Finite Group Databasebeta

← #8093511

Subgroups — #8093511

Order 512.

5778 conjugacy classes of subgroups.

The subgroup lattice has 1075 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53152C214yesmaximal, complemented
2#53129C214yesmaximal, complemented
3#53102C214yesmaximal, complemented
4#53096C214yesmaximal, complemented
5#53063C214yesmaximal, complemented
6#53053C214yesmaximal, complemented
7#52981C214yesmaximal, complemented
8#52971C214yesmaximal, complemented
9#52586C214yesmaximal, complemented
10#52548C214yesmaximal, complemented
11#52313C218yesmaximal, complemented
12#35565C211yesmaximal, characteristic, complemented
13#35564C212yesmaximal, complemented
14#35545C212yesmaximal, complemented
15#35531C212yesmaximal, complemented
16#35518C212yesmaximal, complemented
17#35513C212yesmaximal, complemented
18#35512C211yesmaximal, characteristic, complemented
19#34633C212yesmaximal, complemented
20C2×#2624C211yesmaximal, characteristic, complemented
21C22×H(5,𝔽2)C2211yescharacteristic
22C2×#537C2212yes—
23C2×#537C2211yescharacteristic, complemented
24C2×#535C2212yes—
25C2×#532C2212yes—
26C2×#525C2212yes—
27C2×#525C2212yescomplemented
28C22×#121C2211yescharacteristic
29C2×#520C2212yescomplemented
30C22×#117C2211yescharacteristic, complemented
31#2842C2214yescomplemented
32#2837C2218yescomplemented
33#2837C2218yescomplemented
34#2834C2214yescomplemented
35#2829C2218yescomplemented
36#2829C2218yescomplemented
37#2829C2218yescomplemented
38#2828C2218yescomplemented
39#2828C2218yescomplemented
40#2826C2218yescomplemented
41#2826C2214yescomplemented
42#2825C2218yescomplemented
43#2825C2218yescomplemented
44#2818C2218yescomplemented
45#2813C2218yescomplemented
46#2813C2218yescomplemented
47#2812C2218yescomplemented
48#2812C2214yescomplemented
49#2807C2214yescomplemented
50#2803C2218yescomplemented
51#2778C2218yescomplemented
52#2757C2218yescomplemented
53#2757C2218yescomplemented
54#2756C2218yescomplemented
55#2748C2218yescomplemented
56#2735C2214yescomplemented
57#2709C2218yescomplemented
58#2705C2218yescomplemented
59#2697C2218yescomplemented
60#2693C2214yescomplemented
61#2685C2218yescomplemented
62#2685C2218yescomplemented
63#2678C2218yescomplemented
64#2673C2218yescomplemented
65#2669C2218yescomplemented
66#2668C2214yescomplemented
67#2624C2214yescomplemented
68#2624C2214yescomplemented
69#2624C2214yescomplemented
70#2624C2214yescomplemented
71#2621C2212yescomplemented
72#2621C2212yescomplemented
73#2620C2212yescomplemented
74#2620C2212yescomplemented
75#2620C2212yescomplemented
76#2620C2212yescomplemented
77#2619C2212yescomplemented
78#2619C2212yescomplemented
79#2618C2214yescomplemented
80#2618C2214yescomplemented
81#2617C2214yescomplemented
82#2617C2214yescomplemented
83#2543C2218yescomplemented
84#2541C2214yescomplemented
85#2541C2214yescomplemented
86#2540C2214yescomplemented
87#2540C2214yescomplemented
88#2539C2214yescomplemented
89#2538C2214yescomplemented
90#2537C2214yescomplemented
91#2536C2214yescomplemented
92#2535C2214yescomplemented
93#2514C2214yescomplemented
94#2513C2214yescomplemented
95#2512C2214yescomplemented
96#2511C2214yescomplemented
97#2510C2218yescomplemented
