Finite Group Databasebeta

← #8932639

Subgroups — #8932639

Order 512.

5968 conjugacy classes of subgroups.

The subgroup lattice has 863 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#47096C218yesmaximal, complemented
2#47088C218yesmaximal, complemented
3#47042C218yesmaximal, complemented
4#47002C214yesmaximal, complemented
5#47001C218yesmaximal, complemented
6#46999C211yesmaximal, characteristic, complemented
7#46998C212yesmaximal, complemented
8#46997C212yesmaximal, complemented
9#46996C211yesmaximal, characteristic, complemented
10#35512C212yesmaximal, complemented
11#35446C211yesmaximal, characteristic, complemented
12#35356C214yesmaximal, complemented
13#35355C212yesmaximal, complemented
14#35354C212yesmaximal, complemented
15#35353C218yesmaximal, complemented
16#35351C212yesmaximal, complemented
17C22×H(5,𝔽2)C2211yescharacteristic
18C2×#525C2214yescomplemented
19C22×#123C2211yescharacteristic
20C22×#123C2212yescomplemented
21C22×#121C2212yes—
22C2×#520C2214yescomplemented
23C2×#518C2212yescomplemented
24#2842C2211yescharacteristic, complemented
25#2841C2214yescomplemented
26#2840C2211yescharacteristic, complemented
27#2824C2218yescomplemented
28#2801C2218yescomplemented
29#2787C2218yescomplemented
30#2787C2218yescomplemented
31#2784C2218yescomplemented
32#2771C2214yescomplemented
33#2762C2218yescomplemented
34#2761C2218yescomplemented
35#2761C2218yescomplemented
36#2760C2218yescomplemented
37#2760C2214yescomplemented
38#2752C2218yescomplemented
39#2750C2218yescomplemented
40#2749C2218yescomplemented
41#2743C2218yescomplemented
42#2737C2218yescomplemented
43#2737C2218yescomplemented
44#2736C2218yescomplemented
45#2736C2214yescomplemented
46#2706C2218yescomplemented
47#2703C2218yescomplemented
48#2697C2218yescomplemented
49#2697C2218yescomplemented
50#2668C2214yescomplemented
51#2609C2218yescomplemented
52#2600C2214yescomplemented
53#2599C2218yescomplemented
54#2598C2218yescomplemented
55#2580C2218yescomplemented
56#2579C2218yescomplemented
57#2579C2214yescomplemented
58#2534C2214yescomplemented
59#2487C2214yescomplemented
60#2484C2214yescomplemented
61#2483C2211yescharacteristic, complemented
62#2483C2212yescomplemented
63#2482C2214yescomplemented
64#2482C2214yescomplemented
65#2482C2214yescomplemented
66#2476C2218yescomplemented
67#2476C2218yescomplemented
68#2471C2218yescomplemented
69#2471C2218yescomplemented
70#2470C2218yescomplemented
71#2470C2218yescomplemented
72#2465C2218yescomplemented
73#2464C2218yescomplemented
74#2458C2218yescomplemented
75#2458C2218yescomplemented
76#2458C2218yescomplemented
77#2457C2218yescomplemented
78#2456C2218yescomplemented
79#2456C2218yescomplemented
80#2455C2218yescomplemented
81#2449C2218yescomplemented
82#2444C2218yescomplemented
83#2444C2218yescomplemented
