Finite Group Databasebeta

← #7643624

Subgroups — #7643624

Order 512.

5566 conjugacy classes of subgroups.

The subgroup lattice has 867 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41429C218yesmaximal, complemented
2#40670C218yesmaximal, complemented
3#40669C218yesmaximal, complemented
4#40642C218yesmaximal, complemented
5#37465C214yesmaximal, complemented
6#37459C214yesmaximal, complemented
7#36978C212yesmaximal, complemented
8#36976C212yesmaximal, complemented
9#36731C212yesmaximal, complemented
10#36727C212yesmaximal, complemented
11#35358C214yesmaximal, complemented
12#35351C214yesmaximal, complemented
13#35000C212yesmaximal, complemented
14C2×#2656C211yesmaximal, characteristic, complemented
15C2×#2646C211yesmaximal, characteristic, complemented
16#34205C212yesmaximal, complemented
17C2×#2318C211yesmaximal, characteristic, complemented
18C2×#534C2214yes—
19C22×#121C2212yes—
20C22×#121C2214yes—
21C2×#518C2214yes—
22C22×C4×D4C2211yescharacteristic
23#2854C2214yescomplemented
24#2847C2214yescomplemented
25#2837C2218yescomplemented
26#2836C2218yescomplemented
27#2829C2218yescomplemented
28#2828C2218yescomplemented
29#2777C2218yescomplemented
30#2773C2218yescomplemented
31#2768C2218yescomplemented
32#2756C2218yescomplemented
33#2753C2218yescomplemented
34#2749C2218yescomplemented
35#2748C2218yescomplemented
36#2743C2218yescomplemented
37#2741C2218yescomplemented
38#2740C2218yescomplemented
39#2738C2218yescomplemented
40#2706C2218yescomplemented
41#2703C2218yescomplemented
42#2699C2218yescomplemented
43#2688C2218yescomplemented
44#2671C2218yescomplemented
45#2667C2218yescomplemented
46#2661C2218yescomplemented
47#2656C2214yes—
48#2656C2212yes—
49#2656C2212yes—
50#2656C2218yescomplemented
51#2654C2218yescomplemented
52#2651C2218yescomplemented
53#2649C2218yescomplemented
54#2648C2218yescomplemented
55#2646C2214yescomplemented
56#2646C2212yescomplemented
57#2646C2212yescomplemented
58#2646C2218yescomplemented
59#2635C2218yescomplemented
60#2630C2218yescomplemented
61#2618C2214yescomplemented
62#2617C2214yescomplemented
63#2543C2218yescomplemented
64#2543C2218yescomplemented
65#2543C2218yescomplemented
66#2534C2218yes—
67#2522C2218yescomplemented
68#2516C2218yescomplemented
69#2486C2214yes—
70#2484C2218yescomplemented
71#2483C2218yescomplemented
72#2482C2218yescomplemented
73#2464C2218yescomplemented
74#2457C2218yescomplemented
75#2444C2218yescomplemented
76#2444C2218yescomplemented
77#2444C2218yescomplemented
78#2444C2218yescomplemented
79#2443C2218yescomplemented
80#2443C2218yescomplemented
81#2443C2218yescomplemented
82#2443C2218yescomplemented
83#2425C2218yescomplemented
84#2425C2218yescomplemented
85#2424C2218yescomplemented
86#2424C2218yescomplemented
87#2416C2218yescomplemented
88#2416C2218yescomplemented
89#2416C2214yescomplemented
90#2416C2214yescomplemented
91#2413C2218yes—
92#2412C2218yes—
93#2411C2218yes—
94#2410C2218yes—
95#2408C2214yes—
96#2405C2218yescomplemented
97C2×#400C2214yescomplemented
98C2×#399C2214yescomplemented
99C2×#398C2214yescomplemented
100C2×#392C2214yescomplemented