98#2504C2214yescomplemented
99#2501C2214yescomplemented
100#2500C2214yescomplemented
101#2500C2214yescomplemented
102#2497C2214yescomplemented
103#2496C2214yescomplemented
104#2495C2214yescomplemented
105#2494C2214yescomplemented
106#2481C2218yescomplemented
107#2448C2214yescomplemented
108#2448C2214yescomplemented
109#2445C2214yescomplemented
110#2445C2214yescomplemented
111#2435C2214yescomplemented
112#2433C2214yescomplemented
113#2433C2214yescomplemented
114#2432C2214yescomplemented
115#2431C2214yescomplemented
116#2429C2214yescomplemented
117#2428C2214yescomplemented
118#2427C2214yescomplemented
119#2426C2214yescomplemented
120#2425C2218yescomplemented
121#2424C2218yescomplemented
122#2418C2218yescomplemented
123#2418C2218yescomplemented
124#2417C2214yescomplemented
125#2417C2214yescomplemented
126#2416C2218yescomplemented
127#2416C2214yescomplemented
128#2416C2214yescomplemented
129#2415C2214yescomplemented
130#2415C2214yescomplemented
131#2414C2214yescomplemented
132#2414C2214yescomplemented
133#2410C2218yes—
134#2410C2218yes—
135#2408C2214yes—
136#2408C2214yes—
137#2408C2214yescomplemented
138#2408C2214yescomplemented
139#2407C2214yes—
140#2407C2214yes—
141#2407C2214yescomplemented
142#2407C2214yescomplemented
143#2405C2214yes—
144#2403C2214yes—
145C2×#399C2212yescomplemented
146#2392C2214yescomplemented
147#2392C2214yescomplemented
148#2392C2214yescomplemented
149#2392C2214yescomplemented
150C2×#397C2212yescomplemented
151C2×#394C2214yescomplemented
152#2317C2212yescomplemented
153#2311C2212yes—
154#2311C2212yes—
155#2309C2211yescharacteristic
156#2297C2212yes—
157#2297C2212yescomplemented
158C2×#390C2212yes—
159C2×#389C2212yescomplemented
160#2285C2212yescomplemented
161C2×#380C2211yescharacteristic, complemented
162#2274C2211yescharacteristic, complemented
163C2×H(5,𝔽2)—44no—
164C2×H(5,𝔽2)—48no—
165C22×#41C2312yes—
166C22×#41C2312yes—
167C22×#41C2314yes—
168C23×D4C2311yescharacteristic
169C23×D4C2314yes—
170C23×D4C2314yes—
171C23×D4C2312yes—
172C24×C4C2311yescharacteristic
173#537—48no—
174#537—44no—
175#535—48no—
176#532—48no—
177C2×C4⋊Q8C2312yes—
178C2×#127C2312yes—
179C2×#127C2314yes—
180C2×#127C2318yes—
181C2×#126C2318yes—
182C2×#124C2312yes—
183C2×#124C2312yes—
184C2×#124C2314yes—
185#525—48no—
186#525—48no—
187C2×#123C2314yes—
188C2×#123C2314yes—
189C2×#123C2318yes—
190C2×#123C2318yes—
191C2×C22⋊Q8C2312yes—
192C2×C22⋊Q8C2312yes—
193C2×C22⋊Q8C2312yes—
194C2×C22⋊Q8C2312yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2314yes—
198C2×#121—44no—
199C2×#121C2314yes—
200C2×#121C2314yes—
201C2×#121C2312yes—
202C2×#121C2312yes—
203C2×#121C2312yes—
204C2×#121C2312yes—
205C2×#121C2314yes—
206C2×#121C2314yes—
207C2×#121C2314yes—
208C2×#121C2314yes—
209C2×#121C2314yes—
210C2×#121C2318yes—
211C2×#121C2314yes—
212C2×#121C2314yes—
213C2×#121C2314yes—
214C2×#121C2318yes—
215C2×#121C2318yes—
216C2×#120C2314yes—
217C2×#120C2314yes—
218C2×#120C2318yes—
219C2×#120C2318yes—
220C2×#120C2318yes—
221C2×#120C2318yes—
222#520—48no—
223C2×C4×Q8C2314yes—
224C2×C4×D4C2314yes—
225C2×C4×D4C2314yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2314yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2318yes—
