Finite Group Databasebeta

← #7625841

Subgroups — #7625841

Order 512.

10868 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3489C211yesmaximal, characteristic
2C2×C4×2−1+4C211yesmaximal, characteristic, complemented
3C2×#3428C211yesmaximal, characteristic, complemented
4#34311C212yesmaximal, complemented
5#34309C216yesmaximal, complemented
6#34293C212yesmaximal, complemented
7#34292C216yesmaximal, complemented
8#34291C212yesmaximal, complemented
9#34289C216yesmaximal, complemented
10#34276C213yesmaximal, complemented
11#34274C213yesmaximal, complemented
12#34267C213yesmaximal, complemented
13#34266C213yesmaximal, complemented
14#34259C211yesmaximal, characteristic, complemented
15#34250C211yesmaximal, characteristic, complemented
16#34203C213yesmaximal, complemented
17#34201C213yesmaximal, complemented
18C4×#547C216yesmaximal, complemented
19C4×#548C212yesmaximal, complemented
20#34136C213yesmaximal, complemented
21C2×#2362C213yesmaximal, complemented
22C22⋊C4×#41C211yesmaximal, characteristic, complemented
23C4×#520C211yesmaximal, characteristic, complemented
24C22×2−1+4C2211yescharacteristic
25C23×#41C2211yescharacteristic
26#3489C4132yescomplemented
27C2×D4×Q8C2212yes—
28C2×#548C2212yes—
29C2×#547C2216yes—
30C2×#546C2216yes—
31C2×#537C2213yes—
32C2×#536C2213yes—
33C2×#525C2213yes—
34C22×C22⋊Q8C2213yes—
35C4×2−1+4—216no—
36#3428—216no—
37C2×#520C2211yescharacteristic
38C2×#520C2213yes—
39C2×#520C2213yes—
40C2×#520C2211yescharacteristic
41C2×#520C2211yescharacteristic
42C2×#520C2216yescomplemented
43C2×#520C2213yescomplemented
44C2×#519C2212yes—
45C2×#519C2212yescomplemented
46C2×#519C2213yescomplemented
47C2×#518C2216yes—
48C2×C4×#41C2211yescharacteristic
49C2×C4×#41C2211yescharacteristic
50C2×C4×#41C2212yes—
51C2×C4×#41C2216yes—
52C2×C4×#41C2213yescomplemented
53C2×C4×#41C2216yescomplemented
54C22×C4×Q8C2213yescomplemented
55C22×C4×Q8C2212yescomplemented
56C22×#117C2213yes—
57C22×#117C2213yes—
58#2367C2216yescomplemented
59#2367C2216yescomplemented
60#2365C2216yescomplemented
61#2365C2216yescomplemented
62#2364C22112yescomplemented
63#2363C2211yescharacteristic
64#2363C2213yes—
65#2363C2216yescomplemented
66#2363C2216yescomplemented
67#2362C2216yes—
68#2362C2213yes—
69#2362C2216yes—
70#2362C2216yes—
71#2362C2213yes—
72#2362C2216yescomplemented
73#2362C2216yescomplemented
74#2362C2216yescomplemented
75#2362C2216yescomplemented
76#2362C2216yescomplemented
77#2362C2216yescomplemented
78#2361C2216yescomplemented
79#2361C2213yescomplemented
80#2361C2213yescomplemented
81#2361C22112yescomplemented
82#2360C2213yescomplemented
83#2360C2213yescomplemented
