Finite Group Databasebeta

← #8425178

Subgroups — #8425178

Order 512.

5959 conjugacy classes of subgroups.

The subgroup lattice has 1079 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59816C211yesmaximal, characteristic, complemented
2#59660C211yesmaximal, characteristic, complemented
3#59419C211yesmaximal, characteristic, complemented
4#59095C214yesmaximal, complemented
5#53675C214yesmaximal, complemented
6#53528C214yesmaximal, complemented
7#53116C214yesmaximal, complemented
8#52970C214yesmaximal, complemented
9#52422C214yesmaximal, complemented
10#42566C214yesmaximal, complemented
11#42422C214yesmaximal, complemented
12#40602C214yesmaximal, complemented
13#39361C212yesmaximal, complemented
14#39169C212yesmaximal, complemented
15#38997C214yesmaximal, complemented
16#37748C214yesmaximal, complemented
17#37636C211yesmaximal, characteristic, complemented
18#37629C211yesmaximal, characteristic, complemented
19#37493C214yesmaximal, complemented
20#36595C211yesmaximal, characteristic, complemented
21#36289C212yesmaximal, complemented
22#34925C211yesmaximal, characteristic, complemented
23#34918C212yesmaximal, complemented
24C2×#559C2212yescomplemented
25C2×#554C2212yescomplemented
26C2×#550C2212yescomplemented
27C2×#546C2214yescomplemented
28C2×D42C2214yes—
29C2×D42C2212yes—
30C2×#535C2214yescomplemented
31C2×#532C2214yescomplemented
32#2867C2211yescharacteristic
33#2858C2211yescharacteristic
34#2858C2211yescharacteristic, complemented
35#2850C2214yescomplemented
36#2832C2214yescomplemented
37#2830C2214yescomplemented
38#2829C2218yescomplemented
39#2828C2218yescomplemented
40#2826C2218yescomplemented
41#2824C2218yescomplemented
42#2819C2214yescomplemented
43#2814C2214yescomplemented
44#2812C2218yescomplemented
45#2753C2218yescomplemented
46#2750C2218yescomplemented
47#2749C2218yescomplemented
48#2728C2214yescomplemented
49#2699C2214yescomplemented
50#2688C2218yescomplemented
51#2688C2218yescomplemented
52#2686C2218yescomplemented
53#2684C2218yescomplemented
54#2684C2218yescomplemented
55#2679C2214yes—
56#2676C2218yescomplemented
57#2676C2218yescomplemented
58#2676C2218yescomplemented
59#2671C2218yescomplemented
60#2670C2218yescomplemented
61#2669C2218yescomplemented
62#2669C2218yescomplemented
63#2668C2218yescomplemented
64#2668C2218yescomplemented
65#2661C2214yescomplemented
66#2648C2218yescomplemented
67#2644C2214yescomplemented
68#2641C2214yescomplemented
69#2640C2214yescomplemented
70#2638C2214yescomplemented
71#2632C2214yescomplemented
72#2631C2214yescomplemented
73#2628C2214yescomplemented
74#2624C2214yescomplemented
75#2622C2218yescomplemented
76#2619C2214yescomplemented
77#2617C2218yescomplemented
78#2613C2214yescomplemented
79#2597C2214yescomplemented
80#2595C2214yescomplemented
81#2592C2212yescomplemented
82#2582C2211yescharacteristic, complemented
83#2580C2212yescomplemented
84#2570C2212yescomplemented
85#2566C2214yescomplemented
86#2563C2212yescomplemented
87#2555C2214yescomplemented
88#2551C2211yescharacteristic, complemented
89#2548C2212yes—
90#2548C2212yescomplemented
91#2548C2214yescomplemented
92#2544C2212yes—
93#2544C2212yescomplemented
94#2544C2212yescomplemented
95#2543C2214yescomplemented
96#2541C2214yes—
97#2541C2212yescomplemented
98#2537C2211yescharacteristic
99#2537C2211yescharacteristic
