Finite Group Databasebeta

← #7671990

Subgroups — #7671990

Order 512.

6220 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59680C214yesmaximal, complemented
2#59679C214yesmaximal, complemented
3#59647C214yesmaximal, complemented
4#59646C214yesmaximal, complemented
5#39552C218yesmaximal, complemented
6#39189C218yesmaximal, complemented
7#36640C211yesmaximal, characteristic, complemented
8#36440C218yesmaximal, complemented
9#36211C214yesmaximal, complemented
10#36182C214yesmaximal, complemented
11#35558C212yesmaximal, complemented
12#35533C212yesmaximal, complemented
13#35272C211yesmaximal, characteristic, complemented
14#35272C211yesmaximal, characteristic, complemented
15#35152C212yesmaximal, complemented
16#34265C212yesmaximal, complemented
17#34188C211yesmaximal, characteristic, complemented
18#34183C211yesmaximal, characteristic, complemented
19C4×#532C211yesmaximal, characteristic, complemented
20C2×C4×#127C211yesmaximal, characteristic, complemented
21C2×#553C2218yescomplemented
22C2×#535C2212yes—
23C2×#535C2212yes—
24C2×#532C2211yescharacteristic
25C22×#127C2211yescharacteristic
26C2×#520C2212yes—
27C2×C4×#41C2211yescharacteristic
28C2×C4×#41C2211yescharacteristic
29C22×C4×D4C2212yes—
30C22×C4×D4C2214yes—
31#2864C2214yescomplemented
32#2859C2212yescomplemented
33#2859C2212yescomplemented
34#2856C2212yes—
35#2856C2214yes—
36#2856C2212yes—
37#2851C2214yes—
38#2851C2214yes—
39#2849C2218yes—
40#2803C22116yescomplemented
41#2800C22116yescomplemented
42#2797C22116yescomplemented
43#2714C22116yescomplemented
44#2622C2218yes—
45#2619C2214yes—
46#2619C2214yes—
47#2602C22116yescomplemented
48#2600C22116yescomplemented
49#2566C2218yescomplemented
50#2548C2214yes—
51#2548C2214yes—
52#2548C2214yescomplemented
53#2545C2214yescomplemented
54#2544C2214yescomplemented
55#2541C2214yes—
56#2541C2214yes—
57#2541C2214yescomplemented
58#2535C2218yescomplemented
59#2513C2218yescomplemented
60#2513C2218yescomplemented
61#2513C2218yescomplemented
62#2512C2218yescomplemented
63#2512C2218yescomplemented
64#2512C2218yescomplemented
65#2504C2218yescomplemented
66#2500C2218yescomplemented
67#2490C2218yescomplemented
68#2490C2218yescomplemented
69#2480C22116yes—
70#2466C22116yescomplemented
71#2456C22116yescomplemented
72#2447C2218yescomplemented
73#2445C2218yescomplemented
74#2424C22116yes—
75#2422C2218yescomplemented
76#2422C2218yescomplemented
77#2420C2218yescomplemented
78#2420C2218yescomplemented
79#2416C2218yescomplemented
80#2416C2218yescomplemented
81#2414C2218yescomplemented
82#2414C2218yescomplemented
83#2408C2218yes—
84#2408C2218yes—
85#2367C2218yescomplemented
86#2366C2218yescomplemented
87#2363C2218yescomplemented
88#2363C2218yescomplemented
89#2361C2218yescomplemented
