Finite Group Databasebeta

← #7632098

Subgroups — #7632098

Order 512.

8050 conjugacy classes of subgroups.

The subgroup lattice has 845 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#552C211yesmaximal, characteristic, complemented
2C2×C4×2−1+4C211yesmaximal, characteristic, complemented
3#36232C218yesmaximal, complemented
4#36228C218yesmaximal, complemented
5#35832C218yesmaximal, complemented
6#35772C218yesmaximal, complemented
7#35672C211yesmaximal, characteristic, complemented
8#35672C211yesmaximal, characteristic, complemented
9#35659C211yesmaximal, characteristic, complemented
10#35659C211yesmaximal, characteristic, complemented
11#35453C214yesmaximal, complemented
12#35356C214yesmaximal, complemented
13#35333C212yesmaximal, complemented
14#35143C214yesmaximal, complemented
15#34935C212yesmaximal, complemented
16#34875C214yesmaximal, complemented
17#34201C212yesmaximal, complemented
18#34200C212yesmaximal, complemented
19#34187C211yesmaximal, characteristic, complemented
20C22×2−1+4C2211yescharacteristic
21C2×#552—216no—
22C2×#552C2218yes—
23C2×#552C2218yes—
24C22×#126C2212yes—
25C22×#125C2211yescharacteristic
26C22×#125C2212yes—
27C2×#525C2212yes—
28C2×#525C2212yes—
29C22×#123C2212yes—
30C22×C22⋊Q8C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C4×2−1+4—216no—
33C2×#520C2214yes—
34C2×#520C2212yes—
35C2×#520C2214yescomplemented
36C2×#519C2211yescharacteristic
37C2×#519C2214yescomplemented
38C2×C4×#41C2212yes—
39C2×C4×#41C2214yes—
40C2×C4×#41C2214yescomplemented
41C22×C4×Q8C2211yescharacteristic
42C22×C4×Q8C2214yescomplemented
43C22×C4×D4C2211yescharacteristic
44C22×#117C2212yes—
45C22×#117C2211yescharacteristic
46C23×C4⋊C4C2211yescharacteristic
47#2852C22116yescomplemented
48#2851C2218yescomplemented
49#2637C2218yescomplemented
50#2636C2218yescomplemented
51#2629C2218yescomplemented
52#2609C22116yescomplemented
53#2604C2218yescomplemented
54#2603C2218yescomplemented
55#2601C22116yescomplemented
56#2599C2218yescomplemented
57#2598C2218yescomplemented
58#2579C2218yes—
59#2579C2218yes—
60#2566C2214yescomplemented
61#2566C2214yescomplemented
62#2565C2214yescomplemented
63#2565C2214yescomplemented
64#2538C2214yes—
65#2537C2214yes—
66#2536C2214yes—
67#2535C2214yes—
68#2534C2214yes—
69#2534C2214yes—
70#2486C2214yes—
71#2484C2214yes—
72#2484C2214yes—
73#2482C2214yes—
74#2482C2214yes—
75#2475C22116yescomplemented
76#2473C22116yescomplemented
77#2471C22116yes—
78#2462C22116yescomplemented
79#2460C22116yescomplemented
80#2458C22116yes—
81#2456C22116yes—
82#2443C22116yes—
83#2423C2218yescomplemented
84#2423C2218yescomplemented