101#2364C2218yescomplemented
102#2361C2214yescomplemented
103#2361C2214yescomplemented
104#2344C2214yescomplemented
105#2342C2218yescomplemented
106D4×C22⋊C4C2214yescomplemented
107#2325C2214yescomplemented
108#2325C2214yescomplemented
109#2318C2218yes—
110#2318C2218yescomplemented
111#2308C2214yes—
112#2308C2214yes—
113C4×#121C2214yescomplemented
114C4×#121C2214yescomplemented
115C2×#388C2212yescomplemented
116C2×#387C2212yescomplemented
117C2×#386C2212yes—
118C2×#385C2214yes—
119C2×#385C2212yes—
120C2×#383C2211yescharacteristic, complemented
121C2×#382C2211yescharacteristic, complemented
122C2×#381C2211yescharacteristic, complemented
123C2×#380C2212yes—
124C2×#380C2211yescharacteristic, complemented
125C2×C4×C22⋊C4C2211yescharacteristic
126C22×#95C2211yescharacteristic
127C23×D4C2314yes—
128C23×D4C2311yescharacteristic
129C23×D4C2312yes—
130C23×D4C2314yes—
131C24×C4C2311yescharacteristic
132C24×C4C2312yes—
133C24×C4C2311yescharacteristic
134#534—416no—
135C2×#123C2318yes—
136C2×#123C2318yes—
137C2×#123C2318yes—
138C2×#123C2318yes—
139C2×#121—216no—
140C2×#121—416no—
141C2×#121C2314yes—
142C2×#121C2314yes—
143C2×#121C2314yes—
144C2×#121C2314yes—
145C2×#121C2318yes—
146C2×#121C2318yes—
147C2×#121C2318yes—
148C2×#121C2318yes—
149C2×#121C2318yes—
150C2×#121C2318yes—
151C2×#121C2314yes—
152C2×#121C2314yes—
153C2×#121C2318yes—
154C2×#121C2318yes—
155C2×#120C2318yes—
156C2×#120C2318yes—
157#518—416no—
158C2×C4×D4—28no—
159C2×C4×D4C2314yes—
160C2×C4×D4C2314yes—
161C2×C4×D4C2318yes—
162C2×C4×D4C2318yes—
163C2×C4×D4C2318yes—
164C2×C4×D4C2318yes—
165C2×C4×D4C2314yes—
166C2×C4×D4C2314yes—
167C2×#117C2318yes—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2314yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2314yes—
174C22×C4⋊C4C2314yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C22⋊C4C2311yescharacteristic
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2314yes—
180C22×C22⋊C4C2314yes—
181C22×C22⋊C4C2311yescharacteristic
182C22×C22⋊C4C2318yes—
183C22×C22⋊C4C2314yes—
184C22×C22⋊C4C2314yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C42C2311yescharacteristic
188C22×C42C2312yes—
189#400C2318yes—
190#400C2318yes—
191#400C2318yes—
192#400C2318yes—
193#400C2318yes—
194#400C2318yes—
195#399C2318yes—
196#399C2318yes—
197#399C2318yes—
198#399C2318yes—
199#399C2318yes—
200#399C2318yes—
201#398C2318yes—
202#398C2318yes—
203#398C2318yes—
204#398C2318yes—
205#398C2318yes—
206#398C2318yes—
207#398C2318yes—
208#398C2318yes—
209#398C2318yes—
210#397C2318yes—
211#397C2318yes—
212#397C2318yes—
213#397C2318yes—
214#397C2318yes—
215#397C2318yes—
216#397C2318yes—
217#397C2318yes—
218#397C2318yes—
219#396C2318yes—
220#396C2318yes—
221#396C2318yes—
222#396C2318yes—
223#396C2318yes—
224#396C2318yes—
225#394C2318yes—
226#394C2318yes—
227#394C2318yes—
228#394C2318yes—
229#394C2318yes—
230#394C2318yes—
231#394C2318yes—
232#394C2318yes—
233#394C2318yes—
234#394C2318yes—
235#394C2318yes—
236#394C2318yes—
237#394C2318yes—
238#392C2318yes—
239#392C2318yes—
240#392C2318yes—
241#392C2318yes—
242#392C2318yes—
243#392C2318yes—
244#392C2318yes—