100#2537C2214yes—
101#2536C2214yescomplemented
102#2516C2214yescomplemented
103#2513C2212yescomplemented
104#2511C2212yescomplemented
105#2504C2214yescomplemented
106#2495C2214yescomplemented
107#2491C2214yescomplemented
108#2491C2214yescomplemented
109#2490C2214yescomplemented
110#2490C2214yescomplemented
111#2489C2214yescomplemented
112#2472C2218yescomplemented
113#2472C2218yescomplemented
114#2458C2214yescomplemented
115#2456C2218yescomplemented
116#2452C2214yescomplemented
117#2447C2214yescomplemented
118#2447C2212yescomplemented
119#2445C2212yes—
120#2445C2214yescomplemented
121#2445C2214yescomplemented
122#2444C2218yescomplemented
123#2442C2214yescomplemented
124#2435C2214yescomplemented
125#2433C2214yescomplemented
126#2433C2214yescomplemented
127#2433C2214yescomplemented
128#2431C2214yescomplemented
129#2431C2214yescomplemented
130#2430C2214yescomplemented
131#2428C2214yescomplemented
132#2428C2214yescomplemented
133#2428C2214yescomplemented
134#2428C2214yescomplemented
135#2427C2214yescomplemented
136#2424C2218yescomplemented
137#2424C2218yescomplemented
138#2420C2214yescomplemented
139#2418C2218yescomplemented
140#2416C2214yescomplemented
141#2416C2214yescomplemented
142#2410C2218yescomplemented
143#2408C2214yes—
144#2408C2214yes—
145#2408C2214yes—
146#2407C2214yescomplemented
147#2407C2214yescomplemented
148#2404C2218yescomplemented
149#2398C2214yescomplemented
150#2395C2214yescomplemented
151#2388C2214yescomplemented
152#2366C2214yescomplemented
153#2361C2214yescomplemented
154#2339C2214yescomplemented
155D4×C22⋊C4C2214yescomplemented
156D4×C22⋊C4C2214yescomplemented
157#2328C2214yescomplemented
158#2318C2214yescomplemented
159C4×C4⋊Q8C2211yescharacteristic, complemented
160C4×#127C2212yes—
161C4×#127C2211yescharacteristic
162C4×#127C2211yescharacteristic, complemented
163C4×#124C2212yescomplemented
164C4×#124C2212yescomplemented
165C4×#123C2214yescomplemented
166C4×#121C2214yescomplemented
167#2295C2212yescomplemented
168#2293C2212yescomplemented
169C2×#390C2214yescomplemented
170#2290C2214yescomplemented
171C42×Q8C2211yescharacteristic, complemented
172C42×D4C2212yescomplemented
173C22×#41C2314yes—
174C22×#41C2314yes—
175C23×D4C2314yes—
176C23×D4C2314yes—
177C23×D4C2314yes—
178#559—48no—
179#554—48no—
180#550—48no—
181#546—416no—
182D42—48no—
183D42—416no—
184#535—416no—
185#532—416no—
186C2×C4⋊Q8C2311yescharacteristic
187C2×C4⋊Q8C2314yes—
188C2×#127C2311yescharacteristic
189C2×#127C2312yes—
190C2×#127C2311yescharacteristic
191C2×#127C2314yes—
192C2×#127C2314yes—
193C2×#127C2314yes—
194C2×#127C2312yes—
195C2×#127C2314yes—
196C2×#127C2312yes—
197C2×#125C2314yes—
198C2×#124C2312yes—
199C2×#124C2314yes—
200C2×#124C2314yes—
201C2×#124C2312yes—
202C2×#124C2314yes—
203C2×#124C2312yes—
204C2×#124C2312yes—
205C2×#124C2318yes—
206C2×#124C2312yes—
207C2×#124C2312yes—
208C2×#123C2314yes—
209C2×#123C2314yes—
210C2×#123C2314yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2318yes—
214C2×#121C2314yes—
215C2×#121C2314yes—
216C2×#121C2314yes—
217C2×#121C2314yes—
218C2×#121C2314yes—
219C2×#121C2314yes—
220C2×#121C2314yes—
221C2×#121C2314yes—
222C2×#121C2318yes—
223C2×#121C2318yes—
224C2×#121C2318yes—
225C2×#121C2318yes—
226C2×#121C2318yes—
227C2×#121C2318yes—
228C2×#121C2318yes—
229C2×#120C2318yes—