231C2×C4×D4C2314yes—
232C2×#117—44no—
233C2×#117C2312yes—
234C2×#117C2312yes—
235C2×#117C2312yes—
236C2×#117C2312yes—
237C2×#117C2312yes—
238C2×#117C2312yes—
239C2×#117C2314yes—
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2312yes—
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2314yes—
245C22×C4⋊C4C2314yes—
246C22×C22⋊C4C2312yes—
247C22×C22⋊C4C2312yes—
248C22×C22⋊C4C2312yes—
249C22×C22⋊C4C2314yes—
250C22×C22⋊C4C2314yes—
251C22×C42C2312yes—
252#401C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#399C2318yes—
257#399C2314yes—
258#399C2314yes—
259#399C2318yes—
260#399C2314yes—
261#399C2314yes—
262#399C2318yes—
263#398C2314yes—
264#398C2318yes—
265#398C2318yes—
266#398C2314yes—
267#398C2314yes—
268#398C2314yes—
269#397C2314yes—
270#397C2318yes—
271#397C2318yes—
272#397C2318yes—
273#397C2318yes—
274#397C2318yes—
275#397C2314yes—
276#397C2318yes—
277#397C2314yes—
278#397C2318yes—
279#397C2314yes—
280#397C2314yes—
281#397C2318yes—
282#397C2314yes—
283#396C2314yes—
284#396C2318yes—
285#396C2314yes—
286#396C2318yes—
287#396C2314yes—
288#396C2314yes—
289#396C2318yes—
290#396C2318yes—
291#396C2314yes—
292#396C2314yes—
293#396C2314yes—
294#396C2318yes—
295#396C2314yes—
296#394C2314yes—
297#394C2318yes—
298#394C2318yes—
299#394C2318yes—
300#394C2318yes—
301#394C2318yes—
302#394C2314yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#394C2318yes—
308#394C2314yes—
309#394C2318yes—
310#394C2318yes—
311#394C2314yes—
312#394C2314yes—
313#394C2318yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2314yes—
318#394C2314yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2314yes—
324#394C2314yes—
325#394C2314yes—
326#394C2314yes—
327#394C2314yes—
328#392C2314yes—
329#392C2318yes—
330#392C2318yes—
331#392C2318yes—
332#392C2318yes—
333#392C2318yes—
334#392C2314yes—
335#392C2314yes—
336#392C2318yes—
337#392C2318yes—
338#392C2318yes—
339#392C2318yes—
340#392C2314yes—
341#392C2318yes—
342#392C2314yes—
343#392C2314yes—
344#391C2314yes—
345#391C2314yes—
346#391C2312yes—
347#391C2312yes—
348#391C2312yes—
349#391C2312yes—
350#390C2314yes—
351#390C2314yes—
352#390C2314yes—
353#390C2314yes—
354#390C2318yes—
355#390C2318yes—
356#390C2318yes—
357#390C2318yes—
358#390C2318yes—
359#390C2312yes—
360#390C2312yes—
361#390C2312yes—
362#390C2312yes—
363#390C2314yes—
364#390C2314yes—
365#390C2314yes—
366#390C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2318yes—
370#389C2318yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#386C2318yes—
390#386C2318yes—
391#386C2318yes—
392#386C2318yes—
393#386C2318yes—
394#386C2318yes—
395#386C2318yes—
396#386C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2314yes—
401#386C2314yes—
402#386C2314yes—
403#386C2314yes—
404#385C2314yes—
405#385C2318yes—
406#385C2318yes—
407#385C2314yes—
408#385C2318yes—
409#384C2314yes—
410#384C2312yes—
411#384C2312yes—
412#383C2318yes—
413#382C2314yes—
414#382C2312yes—
415#382C2312yes—
416#380C2314yes—
417#380C2314yes—
418#380C2314yes—
419#380C2314yes—
420#380C2314yes—
421#380C2314yes—
422#380C2314yes—
423#380C2314yes—
424#380C2318yes—
425#380C2318yes—
426#379C2314yes—
427#379C2314yes—
428#379C2318yes—
429#379C2314yes—