245#390C2314yes—
246#390C2314yes—
247#390C2314yes—
248#390C2314yes—
249#390C2318yes—
250#390C2318yes—
251#389C2314yes—
252#389C2314yes—
253#389C2314yes—
254#389C2314yes—
255#389C2318yes—
256#389C2318yes—
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#386C2318yes—
282#386C2318yes—
283#386C2318yes—
284#386C2318yes—
285#386C2318yes—
286#386C2318yes—
287#386C2318yes—
288#386C2318yes—
289#386C2318yes—
290#386C2318yes—
291#386C2318yes—
292#386C2318yes—
293#386C2318yes—
294#386C2318yes—
295#386C2318yes—
296#386C2318yes—
297#386C2318yes—
298#386C2318yes—
299#386C2318yes—
300#386C2318yes—
301#385C2318yes—
302#385C2318yes—
303#385C2318yes—
304#385C2318yes—
305#385C2318yes—
306#385C2318yes—
307#385C2318yes—
308#385C2318yes—
309#385C2318yes—
310#385C2318yes—
311#383C2318yes—
312#382C2318yes—
313#381C2318yes—
314#381C2318yes—
315#381C2318yes—
316#381C2318yes—
317#381C2318yes—
318#380C2318yes—
319#380C2314yes—
320#380C2314yes—
321#380C2314yes—
322#380C2314yes—
323#380C2314yes—
324#380C2314yes—
325#380C2318yes—
326#380C2318yes—
327#379C2318yes—
328#379C2318yes—
329C4×C4⋊C4C2314yes—
330C4×C4⋊C4C2314yes—
331C4×C22⋊C4C2314yes—
332C4×C22⋊C4C2314yes—
333C4×C22⋊C4C2318yes—
334C4×C22⋊C4C2318yes—
335C2×#95C2314yes—
336C2×#95C2314yes—
337C2×#95C2311yescharacteristic
338C2×#95C2311yescharacteristic
339C2×#95C2314yes—
340C2×#95C2311yescharacteristic
341C2×#95C2311yescharacteristic
342C2×#95C2312yes—
343C2×#95C2314yes—
344C2×#95C2314yes—
345C2×#95C2312yes—
346C2×#95C2312yes—
347C2×#95C2312yes—
348C2×#95C2312yes—
349C25C2411yescharacteristic
350C25C2414yes—
351C25C2411yescharacteristic
352C22×D4—24no—
353C22×D4—216no—
354C22×D4—216no—
355C22×D4—216no—
356C22×D4—28no—
357C22×D4—28no—
358C22×D4—48no—
359C22×D4—82no—
360C22×D4—82no—
361C22×D4—84no—
362C22×D4—84no—
363C22×D4C2412yes—
364C22×D4C2418yes—
365C22×D4C2412yes—
366C22×D4C2418yes—
367C22×D4C2414yes—
368C22×D4C2414yes—
369C22×D4C2418yes—
370C22×D4C2418yes—
371C22×D4C2418yes—
372C22×D4C2418yes—
373C23×C4—28no—
374C23×C4—24no—
375C23×C4—82no—
376C23×C4—82no—
377C23×C4—82no—
378C23×C4—82no—
379C23×C4#4118yes—
380C23×C4C2414yes—
381C23×C4C2411yescharacteristic
382C23×C4C2412yes—
383C23×C4C2411yescharacteristic
384C23×C4C2414yes—
385C23×C4C2412yes—
386C23×C4C2414yes—
387C23×C4C2411yescharacteristic
388C23×C4C2414yes—
389C23×C4C2412yes—
390C23×C4C2412yes—
391C23×C4C2414yes—
392C23×C4C2414yes—
393C23×C4C2418yes—
394C23×C4C2418yes—
395C23×C4C2412yes—
396C23×C4C2411yescharacteristic
397C23×C4C2412yes—
398C23×C4C2411yescharacteristic
399#123—416no—
400#123—416no—
401#123—88no—
402#123—88no—
403#121—216no—
404#121—216no—
405#121—216no—
406#121—216no—
407#121—416no—
408#121—416no—
409#121—416no—
410#121—416no—
411#121—416no—
412#121—416no—
413#121—88no—
414#121—88no—
415#121—84no—
416#121—84no—
417#120—416no—
418#120—416no—
419C4×D4—216no—
420C4×D4—216no—
421C4×D4—416no—
422C4×D4—416no—
423C4×D4—416no—
424C4×D4—416no—
425C4×D4—84no—
426C4×D4—84no—
427#117—416no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—28no—
430C2×C4⋊C4—48no—
431C2×C4⋊C4—82no—
432C2×C4⋊C4—82no—
433C2×C4⋊C4—84no—
434C2×C4⋊C4—84no—