84#2360C2216yescomplemented
85#2360C2216yescomplemented
86#2360C2216yescomplemented
87#2359C22112yescomplemented
88#2359C2216yescomplemented
89#2359C2216yescomplemented
90#2359C22112yescomplemented
91#2358C2216yes—
92#2358C2216yes—
93#2354C2216yes—
94#2354C2216yescomplemented
95#2352C2216yes—
96#2352C2216yescomplemented
97#2351C2212yescomplemented
98Q8×C4⋊C4C2212yescomplemented
99#2349C2216yescomplemented
100D4×C4⋊C4C2216yescomplemented
101#2344C22112yescomplemented
102#2342C22112yes—
103#2341C2211yescharacteristic
104#2341C2211yescharacteristic
105Q8×C22⋊C4C2211yescharacteristic
106Q8×C22⋊C4C2211yescharacteristic
107Q8×C22⋊C4C2212yescomplemented
108Q8×C22⋊C4C2212yescomplemented
109#2339C2213yes—
110#2339C2213yes—
111#2339C2216yescomplemented
112#2339C2216yescomplemented
113D4×C22⋊C4C2213yes—
114D4×C22⋊C4C2213yes—
115#2327C2216yescomplemented
116#2326C2216yescomplemented
117#2325C22112yescomplemented
118#2324C2216yescomplemented
119#2323C2216yes—
120#2323C2216yes—
121#2323C2216yescomplemented
122#2322C22112yescomplemented
123#2321C22112yes—
124#2317C2213yescomplemented
125#2316C2213yescomplemented
126#2311C2213yescomplemented
127#2310C2213yescomplemented
128C4×C4⋊Q8C2216yescomplemented
129C4×#124C2216yescomplemented
130C4×C22⋊Q8C2216yescomplemented
131C4×C22⋊Q8C2216yescomplemented
132C4×C22⋊Q8C2216yescomplemented
133C4×#123C22112yescomplemented
134C4×#123C22112yescomplemented
135C4×#121C22112yescomplemented
136C4×#121C2216yescomplemented
137#2297C2213yes—
138#2297C2213yes—
139#2297C2213yescomplemented
140#2296C2213yescomplemented
141C2×#391C2213yescomplemented
142#2293C2216yes—
143C2×#389C2213yescomplemented
144#2290C2216yes—
145#2290C2216yescomplemented
146C2×#388C2216yes—
147C2×#388C2216yes—
148C2×#387C2216yescomplemented
149#2280C2213yes—
150#2276C2212yescomplemented
151#2275C2216yescomplemented
152#2274C2213yescomplemented
153#2274C2213yescomplemented
154C42×Q8C2212yescomplemented
155C42×D4C2216yescomplemented
156C42×D4C2216yescomplemented
157C4×#117C2213yescomplemented
158C2×C4×C4⋊C4C2216yescomplemented
159C2×C4×C4⋊C4C2213yescomplemented
160C2×C4×C22⋊C4C2213yes—
161C2×2−1+4—28no—
162C2×2−1+4—28no—
163C2×2−1+4C2×C4116yescomplemented
164C22×#41—28no—
165C22×#41—28no—
166C22×#41C2×C4116yescomplemented
167C22×#41C2313yes—
168C22×#41C2311yescharacteristic
169C22×#41C2313yes—
170C22×#41C2313yes—
171C22×#41C2316yes—
172C22×#41C2311yescharacteristic
173C23×Q8C2313yes—
174C23×Q8C2311yescharacteristic
175C23×Q8C2312yes—
176C23×D4C2313yes—
177C24×C4C2313yes—
178D4×Q8C2×C4132yescomplemented
179#548C2×C4132yescomplemented
180#547C2×C4196yescomplemented
