Finite Group Databasebeta

← #7630341

Subgroups — #7630341

Order 512.

9232 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3483C211yesmaximal, characteristic, complemented
2C22×C4×#41C211yesmaximal, characteristic, complemented
3#36624C213yesmaximal, complemented
4#36576C211yesmaximal, characteristic, complemented
5Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
6#36456C211yesmaximal, characteristic, complemented
7#36455C211yesmaximal, characteristic, complemented
8#36433C212yesmaximal, complemented
9#36429C212yesmaximal, complemented
10#36411C213yesmaximal, complemented
11#36410C213yesmaximal, complemented
12#36235C216yesmaximal, complemented
13#36231C216yesmaximal, complemented
14#36160C213yesmaximal, complemented
15#36101C213yesmaximal, complemented
16#34977C213yesmaximal, complemented
17#34976C213yesmaximal, complemented
18#34715C216yesmaximal, complemented
19#34681C216yesmaximal, complemented
20C4×#550C212yesmaximal, complemented
21C4×#548C212yesmaximal, complemented
22#34129C211yesmaximal, characteristic, complemented
23C4×#525C213yesmaximal, complemented
24C23×#41C2211yescharacteristic
25#3483—216no—
26C2×Q82C2211yescharacteristic, complemented
27C2×#555C2213yescomplemented
28C2×#555C2216yescomplemented
29C2×#550C2212yes—
30C2×#550C2212yes—
31C2×#550C2213yescomplemented
32C2×#550C2211yescharacteristic, complemented
33C2×#548C2212yes—
34C2×#532C2213yescomplemented
35C2×#532C2216yescomplemented
36C2×#525C2213yes—
37C2×#525C2216yes—
38C2×C4×#41—216no—
39C2×C4×#41C2213yes—
40C2×C4×#41C2211yescharacteristic
41C2×C4×#41C2211yescharacteristic
42C2×C4×#41C2211yescharacteristic
43C2×C4×#41C2213yes—
44C2×C4×#41C2213yes—
45C2×C4×#41C2213yes—
46C2×C4×#41C2211yescharacteristic
47C2×C4×#41C2212yescomplemented
48C2×C4×#41C2213yescomplemented
49C22×C4×Q8C2211yescharacteristic
50C22×C4×Q8C2211yescharacteristic
51C22×C4×D4C2213yes—
52C22×C4×D4C2213yes—
53C22×#117C2213yes—
54C23×C42C2213yes—
55#2857C2213yes—
56#2857C2213yescomplemented
57#2856C2213yes—
58#2856C2213yescomplemented
59#2854C2216yescomplemented
60#2854C2216yescomplemented
61#2850C2216yes—
62#2850C2216yescomplemented
63#2847C2216yes—
64#2847C2216yes—
65#2610C22112yescomplemented
66#2609C22112yescomplemented
67#2582C2213yescomplemented
68#2567C2213yescomplemented
69#2563C2213yescomplemented
70#2548C2213yescomplemented
71#2541C2213yescomplemented
72#2538C2213yescomplemented
73#2538C2213yescomplemented
74#2537C2213yescomplemented
75#2500C2216yescomplemented
76#2485C2216yescomplemented
77#2485C2216yescomplemented
78#2476C22112yescomplemented
79#2474C22112yescomplemented
80#2472C22112yes—
81#2464C22112yescomplemented
82#2461C22112yescomplemented
83#2459C22112yescomplemented
84#2456C22112yescomplemented
85#2452C2216yescomplemented
86#2451C2216yescomplemented
87#2445C2216yescomplemented
88#2445C2216yescomplemented
89#2440C2216yes—
90#2439C2216yescomplemented
91#2433C2216yes—
92#2431C2216yes—
93#2431C2216yes—
94#2428C2216yescomplemented
95#2426C2216yescomplemented
96#2424C22112yes—
97#2422C2216yescomplemented
98#2420C2216yescomplemented
99#2416C2216yes—
100#2414C2216yescomplemented
101#2414C2216yescomplemented
102#2414C2216yescomplemented
