Finite Group Databasebeta

← #7685477

Subgroups — #7685477

Order 512.

4897 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59870C213yesmaximal, complemented
2#59868C216yesmaximal, complemented
3#59322C213yesmaximal, complemented
4#59259C213yesmaximal, complemented
5#45405C216yesmaximal, complemented
6#45278C216yesmaximal, complemented
7#39635C213yesmaximal, complemented
8#39609C213yesmaximal, complemented
9#38101C216yesmaximal
10#36577C211yesmaximal, characteristic, complemented
11#36577C211yesmaximal, characteristic, complemented
12#36552C213yesmaximal, complemented
13#36466C211yesmaximal, characteristic, complemented
14#36435C212yesmaximal, complemented
15#36189C213yesmaximal
16#35971C212yesmaximal, complemented
17#35845C212yesmaximal, complemented
18#34772C213yesmaximal
19#34337C211yesmaximal, characteristic, complemented
20#34291C212yesmaximal
21#34182C211yesmaximal, characteristic, complemented
22C4×D4×Q8C211yesmaximal, characteristic
23C2×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
24C2×#557C2211yescharacteristic
25C2×#557C2212yes—
26C2×D4×Q8C2211yescharacteristic
27C2×#519C2212yes—
28C22×C4×Q8C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30C22×C4×Q8C2212yes—
31#2859C2213yes—
32#2857C2213yes—
33#2857C2213yes—
34#2851C2216yes—
35#2805C22112yes—
36#2802C22112yes—
37#2802C22112yes—
38#2792C22112yes—
39#2774C22112yes—
40#2768C22112yes—
41#2742C22112yes—
42#2647C2216yes—
43#2628C2216yes—
44#2590C22112yes—
45#2585C22112yes—
46#2584C2216yes—
47#2583C22112yes—
48#2582C2213yes—
49#2582C2213yes—
50#2581C2216yes—
51#2581C2216yes—
52#2571C2216yes—
53#2570C2216yes—
54#2568C2213yes—
55#2568C2213yes—
56#2567C2216yes—
57#2567C2216yes—
58#2565C2216yes—
59#2552C2213yes—
60#2551C2213yes—
61#2550C2216yes—
62#2522C2216yes—
63#2520C2216yes—
64#2511C2216yes—
65#2511C2216yes—
66#2511C2213yes—
67#2509C22112yes—
68#2509C2216yes—
69#2508C2216yes—
70#2508C2216yes—
71#2507C2216yes—
72#2507C2216yes—
73#2507C2216yes—
74#2507C2213yes—
75#2505C22112yes—
76#2505C2216yes—
77#2502C2213yes—
78#2497C2216yes—
79#2497C2213yes—
80#2492C2213yes—
81#2487C2216yes—
82#2487C2211yescharacteristic
83#2453C2216yes—
84#2453C2216yes—
85#2453C2216yes—
86#2453C2216yes—
87#2453C2216yes—
88#2451C2216yes—
89#2450C2216yes—
90#2442C2216yes—
91#2442C2216yes—
92#2442C2216yes—
93#2441C2216yes—
94#2441C2216yes—
95#2440C2216yes—
96#2440C2213yes—
97#2423C2216yes—
98#2417C2213yes—
99#2402C2216yes—
100#2396C2216yes—
101#2370C2216yes—
102#2365C2213yes—
103#2365C2213yes—
104#2365C2216yes—
