Finite Group Databasebeta

← #8094873

Subgroups — #8094873

Order 512.

5146 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53122C214yesmaximal, complemented
2#53097C214yesmaximal, complemented
3#53061C214yesmaximal, complemented
4#52963C214yesmaximal, complemented
5#52510C218yesmaximal, complemented
6#46098C214yesmaximal, complemented
7#45976C214yesmaximal, complemented
8#45720C214yesmaximal, complemented
9#45664C214yesmaximal, complemented
10#45631C214yesmaximal, complemented
11#45482C214yesmaximal, complemented
12#35574C212yesmaximal, complemented
13#35518C212yesmaximal, complemented
14#35516C212yesmaximal, complemented
15#35263C212yesmaximal, complemented
16#35253C212yesmaximal, complemented
17#35159C211yesmaximal, characteristic, complemented
18#35158C211yesmaximal, characteristic, complemented
19C2×#2547C211yesmaximal, characteristic, complemented
20#34737C212yesmaximal, complemented
21C2×#562C2214yes—
22C2×#544C2211yescharacteristic
23C2×#537C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25C22×#124C2212yes—
26C2×#525C2212yes—
27C2×#525C2212yes—
28C2×#520C2212yes—
29C22×C4×D4C2211yescharacteristic
30C22×#117C2212yes—
31#2857C2214yescomplemented
32#2855C2214yescomplemented
33#2854C2214yescomplemented
34#2851C2214yes—
35#2851C2214yescomplemented
36#2850C2214yes—
37#2836C2218yescomplemented
38#2836C2218yescomplemented
39#2831C2218yescomplemented
40#2830C2218yescomplemented
41#2829C2218yescomplemented
42#2827C2218yescomplemented
43#2827C2218yescomplemented
44#2826C2218yescomplemented
45#2820C2214yes—
46#2819C2214yes—
47#2814C2218yescomplemented
48#2808C2214yescomplemented
49#2806C2214yescomplemented
50#2806C2214yescomplemented
51#2786C2218yescomplemented
52#2786C2218yescomplemented
53#2755C2218yescomplemented
54#2754C2218yescomplemented
55#2751C2218yescomplemented
56#2747C2218yescomplemented
57#2739C2218yescomplemented
58#2732C2214yescomplemented
59#2730C2218yes—
60#2710C2218yes—
61#2708C2218yescomplemented
62#2704C2218yescomplemented
63#2701C2218yescomplemented
64#2700C2218yes—
65#2700C2218yescomplemented
66#2687C2218yescomplemented
67#2686C2218yes—
68#2676C2218yes—
69#2672C2218yes—
70#2646C2214yes—
71#2639C2214yes—
72#2629C2214yescomplemented
73#2628C2214yescomplemented
74#2625C2214yescomplemented
75#2624C2214yescomplemented
76#2579C2218yes—
77#2547C2214yes—
78#2547C2214yes—
79#2547C2214yes—
80#2547C2214yes—
81#2538C2214yescomplemented
82#2537C2214yescomplemented
83#2536C2214yescomplemented
84#2535C2214yescomplemented
85#2509C2214yescomplemented
86#2508C2214yescomplemented
87#2507C2214yescomplemented
88#2506C2214yescomplemented
89#2498C2218yes—
90#2492C2214yescomplemented
91#2491C2214yescomplemented
92#2490C2214yescomplemented
93#2489C2214yescomplemented
94#2487C2214yescomplemented
95#2487C2214yescomplemented
96#2486C2214yescomplemented
97#2486C2214yescomplemented
98#2485C2214yescomplemented