435C2×C4⋊C4—82no—
436C2×C4⋊C4—82no—
437C2×C4⋊C4C2414yes—
438C2×C4⋊C4C2414yes—
439C2×C4⋊C4C2414yes—
440C2×C4⋊C4C2414yes—
441C2×C4⋊C4C2414yes—
442C2×C4⋊C4C2418yes—
443C2×C4⋊C4C2418yes—
444C2×C4⋊C4C2414yes—
445C2×C4⋊C4C2414yes—
446C2×C4⋊C4C2418yes—
447C2×C4⋊C4C2418yes—
448C2×C4⋊C4C2418yes—
449C2×C4⋊C4C2418yes—
450C2×C4⋊C4C2418yes—
451C2×C4⋊C4C2418yes—
452C2×C4⋊C4C2418yes—
453C2×C4⋊C4C2418yes—
454C2×C4⋊C4C2418yes—
455C2×C4⋊C4C2418yes—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—28no—
458C2×C22⋊C4—216no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—216no—
461C2×C22⋊C4—416no—
462C2×C22⋊C4—48no—
463C2×C22⋊C4—48no—
464C2×C22⋊C4—82no—
465C2×C22⋊C4—82no—
466C2×C22⋊C4C2414yes—
467C2×C22⋊C4C2418yes—
468C2×C22⋊C4C2414yes—
469C2×C22⋊C4C2418yes—
470C2×C22⋊C4C2412yes—
471C2×C22⋊C4C2412yes—
472C2×C22⋊C4C2414yes—
473C2×C22⋊C4C2418yes—
474C2×C22⋊C4C2418yes—
475C2×C22⋊C4C2418yes—
476C2×C22⋊C4C2418yes—
477C2×C22⋊C4C2418yes—
478C2×C22⋊C4C2418yes—
479C2×C22⋊C4C2418yes—
480C2×C22⋊C4C2418yes—
481C2×C22⋊C4C2418yes—
482C2×C22⋊C4C2418yes—
483C2×C22⋊C4C2418yes—
484C2×C22⋊C4C2418yes—
485C2×C22⋊C4C2418yes—
486C2×C22⋊C4C2418yes—
487C2×C22⋊C4C2418yes—
488C2×C22⋊C4C2418yes—
489C2×C22⋊C4C2418yes—
490C2×C22⋊C4C2418yes—
491C2×C22⋊C4C2418yes—
492C2×C22⋊C4C2418yes—
493C2×C22⋊C4C2418yes—
494C2×C22⋊C4C2418yes—
495C2×C42—24no—
496C2×C42—82no—
497C2×C42C2414yes—
498C2×C42C2418yes—
499C2×C42C2418yes—
500C2×C42C2414yes—
501C2×C42C2414yes—
502#95C2414yes—
503#95C2414yes—
504#95C2414yes—
505#95C2414yes—
506#95C2414yes—
507#95C2418yes—
508#95C2414yes—
509#95C2418yes—
510#95C2418yes—
511#95C2418yes—
512#95C2418yes—
513#95C2418yes—
514#95C2418yes—
515#95C2418yes—
516#95C2418yes—
517#95C2418yes—
518#95C2418yes—
519#95C2418yes—
520#95C2418yes—
521#95C2418yes—
522#95C2418yes—
523#95C2418yes—
524#95C2418yes—
525#95C2418yes—
526C24—22no—
527C24—28no—
528C24—28no—
529C24—28no—
530C24—24no—
531C24—42no—
532C24—41no—
533C24—41no—
534C24—41no—
535C24—42no—
536C24—41no—
537C24—44no—
538C24—44no—
539C24—44no—
540C24—44no—
541C24C2×#4114yes—
542C24H(5,𝔽2)18yes—
543C24C2512yes—
544C24C2518yes—
545C24C2511yescharacteristic
546C24C2511yescharacteristic
547C24C2511yescharacteristic
548C2×D4—24no—
549C2×D4—24no—
550C2×D4—216no—
551C2×D4—216no—
552C2×D4—216no—
553C2×D4—216no—
554C2×D4—28no—
555C2×D4—216no—
556C2×D4—216no—
557C2×D4—28no—
558C2×D4—28no—
559C2×D4—28no—
560C2×D4—44no—
561C2×D4—44no—
562C2×D4—48no—
563C2×D4—48no—
564C2×D4—44no—
565C2×D4—44no—
566C2×D4—48no—
567C2×D4—48no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4—48no—
571C2×D4—48no—
572C2×D4—48no—
573C2×D4—48no—
574C2×D4—48no—
575C2×D4—48no—
576C2×D4—416no—
577C2×D4—464no—
578C2×D4—816no—
579C2×D4—832no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—28no—
586C22×C4—28no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—28no—
591C22×C4—28no—
592C22×C4—24no—
593C22×C4—24no—
594C22×C4—28no—
595C22×C4—28no—
596C22×C4—42no—
597C22×C4—41no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—41no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—42no—
622C22×C4—44no—
623C22×C4—48no—