105#2362C2216yes—
106#2360C2216yes—
107#2360C2213yes—
108#2360C2213yes—
109#2360C2216yes—
110#2355C2216yes—
111#2352C2216yes—
112#2351C2212yes—
113#2351C2212yes—
114#2351C2212yes—
115#2351C2212yes—
116#2351C2216yes—
117Q8×C4⋊C4C2212yes—
118Q8×C4⋊C4C2212yes—
119Q8×C4⋊C4C2211yescharacteristic
120Q8×C4⋊C4C2213yes—
121Q8×C4⋊C4C2216yes—
122Q8×C4⋊C4C2211yescharacteristic
123Q8×C4⋊C4C2213yes—
124Q8×C4⋊C4C2213yes—
125Q8×C4⋊C4C2211yescharacteristic
126Q8×C4⋊C4C2211yescharacteristic
127Q8×C4⋊C4C2213yes—
128Q8×C4⋊C4C2213yes—
129D4×C4⋊C4C2213yes—
130#2345C2216yes—
131Q8×C22⋊C4C2211yescharacteristic
132Q8×C22⋊C4C2212yes—
133Q8×C22⋊C4C2211yescharacteristic
134Q8×C22⋊C4C2212yes—
135#2330C2216yes—
136#2327C2216yes—
137#2323C2216yes—
138#2316C2216yes—
139C4×C4⋊Q8C2213yes—
140C4×C4⋊Q8C2213yes—
141C4×C4⋊Q8C2213yes—
142C4×C22⋊Q8C2216yes—
143C4×C22⋊Q8C2213yes—
144C4×C22⋊Q8C2213yes—
145C4×C22⋊Q8C2213yes—
146C4×C22⋊Q8C2213yes—
147C4×C22⋊Q8C2216yes—
148#2295C2213yes—
149C2×#389C2216yes—
150#2290C2216yes—
151#2285C2213yes—
152#2285C2213yes—
153C2×#384C2213yes—
154#2276C2212yes—
155C42×Q8C2211yescharacteristic
156C42×D4C2213yes—
157C2×C4×C4⋊C4C2213yes—
158C23×Q8C2311yescharacteristic
159C23×Q8C2311yescharacteristic
160#557—28no—
161#557—48no—
162D4×Q8Q8116yescomplemented
163C2×C4⋊Q8C2313yes—
164C2×C4⋊Q8C2313yes—
165C2×C4⋊Q8C2316yes—
166C2×C4⋊Q8C2313yes—
167C2×#125C2316yes—
168C2×#125C2316yes—
169C2×#125C2316yes—
170C2×C22⋊Q8C2313yes—
171C2×C22⋊Q8C2316yes—
172C2×C22⋊Q8C2313yes—
173C2×C22⋊Q8C2313yes—
174C2×C22⋊Q8C2313yes—
175#519—48no—
176C2×C4×Q8—28no—
177C2×C4×Q8—28no—
178C2×C4×Q8—48no—
179C2×C4×Q8C2313yes—
180C2×C4×Q8C2313yes—
181C2×C4×Q8C2313yes—
182C2×C4×Q8C2311yescharacteristic
183C2×C4×Q8C2312yes—
184C2×C4×Q8C2311yescharacteristic
185C2×C4×Q8C2312yes—
186C2×C4×Q8C2311yescharacteristic
187C2×C4×Q8C2312yes—
188C2×C4×Q8C2312yes—
189C2×C4×Q8C2313yes—
190C2×C4×Q8C2313yes—
191C2×C4×Q8C2316yes—
192C2×C4×Q8C2316yes—
193C2×C4×Q8C2316yes—
194C2×C4×Q8C2316yes—
195C2×C4×Q8C2316yes—
196C2×C4×Q8C2316yes—
197C2×C4×Q8C2311yescharacteristic
198C2×C4×Q8C2311yescharacteristic
199C2×C4×D4C2311yescharacteristic
200C2×C4×D4C2313yes—
201C2×C4×D4C2313yes—
202C2×#117C2316yes—
203C2×#117C2316yes—
204C22×C4⋊C4C2313yes—
205C22×C4⋊C4C2313yes—
206C22×C4⋊C4C2311yescharacteristic
207C22×C4⋊C4C2316yes—
208C22×C4⋊C4C2316yes—
209C22×C4⋊C4C2313yes—
210C22×C42C2313yes—
211C22×C42C2313yes—
212C22×C42C2316yes—
213#400C23112yes—
214#400C23112yes—
215#400C23112yes—
216#400C2316yes—
217#400C2316yes—
218#400C23112yes—
219#400C2316yes—