430#379C2318yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2314yes—
435C4×C22⋊C4C2314yes—
436C4×C22⋊C4C2314yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2314yes—
439C4×C22⋊C4C2314yes—
440C2×#95C2314yes—
441C2×#95C2312yes—
442C25C2412yes—
443C25C2411yescharacteristic
444C25C2414yes—
445H(5,𝔽2)—464no—
446C2×#41—28no—
447C2×#41—28no—
448C2×#41—28no—
449C2×#41—28no—
450C2×#41—28no—
451C2×#41—28no—
452C2×#41—48no—
453C2×#41—48no—
454C2×#41—48no—
455C22×Q8C2412yes—
456C22×Q8C2412yes—
457C22×D4—24no—
458C22×D4—28no—
459C22×D4—48no—
460C22×D4—48no—
461C22×D4—48no—
462C22×D4—44no—
463C22×D4—416no—
464C22×D4—48no—
465C22×D4—84no—
466C22×D4C2414yes—
467C22×D4C2412yes—
468C22×D4C2414yes—
469C22×D4C2414yes—
470C22×D4C2412yes—
471C22×D4C2414yes—
472C22×D4C2414yes—
473C22×D4C2414yes—
474C22×D4C2414yes—
475C22×D4C2414yes—
476C22×D4C2414yes—
477C22×D4C2418yes—
478C22×D4C2418yes—
479C22×D4C2418yes—
480C22×D4C2418yes—
481C22×D4C2414yes—
482C22×D4C2418yes—
483C23×C4—24no—
484C23×C4—28no—
485C23×C4C2411yescharacteristic
486C23×C4C2414yes—
487C23×C4C2412yes—
488C23×C4C2412yes—
489C23×C4C2414yes—
490C23×C4C2412yes—
491C23×C4C2414yes—
492C23×C4C2412yes—
493C23×C4C2412yes—
494C23×C4C2418yes—
495C23×C4C2414yes—
496C23×C4C2411yescharacteristic
497C4⋊Q8—44no—
498#127—44no—
499#127—48no—
500#127—88no—
501#126—88no—
502#124—44no—
503#124—44no—
504#124—48no—
505#123—48no—
506#123—48no—
507#123—88no—
508#123—88no—
509C22⋊Q8—44no—
510C22⋊Q8—44no—
511C22⋊Q8—44no—
512C22⋊Q8—44no—
513C22⋊Q8—48no—
514C22⋊Q8—48no—
515C22⋊Q8—48no—
516#121—48no—
517#121—48no—
518#121—44no—
519#121—44no—
520#121—44no—
521#121—44no—
522#121—48no—
523#121—48no—
524#121—48no—
525#121—48no—
526#121—48no—
527#121—48no—
528#121—48no—
529#121—48no—
530#121—416no—
531#121—88no—
532#121—88no—
533#120—48no—
534#120—48no—
535#120—416no—
536#120—88no—
537#120—88no—
538#120—88no—
539C4×Q8—48no—
540C4×D4—48no—
541C4×D4—48no—
542C4×D4—48no—
543C4×D4—48no—
544C4×D4—48no—
545C4×D4—48no—
546C4×D4—48no—
547C4×D4—416no—
548#117—28no—
549#117—28no—
550#117—44no—
551#117—44no—
552#117—44no—
553#117—44no—
554#117—48no—
555C2×C4⋊C4—28no—
556C2×C4⋊C4—24no—
557C2×C4⋊C4—48no—
558C2×C4⋊C4—42no—
559C2×C4⋊C4—42no—
560C2×C4⋊C4—84no—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2411yescharacteristic
569C2×C4⋊C4C2411yescharacteristic
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2412yes—
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2414yes—
591C2×C22⋊C4—44no—
592C2×C22⋊C4—44no—
593C2×C22⋊C4—84no—
594C2×C22⋊C4—84no—
595C2×C22⋊C4—82no—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2412yes—
599C2×C22⋊C4C2412yes—
600C2×C22⋊C4C2412yes—
601C2×C22⋊C4C2412yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C42—28no—
643C2×C42C2412yes—
644C2×C42C2412yes—
645C2×C42C2412yes—
646C2×C42C2412yes—
647C2×C42C2414yes—
648C2×C42C2414yes—
649C2×C42C2418yes—
650C2×C42C2418yes—
651#95C2414yes—
652#95C2414yes—
653#95C2418yes—
654#95C2418yes—
655#95C2414yes—
656#95C2414yes—
657#95C2414yes—
658#95C2414yes—
659#95C2414yes—
660#95C2414yes—
661#95C2414yes—
662#95C2414yes—
663#95C2414yes—
664#95C2414yes—
665#95C2414yes—
666#95C2414yes—
667#95C2414yes—
668#95C2414yes—
669#95C2418yes—