103#2408C2216yes—
104#2407C2216yes—
105#2407C2216yes—
106#2407C2216yescomplemented
107#2392C22112yescomplemented
108#2388C22112yescomplemented
109#2367C2216yescomplemented
110#2366C2216yescomplemented
111#2363C2216yescomplemented
112#2363C2216yescomplemented
113#2362C2216yescomplemented
114#2361C2216yes—
115#2354C2213yescomplemented
116#2354C2213yescomplemented
117#2354C2216yescomplemented
118#2352C2216yes—
119#2351C2212yescomplemented
120Q8×C4⋊C4C2211yescharacteristic, complemented
121Q8×C4⋊C4C2211yescharacteristic, complemented
122Q8×C4⋊C4C2212yescomplemented
123#2346C2216yescomplemented
124#2341C2212yes—
125#2341C2212yes—
126#2341C2212yescomplemented
127#2341C2212yescomplemented
128Q8×C22⋊C4C2212yes—
129C4×#127C2216yescomplemented
130C4×#124C2216yescomplemented
131C4×C22⋊Q8C2213yes—
132C4×C22⋊Q8C2211yescharacteristic
133C4×C22⋊Q8C2213yescomplemented
134C4×C22⋊Q8C2216yescomplemented
135C4×C22⋊Q8C2213yescomplemented
136C4×#123C2216yescomplemented
137C4×#123C2216yescomplemented
138C4×#121C2213yes—
139C4×#121C2216yes—
140C4×#121C2213yes—
141C4×#121C2216yescomplemented
142C4×#121C2216yescomplemented
143C4×#121C2213yescomplemented
144C4×#121C2216yescomplemented
145C4×#121C2213yescomplemented
146C4×#120C2216yes—
147C4×#120C2216yes—
148#2297C2216yescomplemented
149#2297C2213yescomplemented
150#2296C2213yescomplemented
151#2293C2216yescomplemented
152#2290C2216yes—
153#2290C2216yescomplemented
154#2285C2213yescomplemented
155#2280C2213yes—
156C42×Q8C2212yescomplemented
157C42×D4C2216yes—
158C42×D4C2216yescomplemented
159C4×#117C2213yescomplemented
160C22×#41—28no—
161C22×#41—28no—
162C22×#41—28no—
163C22×#41C2313yes—
164C22×#41C2313yes—
165C22×#41C2312yes—
166C22×#41C2313yes—
167C22×#41C2311yescharacteristic
168C22×#41C2311yescharacteristic
169C22×#41C2316yes—
170C23×Q8C2311yescharacteristic
171C23×D4C2313yes—
172C24×C4C2313yes—
173C24×C4C2313yes—
174C24×C4C2313yes—
175Q82—28no—
176#555—224no—
177#555—248no—
178#550—216no—
179#550—216no—
180#550—28no—
181#550—224no—
182#548—216no—
183#532—248no—
184#532—224no—
185C2×C4⋊Q8C2313yes—
186C2×C4⋊Q8C2316yes—
187C2×#127C2316yes—
188C2×#127C2313yes—
189C2×#127C2316yes—
190C2×#124C2316yes—
191C2×#124C2316yes—
192C2×#124C23112yes—
193#525—224no—
194#525—424no—
195C2×#123C2316yes—
196C2×#123C23112yes—
197C2×C22⋊Q8C2316yes—
198C2×C22⋊Q8C2313yes—
199C2×C22⋊Q8C2316yes—
200C2×C22⋊Q8C2316yes—
201C2×C22⋊Q8C2311yescharacteristic
202C2×#121C2313yes—
203C2×#121C2316yes—
204C2×#121C2316yes—
205C2×#121C2316yes—
206C2×#121C2316yes—
207C2×#121C2316yes—
208C2×#121C2316yes—
209C2×#121C2313yes—
210C2×#121C2316yes—
211C2×#121C23112yes—
212C2×#121C2316yes—
213C2×#121C2316yes—
214C2×#121C2316yes—
215C2×#120C2316yes—
216C2×#120C23112yes—
217C4×#41—28no—
218C4×#41—28no—
219C4×#41—28no—
220C4×#41—216no—
221C4×#41—224no—
222C4×#41—224no—
223C4×#41—224no—
224C4×#41—224no—
225C4×#41—224no—
226C4×#41D4116yescomplemented
227C2×C4×Q8—28no—
228C2×C4×Q8—28no—
229C2×C4×Q8C2313yes—
230C2×C4×Q8C2313yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2313yes—
237C2×C4×Q8C2313yes—
238C2×C4×Q8C2313yes—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×D4—224no—
243C2×C4×D4—224no—