84#2443C2218yescomplemented
85#2443C2218yescomplemented
86#2443C2218yescomplemented
87#2438C2218yescomplemented
88#2430C2218yescomplemented
89#2424C2218yescomplemented
90#2418C2218yescomplemented
91#2411C2218yescomplemented
92#2408C2218yes—
93#2408C2214yescomplemented
94#2408C2218yescomplemented
95#2407C2218yes—
96#2407C2218yescomplemented
97#2406C2218yescomplemented
98#2406C2214yescomplemented
99#2405C2212yes—
100#2405C2212yes—
101#2405C2212yes—
102#2405C2212yes—
103#2405C2212yescomplemented
104#2405C2218yescomplemented
105#2405C2214yescomplemented
106#2404C2218yescomplemented
107#2404C2214yescomplemented
108#2404C2214yescomplemented
109#2403C2212yes—
110#2403C2212yes—
111#2403C2211yescharacteristic, complemented
112#2403C2214yescomplemented
113#2325C2218yescomplemented
114#2322C2218yescomplemented
115#2322C2214yescomplemented
116#2321C2214yescomplemented
117#2321C2218yescomplemented
118#2318C2218yescomplemented
119#2313C2214yescomplemented
120#2312C2212yescomplemented
121#2312C2212yescomplemented
122#2311C2214yescomplemented
123#2309C2212yes—
124#2308C2211yescharacteristic
125#2308C2212yescomplemented
126#2308C2214yescomplemented
127#2308C2212yescomplemented
128C4×#120C2214yescomplemented
129C4×#120C2214yescomplemented
130C2×#385C2214yescomplemented
131C2×H(5,𝔽2)—44no—
132C2×H(5,𝔽2)—48no—
133C22×#41C2314yes—
134C22×#41C2312yes—
135C22×#41C2314yes—
136C23×D4C2311yescharacteristic
137C23×D4C2312yes—
138C23×D4C2312yes—
139C23×D4C2312yes—
140C23×D4C2312yes—
141C23×D4C2314yes—
142C24×C4C2312yes—
143C24×C4C2311yescharacteristic
144#525—416no—
145C2×#123—44no—
146C2×#123—48no—
147C2×#123C2314yes—
148C2×#123C2318yes—
149C2×#123C2314yes—
150C2×#123C2314yes—
151C2×#123C2314yes—
152C2×#123C2314yes—
153C2×#123C2318yes—
154C2×#123C2318yes—
155C2×C22⋊Q8C2318yes—
156C2×#121—48no—
157C2×#121C2318yes—
158C2×#121C2318yes—
159C2×#121C2318yes—
160C2×#121C2318yes—
161C2×#120C2314yes—
162C2×#120C2318yes—
163C2×#120C2314yes—
164C2×#120C2314yes—
165C2×#120C2314yes—
166C2×#120C2314yes—
167#520—416no—
168#518—48no—
169C2×C4×Q8C2318yes—
170C2×C4×D4C2318yes—
171C2×C4×D4C2314yes—
172C2×C4×D4C2318yes—
173C2×C4×D4C2318yes—
174C2×C4×D4C2314yes—
175C2×C4×D4C2314yes—
176C2×C4×D4C2318yes—
177C2×C4×D4C2314yes—
178C2×#117C2314yes—
179C2×#117C2318yes—
180C2×#117C2314yes—
181C2×#117C2314yes—
182C22×C4⋊C4C2314yes—
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2318yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2314yes—
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2314yes—
192C22×C22⋊C4C2314yes—
193C22×C22⋊C4C2312yes—
194#401C2318yes—
195#400C2318yes—
196#400C2318yes—
197#400C2318yes—
198#400C2318yes—
199#399C2318yes—
200#399C2318yes—
201#399C2314yes—
202#399C2314yes—
203#398C2318yes—
204#398C2318yes—
205#398C2318yes—
