Finite Group Databasebeta

← #8094572

Subgroups — #8094572

Order 512.

5498 conjugacy classes of subgroups.

The subgroup lattice has 1033 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53136C214yesmaximal, complemented
2#53095C214yesmaximal, complemented
3#53051C214yesmaximal, complemented
4#53011C214yesmaximal, complemented
5#52741C218yesmaximal, complemented
6#46335C214yesmaximal, complemented
7#46327C214yesmaximal, complemented
8#45721C214yesmaximal, complemented
9#45677C214yesmaximal, complemented
10#45616C214yesmaximal, complemented
11#45497C214yesmaximal, complemented
12#35674C211yesmaximal, characteristic, complemented
13#35666C211yesmaximal, characteristic, complemented
14#35661C212yesmaximal, complemented
15#35659C212yesmaximal, complemented
16#35311C212yesmaximal, complemented
17#35306C212yesmaximal, complemented
18#35160C212yesmaximal, complemented
19C2×#2542C211yesmaximal, characteristic, complemented
20#34737C212yesmaximal, complemented
21C22×2−1+4C2211yescharacteristic
22C2×#536C2212yes—
23C22×C4⋊Q8C2211yescharacteristic
24C2×#525C2212yes—
25C2×#525C2212yes—
26C22×C22⋊Q8C2212yes—
27C22×C22⋊Q8C2212yes—
28C2×#519C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×#117C2212yes—
31#2857C2214yescomplemented
32#2855C2214yescomplemented
33#2855C2214yescomplemented
34#2852C2218yes—
35#2850C2214yescomplemented
36#2843C2214yescomplemented
37#2841C2218yescomplemented
38#2838C2218yescomplemented
39#2838C2218yescomplemented
40#2830C2214yes—
41#2829C2218yescomplemented
42#2829C2218yescomplemented
43#2828C2214yes—
44#2827C2218yescomplemented
45#2827C2218yescomplemented
46#2826C2218yescomplemented
47#2823C2214yescomplemented
48#2797C2218yes—
49#2796C2218yescomplemented
50#2796C2218yescomplemented
51#2795C2218yescomplemented
52#2795C2214yescomplemented
53#2792C2214yescomplemented
54#2792C2218yescomplemented
55#2790C2218yescomplemented
56#2790C2218yescomplemented
57#2790C2218yescomplemented
58#2784C2214yes—
59#2780C2218yescomplemented
60#2780C2218yescomplemented
61#2752C2218yescomplemented
62#2749C2218yes—
63#2746C2218yescomplemented
64#2746C2218yescomplemented
65#2742C2218yescomplemented
66#2737C2218yes—
67#2714C2218yes—
68#2699C2214yes—
69#2691C2218yes—
70#2643C2218yes—
71#2625C2214yescomplemented
72#2625C2214yescomplemented
73#2621C2214yescomplemented
74#2620C2214yescomplemented
75#2542C2214yes—
76#2542C2214yes—
77#2542C2214yes—
78#2542C2214yes—
79#2538C2214yescomplemented
80#2538C2214yescomplemented
81#2536C2214yescomplemented
82#2536C2214yescomplemented
83#2514C2214yescomplemented
84#2513C2214yescomplemented
85#2512C2214yescomplemented
86#2511C2214yescomplemented
87#2503C2214yescomplemented
88#2502C2214yescomplemented
89#2499C2214yescomplemented
90#2499C2214yescomplemented
91#2497C2214yescomplemented
92#2496C2214yescomplemented
93#2495C2214yescomplemented
94#2494C2214yescomplemented
95#2484C2214yes—
96#2484C2218yes—