244C2×C4×D4C2313yes—
245C2×C4×D4C2316yes—
246C2×C4×D4C2313yes—
247C2×C4×D4C2316yes—
248C2×C4×D4C2316yes—
249C2×C4×D4C2316yes—
250C2×C4×D4C2316yes—
251C2×C4×D4C2313yes—
252C2×C4×D4C2316yes—
253C2×C4×D4C2316yes—
254C2×C4×D4C2316yes—
255C2×C4×D4C2316yes—
256C2×C4×D4C2313yes—
257C2×C4×D4C2313yes—
258C2×C4×D4C2313yes—
259C2×C4×D4C2316yes—
260C2×C4×D4C2316yes—
261C2×C4×D4C2316yes—
262C2×C4×D4C2313yes—
263C2×C4×D4C2313yes—
264C2×C4×D4C2316yes—
265C2×C4×D4C2316yes—
266C2×C4×D4C23112yes—
267C2×C4×D4C2313yes—
268C2×C4×D4C2313yes—
269C2×#117—224no—
270C2×#117C2316yes—
271C2×#117C2316yes—
272C2×#117C2316yes—
273C2×#117C2313yes—
274C2×#117C2313yes—
275C2×#117C2313yes—
276C2×#117C2316yes—
277C2×#117C2313yes—
278C2×#117C2313yes—
279C2×#117C2313yes—
280C2×#117C2316yes—
281C2×#117C2313yes—
282C22×C4⋊C4C2313yes—
283C22×C4⋊C4C2313yes—
284C22×C22⋊C4C2316yes—
285C22×C42—224no—
286C22×C42C2313yes—
287C22×C42C2313yes—
288C22×C42C2313yes—
289C22×C42C2313yes—
290C22×C42C2313yes—
291C22×C42C2313yes—
292C22×C42C2311yescharacteristic
293C22×C42C2313yes—
294C22×C42C2313yes—
295C22×C42C2313yes—
296C22×C42C2313yes—
297C22×C42C2316yes—
298C22×C42C2313yes—
299#398C23112yes—
300#397C23112yes—
301#396C23112yes—
302#396C23112yes—
303#395C23112yes—
304#394C23112yes—
305#394C23112yes—
306#394C23112yes—
307#394C23112yes—
308#394C23112yes—
309#394C23112yes—
310#393C23112yes—
311#392C23112yes—
312#392C23112yes—
313#392C23112yes—
314#392C23112yes—
315#391C2316yes—
316#391C2313yes—
317#391C2316yes—
318#391C2316yes—
319#391C2316yes—
320#391C2311yescharacteristic
321#390C2316yes—
322#390C2316yes—
323#390C23112yes—
324#390C23112yes—
325#390C2316yes—
326#390C2316yes—
327#390C2316yes—
328#390C2316yes—
329#390C2316yes—
330#390C2316yes—
331#390C2316yes—
332#390C2316yes—
333#390C2313yes—
334#390C2316yes—
335#390C2313yes—
336#389C2313yes—
337#389C2316yes—
338#389C2316yes—
339#389C2313yes—
340#389C2316yes—
341#389C2316yes—
342#389C2316yes—
343#389C2316yes—
344#389C2316yes—
345#389C2313yes—
346#389C2311yescharacteristic
347#388C23112yes—
348#388C23112yes—
349#388C2316yes—
350#388C23112yes—
351#388C23112yes—
352#388C23112yes—
353#388C23112yes—
354#388C23112yes—
355#388C2316yes—
356#388C23112yes—
357#388C2316yes—
358#388C2316yes—
359#387C23112yes—
360#387C2316yes—
361#387C2316yes—
362#387C2316yes—
363#387C2312yes—
364#386C2316yes—
365#386C23112yes—
366#386C23112yes—
367#386C23112yes—
368#386C23112yes—
369#386C23112yes—
370#386C23112yes—
371#386C2316yes—
372#386C2316yes—
373#386C2316yes—
374#386C2316yes—
375#386C2316yes—
376#385C2316yes—
377#385C23112yes—
378#385C2316yes—
379#385C2316yes—
380#385C2316yes—
381#385C2316yes—
382#385C2312yes—
383#384C2316yes—
384#384C2313yes—
385#384C2313yes—
386#382C2316yes—
387#382C2316yes—
388#381C2316yes—
389#380C2313yes—
390#380C2316yes—
391#380C2313yes—
392#380C2316yes—
393#380C2316yes—
394#380C2316yes—
395#380C2316yes—
396#380C2316yes—
397#380C2316yes—
398#380C2313yes—
399#380C2311yescharacteristic
400#379C2316yes—
401C4×C4⋊C4C2313yes—
402C4×C4⋊C4C2313yes—
403C4×C4⋊C4C2316yes—
404C4×C4⋊C4C2316yes—
405C4×C4⋊C4C2316yes—
406C4×C4⋊C4C2316yes—
407C4×C4⋊C4C2316yes—
408C4×C4⋊C4C2316yes—
409C4×C4⋊C4C2316yes—