99#2485C2214yescomplemented
100#2485C2214yescomplemented
101#2485C2214yescomplemented
102#2452C2214yescomplemented
103#2452C2214yescomplemented
104#2451C2214yescomplemented
105#2451C2214yescomplemented
106#2442C2214yescomplemented
107#2441C2214yescomplemented
108#2440C2214yescomplemented
109#2440C2214yescomplemented
110#2440C2214yescomplemented
111#2439C2214yescomplemented
112#2439C2214yescomplemented
113#2439C2214yescomplemented
114#2438C2218yes—
115#2437C2218yes—
116#2425C2218yes—
117#2424C2218yes—
118#2423C2214yescomplemented
119#2422C2214yescomplemented
120#2421C2214yescomplemented
121#2420C2214yescomplemented
122#2419C2218yes—
123#2418C2218yes—
124#2417C2212yes—
125#2417C2212yes—
126#2417C2214yescomplemented
127#2416C2212yes—
128#2416C2212yes—
129#2416C2214yescomplemented
130#2415C2212yes—
131#2415C2212yes—
132#2415C2214yescomplemented
133#2414C2212yes—
134#2414C2212yes—
135#2414C2214yescomplemented
136#2413C2214yes—
137#2412C2214yes—
138#2412C2218yes—
139#2411C2214yes—
140#2410C2214yes—
141#2409C2218yes—
142#2392C2214yes—
143#2392C2214yes—
144C2×#397C2214yes—
145#2379C2214yes—
146#2378C2218yescomplemented
147#2317C2212yes—
148#2317C2212yes—
149#2316C2211yescharacteristic
150#2316C2211yescharacteristic
151#2316C2212yes—
152#2311C2212yes—
153#2311C2212yes—
154C4×#121C2214yes—
155C4×#121C2214yes—
156#2297C2212yes—
157#2296C2212yes—
158C2×#391C2212yes—
159#2280C2212yes—
160C2×#380C2212yes—
161C2×#380C2212yes—
162C2×C4×C4⋊C4C2211yescharacteristic
163C22×#41C2312yes—
164C23×Q8C2312yes—
165C23×D4C2311yescharacteristic
166C24×C4C2312yes—
167#562—416no—
168#544—44no—
169#537—44no—
170C2×C4⋊Q8—44no—
171C2×C4⋊Q8C2314yes—
172C2×C4⋊Q8C2314yes—
173C2×C4⋊Q8C2314yes—
174C2×#125C2314yes—
175C2×#125C2314yes—
176C2×#124—48no—
177C2×#124C2314yes—
178C2×#124C2314yes—
179C2×#124C2314yes—
180C2×#124C2318yes—
181#525—48no—
182#525—48no—
183C2×#123C2318yes—
184C2×#123C2314yes—
185C2×#123C2314yes—
186C2×#123C2318yes—
187C2×C22⋊Q8C2314yes—
188C2×C22⋊Q8C2312yes—
189C2×C22⋊Q8C2318yes—
190C2×C22⋊Q8C2312yes—
191C2×C22⋊Q8C2318yes—
192C2×C22⋊Q8C2318yes—
193C2×C22⋊Q8C2312yes—
194C2×C22⋊Q8C2312yes—
195C2×C22⋊Q8C2314yes—
196C2×#121C2314yes—
197C2×#121C2314yes—
198C2×#121C2312yes—
199C2×#121C2312yes—
200C2×#121C2314yes—
201C2×#121C2312yes—
202C2×#121C2312yes—
203C2×#121C2314yes—
204C2×#121C2318yes—
205C2×#120C2314yes—
206C2×#120C2314yes—
207#520—48no—
208C2×C4×Q8C2314yes—
209C2×C4×D4—44no—
210C2×C4×D4C2318yes—
211C2×C4×D4C2312yes—
212C2×C4×D4C2312yes—
213C2×C4×D4C2314yes—
214C2×C4×D4C2314yes—
215C2×C4×D4C2314yes—
216C2×C4×D4C2312yes—
217C2×C4×D4C2312yes—
218C2×C4×D4C2314yes—
219C2×C4×D4C2314yes—
220C2×#117—48no—
221C2×#117C2312yes—
222C2×#117C2312yes—
223C2×#117C2312yes—
224C2×#117C2314yes—
225C2×#117C2314yes—
226C2×#117C2312yes—
227C2×#117C2312yes—
228C2×#117C2314yes—
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2312yes—