97#2484C2214yes—
98#2483C2218yes—
99#2446C2214yescomplemented
100#2446C2214yescomplemented
101#2446C2214yescomplemented
102#2446C2214yescomplemented
103#2434C2214yescomplemented
104#2434C2214yescomplemented
105#2432C2214yescomplemented
106#2432C2214yescomplemented
107#2429C2214yescomplemented
108#2429C2214yescomplemented
109#2426C2214yescomplemented
110#2426C2214yescomplemented
111#2417C2212yes—
112#2417C2212yes—
113#2417C2214yescomplemented
114#2417C2214yescomplemented
115#2416C2212yes—
116#2416C2212yes—
117#2415C2212yes—
118#2415C2212yes—
119#2415C2214yescomplemented
120#2415C2214yescomplemented
121#2414C2212yes—
122#2414C2212yes—
123#2413C2218yes—
124#2413C2218yes—
125#2413C2214yes—
126#2412C2214yes—
127#2412C2218yes—
128#2411C2214yes—
129#2411C2218yes—
130#2410C2214yes—
131#2409C2214yescomplemented
132#2409C2214yescomplemented
133#2409C2214yescomplemented
134#2409C2214yescomplemented
135#2407C2214yescomplemented
136#2407C2214yescomplemented
137#2407C2214yescomplemented
138#2407C2214yescomplemented
139#2406C2214yes—
140#2406C2218yes—
141#2406C2214yes—
142#2404C2218yes—
143C2×#399C2214yes—
144#2392C2214yes—
145#2392C2214yes—
146#2383C2218yescomplemented
147#2377C2218yes—
148#2317C2212yes—
149#2317C2212yes—
150#2311C2212yes—
151#2311C2212yes—
152#2310C2212yes—
153#2310C2211yescharacteristic
154#2310C2211yescharacteristic
155C4×#121C2214yes—
156C4×#121C2214yes—
157#2297C2212yes—
158#2296C2212yes—
159C2×#390C2212yes—
160C2×#384C2212yes—
161#2280C2212yes—
162C2×C4×C4⋊C4C2211yescharacteristic
163C2×2−1+4—48no—
164C2×2−1+4—44no—
165C22×#41C2312yes—
166C22×#41C2314yes—
167C22×#41C2314yes—
168C23×Q8C2311yescharacteristic
169C23×Q8C2311yescharacteristic
170C23×Q8C2314yes—
171C23×D4C2311yescharacteristic
172C24×C4C2312yes—
173#536—48no—
174C2×C4⋊Q8—44no—
175C2×C4⋊Q8C2314yes—
176C2×C4⋊Q8C2314yes—
177C2×C4⋊Q8C2314yes—
178C2×#126C2318yes—
179C2×#124C2314yes—
180#525—48no—
181#525—48no—
182C2×#123C2314yes—
183C2×#123C2318yes—
184C2×#123C2314yes—
185C2×C22⋊Q8—48no—
186C2×C22⋊Q8—48no—
187C2×C22⋊Q8C2314yes—
188C2×C22⋊Q8C2314yes—
189C2×C22⋊Q8C2312yes—
190C2×C22⋊Q8C2314yes—
191C2×C22⋊Q8C2312yes—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2312yes—
196C2×C22⋊Q8C2312yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2314yes—
199C2×C22⋊Q8C2314yes—
200C2×C22⋊Q8C2314yes—
201C2×#121C2314yes—
202C2×#121C2312yes—
203C2×#121C2312yes—
204C2×#121C2312yes—
205C2×#121C2312yes—
206C2×#121C2314yes—
207C2×#120C2314yes—
208C2×#120C2314yes—
209#519—44no—
210C2×C4×Q8C2314yes—
211C2×C4×Q8C2314yes—
212C2×C4×D4—44no—
213C2×C4×D4C2312yes—
214C2×C4×D4C2312yes—
215C2×C4×D4C2314yes—
216C2×C4×D4C2314yes—
217C2×C4×D4C2314yes—
218C2×C4×D4C2312yes—
219C2×C4×D4C2312yes—
220C2×C4×D4C2314yes—
221C2×#117—48no—
222C2×#117C2312yes—
223C2×#117C2312yes—
224C2×#117C2312yes—
225C2×#117C2314yes—
226C2×#117C2314yes—
227C2×#117C2312yes—
228C2×#117C2312yes—