206#398C2318yes—
207#397C2318yes—
208#397C2318yes—
209#397C2318yes—
210#397C2314yes—
211#397C2318yes—
212#397C2318yes—
213#397C2318yes—
214#397C2314yes—
215#396C2318yes—
216#396C2318yes—
217#396C2318yes—
218#396C2318yes—
219#396C2318yes—
220#395C2318yes—
221#395C2318yes—
222#394C2318yes—
223#394C2318yes—
224#394C2318yes—
225#394C2318yes—
226#394C2318yes—
227#394C2318yes—
228#394C2318yes—
229#394C2318yes—
230#394C2318yes—
231#394C2318yes—
232#394C2318yes—
233#393C2318yes—
234#393C2318yes—
235#393C2318yes—
236#393C2318yes—
237#393C2314yes—
238#393C2314yes—
239#392C2318yes—
240#392C2318yes—
241#392C2314yes—
242#392C2318yes—
243#392C2318yes—
244#392C2314yes—
245#392C2318yes—
246#391C2318yes—
247#390C2318yes—
248#390C2318yes—
249#390C2318yes—
250#390C2318yes—
251#390C2318yes—
252#390C2318yes—
253#389C2318yes—
254#389C2318yes—
255#389C2318yes—
256#388C2318yes—
257#388C2318yes—
258#388C2318yes—
259#388C2318yes—
260#388C2318yes—
261#388C2318yes—
262#388C2318yes—
263#388C2318yes—
264#388C2318yes—
265#388C2318yes—
266#388C2318yes—
267#388C2318yes—
268#388C2318yes—
269#388C2318yes—
270#388C2318yes—
271#388C2318yes—
272#388C2318yes—
273#387C2318yes—
274#387C2318yes—
275#387C2318yes—
276#387C2318yes—
277#387C2318yes—
278#387C2318yes—
279#387C2318yes—
280#387C2318yes—
281#387C2318yes—
282#387C2318yes—
283#387C2318yes—
284#386C2318yes—
285#386C2318yes—
286#386C2318yes—
287#386C2318yes—
288#386C2318yes—
289#386C2318yes—
290#386C2314yes—
291#386C2314yes—
292#386C2318yes—
293#386C2318yes—
294#386C2314yes—
295#386C2314yes—
296#386C2314yes—
297#386C2314yes—
298#386C2318yes—
299#386C2318yes—
300#386C2318yes—
301#386C2314yes—
302#386C2318yes—
303#386C2314yes—
304#386C2314yes—
305#386C2318yes—
306#386C2318yes—
307#386C2318yes—
308#386C2318yes—
309#386C2318yes—
310#386C2314yes—
311#385C2318yes—
312#385C2318yes—
313#385C2318yes—
314#385C2314yes—
315#385C2318yes—
316#385C2318yes—
317#385C2318yes—
318#385C2314yes—
319#385C2318yes—
320#385C2318yes—
321#385C2314yes—
322#385C2318yes—
323#385C2318yes—
324#385C2318yes—
325#385C2314yes—
326#385C2314yes—
327#385C2314yes—
328#385C2314yes—
329#385C2314yes—
330#383C2318yes—
331#382C2318yes—
332#381C2312yes—
333#381C2314yes—
334#381C2314yes—
335#381C2314yes—
336#381C2314yes—
337#381C2314yes—
338#381C2314yes—
339#381C2318yes—
340#381C2314yes—
341#380C2318yes—
342#380C2318yes—
343#380C2314yes—
344#380C2314yes—
345#380C2318yes—
346#379C2311yescharacteristic
347#379C2311yescharacteristic
348#379C2312yes—
349#379C2314yes—
350#379C2314yes—
351#379C2314yes—
352#379C2312yes—
353#379C2314yes—
354#379C2314yes—
355#379C2318yes—
356#379C2314yes—
357#379C2314yes—
358C4×C22⋊C4C2314yes—
359C4×C22⋊C4C2314yes—
360C4×C22⋊C4C2318yes—
361C4×C22⋊C4C2318yes—
362C2×#95C2318yes—
363C25C2412yes—
364C25C2411yescharacteristic