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2312yes—
233C22×C4⋊C4C2312yes—
234C22×C4⋊C4C2312yes—
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2314yes—
237C22×C22⋊C4C2312yes—
238C22×C22⋊C4C2314yes—
239C22×C22⋊C4C2314yes—
240C22×C22⋊C4C2314yes—
241C22×C42C2311yescharacteristic
242C22×C42C2312yes—
243C22×C42C2314yes—
244#400C2318yes—
245#400C2318yes—
246#400C2318yes—
247#400C2318yes—
248#400C2318yes—
249#400C2318yes—
250#399C2318yes—
251#399C2318yes—
252#399C2318yes—
253#398C2318yes—
254#398C2318yes—
255#398C2318yes—
256#398C2314yes—
257#398C2318yes—
258#398C2318yes—
259#398C2318yes—
260#398C2318yes—
261#398C2318yes—
262#398C2318yes—
263#398C2314yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2314yes—
268#397C2318yes—
269#397C2318yes—
270#397C2318yes—
271#397C2318yes—
272#397C2318yes—
273#397C2318yes—
274#397C2318yes—
275#397C2314yes—
276#397C2318yes—
277#397C2318yes—
278#396C2318yes—
279#396C2318yes—
280#396C2318yes—
281#396C2318yes—
282#396C2314yes—
283#396C2318yes—
284#396C2318yes—
285#396C2314yes—
286#396C2314yes—
287#396C2314yes—
288#395C2318yes—
289#395C2318yes—
290#395C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2314yes—
294#394C2314yes—
295#394C2314yes—
296#394C2318yes—
297#394C2318yes—
298#394C2318yes—
299#394C2318yes—
300#394C2314yes—
301#394C2318yes—
302#394C2314yes—
303#394C2314yes—
304#394C2318yes—
305#393C2318yes—
306#393C2318yes—
307#393C2318yes—
308#393C2318yes—
309#392C2314yes—
310#392C2318yes—
311#392C2314yes—
312#391C2314yes—
313#391C2314yes—
314#391C2314yes—
315#391C2314yes—
316#391C2318yes—
317#391C2314yes—
318#391C2318yes—
319#391C2318yes—
320#391C2312yes—
321#391C2312yes—
322#391C2318yes—
323#390C2314yes—
324#390C2314yes—
325#390C2314yes—
326#390C2318yes—
327#390C2314yes—
328#390C2314yes—
329#390C2312yes—
330#390C2312yes—
331#389C2314yes—
332#389C2314yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2318yes—
344#389C2318yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2312yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#388C2318yes—
354#388C2318yes—
355#388C2314yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2314yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2314yes—
364#388C2314yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#386C2318yes—
376#386C2318yes—
377#386C2318yes—
378#386C2318yes—
379#386C2314yes—
380#386C2318yes—
381#386C2314yes—
382#386C2314yes—
383#386C2318yes—
384#386C2314yes—
385#386C2314yes—
386#386C2314yes—
387#385C2318yes—
388#385C2318yes—
389#385C2318yes—
390#385C2318yes—
391#385C2318yes—
392#385C2318yes—
393#385C2318yes—
394#385C2314yes—
395#385C2314yes—
396#385C2318yes—
397#384C2314yes—
398#384C2314yes—
399#382C2314yes—
400#382C2314yes—
401#382C2314yes—
402#382C2314yes—
403#381C2318yes—
404#381C2318yes—
405#381C2314yes—
406#380C2314yes—
407#380C2314yes—
408#380C2314yes—
409#380C2314yes—