229C2×#117C2314yes—
230C22×C4⋊C4C2312yes—
231C22×C4⋊C4C2312yes—
232C22×C4⋊C4C2314yes—
233C22×C4⋊C4C2314yes—
234C22×C4⋊C4C2312yes—
235C22×C4⋊C4C2312yes—
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2312yes—
238C22×C22⋊C4C2312yes—
239C22×C22⋊C4C2314yes—
240C22×C22⋊C4C2314yes—
241C22×C22⋊C4C2314yes—
242C22×C42C2311yescharacteristic
243C22×C42C2314yes—
244C22×C42C2312yes—
245#401C2318yes—
246#400C2318yes—
247#400C2318yes—
248#400C2318yes—
249#400C2318yes—
250#400C2318yes—
251#400C2314yes—
252#400C2318yes—
253#400C2314yes—
254#399C2318yes—
255#399C2318yes—
256#399C2318yes—
257#399C2318yes—
258#398C2318yes—
259#398C2314yes—
260#398C2318yes—
261#398C2318yes—
262#398C2318yes—
263#398C2318yes—
264#398C2314yes—
265#398C2318yes—
266#398C2318yes—
267#398C2314yes—
268#398C2314yes—
269#397C2318yes—
270#397C2318yes—
271#397C2314yes—
272#397C2318yes—
273#397C2318yes—
274#397C2318yes—
275#397C2318yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2314yes—
280#396C2314yes—
281#396C2318yes—
282#396C2318yes—
283#396C2318yes—
284#396C2314yes—
285#396C2318yes—
286#396C2318yes—
287#396C2318yes—
288#396C2314yes—
289#396C2318yes—
290#396C2314yes—
291#395C2314yes—
292#395C2318yes—
293#395C2318yes—
294#395C2318yes—
295#395C2314yes—
296#394C2318yes—
297#394C2314yes—
298#394C2314yes—
299#394C2318yes—
300#394C2318yes—
301#394C2314yes—
302#394C2314yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2314yes—
307#394C2314yes—
308#394C2318yes—
309#394C2314yes—
310#394C2314yes—
311#393C2318yes—
312#393C2318yes—
313#392C2318yes—
314#392C2314yes—
315#392C2318yes—
316#392C2314yes—
317#391C2314yes—
318#391C2314yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2312yes—
328#391C2312yes—
329#390C2314yes—
330#390C2314yes—
331#390C2314yes—
332#390C2314yes—
333#390C2318yes—
334#390C2314yes—
335#390C2318yes—
336#390C2314yes—
337#390C2312yes—
338#390C2312yes—
339#390C2318yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2318yes—
345#389C2318yes—
346#389C2318yes—
347#389C2314yes—
348#389C2318yes—
349#389C2314yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2314yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2314yes—
364#388C2318yes—
365#388C2314yes—
366#388C2314yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#386C2318yes—
379#386C2318yes—
380#386C2314yes—
381#386C2318yes—
382#386C2318yes—
383#386C2318yes—
384#386C2318yes—
385#386C2314yes—
386#386C2314yes—
387#386C2318yes—
388#386C2318yes—
389#386C2314yes—
390#386C2314yes—
391#386C2314yes—
392#385C2318yes—
393#385C2318yes—
394#385C2318yes—
395#385C2318yes—
396#385C2318yes—
397#385C2318yes—
398#385C2318yes—
399#385C2314yes—
400#385C2318yes—
401#385C2318yes—
402#385C2318yes—
403#385C2318yes—
404#385C2318yes—
405#385C2314yes—
406#384C2314yes—
407#384C2314yes—
408#384C2314yes—
409#384C2314yes—
410#384C2318yes—
411#383C2318yes—
412#382C2314yes—
413#382C2314yes—
414#381C2318yes—
415#381C2314yes—