670#95C2418yes—
671#95C2418yes—
672#95C2418yes—
673#95C2418yes—
674#95C2418yes—
675C24—22no—
676C24—24no—
677C24—24no—
678C24—28no—
679C24—41no—
680C24—42no—
681C24—41no—
682C24—44no—
683C24—48no—
684C24—42no—
685C24—44no—
686C24—42no—
687C24—48no—
688C24—44no—
689C24—44no—
690C24C2514yes—
691C24C2514yes—
692C24C2512yes—
693C24C2514yes—
694C24C2511yescharacteristic
695#41—464no—
696#41—432no—
697#41—432no—
698C2×Q8—24no—
699C2×Q8—24no—
700C2×Q8—24no—
701C2×Q8—24no—
702C2×Q8—24no—
703C2×Q8—24no—
704C2×D4—28no—
705C2×D4—28no—
706C2×D4—28no—
707C2×D4—28no—
708C2×D4—28no—
709C2×D4—28no—
710C2×D4—24no—
711C2×D4—24no—
712C2×D4—24no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—24no—
716C2×D4—24no—
717C2×D4—28no—
718C2×D4—24no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C2×D4—44no—
726C2×D4—44no—
727C2×D4—44no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—44no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—44no—
739C2×D4—48no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—48no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—48no—
750C2×D4—44no—
751C2×D4—48no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—464no—
755C2×D4—464no—
756C2×D4—416no—
757C2×D4—816no—
758C22×C4—22no—
759C22×C4—24no—
760C22×C4—24no—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—28no—
764C22×C4—28no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—28no—
770C22×C4—28no—
771C22×C4—28no—
772C22×C4—28no—
773C22×C4—24no—
774C22×C4—24no—
775C22×C4—28no—
776C22×C4—44no—
777C22×C4—48no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—44no—
781C22×C4—44no—
782C22×C4—42no—
783C22×C4—44no—
784C22×C4—42no—
785C22×C4—48no—
786C22×C4—48no—
787C22×C4—48no—
788C22×C4—416no—
789C22×C4H(5,𝔽2)14yes—
790C22×C4H(5,𝔽2)18yes—
791C22×C4C2514yes—
792C22×C4C2512yes—
793C22×C4C2514yes—
794C22×C4C2514yes—
795C22×C4C2514yes—
796C22×C4C2514yes—
797C22×C4C2512yes—
798C22×C4C2512yes—
799C22×C4C2514yes—
800C22×C4C2518yes—
801C22×C4C2512yes—
802C22×C4C2514yes—
803C22×C4C2511yescharacteristic
804C22×C4C2511yescharacteristic
805C22×C4C2512yes—
806C4⋊C4—28no—
807C4⋊C4—28no—
808C4⋊C4—28no—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—41no—
814C4⋊C4—41no—
815C4⋊C4—42no—
816C4⋊C4—42no—
817C4⋊C4—41no—
818C4⋊C4—41no—
819C4⋊C4—48no—
820C4⋊C4—48no—
821C4⋊C4—48no—
822C4⋊C4—44no—
823C4⋊C4—44no—
824C4⋊C4—44no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—44no—
829C4⋊C4—48no—
830C4⋊C4—44no—
831C4⋊C4—48no—
832C4⋊C4—44no—
833C4⋊C4—44no—
834C4⋊C4—48no—
835C4⋊C4—44no—
836C22⋊C4—28no—
837C22⋊C4—28no—
838C22⋊C4—42no—
839C22⋊C4—42no—
840C22⋊C4—42no—
841C22⋊C4—42no—
842C22⋊C4—44no—
843C22⋊C4—44no—
844C22⋊C4—48no—
845C22⋊C4—48no—
846C22⋊C4—48no—
847C22⋊C4—48no—
848C22⋊C4—48no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4—48no—
853C22⋊C4—44no—
854C22⋊C4—44no—
855C22⋊C4—44no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C22⋊C4—48no—
866C22⋊C4—48no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C22⋊C4—48no—
870C22⋊C4—48no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4—48no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C22⋊C4—48no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C42—24no—