220#400C23112yes—
221#400C23112yes—
222#400C2312yes—
223#400C2316yes—
224#399C23112yes—
225#399C2312yes—
226#398C23112yes—
227#398C23112yes—
228#398C2316yes—
229#398C23112yes—
230#398C23112yes—
231#398C23112yes—
232#398C23112yes—
233#398C2316yes—
234#398C2316yes—
235#398C2316yes—
236#398C2316yes—
237#398C2316yes—
238#396C2316yes—
239#396C2316yes—
240#395C23112yes—
241#395C2316yes—
242#395C23112yes—
243#395C23112yes—
244#393C2316yes—
245#391C2313yes—
246#391C2313yes—
247#391C2313yes—
248#391C2316yes—
249#391C2313yes—
250#391C2316yes—
251#391C2313yes—
252#391C2313yes—
253#391C2316yes—
254#391C2316yes—
255#391C2313yes—
256#391C2316yes—
257#391C2316yes—
258#391C2316yes—
259#391C2313yes—
260#391C2316yes—
261#389C2311yescharacteristic
262#389C2316yes—
263#389C2316yes—
264#389C2316yes—
265#389C2313yes—
266#389C2316yes—
267#389C2316yes—
268#389C23112yes—
269#389C23112yes—
270#389C23112yes—
271#389C23112yes—
272#389C2316yes—
273#389C2316yes—
274#389C2316yes—
275#389C2316yes—
276#389C23112yes—
277#389C2316yes—
278#389C2316yes—
279#389C23112yes—
280#389C2316yes—
281#389C2316yes—
282#389C2313yes—
283#389C2313yes—
284#389C2316yes—
285#389C2316yes—
286#389C23112yes—
287#389C2316yes—
288#389C2316yes—
289#389C2316yes—
290#389C23112yes—
291#389C2316yes—
292#389C2316yes—
293#389C2316yes—
294#389C2316yes—
295#389C2316yes—
296#389C2316yes—
297#389C2313yes—
298#389C23112yes—
299#389C2313yes—
300#389C2313yes—
301#389C2316yes—
302#389C2311yescharacteristic
303#388C2316yes—
304#388C23112yes—
305#388C2316yes—
306#387C2316yes—
307#387C23112yes—
308#387C23112yes—
309#387C23112yes—
310#387C23112yes—
311#387C2316yes—
312#387C23112yes—
313#387C23112yes—
314#387C2316yes—
315#387C23112yes—
316#387C23112yes—
317#387C2316yes—
318#387C2316yes—
319#387C2316yes—
320#387C23112yes—
321#387C2316yes—
322#387C23112yes—
323#387C2316yes—
324#387C2316yes—
325#387C2316yes—
326#386C2316yes—
327#386C2312yes—
328#385C2316yes—
329#385C2316yes—
330#385C2316yes—
331#385C23112yes—
332#385C2316yes—
333#385C2316yes—
334#385C2316yes—
335#385C2312yes—
336#385C2316yes—
337#384C2313yes—
338#384C2313yes—
339#384C2313yes—
340#384C2316yes—
341#384C2313yes—
342#384C2316yes—
343#384C2316yes—
344#384C2313yes—
345#384C2313yes—
346#384C2316yes—
347#384C2313yes—
348#382C2316yes—
349#382C2316yes—
350#382C2316yes—
351#382C2316yes—
352#382C23112yes—
353#382C2316yes—
354#380C2316yes—
355#380C2316yes—
356#380C2316yes—
357#380C2313yes—
358#380C2316yes—
359#380C2313yes—
360#380C2316yes—
361#380C2316yes—
362#380C2316yes—
363#380C2313yes—