416#381C2314yes—
417#381C2318yes—
418#381C2318yes—
419#381C2314yes—
420#380C2314yes—
421#380C2314yes—
422#380C2314yes—
423#380C2314yes—
424#380C2314yes—
425#380C2318yes—
426#380C2312yes—
427#380C2312yes—
428#380C2318yes—
429#380C2312yes—
430#380C2312yes—
431#380C2314yes—
432#379C2314yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2314yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2314yes—
439C4×C22⋊C4C2314yes—
440C4×C22⋊C4C2314yes—
441C2×#95C2312yes—
442C25C2412yes—
4432−1+4—464no—
444C2×#41—28no—
445C2×#41—28no—
446C2×#41—28no—
447C2×#41—416no—
448C2×#41—48no—
449C2×#41—48no—
450C2×#41—48no—
451C2×#41—48no—
452C22×Q8—24no—
453C22×Q8—28no—
454C22×Q8—28no—
455C22×Q8—24no—
456C22×Q8—48no—
457C22×Q8—48no—
458C22×Q8—48no—
459C22×Q8C2414yes—
460C22×Q8C2414yes—
461C22×Q8C2412yes—
462C22×Q8C2414yes—
463C22×D4—24no—
464C22×D4—42no—
465C22×D4—42no—
466C22×D4C2414yes—
467C22×D4C2412yes—
468C22×D4C2412yes—
469C22×D4C2411yescharacteristic
470C22×D4C2414yes—
471C22×D4C2414yes—
472C22×D4C2414yes—
473C22×D4C2414yes—
474C22×D4C2414yes—
475C22×D4C2411yescharacteristic
476C23×C4—28no—
477C23×C4—28no—
478C23×C4—28no—
479C23×C4C2412yes—
480C23×C4C2412yes—
481C23×C4C2412yes—
482C23×C4C2411yescharacteristic
483C23×C4C2412yes—
484C23×C4C2412yes—
485C23×C4C2412yes—
486C23×C4C2412yes—
487C23×C4C2414yes—
488C23×C4C2414yes—
489C23×C4C2411yescharacteristic
490C23×C4C2414yes—
491C23×C4C2414yes—
492C23×C4C2418yes—
493C23×C4C2411yescharacteristic
494C4⋊Q8—48no—
495C4⋊Q8—48no—
496C4⋊Q8—48no—
497#126—416no—
498#124—48no—
499#123—48no—
500#123—48no—
501#123—416no—
502C22⋊Q8—48no—
503C22⋊Q8—48no—
504C22⋊Q8—48no—
505C22⋊Q8—48no—
506C22⋊Q8—48no—
507C22⋊Q8—48no—
508C22⋊Q8—48no—
509C22⋊Q8—48no—
510C22⋊Q8—44no—
511C22⋊Q8—44no—
512C22⋊Q8—44no—
513C22⋊Q8—44no—
514C22⋊Q8—48no—
515C22⋊Q8—48no—
516#121—216no—
517#121—48no—
518#121—44no—
519#121—44no—
520#121—44no—
521#121—44no—
522#120—48no—
523#120—48no—
524C4×Q8—48no—
525C4×Q8—48no—
526C4×D4—44no—
527C4×D4—44no—
528C4×D4—44no—
529C4×D4—44no—
530C4×D4—48no—
531C4×D4—48no—
532C4×D4—48no—
533C4×D4—48no—
534#117—28no—
535#117—28no—
536#117—28no—
537#117—48no—
538#117—48no—
539#117—48no—
540#117—44no—
541#117—44no—
542C2×C4⋊C4—28no—
543C2×C4⋊C4—44no—
544C2×C4⋊C4—44no—
545C2×C4⋊C4—42no—
546C2×C4⋊C4—48no—
547C2×C4⋊C4—48no—
548C2×C4⋊C4—44no—
549C2×C4⋊C4—44no—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2411yescharacteristic
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2411yescharacteristic
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2418yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2418yes—
579C2×C4⋊C4C2418yes—
580C2×C4⋊C4C2418yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2418yes—
585C2×C4⋊C4C2418yes—
586C2×C22⋊C4—48no—
587C2×C22⋊C4—44no—
588C2×C22⋊C4—48no—
589C2×C22⋊C4—48no—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