365C25C2412yes—
366C25C2412yes—
367C25C2411yescharacteristic
368H(5,𝔽2)—464no—
369C2×#41—216no—
370C2×#41—48no—
371C2×#41—416no—
372C2×#41—48no—
373C2×#41—44no—
374C2×#41—48no—
375C2×#41—48no—
376C22×Q8C2412yes—
377C22×Q8C2414yes—
378C22×D4—28no—
379C22×D4—28no—
380C22×D4—24no—
381C22×D4—28no—
382C22×D4—48no—
383C22×D4—48no—
384C22×D4—44no—
385C22×D4—48no—
386C22×D4—44no—
387C22×D4—48no—
388C22×D4—44no—
389C22×D4—48no—
390C22×D4—44no—
391C22×D4—48no—
392C22×D4C2418yes—
393C22×D4C2414yes—
394C22×D4C2414yes—
395C22×D4C2414yes—
396C22×D4C2414yes—
397C22×D4C2414yes—
398C22×D4C2414yes—
399C22×D4C2414yes—
400C22×D4C2418yes—
401C22×D4C2418yes—
402C22×D4C2412yes—
403C23×C4—48no—
404C23×C4—44no—
405C23×C4—42no—
406C23×C4—44no—
407C23×C4C2412yes—
408C23×C4C2414yes—
409C23×C4C2412yes—
410C23×C4C2412yes—
411C23×C4C2412yes—
412C23×C4C2418yes—
413C23×C4C2412yes—
414C23×C4C2414yes—
415C23×C4C2412yes—
416C23×C4C2411yescharacteristic
417C23×C4C2418yes—
418C23×C4C2414yes—
419C23×C4C2414yes—
420C23×C4C2414yes—
421C23×C4C2412yes—
422#123—416no—
423#123—48no—
424#123—48no—
425#123—416no—
426#123—48no—
427#123—416no—
428#123—48no—
429#123—48no—
430C22⋊Q8—416no—
431#121—416no—
432#121—416no—
433#121—416no—
434#121—416no—
435#120—48no—
436#120—48no—
437#120—48no—
438#120—48no—
439#120—416no—
440#120—48no—
441C4×Q8—416no—
442C4×D4—232no—
443C4×D4—416no—
444C4×D4—416no—
445C4×D4—48no—
446C4×D4—48no—
447C4×D4—48no—
448C4×D4—48no—
449C4×D4—416no—
450#117—48no—
451#117—416no—
452#117—48no—
453#117—48no—
454C2×C4⋊C4—216no—
455C2×C4⋊C4—416no—
456C2×C4⋊C4—44no—
457C2×C4⋊C4—44no—
458C2×C4⋊C4C2418yes—
459C2×C4⋊C4C2418yes—
460C2×C4⋊C4C2418yes—
461C2×C4⋊C4C2414yes—
462C2×C4⋊C4C2418yes—
463C2×C4⋊C4C2418yes—
464C2×C4⋊C4C2418yes—
465C2×C4⋊C4C2414yes—
466C2×C4⋊C4C2414yes—
467C2×C4⋊C4C2414yes—
468C2×C4⋊C4C2418yes—
469C2×C4⋊C4C2418yes—
470C2×C4⋊C4C2418yes—
471C2×C4⋊C4C2418yes—
472C2×C4⋊C4C2418yes—
473C2×C4⋊C4C2418yes—
474C2×C22⋊C4—28no—
475C2×C22⋊C4—28no—
476C2×C22⋊C4—48no—
477C2×C22⋊C4—48no—
478C2×C22⋊C4—44no—
479C2×C22⋊C4—44no—
480C2×C22⋊C4—48no—
481C2×C22⋊C4—42no—
482C2×C22⋊C4C2414yes—
483C2×C22⋊C4C2414yes—
484C2×C22⋊C4C2414yes—
485C2×C22⋊C4C2414yes—
486C2×C22⋊C4C2418yes—
487C2×C22⋊C4C2418yes—
488C2×C22⋊C4C2418yes—
489C2×C22⋊C4C2414yes—
490C2×C22⋊C4C2414yes—
491C2×C22⋊C4C2418yes—
492C2×C22⋊C4C2412yes—
493C2×C22⋊C4C2414yes—
494C2×C22⋊C4C2414yes—
495C2×C22⋊C4C2412yes—
496C2×C22⋊C4C2418yes—
497C2×C22⋊C4C2418yes—
498C2×C22⋊C4C2414yes—
499C2×C22⋊C4C2414yes—
500C2×C22⋊C4C2418yes—
501C2×C22⋊C4C2418yes—
502C2×C22⋊C4C2414yes—
503C2×C22⋊C4C2414yes—
504C2×C22⋊C4C2418yes—
505C2×C22⋊C4C2418yes—
506C2×C22⋊C4C2414yes—
507C2×C22⋊C4C2414yes—
508C2×C22⋊C4C2418yes—
509C2×C22⋊C4C2418yes—
510C2×C22⋊C4C2414yes—
511C2×C22⋊C4C2418yes—
512C2×C22⋊C4C2418yes—
513C2×C22⋊C4C2418yes—