364#380C2311yescharacteristic
365#380C2311yescharacteristic
366#380C2311yescharacteristic
367C4×C4⋊C4C2313yes—
368C4×C4⋊C4C2316yes—
369C4×C4⋊C4C2313yes—
370C4×C4⋊C4C2313yes—
371C4×C4⋊C4C2316yes—
372C4×C4⋊C4C2316yes—
373C4×C4⋊C4C2316yes—
374C4×C4⋊C4C2316yes—
375C4×C4⋊C4C2316yes—
376C4×C4⋊C4C2313yes—
377C4×C4⋊C4C2316yes—
378C4×C4⋊C4C2313yes—
379C4×C4⋊C4C2316yes—
380C4×C4⋊C4C23112yes—
381C4×C4⋊C4C2313yes—
382C4×C4⋊C4C2316yes—
383C4×C4⋊C4C2313yes—
384C4×C4⋊C4C2313yes—
385C4×C4⋊C4C2316yes—
386C4×C4⋊C4C2316yes—
387C4×C4⋊C4C2313yes—
388C4×C4⋊C4C2316yes—
389C4×C4⋊C4C2313yes—
390C4×C4⋊C4C2316yes—
391C4×C4⋊C4C2316yes—
392C4×C4⋊C4C2313yes—
393C4×C22⋊C4C23112yes—
394C4×C22⋊C4C2313yes—
395C4×C22⋊C4C2316yes—
396C4×C22⋊C4C2313yes—
397C4×C22⋊C4C2316yes—
398C4×C22⋊C4C2313yes—
399C4×C22⋊C4C2313yes—
400C4×C22⋊C4C2313yes—
401C4×C22⋊C4C2313yes—
402#376C2316yes—
403C2×#95C2316yes—
404C43C2313yes—
405C22×Q8—24no—
406C22×Q8—24no—
407C22×Q8—24no—
408C22×Q8—24no—
409C22×Q8C2×Q818yes—
410C22×Q8C2×Q818yes—
411C22×Q8C2413yes—
412C22×Q8C2413yes—
413C22×Q8C2413yes—
414C22×Q8C2416yes—
415C22×Q8C2411yescharacteristic
416C22×D4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2413yes—
419C23×C4C2413yes—
420C23×C4C2413yes—
421C23×C4C2411yescharacteristic
422C23×C4C2416yes—
423C23×C4C2413yes—
424C23×C4C2412yes—
425C4⋊Q8—212no—
426C4⋊Q8—46no—
427C4⋊Q8—412no—
428C4⋊Q8C2×Q8124yes—
429#125—224no—
430#125—412no—
431#125—412no—
432C22⋊Q8—212no—
433C22⋊Q8—412no—
434C22⋊Q8—46no—
435C22⋊Q8C2×Q8124yes—
436C22⋊Q8C2×Q8124yes—
437C4×Q8—24no—
438C4×Q8—24no—
439C4×Q8—28no—
440C4×Q8—28no—
441C4×Q8—28no—
442C4×Q8—28no—
443C4×Q8—24no—
444C4×Q8—212no—
445C4×Q8—212no—
446C4×Q8—212no—
447C4×Q8—212no—
448C4×Q8—212no—
449C4×Q8—412no—
450C4×Q8—412no—
451C4×Q8—412no—
452C4×Q8—412no—
453C4×Q8—412no—
454C4×Q8—412no—
455C4×Q8C2×Q818yes—
456C4×Q8#4118yes—
457C4×D4—24no—
458C4×D4—46no—
459C4×D4C2×Q8124yes—
460#117—412no—
461#117—412no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—212no—
464C2×C4⋊C4—212no—
465C2×C4⋊C4—46no—
466C2×C4⋊C4—412no—
467C2×C4⋊C4—412no—
468C2×C4⋊C4C2416yes—
469C2×C4⋊C4C2416yes—
470C2×C4⋊C4C2413yes—
471C2×C4⋊C4C2413yes—
472C2×C4⋊C4C2413yes—
473C2×C4⋊C4C2416yes—
474C2×C4⋊C4C2416yes—
475C2×C4⋊C4C2413yes—
476C2×C4⋊C4C2411yescharacteristic
477C2×C4⋊C4C2411yescharacteristic
478C2×C4⋊C4C2412yes—
479C2×C4⋊C4C2416yes—
480C2×C4⋊C4C2411yescharacteristic
481C2×C4⋊C4C2411yescharacteristic
482C2×C4⋊C4C2413yes—
483C2×C4⋊C4C2416yes—
484C2×C4⋊C4C2416yes—
485C2×C4⋊C4C2413yes—
486C2×C4⋊C4C2416yes—
487C2×C4⋊C4C2416yes—