90#2361C2218yescomplemented
91#2357C2218yescomplemented
92#2355C2214yescomplemented
93#2354C2214yescomplemented
94#2352C2218yes—
95Q8×C4⋊C4C2214yescomplemented
96D4×C4⋊C4C2218yes—
97D4×C4⋊C4C2214yescomplemented
98#2321C2218yes—
99#2317C2212yes—
100#2317C2214yescomplemented
101#2314C2214yescomplemented
102#2311C2212yes—
103#2309C2212yes—
104#2309C2212yes—
105C4×C4⋊Q8C2212yescomplemented
106C4×#127C2214yes—
107C4×#127C2214yes—
108C4×#127C2214yes—
109C4×#127C2214yes—
110C4×#127C2212yescomplemented
111C4×#125C2214yescomplemented
112C4×#125C2214yescomplemented
113C4×#124C2212yescomplemented
114C4×#124C2212yescomplemented
115C4×#121C2214yes—
116C4×#121C2214yes—
117C4×#120C2218yes—
118#2297C2211yescharacteristic
119#2297C2211yescharacteristic
120#2296C2212yes—
121#2296C2212yes—
122#2293C2214yescomplemented
123C2×#390C2214yes—
124C2×#390C2212yes—
125#2285C2211yescharacteristic
126#2285C2211yescharacteristic
127#2285C2211yescharacteristic
128#2285C2214yescomplemented
129#2285C2212yescomplemented
130C2×#384C2211yescharacteristic
131C2×#384C2212yescomplemented
132#2274C2212yes—
133C42×D4C2214yescomplemented
134C2×C43C2211yescharacteristic
135C22×#41C2311yescharacteristic
136C22×#41C2311yescharacteristic
137C23×D4C2312yes—
138C23×D4C2314yes—
139C24×C4C2314yes—
140#553—432no—
141#535—216no—
142#535—48no—
143#532—28no—
144C2×C4⋊Q8C2311yescharacteristic
145C2×#127—28no—
146C2×#127C2312yes—
147C2×#127C2312yes—
148C2×#127C2314yes—
149C2×#127C2311yescharacteristic
150C2×#127C2314yes—
151C2×#127C2314yes—
152C2×#126C23116yes—
153C2×#125C2314yes—
154C2×#125C2314yes—
155C2×#124C2314yes—
156C2×#124C2311yescharacteristic
157C2×#124C2311yescharacteristic
158C2×#124C2314yes—
159C2×#123C23116yes—
160C2×#121C2318yes—
161C2×#121C2314yes—
162C2×#121C2318yes—
163C2×#121C2318yes—
164C2×#121C2314yes—
165C2×#121C2314yes—
166C2×#121C2318yes—
167C2×#121C2318yes—
168C2×#121C23116yes—
169C2×#120C2318yes—
170C2×#120C2318yes—
171#520—48no—
172C4×#41—28no—
173C4×#41—28no—
174C2×C4×Q8C2312yes—
175C2×C4×Q8C2312yes—
176C2×C4×Q8C2314yes—
177C2×C4×D4—48no—
178C2×C4×D4—416no—
179C2×C4×D4C2318yes—
180C2×C4×D4C2312yes—
181C2×C4×D4C2312yes—
182C2×C4×D4C2314yes—
183C2×C4×D4C2314yes—
184C2×C4×D4C2314yes—
185C2×C4×D4C2314yes—
186C2×C4×D4C2318yes—
187C2×C4×D4C2318yes—
188C2×C4×D4C2318yes—
189C2×C4×D4C2318yes—
190C2×C4×D4C2318yes—
191C2×C4×D4C2314yes—
192C2×C4×D4C2318yes—
193C2×C4×D4C23116yes—
194C2×C4×D4C2314yes—
195C2×#117C2311yescharacteristic
196C2×#117C2311yescharacteristic
197C2×#117C2312yes—
198C2×#117C2312yes—
199C2×#117C2312yes—
200C2×#117C2312yes—
201C2×#117C2314yes—
202C2×#117C2318yes—
203C22×C4⋊C4C2312yes—
204C22×C4⋊C4C2314yes—
205C22×C4⋊C4C2314yes—
206C22×C4⋊C4C2318yes—