85#2421C2218yescomplemented
86#2421C2218yescomplemented
87#2409C2218yescomplemented
88#2409C2218yescomplemented
89#2408C2214yes—
90#2407C2218yescomplemented
91#2407C2218yescomplemented
92#2406C2214yes—
93#2406C2214yes—
94#2404C2214yes—
95#2404C2214yes—
96#2396C2218yescomplemented
97#2392C2218yes—
98#2392C2218yescomplemented
99#2363C2218yescomplemented
100#2362C2218yescomplemented
101#2361C2218yescomplemented
102#2360C2218yescomplemented
103#2356C2218yescomplemented
104#2355C2218yescomplemented
105#2354C2218yescomplemented
106#2352C2218yescomplemented
107#2352C2218yescomplemented
108D4×C4⋊C4C2218yescomplemented
109#2322C2218yes—
110#2321C2218yes—
111#2317C2212yes—
112#2317C2212yes—
113#2313C2214yes—
114#2311C2212yes—
115#2311C2212yes—
116#2310C2211yescharacteristic
117#2310C2211yescharacteristic
118C4×#123C2218yes—
119C4×#121C2218yes—
120C4×#120C2218yes—
121#2290C22116yescomplemented
122#2285C2212yes—
123#2283C2214yes—
124#2280C2212yes—
125#2280C2212yes—
126#2274C2212yes—
127C2×2−1+4—216no—
128C2×2−1+4—28no—
129C22×#41C2314yes—
130C22×#41C2314yes—
131C22×#41C2312yes—
132C23×Q8C2314yes—
133C23×Q8C2311yescharacteristic
134C23×D4C2311yescharacteristic
135C24×C4C2311yescharacteristic
136C24×C4C2311yescharacteristic
137C24×C4C2312yes—
138#552—264no—
139#552—264no—
140C2×#126—216no—
141C2×#126C2318yes—
142C2×#126C2318yes—
143C2×#125—216no—
144C2×#125—28no—
145C2×#125C2314yes—
146C2×#125C2314yes—
147C2×#125C23116yes—
148#525—216no—
149#525—216no—
150C2×#123—216no—
151C2×#123C2314yes—
152C2×#123C2314yes—
153C2×#123C23116yes—
154C2×C22⋊Q8—28no—
155C2×C22⋊Q8—28no—
156C2×C22⋊Q8C2314yes—
157C2×C22⋊Q8C2314yes—
158C2×C22⋊Q8C2318yes—
159C2×C22⋊Q8C2318yes—
160C2×#121C2314yes—
161C2×#121C2314yes—
162C2×#121C2318yes—
163C2×#120C2314yes—
164C2×#120C2314yes—
165#520—232no—
166#520—216no—
167#520—232no—
168#519—28no—
169#519—232no—
170C4×#41—232no—
171C4×#41—232no—
172C4×#41—216no—
173C2×C4×Q8—232no—
174C2×C4×Q8D4116yescomplemented
175C2×C4×Q8C2312yes—
176C2×C4×Q8C2312yes—
177C2×C4×Q8C2314yes—
178C2×C4×Q8C2314yes—
179C2×C4×Q8C2314yes—
180C2×C4×Q8C2314yes—
181C2×C4×Q8C2318yes—
182C2×C4×Q8C2314yes—
183C2×C4×Q8C2314yes—
184C2×C4×Q8C2314yes—
185C2×C4×D4—28no—
186C2×C4×D4C2312yes—
187C2×C4×D4C2312yes—
188C2×C4×D4C2318yes—
189C2×C4×D4C2314yes—
190C2×C4×D4C2314yes—
191C2×C4×D4C2314yes—
192C2×C4×D4C2318yes—
193C2×C4×D4C2318yes—
194C2×C4×D4C2314yes—
195C2×C4×D4C2314yes—
196C2×C4×D4C2314yes—
197C2×C4×D4C2314yes—
198C2×C4×D4C2318yes—
199C2×C4×D4C23116yes—
200C2×#117—28no—
201C2×#117—216no—
202C2×#117C2312yes—
203C2×#117C2312yes—
204C2×#117C2312yes—
205C2×#117C2318yes—
206C2×#117C2318yes—