230C2×#120C2318yes—
231C2×#120C2318yes—
232C2×#120C2318yes—
233C2×#120C2318yes—
234C2×#120C2318yes—
235C2×#120C2318yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2312yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2318yes—
255C2×#117C2314yes—
256C22×C4⋊C4C2314yes—
257C22×C22⋊C4C2318yes—
258C22×C22⋊C4C2318yes—
259C22×C42C2314yes—
260#400C2314yes—
261#400C2318yes—
262#400C2318yes—
263#400C2314yes—
264#400C2314yes—
265#399C2314yes—
266#399C2318yes—
267#398C2314yes—
268#398C2314yes—
269#398C2314yes—
270#397C2314yes—
271#397C2318yes—
272#397C2314yes—
273#397C2314yes—
274#397C2318yes—
275#397C2314yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2314yes—
281#397C2314yes—
282#397C2314yes—
283#397C2318yes—
284#396C2318yes—
285#396C2318yes—
286#396C2318yes—
287#395C2314yes—
288#395C2314yes—
289#394C2318yes—
290#394C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2318yes—
294#394C2318yes—
295#394C2318yes—
296#394C2318yes—
297#394C2318yes—
298#394C2318yes—
299#394C2318yes—
300#394C2318yes—
301#394C2318yes—
302#394C2318yes—
303#394C2318yes—
304#394C2318yes—
305#394C2314yes—
306#394C2314yes—
307#394C2314yes—
308#394C2314yes—
309#394C2314yes—
310#394C2314yes—
311#394C2318yes—
312#394C2314yes—
313#394C2314yes—
314#393C2318yes—
315#393C2314yes—
316#393C2314yes—
317#393C2314yes—
318#393C2318yes—
319#393C2318yes—
320#393C2314yes—
321#392C2314yes—
322#392C2314yes—
323#392C2318yes—
324#392C2318yes—
325#392C2318yes—
326#392C2318yes—
327#392C2318yes—
328#392C2318yes—
329#392C2314yes—
330#392C2318yes—
331#392C2314yes—
332#392C2318yes—
333#392C2318yes—
334#392C2318yes—
335#391C2312yes—
336#391C2314yes—
337#391C2312yes—
338#391C2312yes—
339#391C2312yes—
340#391C2312yes—
341#390C2312yes—
342#390C2312yes—
343#390C2312yes—
344#390C2314yes—
345#390C2314yes—
346#390C2314yes—
347#390C2314yes—
348#390C2312yes—
349#390C2314yes—
350#390C2314yes—
351#390C2314yes—
352#390C2318yes—
353#390C2312yes—
354#390C2314yes—
355#390C2312yes—
356#390C2314yes—
357#390C2314yes—
358#390C2314yes—
359#390C2314yes—
360#390C2314yes—
361#390C2318yes—
362#390C2312yes—
363#390C2318yes—
364#390C2312yes—
365#389C2314yes—
366#389C2312yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2314yes—
371#389C2314yes—
372#388C2314yes—
373#388C2318yes—
374#388C2318yes—
375#388C2314yes—
376#388C2314yes—
377#388C2318yes—
378#388C2314yes—
379#388C2314yes—
380#388C2314yes—
381#388C2314yes—
382#388C2318yes—
383#388C2318yes—
384#388C2314yes—
385#388C2314yes—
386#388C2314yes—
387#387C2314yes—
388#387C2314yes—
389#387C2314yes—
390#387C2314yes—
391#387C2314yes—
392#387C2314yes—
393#386C2318yes—
394#386C2318yes—
395#386C2318yes—
396#386C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2318yes—
401#386C2318yes—
402#386C2318yes—
403#386C2318yes—
404#386C2318yes—
405#386C2318yes—
406#386C2314yes—
407#386C2314yes—
408#386C2318yes—
409#386C2318yes—
410#386C2318yes—
411#386C2318yes—
412#386C2314yes—
413#385C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2314yes—
417#385C2314yes—
418#385C2318yes—
419#385C2314yes—
420#384C2311yescharacteristic
421#384C2312yes—
422#383C2314yes—
423#382C2314yes—
424#382C2314yes—
425#382C2312yes—
426#382C2312yes—
427#381C2314yes—
428#381C2318yes—
429#381C2314yes—
430#380C2314yes—
431#380C2314yes—
432#380C2314yes—
433#380C2314yes—
434#380C2318yes—