514C2×C22⋊C4C2418yes—
515C2×C22⋊C4C2418yes—
516C2×C22⋊C4C2414yes—
517C2×C22⋊C4C2418yes—
518C2×C22⋊C4C2418yes—
519C2×C42C2418yes—
520C2×C42C2414yes—
521C2×C42C2414yes—
522C2×C42C2418yes—
523C2×C42C2418yes—
524#95C2418yes—
525#95C2418yes—
526#95C2418yes—
527#95C2418yes—
528#95C2418yes—
529#95C2418yes—
530#95C2418yes—
531#95C2418yes—
532#95C2418yes—
533#95C2418yes—
534#95C2418yes—
535#95C2418yes—
536#95C2418yes—
537#95C2418yes—
538#95C2414yes—
539#95C2414yes—
540#95C2418yes—
541#95C2418yes—
542#95C2418yes—
543#95C2418yes—
544#95C2414yes—
545#95C2414yes—
546#95C2418yes—
547C24—24no—
548C24—22no—
549C24—24no—
550C24—28no—
551C24—24no—
552C24—24no—
553C24—42no—
554C24—44no—
555C24—42no—
556C24—42no—
557C24—44no—
558C24—44no—
559C24—44no—
560C24—44no—
561C24—48no—
562C24—44no—
563C24—44no—
564C24H(5,𝔽2)14yes—
565C24C2514yes—
566C24C2512yes—
567C24C2511yescharacteristic
568C24C2512yes—
569C24C2514yes—
570#41—464no—
571#41—464no—
572#41—432no—
573C2×Q8—28no—
574C2×Q8—44no—
575C2×Q8—48no—
576C2×Q8—42no—
577C2×D4—216no—
578C2×D4—28no—
579C2×D4—28no—
580C2×D4—28no—
581C2×D4—28no—
582C2×D4—28no—
583C2×D4—28no—
584C2×D4—28no—
585C2×D4—28no—
586C2×D4—216no—
587C2×D4—216no—
588C2×D4—28no—
589C2×D4—216no—
590C2×D4—216no—
591C2×D4—28no—
592C2×D4—28no—
593C2×D4—28no—
594C2×D4—44no—
595C2×D4—44no—
596C2×D4—44no—
597C2×D4—44no—
598C2×D4—44no—
599C2×D4—44no—
600C2×D4—42no—
601C2×D4—44no—
602C2×D4—44no—
603C2×D4—48no—
604C2×D4—432no—
605C2×D4—48no—
606C2×D4—48no—
607C2×D4—48no—
608C2×D4—48no—
609C2×D4—432no—
610C2×D4—432no—
611C2×D4—416no—
612C2×D4—464no—
613C2×D4—816no—
614C22×C4—24no—
615C22×C4—28no—
616C22×C4—28no—
617C22×C4—24no—
618C22×C4—22no—
619C22×C4—216no—
620C22×C4—24no—
621C22×C4—24no—
622C22×C4—24no—
623C22×C4—24no—
624C22×C4—28no—
625C22×C4—28no—
626C22×C4—216no—
627C22×C4—48no—
628C22×C4—44no—
629C22×C4—42no—
630C22×C4—44no—
631C22×C4—42no—
632C22×C4—44no—
633C22×C4—42no—
634C22×C4—48no—
635C22×C4—48no—
636C22×C4—48no—
637C22×C4—48no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—44no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—48no—
647C22×C4—48no—
648C22×C4—816no—
649C22×C4—88no—
650C22×C4H(5,𝔽2)18yes—
651C22×C4C2514yes—
652C22×C4C2518yes—
653C22×C4C2514yes—
654C22×C4C2514yes—
655C22×C4C2514yes—
656C22×C4C2512yes—
657C22×C4C2514yes—
658C22×C4C2518yes—
659C22×C4C2514yes—
660C22×C4C2514yes—
661C22×C4C2514yes—
662C4⋊C4—216no—
663C4⋊C4—216no—
664C4⋊C4—216no—
665C4⋊C4—44no—
666C4⋊C4—48no—
667C4⋊C4—48no—
668C4⋊C4—48no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—48no—
673C4⋊C4—48no—
674C4⋊C4—48no—
675C4⋊C4—48no—
676C4⋊C4—48no—
677C4⋊C4—48no—
678C22⋊C4—28no—
679C22⋊C4—28no—
680C22⋊C4—28no—
681C22⋊C4—28no—
682C22⋊C4—216no—
683C22⋊C4—216no—
684C22⋊C4—216no—
685C22⋊C4—44no—
