Finite Group Databasebeta

← #8932887

Subgroups — #8932887

Order 512.

5814 conjugacy classes of subgroups.

The subgroup lattice has 859 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59620C214yesmaximal, complemented
2#59223C218yesmaximal, complemented
3#51573C218yesmaximal, complemented
4#51541C214yesmaximal, complemented
5#49190C218yesmaximal, complemented
6#48482C218yesmaximal, complemented
7#47854C218yesmaximal, complemented
8#47563C211yesmaximal, characteristic, complemented
9#47195C211yesmaximal, characteristic, complemented
10#46997C212yesmaximal, complemented
11#46837C212yesmaximal, complemented
12#35616C211yesmaximal, characteristic, complemented
13#35540C212yesmaximal, complemented
14#35451C212yesmaximal, complemented
15#35355C212yesmaximal, complemented
16#35347C212yesmaximal, complemented
17C22×H(5,𝔽2)C2211yescharacteristic
18C2×#562C2214yescomplemented
19C2×#536C2212yescomplemented
20C2×#534C2214yescomplemented
21C22×#124C2211yescharacteristic
22C22×#121C2212yes—
23C2×#518C2212yescomplemented
24#2842C2211yescharacteristic, complemented
25#2840C2211yescharacteristic, complemented
26#2790C2218yescomplemented
27#2784C2214yescomplemented
28#2781C2218yescomplemented
29#2775C2218yescomplemented
30#2764C2218yescomplemented
31#2761C2218yescomplemented
32#2757C2218yescomplemented
33#2756C2218yescomplemented
34#2749C2218yescomplemented
35#2735C2214yescomplemented
36#2729C2218yescomplemented
37#2707C2218yescomplemented
38#2706C2218yescomplemented
39#2701C2218yescomplemented
40#2699C2214yescomplemented
41#2697C2218yescomplemented
42#2688C2218yescomplemented
43#2687C2218yescomplemented
44#2687C2218yescomplemented
45#2686C2218yescomplemented
46#2681C2218yescomplemented
47#2680C2218yescomplemented
48#2678C2218yescomplemented
49#2670C2218yescomplemented
50#2670C2214yescomplemented
51#2661C2218yescomplemented
52#2660C2214yescomplemented
53#2640C2214yescomplemented
54#2620C2218yescomplemented
55#2611C2214yescomplemented
56#2610C2214yescomplemented
57#2610C2218yescomplemented
58#2609C2218yescomplemented
59#2586C2214yescomplemented
60#2579C2214yescomplemented
61#2572C2214yescomplemented
62#2572C2218yescomplemented
63#2572C2218yescomplemented
64#2561C2218yescomplemented
65#2558C2218yescomplemented
66#2557C2218yescomplemented
67#2549C2218yescomplemented
68#2534C2218yescomplemented
69#2534C2214yescomplemented
70#2526C2218yescomplemented
71#2518C2218yescomplemented
72#2488C2218yescomplemented
73#2483C2214yescomplemented
74#2483C2211yescharacteristic, complemented
75#2483C2212yescomplemented
76#2476C2218yescomplemented
77#2474C2218yescomplemented
78#2472C2218yescomplemented
79#2472C2218yescomplemented
80#2471C2218yescomplemented
81#2464C2218yescomplemented
82#2461C2218yescomplemented
83#2459C2218yescomplemented