435#380C2314yes—
436#379C2318yes—
437#379C2318yes—
438#379C2318yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2312yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2312yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4C2314yes—
451C4×C22⋊C4C2314yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2314yes—
454C4×C22⋊C4C2314yes—
455C4×C22⋊C4C2314yes—
456C4×C22⋊C4C2314yes—
457C4×C22⋊C4C2314yes—
458C4×C22⋊C4C2314yes—
459#376C2314yes—
460C2×#95C2314yes—
461C43C2311yescharacteristic
462C43C2311yescharacteristic
463C43C2311yescharacteristic
464C25C2418yes—
465C2×#41—48no—
466C2×#41—416no—
467C2×#41—48no—
468C2×#41—48no—
469C2×#41—48no—
470C22×Q8C2412yes—
471C22×Q8C2411yescharacteristic
472C22×Q8C2412yes—
473C22×Q8C2414yes—
474C22×D4—216no—
475C22×D4—48no—
476C22×D4—48no—
477C22×D4—48no—
478C22×D4—48no—
479C22×D4—48no—
480C22×D4—48no—
481C22×D4—416no—
482C22×D4C2414yes—
483C22×D4C2412yes—
484C22×D4C2414yes—
485C22×D4C2414yes—
486C22×D4C2414yes—
487C22×D4C2412yes—
488C22×D4C2414yes—
489C22×D4C2412yes—
490C22×D4C2418yes—
491C22×D4C2414yes—
492C22×D4C2412yes—
493C22×D4C2418yes—
494C22×D4C2418yes—
495C22×D4C2418yes—
496C22×D4C2414yes—
497C22×D4C2414yes—
498C22×D4C2418yes—
499C22×D4C2418yes—
500C22×D4C2418yes—
501C23×C4C2414yes—
502C23×C4C2414yes—
503C23×C4C2414yes—
504C23×C4C2414yes—
505C23×C4C2414yes—
506C23×C4C2418yes—
507C23×C4C2414yes—
508C23×C4C2418yes—
509C4⋊Q8—24no—
510C4⋊Q8—48no—
511#127—216no—
512#127—28no—
513#127—24no—
514#127—24no—
515#127—48no—
516#127—48no—
517#127—48no—
518#127—44no—
519#127—82no—
520#125—48no—
521#124—28no—
522#124—48no—
523#124—44no—
524#124—44no—
525#124—44no—
526#124—48no—
527#124—48no—
528#124—416no—
529#124—82no—
530#124—82no—
531#123—216no—
532#123—48no—
533#123—48no—
534C22⋊Q8—416no—
535C22⋊Q8—48no—
536C22⋊Q8—48no—
537#121—216no—
538#121—48no—
539#121—416no—
540#121—416no—
541#121—416no—
542#121—416no—
543#121—416no—
544#121—416no—
545#121—48no—
546#121—48no—
547#121—48no—
548#121—48no—
549#121—48no—
550#121—48no—
551#121—88no—
552#120—416no—
553#120—416no—
554#120—416no—
555#120—416no—
556#120—416no—
557#120—416no—
558#120—88no—
559C4×Q8—24no—
560C4×Q8—28no—
561C4×Q8—44no—
562C4×Q8—44no—
563C4×D4—28no—
564C4×D4—216no—
565C4×D4—28no—
566C4×D4—28no—
567C4×D4—48no—
568C4×D4—44no—
569C4×D4—48no—
570C4×D4—48no—
571C4×D4—48no—
572C4×D4—48no—
573C4×D4—48no—
574C4×D4—48no—
575C4×D4—44no—
576C4×D4—44no—
577C4×D4—416no—
578#117—48no—
579C2×C4⋊C4—48no—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2411yescharacteristic
606C2×C22⋊C4—416no—
607C2×C22⋊C4—88no—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2414yes—
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⋊C4C2418yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C42—48no—
652C2×C42C2412yes—
653C2×C42C2414yes—
654C2×C42C2412yes—
655C2×C42C2412yes—
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2414yes—
659C2×C42C2414yes—
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2411yescharacteristic
663C2×C42C2412yes—
664C2×C42C2414yes—
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2414yes—
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670#95C2414yes—
671#95C2414yes—
672#95C2414yes—
673#95C2414yes—
674#95C2414yes—
675#95C2414yes—
676#95C2414yes—
677#95C2414yes—
678#95C2414yes—