410#380C2318yes—
411#380C2314yes—
412#380C2314yes—
413#380C2312yes—
414#380C2314yes—
415#380C2314yes—
416#380C2312yes—
417#380C2318yes—
418#380C2314yes—
419#380C2312yes—
420#380C2314yes—
421#380C2312yes—
422#380C2318yes—
423#380C2314yes—
424#380C2314yes—
425#380C2314yes—
426#380C2314yes—
427#380C2314yes—
428#380C2314yes—
429#379C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2314yes—
436C4×C22⋊C4C2314yes—
437C4×C22⋊C4C2314yes—
438C2×#95C2312yes—
439C2×#95C2314yes—
440C2×#95C2314yes—
441C25C2412yes—
442C2×#41—28no—
443C2×#41—28no—
444C2×#41—28no—
445C22×Q8—44no—
446C22×Q8—44no—
447C22×Q8—44no—
448C22×Q8C2412yes—
449C22×Q8C2414yes—
450C22×Q8C2414yes—
451C22×Q8C2414yes—
452C22×D4—24no—
453C22×D4—42no—
454C22×D4—42no—
455C22×D4C2414yes—
456C22×D4C2412yes—
457C22×D4C2412yes—
458C22×D4C2411yescharacteristic
459C22×D4C2414yes—
460C22×D4C2414yes—
461C22×D4C2414yes—
462C22×D4C2414yes—
463C22×D4C2414yes—
464C22×D4C2411yescharacteristic
465C23×C4—28no—
466C23×C4—28no—
467C23×C4—28no—
468C23×C4C2412yes—
469C23×C4C2412yes—
470C23×C4C2414yes—
471C23×C4C2411yescharacteristic
472C23×C4C2412yes—
473C23×C4C2412yes—
474C23×C4C2412yes—
475C23×C4C2414yes—
476C23×C4C2411yescharacteristic
477C23×C4C2412yes—
478C23×C4C2412yes—
479C23×C4C2414yes—
480C23×C4C2414yes—
481C23×C4C2418yes—
482C23×C4C2411yescharacteristic
483C4⋊Q8—48no—
484C4⋊Q8—48no—
485C4⋊Q8—48no—
486#125—48no—
487#125—48no—
488#124—216no—
489#124—48no—
490#124—48no—
491#124—416no—
492#123—416no—
493#123—48no—
494#123—48no—
495#123—416no—
496C22⋊Q8—48no—
497C22⋊Q8—416no—
498C22⋊Q8—416no—
499C22⋊Q8—416no—
500C22⋊Q8—44no—
501C22⋊Q8—44no—
502C22⋊Q8—44no—
503C22⋊Q8—44no—
504C22⋊Q8—48no—
505#121—216no—
506#121—48no—
507#121—416no—
508#121—44no—
509#121—44no—
510#121—44no—
511#121—44no—
512#121—48no—
513#121—48no—
514#120—48no—
515#120—48no—
516C4×Q8—48no—
517C4×D4—48no—
518C4×D4—44no—
519C4×D4—44no—
520C4×D4—44no—
521C4×D4—44no—
522C4×D4—48no—
523C4×D4—48no—
524C4×D4—48no—
525C4×D4—48no—
526C4×D4—416no—
527#117—28no—
528#117—28no—
529#117—28no—
530#117—48no—
531#117—48no—
532#117—44no—
533#117—44no—
534#117—48no—
535C2×C4⋊C4—28no—
536C2×C4⋊C4—24no—
537C2×C4⋊C4—24no—
538C2×C4⋊C4—44no—
539C2×C4⋊C4—44no—
540C2×C4⋊C4—48no—
541C2×C4⋊C4—42no—
542C2×C4⋊C4—44no—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2411yescharacteristic
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2411yescharacteristic
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2418yes—
581C2×C22⋊C4—48no—
582C2×C22⋊C4—48no—
583C2×C22⋊C4—48no—
584C2×C22⋊C4—44no—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2412yes—
596C2×C22⋊C4C2412yes—
597C2×C22⋊C4C2412yes—
598C2×C22⋊C4C2412yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2418yes—
620C2×C42—24no—
621C2×C42—48no—
622C2×C42—44no—
623C2×C42C2414yes—
624C2×C42C2414yes—
625C2×C42C2414yes—
626C2×C42C2412yes—
627C2×C42C2412yes—
