Finite Group Databasebeta

← #7633233

Subgroups — #7633233

Order 512.

22517 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×2−1+4C211yesmaximal, characteristic, complemented
2C2×#3489C212yesmaximal, complemented
3C2×D4×#41C211yesmaximal, characteristic, complemented
4#36575C212yesmaximal, complemented
5Q8×#120C212yesmaximal, complemented
6#36213C216yesmaximal, complemented
7#36212C216yesmaximal, complemented
8#36085C216yesmaximal, complemented
9#36078C216yesmaximal, complemented
10#35757C212yesmaximal, complemented
11#35687C212yesmaximal, complemented
12#35660C216yesmaximal, complemented
13#35659C216yesmaximal, complemented
14#35251C213yesmaximal, complemented
15#35242C213yesmaximal, complemented
16#34736C213yesmaximal, complemented
17C2×#2409C213yesmaximal, complemented
18#34259C212yesmaximal, complemented
19#34175C211yesmaximal, characteristic, complemented
20C22×2−1+4—232no—
21C22×2−1+4—216no—
22C22×2−1+4C2212yes—
23C22×2−1+4C2216yescomplemented
24C22×2−1+4C2212yescomplemented
25C22×2−1+4C2216yescomplemented
26C23×#41C2211yescharacteristic
27C23×#41C2211yescharacteristic, complemented
28C23×#41C2216yescomplemented
29C23×#41C2213yescomplemented
30C24×Q8C2213yescomplemented
31C24×Q8C2212yescomplemented
32#3489—232no—
33D4×#41—216no—
34C2×#550C2211yescharacteristic, complemented
35C2×D4×Q8C2211yescharacteristic
36C2×D4×Q8C2214yescomplemented
37C2×#548C2211yescharacteristic
38C2×#548C2214yescomplemented
39C2×#548C2211yescharacteristic, complemented
40C2×#547C22112yescomplemented
41C2×#547C2213yescomplemented
42C2×#546C2213yes—
43C2×#546C22112yescomplemented
44C2×#546C2213yescomplemented
45C2×D42C2213yes—
46C2×#537C2216yescomplemented
47C2×#536C2216yescomplemented
48C2×#532C2213yescomplemented
49C2×#525C2213yes—
50C2×#525C2213yescomplemented
51C2×#525C2216yescomplemented
52C22×C22⋊Q8C2216yescomplemented
53C2×#520C2212yescomplemented
54C2×C4×#41C2211yescharacteristic, complemented
55C22×C4×D4C2213yes—
56#2849C22112yescomplemented
57#2848C2216yescomplemented
58#2847C2216yescomplemented
59#2616C2216yescomplemented
60#2615C2216yescomplemented
61#2614C22112yescomplemented
62#2436C22112yescomplemented
63#2436C2216yescomplemented
64#2436C2216yescomplemented
65#2434C22112yescomplemented
66#2434C2216yescomplemented
67#2434C2216yescomplemented
68#2432C22112yescomplemented
69#2431C22112yescomplemented
70#2430C22124yescomplemented
71#2430C22124yescomplemented
72#2430C22112yescomplemented
73#2410C22112yescomplemented
74#2409C2216yes—
75#2409C2213yes—
76#2409C2216yescomplemented
77#2409C22112yescomplemented
78#2409C22112yescomplemented
79#2409C22112yescomplemented
80#2409C2216yescomplemented
81#2409C2216yescomplemented
82#2409C2216yescomplemented
83#2409C2216yescomplemented
84#2409C2216yescomplemented
85#2409C2213yescomplemented