883C42—24no—
884C42—24no—
885C42—24no—
886C42—28no—
887C42—28no—
888C42—48no—
889C42—48no—
890C23—22no—
891C23—21no—
892C23—21no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—24no—
897C23—24no—
898C23—24no—
899C23—24no—
900C23—24no—
901C23—24no—
902C23—24no—
903C23—28no—
904C23—24no—
905C23—24no—
906C23—22no—
907C23—28no—
908C23—24no—
909C23—24no—
910C23—24no—
911C23—24no—
912C23—24no—
913C23—22no—
914C23—22no—
915C23—24no—
916C23—24no—
917C23—24no—
918C23—22no—
919C23—44no—
920C23—44no—
921C23—416no—
922C23—44no—
923C23—48no—
924C23—84no—
925C23—84no—
926C23—84no—
927C23—84no—
928C23—88no—
929C23—88no—
930C23—164no—
931C23—164no—
932C23—168no—
933C23—168no—
934C23C2×H(5,𝔽2)14yes—
935C23C2×H(5,𝔽2)12yes—
936C23C2611yescharacteristic
937Q8—48no—
938Q8—48no—
939D4—432no—
940D4—416no—
941D4—416no—
942D4—416no—
943D4—48no—
944D4—48no—
945D4—88no—
946D4—88no—
947D4—88no—
948D4—88no—
949D4—88no—
950D4—88no—
951D4—816no—
952D4—164no—
953D4—168no—
954D4—168no—
955D4—168no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—28no—
966C2×C4—24no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—28no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—24no—
984C2×C4—28no—
985C2×C4—24no—
986C2×C4—28no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—24no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—24no—
995C2×C4—416no—
996C2×C4—44no—
997C2×C4—48no—
998C2×C4—48no—
999C2×C4—416no—
1000C2×C4—416no—
1001C2×C4—84no—
1002C2×C4—84no—
1003C2×C4—88no—
1004C2×C4—84no—
1005C2×C4—168no—
1006C2×C4#560116yes—
1007C2×C4C2×H(5,𝔽2)14yes—
1008C2×C4C2×H(5,𝔽2)14yes—
1009C2×C4C2×H(5,𝔽2)14yes—
1010C22—22no—
1011C22—22no—
1012C22—24no—
1013C22—24no—
1014C22—42no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—44no—
1020C22—42no—
1021C22—44no—
1022C22—42no—
1023C22—42no—
1024C22—44no—
1025C22—44no—
1026C22—44no—
1027C22—48no—
1028C22—44no—
1029C22—44no—
1030C22—42no—
1031C22—42no—
1032C22—44no—
1033C22—44no—
1034C22—44no—
1035C22—48no—
1036C22—42no—
1037C22—44no—
1038C22—44no—
1039C22—44no—
1040C22—88no—
1041C22—168no—
1042C22—1616no—
1043C22C2×#56014yes—
1044C22C22×H(5,𝔽2)11yescharacteristic
1045C22C22×H(5,𝔽2)12yes—
1046C22H(7,𝔽2)12yes—
1047C22H(7,𝔽2)11yescharacteristic
1048C222−1+611yescharacteristic
1049C4—42no—
1050C4—42no—
1051C4—44no—
1052C4—42no—
1053C4—42no—
1054C4—44no—
1055C4—44no—
1056C4—48no—
1057C4—44no—
1058C4—44no—
1059C4—41no—
1060C4—41no—
1061C4—44no—
1062C4—44no—
1063C4C2×#56018yes—
1064C2—24no—
1065C2—84no—
1066C2—82no—
1067C2—84no—
1068C2—84no—
1069C2C22×#56011yescharacteristic
1070C2#6287411yescharacteristic
1071C2#6287511yescharacteristic
1072C2#6287812yes—
1073C2#6288012yes—
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. #53152C2semidirect
2. #53129C2semidirect
3. #53102C2semidirect
4. #53096C2semidirect
5. #53063C2semidirect
6. #53053C2semidirect
7. #52981C2semidirect
8. #52971C2semidirect
9. #52586C2semidirect
10. #52548C2semidirect
11. #52313C2semidirect
12. #35565C2semidirect
13. #35564C2semidirect
14. #35545C2semidirect
15. #35531C2semidirect
16. #35518C2semidirect
17. #35513C2semidirect
18. #35512C2semidirect
19. #34633C2semidirect
20. C2×#2624C2semidirect