207C22×C22⋊C4C2314yes—
208C22×C22⋊C4C2318yes—
209C22×C42C2312yes—
210C22×C42C2312yes—
211C22×C42C2312yes—
212C22×C42C2311yescharacteristic
213C22×C42C2311yescharacteristic
214C22×C42C2312yes—
215C22×C42C2311yescharacteristic
216#397C23116yes—
217#397C23116yes—
218#397C23116yes—
219#397C23116yes—
220#397C23116yes—
221#396C23116yes—
222#396C23116yes—
223#394C23116yes—
224#394C23116yes—
225#394C23116yes—
226#394C23116yes—
227#394C23116yes—
228#394C23116yes—
229#392C23116yes—
230#392C23116yes—
231#392C23116yes—
232#391C2312yes—
233#391C2312yes—
234#391C2314yes—
235#390C2318yes—
236#390C2318yes—
237#390C2318yes—
238#390C2318yes—
239#390C2314yes—
240#390C2314yes—
241#390C2318yes—
242#390C2312yes—
243#390C2312yes—
244#390C2314yes—
245#390C2314yes—
246#390C2314yes—
247#390C2314yes—
248#390C2318yes—
249#390C2318yes—
250#390C2318yes—
251#390C2318yes—
252#390C2318yes—
253#390C2314yes—
254#390C23116yes—
255#390C2318yes—
256#390C2318yes—
257#390C23116yes—
258#389C2314yes—
259#389C2314yes—
260#389C2314yes—
261#389C2314yes—
262#389C2314yes—
263#389C2314yes—
264#389C2318yes—
265#389C23116yes—
266#389C2314yes—
267#389C2314yes—
268#389C2314yes—
269#389C2314yes—
270#388C23116yes—
271#388C23116yes—
272#388C23116yes—
273#388C2314yes—
274#388C23116yes—
275#388C2314yes—
276#388C23116yes—
277#388C23116yes—
278#388C23116yes—
279#388C2314yes—
280#388C2314yes—
281#387C2318yes—
282#387C2318yes—
283#387C2318yes—
284#387C2318yes—
285#387C23116yes—
286#386C2318yes—
287#386C2312yes—
288#386C23116yes—
289#386C2312yes—
290#386C23116yes—
291#386C23116yes—
292#386C23116yes—
293#386C2312yes—
294#386C2312yes—
295#385C23116yes—
296#385C23116yes—
297#385C2318yes—
298#385C23116yes—
299#385C2314yes—
300#385C2314yes—
301#385C2318yes—
302#384C2312yes—
303#384C2314yes—
304#384C2312yes—
305#384C2312yes—
306#384C2318yes—
307#384C2314yes—
308#384C2311yescharacteristic
309#384C2311yescharacteristic
310#384C2312yes—
311#382C2314yes—
312#382C2314yes—
313#382C2318yes—
314#382C2312yes—
315#382C2314yes—
316#382C2312yes—
317#382C2312yes—
318#381C23116yes—
319#380C2318yes—
320#380C2314yes—
321#380C2314yes—
322#380C2318yes—
323#380C2318yes—
324#380C2314yes—
325#379C2318yes—
326#379C2318yes—
327C4×C4⋊C4C2314yes—
328C4×C4⋊C4C2314yes—
329C4×C4⋊C4C2318yes—
330C4×C4⋊C4C2314yes—
331C4×C4⋊C4C2314yes—
332C4×C4⋊C4C2314yes—
333C4×C4⋊C4C2314yes—
334C4×C4⋊C4C2318yes—
335C4×C4⋊C4C2318yes—
336C4×C4⋊C4C2318yes—
337C4×C4⋊C4C2318yes—
338C4×C4⋊C4C2314yes—
339C4×C22⋊C4C2318yes—
340C4×C22⋊C4C23116yes—
341C4×C22⋊C4C2314yes—
342C4×C22⋊C4C2314yes—
343C4×C22⋊C4C2314yes—
344C4×C22⋊C4C2314yes—
345C4×C22⋊C4C2314yes—
346C4×C22⋊C4C2314yes—
347C43C2312yes—
348C43C2312yes—
349C43C2312yes—
350C43C2312yes—
351C25C2414yes—
352C2×#41—24no—
353C2×#41—24no—