86#2408C2211yescharacteristic
87#2408C2213yescomplemented
88#2407C2216yescomplemented
89#2407C22112yescomplemented
90#2407C22112yescomplemented
91#2407C22112yescomplemented
92#2407C2216yescomplemented
93#2406C22124yescomplemented
94#2406C2216yescomplemented
95#2405C2216yescomplemented
96#2404C22124yescomplemented
97#2404C2216yescomplemented
98#2403C2216yes—
99#2388C2216yescomplemented
100#2388C2216yescomplemented
101C2×#395C2216yescomplemented
102C2×#393C2216yescomplemented
103#2341C2212yescomplemented
104Q8×C22⋊C4C2214yescomplemented
105Q8×C22⋊C4C2212yescomplemented
106Q8×C22⋊C4C2214yescomplemented
107#2339C22112yescomplemented
108#2339C22112yescomplemented
109#2339C2216yescomplemented
110D4×C22⋊C4C2216yescomplemented
111#2311C2216yescomplemented
112#2311C2216yescomplemented
113#2310C2216yescomplemented
114C4×#120C2216yes—
115C4×#120C2216yescomplemented
116#2297C2216yescomplemented
117C2×#391C2216yescomplemented
118C2×#386C2216yes—
119C2×#385C2216yescomplemented
120#2280C2213yescomplemented
121C2×#380C2213yescomplemented
122C2×2−1+4—2512no—
123C2×2−1+4—216no—
124C2×2−1+4—216no—
125C2×2−1+4—248no—
126C2×2−1+4—248no—
127C2×2−1+4—216no—
128C2×2−1+4—248no—
129C2×2−1+4—296no—
130C2×2−1+4—248no—
131C2×2−1+4—232no—
132C2×2−1+4D4132yescomplemented
133C22×#41—216no—
134C22×#41—248no—
135C22×#41—296no—
136C22×#41—28no—
137C22×#41—216no—
138C22×#41—248no—
139C22×#41—224no—
140C22×#41D4116yescomplemented
141C22×#41C2316yes—
142C22×#41C23124yes—
143C22×#41C2316yes—
144C22×#41C2316yes—
145C22×#41C23112yes—
146C22×#41C2313yes—
147C22×#41C2313yes—
148C22×#41C2311yescharacteristic
149C22×#41C2313yes—
150C22×#41C2313yes—
151C22×#41C2311yescharacteristic
152C22×#41C2316yes—
153C22×#41C23112yes—
154C22×#41C2311yescharacteristic
155C23×Q8—216no—
156C23×Q8—248no—
157C23×Q8—232no—
158C23×Q8—224no—
159C23×Q8C2313yes—
160C23×Q8C2316yes—
161C23×Q8C2316yes—
162C23×Q8C2316yes—
163C23×Q8C2316yes—
164C23×Q8C23112yes—
165C23×Q8C2311yescharacteristic
166C23×Q8C2311yescharacteristic
167C23×Q8C2316yes—
168C23×Q8C2314yes—
169C23×D4C2316yes—
170C23×D4C2311yescharacteristic
171C23×D4C2313yes—
172C23×D4C2313yes—
173C23×D4C2313yes—
174C24×C4C2316yes—
175C24×C4C2316yes—
176C24×C4C2313yes—
177C24×C4C2313yes—
178#550—28no—
179D4×Q8—28no—
180D4×Q8—232no—
181#548—28no—
182#548—28no—
183#548—232no—
184#547—224no—
185#547—296no—
186#546—224no—
187#546—296no—
188#546—224no—
189D42—224no—
190#537—248no—
191#536—248no—
192#532—224no—
193C2×C4⋊Q8C2313yes—
194C2×C4⋊Q8C23112yes—
195C2×#127C2313yes—
196C2×#124C2313yes—
197C2×#124C2313yes—
198C2×#124C23112yes—
199#525—224no—
200#525—248no—
201#525—224no—
202C2×#123C23124yes—
203C2×#123C2316yes—
204C2×#123C23112yes—
205C2×#123C2316yes—
206C2×C22⋊Q8—248no—
207C2×C22⋊Q8C2313yes—
208C2×C22⋊Q8C23112yes—
209C2×C22⋊Q8C2313yes—
210C2×C22⋊Q8C2316yes—