679#95C2414yes—
680#95C2414yes—
681#95C2414yes—
682#95C2414yes—
683#95C2414yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2414yes—
689#95C2414yes—
690#95C2414yes—
691#95C2412yes—
692#95C2412yes—
693#95C2412yes—
694#95C2414yes—
695#95C2414yes—
696#95C2418yes—
697#95C2418yes—
698#95C2418yes—
699#95C2418yes—
700C24—216no—
701C24—48no—
702C24—48no—
703C24—48no—
704C24—48no—
705C24—48no—
706C24—48no—
707C24C2514yes—
708C24C2514yes—
709C24C2514yes—
710C24C2514yes—
711#41—832no—
712#41—832no—
713C2×Q8—24no—
714C2×Q8—22no—
715C2×Q8—24no—
716C2×Q8—24no—
717C2×Q8—24no—
718C2×Q8—42no—
719C2×Q8—42no—
720C2×Q8—44no—
721C2×Q8—48no—
722C2×Q8—42no—
723C2×D4—216no—
724C2×D4—28no—
725C2×D4—216no—
726C2×D4—28no—
727C2×D4—216no—
728C2×D4—216no—
729C2×D4—24no—
730C2×D4—24no—
731C2×D4—28no—
732C2×D4—28no—
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—24no—
736C2×D4—28no—
737C2×D4—28no—
738C2×D4—24no—
739C2×D4—24no—
740C2×D4—24no—
741C2×D4—28no—
742C2×D4—24no—
743C2×D4—28no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—44no—
749C2×D4—48no—
750C2×D4—48no—
751C2×D4—48no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—44no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—44no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—48no—
764C2×D4—48no—
765C2×D4—48no—
766C2×D4—48no—
767C2×D4—48no—
768C2×D4—48no—
769C2×D4—48no—
770C2×D4—48no—
771C2×D4—48no—
772C2×D4—48no—
773C2×D4—44no—
774C2×D4—48no—
775C2×D4—832no—
776C2×D4—832no—
777C2×D4—832no—
778C2×D4H(5,𝔽2)18yes—
779C22×C4—28no—
780C22×C4—28no—
781C22×C4—28no—
782C22×C4—28no—
783C22×C4—28no—
784C22×C4—28no—
785C22×C4—28no—
786C22×C4—28no—
787C22×C4—28no—
788C22×C4—28no—
789C22×C4—44no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—48no—
793C22×C4—48no—
794C22×C4—48no—
795C22×C4—44no—
796C22×C4—48no—
797C22×C4—48no—
798C22×C4—48no—
799C22×C4—48no—
800C22×C4—48no—
801C22×C4C2512yes—
802C22×C4C2514yes—
803C22×C4C2514yes—
804C22×C4C2514yes—
805C22×C4C2512yes—
806C22×C4C2511yescharacteristic
807C22×C4C2511yescharacteristic
808C22×C4C2512yes—
809C22×C4C2514yes—
810C22×C4C2514yes—
811C22×C4C2514yes—
812C22×C4C2514yes—
813C22×C4C2511yescharacteristic
814C22×C4C2514yes—
815C22×C4C2511yescharacteristic
816C22×C4C2511yescharacteristic
817C22×C4C2511yescharacteristic
818C22×C4C2511yescharacteristic
819C22×C4C2512yes—
820C4⋊C4—24no—
821C4⋊C4—28no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—28no—
826C4⋊C4—28no—
827C4⋊C4—22no—
828C4⋊C4—22no—
829C4⋊C4—28no—
830C4⋊C4—24no—
831C4⋊C4—48no—
832C4⋊C4—44no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4—42no—
836C4⋊C4—44no—
837C4⋊C4—44no—
838C4⋊C4—48no—
839C4⋊C4—42no—
840C4⋊C4—42no—
841C4⋊C4—42no—
842C4⋊C4—44no—
843C4⋊C4—44no—
844C4⋊C4—48no—
845C4⋊C4H(5,𝔽2)14yes—
846C22⋊C4—28no—
847C22⋊C4—216no—
848C22⋊C4—28no—
849C22⋊C4—28no—
850C22⋊C4—28no—
851C22⋊C4—28no—
852C22⋊C4—28no—
853C22⋊C4—28no—
854C22⋊C4—28no—
855C22⋊C4—28no—
856C22⋊C4—28no—
857C22⋊C4—48no—
858C22⋊C4—48no—
859C22⋊C4—44no—
860C22⋊C4—48no—
861C22⋊C4—48no—
862C22⋊C4—48no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C22⋊C4—44no—
866C22⋊C4—44no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C22⋊C4—48no—
870C22⋊C4—44no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4—48no—
874C22⋊C4—48no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C22⋊C4—48no—