354C2×#41—24no—
355C2×#41—24no—
356C2×#41—24no—
357C2×#41#4118yes—
358C22×Q8C2411yescharacteristic
359C22×Q8C2411yescharacteristic
360C22×D4—216no—
361C22×D4—28no—
362C22×D4—28no—
363C22×D4—28no—
364C22×D4—48no—
365C22×D4—48no—
366C22×D4C2412yes—
367C22×D4C2414yes—
368C22×D4C2418yes—
369C22×D4C2414yes—
370C22×D4C2411yescharacteristic
371C22×D4C2414yes—
372C22×D4C2412yes—
373C22×D4C2411yescharacteristic
374C22×D4C2418yes—
375C22×D4C24116yes—
376C22×D4C2418yes—
377C22×D4C2418yes—
378C23×C4—416no—
379C23×C4—48no—
380C23×C4C2414yes—
381C23×C4C2414yes—
382C23×C4C2412yes—
383C23×C4C2411yescharacteristic
384C23×C4C2412yes—
385C23×C4C2412yes—
386C23×C4C2412yes—
387C23×C4C2411yescharacteristic
388C23×C4C2414yes—
389C23×C4C24116yes—
390C23×C4C2418yes—
391C23×C4C2411yescharacteristic
392C4⋊Q8—24no—
393#127—24no—
394#127—216no—
395#127—28no—
396#127—28no—
397#127—216no—
398#127—48no—
399#126—432no—
400#125—216no—
401#125—48no—
402#124—24no—
403#124—216no—
404#124—24no—
405#124—48no—
406#123—432no—
407#121—216no—
408#121—232no—
409#121—432no—
410#121—416no—
411#121—416no—
412#121—48no—
413#121—48no—
414#121—416no—
415#121—416no—
416#120—232no—
417#120—416no—
418C4×Q8—28no—
419C4×Q8—28no—
420C4×Q8—48no—
421C4×D4—216no—
422C4×D4—216no—
423C4×D4—216no—
424C4×D4—28no—
425C4×D4—28no—
426C4×D4—232no—
427C4×D4—216no—
428C4×D4—416no—
429C4×D4—416no—
430C4×D4—416no—
431C4×D4—416no—
432C4×D4—48no—
433C4×D4—416no—
434C4×D4—48no—
435C4×D4—432no—
436C4×D4—416no—
437#117—24no—
438#117—24no—
439#117—28no—
440#117—28no—
441#117—28no—
442#117—28no—
443#117—48no—
444#117—416no—
445C2×C4⋊C4—28no—
446C2×C4⋊C4—48no—
447C2×C4⋊C4—48no—
448C2×C4⋊C4—416no—
449C2×C4⋊C4C2414yes—
450C2×C4⋊C4C2418yes—
451C2×C4⋊C4C2412yes—
452C2×C4⋊C4C2414yes—
453C2×C4⋊C4C2414yes—
454C2×C4⋊C4C2412yes—
455C2×C4⋊C4C2414yes—
456C2×C4⋊C4C2412yes—
457C2×C4⋊C4C2412yes—
458C2×C4⋊C4C2414yes—
459C2×C4⋊C4C2414yes—
460C2×C4⋊C4C2414yes—
461C2×C4⋊C4C2418yes—
462C2×C4⋊C4C2414yes—
463C2×C4⋊C4C2414yes—
464C2×C4⋊C4C2418yes—
465C2×C4⋊C4C2414yes—
466C2×C4⋊C4C2414yes—
467C2×C4⋊C4C2418yes—
468C2×C4⋊C4C2418yes—
469C2×C4⋊C4C24116yes—
470C2×C4⋊C4C2414yes—
471C2×C4⋊C4C2418yes—
472C2×C4⋊C4C2418yes—
473C2×C22⋊C4—416no—
474C2×C22⋊C4—48no—
475C2×C22⋊C4C24116yes—
476C2×C22⋊C4C2414yes—
477C2×C22⋊C4C2412yes—
478C2×C22⋊C4C2412yes—
479C2×C22⋊C4C2414yes—
480C2×C22⋊C4C2414yes—
481C2×C22⋊C4C2414yes—
482C2×C22⋊C4C2414yes—
483C2×C22⋊C4C2414yes—
484C2×C22⋊C4C2414yes—
485C2×C22⋊C4C2414yes—
486C2×C22⋊C4C24116yes—
487C2×C22⋊C4C24116yes—
488C2×C22⋊C4C24116yes—
489C2×C22⋊C4C2418yes—
490C2×C22⋊C4C24116yes—
491C2×C22⋊C4C24116yes—
492C2×C22⋊C4C2414yes—
493C2×C22⋊C4C2414yes—
494C2×C22⋊C4C2418yes—
495C2×C22⋊C4C2418yes—
496C2×C22⋊C4C24116yes—
497C2×C22⋊C4C24116yes—