686C22⋊C4—48no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—48no—
691C22⋊C4—42no—
692C22⋊C4—48no—
693C22⋊C4—44no—
694C22⋊C4—44no—
695C22⋊C4—48no—
696C22⋊C4—42no—
697C22⋊C4—48no—
698C22⋊C4—44no—
699C22⋊C4—44no—
700C22⋊C4—48no—
701C22⋊C4—48no—
702C22⋊C4—44no—
703C22⋊C4—48no—
704C22⋊C4—48no—
705C22⋊C4—48no—
706C22⋊C4—48no—
707C22⋊C4—44no—
708C22⋊C4—48no—
709C22⋊C4—48no—
710C22⋊C4—44no—
711C22⋊C4—48no—
712C22⋊C4—44no—
713C22⋊C4—48no—
714C22⋊C4—48no—
715C42—216no—
716C42—44no—
717C42—44no—
718C42—48no—
719C42—48no—
720C23—28no—
721C23—216no—
722C23—28no—
723C23—24no—
724C23—24no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—24no—
729C23—24no—
730C23—28no—
731C23—24no—
732C23—24no—
733C23—28no—
734C23—24no—
735C23—24no—
736C23—24no—
737C23—28no—
738C23—28no—
739C23—44no—
740C23—48no—
741C23—48no—
742C23—48no—
743C23—84no—
744C23—84no—
745C23—84no—
746C23—816no—
747C23—88no—
748C23—84no—
749C23—84no—
750C23—88no—
751C23—164no—
752C23—164no—
753C23—164no—
754C23—168no—
755C23C2×H(5,𝔽2)14yes—
756C23C2×H(5,𝔽2)12yes—
757C23C2×H(5,𝔽2)14yes—
758C23#58518yes—
759C23C2611yescharacteristic
760Q8—48no—
761Q8—416no—
762D4—416no—
763D4—416no—
764D4—416no—
765D4—416no—
766D4—416no—
767D4—416no—
768D4—416no—
769D4—432no—
770D4—48no—
771D4—816no—
772D4—816no—
773C2×C4—216no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—28no—
777C2×C4—28no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—28no—
785C2×C4—28no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—22no—
789C2×C4—28no—
790C2×C4—28no—
791C2×C4—28no—
792C2×C4—24no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—24no—
798C2×C4—28no—
799C2×C4—48no—
800C2×C4—416no—
801C2×C4—48no—
802C2×C4—44no—
803C2×C4—432no—
804C2×C4—416no—
805C2×C4—816no—
806C2×C4—84no—
807C2×C4—84no—
808C2×C4—84no—
809C2×C4—88no—
810C2×C4—84no—
811C2×C4—164no—
812C2×C4—164no—
813C2×C4C2×H(5,𝔽2)18yes—
814C22—24no—
815C22—24no—
816C22—22no—
817C22—24no—
818C22—24no—
819C22—28no—
820C22—24no—
821C22—216no—
822C22—28no—
823C22—44no—
824C22—44no—
825C22—44no—
826C22—48no—
827C22—44no—
828C22—44no—
829C22—48no—
830C22—44no—
831C22—44no—
832C22—44no—
833C22—48no—
834C22—48no—
835C22—816no—
836C22—88no—
837C22—164no—
838C22—168no—
839C22—168no—
840C22C22×H(5,𝔽2)11yescharacteristic
841C22C22×H(5,𝔽2)12yes—
842C22C2×#58514yes—
843C4—28no—
844C4—42no—
845C4—44no—
846C4—44no—
847C4—44no—
848C4—44no—
849C4—44no—
850C4—44no—
851C4—48no—
852C4—44no—
853C4—48no—
854C2—48no—
855C2—42no—
856C2—44no—
857C2—44no—
858C2—84no—
859C2#6281711yescharacteristic
860C2#6282012yes—
861C2#6282114yes—
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. #47096C2semidirect
2. #47088C2semidirect
3. #47042C2semidirect
4. #47002C2semidirect
5. #47001C2semidirect
6. #46999C2semidirect
7. #46998C2semidirect
8. #46997C2semidirect