878C22⋊C4—48no—
879C22⋊C4—48no—
880C22⋊C4—48no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C42—24no—
890C42—28no—
891C42—24no—
892C42—28no—
893C42—24no—
894C42—22no—
895C42—22no—
896C42—28no—
897C42—22no—
898C42—24no—
899C42—24no—
900C42—24no—
901C42—44no—
902C42—44no—
903C42—41no—
904C42—41no—
905C42—41no—
906C42H(5,𝔽2)14yes—
907C23—24no—
908C23—24no—
909C23—24no—
910C23—24no—
911C23—24no—
912C23—24no—
913C23—24no—
914C23—24no—
915C23—24no—
916C23—24no—
917C23—24no—
918C23—28no—
919C23—24no—
920C23—28no—
921C23—24no—
922C23—24no—
923C23—24no—
924C23—24no—
925C23—28no—
926C23—28no—
927C23—24no—
928C23—24no—
929C23—24no—
930C23—816no—
931C23—816no—
932C23—816no—
933C23—816no—
934C23—816no—
935C23—168no—
936C23—168no—
937C23C2×H(5,𝔽2)18yes—
938C23C2611yescharacteristic
939Q8—44no—
940Q8—48no—
941Q8—84no—
942Q8—88no—
943D4—216no—
944D4—416no—
945D4—416no—
946D4—48no—
947D4—416no—
948D4—416no—
949D4—88no—
950D4—84no—
951D4—84no—
952D4—816no—
953D4—88no—
954D4—816no—
955D4—816no—
956D4—816no—
957D4—88no—
958D4—816no—
959D4—164no—
960D4—168no—
961D4—168no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—22no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—22no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—21no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—28no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—416no—
1006C2×C4—416no—
1007C2×C4—416no—
1008C2×C4—88no—
1009C2×C4—88no—
1010C2×C4—88no—
1011C2×C4—816no—
1012C2×C4—168no—
1013C2×C4C2×H(5,𝔽2)12yes—
1014C2×C4C2×H(5,𝔽2)12yes—
1015C2×C4C2×H(5,𝔽2)12yes—
1016C2×C4C2×H(5,𝔽2)12yes—
1017C2×C4C2×H(5,𝔽2)14yes—
1018C2×C4C2×H(5,𝔽2)14yes—
1019C2×C4#58514yes—
1020C22—28no—
1021C22—28no—
1022C22—28no—
1023C22—44no—
1024C22—44no—
1025C22—44no—
1026C22—44no—
1027C22—44no—
1028C22—48no—
1029C22—48no—
1030C22—44no—
1031C22—44no—
1032C22—44no—
1033C22—44no—
1034C22—44no—
1035C22—44no—
1036C22—44no—
1037C22—44no—
1038C22—44no—
1039C22—44no—
1040C22—48no—
1041C22—44no—
1042C22—48no—
1043C22—44no—
1044C22—1632no—
1045C22C22×H(5,𝔽2)11yescharacteristic
1046C22C22×H(5,𝔽2)12yes—
1047C22C22×H(5,𝔽2)11yescharacteristic
1048C22C2×#58512yes—
1049C22H(7,𝔽2)11yescharacteristic
1050C4—22no—
1051C4—22no—
1052C4—22no—
1053C4—22no—
1054C4—44no—
1055C4—44no—
1056C4—44no—
1057C4—44no—
1058C4—44no—
1059C4—41no—
1060C4—41no—
1061C4—41no—
1062C4—44no—
1063C4—44no—
1064C4—42no—
1065C4—44no—
1066C4—42no—
1067C4—42no—
1068C4#355818yes—
1069C2—48no—
1070C2—84no—
1071C2—84no—
1072C2—84no—
1073C2C2×#355812yes—
1074C2#6275911yescharacteristic
1075C2#6291611yescharacteristic
1076C2#6292012yes—
1077C2#6301111yescharacteristic
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. #59816C2semidirect
2. #59660C2semidirect
3. #59419C2semidirect
4. #59095C2semidirect
5. #53675C2semidirect
6. #53528C2semidirect
7. #53116C2semidirect
8. #52970C2semidirect
9. #52422C2semidirect
10. #42566C2semidirect
11. #42422C2semidirect
12. #40602C2semidirect
13. #39361C2semidirect
14. #39169C2semidirect
15. #38997C2semidirect
16. #37748C2semidirect
17. #37636C2semidirect
18. #37629C2semidirect
19. #37493C2semidirect
20. #36595C2semidirect
21. #36289C2semidirect
22. #34925C2semidirect
23. #34918C2semidirect
24. C2×#559C22semidirect
25. C2×#554C22semidirect
26. C2×#550C22semidirect