624C22×C4—48no—
625C22×C4—48no—
626C22×C4—48no—
627C22×C4—48no—
628C22×C4—48no—
629C22×C4—88no—
630C22×C4—88no—
631C22×C4—816no—
632C22×C4C2×#4114yes—
633C22×C4C2×#4118yes—
634C22×C4C2×#4114yes—
635C22×C4C2×#4118yes—
636C22×C4C2514yes—
637C22×C4C2512yes—
638C22×C4C2518yes—
639C22×C4C2512yes—
640C22×C4C2514yes—
641C22×C4C2514yes—
642C22×C4C2514yes—
643C22×C4C2512yes—
644C22×C4C2518yes—
645C22×C4C2518yes—
646C22×C4C2512yes—
647C22×C4C2512yes—
648C4⋊C4—28no—
649C4⋊C4—28no—
650C4⋊C4—28no—
651C4⋊C4—48no—
652C4⋊C4—48no—
653C4⋊C4—44no—
654C4⋊C4—44no—
655C4⋊C4—44no—
656C4⋊C4—44no—
657C4⋊C4—48no—
658C4⋊C4—48no—
659C4⋊C4—48no—
660C4⋊C4—48no—
661C4⋊C4—48no—
662C4⋊C4—48no—
663C4⋊C4—48no—
664C4⋊C4—48no—
665C4⋊C4—48no—
666C4⋊C4—48no—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—28no—
670C22⋊C4—216no—
671C22⋊C4—28no—
672C22⋊C4—216no—
673C22⋊C4—28no—
674C22⋊C4—216no—
675C22⋊C4—216no—
676C22⋊C4—48no—
677C22⋊C4—48no—
678C22⋊C4—48no—
679C22⋊C4—48no—
680C22⋊C4—48no—
681C22⋊C4—48no—
682C22⋊C4—48no—
683C22⋊C4—48no—
684C22⋊C4—48no—
685C22⋊C4—48no—
686C22⋊C4—48no—
687C22⋊C4—48no—
688C22⋊C4—48no—
689C22⋊C4—48no—
690C22⋊C4—48no—
691C22⋊C4—48no—
692C22⋊C4—48no—
693C22⋊C4—48no—
694C22⋊C4—48no—
695C22⋊C4—48no—
696C42—28no—
697C42—44no—
698C42—44no—
699C42—48no—
700C42—48no—
701C23—22no—
702C23—21no—
703C23—22no—
704C23—21no—
705C23—22no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—22no—
711C23—28no—
712C23—28no—
713C23—28no—
714C23—24no—
715C23—22no—
716C23—24no—
717C23—28no—
718C23—28no—
719C23—28no—
720C23—28no—
721C23—22no—
722C23—44no—
723C23—48no—
724C23—44no—
725C23—48no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—416no—
730C23—84no—
731C23—84no—
732C23—88no—
733C23—88no—
734C23—88no—
735C23—88no—
736C23—88no—
737C23—88no—
738C23#540116yes—
739C23C22×#4112yes—
740C23C22×#4112yes—
741C23C22×#4112yes—
742C23C2×H(5,𝔽2)14yes—
743C23C2×H(5,𝔽2)14yes—
744C23C2×H(5,𝔽2)14yes—
745C23C2611yescharacteristic
746D4—416no—
747D4—48no—
748D4—432no—
749D4—48no—
750D4—432no—
751D4—88no—
752D4—816no—
753D4—816no—
754D4—168no—
755D4—168no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—28no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—28no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—28no—
779C2×C4—28no—
780C2×C4—28no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—28no—
788C2×C4—44no—
789C2×C4—48no—
790C2×C4—44no—
791C2×C4—48no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—416no—
795C2×C4—416no—
796C2×C4—44no—
797C2×C4—88no—
798C2×C4—84no—
799C2×C4—88no—
800C2×C4—84no—
801C2×C4—88no—
802C2×C4—88no—
803C2×C4—84no—
804C2×C4—84no—
805C2×C4—168no—
806C2×C4—168no—
807C2×C4C22×#4114yes—
808C2×C4C22×#4114yes—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—24no—
820C22—24no—
821C22—416no—
822C22—42no—
823C22—48no—
824C22—42no—
825C22—48no—
826C22—48no—
827C22—48no—
828C22—44no—
829C22—48no—
830C22—44no—
831C22—48no—
832C22—42no—
833C22—48no—
834C22—88no—
835C22—1616no—
836C22C2×#54014yes—
837C22C2×#54014yes—
838C22C2×#54014yes—
839C22C23×#4111yescharacteristic
840C22C22×H(5,𝔽2)12yes—
841C22H(7,𝔽2)12yes—