211C2×C22⋊Q8C23112yes—
212C2×C22⋊Q8C23112yes—
213C2×C22⋊Q8C23112yes—
214C2×C22⋊Q8C2316yes—
215C2×C22⋊Q8C2313yes—
216C2×C22⋊Q8C2313yes—
217C2×#121C2313yes—
218C2×#121C23112yes—
219C2×#121C2313yes—
220C2×#121C2313yes—
221C2×#121C2313yes—
222C2×#121C2312yes—
223C2×#121C2316yes—
224C2×#121C23124yes—
225C2×#121C2316yes—
226C2×#121C2316yes—
227C2×#120C2316yes—
228C2×#120C2312yes—
229C2×#120C23112yes—
230C2×#120C2316yes—
231C2×#120C2316yes—
232#520—216no—
233C4×#41—28no—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2314yes—
237C2×C4×D4—224no—
238C2×C4×D4C23112yes—
239C2×C4×D4C2313yes—
240C2×C4×D4C2313yes—
241C2×C4×D4C2313yes—
242C2×C4×D4C2313yes—
243C2×C4×D4C23112yes—
244C2×C4×D4C23112yes—
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2313yes—
247C2×C4×D4C2313yes—
248C2×C4×D4C2313yes—
249C2×C4×D4C2313yes—
250C2×C4×D4C2313yes—
251C2×C4×D4C2316yes—
252C2×#117C2313yes—
253C2×#117C2316yes—
254C22×C4⋊C4C2316yes—
255C22×C4⋊C4C2313yes—
256C22×C4⋊C4C23112yes—
257C22×C22⋊C4C2313yes—
258C22×C22⋊C4C23112yes—
259C22×C22⋊C4C2313yes—
260C22×C22⋊C4C2316yes—
261C22×C42C2313yes—
262#395C2316yes—
263#395C23112yes—
264#395C23124yes—
265#395C2316yes—
266#395C23112yes—
267#395C23112yes—
268#394C2316yes—
269#394C23124yes—
270#394C2312yes—
271#394C23112yes—
272#394C23112yes—
273#393C2316yes—
274#393C23112yes—
275#393C23124yes—
276#393C2316yes—
277#393C23112yes—
278#393C23112yes—
279#392C2316yes—
280#392C23124yes—
281#392C2312yes—
282#392C23112yes—
283#392C23112yes—
284#391C2316yes—
285#391C23112yes—
286#391C23112yes—
287#391C23112yes—
288#391C23112yes—
289#391C23112yes—
290#391C23112yes—
291#391C2316yes—
292#390C2316yes—
293#390C23112yes—
294#390C2312yes—
295#386C23124yes—
296#386C23124yes—
297#386C23112yes—
298#386C23124yes—
299#386C2316yes—
300#386C23124yes—
301#386C23112yes—
302#386C23112yes—
303#386C2316yes—
304#386C23112yes—
305#386C23112yes—
306#386C23112yes—
307#386C23112yes—
308#385C23112yes—
309#385C23124yes—
310#385C2316yes—
311#385C23124yes—
312#385C2316yes—
313#385C23112yes—
314#385C23112yes—
315#385C23112yes—
316#385C23112yes—
317#381C23124yes—
318#381C2316yes—
319#380C2316yes—
320#380C2316yes—
321#380C23112yes—
322#380C23112yes—
323#380C2316yes—
324#380C2316yes—
325#380C2311yescharacteristic
326#380C2313yes—
327#379C2316yes—
328#379C2316yes—
329#379C2312yes—
330C4×C22⋊C4C2316yes—
331C4×C22⋊C4C23112yes—
332C4×C22⋊C4C23112yes—
333C4×C22⋊C4C2316yes—
334C2×#95C2316yes—
335C2×#95C23112yes—
336C2×#95C23112yes—
337C25C2412yes—
338C25C2413yes—
339C25C2413yes—
3402−1+4—2768no—
3412−1+4—2768no—
3422−1+4—2256no—
3432−1+4—2256no—
344C2×#41—2768no—
345C2×#41—2384no—
346C2×#41—2128no—
347C2×#41—224no—
348C2×#41—248no—
349C2×#41—28no—
350C2×#41—28no—
351C2×#41—24no—
352C2×#41—248no—
353C2×#41—296no—
354C2×#41—296no—
355C2×#41—224no—