84#2459C2218yescomplemented
85#2456C2218yescomplemented
86#2435C2218yescomplemented
87#2432C2218yescomplemented
88#2430C2218yes—
89#2430C2218yescomplemented
90#2424C2218yescomplemented
91#2422C2218yescomplemented
92#2422C2218yescomplemented
93#2420C2218yescomplemented
94#2420C2218yescomplemented
95#2411C2218yescomplemented
96#2410C2218yes—
97#2410C2218yescomplemented
98#2409C2214yescomplemented
99#2408C2214yescomplemented
100#2406C2214yescomplemented
101#2405C2212yes—
102#2405C2212yes—
103#2405C2212yes—
104#2405C2212yes—
105#2405C2212yescomplemented
106#2405C2214yescomplemented
107#2405C2214yescomplemented
108#2404C2214yescomplemented
109#2403C2212yes—
110#2403C2212yes—
111#2403C2211yescharacteristic, complemented
112#2379C2218yescomplemented
113#2372C2214yescomplemented
114#2363C2218yescomplemented
115#2353C2218yescomplemented
116#2343C2218yescomplemented
117#2342C2218yescomplemented
118#2321C2214yescomplemented
119#2321C2214yescomplemented
120#2317C2214yescomplemented
121#2312C2212yescomplemented
122#2312C2212yescomplemented
123#2309C2211yescharacteristic
124#2309C2212yescomplemented
125#2308C2212yes—
126C4×#123C2214yescomplemented
127C4×#120C2214yescomplemented
128#2297C2212yescomplemented
129C2×#386C2214yescomplemented
130#2280C2214yescomplemented
131C2×H(5,𝔽2)—44no—
132C2×H(5,𝔽2)—48no—
133C22×#41C2312yes—
134C22×#41C2314yes—
135C23×Q8C2311yescharacteristic
136C23×D4C2312yes—
137C23×D4C2311yescharacteristic
138C23×D4C2312yes—
139C23×D4C2314yes—
140C23×D4C2312yes—
141C23×D4C2312yes—
142C24×C4C2312yes—
143#562—416no—
144#536—48no—
145#534—416no—
146C2×C4⋊Q8C2314yes—
147C2×#125C2314yes—
148C2×#124—44no—
149C2×#124C2314yes—
150C2×#124C2318yes—
151C2×#124C2314yes—
152C2×#124C2318yes—
153C2×#123C2314yes—
154C2×#123C2314yes—
155C2×#123C2314yes—
156C2×#123C2314yes—
157C2×#123C2318yes—
158C2×#123C2314yes—
159C2×#123C2318yes—
160C2×#123C2318yes—
161C2×C22⋊Q8C2318yes—
162C2×C22⋊Q8C2318yes—
163C2×C22⋊Q8C2318yes—
164C2×#121—48no—
165C2×#121C2318yes—
166C2×#121C2318yes—
167C2×#121C2318yes—
168C2×#121C2318yes—
169C2×#121C2318yes—
170C2×#120C2314yes—
171C2×#120C2314yes—
172C2×#120C2314yes—
173C2×#120C2314yes—
174C2×#120C2314yes—
175C2×#120C2318yes—
176#518—48no—
177C2×C4×D4C2314yes—
178C2×C4×D4C2314yes—
179C2×C4×D4C2314yes—
180C2×C4×D4C2318yes—
181C2×C4×D4C2314yes—
182C2×#117C2312yes—
183C2×#117C2314yes—
184C2×#117C2314yes—
185C2×#117C2318yes—
186C22×C4⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2314yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2318yes—
193C22×C22⋊C4C2314yes—
194C22×C42C2311yescharacteristic
195#400C2314yes—
196#400C2318yes—
197#400C2318yes—
198#399C2314yes—
199#398C2318yes—
200#398C2314yes—
201#398C2318yes—
202#398C2318yes—
203#398C2318yes—
204#397C2318yes—