488C2×C4⋊C4C2411yescharacteristic
489C2×C4⋊C4C24112yes—
490C2×C4⋊C4C2416yes—
491C2×C4⋊C4C2416yes—
492C2×C4⋊C4C2416yes—
493C2×C4⋊C4C24112yes—
494C2×C4⋊C4C2416yes—
495C2×C4⋊C4C2416yes—
496C2×C4⋊C4C2413yes—
497C2×C4⋊C4C2412yes—
498C2×C4⋊C4C2416yes—
499C2×C4⋊C4C2416yes—
500C2×C4⋊C4C24112yes—
501C2×C4⋊C4C2416yes—
502C2×C4⋊C4C2416yes—
503C2×C4⋊C4C2416yes—
504C2×C4⋊C4C2416yes—
505C2×C4⋊C4C24112yes—
506C2×C4⋊C4C2416yes—
507C2×C4⋊C4C2416yes—
508C2×C4⋊C4C2412yes—
509C2×C4⋊C4C2416yes—
510C2×C4⋊C4C2416yes—
511C2×C4⋊C4C2416yes—
512C2×C4⋊C4C2416yes—
513C2×C4⋊C4C2413yes—
514C2×C4⋊C4C2413yes—
515C2×C4⋊C4C2416yes—
516C2×C4⋊C4C2413yes—
517C2×C22⋊C4C2413yes—
518C2×C22⋊C4C2411yescharacteristic
519C2×C22⋊C4C2411yescharacteristic
520C2×C22⋊C4C2412yes—
521C2×C22⋊C4C2416yes—
522C2×C22⋊C4C2412yes—
523C2×C22⋊C4C2416yes—
524C2×C22⋊C4C2413yes—
525C2×C22⋊C4C2416yes—
526C2×C22⋊C4C2412yes—
527C2×C22⋊C4C2413yes—
528C2×C22⋊C4C2413yes—
529C2×C42—212no—
530C2×C42—212no—
531C2×C42—412no—
532C2×C42C2416yes—
533C2×C42C2416yes—
534C2×C42C2411yescharacteristic
535C2×C42C2413yes—
536C2×C42C2416yes—
537C2×C42C2416yes—
538C2×C42C2413yes—
539C2×C42C2413yes—
540C2×C42C2413yes—
541C2×C42C2413yes—
542C2×C42C2413yes—
543C2×C42C2413yes—
544C2×C42C2413yes—
545C2×C42C24112yes—
546C2×C42C2413yes—
547C2×C42C2416yes—
548C2×C42C2416yes—
549C2×C42C24112yes—
550C2×C42C2413yes—
551C2×C42C2413yes—
552C2×C42C2413yes—
553#95C2416yes—
554#95C2416yes—
555#95C2416yes—
556#95C2416yes—
557#95C2412yes—
558#95C2416yes—
559#95C2416yes—
560#95C2416yes—
561#95C2413yes—
562#95C2413yes—
563#95C2413yes—
564#95C2413yes—
565#95C2413yes—
566#95C2413yes—
567#95C2416yes—
568#95C24112yes—
569#95C24112yes—
570#95C2416yes—
571#95C2416yes—
572#95C2416yes—
573#95C2416yes—
574#95C2412yes—
575#95C2412yes—
576#95C2416yes—
577#95C2412yes—
578#95C2416yes—
579#95C2412yes—
580#95C24112yes—
581#95C2416yes—
582#95C2416yes—
583#95C2416yes—
584#95C24112yes—
585#95C2416yes—
586#95C2416yes—
587#95C2416yes—
588#95C2416yes—
589#95C24112yes—
590#95C24112yes—
591C24C2511yescharacteristic
592C24C2511yescharacteristic
593C2×Q8—232no—
594C2×Q8—232no—
595C2×Q8—26no—
596C2×Q8—26no—
597C2×Q8—26no—
598C2×Q8—26no—
599C2×Q8—26no—
600C2×Q8—26no—
601C2×Q8—26no—
602C2×Q8—46no—
603C2×Q8—46no—
604C2×Q8—46no—
605C2×Q8C22×Q8112yes—
606C2×Q8C22×Q8112yes—
607C2×Q8C22×Q814yes—
608C2×Q8C2×#4114yes—
609C2×Q8H(5,𝔽2)14yes—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4C22×Q814yes—
613C22×C4—22no—
614C22×C4—26no—
615C22×C4—26no—
616C22×C4—26no—
617C22×C4—26no—
618C22×C4—22no—