410C4×C4⋊C4C2311yescharacteristic
411C4×C4⋊C4C2313yes—
412C4×C4⋊C4C2312yes—
413C4×C4⋊C4C2316yes—
414C4×C22⋊C4C2316yes—
415C4×C22⋊C4C2316yes—
416C4×C22⋊C4C2316yes—
417C4×C22⋊C4C2316yes—
418C4×C22⋊C4C2316yes—
419C4×C22⋊C4C2316yes—
420C4×C22⋊C4C2316yes—
421C4×C22⋊C4C2316yes—
422C4×C22⋊C4C2316yes—
423C4×C22⋊C4C2316yes—
424C4×C22⋊C4C2316yes—
425C4×C22⋊C4C23112yes—
426C4×C22⋊C4C2316yes—
427C4×C22⋊C4C2312yes—
428C4×C22⋊C4C2316yes—
429#376C2316yes—
430C43C2316yes—
431C25C2413yes—
432C2×#41—2128no—
433C2×#41—24no—
434C2×#41—28no—
435C2×#41—212no—
436C2×#41—212no—
437C2×#41—24no—
438C2×#41—24no—
439C2×#41—24no—
440C2×#41—28no—
441C2×#41—28no—
442C2×#41—212no—
443C2×#41—212no—
444C2×#41—212no—
445C2×#41—212no—
446C2×#41—212no—
447C2×#41—224no—
448C2×#41—212no—
449C2×#41—412no—
450C2×#41—412no—
451C2×#41—46no—
452C2×#41C2×D418yes—
453C2×#41#4118yescomplemented
454C22×Q8—24no—
455C22×Q8—24no—
456C22×Q8#4118yescomplemented
457C22×Q8C2413yes—
458C22×Q8C2411yescharacteristic
459C22×Q8C2416yes—
460C22×Q8C2411yescharacteristic
461C22×D4—212no—
462C22×D4—212no—
463C22×D4—212no—
464C22×D4C2416yes—
465C22×D4C2416yes—
466C22×D4C2413yes—
467C22×D4C2416yes—
468C22×D4C2416yes—
469C22×D4C2416yes—
470C22×D4C2413yes—
471C22×D4C2413yes—
472C22×D4C24112yes—
473C22×D4C24112yes—
474C22×D4C2416yes—
475C23×C4—212no—
476C23×C4—212no—
477C23×C4—212no—
478C23×C4—212no—
479C23×C4—212no—
480C23×C4—212no—
481C23×C4—212no—
482C23×C4—46no—
483C23×C4—46no—
484C23×C4C2413yes—
485C23×C4C2413yes—
486C23×C4C2416yes—
487C23×C4C2413yes—
488C23×C4C2411yescharacteristic
489C23×C4C2413yes—
490C23×C4C2416yes—
491C23×C4C2413yes—
492C23×C4C2413yes—
493C23×C4C2416yes—
494C23×C4C2413yes—
495C23×C4C2413yes—
496C23×C4C2413yes—
497C23×C4C2413yes—
498C23×C4C2413yes—
499C23×C4C2413yes—
500C23×C4C2413yes—
501C23×C4C2413yes—
502C23×C4C2413yes—
503C23×C4C2411yescharacteristic
504C23×C4C2411yescharacteristic
505C4⋊Q8—224no—
506C4⋊Q8—212no—
507#127—224no—
508#127—224no—
509#127—212no—
510#124—224no—
511#124—248no—
512#124—224no—
513#123—224no—
514#123—424no—
515C22⋊Q8—224no—
516C22⋊Q8—212no—
517C22⋊Q8—412no—
518C22⋊Q8—412no—
519C22⋊Q8#4118yescomplemented
520#121—224no—
521#121—224no—
522#121—224no—
523#121—224no—
524#121—212no—
525#121—224no—
526#121—224no—
527#121—224no—
528#121—212no—
529#121—248no—
530#121—412no—
531#121—412no—
532#121—412no—
533#120—224no—
534#120—424no—
535C4×Q8—24no—
536C4×Q8—24no—
537C4×Q8—28no—
538C4×Q8—28no—
539C4×Q8—28no—
540C4×Q8—212no—
541C4×Q8—212no—
542C4×Q8—212no—
543C4×Q8—212no—
544C4×Q8—24no—
545C4×Q8—212no—
546C4×Q8C2×D418yes—
547C4×Q8C2×D418yes—
548C4×D4—212no—
549C4×D4—212no—
550C4×D4—224no—
551C4×D4—224no—
552C4×D4—224no—
553C4×D4—224no—
554C4×D4—224no—
555C4×D4—224no—
556C4×D4—224no—
557C4×D4—212no—
558C4×D4—212no—
559C4×D4—224no—
560C4×D4—224no—
561C4×D4—224no—
562C4×D4—224no—
563C4×D4—224no—
564C4×D4—212no—
565C4×D4—212no—
566C4×D4—212no—
567C4×D4—224no—
568C4×D4—212no—
569C4×D4—412no—
570C4×D4—424no—
571C4×D4C2×D4124yes—
572C4×D4C2×D4124yes—
573#117—212no—
574#117—212no—
575#117—212no—
576#117—212no—
577#117—224no—
578#117—212no—
579#117—224no—
580#117—224no—
581#117—224no—
582#117—412no—
583#117—46no—
584#117C2×D4124yes—