205#397C2318yes—
206#397C2314yes—
207#397C2318yes—
208#397C2318yes—
209#397C2318yes—
210#397C2318yes—
211#397C2318yes—
212#396C2318yes—
213#396C2318yes—
214#396C2318yes—
215#396C2318yes—
216#396C2318yes—
217#396C2318yes—
218#395C2314yes—
219#395C2318yes—
220#395C2318yes—
221#394C2314yes—
222#394C2318yes—
223#394C2318yes—
224#394C2318yes—
225#394C2318yes—
226#394C2318yes—
227#394C2318yes—
228#394C2318yes—
229#394C2318yes—
230#394C2318yes—
231#394C2318yes—
232#394C2318yes—
233#394C2318yes—
234#394C2318yes—
235#394C2318yes—
236#393C2318yes—
237#393C2318yes—
238#393C2314yes—
239#393C2318yes—
240#393C2318yes—
241#392C2318yes—
242#392C2314yes—
243#392C2318yes—
244#392C2318yes—
245#392C2318yes—
246#392C2318yes—
247#391C2318yes—
248#391C2314yes—
249#391C2318yes—
250#391C2318yes—
251#390C2318yes—
252#390C2318yes—
253#390C2318yes—
254#390C2318yes—
255#390C2318yes—
256#390C2314yes—
257#390C2318yes—
258#390C2318yes—
259#389C2318yes—
260#389C2318yes—
261#389C2318yes—
262#388C2318yes—
263#388C2318yes—
264#388C2318yes—
265#388C2318yes—
266#388C2318yes—
267#388C2318yes—
268#388C2318yes—
269#388C2318yes—
270#388C2318yes—
271#388C2318yes—
272#388C2318yes—
273#388C2318yes—
274#388C2318yes—
275#388C2318yes—
276#388C2318yes—
277#388C2318yes—
278#388C2318yes—
279#388C2318yes—
280#388C2318yes—
281#387C2318yes—
282#387C2318yes—
283#387C2318yes—
284#387C2318yes—
285#387C2318yes—
286#386C2318yes—
287#386C2318yes—
288#386C2314yes—
289#386C2314yes—
290#386C2318yes—
291#386C2314yes—
292#386C2314yes—
293#386C2318yes—
294#386C2314yes—
295#386C2318yes—
296#386C2318yes—
297#386C2314yes—
298#386C2314yes—
299#386C2314yes—
300#386C2318yes—
301#386C2318yes—
302#386C2318yes—
303#386C2318yes—
304#386C2314yes—
305#386C2314yes—
306#386C2318yes—
307#386C2318yes—
308#385C2314yes—
309#385C2314yes—
310#385C2314yes—
311#385C2314yes—
312#385C2314yes—
313#385C2314yes—
314#385C2314yes—
315#385C2318yes—
316#385C2318yes—
317#385C2318yes—
318#385C2318yes—
319#385C2314yes—
320#385C2318yes—
321#385C2318yes—
322#385C2318yes—
323#384C2318yes—
324#383C2318yes—
325#383C2318yes—
326#382C2318yes—
327#382C2318yes—
328#381C2318yes—
329#381C2318yes—
330#381C2314yes—
331#381C2314yes—
332#381C2314yes—
333#381C2318yes—
334#381C2314yes—
335#380C2314yes—
336#380C2314yes—
337#380C2318yes—
338#380C2318yes—
339#379C2314yes—
340#379C2314yes—
341#379C2312yes—
342#379C2312yes—
343#379C2311yescharacteristic
344#379C2311yescharacteristic
345#379C2312yes—
346#379C2314yes—
347#379C2314yes—
348#379C2314yes—
349#379C2318yes—
350#379C2314yes—
351C4×C4⋊C4C2318yes—
352C4×C22⋊C4C2318yes—
353C4×C22⋊C4C2314yes—
354C4×C22⋊C4C2314yes—
355C4×C22⋊C4C2318yes—
356C4×C22⋊C4C2318yes—
357C4×C22⋊C4C2318yes—
358C4×C22⋊C4C2318yes—
359C4×C22⋊C4C2318yes—
360#376C2314yes—
361#376C2314yes—
362C2×#95C2318yes—