619C22×C4—24no—
620C22×C4—26no—
621C22×C4—212no—
622C22×C4—22no—
623C22×C4—26no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—26no—
627C22×C4—42no—
628C22×C4—43no—
629C22×C4—42no—
630C22×C4—46no—
631C22×C4—46no—
632C22×C4—43no—
633C22×C4—43no—
634C22×C4C22×Q8112yes—
635C22×C4C22×Q8112yes—
636C22×C42−1+414yes—
637C22×C4C2511yescharacteristic
638C22×C4C2516yes—
639C22×C4C2512yes—
640C22×C4C2512yes—
641C22×C4C2513yes—
642C22×C4C2513yes—
643C22×C4C2511yescharacteristic
644C22×C4C2512yes—
645C22×C4C2516yes—
646C22×C4C2512yes—
647C22×C4C2513yes—
648C22×C4C2516yes—
649C22×C4C2516yes—
650C22×C4C2511yescharacteristic
651C22×C4C2513yes—
652C22×C4C2513yes—
653C22×C4C2513yes—
654C22×C4C2513yes—
655C22×C4C2511yescharacteristic
656C22×C4C2513yes—
657C22×C4C2511yescharacteristic
658C4⋊C4—212no—
659C4⋊C4—212no—
660C4⋊C4—26no—
661C4⋊C4—26no—
662C4⋊C4—22no—
663C4⋊C4—212no—
664C4⋊C4—212no—
665C4⋊C4—212no—
666C4⋊C4—212no—
667C4⋊C4—212no—
668C4⋊C4—212no—
669C4⋊C4—26no—
670C4⋊C4—24no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—26no—
675C4⋊C4—212no—
676C4⋊C4—26no—
677C4⋊C4—26no—
678C4⋊C4—22no—
679C4⋊C4—46no—
680C4⋊C4—46no—
681C4⋊C4—46no—
682C4⋊C4—412no—
683C4⋊C4—412no—
684C4⋊C4—46no—
685C4⋊C4—46no—
686C4⋊C4—46no—
687C4⋊C4—42no—
688C4⋊C4—46no—
689C4⋊C4—46no—
690C4⋊C4—46no—
691C4⋊C4—46no—
692C4⋊C4—43no—
693C4⋊C4—412no—
694C4⋊C4—42no—
695C4⋊C4—46no—
696C4⋊C4—46no—
697C4⋊C4—46no—
698C4⋊C4—46no—
699C4⋊C4—46no—
700C4⋊C4—46no—
701C4⋊C4—412no—
702C4⋊C4—46no—
703C4⋊C4C22×Q8112yes—
704C4⋊C4C22×Q8112yes—
705C4⋊C4C22×Q8124yes—
706C4⋊C4C2×#41112yes—
707C22⋊C4—22no—
708C22⋊C4—212no—
709C22⋊C4—26no—
710C22⋊C4—24no—
711C22⋊C4—22no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—46no—
715C22⋊C4—43no—
716C22⋊C4—46no—
717C22⋊C4C22×Q8112yes—
718C22⋊C4C22×Q8112yes—
719C42—26no—
720C42—26no—
721C42—26no—
722C42—26no—
723C42—26no—
724C42—26no—
725C42—212no—
726C42—212no—
727C42—212no—
728C42—212no—
729C42—26no—
730C42—22no—
731C42—26no—
732C42—46no—
733C42—46no—
734C42—43no—
735C42—412no—
736C42—43no—
737C42—412no—
738C42C22×Q8112yes—
739C42C2×#41112yes—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23C23×Q812yes—
751C23C23×Q812yes—
752C23C2×2−1+412yes—
753C23#58512yes—
754C23C2611yescharacteristic
755Q8—224no—
756Q8—224no—
757Q8—412no—
758Q8—812no—
759Q8#554116yes—
760D4—28no—
761C2×C4—21no—
762C2×C4—23no—
763C2×C4—23no—
764C2×C4—23no—
765C2×C4—23no—
766C2×C4—21no—
767C2×C4—23no—
768C2×C4—21no—
769C2×C4—23no—
770C2×C4—21no—
771C2×C4—23no—
772C2×C4—23no—
773C2×C4—224no—