356C2×#41—248no—
357C2×#41—224no—
358C2×#41—248no—
359C2×#41—248no—
360C2×#41—212no—
361C2×#41—224no—
362C2×#41—296no—
363C2×#41—224no—
364C2×#41—224no—
365C2×#41—248no—
366C2×#41—248no—
367C2×#41—224no—
368C2×#41—224no—
369C2×#41—224no—
370C2×#41—224no—
371C2×#41—212no—
372C2×#41—224no—
373C2×#41—464no—
374C2×#41C2×D4124yes—
375C2×#41C2×D4124yes—
376C2×#41C2×D418yes—
377C2×#41C2×D418yes—
378C2×#41C2×D4116yes—
379C2×#41C2×D4148yescomplemented
380C2×#41C2×D4196yescomplemented
381C22×Q8—2256no—
382C22×Q8—2384no—
383C22×Q8—224no—
384C22×Q8—248no—
385C22×Q8—28no—
386C22×Q8—248no—
387C22×Q8—248no—
388C22×Q8—248no—
389C22×Q8—248no—
390C22×Q8—216no—
391C22×Q8—216no—
392C22×Q8—24no—
393C22×Q8—28no—
394C22×Q8—212no—
395C22×Q8—224no—
396C22×Q8—248no—
397C22×Q8—224no—
398C22×Q8—224no—
399C22×Q8—248no—
400C22×Q8—224no—
401C22×Q8—224no—
402C22×Q8—224no—
403C22×Q8C2×D418yes—
404C22×Q8C2×D4148yescomplemented
405C22×Q8C2×D4132yescomplemented
406C22×Q8C2413yes—
407C22×Q8C2416yes—
408C22×Q8C24112yes—
409C22×Q8C2416yes—
410C22×Q8C2413yes—
411C22×Q8C24112yes—
412C22×Q8C2411yescharacteristic
413C22×D4—224no—
414C22×D4—248no—
415C22×D4—28no—
416C22×D4—224no—
417C22×D4—212no—
418C22×D4—212no—
419C22×D4—224no—
420C22×D4—212no—
421C22×D4—24no—
422C22×D4—46no—
423C22×D4C2×D4124yes—
424C22×D4C2413yes—
425C22×D4C2416yes—
426C22×D4C2413yes—
427C22×D4C24112yes—
428C22×D4C2412yes—
429C22×D4C2414yes—
430C22×D4C2413yes—
431C22×D4C2413yes—
432C22×D4C24112yes—
433C22×D4C2416yes—
434C22×D4C2412yes—
435C22×D4C2413yes—
436C22×D4C2411yescharacteristic
437C22×D4C24112yes—
438C22×D4C2416yes—
439C22×D4C2413yes—
440C23×C4—224no—
441C23×C4—224no—
442C23×C4—248no—
443C23×C4—248no—
444C23×C4—224no—
445C23×C4—212no—
446C23×C4—224no—
447C23×C4C2×D4124yes—
448C23×C4C2413yes—
449C23×C4C2413yes—
450C23×C4C2413yes—
451C23×C4C2411yescharacteristic
452C23×C4C2413yes—
453C23×C4C2416yes—
454C23×C4C24112yes—
455C23×C4C24112yes—
456C23×C4C2413yes—
457C23×C4C24112yes—
458C23×C4C2413yes—
459C23×C4C2411yescharacteristic
460C23×C4C2413yes—
461C23×C4C2413yes—
462C23×C4C24112yes—
463C23×C4C2413yes—
464C23×C4C24112yes—
465C23×C4C2413yes—
466C23×C4C2413yes—
467C4⋊Q8—212no—
468C4⋊Q8—248no—
469#127—212no—
470#124—212no—
471#124—248no—
472#124—212no—
473#123—224no—
474#123—248no—
475#123—224no—
476#123—296no—
477C22⋊Q8—224no—
478C22⋊Q8—248no—
479C22⋊Q8—248no—
480C22⋊Q8—248no—
481C22⋊Q8—224no—
482C22⋊Q8—212no—
483C22⋊Q8—212no—
484C22⋊Q8—212no—
485C22⋊Q8—212no—
486C22⋊Q8—248no—
487#121—28no—
488#121—224no—
489#121—212no—
490#121—212no—
491#121—224no—
492#121—224no—
493#121—296no—
494#121—212no—
495#121—212no—
496#121—248no—
497#120—224no—
498#120—224no—
499#120—248no—
500#120—28no—
501#120—412no—
502C4×Q8—24no—
503C4×Q8—24no—
504C4×Q8—216no—
505C4×D4—212no—
506C4×D4—212no—
507C4×D4—248no—