585C2×C4⋊C4—212no—
586C2×C4⋊C4—212no—
587C2×C4⋊C4C2413yes—
588C2×C4⋊C4C2413yes—
589C2×C4⋊C4C2416yes—
590C2×C4⋊C4C2416yes—
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2413yes—
595C2×C4⋊C4C2416yes—
596C2×C4⋊C4C2416yes—
597C2×C4⋊C4C2413yes—
598C2×C4⋊C4C2413yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2416yes—
601C2×C4⋊C4C2416yes—
602C2×C4⋊C4C2416yes—
603C2×C4⋊C4C2416yes—
604C2×C4⋊C4C2416yes—
605C2×C4⋊C4C2416yes—
606C2×C4⋊C4C2416yes—
607C2×C4⋊C4C24112yes—
608C2×C4⋊C4C2416yes—
609C2×C4⋊C4C2413yes—
610C2×C4⋊C4C2413yes—
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2412yes—
613C2×C22⋊C4—224no—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C2416yes—
618C2×C22⋊C4C2416yes—
619C2×C22⋊C4C24112yes—
620C2×C22⋊C4C2416yes—
621C2×C22⋊C4C2416yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2416yes—
624C2×C22⋊C4C2416yes—
625C2×C22⋊C4C2416yes—
626C2×C22⋊C4C2416yes—
627C2×C22⋊C4C2416yes—
628C2×C22⋊C4C2416yes—
629C2×C22⋊C4C2416yes—
630C2×C22⋊C4C2416yes—
631C2×C22⋊C4C24112yes—
632C2×C22⋊C4C24112yes—
633C2×C22⋊C4C2416yes—
634C2×C22⋊C4C24112yes—
635C2×C22⋊C4C24112yes—
636C2×C22⋊C4C2416yes—
637C2×C22⋊C4C2416yes—
638C2×C22⋊C4C24112yes—
639C2×C22⋊C4C2416yes—
640C2×C22⋊C4C2412yes—
641C2×C42—212no—
642C2×C42—212no—
643C2×C42—212no—
644C2×C42—212no—
645C2×C42—212no—
646C2×C42—212no—
647C2×C42—224no—
648C2×C42—212no—
649C2×C42—212no—
650C2×C42—212no—
651C2×C42—212no—
652C2×C42—24no—
653C2×C42C2×D4124yes—
654C2×C42C2416yes—
655C2×C42C2413yes—
656C2×C42C2413yes—
657C2×C42C2413yes—
658C2×C42C2416yes—
659C2×C42C2416yes—
660C2×C42C2413yes—
661C2×C42C2413yes—
662C2×C42C2413yes—
663C2×C42C2413yes—
664C2×C42C2413yes—
665C2×C42C2416yes—
666C2×C42C2416yes—
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2416yes—
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2413yes—
673C2×C42C2411yescharacteristic
674C2×C42C2416yes—
675C2×C42C2413yes—
676C2×C42C2413yes—
677C2×C42C2413yes—
678C2×C42C2411yescharacteristic
679#95C2412yes—
680#95C2416yes—
681#95C2416yes—
682#95C2416yes—
683#95C2412yes—
684#95C2412yes—
685#95C2412yes—
686#95C2412yes—
687#95C2416yes—
688#95C2416yes—
689#95C2416yes—
690#95C2416yes—
691#95C2416yes—
692#95C2416yes—
693#95C2416yes—
694#95C2416yes—
695#95C24112yes—
696#95C24112yes—
697#95C24112yes—
698C24—26no—
699C24—26no—
700C24—26no—
701C24—26no—
702C24—26no—
703C24—43no—
704C24—43no—
705C24C2516yes—
706C24C2513yes—
707C24C2513yes—
708C24C2511yescharacteristic
709#41—296no—
710#41—296no—
711#41—232no—
712#41—232no—
713#41—448no—
714#41—432no—
715#41—848no—
716C2×Q8—232no—
717C2×Q8—26no—
718C2×Q8—22no—
719C2×Q8—212no—
720C2×Q8—26no—
721C2×Q8—22no—
722C2×Q8—46no—
723C2×Q8—46no—
724C2×Q8C22×D414yes—
725C2×Q8C2×#41112yes—
726C2×Q8C2×#4114yes—
727C2×Q8C2×#4114yes—
728C2×Q8C2×#4114yescomplemented
729C2×D4—296no—
730C2×D4—212no—
731C2×D4—212no—
732C2×D4—212no—
733C2×D4—212no—
734C2×D4—212no—
735C2×D4—212no—
736C2×D4—212no—
737C2×D4—224no—
738C2×D4—224no—
739C2×D4—26no—
740C2×D4—212no—
741C2×D4—26no—
742C2×D4—212no—
743C2×D4—212no—
744C2×D4—26no—
745C2×D4—26no—
746C2×D4—26no—
747C2×D4—212no—
748C2×D4—212no—
749C2×D4—26no—
750C2×D4—212no—
751C2×D4—212no—
752C2×D4—26no—
753C2×D4—46no—