181#546C2×C4196yescomplemented
182#537C2×C4148yescomplemented
183#536C2×C4148yescomplemented
184C2×C4⋊Q8C2316yes—
185C2×#124C2316yes—
186#525C2×C4148yescomplemented
187C2×#123C23112yes—
188C2×#123C2316yes—
189C2×C22⋊Q8C2×C4148yescomplemented
190C2×C22⋊Q8C2316yes—
191C2×C22⋊Q8C2316yes—
192C2×C22⋊Q8C2316yes—
193C2×C22⋊Q8C2313yes—
194C2×C22⋊Q8C2313yes—
195C2×C22⋊Q8C2316yes—
196C2×#121C2316yes—
197C2×#121C23112yes—
198C2×#121C2313yes—
199C2×#121C2311yescharacteristic
200C2×#120C2316yes—
201#520—28no—
202#520—248no—
203#520—224no—
204#520—224no—
205#520—224no—
206#520C2×C4116yescomplemented
207#520D4116yescomplemented
208#519—216no—
209#519—216no—
210#519—224no—
211#518—248no—
212C4×#41—28no—
213C4×#41—28no—
214C4×#41—216no—
215C4×#41—248no—
216C4×#41—248no—
217C4×#41—224no—
218C2×C4×Q8—216no—
219C2×C4×Q8—224no—
220C2×C4×Q8C2316yes—
221C2×C4×Q8C2316yes—
222C2×C4×Q8C2316yes—
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2313yes—
229C2×C4×Q8C2313yes—
230C2×C4×Q8C2316yes—
231C2×C4×Q8C2316yes—
232C2×C4×Q8C2316yes—
233C2×C4×Q8C2316yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×D4C23112yes—
237C2×C4×D4C23112yes—
238C2×C4×D4C2316yes—
239C2×C4×D4C2313yes—
240C2×C4×D4C2313yes—
241C2×C4×D4C2313yes—
242C2×C4×D4C2313yes—
243C2×C4×D4C2316yes—
244C2×C4×D4C2316yes—
245C2×C4×D4C2316yes—
246C2×C4×D4C23112yes—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2313yes—
249C2×C4×D4C2316yes—
250C2×C4×D4C2316yes—
251C2×C4×D4C2316yes—
252C2×C4×D4C2316yes—
253C2×C4×D4C2316yes—
254C2×C4×D4C2316yes—
255C2×C4×D4C2316yes—
256C2×#117—224no—
257C2×#117—224no—
258C2×#117C2313yes—
259C2×#117C2313yes—
260C2×#117C2313yes—
261C2×#117C2316yes—
262C2×#117C2316yes—
263C2×#117C23112yes—
264C2×#117C2316yes—
265C2×#117C2316yes—
266C2×#117C2316yes—
267C2×#117C2316yes—
268C2×#117C2313yes—
269C2×#117C2311yescharacteristic
270C2×#117C2316yes—
271C2×#117C2313yes—
272C2×#117C2313yes—
273C22×C4⋊C4C2313yes—
274C22×C4⋊C4C2316yes—
275C22×C4⋊C4C2316yes—
276C22×C4⋊C4C2313yes—
277C22×C4⋊C4C2313yes—
278C22×C4⋊C4C2316yes—
279C22×C4⋊C4C2313yes—
280C22×C4⋊C4C2316yes—
281C22×C4⋊C4C2313yes—
282C22×C22⋊C4C2316yes—
283C22×C22⋊C4C2316yes—
284C22×C22⋊C4C2313yes—
285C22×C22⋊C4C2313yes—
286C22×C22⋊C4C2316yes—
287C22×C42C2316yes—
288C22×C42C2316yes—
289C22×C42C2313yes—
290C22×C42C2316yes—
291C22×C42C2316yes—
292C22×C42C2313yes—
293C22×C42C2316yes—
294#391C2313yes—
295#391C2316yes—
296#391C2313yes—
297#391C2316yes—
298#391C2316yes—
299#391C2316yes—
300#391C2313yes—
301#391C2316yes—
302#391C2313yes—
303#391C2313yes—
304#391C2313yes—
305#390C2313yes—
306#390C2316yes—
307#390C23112yes—
308#390C2313yes—