508C4×D4—24no—
509C4×D4—212no—
510C4×D4—212no—
511C4×D4—212no—
512C4×D4—212no—
513C4×D4—212no—
514C4×D4—212no—
515C4×D4—212no—
516C4×D4—224no—
517C4×D4—248no—
518C4×D4—248no—
519#117—212no—
520#117—224no—
521C2×C4⋊C4—212no—
522C2×C4⋊C4—224no—
523C2×C4⋊C4—248no—
524C2×C4⋊C4C2411yescharacteristic
525C2×C4⋊C4C2416yes—
526C2×C4⋊C4C24112yes—
527C2×C4⋊C4C2413yes—
528C2×C4⋊C4C2413yes—
529C2×C4⋊C4C2413yes—
530C2×C4⋊C4C24112yes—
531C2×C4⋊C4C24124yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2413yes—
534C2×C4⋊C4C2413yes—
535C2×C4⋊C4C2416yes—
536C2×C4⋊C4C24112yes—
537C2×C22⋊C4—212no—
538C2×C22⋊C4—212no—
539C2×C22⋊C4—248no—
540C2×C22⋊C4—412no—
541C2×C22⋊C4C2411yescharacteristic
542C2×C22⋊C4C2411yescharacteristic
543C2×C22⋊C4C24112yes—
544C2×C22⋊C4C2416yes—
545C2×C22⋊C4C2413yes—
546C2×C22⋊C4C2413yes—
547C2×C22⋊C4C2413yes—
548C2×C22⋊C4C2413yes—
549C2×C22⋊C4C2413yes—
550C2×C22⋊C4C2413yes—
551C2×C22⋊C4C24124yes—
552C2×C22⋊C4C2416yes—
553C2×C22⋊C4C24112yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2416yes—
556C2×C22⋊C4C2416yes—
557C2×C22⋊C4C24112yes—
558C2×C22⋊C4C24112yes—
559C2×C22⋊C4C2412yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C24112yes—
562C2×C22⋊C4C24112yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C24112yes—
565C2×C22⋊C4C24112yes—
566C2×C42—212no—
567C2×C42C2413yes—
568C2×C42C24112yes—
569C2×C42C2411yescharacteristic
570C2×C42C2413yes—
571C2×C42C2413yes—
572#95C2416yes—
573#95C24112yes—
574#95C24112yes—
575#95C24112yes—
576#95C24124yes—
577#95C24124yes—
578#95C2412yes—
579#95C24112yes—
580#95C24112yes—
581#95C24112yes—
582C24—28no—
583C24—212no—
584C24—24no—
585C24—26no—
586C24—26no—
587C24—24no—
588C24—26no—
589C24—24no—
590C24—212no—
591C24—26no—
592C24—46no—
593C24—44no—
594C24—43no—
595C24—46no—
596C24C22×D4112yes—
597C24C2513yes—
598C24C2514yes—
599C24C2513yes—
600C24C2511yescharacteristic
601C24C2513yes—
602C24C2511yescharacteristic
603#41—2768no—
604#41—2192no—
605#41—2384no—
606#41—2192no—
607#41—2192no—
608#41—232no—
609#41—296no—
610#41—2384no—
611#41—296no—
612#41—2192no—
613#41—416no—
614#41—448no—
615#41—448no—
616#41#120164yescomplemented
617C2×Q8—2192no—
618C2×Q8—296no—
619C2×Q8—2384no—
620C2×Q8—2192no—
621C2×Q8—2192no—
622C2×Q8—2192no—
623C2×Q8—232no—
624C2×Q8—2128no—
625C2×Q8—2192no—
626C2×Q8—224no—
627C2×Q8—248no—
628C2×Q8—224no—
629C2×Q8—212no—
630C2×Q8—212no—
631C2×Q8—224no—
632C2×Q8—212no—
633C2×Q8—224no—
634C2×Q8—212no—
635C2×Q8—26no—
636C2×Q8—212no—
637C2×Q8—416no—
638C2×Q8C22×D4124yes—
639C2×Q8C22×D4112yes—
640C2×Q8C22×D4148yes—
641C2×Q8C22×D414yes—
642C2×Q8C22×D418yes—
643C2×D4—2192no—
644C2×D4—232no—
645C2×D4—22no—
646C2×D4—224no—
647C2×D4—224no—
648C2×D4—28no—
649C2×D4—224no—
650C2×D4—224no—
651C2×D4—224no—
652C2×D4—22no—
653C2×D4—296no—
654C2×D4—28no—
655C2×D4—26no—
656C2×D4—26no—