207C2×#117C2314yes—
208C2×#117C2318yes—
209C2×#117C2318yes—
210C2×#117C2314yes—
211C2×#117C2314yes—
212C2×#117C2318yes—
213C22×C4⋊C4—28no—
214C22×C4⋊C4C2311yescharacteristic
215C22×C4⋊C4C2311yescharacteristic
216C22×C4⋊C4C2312yes—
217C22×C4⋊C4C2312yes—
218C22×C4⋊C4C2312yes—
219C22×C4⋊C4C2314yes—
220C22×C4⋊C4C2318yes—
221C22×C4⋊C4C2312yes—
222C22×C4⋊C4C2311yescharacteristic
223C22×C4⋊C4C2318yes—
224C22×C4⋊C4C2312yes—
225C22×C4⋊C4C2312yes—
226C22×C4⋊C4C2311yescharacteristic
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2311yescharacteristic
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2311yescharacteristic
231C22×C22⋊C4C2312yes—
232C22×C42C2314yes—
233C22×C42C2318yes—
234C22×C42C2312yes—
235C22×C42C2312yes—
236C22×C42C2311yescharacteristic
237#400C2318yes—
238#400C2318yes—
239#399C2318yes—
240#399C2318yes—
241#398C23116yes—
242#398C23116yes—
243#398C2318yes—
244#398C2318yes—
245#398C2318yes—
246#397C2318yes—
247#397C2318yes—
248#397C2318yes—
249#396C23116yes—
250#396C23116yes—
251#396C2318yes—
252#396C2318yes—
253#395C2318yes—
254#395C2318yes—
255#394C2318yes—
256#394C2318yes—
257#394C2318yes—
258#394C2318yes—
259#394C2318yes—
260#393C2318yes—
261#393C2318yes—
262#392C2318yes—
263#392C2318yes—
264#392C2318yes—
265#391C2314yes—
266#391C2314yes—
267#391C2318yes—
268#391C2318yes—
269#390C2314yes—
270#390C2314yes—
271#390C23116yes—
272#390C2318yes—
273#389C2318yes—
274#389C2318yes—
275#389C23116yes—
276#389C2318yes—
277#388C23116yes—
278#388C23116yes—
279#388C23116yes—
280#388C2318yes—
281#388C23116yes—
282#388C23116yes—
283#388C2318yes—
284#388C23116yes—
285#387C23116yes—
286#387C23116yes—
287#387C23116yes—
288#387C23116yes—
289#387C23116yes—
290#387C23116yes—
291#387C23116yes—
292#387C23116yes—
293#386C2318yes—
294#386C2318yes—
295#386C23116yes—
296#386C2318yes—
297#386C23116yes—
298#386C2318yes—
299#386C23116yes—
300#386C23116yes—
301#385C23116yes—
302#385C23116yes—
303#385C2318yes—
304#385C2318yes—
305#385C23116yes—
306#385C23116yes—
307#385C23116yes—
308#385C23116yes—
309#384C2314yes—
310#384C2314yes—
311#384C2314yes—
312#383C2318yes—
313#382C2314yes—
314#382C2314yes—
315#382C2314yes—
316#382C2318yes—
317#381C2314yes—
318#381C2314yes—
319#381C2314yes—
320#381C2314yes—
321#380C2318yes—
322#380C2318yes—
323#380C2314yes—
324#380C2314yes—
325#380C2314yes—
326#380C2314yes—
327#380C2314yes—
328#380C2314yes—
329#380C2318yes—
330#379C2314yes—
331#379C2314yes—
332C4×C4⋊C4C2314yes—
333C4×C4⋊C4C2314yes—
334C4×C4⋊C4C2318yes—
335C4×C4⋊C4C2318yes—
336C4×C4⋊C4C2318yes—
337C4×C4⋊C4C23116yes—
338C4×C22⋊C4C2318yes—
339C4×C22⋊C4C23116yes—
340C4×C22⋊C4C23116yes—