363C25C2412yes—
364C25C2412yes—
365C25C2412yes—
366C25C2411yescharacteristic
367C25C2411yescharacteristic
368H(5,𝔽2)—464no—
369C2×#41—28no—
370C2×#41—44no—
371C2×#41—44no—
372C2×#41—48no—
373C2×#41—48no—
374C2×#41—48no—
375C22×Q8—42no—
376C22×Q8—44no—
377C22×Q8C2414yes—
378C22×Q8C2412yes—
379C22×Q8C2414yes—
380C22×D4—28no—
381C22×D4—28no—
382C22×D4—24no—
383C22×D4—216no—
384C22×D4—48no—
385C22×D4—44no—
386C22×D4—48no—
387C22×D4—44no—
388C22×D4—48no—
389C22×D4—44no—
390C22×D4—48no—
391C22×D4—48no—
392C22×D4—48no—
393C22×D4C2414yes—
394C22×D4C2414yes—
395C22×D4C2414yes—
396C22×D4C2414yes—
397C22×D4C2414yes—
398C22×D4C2418yes—
399C22×D4C2418yes—
400C22×D4C2414yes—
401C22×D4C2418yes—
402C22×D4C2414yes—
403C22×D4C2412yes—
404C23×C4—48no—
405C23×C4—44no—
406C23×C4C2412yes—
407C23×C4C2411yescharacteristic
408C23×C4C2414yes—
409C23×C4C2418yes—
410C23×C4C2412yes—
411C23×C4C2412yes—
412C23×C4C2412yes—
413C23×C4C2412yes—
414C23×C4C2412yes—
415C23×C4C2418yes—
416C23×C4C2414yes—
417C23×C4C2414yes—
418C23×C4C2412yes—
419C4⋊Q8—48no—
420#125—48no—
421#124—216no—
422#124—416no—
423#124—48no—
424#124—416no—
425#123—48no—
426#123—48no—
427#123—48no—
428#123—416no—
429#123—416no—
430#123—416no—
431#123—48no—
432#123—48no—
433C22⋊Q8—416no—
434C22⋊Q8—416no—
435C22⋊Q8—416no—
436#121—232no—
437#121—416no—
438#121—416no—
439#121—416no—
440#121—416no—
441#120—48no—
442#120—48no—
443#120—48no—
444#120—48no—
445#120—416no—
446#120—48no—
447C4×D4—416no—
448C4×D4—48no—
449C4×D4—48no—
450C4×D4—48no—
451C4×D4—48no—
452#117—48no—
453#117—44no—
454#117—416no—
455#117—48no—
456C2×C4⋊C4—44no—
457C2×C4⋊C4C2418yes—
458C2×C4⋊C4C2418yes—
459C2×C4⋊C4C2418yes—
460C2×C4⋊C4C2414yes—
461C2×C4⋊C4C2414yes—
462C2×C4⋊C4C2414yes—
463C2×C4⋊C4C2418yes—
464C2×C4⋊C4C2418yes—
465C2×C4⋊C4C2418yes—
466C2×C4⋊C4C2418yes—
467C2×C4⋊C4C2418yes—
468C2×C4⋊C4C2418yes—
469C2×C4⋊C4C2418yes—
470C2×C4⋊C4C2418yes—
471C2×C4⋊C4C2414yes—
472C2×C4⋊C4C2414yes—
473C2×C22⋊C4—28no—
474C2×C22⋊C4—28no—
475C2×C22⋊C4—416no—
476C2×C22⋊C4—48no—
477C2×C22⋊C4—44no—
478C2×C22⋊C4—44no—
479C2×C22⋊C4—48no—
480C2×C22⋊C4C2414yes—
481C2×C22⋊C4C2414yes—
482C2×C22⋊C4C2418yes—
483C2×C22⋊C4C2414yes—
484C2×C22⋊C4C2414yes—
485C2×C22⋊C4C2418yes—
486C2×C22⋊C4C2418yes—
487C2×C22⋊C4C2418yes—
488C2×C22⋊C4C2418yes—
489C2×C22⋊C4C2418yes—
490C2×C22⋊C4C2418yes—
491C2×C22⋊C4C2414yes—
492C2×C22⋊C4C2414yes—
493C2×C22⋊C4C2414yes—
494C2×C22⋊C4C2414yes—
495C2×C22⋊C4C2418yes—
496C2×C22⋊C4C2418yes—
497C2×C22⋊C4C2418yes—
498C2×C22⋊C4C2418yes—
499C2×C22⋊C4C2418yes—
500C2×C22⋊C4C2412yes—
501C2×C22⋊C4C2412yes—
502C2×C22⋊C4C2418yes—
503C2×C22⋊C4C2414yes—
504C2×C22⋊C4C2414yes—
505C2×C22⋊C4C2418yes—
506C2×C22⋊C4C2418yes—
507C2×C22⋊C4C2418yes—
508C2×C22⋊C4C2414yes—
509C2×C22⋊C4C2414yes—
510C2×C22⋊C4C2414yes—