657C2×D4—26no—
658C2×D4—212no—
659C2×D4—224no—
660C2×D4—26no—
661C2×D4—28no—
662C2×D4—26no—
663C2×D4—26no—
664C2×D4—212no—
665C2×D4—224no—
666C2×D4—224no—
667C2×D4—24no—
668C2×D4—24no—
669C2×D4—212no—
670C2×D4—24no—
671C2×D4—212no—
672C2×D4—26no—
673C2×D4—26no—
674C2×D4—43no—
675C2×D4—43no—
676C2×D4—44no—
677C2×D4—412no—
678C2×D4—412no—
679C2×D4—412no—
680C2×D4—448no—
681C2×D4—448no—
682C2×D4C22×D4148yes—
683C2×D4C22×D4124yes—
684C2×D4C22×D418yes—
685C2×D4C22×D4112yes—
686C2×D4C22×D4124yes—
687C2×D4C22×D4112yes—
688C2×D42−1+414yescomplemented
689C22×C4—2192no—
690C22×C4—2192no—
691C22×C4—212no—
692C22×C4—224no—
693C22×C4—224no—
694C22×C4—224no—
695C22×C4—224no—
696C22×C4—212no—
697C22×C4—296no—
698C22×C4—224no—
699C22×C4—212no—
700C22×C4—24no—
701C22×C4—248no—
702C22×C4—224no—
703C22×C4—224no—
704C22×C4—224no—
705C22×C4—212no—
706C22×C4—224no—
707C22×C4—212no—
708C22×C4—26no—
709C22×C4—26no—
710C22×C4—212no—
711C22×C4—26no—
712C22×C4—224no—
713C22×C4—22no—
714C22×C4—26no—
715C22×C4—26no—
716C22×C4—26no—
717C22×C4—212no—
718C22×C4—212no—
719C22×C4—24no—
720C22×C4—212no—
721C22×C4—26no—
722C22×C4—43no—
723C22×C4—412no—
724C22×C4—46no—
725C22×C4—412no—
726C22×C4—448no—
727C22×C4C22×D4148yes—
728C22×C4C22×D4112yes—
729C22×C4C22×D414yes—
730C22×C4C22×D4112yes—
731C22×C4C22×D4112yes—
732C22×C4C22×D4148yes—
733C22×C4C22×D4112yes—
734C22×C4C22×D4112yes—
735C22×C4C22×D4124yes—
736C22×C4C2511yescharacteristic
737C22×C4C2513yes—
738C22×C4C2513yes—
739C22×C4C2514yes—
740C22×C4C25112yes—
741C22×C4C2511yescharacteristic
742C22×C4C2513yes—
743C22×C4C25112yes—
744C22×C4C2513yes—
745C22×C4C2511yescharacteristic
746C22×C4C2511yescharacteristic
747C22×C4C2513yes—
748C22×C4C2511yescharacteristic
749C4⋊C4—22no—
750C4⋊C4—212no—
751C4⋊C4—224no—
752C4⋊C4—26no—
753C4⋊C4—26no—
754C4⋊C4—26no—
755C4⋊C4—224no—
756C4⋊C4—248no—
757C4⋊C4—24no—
758C4⋊C4—26no—
759C4⋊C4—26no—
760C4⋊C4—212no—
761C4⋊C4—224no—
762C22⋊C4—22no—
763C22⋊C4—26no—
764C22⋊C4—26no—
765C22⋊C4—26no—
766C22⋊C4—212no—
767C22⋊C4—224no—
768C22⋊C4—28no—
769C22⋊C4—212no—
770C22⋊C4—224no—
771C22⋊C4—24no—
772C22⋊C4—212no—
773C22⋊C4—22no—
774C22⋊C4—224no—
775C22⋊C4—26no—
776C22⋊C4—26no—
777C22⋊C4—26no—
778C22⋊C4—248no—
779C22⋊C4—212no—
780C22⋊C4—224no—
781C22⋊C4—28no—
782C22⋊C4—412no—
783C22⋊C4—44no—
784C22⋊C4—412no—
785C22⋊C4—412no—
786C22⋊C4—412no—
787C42—22no—
788C42—26no—
789C42—26no—
790C42—26no—
791C42—224no—
792C23—22no—
793C23—23no—
794C23—23no—
795C23—26no—
796C23—22no—
797C23—216no—
798C23—22no—
799C23—21no—
800C23—26no—
801C23—24no—
802C23—24no—
803C23—24no—
804C23—23no—
805C23—23no—
806C23—24no—
807C23—21no—
808C23—24no—
809C23—26no—
810C23—24no—
811C23—22no—
812C23—224no—
813C23—224no—
814C23—26no—
815C23—23no—
816C23—23no—
817C23—23no—
818C23—26no—
819C23—412no—
820C23—424no—