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⋊C4C2418yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2418yes—
625C2×C42—24no—
626C2×C42—48no—
627C2×C42—44no—
628C2×C42C2414yes—
629C2×C42C2414yes—
630C2×C42C2414yes—
631C2×C42C2412yes—
632C2×C42C2412yes—
633C2×C42C2414yes—
634C2×C42C2414yes—
635C2×C42C2414yes—
636C2×C42C2418yes—
637C2×C42C2414yes—
638#95C2418yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2414yes—
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2414yes—
651#95C2414yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656#95C2418yes—
657#95C2414yes—
658#95C2418yes—
659#95C2418yes—
660#95C2418yes—
661#95C2418yes—
662#95C2418yes—
663#95C2418yes—
664#95C2418yes—
665#95C2414yes—
666#95C2418yes—
667#95C2418yes—
668#95C2414yes—
669C24—24no—
670C24—24no—
671C24—24no—
672C24—24no—
673C24—42no—
674C24—42no—
675C24—42no—
676C24C2512yes—
677C24C2514yes—
678C24C2512yes—
679C24C2511yescharacteristic
680#41—464no—
681#41—464no—
682#41—432no—
683C2×Q8—28no—
684C2×Q8—28no—
685C2×Q8—28no—
686C2×Q8—28no—
687C2×Q8—28no—
688C2×Q8—24no—
689C2×Q8—24no—
690C2×Q8—28no—
691C2×Q8—24no—
692C2×Q8—44no—
693C2×Q8—48no—
694C2×Q8—464no—
695C2×Q8—416no—
696C2×Q8—416no—
697C2×D4—28no—
698C2×D4—28no—
699C2×D4—28no—
700C2×D4—24no—
701C2×D4—28no—
702C2×D4—28no—
703C2×D4—24no—
704C2×D4—24no—
705C2×D4—24no—
706C2×D4—22no—
707C2×D4—24no—
708C2×D4—41no—
709C2×D4—42no—
710C2×D4—41no—
711C2×D4—41no—
712C2×D4—41no—
713C2×D4—48no—
714C2×D4—44no—
715C2×D4—416no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—44no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C2×D4—44no—
726C2×D42−1+414yescomplemented
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—28no—
732C22×C4—24no—
733C22×C4—28no—
734C22×C4—28no—
735C22×C4—24no—
736C22×C4—24no—
737C22×C4—24no—
738C22×C4—24no—
739C22×C4—28no—
740C22×C4—24no—
741C22×C4—24no—
742C22×C4—24no—
743C22×C4—24no—
744C22×C4—24no—
745C22×C4—24no—
746C22×C4—24no—
747C22×C4—24no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—28no—
751C22×C4—28no—
752C22×C4—24no—
753C22×C4—24no—
754C22×C4—28no—
755C22×C4—44no—
756C22×C4—42no—
757C22×C4—44no—
758C22×C4—48no—
759C22×C4—48no—
760C22×C4—48no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—432no—
767C22×C4H(5,𝔽2)14yes—
768C22×C4H(5,𝔽2)18yes—
769C22×C4C2514yes—
770C22×C4C2514yes—
771C22×C4C2514yes—
772C22×C4C2514yes—
773C22×C4C2512yes—
774C22×C4C2514yes—
775C22×C4C2514yes—
776C22×C4C2514yes—
777C22×C4C2514yes—
778C22×C4C2518yes—
779C22×C4C2512yes—
780C22×C4C2514yes—
781C22×C4C2512yes—
782C22×C4C2511yescharacteristic
783C22×C4C2511yescharacteristic
784C22×C4C2512yes—
785C4⋊C4—28no—
786C4⋊C4—28no—
787C4⋊C4—24no—
788C4⋊C4—24no—
789C4⋊C4—24no—
790C4⋊C4—24no—
791C4⋊C4—24no—
792C4⋊C4—24no—
793C4⋊C4—28no—
794C4⋊C4—28no—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—41no—
798C4⋊C4—42no—
799C4⋊C4—41no—
800C4⋊C4—48no—
801C4⋊C4—48no—
802C4⋊C4—48no—
803C4⋊C4—48no—
804C4⋊C4—44no—