341C4×C22⋊C4C2318yes—
342C4×C22⋊C4C2318yes—
343#376C2318yes—
344C25C2411yescharacteristic
345C25C2411yescharacteristic
3462−1+4—2128no—
347C2×#41—216no—
348C2×#41—232no—
349C2×#41—216no—
350C2×#41—216no—
351C2×#41—28no—
352C2×#41—216no—
353C2×#41—28no—
354C2×#41#41116yes—
355C22×Q8—216no—
356C22×Q8—216no—
357C22×Q8—216no—
358C22×Q8—28no—
359C22×Q8C2×D418yes—
360C22×Q8C2414yes—
361C22×Q8C2414yes—
362C22×Q8C2412yes—
363C22×D4—24no—
364C22×D4—44no—
365C22×D4C2414yes—
366C22×D4C2418yes—
367C22×D4C2414yes—
368C22×D4C2414yes—
369C22×D4C2412yes—
370C22×D4C2418yes—
371C23×C4—28no—
372C23×C4—24no—
373C23×C4—24no—
374C23×C4—28no—
375C23×C4—28no—
376C23×C4—48no—
377C23×C4C2411yescharacteristic
378C23×C4C2411yescharacteristic
379C23×C4C2414yes—
380C23×C4C2418yes—
381C23×C4C2414yes—
382C23×C4C2418yes—
383C23×C4C2412yes—
384C23×C4C2414yes—
385C23×C4C2412yes—
386C23×C4C2412yes—
387C23×C4C2418yes—
388C23×C4C2414yes—
389C23×C4C2414yes—
390C23×C4C2411yescharacteristic
391C23×C4C2412yes—
392C23×C4C2411yescharacteristic
393C23×C4C2411yescharacteristic
394#126—232no—
395#126—232no—
396#125—264no—
397#125—216no—
398#125—216no—
399#123—216no—
400#123—216no—
401#123—264no—
402C22⋊Q8—232no—
403C22⋊Q8—232no—
404C22⋊Q8—216no—
405C22⋊Q8—216no—
406#121—216no—
407#121—216no—
408#121—416no—
409#120—216no—
410#120—216no—
411C4×Q8—216no—
412C4×Q8—216no—
413C4×Q8—216no—
414C4×Q8—232no—
415C4×Q8—216no—
416C4×Q8—28no—
417C4×Q8—216no—
418C4×Q8—28no—
419C4×Q8C2×D4132yes—
420C4×Q8C2×D4132yes—
421C4×D4—216no—
422C4×D4—232no—
423C4×D4—216no—
424C4×D4—232no—
425C4×D4—232no—
426C4×D4—216no—
427C4×D4—232no—
428C4×D4—216no—
429C4×D4—216no—
430C4×D4—216no—
431C4×D4—28no—
432C4×D4—216no—
433C4×D4—28no—
434C4×D4—432no—
435#117—216no—
436#117—28no—
437#117—28no—
438#117—28no—
439#117—232no—
440#117—216no—
441#117—232no—
442#117—232no—
443#117—232no—
444#117—232no—
445#117—216no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—28no—
448C2×C4⋊C4—28no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—28no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—28no—
453C2×C4⋊C4—28no—
454C2×C4⋊C4—232no—
455C2×C4⋊C4—216no—
456C2×C4⋊C4—232no—
457C2×C4⋊C4C2×D418yes—
458C2×C4⋊C4C2×D4116yes—
459C2×C4⋊C4C2414yes—
460C2×C4⋊C4C2418yes—
461C2×C4⋊C4C2412yes—
462C2×C4⋊C4C2418yes—
463C2×C4⋊C4C2414yes—
464C2×C4⋊C4C2414yes—
465C2×C4⋊C4C2414yes—
466C2×C4⋊C4C2418yes—
467C2×C4⋊C4C2414yes—
468C2×C4⋊C4C2414yes—
469C2×C4⋊C4C2414yes—
470C2×C4⋊C4C2418yes—
471C2×C4⋊C4C2418yes—
472C2×C4⋊C4C2412yes—
473C2×C4⋊C4C2414yes—
474C2×C4⋊C4C2414yes—
475C2×C4⋊C4C2414yes—
476C2×C4⋊C4C2414yes—
477C2×C4⋊C4C2418yes—