498C2×C22⋊C4C24116yes—
499C2×C42—24no—
500C2×C42—24no—
501C2×C42—28no—
502C2×C42—28no—
503C2×C42—28no—
504C2×C42—44no—
505C2×C42#4118yes—
506C2×C42C2412yes—
507C2×C42C2412yes—
508C2×C42C2414yes—
509C2×C42C2414yes—
510C2×C42C2412yes—
511C2×C42C2412yes—
512C2×C42C2412yes—
513C2×C42C2412yes—
514C2×C42C2412yes—
515C2×C42C2412yes—
516C2×C42C2412yes—
517C2×C42C2414yes—
518C2×C42C2414yes—
519C2×C42C2411yescharacteristic
520C2×C42C2412yes—
521C2×C42C2411yescharacteristic
522C2×C42C2418yes—
523C2×C42C24116yes—
524C2×C42C2412yes—
525C2×C42C2412yes—
526C2×C42C2411yescharacteristic
527C2×C42C2412yes—
528C2×C42C2411yescharacteristic
529C2×C42C2412yes—
530#95C2414yes—
531#95C2414yes—
532#95C2414yes—
533#95C2414yes—
534#95C2418yes—
535#95C2414yes—
536#95C2414yes—
537#95C24116yes—
538#95C24116yes—
539#95C24116yes—
540#95C2418yes—
541#95C2418yes—
542#95C2418yes—
543#95C2418yes—
544#95C2418yes—
545C24—28no—
546C24—28no—
547C24—28no—
548C24—48no—
549C24—48no—
550C24C2518yes—
551C24C2512yes—
552C24C2512yes—
553C24C2511yescharacteristic
554#41—232no—
555#41—416no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8C2×#4114yes—
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—28no—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—232no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—28no—
572C2×D4—28no—
573C2×D4—22no—
574C2×D4—216no—
575C2×D4—28no—
576C2×D4—28no—
577C2×D4—216no—
578C2×D4—22no—
579C2×D4—216no—
580C2×D4—28no—
581C2×D4—28no—
582C2×D4—28no—
583C2×D4—22no—
584C2×D4—216no—
585C2×D4—48no—
586C2×D4—44no—
587C2×D4—48no—
588C2×D4—464no—
589C2×D4—416no—
590C2×D4—416no—
591C2×D4—48no—
592C2×D4—48no—
593C2×D4—416no—
594C2×D4—416no—
595C2×D4—432no—
596C2×D4C2×#4118yes—
597C2×D4C2×#4114yes—
598C22×C4—22no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—22no—
606C22×C4—28no—
607C22×C4—24no—
608C22×C4—28no—
609C22×C4—28no—
610C22×C4—24no—
611C22×C4—24no—
612C22×C4—28no—
613C22×C4—28no—
614C22×C4—24no—
615C22×C4—28no—
616C22×C4—28no—
617C22×C4—232no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—48no—
621C22×C4—416no—
622C22×C4—416no—
623C22×C4—48no—
624C22×C4—416no—
625C22×C4—832no—
626C22×C4C2×#4118yes—
627C22×C4C2×#4118yes—
628C22×C4C2×#4114yes—
629C22×C4C2×#4114yes—
630C22×C4H(5,𝔽2)14yes—
631C22×C4C2512yes—
632C22×C4C2518yes—
633C22×C4C2514yes—
634C22×C4C2512yes—
635C22×C4C2514yes—
636C22×C4C2512yes—
637C22×C4C2514yes—
638C22×C4C2518yes—
639C22×C4C2514yes—
640C22×C4C2512yes—
641C22×C4C2512yes—
642C22×C4C2512yes—
643C22×C4C2512yes—
644C22×C4C2511yescharacteristic
645C22×C4C2511yescharacteristic
646C22×C4C2512yes—
647C4⋊C4—28no—
648C4⋊C4—24no—
649C4⋊C4—24no—
650C4⋊C4—28no—
651C4⋊C4—28no—
652C4⋊C4—28no—
653C4⋊C4—28no—
654C4⋊C4—28no—
655C4⋊C4—24no—