805C4⋊C4—44no—
806C4⋊C4—48no—
807C4⋊C4—44no—
808C4⋊C4—48no—
809C4⋊C4—48no—
810C4⋊C4—44no—
811C4⋊C4—44no—
812C4⋊C4—44no—
813C4⋊C4—44no—
814C4⋊C4—44no—
815C4⋊C4—44no—
816C4⋊C4—44no—
817C4⋊C4—48no—
818C4⋊C4—48no—
819C4⋊C4—48no—
820C4⋊C4—48no—
821C22⋊C4—28no—
822C22⋊C4—28no—
823C22⋊C4—28no—
824C22⋊C4—28no—
825C22⋊C4—28no—
826C22⋊C4—28no—
827C22⋊C4—44no—
828C22⋊C4—44no—
829C22⋊C4—42no—
830C22⋊C4—42no—
831C22⋊C4—42no—
832C22⋊C4—42no—
833C22⋊C4—48no—
834C22⋊C4—48no—
835C22⋊C4—48no—
836C22⋊C4—48no—
837C22⋊C4—44no—
838C22⋊C4—44no—
839C22⋊C4—44no—
840C22⋊C4—48no—
841C22⋊C4—48no—
842C22⋊C4—44no—
843C22⋊C4—44no—
844C22⋊C4—44no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—44no—
848C22⋊C4—44no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4—48no—
853C22⋊C4—48no—
854C22⋊C4—48no—
855C22⋊C4—48no—
856C42—24no—
857C42—24no—
858C42—28no—
859C42—28no—
860C42—28no—
861C42—28no—
862C42—44no—
863C42—44no—
864C42—44no—
865C42—48no—
866C23—21no—
867C23—21no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—24no—
879C23—24no—
880C23—24no—
881C23—24no—
882C23—22no—
883C23—24no—
884C23—22no—
885C23—24no—
886C23—24no—
887C23—22no—
888C23—22no—
889C23—48no—
890C23—48no—
891C23—48no—
892C23—48no—
893C23—84no—
894C23—84no—
895C23—84no—
896C23C2×H(5,𝔽2)12yes—
897C23C2×H(5,𝔽2)14yes—
898C23C2×2−1+414yes—
899C23C2611yescharacteristic
900Q8—416no—
901Q8—416no—
902Q8—416no—
903Q8—48no—
904D4—44no—
905D4—48no—
906D4—44no—
907D4—416no—
908D4—416no—
909D4—48no—
910D4—88no—
911D4—88no—
912D4—88no—
913D4—88no—
914C2×C4—28no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—22no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—22no—
927C2×C4—24no—
928C2×C4—28no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—28no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—28no—
937C2×C4—22no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—28no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—28no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—22no—
955C2×C4—24no—
956C2×C4—44no—
957C2×C4—416no—
958C2×C4—432no—
959C2×C4—48no—
960C2×C4—48no—
961C2×C4—48no—
962C2×C4—48no—
963C2×C4—48no—
964C2×C4—48no—
965C2×C4—48no—
966C2×C4—416no—
967C2×C4—88no—
968C2×C4—88no—
969C2×C4#560116yes—
970C2×C4C2×H(5,𝔽2)14yes—
971C2×C4C2×H(5,𝔽2)14yes—
972C2×C4C2×H(5,𝔽2)14yes—
973C2×C4C2×2−1+412yes—
974C2×C4#58512yes—
975C22—22no—
976C22—22no—
977C22—24no—
978C22—24no—
979C22—24no—
980C22—24no—
981C22—24no—
982C22—42no—
983C22—42no—
984C22—42no—
985C22—42no—
986C22—42no—
987C22—44no—
988C22—42no—
989C22—44no—
990C22—42no—
991C22—44no—
992C22—44no—
993C22—42no—
994C22—44no—
995C22—44no—
996C22—42no—
997C22—42no—
998C22—44no—
999C22—42no—
1000C22—816no—
1001C22C2×#56014yes—
1002C22C22×H(5,𝔽2)11yescharacteristic
1003C22C22×H(5,𝔽2)12yes—
1004C22C22×2−1+411yescharacteristic
1005C22C2×#58511yescharacteristic
1006C222−1+612yes—
1007C4—22no—
1008C4—22no—
1009C4—44no—