478C2×C4⋊C4C2418yes—
479C2×C4⋊C4C24116yes—
480C2×C4⋊C4C2418yes—
481C2×C4⋊C4C2418yes—
482C2×C4⋊C4C24116yes—
483C2×C4⋊C4C2414yes—
484C2×C4⋊C4C2418yes—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—28no—
487C2×C22⋊C4—28no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—28no—
490C2×C22⋊C4C2412yes—
491C2×C22⋊C4C2412yes—
492C2×C22⋊C4C2418yes—
493C2×C22⋊C4C2418yes—
494C2×C22⋊C4C2412yes—
495C2×C22⋊C4C2412yes—
496C2×C22⋊C4C2418yes—
497C2×C22⋊C4C2414yes—
498C2×C22⋊C4C2418yes—
499C2×C22⋊C4C2414yes—
500C2×C22⋊C4C2414yes—
501C2×C22⋊C4C2414yes—
502C2×C22⋊C4C2414yes—
503C2×C22⋊C4C2418yes—
504C2×C22⋊C4C2418yes—
505C2×C22⋊C4C2418yes—
506C2×C22⋊C4C2418yes—
507C2×C22⋊C4C2418yes—
508C2×C22⋊C4C24116yes—
509C2×C22⋊C4C2418yes—
510C2×C22⋊C4C2418yes—
511C2×C22⋊C4C2418yes—
512C2×C22⋊C4C24116yes—
513C2×C42—28no—
514C2×C42—232no—
515C2×C42—216no—
516C2×C42C2×D4116yes—
517C2×C42C2×D418yes—
518C2×C42C2418yes—
519C2×C42C2414yes—
520C2×C42C2418yes—
521C2×C42C2418yes—
522C2×C42C2414yes—
523C2×C42C2414yes—
524C2×C42C2414yes—
525C2×C42C2414yes—
526C2×C42C24116yes—
527C2×C42C2414yes—
528C2×C42C2412yes—
529C2×C42C2414yes—
530C2×C42C2412yes—
531#95C2418yes—
532#95C2418yes—
533#95C2418yes—
534#95C2418yes—
535#95C2418yes—
536#95C24116yes—
537#95C2418yes—
538#95C2418yes—
539#95C24116yes—
540#95C24116yes—
541#95C24116yes—
542#95C2418yes—
543#95C24116yes—
544#95C2418yes—
545#95C2418yes—
546C24—22no—
547C24—24no—
548C24—22no—
549C24—24no—
550C24—24no—
551C24—42no—
552C24—42no—
553C24—42no—
554C24C2512yes—
555C24C2514yes—
556C24C2512yes—
557C24C2511yescharacteristic
558#41—2128no—
559#41—2128no—
560#41—264no—
561C2×Q8—2128no—
562C2×Q8—232no—
563C2×Q8—28no—
564C2×Q8—24no—
565C2×Q8—216no—
566C2×Q8—28no—
567C2×Q8—24no—
568C2×Q8—28no—
569C2×Q8C22×D4116yes—
570C2×Q8C2×#4118yes—
571C2×D4—28no—
572C2×D4—216no—
573C2×D4—28no—
574C2×D4—216no—
575C2×D4—216no—
576C2×D4—28no—
577C2×D4—216no—
578C2×D4—28no—
579C2×D4—24no—
580C2×D4—28no—
581C2×D4—24no—
582C2×D4—44no—
583C2×D4—48no—
584C2×D4—48no—
585C2×D4—48no—
586C2×D4—416no—
587C2×D4C2×#41116yes—
588C2×D4C2×#4118yes—
589C22×C4—216no—
590C22×C4—28no—
591C22×C4—216no—
592C22×C4—28no—
593C22×C4—216no—
594C22×C4—28no—
595C22×C4—22no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—22no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—216no—
602C22×C4—28no—
603C22×C4—216no—
604C22×C4—28no—
605C22×C4—28no—
606C22×C4—28no—
607C22×C4—28no—
608C22×C4—28no—
609C22×C4—28no—
610C22×C4—216no—
611C22×C4—28no—
612C22×C4—44no—
613C22×C4—48no—
614C22×C4—44no—
615C22×C4—42no—
616C22×C4—48no—
617C22×C4—44no—
618C22×C4—42no—
619C22×C4—416no—
620C22×C4—48no—