309#390C2313yes—
310#390C2313yes—
311#390C2313yes—
312#390C2312yes—
313#390C2311yescharacteristic
314#389C2316yes—
315#389C23112yes—
316#389C2313yes—
317#389C2316yes—
318#389C2316yes—
319#389C2316yes—
320#389C2313yes—
321#389C2316yes—
322#389C23112yes—
323#389C2316yes—
324#389C2316yes—
325#389C2311yescharacteristic
326#389C2313yes—
327#388C23112yes—
328#388C23112yes—
329#388C23112yes—
330#388C23112yes—
331#388C23112yes—
332#388C2316yes—
333#388C2316yes—
334#388C2316yes—
335#388C23112yes—
336#388C23112yes—
337#388C2316yes—
338#388C2316yes—
339#388C2316yes—
340#388C2312yes—
341#388C23112yes—
342#388C2316yes—
343#388C23112yes—
344#387C23112yes—
345#387C23112yes—
346#387C23112yes—
347#387C23112yes—
348#387C23112yes—
349#387C2316yes—
350#387C2316yes—
351#387C23112yes—
352#387C2316yes—
353#387C2316yes—
354#386C23112yes—
355#386C2316yes—
356#386C23112yes—
357#386C2316yes—
358#386C2316yes—
359#386C2316yes—
360#386C2316yes—
361#386C2316yes—
362#386C2316yes—
363#386C2316yes—
364#386C2316yes—
365#386C2312yes—
366#385C23112yes—
367#385C2316yes—
368#385C2316yes—
369#385C23112yes—
370#385C23112yes—
371#385C2316yes—
372#385C2316yes—
373#385C2316yes—
374#385C2316yes—
375#384C2316yes—
376#382C2316yes—
377#381C23112yes—
378#381C2316yes—
379#380C2316yes—
380#380C2316yes—
381#380C23112yes—
382#380C2313yes—
383#380C2313yes—
384#380C2313yes—
385#380C2313yes—
386#379C2316yes—
387C4×C4⋊C4C23112yes—
388C4×C4⋊C4C23112yes—
389C4×C4⋊C4C2316yes—
390C4×C4⋊C4C2316yes—
391C4×C4⋊C4C2316yes—
392C4×C4⋊C4C23112yes—
393C4×C4⋊C4C2316yes—
394C4×C4⋊C4C2316yes—
395C4×C4⋊C4C2316yes—
396C4×C4⋊C4C2316yes—
397C4×C4⋊C4C2316yes—
398C4×C4⋊C4C2311yescharacteristic
399C4×C4⋊C4C2313yes—
400C4×C4⋊C4C2316yes—
401C4×C4⋊C4C2316yes—
402C4×C4⋊C4C2313yes—
403C4×C4⋊C4C2313yes—
404C4×C4⋊C4C2316yes—
405C4×C4⋊C4C23112yes—
406C4×C22⋊C4C23112yes—
407C4×C22⋊C4C2313yes—
408C4×C22⋊C4C2313yes—
409C4×C22⋊C4C2313yes—
410C4×C22⋊C4C2313yes—
411C4×C22⋊C4C2316yes—
412C4×C22⋊C4C2316yes—
413C4×C22⋊C4C23112yes—
414C4×C22⋊C4C23112yes—
415C4×C22⋊C4C23112yes—
416C4×C22⋊C4C23112yes—
417C4×C22⋊C4C2316yes—
418C4×C22⋊C4C2316yes—
419C4×C22⋊C4C2316yes—
420C4×C22⋊C4C2316yes—
421C4×C22⋊C4C2316yes—
422C4×C22⋊C4C2312yes—
423C4×C22⋊C4C2316yes—
424C4×C22⋊C4C2313yes—
425C4×C22⋊C4C2313yes—
426C4×C22⋊C4C2311yescharacteristic
427C4×C22⋊C4C2313yes—
428#376C2316yes—
429C2×#95C2316yes—
430C2×#95C2313yes—
431C2×#95C2313yes—
432C2×#95C2316yes—
433C2×#95C2316yes—
434C2×#95C2316yes—
435C43C2316yes—
436C25C2413yes—
4372−1+4—2128no—
438C2×#41—2128no—
439C2×#41—24no—
440C2×#41—24no—
441C2×#41—212no—
442C2×#41—224no—
443C2×#41—212no—
444C2×#41—224no—