23. C2×#537C22semidirect
27. C2×#525C22semidirect
29. C2×#520C22semidirect
30. C22×#117C22semidirect
31. #2842C22semidirect
32. #2837C22semidirect
33. #2837C22semidirect
34. #2834C22semidirect
35. #2829C22semidirect
36. #2829C22semidirect
37. #2829C22semidirect
38. #2828C22semidirect
39. #2828C22semidirect
40. #2826C22semidirect
41. #2826C22semidirect
42. #2825C22semidirect
43. #2825C22semidirect
44. #2818C22semidirect
45. #2813C22semidirect
46. #2813C22semidirect
47. #2812C22semidirect
48. #2812C22semidirect
49. #2807C22semidirect
50. #2803C22semidirect
51. #2778C22semidirect
52. #2757C22semidirect
53. #2757C22semidirect
54. #2756C22semidirect
55. #2748C22semidirect
56. #2735C22semidirect
57. #2709C22semidirect
58. #2705C22semidirect
59. #2697C22semidirect
60. #2693C22semidirect
61. #2685C22semidirect
62. #2685C22semidirect
63. #2678C22semidirect
64. #2673C22semidirect
65. #2669C22semidirect
66. #2668C22semidirect
67. #2624C22semidirect
68. #2624C22semidirect
69. #2624C22semidirect
70. #2624C22semidirect
71. #2621C22semidirect
72. #2621C22semidirect
73. #2620C22semidirect
74. #2620C22semidirect
75. #2620C22semidirect
76. #2620C22semidirect
77. #2619C22semidirect
78. #2619C22semidirect
79. #2618C22semidirect
80. #2618C22semidirect
81. #2617C22semidirect
82. #2617C22semidirect
83. #2543C22semidirect
84. #2541C22semidirect
85. #2541C22semidirect
86. #2540C22semidirect
87. #2540C22semidirect
88. #2539C22semidirect
89. #2538C22semidirect
90. #2537C22semidirect
91. #2536C22semidirect
92. #2535C22semidirect
93. #2514C22semidirect
94. #2513C22semidirect
95. #2512C22semidirect
96. #2511C22semidirect
97. #2510C22semidirect
98. #2504C22semidirect
99. #2501C22semidirect
100. #2500C22semidirect
101. #2500C22semidirect
102. #2497C22semidirect
103. #2496C22semidirect
104. #2495C22semidirect
105. #2494C22semidirect
106. #2481C22semidirect
107. #2448C22semidirect
108. #2448C22semidirect
109. #2445C22semidirect
110. #2445C22semidirect
111. #2435C22semidirect
112. #2433C22semidirect
113. #2433C22semidirect
114. #2432C22semidirect
115. #2431C22semidirect
116. #2429C22semidirect
117. #2428C22semidirect
118. #2427C22semidirect
119. #2426C22semidirect
120. #2425C22semidirect
121. #2424C22semidirect
122. #2418C22semidirect
123. #2418C22semidirect
124. #2417C22semidirect
125. #2417C22semidirect
126. #2416C22semidirect
127. #2416C22semidirect
128. #2416C22semidirect
129. #2415C22semidirect
130. #2415C22semidirect
131. #2414C22semidirect
132. #2414C22semidirect
137. #2408C22semidirect
138. #2408C22semidirect
141. #2407C22semidirect
142. #2407C22semidirect
145. C2×#399C22semidirect
146. #2392C22semidirect
147. #2392C22semidirect
148. #2392C22semidirect
149. #2392C22semidirect
150. C2×#397C22semidirect
151. C2×#394C22semidirect
152. #2317C22semidirect
157. #2297C22semidirect
159. C2×#389C22semidirect
160. #2285C22semidirect
161. C2×#380C22semidirect
162. #2274C22semidirect

Maximal subgroups

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

subgroupindex
#531522
#531292
#531022
#530962
#530632
#530532
#529812
#529712
#525862
#525482
#523132
#355652
#355642
#355452
#355312
#355182
#355132
#355122
#346332
C2×#26242