628C2×C42C2414yes—
629C2×C42C2414yes—
630C2×C42C2414yes—
631C2×C42C2418yes—
632C2×C42C2414yes—
633#95C2418yes—
634#95C2418yes—
635#95C2418yes—
636#95C2418yes—
637#95C2418yes—
638#95C2414yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2414yes—
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2418yes—
651#95C2418yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656#95C2418yes—
657#95C2418yes—
658#95C2418yes—
659#95C2418yes—
660#95C2418yes—
661#95C2418yes—
662C24—24no—
663C24—24no—
664C24—24no—
665C24—24no—
666C24—42no—
667C24—42no—
668C24—42no—
669C24C2512yes—
670C24C2514yes—
671C24C2512yes—
672C24C2511yescharacteristic
673#41—432no—
674C2×Q8—24no—
675C2×Q8—24no—
676C2×Q8—28no—
677C2×Q8—24no—
678C2×Q8—28no—
679C2×Q8—44no—
680C2×Q8—44no—
681C2×Q8—44no—
682C2×Q8—44no—
683C2×Q8—44no—
684C2×Q8—44no—
685C2×Q8—44no—
686C2×Q8—816no—
687C2×D4—28no—
688C2×D4—28no—
689C2×D4—24no—
690C2×D4—28no—
691C2×D4—28no—
692C2×D4—28no—
693C2×D4—24no—
694C2×D4—24no—
695C2×D4—22no—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—41no—
699C2×D4—42no—
700C2×D4—41no—
701C2×D4—41no—
702C2×D4—41no—
703C2×D4—416no—
704C2×D4—44no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—44no—
709C2×D4—44no—
710C2×D4—44no—
711C2×D4—44no—
712C2×D4—44no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4H(5,𝔽2)14yes—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—24no—
723C22×C4—24no—
724C22×C4—24no—
725C22×C4—28no—
726C22×C4—24no—
727C22×C4—28no—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—24no—
731C22×C4—28no—
732C22×C4—24no—
733C22×C4—24no—
734C22×C4—24no—
735C22×C4—24no—
736C22×C4—24no—
737C22×C4—24no—
738C22×C4—28no—
739C22×C4—24no—
740C22×C4—24no—
741C22×C4—24no—
742C22×C4—24no—
743C22×C4—28no—
744C22×C4—41no—
745C22×C4—41no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—42no—
754C22×C4—44no—
755C22×C4—42no—
756C22×C4—44no—
757C22×C4—48no—
758C22×C4—48no—
759C22×C4—48no—
760C22×C4—432no—
761C22×C4H(5,𝔽2)14yes—
762C22×C4H(5,𝔽2)14yes—
763C22×C42−1+414yes—
764C22×C4C2514yes—
765C22×C4C2512yes—
766C22×C4C2514yes—
767C22×C4C2512yes—
768C22×C4C2514yes—
769C22×C4C2514yes—
770C22×C4C2512yes—
771C22×C4C2514yes—
772C22×C4C2514yes—
773C22×C4C2514yes—
774C22×C4C2518yes—
775C22×C4C2514yes—
776C22×C4C2514yes—
777C22×C4C2511yescharacteristic
778C22×C4C2511yescharacteristic
779C22×C4C2512yes—
780C4⋊C4—28no—
781C4⋊C4—28no—
782C4⋊C4—28no—
783C4⋊C4—24no—
784C4⋊C4—24no—
785C4⋊C4—24no—
786C4⋊C4—24no—
787C4⋊C4—24no—
788C4⋊C4—24no—
789C4⋊C4—28no—
790C4⋊C4—28no—
791C4⋊C4—28no—
792C4⋊C4—44no—
793C4⋊C4—44no—
794C4⋊C4—41no—
795C4⋊C4—42no—
796C4⋊C4—41no—
797C4⋊C4—48no—
798C4⋊C4—48no—
799C4⋊C4—44no—
800C4⋊C4—44no—
801C4⋊C4—44no—
802C4⋊C4—44no—
803C4⋊C4—48no—
804C4⋊C4—44no—
805C4⋊C4—44no—
806C4⋊C4—44no—
807C4⋊C4—44no—
808C4⋊C4—44no—
809C4⋊C4—48no—
810C4⋊C4—48no—
811C4⋊C4—48no—
812C4⋊C4—48no—
813C4⋊C4—48no—
814C4⋊C4—44no—