445C2×#41—212no—
446C2×#41—212no—
447C2×#41—212no—
448C2×#41—212no—
449C2×#41C22×C4124yes—
450C2×#41C22×C4124yes—
451C2×#41C22×C4148yes—
452C2×#41C22×C4124yes—
453C2×#41C22×C418yes—
454C2×#41C22×C418yes—
455C2×#41C2×D418yes—
456C2×#41#4118yes—
457C22×Q8—28no—
458C22×Q8—24no—
459C22×Q8—24no—
460C22×Q8—28no—
461C22×Q8—212no—
462C22×Q8—212no—
463C22×Q8C22×C4124yes—
464C22×Q8C22×C4116yes—
465C22×Q8C22×C418yes—
466C22×Q8C2413yes—
467C22×Q8C2416yes—
468C22×Q8C2413yes—
469C22×Q8C2411yescharacteristic
470C22×D4—212no—
471C22×D4—212no—
472C22×D4C22×C4124yes—
473C22×D4C2416yes—
474C22×D4C2411yescharacteristic
475C22×D4C2416yes—
476C22×D4C2413yes—
477C22×D4C2412yes—
478C22×D4C2416yes—
479C22×D4C2413yes—
480C23×C4—212no—
481C23×C4—212no—
482C23×C4C22×C4124yes—
483C23×C4C2413yes—
484C23×C4C2413yes—
485C23×C4C2412yes—
486C23×C4C2416yes—
487C23×C4C2413yes—
488C23×C4C2413yes—
489C23×C4C2416yes—
490C23×C4C2413yes—
491C23×C4C2411yescharacteristic
492C23×C4C2413yes—
493C23×C4C2416yes—
494C23×C4C2413yes—
495C23×C4C2416yes—
496C23×C4C2416yes—
497C23×C4C2413yes—
498C23×C4C2416yes—
499C23×C4C2416yes—
500C23×C4C2416yes—
501C23×C4C2413yes—
502C4⋊Q8C22×C4148yes—
503#124C22×C4148yes—
504#123C22×C4148yes—
505#123C22×C4196yes—
506C22⋊Q8C22×C4124yes—
507C22⋊Q8C22×C4148yes—
508C22⋊Q8C22×C4148yes—
509C22⋊Q8C22×C4148yes—
510C22⋊Q8C22×C4124yes—
511C22⋊Q8C22×C4148yes—
512#121C22×C418yes—
513#121C22×C4124yes—
514#121C22×C4196yes—
515#121C22×C4148yes—
516#120C22×C4148yes—
517C4×Q8—24no—
518C4×Q8—24no—
519C4×Q8—28no—
520C4×Q8—24no—
521C4×Q8—24no—
522C4×Q8—212no—
523C4×Q8—224no—
524C4×Q8—224no—
525C4×Q8—224no—
526C4×Q8—212no—
527C4×Q8—224no—
528C4×Q8—224no—
529C4×Q8—224no—
530C4×Q8—224no—
531C4×Q8C22×C4116yes—
532C4×Q8C2×D4116yes—
533C4×D4—212no—
534C4×D4—224no—
535C4×D4—212no—
536C4×D4—212no—
537C4×D4—212no—
538C4×D4—248no—
539C4×D4—248no—
540C4×D4—24no—
541C4×D4—224no—
542C4×D4—212no—
543C4×D4—224no—
544C4×D4—248no—
545C4×D4—224no—
546C4×D4—224no—
547C4×D4—412no—
548C4×D4—412no—
549C4×D4C22×C4148yes—
550C4×D4C22×C4148yes—
551C4×D4C22×C4148yes—
552C4×D4C2×D4148yes—
553#117—212no—
554#117—212no—
555#117—212no—
556#117—24no—
557#117—212no—
558#117—224no—
559#117—224no—
560#117—224no—
561#117—224no—
562#117—224no—
563#117—248no—
564#117—224no—
565#117—224no—
566#117C22×C4124yes—
567#117C2×D4124yes—
568C2×C4⋊C4—212no—
569C2×C4⋊C4—224no—
570C2×C4⋊C4—212no—
571C2×C4⋊C4—212no—
572C2×C4⋊C4—224no—
573C2×C4⋊C4—412no—
574C2×C4⋊C4C22×C4124yes—
575C2×C4⋊C4C22×C4148yes—
576C2×C4⋊C4C2×D4124yes—
577C2×C4⋊C4C2413yes—
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2413yes—
580C2×C4⋊C4C2416yes—
