24no—
916C2×D4—24no—
917C2×D4—24no—
918C2×D4—24no—
919C2×D4—24no—
920C2×D4—24no—
921C2×D4—44no—
922C2×D4—48no—
923C2×D4—42no—
924C2×D4—48no—
925C2×D4—48no—
926C2×D4—48no—
927C2×D4—44no—
928C2×D4—48no—
929C2×D4—44no—
930C2×D4—48no—
931C2×D4—48no—
932C2×D4—48no—
933C2×D4—44no—
934C2×D4—44no—
935C2×D4—48no—
936C2×D4—44no—
937C2×D4—44no—
938C2×D4—44no—
939C2×D4—44no—
940C2×D4—44no—
941C2×D4—44no—
942C2×D4—44no—
943C2×D4—48no—
944C2×D4—48no—
945C2×D4—48no—
946C2×D4—48no—
947C2×D4—48no—
948C2×D4—48no—
949C2×D4—48no—
950C2×D4—48no—
951C2×D4—48no—
952C2×D4—88no—
953C2×D4—816no—
954C2×D4—832no—
955C2×D4C22×D414yes—
956C2×D4C22×D418yes—
957C22×C4—24no—
958C22×C4—24no—
959C22×C4—24no—
960C22×C4—24no—
961C22×C4—28no—
962C22×C4—24no—
963C22×C4—24no—
964C22×C4—28no—
965C22×C4—28no—
966C22×C4—28no—
967C22×C4—28no—
968C22×C4—28no—
969C22×C4—44no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—44no—
973C22×C4—44no—
974C22×C4—44no—
975C22×C4—48no—
976C22×C4—48no—
977C22×C4—48no—
978C22×C4—44no—
979C22×C4—48no—
980C22×C4—48no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4C22×D414yes—
985C22×C4C22×D418yes—
986C22×C4C22×D414yes—
987C22×C4C22×D414yes—
988C22×C4C2514yes—
989C22×C4C2514yes—
990C22×C4C2514yes—
991C22×C4C2514yes—
992C22×C4C2514yes—
993C22×C4C2512yes—
994C22×C4C2514yes—
995C22×C4C2514yes—
996C22×C4C2512yes—
997C22×C4C2514yes—
998C22×C4C2511yescharacteristic
999C22×C4C2511yescharacteristic
1000C22×C4C2511yescharacteristic
1001C22×C4C2511yescharacteristic
1002C22×C4C2512yes—
1003C22×C4C2512yes—
1004C22×C4C2512yes—
1005C22×C4C2511yescharacteristic
1006C22×C4C2511yescharacteristic
1007C4⋊C4—22no—
1008C4⋊C4—24no—
1009C4⋊C4—24no—
1010C4⋊C4—28no—
1011C4⋊C4—28no—
1012C4⋊C4—24no—
1013C4⋊C4—22no—
1014C4⋊C4—28no—
1015C4⋊C4—24no—
1016C4⋊C4—28no—
1017C4⋊C4—24no—
1018C4⋊C4—24no—
1019C4⋊C4—28no—
1020C4⋊C4—28no—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—24no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C4⋊C4—48no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—48no—
1030C4⋊C4—44no—
1031C4⋊C4C22×D414yes—
1032C4⋊C4C22×D418yes—
1033C4⋊C4C22×D414yes—
1034C4⋊C4C22×D418yes—
1035C4⋊C4C22×D418yes—
1036C4⋊C4C22×D418yes—
1037C22⋊C4—28no—
1038C22⋊C4—28no—
1039C22⋊C4—28no—
1040C22⋊C4—28no—
1041C22⋊C4—28no—
1042C22⋊C4—28no—
1043C22⋊C4—28no—
1044C22⋊C4—28no—
1045C22⋊C4—24no—
1046C22⋊C4—28no—
1047C22⋊C4—28no—
1048C22⋊C4—24no—
1049C22⋊C4—28no—
1050C22⋊C4—28no—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—28no—
1054C22⋊C4—28no—
1055C22⋊C4—24no—
1056C22⋊C4—28no—
1057C22⋊C4—24no—
1058C22⋊C4—48no—
1059C22⋊C4—48no—
1060C22⋊C4—48no—
1061C22⋊C4—48no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—48no—
1065C22⋊C4—48no—
1066C22⋊C4—42no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—42no—
1070C22⋊C4—48no—
1071C22⋊C4—48no—
1072C22⋊C4—48no—
1073C22⋊C4—48no—
1074C22⋊C4—48no—
1075C22⋊C4—48no—
1076C22⋊C4—48no—
1077C22⋊C4—48no—
1078C22⋊C4—48no—
1079C22⋊C4—48no—
1080C22⋊C4C22×D418yes—
1081C22⋊C4C22×D418yes—
1082C22⋊C4C22×D418yes—
1083C22⋊C4C22×D418yes—
1084C22⋊C4C22×D418yes—
1085C42—28no—
1086C42—28no—
1087C42—28no—
1088C42—24no—
1089C42—24no—
1090C42—24no—
1091C42—24no—
1092C42—44no—
1093C42—44no—
1094C42—42no—
1095C42—42no—
1096C42—44no—
1097C42—42no—
1098C42—42no—
1099C42C22×D414yes—
1100C42C22×D414yes—
1101C42C22×D414yes—
1102C42C22×D414yes—
1103C42C22×D418yes—
1104C23—22no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23—24no—
1109C23—24no—
1110C23—22no—
1111C23—22no—
1112C23—22no—