511C2×C22⋊C4C2418yes—
512C2×C22⋊C4C2418yes—
513C2×C22⋊C4C2414yes—
514C2×C22⋊C4C2418yes—
515C2×C22⋊C4C2418yes—
516C2×C22⋊C4C2418yes—
517C2×C42—42no—
518C2×C42C2418yes—
519C2×C42C2414yes—
520C2×C42C2414yes—
521C2×C42C2414yes—
522C2×C42C2418yes—
523C2×C42C2418yes—
524C2×C42C2414yes—
525#95C2418yes—
526#95C2418yes—
527#95C2418yes—
528#95C2418yes—
529#95C2414yes—
530#95C2414yes—
531#95C2414yes—
532#95C2414yes—
533#95C2418yes—
534#95C2418yes—
535#95C2418yes—
536#95C2418yes—
537#95C2418yes—
538#95C2418yes—
539#95C2418yes—
540#95C2418yes—
541#95C2418yes—
542#95C2418yes—
543#95C2418yes—
544#95C2418yes—
545#95C2418yes—
546#95C2418yes—
547C24—28no—
548C24—24no—
549C24—24no—
550C24—22no—
551C24—28no—
552C24—42no—
553C24—42no—
554C24—42no—
555C24—44no—
556C24—44no—
557C24—44no—
558C24—44no—
559C24—48no—
560C24—44no—
561C24—44no—
562C24—44no—
563C24H(5,𝔽2)14yes—
564C24C2512yes—
565C24C2514yes—
566C24C2512yes—
567C24C2511yescharacteristic
568C24C2514yes—
569#41—432no—
570#41—464no—
571C2×Q8—24no—
572C2×Q8—28no—
573C2×Q8—42no—
574C2×Q8—42no—
575C2×Q8—44no—
576C2×Q8—44no—
577C2×Q8—44no—
578C2×Q8—48no—
579C2×Q8—88no—
580C2×D4—28no—
581C2×D4—28no—
582C2×D4—28no—
583C2×D4—28no—
584C2×D4—28no—
585C2×D4—28no—
586C2×D4—28no—
587C2×D4—28no—
588C2×D4—216no—
589C2×D4—216no—
590C2×D4—28no—
591C2×D4—28no—
592C2×D4—28no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—44no—
596C2×D4—44no—
597C2×D4—44no—
598C2×D4—44no—
599C2×D4—44no—
600C2×D4—44no—
601C2×D4—44no—
602C2×D4—432no—
603C2×D4—416no—
604C2×D4—48no—
605C2×D4—48no—
606C2×D4—48no—
607C2×D4—48no—
608C2×D4—48no—
609C2×D4—48no—
610C2×D4—48no—
611C2×D4—44no—
612C2×D4—48no—
613C2×D4—464no—
614C2×D4—432no—
615C2×D4—432no—
616C2×D4—816no—
617C2×D4H(5,𝔽2)18yes—
618C22×C4—22no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—28no—
622C22×C4—24no—
623C22×C4—28no—
624C22×C4—24no—
625C22×C4—24no—
626C22×C4—24no—
627C22×C4—24no—
628C22×C4—216no—
629C22×C4—28no—
630C22×C4—216no—
631C22×C4—44no—
632C22×C4—42no—
633C22×C4—44no—
634C22×C4—44no—
635C22×C4—48no—
636C22×C4—48no—
637C22×C4—48no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4—48no—
642C22×C4—44no—
643C22×C4—44no—
644C22×C4—44no—
645C22×C4—48no—
646C22×C4—48no—
647C22×C4—816no—
648C22×C4C2514yes—
649C22×C4C2518yes—
650C22×C4C2514yes—
651C22×C4C2514yes—
652C22×C4C2514yes—
653C22×C4C2518yes—
654C22×C4C2514yes—
655C22×C4C2514yes—
656C22×C4C2514yes—
657C22×C4C2512yes—
658C22×C4C2514yes—
659C4⋊C4—216no—
660C4⋊C4—216no—
661C4⋊C4—48no—
662C4⋊C4—48no—
663C4⋊C4—48no—
664C4⋊C4—44no—
665C4⋊C4—44no—
666C4⋊C4—44no—
667C4⋊C4—48no—
668C4⋊C4—48no—
669C4⋊C4—48no—
670C4⋊C4—48no—
671C4⋊C4—48no—
672C4⋊C4—48no—
673C4⋊C4—44no—
674C4⋊C4—44no—
675C22⋊C4—28no—
676C22⋊C4—28no—
677C22⋊C4—28no—
678C22⋊C4—28no—
679C22⋊C4—216no—
680C22⋊C4—216no—