27. C2×#546C22semidirect
30. C2×#535C22semidirect
31. C2×#532C22semidirect
34. #2858C22semidirect
35. #2850C22semidirect
36. #2832C22semidirect
37. #2830C22semidirect
38. #2829C22semidirect
39. #2828C22semidirect
40. #2826C22semidirect
41. #2824C22semidirect
42. #2819C22semidirect
43. #2814C22semidirect
44. #2812C22semidirect
45. #2753C22semidirect
46. #2750C22semidirect
47. #2749C22semidirect
48. #2728C22semidirect
49. #2699C22semidirect
50. #2688C22semidirect
51. #2688C22semidirect
52. #2686C22semidirect
53. #2684C22semidirect
54. #2684C22semidirect
56. #2676C22semidirect
57. #2676C22semidirect
58. #2676C22semidirect
59. #2671C22semidirect
60. #2670C22semidirect
61. #2669C22semidirect
62. #2669C22semidirect
63. #2668C22semidirect
64. #2668C22semidirect
65. #2661C22semidirect
66. #2648C22semidirect
67. #2644C22semidirect
68. #2641C22semidirect
69. #2640C22semidirect
70. #2638C22semidirect
71. #2632C22semidirect
72. #2631C22semidirect
73. #2628C22semidirect
74. #2624C22semidirect
75. #2622C22semidirect
76. #2619C22semidirect
77. #2617C22semidirect
78. #2613C22semidirect
79. #2597C22semidirect
80. #2595C22semidirect
81. #2592C22semidirect
82. #2582C22semidirect
83. #2580C22semidirect
84. #2570C22semidirect
85. #2566C22semidirect
86. #2563C22semidirect
87. #2555C22semidirect
88. #2551C22semidirect
90. #2548C22semidirect
91. #2548C22semidirect
93. #2544C22semidirect
94. #2544C22semidirect
95. #2543C22semidirect
97. #2541C22semidirect
101. #2536C22semidirect
102. #2516C22semidirect
103. #2513C22semidirect
104. #2511C22semidirect
105. #2504C22semidirect
106. #2495C22semidirect
107. #2491C22semidirect
108. #2491C22semidirect
109. #2490C22semidirect
110. #2490C22semidirect
111. #2489C22semidirect
112. #2472C22semidirect
113. #2472C22semidirect
114. #2458C22semidirect
115. #2456C22semidirect
116. #2452C22semidirect
117. #2447C22semidirect
118. #2447C22semidirect
120. #2445C22semidirect
121. #2445C22semidirect
122. #2444C22semidirect
123. #2442C22semidirect
124. #2435C22semidirect
125. #2433C22semidirect
126. #2433C22semidirect
127. #2433C22semidirect
128. #2431C22semidirect
129. #2431C22semidirect
130. #2430C22semidirect
131. #2428C22semidirect
132. #2428C22semidirect
133. #2428C22semidirect
134. #2428C22semidirect
135. #2427C22semidirect
136. #2424C22semidirect
137. #2424C22semidirect
138. #2420C22semidirect
139. #2418C22semidirect
140. #2416C22semidirect
141. #2416C22semidirect
142. #2410C22semidirect
146. #2407C22semidirect
147. #2407C22semidirect
148. #2404C22semidirect
149. #2398C22semidirect
150. #2395C22semidirect
151. #2388C22semidirect
152. #2366C22semidirect
153. #2361C22semidirect
154. #2339C22semidirect
155. D4×C22⋊C4C22semidirect
156. D4×C22⋊C4C22semidirect
157. #2328C22semidirect
158. #2318C22semidirect
159. C4×C4⋊Q8C22semidirect
162. C4×#127C22semidirect
163. C4×#124C22semidirect
164. C4×#124C22semidirect
165. C4×#123C22semidirect
166. C4×#121C22semidirect
167. #2295C22semidirect
168. #2293C22semidirect
169. C2×#390C22semidirect
170. #2290C22semidirect
171. C42×Q8C22semidirect
172. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#598162
#596602
#594192
#590952
#536752
#535282
#531162
#529702
#524222
#425662
#424222
#406022
#393612
#391692
#389972
#377482
#376362
#376292
#374932
#365952
#362892
#349252
#349182