581C2×C4⋊C4C24112yes—
582C2×C4⋊C4C2416yes—
583C2×C4⋊C4C2416yes—
584C2×C4⋊C4C2416yes—
585C2×C4⋊C4C2416yes—
586C2×C4⋊C4C2413yes—
587C2×C4⋊C4C2416yes—
588C2×C4⋊C4C2413yes—
589C2×C4⋊C4C2413yes—
590C2×C4⋊C4C24112yes—
591C2×C4⋊C4C2416yes—
592C2×C4⋊C4C2416yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2413yes—
595C2×C4⋊C4C2416yes—
596C2×C4⋊C4C2416yes—
597C2×C4⋊C4C24112yes—
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2416yes—
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2413yes—
602C2×C4⋊C4C2416yes—
603C2×C22⋊C4—224no—
604C2×C22⋊C4—224no—
605C2×C22⋊C4—46no—
606C2×C22⋊C4—46no—
607C2×C22⋊C4C22×C4148yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C2412yes—
610C2×C22⋊C4C2411yescharacteristic
611C2×C22⋊C4C2411yescharacteristic
612C2×C22⋊C4C2416yes—
613C2×C22⋊C4C24112yes—
614C2×C22⋊C4C2413yes—
615C2×C22⋊C4C2413yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C2412yes—
618C2×C22⋊C4C2416yes—
619C2×C22⋊C4C2416yes—
620C2×C22⋊C4C2412yes—
621C2×C22⋊C4C2413yes—
622C2×C22⋊C4C2413yes—
623C2×C22⋊C4C2413yes—
624C2×C22⋊C4C2413yes—
625C2×C22⋊C4C2416yes—
626C2×C22⋊C4C2416yes—
627C2×C22⋊C4C2416yes—
628C2×C22⋊C4C2416yes—
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2416yes—
631C2×C22⋊C4C24112yes—
632C2×C22⋊C4C2416yes—
633C2×C22⋊C4C2412yes—
634C2×C22⋊C4C2416yes—
635C2×C22⋊C4C2416yes—
636C2×C22⋊C4C2416yes—
637C2×C42—224no—
638C2×C42—224no—
639C2×C42—212no—
640C2×C42—212no—
641C2×C42—224no—
642C2×C42—224no—
643C2×C42—412no—
644C2×C42C2412yes—
645C2×C42C2416yes—
646C2×C42C2416yes—
647C2×C42C24112yes—
648C2×C42C2413yes—
649C2×C42C2416yes—
650C2×C42C2413yes—
651C2×C42C24112yes—
652C2×C42C2413yes—
653C2×C42C2411yescharacteristic
654C2×C42C2413yes—
655C2×C42C2416yes—
656C2×C42C2413yes—
657C2×C42C2413yes—
658C2×C42C2416yes—
659C2×C42C2411yescharacteristic
660C2×C42C2416yes—
661C2×C42C2412yes—
662C2×C42C2416yes—
663C2×C42C24112yes—
664C2×C42C2416yes—
665C2×C42C2416yes—
666#95C2411yescharacteristic
667#95C2411yescharacteristic
668#95C2416yes—
669#95C2416yes—
670#95C2416yes—
671#95C2416yes—
672#95C2413yes—
673#95C2413yes—
674#95C2413yes—
675#95C24112yes—
676#95C2413yes—
677#95C24112yes—
678#95C2413yes—
679#95C2413yes—
680#95C24112yes—
681#95C24112yes—
682#95C2412yes—
683#95C2416yes—
684#95C2416yes—
685#95C2412yes—
686#95C2416yes—
687#95C2416yes—
688#95C2416yes—
689#95C2416yes—
690#95C2416yes—
691#95C2416yes—
692C24—26no—
693C24—26no—
694C24—43no—
695C24—43no—
696C24—43no—
697C24—43no—
698C24C23×C4112yes—
699C24C2511yescharacteristic
700C24C2513yes—
701C24C2512yes—
702C24C2513yes—
703#41—232no—
704#41—296no—
705#41—2192no—
706#41—296no—