1113C23—24no—
1114C23—24no—
1115C23—24no—
1116C23—24no—
1117C23—24no—
1118C23—24no—
1119C23—24no—
1120C23—24no—
1121C23—28no—
1122C23—28no—
1123C23—24no—
1124C23—28no—
1125C23—28no—
1126C23—24no—
1127C23—24no—
1128C23—24no—
1129C23—48no—
1130C23—84no—
1131C23—88no—
1132C23—88no—
1133C23—84no—
1134C23—88no—
1135C23—816no—
1136C23—168no—
1137C23—168no—
1138C23C23×D414yes—
1139C23C23×D412yes—
1140C23C2611yescharacteristic
1141Q8—44no—
1142Q8—48no—
1143Q8—48no—
1144Q8—84no—
1145Q8—84no—
1146Q8—88no—
1147Q8—84no—
1148Q8—84no—
1149D4—48no—
1150D4—44no—
1151D4—416no—
1152D4—44no—
1153D4—44no—
1154D4—48no—
1155D4—48no—
1156D4—84no—
1157D4—84no—
1158D4—88no—
1159D4—88no—
1160D4—84no—
1161D4—88no—
1162D4—84no—
1163D4—84no—
1164D4—88no—
1165D4—88no—
1166D4—88no—
1167D4—84no—
1168D4—84no—
1169D4—88no—
1170D4—816no—
1171D4—168no—
1172D4—168no—
1173D4—168no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—28no—
1184C2×C4—216no—
1185C2×C4—24no—
1186C2×C4—22no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—22no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—24no—
1196C2×C4—24no—
1197C2×C4—24no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—24no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—28no—
1205C2×C4—24no—
1206C2×C4—28no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—28no—
1210C2×C4—44no—
1211C2×C4—44no—
1212C2×C4—48no—
1213C2×C4—48no—
1214C2×C4—88no—
1215C2×C4—88no—
1216C2×C4—88no—
1217C2×C4—88no—
1218C2×C4—88no—
1219C2×C4—84no—
1220C2×C4—88no—
1221C2×C4—88no—
1222C2×C4C23×D412yes—
1223C2×C4C23×D414yes—
1224C2×C4C23×D414yes—
1225C2×C4C23×D412yes—
1226C2×C4C23×D412yes—
1227C2×C4C23×D412yes—
1228C2×C4C23×D412yes—
1229C2×C4C23×D414yes—
1230C2×C4C23×D412yes—
1231C2×C4#58514yes—
1232C22—22no—
1233C22—24no—
1234C22—22no—
1235C22—22no—
1236C22—24no—
1237C22—24no—
1238C22—44no—
1239C22—44no—
1240C22—44no—
1241C22—44no—
1242C22—44no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—44no—
1249C22—44no—
1250C22—42no—
1251C22—44no—
1252C22—44no—
1253C22—48no—
1254C22—48no—
1255C22—48no—
1256C22—48no—
1257C22—48no—
1258C22—48no—
1259C22—168no—
1260C22—1616no—
1261C22C24×D411yescharacteristic
1262C22C2×#58512yes—
1263C22H(7,𝔽2)12yes—
1264C22H(7,𝔽2)12yes—
1265C4—24no—
1266C4—22no—
1267C4—22no—
1268C4—22no—
1269C4—22no—
1270C4—22no—
1271C4—24no—
1272C4—24no—
1273C4—44no—
1274C4—42no—
1275C4—42no—
1276C4—44no—
1277C4—44no—
1278C4—44no—
1279C4—44no—
1280C4—44no—
1281C4—44no—
1282C4—44no—
1283C4#350014yes—
1284C2—42no—
1285C2—44no—
1286C2—82no—
1287C2—82no—
1288C2—84no—
1289C2—84no—
1290C2C2×#350011yescharacteristic
1291C2#6285211yescharacteristic
1292C2#6285211yescharacteristic
1293C2#6288514yes—
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×#3547C2semidirect
2. C2×#3558C2semidirect
3. #51070C2semidirect
4. #50693C2semidirect
5. #47955C2semidirect
6. #47686C2semidirect
7. #46430C2semidirect
8. #46354C2semidirect
9. #39171C2semidirect
10. #39161C2semidirect
11. #38953C2semidirect
12. #38948C2semidirect
13. #38095C2semidirect
14. #38090C2semidirect
15. #38082C2semidirect
16. #38080C2semidirect
17. #37634C2semidirect
18. #37536C2semidirect
19. #37423C2semidirect
20. #37302C2semidirect
21. #35338C2semidirect
22. #35293C2semidirect
23. #35276C2semidirect
24. #35264C2semidirect
25. #34081C2semidirect
29. C2×#562C22semidirect
32. C2×#555C22semidirect
33. C2×#555C22semidirect
34. C2×#554C22semidirect
35. C2×#553C22semidirect
36. C2×#552C22semidirect
37. C2×D4×Q8C22semidirect