754C2×D4—46no—
755C2×D4—412no—
756C2×D4—412no—
757C2×D4—46no—
758C2×D4—412no—
759C2×D4—46no—
760C2×D4—412no—
761C2×D4C22×D4112yes—
762C2×D4C2×#41112yes—
763C22×C4—296no—
764C22×C4—26no—
765C22×C4—22no—
766C22×C4—26no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—26no—
771C22×C4—26no—
772C22×C4—26no—
773C22×C4—26no—
774C22×C4—22no—
775C22×C4—26no—
776C22×C4—26no—
777C22×C4—26no—
778C22×C4—26no—
779C22×C4—26no—
780C22×C4—26no—
781C22×C4—26no—
782C22×C4—26no—
783C22×C4—26no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—26no—
787C22×C4—26no—
788C22×C4—26no—
789C22×C4—26no—
790C22×C4—26no—
791C22×C4—26no—
792C22×C4—26no—
793C22×C4—26no—
794C22×C4—26no—
795C22×C4—26no—
796C22×C4—26no—
797C22×C4—212no—
798C22×C4—212no—
799C22×C4—212no—
800C22×C4—26no—
801C22×C4—212no—
802C22×C4—212no—
803C22×C4—212no—
804C22×C4—26no—
805C22×C4—26no—
806C22×C4—212no—
807C22×C4—26no—
808C22×C4—26no—
809C22×C4—26no—
810C22×C4—26no—
811C22×C4—212no—
812C22×C4—26no—
813C22×C4—43no—
814C22×C4—43no—
815C22×C4—43no—
816C22×C4—43no—
817C22×C4—43no—
818C22×C4—43no—
819C22×C4—46no—
820C22×C4—448no—
821C22×C4—448no—
822C22×C4C22×D4112yes—
823C22×C4C22×D4112yes—
824C22×C4C22×D4112yes—
825C22×C4C2×#41112yes—
826C22×C4C2×#41112yes—
827C22×C4C2×#4114yes—
828C22×C4H(5,𝔽2)14yes—
829C22×C4C2512yes—
830C22×C4C2516yes—
831C22×C4C2512yes—
832C22×C4C2513yes—
833C22×C4C2516yes—
834C22×C4C2516yes—
835C22×C4C2513yes—
836C22×C4C2511yescharacteristic
837C22×C4C2513yes—
838C22×C4C2513yes—
839C22×C4C2511yescharacteristic
840C22×C4C2511yescharacteristic
841C22×C4C2512yes—
842C22×C4C2513yes—
843C22×C4C2512yes—
844C22×C4C2511yescharacteristic
845C22×C4C2513yes—
846C22×C4C2511yescharacteristic
847C22×C4C2511yescharacteristic
848C4⋊C4—212no—
849C4⋊C4—212no—
850C4⋊C4—26no—
851C4⋊C4—26no—
852C4⋊C4—24no—
853C4⋊C4—22no—
854C4⋊C4—212no—
855C4⋊C4—212no—
856C4⋊C4—26no—
857C4⋊C4—26no—
858C4⋊C4—24no—
859C4⋊C4—212no—
860C4⋊C4—212no—
861C4⋊C4—212no—
862C4⋊C4—212no—
863C4⋊C4—212no—
864C4⋊C4—22no—
865C4⋊C4—26no—
866C4⋊C4—46no—
867C4⋊C4—46no—
868C4⋊C4—46no—
869C4⋊C4—412no—
870C4⋊C4C22×D4112yes—
871C4⋊C4C22×D4112yes—
872C4⋊C4C2×#4114yescomplemented
873C4⋊C4C2×#4118yescomplemented
874C22⋊C4—212no—
875C22⋊C4—212no—
876C22⋊C4—24no—
877C22⋊C4—212no—
878C22⋊C4—212no—
879C22⋊C4—212no—
880C22⋊C4—212no—
881C22⋊C4—212no—
882C22⋊C4—212no—
883C22⋊C4—224no—
884C22⋊C4—212no—
885C22⋊C4—212no—
886C22⋊C4—212no—
887C22⋊C4—212no—
888C22⋊C4—212no—
889C22⋊C4—212no—
890C22⋊C4—224no—
891C22⋊C4—212no—
892C22⋊C4—46no—
893C22⋊C4—412no—
894C22⋊C4—46no—
895C22⋊C4—46no—
896C22⋊C4—412no—
897C22⋊C4—412no—
898C22⋊C4—412no—
899C22⋊C4C22×D4124yes—
900C22⋊C4C2×#4118yes—
901C42—22no—
902C42—22no—
903C42—22no—
904C42—26no—
905C42—26no—
906C42—26no—
907C42—24no—
908C42—26no—
909C42—26no—
910C42—26no—
911C42—26no—
912C42—26no—
913C42—26no—
914C42—212no—
915C42—212no—
916C42—212no—
917C42—212no—
918C42—212no—
919C42—212no—
920C42—24no—
921C42—46no—
922C42C22×D414yes—
923C42C22×D4112yes—
924C42C22×D4112yes—
925C42C22×D4112yes—
926C23—21no—
927C23—21no—
928C23—21no—
929C23—21no—
930C23—224no—
931C23—23no—
932C23—23no—
933C23—23no—
934C23—23no—
935C23—23no—
936C23—23no—
937C23—23no—
938C23—23no—