821C23—416no—
822C23—424no—
823C23—416no—
824C23—412no—
825C23—424no—
826C23—48no—
827C23—48no—
828C23—412no—
829C23—812no—
830C23—86no—
831C23C23×D416yes—
832C23C23×D418yes—
833C23C23×D416yes—
834C23C23×D4112yes—
835C23C23×D412yes—
836C23C2×2−1+412yes—
837C23C2×2−1+412yescomplemented
838C23#58512yes—
839C23C2611yescharacteristic
840Q8—296no—
841Q8—248no—
842Q8—296no—
843Q8—224no—
844Q8—248no—
845Q8—412no—
846Q8C2×#120116yes—
847D4—296no—
848D4—216no—
849D4—296no—
850D4—248no—
851D4—28no—
852D4—224no—
853D4—216no—
854D4—412no—
855D4—416no—
856D4—412no—
857D4—424no—
858D4—412no—
859D4—412no—
860D4—824no—
861D4—812no—
862D4C2×#120148yes—
863C2×C4—248no—
864C2×C4—296no—
865C2×C4—296no—
866C2×C4—21no—
867C2×C4—212no—
868C2×C4—26no—
869C2×C4—22no—
870C2×C4—212no—
871C2×C4—21no—
872C2×C4—296no—
873C2×C4—224no—
874C2×C4—224no—
875C2×C4—28no—
876C2×C4—296no—
877C2×C4—224no—
878C2×C4—224no—
879C2×C4—21no—
880C2×C4—24no—
881C2×C4—23no—
882C2×C4—23no—
883C2×C4—212no—
884C2×C4—21no—
885C2×C4—23no—
886C2×C4—22no—
887C2×C4—26no—
888C2×C4—24no—
889C2×C4—23no—
890C2×C4—212no—
891C2×C4—23no—
892C2×C4—24no—
893C2×C4—22no—
894C2×C4—212no—
895C2×C4—26no—
896C2×C4—412no—
897C2×C4—412no—
898C2×C4—44no—
899C2×C4—412no—
900C2×C4—412no—
901C2×C4—412no—
902C2×C4—824no—
903C2×C4—86no—
904C2×C4C2×#120148yes—
905C2×C4C23×D4124yes—
906C2×C4C23×D416yes—
907C2×C4C23×D412yes—
908C2×C4C23×D412yes—
909C2×C4C23×D4112yes—
910C2×C4C23×D416yes—
911C2×C4C23×D414yes—
912C2×C4C2×2−1+412yescomplemented
913C22—24no—
914C22—212no—
915C22—212no—
916C22—24no—
917C22—26no—
918C22—26no—
919C22—22no—
920C22—22no—
921C22—24no—
922C22—28no—
923C22—28no—
924C22—22no—
925C22—26no—
926C22—26no—
927C22—26no—
928C22—28no—
929C22—448no—
930C22—432no—
931C22—44no—
932C22—46no—
933C22—46no—
934C22—44no—
935C22—42no—
936C22—44no—
937C22—44no—
938C22—41no—
939C22—41no—
940C22—46no—
941C22—46no—
942C22—43no—
943C22—43no—
944C22—43no—
945C22—824no—
946C22C22×#120112yes—
947C22#348914yescomplemented
948C22C24×D412yes—
949C22C24×D411yescharacteristic
950C22C22×2−1+411yescharacteristic
951C22C2×#58511yescharacteristic
952C222−1+612yes—
953C4—22no—
954C4—224no—
955C4—26no—
956C4—22no—
957C4—44no—
958C4—412no—
959C4—43no—
960C4—41no—
961C4—43no—
962C4—41no—
963C4—43no—
964C4C22×#120112yes—
965C4C22×#12014yes—
966C2—24no—
967C2—212no—
968C2—48no—
969C2—46no—
970C2—42no—
971C2—83no—
972C2C23×#12011yescharacteristic
973C2C2×#348911yescharacteristic
974C2#6285911yescharacteristic
975C2D4×2−1+412yes—
976C2#6300212yes—
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. C23×2−1+4C2semidirect
2. C2×#3489C2semidirect
3. C2×D4×#41C2semidirect
4. #36575C2semidirect
5. Q8×#120C2semidirect
6. #36213C2semidirect
7. #36212C2semidirect
8. #36085C2semidirect
9. #36078C2semidirect
10. #35757C2semidirect