1010C4—42no—
1011C4—44no—
1012C4—48no—
1013C4—44no—
1014C4—44no—
1015C4—44no—
1016C4—44no—
1017C4—42no—
1018C4—42no—
1019C4—44no—
1020C4—44no—
1021C4—44no—
1022C4C2×#56018yes—
1023C2—24no—
1024C2—44no—
1025C2—84no—
1026C2—82no—
1027C2C22×#56011yescharacteristic
1028C2#6281911yescharacteristic
1029C2#6288611yescharacteristic
1030C2#6292512yes—
1031C2#6294212yes—
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. #53136C2semidirect
2. #53095C2semidirect
3. #53051C2semidirect
4. #53011C2semidirect
5. #52741C2semidirect
6. #46335C2semidirect
7. #46327C2semidirect
8. #45721C2semidirect
9. #45677C2semidirect
10. #45616C2semidirect
11. #45497C2semidirect
12. #35674C2semidirect
13. #35666C2semidirect
14. #35661C2semidirect
15. #35659C2semidirect
16. #35311C2semidirect
17. #35306C2semidirect
18. #35160C2semidirect
19. C2×#2542C2semidirect
20. #34737C2semidirect
31. #2857C22semidirect
32. #2855C22semidirect
33. #2855C22semidirect
35. #2850C22semidirect
36. #2843C22semidirect
37. #2841C22semidirect
38. #2838C22semidirect
39. #2838C22semidirect
41. #2829C22semidirect
42. #2829C22semidirect
44. #2827C22semidirect
45. #2827C22semidirect
46. #2826C22semidirect
47. #2823C22semidirect
49. #2796C22semidirect
50. #2796C22semidirect
51. #2795C22semidirect
52. #2795C22semidirect
53. #2792C22semidirect
54. #2792C22semidirect
55. #2790C22semidirect
56. #2790C22semidirect
57. #2790C22semidirect
59. #2780C22semidirect
60. #2780C22semidirect
61. #2752C22semidirect
63. #2746C22semidirect
64. #2746C22semidirect
65. #2742C22semidirect
71. #2625C22semidirect
72. #2625C22semidirect
73. #2621C22semidirect
74. #2620C22semidirect
79. #2538C22semidirect
80. #2538C22semidirect
81. #2536C22semidirect
82. #2536C22semidirect
83. #2514C22semidirect
84. #2513C22semidirect
85. #2512C22semidirect
86. #2511C22semidirect
87. #2503C22semidirect
88. #2502C22semidirect
89. #2499C22semidirect
90. #2499C22semidirect
91. #2497C22semidirect
92. #2496C22semidirect
93. #2495C22semidirect
94. #2494C22semidirect
99. #2446C22semidirect
100. #2446C22semidirect
101. #2446C22semidirect
102. #2446C22semidirect
103. #2434C22semidirect
104. #2434C22semidirect
105. #2432C22semidirect
106. #2432C22semidirect
107. #2429C22semidirect
108. #2429C22semidirect
109. #2426C22semidirect
110. #2426C22semidirect
113. #2417C22semidirect
114. #2417C22semidirect
119. #2415C22semidirect
120. #2415C22semidirect
131. #2409C22semidirect
132. #2409C22semidirect
133. #2409C22semidirect
134. #2409C22semidirect
135. #2407C22semidirect
136. #2407C22semidirect
137. #2407C22semidirect
138. #2407C22semidirect
146. #2383C22semidirect
726. C2×D42−1+4semidirect

Maximal subgroups

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

subgroupindex
#531362
#530952
#530512
#530112
#527412
#463352
#463272
#457212
#456772
#456162
#454972
#356742
#356662
#356612
#356592
#353112
#353062
#351602
C2×#25422
#347372