656C4⋊C4—216no—
657C4⋊C4—28no—
658C4⋊C4—24no—
659C4⋊C4—28no—
660C4⋊C4—28no—
661C4⋊C4—216no—
662C4⋊C4—216no—
663C4⋊C4—28no—
664C4⋊C4—28no—
665C4⋊C4—48no—
666C4⋊C4—48no—
667C4⋊C4—416no—
668C4⋊C4—44no—
669C4⋊C4—48no—
670C4⋊C4—48no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—28no—
674C22⋊C4—28no—
675C22⋊C4—28no—
676C22⋊C4—28no—
677C22⋊C4—28no—
678C22⋊C4—28no—
679C22⋊C4—232no—
680C22⋊C4—232no—
681C22⋊C4—28no—
682C22⋊C4—28no—
683C22⋊C4—416no—
684C22⋊C4—416no—
685C22⋊C4—48no—
686C22⋊C4—416no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—416no—
690C22⋊C4—48no—
691C22⋊C4—48no—
692C22⋊C4—416no—
693C22⋊C4—416no—
694C22⋊C4—416no—
695C42—24no—
696C42—24no—
697C42—24no—
698C42—28no—
699C42—28no—
700C42—22no—
701C42—22no—
702C42—28no—
703C42—24no—
704C42—24no—
705C42—24no—
706C42—24no—
707C42—24no—
708C42—28no—
709C42—24no—
710C42—24no—
711C42—42no—
712C42—42no—
713C42—48no—
714C42—416no—
715C42C2×#4114yes—
716C42C2×#4114yes—
717C42C2×#4118yes—
718C42H(5,𝔽2)18yes—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—24no—
723C23—22no—
724C23—24no—
725C23—22no—
726C23—22no—
727C23—28no—
728C23—28no—
729C23—24no—
730C23—216no—
731C23—28no—
732C23—22no—
733C23—216no—
734C23—24no—
735C23—432no—
736C23—416no—
737C23—88no—
738C23—816no—
739C23—88no—
740C23C22×#4114yes—
741C23C22×#4112yes—
742C23C22×#4112yes—
743C23C2×H(5,𝔽2)12yes—
744C23C2611yescharacteristic
745Q8—28no—
746Q8—44no—
747D4—216no—
748D4—28no—
749D4—416no—
750D4—432no—
751D4—48no—
752D4—416no—
753D4—416no—
754D4—44no—
755D4—432no—
756D4—832no—
757D4—168no—
758D4—168no—
759C2×C4—28no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—216no—
769C2×C4—216no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—28no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—28no—
782C2×C4—216no—
783C2×C4—28no—
784C2×C4—24no—
785C2×C4—22no—
786C2×C4—28no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—48no—
795C2×C4—44no—
796C2×C4—48no—
797C2×C4—416no—
798C2×C4—416no—
799C2×C4—832no—
800C2×C4—88no—
801C2×C4—168no—
802C2×C4#553116yescomplemented
803C2×C4C22×#4114yes—
804C2×C4C22×#4114yes—
805C2×C4C22×#4112yes—
806C2×C4C22×#4112yes—
807C2×C4C22×#4112yes—
808C2×C4C22×#4112yes—
809C2×C4C22×#4114yes—
810C2×C4C2×H(5,𝔽2)14yes—
811C2×C4C2×H(5,𝔽2)14yes—
812C2×C4C2×H(5,𝔽2)12yes—
813C2×C4C2×H(5,𝔽2)12yes—
814C2×C4C2×H(5,𝔽2)14yes—
815C2×C4#58514yes—
816C22—24no—
817C22—24no—
818C22—22no—
819C22—22no—
820C22—28no—
821C22—24no—
822C22—44no—
823C22—42no—
824C22—42no—
825C22—44no—
826C22—416no—
827C22—44no—
828C22—416no—
829C22—48no—
830C22—42no—
831C22—42no—
832C22—48no—
833C22—42no—
834C22—48no—
835C22—832no—
836C22C2×#55314yes—
837C22C23×#4111yescharacteristic
838C22C23×#4111yescharacteristic
839C22C22×H(5,𝔽2)12yes—