939C23—23no—
940C23—23no—
941C23—23no—
942C23—23no—
943C23—26no—
944C23—26no—
945C23—26no—
946C23—26no—
947C23—26no—
948C23—26no—
949C23—26no—
950C23—412no—
951C23—412no—
952C23—412no—
953C23—412no—
954C23—412no—
955C23—412no—
956C23C23×D416yes—
957C23C22×#4116yes—
958C23C22×#4112yes—
959C23C22×#4112yes—
960C23C2×H(5,𝔽2)12yes—
961C23C2611yescharacteristic
962Q8—224no—
963Q8—28no—
964Q8—812no—
965Q8#525116yescomplemented
966D4—248no—
967D4—224no—
968D4—224no—
969D4—424no—
970D4—424no—
971D4—424no—
972D4—424no—
973D4—412no—
974D4—812no—
975D4—824no—
976D4—824no—
977C2×C4—28no—
978C2×C4—224no—
979C2×C4—224no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—22no—
984C2×C4—23no—
985C2×C4—22no—
986C2×C4—23no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—23no—
991C2×C4—23no—
992C2×C4—22no—
993C2×C4—23no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—23no—
997C2×C4—22no—
998C2×C4—224no—
999C2×C4—224no—
1000C2×C4—224no—
1001C2×C4—28no—
1002C2×C4—224no—
1003C2×C4—28no—
1004C2×C4—224no—
1005C2×C4—22no—
1006C2×C4—23no—
1007C2×C4—23no—
1008C2×C4—26no—
1009C2×C4—22no—
1010C2×C4—26no—
1011C2×C4—26no—
1012C2×C4—26no—
1013C2×C4—22no—
1014C2×C4—23no—
1015C2×C4—22no—
1016C2×C4—26no—
1017C2×C4—26no—
1018C2×C4—26no—
1019C2×C4—23no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—26no—
1023C2×C4—23no—
1024C2×C4—23no—
1025C2×C4—26no—
1026C2×C4—412no—
1027C2×C4—412no—
1028C2×C4—424no—
1029C2×C4—412no—
1030C2×C4—412no—
1031C2×C4—412no—
1032C2×C4—412no—
1033C2×C4—424no—
1034C2×C4—412no—
1035C2×C4—412no—
1036C2×C4—424no—
1037C2×C4C23×D412yes—
1038C2×C4C23×D416yes—
1039C2×C4C23×D416yes—
1040C2×C4C23×D416yes—
1041C2×C4C23×D412yes—
1042C2×C4C23×D412yes—
1043C2×C4C22×#4114yes—
1044C2×C4C22×#4112yes—
1045C2×C4C22×#4116yes—
1046C2×C4C22×#4112yes—
1047C2×C4C22×#4114yes—
1048C2×C4C22×#4116yes—
1049C2×C4C22×#4116yes—
1050C2×C4C22×#4112yes—
1051C2×C4C2×H(5,𝔽2)12yes—
1052C2×C4C2×H(5,𝔽2)12yes—
1053C2×C4#58512yes—
1054C2×C4#58512yes—
1055C22—22no—
1056C22—22no—
1057C22—22no—
1058C22—22no—
1059C22—22no—
1060C22—22no—
1061C22—26no—
1062C22—26no—
1063C22—26no—
1064C22—26no—
1065C22—26no—
1066C22—26no—
1067C22—448no—
1068C22—43no—
1069C22—43no—
1070C22—43no—
1071C22—43no—
1072C22—43no—
1073C22—43no—
1074C22—43no—
1075C22—43no—
1076C22—46no—
1077C22—46no—
1078C22—46no—
1079C22—46no—
1080C22—46no—
1081C22—46no—
1082C22—46no—
1083C22#348314yescomplemented
1084C22C24×D411yescharacteristic
1085C22C23×#4111yescharacteristic
1086C22C23×#4111yescharacteristic
1087C22C23×#4111yescharacteristic
1088C22C22×H(5,𝔽2)11yescharacteristic
1089C22C2×#58511yescharacteristic
1090C22C2×#58511yescharacteristic
1091C4—22no—
1092C4—26no—
1093C4—22no—
1094C4—22no—
1095C4—26no—
1096C4—22no—
1097C4—26no—
1098C4—24no—
1099C4—24no—
1100C4—42no—
1101C4—43no—
1102C4—46no—
1103C4—46no—
1104C4—42no—
1105C4—43no—
1106C4—46no—
1107C4C2×#525112yes—
1108C4D4×#4114yes—
1109C4#348814yes—
1110C2—24no—
1111C2—46no—
1112C2—46no—
1113C2—86no—
1114C2C22×#52511yescharacteristic
1115C2C2×D4×#4111yescharacteristic
1116C2C2×#348311yescharacteristic
1117C2#41211yescharacteristic
1118C2#6279311yescharacteristic
1119C2C2×#348811yescharacteristic