774C2×C4—224no—
775C2×C4—28no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—23no—
779C2×C4—23no—
780C2×C4—26no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—26no—
786C2×C4—26no—
787C2×C4—26no—
788C2×C4—23no—
789C2×C4—21no—
790C2×C4—26no—
791C2×C4—21no—
792C2×C4—26no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—23no—
796C2×C4—26no—
797C2×C4—26no—
798C2×C4—23no—
799C2×C4—22no—
800C2×C4—23no—
801C2×C4—22no—
802C2×C4—26no—
803C2×C4—23no—
804C2×C4—22no—
805C2×C4—26no—
806C2×C4—21no—
807C2×C4—26no—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—26no—
812C2×C4—23no—
813C2×C4—23no—
814C2×C4—22no—
815C2×C4—412no—
816C2×C4—48no—
817C2×C4—44no—
818C2×C4—86no—
819C2×C4—812no—
820C2×C4C23×Q812yes—
821C2×C4C23×Q816yes—
822C2×C4C23×Q816yes—
823C2×C4C23×Q816yes—
824C2×C4C23×Q816yes—
825C2×C4C22×#4116yes—
826C2×C4C22×#4116yes—
827C2×C4C22×#4112yes—
828C2×C4C2×H(5,𝔽2)16yes—
829C2×C4C2×2−1+412yes—
830C2×C4C2×2−1+412yes—
831C2×C4#58512yes—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22#350214yes—
846C22C24×Q811yescharacteristic
847C22C23×#4111yescharacteristic
848C22C22×H(5,𝔽2)11yescharacteristic
849C22C22×2−1+411yescharacteristic
850C22C2×#58511yescharacteristic
851C22C2×#58511yescharacteristic
852C222−1+611yescharacteristic
853C4—26no—
854C4—26no—
855C4—22no—
856C4—22no—
857C4—26no—
858C4—26no—
859C4—42no—
860C4—43no—
861C4—43no—
862C4—46no—
863C4—46no—
864C4—43no—
865C4—42no—
866C4—41no—
867C4—46no—
868C4—41no—
869C4—46no—
870C4—42no—
871C4—42no—
872C4C2×#554112yes—
873C4#351614yes—
874C2—24no—
875C2—42no—
876C2C22×#55411yescharacteristic
877C2C2×#350211yescharacteristic
878C2C2×#351611yescharacteristic
879C2#6291311yescharacteristic
880C2#6299311yescharacteristic
881C2#6300411yescharacteristic
882C2#6301911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59870C2semidirect
2. #59868C2semidirect
3. #59322C2semidirect
4. #59259C2semidirect
5. #45405C2semidirect
6. #45278C2semidirect
7. #39635C2semidirect
8. #39609C2semidirect
10. #36577C2semidirect
11. #36577C2semidirect
12. #36552C2semidirect
13. #36466C2semidirect
14. #36435C2semidirect
16. #35971C2semidirect
17. #35845C2semidirect
19. #34337C2semidirect
21. #34182C2semidirect
23. C2×Q8×C4⋊C4C2semidirect
162. D4×Q8Q8semidirect

Maximal subgroups

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

subgroupindex
#598702
#598682
#593222
#592592
#454052
#452782
#396352
#396092
#381012
#365772
#365522
#364662
#364352
#361892
#359712
#358452
#347722
#343372
#342912
#341822
C4×D4×Q82
C2×Q8×C4⋊C42