9. #46996C2semidirect
10. #35512C2semidirect
11. #35446C2semidirect
12. #35356C2semidirect
13. #35355C2semidirect
14. #35354C2semidirect
15. #35353C2semidirect
16. #35351C2semidirect
18. C2×#525C22semidirect
20. C22×#123C22semidirect
22. C2×#520C22semidirect
23. C2×#518C22semidirect
24. #2842C22semidirect
25. #2841C22semidirect
26. #2840C22semidirect
27. #2824C22semidirect
28. #2801C22semidirect
29. #2787C22semidirect
30. #2787C22semidirect
31. #2784C22semidirect
32. #2771C22semidirect
33. #2762C22semidirect
34. #2761C22semidirect
35. #2761C22semidirect
36. #2760C22semidirect
37. #2760C22semidirect
38. #2752C22semidirect
39. #2750C22semidirect
40. #2749C22semidirect
41. #2743C22semidirect
42. #2737C22semidirect
43. #2737C22semidirect
44. #2736C22semidirect
45. #2736C22semidirect
46. #2706C22semidirect
47. #2703C22semidirect
48. #2697C22semidirect
49. #2697C22semidirect
50. #2668C22semidirect
51. #2609C22semidirect
52. #2600C22semidirect
53. #2599C22semidirect
54. #2598C22semidirect
55. #2580C22semidirect
56. #2579C22semidirect
57. #2579C22semidirect
58. #2534C22semidirect
59. #2487C22semidirect
60. #2484C22semidirect
61. #2483C22semidirect
62. #2483C22semidirect
63. #2482C22semidirect
64. #2482C22semidirect
65. #2482C22semidirect
66. #2476C22semidirect
67. #2476C22semidirect
68. #2471C22semidirect
69. #2471C22semidirect
70. #2470C22semidirect
71. #2470C22semidirect
72. #2465C22semidirect
73. #2464C22semidirect
74. #2458C22semidirect
75. #2458C22semidirect
76. #2458C22semidirect
77. #2457C22semidirect
78. #2456C22semidirect
79. #2456C22semidirect
80. #2455C22semidirect
81. #2449C22semidirect
82. #2444C22semidirect
83. #2444C22semidirect
84. #2443C22semidirect
85. #2443C22semidirect
86. #2443C22semidirect
87. #2438C22semidirect
88. #2430C22semidirect
89. #2424C22semidirect
90. #2418C22semidirect
91. #2411C22semidirect
93. #2408C22semidirect
94. #2408C22semidirect
96. #2407C22semidirect
97. #2406C22semidirect
98. #2406C22semidirect
103. #2405C22semidirect
104. #2405C22semidirect
105. #2405C22semidirect
106. #2404C22semidirect
107. #2404C22semidirect
108. #2404C22semidirect
111. #2403C22semidirect
112. #2403C22semidirect
113. #2325C22semidirect
114. #2322C22semidirect
115. #2322C22semidirect
116. #2321C22semidirect
117. #2321C22semidirect
118. #2318C22semidirect
119. #2313C22semidirect
120. #2312C22semidirect
121. #2312C22semidirect
122. #2311C22semidirect
125. #2308C22semidirect
126. #2308C22semidirect
127. #2308C22semidirect
128. C4×#120C22semidirect
129. C4×#120C22semidirect
130. C2×#385C22semidirect

Maximal subgroups

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

subgroupindex
#470962
#470882
#470422
#470022
#470012
#469992
#469982
#469972
#469962
#355122
#354462
#353562
#353552
#353542
#353532
#353512