621C22×C4—432no—
622C22×C4—416no—
623C22×C4—416no—
624C22×C4C22×D418yes—
625C22×C4C22×D418yes—
626C22×C4C22×D414yes—
627C22×C4C22×D414yes—
628C22×C4C22×D414yes—
629C22×C4C2×#41116yes—
630C22×C4C2×#4118yes—
631C22×C4C2518yes—
632C22×C4C2518yes—
633C22×C4C2514yes—
634C22×C4C2512yes—
635C22×C4C2514yes—
636C22×C4C2514yes—
637C22×C4C2512yes—
638C22×C4C2514yes—
639C22×C4C2511yescharacteristic
640C22×C4C2514yes—
641C22×C4C2514yes—
642C22×C4C2512yes—
643C22×C4C2511yescharacteristic
644C22×C4C2514yes—
645C22×C4C2512yes—
646C4⋊C4—28no—
647C4⋊C4—216no—
648C4⋊C4—216no—
649C4⋊C4—28no—
650C4⋊C4—28no—
651C4⋊C4—24no—
652C4⋊C4—216no—
653C4⋊C4—28no—
654C4⋊C4—28no—
655C4⋊C4—28no—
656C4⋊C4—28no—
657C4⋊C4—216no—
658C4⋊C4—216no—
659C4⋊C4—28no—
660C4⋊C4—28no—
661C4⋊C4—24no—
662C4⋊C4—28no—
663C4⋊C4—28no—
664C4⋊C4—216no—
665C4⋊C4—216no—
666C4⋊C4—48no—
667C4⋊C4—416no—
668C4⋊C4—416no—
669C4⋊C4—48no—
670C4⋊C4C22×D4116yes—
671C4⋊C4C22×D4132yes—
672C22⋊C4—28no—
673C22⋊C4—28no—
674C22⋊C4—28no—
675C22⋊C4—216no—
676C22⋊C4—216no—
677C22⋊C4—216no—
678C22⋊C4—24no—
679C22⋊C4—24no—
680C22⋊C4—216no—
681C22⋊C4—216no—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—216no—
685C22⋊C4—216no—
686C22⋊C4—28no—
687C22⋊C4—28no—
688C22⋊C4—216no—
689C22⋊C4—216no—
690C22⋊C4—416no—
691C22⋊C4—48no—
692C22⋊C4—48no—
693C22⋊C4—416no—
694C22⋊C4—48no—
695C42—28no—
696C42—216no—
697C42—216no—
698C42—28no—
699C42—216no—
700C42—28no—
701C42—28no—
702C42—28no—
703C42—416no—
704C42C22×D4116yes—
705C42C22×D418yes—
706C42C22×D4116yes—
707C42C22×D418yes—
708C23—22no—
709C23—22no—
710C23—28no—
711C23—22no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—28no—
716C23—22no—
717C23—28no—
718C23—24no—
719C23—22no—
720C23—24no—
721C23—24no—
722C23—22no—
723C23—22no—
724C23—416no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—88no—
731C23C23×D412yes—
732C23C22×#4118yes—
733C23C22×#4114yes—
734C23#58514yes—
735C23C2611yescharacteristic
736Q8—232no—
737Q8—232no—
738Q8—216no—
739D4—232no—
740D4—232no—
741D4—216no—
742D4—416no—
743D4—432no—
744D4—816no—
745C2×C4—264no—
746C2×C4—24no—
747C2×C4—28no—
748C2×C4—24no—
749C2×C4—28no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—216no—
754C2×C4—232no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—28no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—28no—
772C2×C4—28no—
773C2×C4—48no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—432no—
777C2×C4—416no—
778C2×C4—48no—
779C2×C4—48no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—416no—
783C2×C4—416no—
784C2×C4—816no—
785C2×C4—88no—
786C2×C4#525116yes—
787C2×C4C23×D412yes—
788C2×C4C23×D418yes—