842C22H(7,𝔽2)11yescharacteristic
843C222−1+611yescharacteristic
844C4—24no—
845C4—24no—
846C4—42no—
847C4—42no—
848C4—44no—
849C4—44no—
850C4—44no—
851C4—48no—
852C4—44no—
853C4—48no—
854C4—42no—
855C4—48no—
856C2—24no—
857C2—24no—
858C2—24no—
859C2—82no—
860C2—88no—
861C2C22×#54011yescharacteristic
862C2#6284411yescharacteristic
863C2#6285611yescharacteristic
864C2#6286312yes—
865C2#6286612yes—
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. #41429C2semidirect
2. #40670C2semidirect
3. #40669C2semidirect
4. #40642C2semidirect
5. #37465C2semidirect
6. #37459C2semidirect
7. #36978C2semidirect
8. #36976C2semidirect
9. #36731C2semidirect
10. #36727C2semidirect
11. #35358C2semidirect
12. #35351C2semidirect
13. #35000C2semidirect
14. C2×#2656C2semidirect
15. C2×#2646C2semidirect
16. #34205C2semidirect
17. C2×#2318C2semidirect
23. #2854C22semidirect
24. #2847C22semidirect
25. #2837C22semidirect
26. #2836C22semidirect
27. #2829C22semidirect
28. #2828C22semidirect
29. #2777C22semidirect
30. #2773C22semidirect
31. #2768C22semidirect
32. #2756C22semidirect
33. #2753C22semidirect
34. #2749C22semidirect
35. #2748C22semidirect
36. #2743C22semidirect
37. #2741C22semidirect
38. #2740C22semidirect
39. #2738C22semidirect
40. #2706C22semidirect
41. #2703C22semidirect
42. #2699C22semidirect
43. #2688C22semidirect
44. #2671C22semidirect
45. #2667C22semidirect
46. #2661C22semidirect
50. #2656C22semidirect
51. #2654C22semidirect
52. #2651C22semidirect
53. #2649C22semidirect
54. #2648C22semidirect
55. #2646C22semidirect
56. #2646C22semidirect
57. #2646C22semidirect
58. #2646C22semidirect
59. #2635C22semidirect
60. #2630C22semidirect
61. #2618C22semidirect
62. #2617C22semidirect
63. #2543C22semidirect
64. #2543C22semidirect
65. #2543C22semidirect
67. #2522C22semidirect
68. #2516C22semidirect
70. #2484C22semidirect
71. #2483C22semidirect
72. #2482C22semidirect
73. #2464C22semidirect
74. #2457C22semidirect
75. #2444C22semidirect
76. #2444C22semidirect
77. #2444C22semidirect
78. #2444C22semidirect
79. #2443C22semidirect
80. #2443C22semidirect
81. #2443C22semidirect
82. #2443C22semidirect
83. #2425C22semidirect
84. #2425C22semidirect
85. #2424C22semidirect
86. #2424C22semidirect
87. #2416C22semidirect
88. #2416C22semidirect
89. #2416C22semidirect
90. #2416C22semidirect
96. #2405C22semidirect
97. C2×#400C22semidirect
98. C2×#399C22semidirect
99. C2×#398C22semidirect
100. C2×#392C22semidirect
101. #2364C22semidirect
102. #2361C22semidirect
103. #2361C22semidirect
104. #2344C22semidirect
105. #2342C22semidirect
106. D4×C22⋊C4C22semidirect
107. #2325C22semidirect
108. #2325C22semidirect
110. #2318C22semidirect
113. C4×#121C22semidirect
114. C4×#121C22semidirect
115. C2×#388C22semidirect
116. C2×#387C22semidirect
120. C2×#383C22semidirect
121. C2×#382C22semidirect
122. C2×#381C22semidirect
124. C2×#380C22semidirect

Maximal subgroups

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

subgroupindex
#414292
#406702
#406692
#406422
#374652
#374592
#369782
#369762
#367312
#367272
#353582
#353512
#350002
C2×#26562
C2×#26462
#342052
C2×#23182