681C22⋊C4—216no—
682C22⋊C4—216no—
683C22⋊C4—216no—
684C22⋊C4—216no—
685C22⋊C4—216no—
686C22⋊C4—48no—
687C22⋊C4—48no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—48no—
692C22⋊C4—44no—
693C22⋊C4—48no—
694C22⋊C4—48no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—48no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—48no—
701C22⋊C4—44no—
702C22⋊C4—44no—
703C22⋊C4—44no—
704C22⋊C4—48no—
705C22⋊C4—48no—
706C22⋊C4—48no—
707C22⋊C4—48no—
708C22⋊C4—44no—
709C22⋊C4—48no—
710C22⋊C4—48no—
711C22⋊C4—48no—
712C42—28no—
713C42—216no—
714C42—44no—
715C42—48no—
716C42—44no—
717C42—44no—
718C42—48no—
719C23—216no—
720C23—22no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—28no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—28no—
729C23—28no—
730C23—24no—
731C23—22no—
732C23—24no—
733C23—28no—
734C23—28no—
735C23—24no—
736C23—24no—
737C23—44no—
738C23—48no—
739C23—48no—
740C23—44no—
741C23—48no—
742C23—84no—
743C23—816no—
744C23—84no—
745C23—84no—
746C23—816no—
747C23—84no—
748C23—84no—
749C23—164no—
750C23—168no—
751C23—164no—
752C23—164no—
753C23C2×H(5,𝔽2)14yes—
754C23C2×H(5,𝔽2)18yes—
755C23C2×H(5,𝔽2)12yes—
756C23C2611yescharacteristic
757Q8—48no—
758Q8—88no—
759Q8—164no—
760D4—48no—
761D4—416no—
762D4—416no—
763D4—416no—
764D4—416no—
765D4—416no—
766D4—416no—
767D4—816no—
768D4—816no—
769D4—168no—
770D4—164no—
771C2×C4—216no—
772C2×C4—28no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—28no—
784C2×C4—28no—
785C2×C4—28no—
786C2×C4—28no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—28no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—28no—
798C2×C4—416no—
799C2×C4—48no—
800C2×C4—48no—
801C2×C4—816no—
802C2×C4—816no—
803C2×C4—84no—
804C2×C4—84no—
805C2×C4—84no—
806C2×C4—84no—
807C2×C4—164no—
808C2×C4—164no—
809C2×C4C2×H(5,𝔽2)14yes—
810C2×C4#58518yes—
811C22—216no—
812C22—22no—
813C22—24no—
814C22—28no—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—48no—
819C22—48no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—48no—
824C22—48no—
825C22—48no—
826C22—42no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—44no—
831C22—816no—
832C22—164no—
833C22—168no—
834C22—168no—
835C22—164no—
836C22C22×H(5,𝔽2)12yes—
837C22C22×H(5,𝔽2)11yescharacteristic
838C22C2×#58514yes—
839C4—24no—
840C4—28no—
841C4—44no—
842C4—48no—
843C4—48no—
844C4—44no—
845C4—44no—
846C4—44no—
847C4—44no—
848C4—44no—
849C4—44no—
850C2—48no—
851C2—44no—
852C2—42no—
853C2—84no—
854C2—82no—
855C2#6281711yescharacteristic
856C2#6282012yes—
857C2#6302414yes—
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. #59620C2semidirect
2. #59223C2semidirect
3. #51573C2semidirect
4. #51541C2semidirect
5. #49190C2semidirect
6. #48482C2semidirect
7. #47854C2semidirect
8. #47563C2semidirect
9. #47195C2semidirect