39. C2×#548C22semidirect
40. C2×#547C22semidirect
44. C2×#544C22semidirect
46. C2×#542C22semidirect
47. C2×#540C22semidirect
51. C2×#536C22semidirect
54. C2×#533C22semidirect
56. C2×#532C22semidirect
59. #2867C22semidirect
60. #2862C22semidirect
61. #2861C22semidirect
62. #2861C22semidirect
63. #2861C22semidirect
65. #2858C22semidirect
66. #2858C22semidirect
68. #2850C22semidirect
69. #2819C22semidirect
70. #2816C22semidirect
71. #2730C22semidirect
72. #2716C22semidirect
73. #2714C22semidirect
74. #2712C22semidirect
75. #2703C22semidirect
76. #2702C22semidirect
77. #2700C22semidirect
78. #2699C22semidirect
79. #2696C22semidirect
80. #2696C22semidirect
81. #2696C22semidirect
82. #2690C22semidirect
83. #2688C22semidirect
84. #2687C22semidirect
85. #2681C22semidirect
86. #2678C22semidirect
87. #2676C22semidirect
88. #2673C22semidirect
89. #2673C22semidirect
90. #2670C22semidirect
91. #2670C22semidirect
92. #2669C22semidirect
93. #2669C22semidirect
94. #2668C22semidirect
95. #2660C22semidirect
96. #2657C22semidirect
98. #2641C22semidirect
99. #2640C22semidirect
100. #2640C22semidirect
101. #2640C22semidirect
102. #2640C22semidirect
103. #2632C22semidirect
104. #2631C22semidirect
105. #2620C22semidirect
107. #2619C22semidirect
108. #2619C22semidirect
109. #2617C22semidirect
110. #2616C22semidirect
111. #2592C22semidirect
112. #2592C22semidirect
113. #2568C22semidirect
114. #2566C22semidirect
115. #2565C22semidirect
116. #2563C22semidirect
117. #2563C22semidirect
118. #2561C22semidirect
119. #2561C22semidirect
120. #2555C22semidirect
121. #2554C22semidirect
122. #2544C22semidirect
123. #2544C22semidirect
124. #2544C22semidirect
125. #2544C22semidirect
126. #2544C22semidirect
127. #2544C22semidirect
128. #2542C22semidirect
131. #2536C22semidirect
133. #2503C22semidirect
135. #2500C22semidirect
136. #2500C22semidirect
137. #2499C22semidirect
138. #2491C22semidirect
139. #2490C22semidirect
140. #2477C22semidirect
141. #2472C22semidirect
142. #2472C22semidirect
143. #2472C22semidirect
144. #2471C22semidirect
145. #2464C22semidirect
146. #2463C22semidirect
147. #2461C22semidirect
148. #2459C22semidirect
149. #2459C22semidirect
150. #2457C22semidirect
151. #2443C22semidirect
152. #2436C22semidirect
153. #2436C22semidirect
154. #2436C22semidirect
157. #2433C22semidirect
158. #2433C22semidirect
159. #2431C22semidirect
160. #2431C22semidirect
161. #2431C22semidirect
162. #2431C22semidirect
163. #2427C22semidirect
164. #2424C22semidirect
165. #2414C22semidirect
166. #2412C22semidirect
167. #2410C22semidirect
168. #2408C22semidirect
169. #2404C22semidirect
170. #2404C22semidirect
171. #2337C22semidirect
172. #2336C22semidirect
173. #2335C22semidirect
174. #2334C22semidirect
176. #2332C22semidirect
177. #2328C22semidirect
178. #2328C22semidirect
179. #2328C22semidirect
180. #2326C22semidirect
181. #2311C22semidirect
182. #2310C22semidirect
184. #2309C22semidirect
185. C4×#127C22semidirect
186. C4×#124C22semidirect
187. #2298C22semidirect
188. #2297C22semidirect
189. #2295C22semidirect
190. #2293C22semidirect
191. C2×#390C22semidirect
192. #2290C22semidirect
193. #2290C22semidirect
194. #2283C22semidirect
195. C4×#117C22semidirect
196. C4×#117C22semidirect
250. #529D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35472
C2×#35582
#510702
#506932
#479552
#476862
#464302
#463542
#391712
#391612
#389532
#389482
#380952
#380902
#380822
#380802
#376342
#375362
#374232
#373022
#353382
#352932
#352762
#352642
#340812