789C2×C4C23×D418yes—
790C2×C4C23×D414yes—
791C2×C4C23×D412yes—
792C2×C4C23×D414yes—
793C2×C4C22×#4118yes—
794C2×C4C22×#4114yes—
795C2×C4C22×#4114yes—
796C22—28no—
797C22—22no—
798C22—22no—
799C22—28no—
800C22—216no—
801C22—24no—
802C22—28no—
803C22—416no—
804C22—48no—
805C22—44no—
806C22—44no—
807C22—44no—
808C22—42no—
809C22—42no—
810C22—44no—
811C22—44no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—88no—
816C22C2×#52514yes—
817C22C24×D411yescharacteristic
818C22C23×#4112yes—
819C22C2×#58512yes—
820C222−1+612yes—
821C4—28no—
822C4—24no—
823C4—22no—
824C4—22no—
825C4—28no—
826C4—28no—
827C4—48no—
828C4—48no—
829C4—44no—
830C4—44no—
831C4—44no—
832C4—44no—
833C4—42no—
834C4—42no—
835C4C2×#52518yes—
836C2—24no—
837C2—48no—
838C2—44no—
839C2—82no—
840C2C22×#52511yescharacteristic
841C2#6281111yescharacteristic
842C2#6284811yescharacteristic
843C2#6299314yes—
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. C22×#552C2semidirect
2. C2×C4×2−1+4C2semidirect
3. #36232C2semidirect
4. #36228C2semidirect
5. #35832C2semidirect
6. #35772C2semidirect
7. #35672C2semidirect
8. #35672C2semidirect
9. #35659C2semidirect
10. #35659C2semidirect
11. #35453C2semidirect
12. #35356C2semidirect
13. #35333C2semidirect
14. #35143C2semidirect
15. #34935C2semidirect
16. #34875C2semidirect
17. #34201C2semidirect
18. #34200C2semidirect
19. #34187C2semidirect
35. C2×#520C22semidirect
37. C2×#519C22semidirect
40. C2×C4×#41C22semidirect
42. C22×C4×Q8C22semidirect
47. #2852C22semidirect
48. #2851C22semidirect
49. #2637C22semidirect
50. #2636C22semidirect
51. #2629C22semidirect
52. #2609C22semidirect
53. #2604C22semidirect
54. #2603C22semidirect
55. #2601C22semidirect
56. #2599C22semidirect
57. #2598C22semidirect
60. #2566C22semidirect
61. #2566C22semidirect
62. #2565C22semidirect
63. #2565C22semidirect
75. #2475C22semidirect
76. #2473C22semidirect
78. #2462C22semidirect
79. #2460C22semidirect
83. #2423C22semidirect
84. #2423C22semidirect
85. #2421C22semidirect
86. #2421C22semidirect
87. #2409C22semidirect
88. #2409C22semidirect
90. #2407C22semidirect
91. #2407C22semidirect
96. #2396C22semidirect
98. #2392C22semidirect
99. #2363C22semidirect
100. #2362C22semidirect
101. #2361C22semidirect
102. #2360C22semidirect
103. #2356C22semidirect
104. #2355C22semidirect
105. #2354C22semidirect
106. #2352C22semidirect
107. #2352C22semidirect
108. D4×C4⋊C4C22semidirect
121. #2290C22semidirect
174. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5522
C2×C4×2−1+42
#362322
#362282
#358322
#357722
#356722
#356592
#354532
#353562
#353332
#351432
#349352
#348752
#342012
#342002
#341872