10. #46997C2semidirect
11. #46837C2semidirect
12. #35616C2semidirect
13. #35540C2semidirect
14. #35451C2semidirect
15. #35355C2semidirect
16. #35347C2semidirect
18. C2×#562C22semidirect
19. C2×#536C22semidirect
20. C2×#534C22semidirect
23. C2×#518C22semidirect
24. #2842C22semidirect
25. #2840C22semidirect
26. #2790C22semidirect
27. #2784C22semidirect
28. #2781C22semidirect
29. #2775C22semidirect
30. #2764C22semidirect
31. #2761C22semidirect
32. #2757C22semidirect
33. #2756C22semidirect
34. #2749C22semidirect
35. #2735C22semidirect
36. #2729C22semidirect
37. #2707C22semidirect
38. #2706C22semidirect
39. #2701C22semidirect
40. #2699C22semidirect
41. #2697C22semidirect
42. #2688C22semidirect
43. #2687C22semidirect
44. #2687C22semidirect
45. #2686C22semidirect
46. #2681C22semidirect
47. #2680C22semidirect
48. #2678C22semidirect
49. #2670C22semidirect
50. #2670C22semidirect
51. #2661C22semidirect
52. #2660C22semidirect
53. #2640C22semidirect
54. #2620C22semidirect
55. #2611C22semidirect
56. #2610C22semidirect
57. #2610C22semidirect
58. #2609C22semidirect
59. #2586C22semidirect
60. #2579C22semidirect
61. #2572C22semidirect
62. #2572C22semidirect
63. #2572C22semidirect
64. #2561C22semidirect
65. #2558C22semidirect
66. #2557C22semidirect
67. #2549C22semidirect
68. #2534C22semidirect
69. #2534C22semidirect
70. #2526C22semidirect
71. #2518C22semidirect
72. #2488C22semidirect
73. #2483C22semidirect
74. #2483C22semidirect
75. #2483C22semidirect
76. #2476C22semidirect
77. #2474C22semidirect
78. #2472C22semidirect
79. #2472C22semidirect
80. #2471C22semidirect
81. #2464C22semidirect
82. #2461C22semidirect
83. #2459C22semidirect
84. #2459C22semidirect
85. #2456C22semidirect
86. #2435C22semidirect
87. #2432C22semidirect
89. #2430C22semidirect
90. #2424C22semidirect
91. #2422C22semidirect
92. #2422C22semidirect
93. #2420C22semidirect
94. #2420C22semidirect
95. #2411C22semidirect
97. #2410C22semidirect
98. #2409C22semidirect
99. #2408C22semidirect
100. #2406C22semidirect
105. #2405C22semidirect
106. #2405C22semidirect
107. #2405C22semidirect
108. #2404C22semidirect
111. #2403C22semidirect
112. #2379C22semidirect
113. #2372C22semidirect
114. #2363C22semidirect
115. #2353C22semidirect
116. #2343C22semidirect
117. #2342C22semidirect
118. #2321C22semidirect
119. #2321C22semidirect
120. #2317C22semidirect
121. #2312C22semidirect
122. #2312C22semidirect
124. #2309C22semidirect
126. C4×#123C22semidirect
127. C4×#120C22semidirect
128. #2297C22semidirect
129. C2×#386C22semidirect
130. #2280C22semidirect

Maximal subgroups

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

subgroupindex
#596202
#592232
#515732
#515412
#491902
#484822
#478542
#475632
#471952
#469972
#468372
#356162
#355402
#354512
#353552
#353472