815C4⋊C4—48no—
816C4⋊C4—44no—
817C4⋊C4—44no—
818C22⋊C4—28no—
819C22⋊C4—28no—
820C22⋊C4—216no—
821C22⋊C4—216no—
822C22⋊C4—28no—
823C22⋊C4—28no—
824C22⋊C4—28no—
825C22⋊C4—28no—
826C22⋊C4—44no—
827C22⋊C4—44no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—42no—
831C22⋊C4—42no—
832C22⋊C4—48no—
833C22⋊C4—48no—
834C22⋊C4—44no—
835C22⋊C4—48no—
836C22⋊C4—44no—
837C22⋊C4—44no—
838C22⋊C4—44no—
839C22⋊C4—48no—
840C22⋊C4—44no—
841C22⋊C4—44no—
842C22⋊C4—44no—
843C22⋊C4—44no—
844C22⋊C4—44no—
845C22⋊C4—44no—
846C22⋊C4—44no—
847C22⋊C4—44no—
848C22⋊C4—44no—
849C22⋊C4—48no—
850C22⋊C4—48no—
851C22⋊C4—48no—
852C22⋊C4—48no—
853C42—24no—
854C42—24no—
855C42—28no—
856C42—28no—
857C42—28no—
858C42—28no—
859C42—44no—
860C42—44no—
861C42—44no—
862C42—48no—
863C23—21no—
864C23—21no—
865C23—21no—
866C23—21no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—24no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—24no—
878C23—24no—
879C23—22no—
880C23—24no—
881C23—24no—
882C23—22no—
883C23—24no—
884C23—22no—
885C23—24no—
886C23—22no—
887C23—48no—
888C23—48no—
889C23—48no—
890C23—48no—
891C23—84no—
892C23—84no—
893C23—84no—
894C23C2×H(5,𝔽2)14yes—
895C23C2×H(5,𝔽2)12yes—
896C23C2×H(5,𝔽2)12yes—
897C23C2×2−1+412yes—
898C23C2611yescharacteristic
899Q8—48no—
900Q8—88no—
901Q8—88no—
902Q8—164no—
903D4—44no—
904D4—48no—
905D4—44no—
906D4—416no—
907D4—48no—
908D4—88no—
909D4—88no—
910D4—88no—
911D4—88no—
912D4—164no—
913C2×C4—28no—
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—22no—
928C2×C4—24no—
929C2×C4—28no—
930C2×C4—28no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—22no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—28no—
947C2×C4—24no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—44no—
958C2×C4—48no—
959C2×C4—48no—
960C2×C4—48no—
961C2×C4—48no—
962C2×C4—48no—
963C2×C4—416no—
964C2×C4—88no—
965C2×C4—84no—
966C2×C4—84no—
967C2×C4—88no—
968C2×C4—88no—
969C2×C4—168no—
970C2×C4#562116yescomplemented
971C2×C4C2×H(5,𝔽2)12yes—
972C2×C4C2×H(5,𝔽2)14yes—
973C2×C4C2×H(5,𝔽2)14yes—
974C2×C4C2×2−1+414yes—
975C2×C4#58512yes—
976C22—22no—
977C22—22no—
978C22—22no—
979C22—22no—
980C22—22no—
981C22—22no—
982C22—24no—
983C22—24no—
984C22—24no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—42no—
989C22—44no—
990C22—42no—
991C22—42no—
992C22—44no—
993C22—44no—
994C22—42no—
995C22—44no—
996C22—42no—
997C22—42no—
998C22—44no—
999C22—44no—
1000C22—42no—
1001C22—42no—
1002C22—44no—
1003C22—816no—
1004C22C2×#56214yes—
1005C22C22×H(5,𝔽2)11yescharacteristic
1006C22C22×H(5,𝔽2)11yescharacteristic
1007C22C22×H(5,𝔽2)11yescharacteristic
1008C22C22×2−1+411yescharacteristic
1009C22C2×#58511yescharacteristic
1010C222−1+611yescharacteristic
1011C222−1+611yescharacteristic
1012C4—22no—
1013C4—22no—
1014C4—48no—
1015C4—44no—
1016C4—42no—
1017C4—44no—
1018C4—44no—
1019C4—44no—
1020C4—44no—
1021C4—44no—
1022C4—42no—