1120C2#6280011yescharacteristic
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3483C2semidirect
2. C22×C4×#41C2semidirect
3. #36624C2semidirect
4. #36576C2semidirect
5. Q8×C22⋊Q8C2semidirect
6. #36456C2semidirect
7. #36455C2semidirect
8. #36433C2semidirect
9. #36429C2semidirect
10. #36411C2semidirect
11. #36410C2semidirect
12. #36235C2semidirect
13. #36231C2semidirect
14. #36160C2semidirect
15. #36101C2semidirect
16. #34977C2semidirect
17. #34976C2semidirect
18. #34715C2semidirect
19. #34681C2semidirect
20. C4×#550C2semidirect
21. C4×#548C2semidirect
22. #34129C2semidirect
23. C4×#525C2semidirect
26. C2×Q82C22semidirect
27. C2×#555C22semidirect
28. C2×#555C22semidirect
31. C2×#550C22semidirect
32. C2×#550C22semidirect
34. C2×#532C22semidirect
35. C2×#532C22semidirect
47. C2×C4×#41C22semidirect
48. C2×C4×#41C22semidirect
56. #2857C22semidirect
58. #2856C22semidirect
59. #2854C22semidirect
60. #2854C22semidirect
62. #2850C22semidirect
65. #2610C22semidirect
66. #2609C22semidirect
67. #2582C22semidirect
68. #2567C22semidirect
69. #2563C22semidirect
70. #2548C22semidirect
71. #2541C22semidirect
72. #2538C22semidirect
73. #2538C22semidirect
74. #2537C22semidirect
75. #2500C22semidirect
76. #2485C22semidirect
77. #2485C22semidirect
78. #2476C22semidirect
79. #2474C22semidirect
81. #2464C22semidirect
82. #2461C22semidirect
83. #2459C22semidirect
84. #2456C22semidirect
85. #2452C22semidirect
86. #2451C22semidirect
87. #2445C22semidirect
88. #2445C22semidirect
90. #2439C22semidirect
94. #2428C22semidirect
95. #2426C22semidirect
97. #2422C22semidirect
98. #2420C22semidirect
100. #2414C22semidirect
101. #2414C22semidirect
102. #2414C22semidirect
106. #2407C22semidirect
107. #2392C22semidirect
108. #2388C22semidirect
109. #2367C22semidirect
110. #2366C22semidirect
111. #2363C22semidirect
112. #2363C22semidirect
113. #2362C22semidirect
115. #2354C22semidirect
116. #2354C22semidirect
117. #2354C22semidirect
119. #2351C22semidirect
120. Q8×C4⋊C4C22semidirect
121. Q8×C4⋊C4C22semidirect
122. Q8×C4⋊C4C22semidirect
123. #2346C22semidirect
126. #2341C22semidirect
127. #2341C22semidirect
129. C4×#127C22semidirect
130. C4×#124C22semidirect
133. C4×C22⋊Q8C22semidirect
134. C4×C22⋊Q8C22semidirect
135. C4×C22⋊Q8C22semidirect
136. C4×#123C22semidirect
137. C4×#123C22semidirect
141. C4×#121C22semidirect
142. C4×#121C22semidirect
143. C4×#121C22semidirect
144. C4×#121C22semidirect
145. C4×#121C22semidirect
148. #2297C22semidirect
149. #2297C22semidirect
150. #2296C22semidirect
151. #2293C22semidirect
153. #2290C22semidirect
154. #2285C22semidirect
156. C42×Q8C22semidirect
158. C42×D4C22semidirect
159. C4×#117C22semidirect
226. C4×#41D4semidirect
453. C2×#41#41semidirect
456. C22×Q8#41semidirect
519. C22⋊Q8#41semidirect
728. C2×Q8C2×#41semidirect
872. C4⋊C4C2×#41semidirect
873. C4⋊C4C2×#41semidirect
965. Q8#525semidirect
1083. C22#3483semidirect

Maximal subgroups

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

subgroupindex
C2×#34832
C22×C4×#412
#366242
#365762
Q8×C22⋊Q82
#364562
#364552
#364332
#364292
#364112
#364102
#362352
#362312
#361602
#361012
#349772
#349762
#347152
#346812
C4×#5502
C4×#5482
#341292
C4×#5252