840C22C22×H(5,𝔽2)11yescharacteristic
841C22C2×#58512yes—
842C4—24no—
843C4—24no—
844C4—24no—
845C4—24no—
846C4—44no—
847C4—44no—
848C4—42no—
849C4—48no—
850C4—48no—
851C4—44no—
852C4—42no—
853C4—44no—
854C4—42no—
855C4C2×#55314yes—
856C4C2×#55314yes—
857C4#350618yes—
858C2—24no—
859C2—44no—
860C2—82no—
861C2—88no—
862C2C22×#55311yescharacteristic
863C2C2×#350612yes—
864C2#6280012yes—
865C2#6283211yescharacteristic
866C2#6283611yescharacteristic
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. #59680C2semidirect
2. #59679C2semidirect
3. #59647C2semidirect
4. #59646C2semidirect
5. #39552C2semidirect
6. #39189C2semidirect
7. #36640C2semidirect
8. #36440C2semidirect
9. #36211C2semidirect
10. #36182C2semidirect
11. #35558C2semidirect
12. #35533C2semidirect
13. #35272C2semidirect
14. #35272C2semidirect
15. #35152C2semidirect
16. #34265C2semidirect
17. #34188C2semidirect
18. #34183C2semidirect
19. C4×#532C2semidirect
20. C2×C4×#127C2semidirect
21. C2×#553C22semidirect
31. #2864C22semidirect
32. #2859C22semidirect
33. #2859C22semidirect
40. #2803C22semidirect
41. #2800C22semidirect
42. #2797C22semidirect
43. #2714C22semidirect
47. #2602C22semidirect
48. #2600C22semidirect
49. #2566C22semidirect
52. #2548C22semidirect
53. #2545C22semidirect
54. #2544C22semidirect
57. #2541C22semidirect
58. #2535C22semidirect
59. #2513C22semidirect
60. #2513C22semidirect
61. #2513C22semidirect
62. #2512C22semidirect
63. #2512C22semidirect
64. #2512C22semidirect
65. #2504C22semidirect
66. #2500C22semidirect
67. #2490C22semidirect
68. #2490C22semidirect
70. #2466C22semidirect
71. #2456C22semidirect
72. #2447C22semidirect
73. #2445C22semidirect
75. #2422C22semidirect
76. #2422C22semidirect
77. #2420C22semidirect
78. #2420C22semidirect
79. #2416C22semidirect
80. #2416C22semidirect
81. #2414C22semidirect
82. #2414C22semidirect
85. #2367C22semidirect
86. #2366C22semidirect
87. #2363C22semidirect
88. #2363C22semidirect
89. #2361C22semidirect
90. #2361C22semidirect
91. #2357C22semidirect
92. #2355C22semidirect
93. #2354C22semidirect
95. Q8×C4⋊C4C22semidirect
97. D4×C4⋊C4C22semidirect
100. #2317C22semidirect
101. #2314C22semidirect
105. C4×C4⋊Q8C22semidirect
110. C4×#127C22semidirect
111. C4×#125C22semidirect
112. C4×#125C22semidirect
113. C4×#124C22semidirect
114. C4×#124C22semidirect
122. #2293C22semidirect
128. #2285C22semidirect
129. #2285C22semidirect
131. C2×#384C22semidirect
133. C42×D4C22semidirect
802. C2×C4#553semidirect

Maximal subgroups

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

subgroupindex
#596802
#596792
#596472
#596462
#395522
#391892
#366402
#364402
#362112
#361822
#355582
#355332
#352722
#351522
#342652
#341882
#341832
C4×#5322
C2×C4×#1272