1023C4—42no—
1024C4—44no—
1025C4—44no—
1026C4—44no—
1027C4C2×#56218yes—
1028C2—24no—
1029C2—44no—
1030C2—84no—
1031C2—82no—
1032C2C22×#56211yescharacteristic
1033C2#6281811yescharacteristic
1034C2#6288611yescharacteristic
1035C2#6291411yescharacteristic
1036C2#6291511yescharacteristic
1037C2#6295911yescharacteristic
1038C2#6296011yescharacteristic
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. #53122C2semidirect
2. #53097C2semidirect
3. #53061C2semidirect
4. #52963C2semidirect
5. #52510C2semidirect
6. #46098C2semidirect
7. #45976C2semidirect
8. #45720C2semidirect
9. #45664C2semidirect
10. #45631C2semidirect
11. #45482C2semidirect
12. #35574C2semidirect
13. #35518C2semidirect
14. #35516C2semidirect
15. #35263C2semidirect
16. #35253C2semidirect
17. #35159C2semidirect
18. #35158C2semidirect
19. C2×#2547C2semidirect
20. #34737C2semidirect
31. #2857C22semidirect
32. #2855C22semidirect
33. #2854C22semidirect
35. #2851C22semidirect
37. #2836C22semidirect
38. #2836C22semidirect
39. #2831C22semidirect
40. #2830C22semidirect
41. #2829C22semidirect
42. #2827C22semidirect
43. #2827C22semidirect
44. #2826C22semidirect
47. #2814C22semidirect
48. #2808C22semidirect
49. #2806C22semidirect
50. #2806C22semidirect
51. #2786C22semidirect
52. #2786C22semidirect
53. #2755C22semidirect
54. #2754C22semidirect
55. #2751C22semidirect
56. #2747C22semidirect
57. #2739C22semidirect
58. #2732C22semidirect
61. #2708C22semidirect
62. #2704C22semidirect
63. #2701C22semidirect
65. #2700C22semidirect
66. #2687C22semidirect
72. #2629C22semidirect
73. #2628C22semidirect
74. #2625C22semidirect
75. #2624C22semidirect
81. #2538C22semidirect
82. #2537C22semidirect
83. #2536C22semidirect
84. #2535C22semidirect
85. #2509C22semidirect
86. #2508C22semidirect
87. #2507C22semidirect
88. #2506C22semidirect
90. #2492C22semidirect
91. #2491C22semidirect
92. #2490C22semidirect
93. #2489C22semidirect
94. #2487C22semidirect
95. #2487C22semidirect
96. #2486C22semidirect
97. #2486C22semidirect
98. #2485C22semidirect
99. #2485C22semidirect
100. #2485C22semidirect
101. #2485C22semidirect
102. #2452C22semidirect
103. #2452C22semidirect
104. #2451C22semidirect
105. #2451C22semidirect
106. #2442C22semidirect
107. #2441C22semidirect
108. #2440C22semidirect
109. #2440C22semidirect
110. #2440C22semidirect
111. #2439C22semidirect
112. #2439C22semidirect
113. #2439C22semidirect
118. #2423C22semidirect
119. #2422C22semidirect
120. #2421C22semidirect
121. #2420C22semidirect
126. #2417C22semidirect
129. #2416C22semidirect
132. #2415C22semidirect
135. #2414C22semidirect
146. #2378C22semidirect
970. C2×C4#562semidirect

Maximal subgroups

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

subgroupindex
#531222
#530972
#530612
#529632
#525102
#460982
#459762
#457202
#456642
#456312
#454822
#355742
#355182
#355162
#352632
#352532
#351592
#351582
C2×#25472
#347372