11. #35687C2semidirect
12. #35660C2semidirect
13. #35659C2semidirect
14. #35251C2semidirect
15. #35242C2semidirect
16. #34736C2semidirect
17. C2×#2409C2semidirect
18. #34259C2semidirect
19. #34175C2semidirect
23. C22×2−1+4C22semidirect
24. C22×2−1+4C22semidirect
25. C22×2−1+4C22semidirect
27. C23×#41C22semidirect
28. C23×#41C22semidirect
29. C23×#41C22semidirect
30. C24×Q8C22semidirect
31. C24×Q8C22semidirect
34. C2×#550C22semidirect
36. C2×D4×Q8C22semidirect
38. C2×#548C22semidirect
39. C2×#548C22semidirect
40. C2×#547C22semidirect
41. C2×#547C22semidirect
43. C2×#546C22semidirect
44. C2×#546C22semidirect
46. C2×#537C22semidirect
47. C2×#536C22semidirect
48. C2×#532C22semidirect
50. C2×#525C22semidirect
51. C2×#525C22semidirect
52. C22×C22⋊Q8C22semidirect
53. C2×#520C22semidirect
54. C2×C4×#41C22semidirect
56. #2849C22semidirect
57. #2848C22semidirect
58. #2847C22semidirect
59. #2616C22semidirect
60. #2615C22semidirect
61. #2614C22semidirect
62. #2436C22semidirect
63. #2436C22semidirect
64. #2436C22semidirect
65. #2434C22semidirect
66. #2434C22semidirect
67. #2434C22semidirect
68. #2432C22semidirect
69. #2431C22semidirect
70. #2430C22semidirect
71. #2430C22semidirect
72. #2430C22semidirect
73. #2410C22semidirect
76. #2409C22semidirect
77. #2409C22semidirect
78. #2409C22semidirect
79. #2409C22semidirect
80. #2409C22semidirect
81. #2409C22semidirect
82. #2409C22semidirect
83. #2409C22semidirect
84. #2409C22semidirect
85. #2409C22semidirect
87. #2408C22semidirect
88. #2407C22semidirect
89. #2407C22semidirect
90. #2407C22semidirect
91. #2407C22semidirect
92. #2407C22semidirect
93. #2406C22semidirect
94. #2406C22semidirect
95. #2405C22semidirect
96. #2404C22semidirect
97. #2404C22semidirect
99. #2388C22semidirect
100. #2388C22semidirect
101. C2×#395C22semidirect
102. C2×#393C22semidirect
103. #2341C22semidirect
104. Q8×C22⋊C4C22semidirect
105. Q8×C22⋊C4C22semidirect
106. Q8×C22⋊C4C22semidirect
107. #2339C22semidirect
108. #2339C22semidirect
109. #2339C22semidirect
110. D4×C22⋊C4C22semidirect
111. #2311C22semidirect
112. #2311C22semidirect
113. #2310C22semidirect
115. C4×#120C22semidirect
116. #2297C22semidirect
117. C2×#391C22semidirect
119. C2×#385C22semidirect
120. #2280C22semidirect
121. C2×#380C22semidirect
132. C2×2−1+4D4semidirect
140. C22×#41D4semidirect
379. C2×#41C2×D4semidirect
380. C2×#41C2×D4semidirect
404. C22×Q8C2×D4semidirect
405. C22×Q8C2×D4semidirect
616. #41#120semidirect
688. C2×D42−1+4semidirect
837. C23C2×2−1+4semidirect
912. C2×C4C2×2−1+4semidirect
947. C22#3489semidirect

Maximal subgroups

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

subgroupindex
C23×2−1+42
C2×#34892
C2×D4×#412
#365752
Q8×#1202
#362132
#362122
#360852
#360782
#357572
#356872
#356602
#356592
#352512
#352422
#347362
C2×#24092
#342592
#341752