707#41—296no—
708#41C4×D4164yescomplemented
709C2×Q8—232no—
710C2×Q8—264no—
711C2×Q8—296no—
712C2×Q8—212no—
713C2×Q8—26no—
714C2×Q8—26no—
715C2×Q8—26no—
716C2×Q8—212no—
717C2×Q8—26no—
718C2×Q8C23×C4112yes—
719C2×Q8C23×C4124yes—
720C2×Q8C23×C4112yes—
721C2×Q8C23×C414yes—
722C2×Q8C22×D414yes—
723C2×Q8C2×#4114yes—
724C2×D4—212no—
725C2×D4—212no—
726C2×D4—212no—
727C2×D4—212no—
728C2×D4—296no—
729C2×D4—26no—
730C2×D4—22no—
731C2×D4—26no—
732C2×D4—22no—
733C2×D4—46no—
734C2×D4—46no—
735C2×D4—42no—
736C2×D4—42no—
737C2×D4C23×C4124yes—
738C2×D4C23×C414yes—
739C2×D4C23×C4124yes—
740C2×D4C23×C4112yes—
741C2×D4C23×C418yes—
742C2×D4C23×C4124yes—
743C2×D4C23×C4112yes—
744C2×D4C22×D4112yes—
745C2×D4C2×#41112yes—
746C22×C4—26no—
747C22×C4—212no—
748C22×C4—26no—
749C22×C4—212no—
750C22×C4—296no—
751C22×C4—26no—
752C22×C4—212no—
753C22×C4—26no—
754C22×C4—22no—
755C22×C4—26no—
756C22×C4—22no—
757C22×C4—26no—
758C22×C4—26no—
759C22×C4—26no—
760C22×C4—212no—
761C22×C4—26no—
762C22×C4—26no—
763C22×C4—212no—
764C22×C4—26no—
765C22×C4—26no—
766C22×C4—24no—
767C22×C4—26no—
768C22×C4—26no—
769C22×C4—24no—
770C22×C4—212no—
771C22×C4—212no—
772C22×C4—212no—
773C22×C4—46no—
774C22×C4—46no—
775C22×C4—46no—
776C22×C4—43no—
777C22×C4—46no—
778C22×C4—42no—
779C22×C4—43no—
780C22×C4—43no—
781C22×C4—43no—
782C22×C4—46no—
783C22×C4—46no—
784C22×C4—46no—
785C22×C4—46no—
786C22×C4—46no—
787C22×C4—46no—
788C22×C4—46no—
789C22×C4—43no—
790C22×C4—43no—
791C22×C4—46no—
792C22×C4C23×C4124yes—
793C22×C4C23×C4112yes—
794C22×C4C23×C4124yes—
795C22×C4C23×C4112yes—
796C22×C4C23×C4112yes—
797C22×C4C23×C414yes—
798C22×C4C23×C4112yes—
799C22×C4C23×C4124yes—
800C22×C4C23×C4112yes—
801C22×C4C22×D4124yes—
802C22×C4C22×D4112yes—
803C22×C4C2×#41112yes—
804C22×C4C2511yescharacteristic
805C22×C4C2513yes—
806C22×C4C2513yes—
807C22×C4C2512yes—
808C22×C4C2516yes—
809C22×C4C2511yescharacteristic
810C22×C4C2513yes—
811C22×C4C2513yes—
812C22×C4C2511yescharacteristic
813C22×C4C2512yes—
814C22×C4C2516yes—
815C22×C4C2516yes—
816C22×C4C2513yes—
817C22×C4C2516yes—
818C22×C4C2512yes—
819C22×C4C2511yescharacteristic
820C22×C4C2511yescharacteristic
821C22×C4C2513yes—
822C22×C4C2511yescharacteristic
823C4⋊C4—26no—
824C4⋊C4—22no—
825C4⋊C4—212no—
826C4⋊C4—224no—
827C4⋊C4—26no—
828C4⋊C4—212no—
829C4⋊C4—212no—
830C4⋊C4—212no—
831C4⋊C4—212no—
832C4⋊C4—26no—
833C4⋊C4—26no—
834C4⋊C4—26no—
835C4⋊C4—212no—
836C4⋊C4—412no—
837C4⋊C4—42no—
838C4⋊C4—46no—
839C4⋊C4—46no—
840C4⋊C4C23×C4112yes—
841C4⋊C4C23×C4124yes—
842C4⋊C4C23×C4124yes—
843C4⋊C4C23×C4148yes—
844C4⋊C4C23×C414yes—
845C4⋊C4C23×C4124yes—
846C4⋊C4C22×D414yes—
847C4⋊C4C22×D4112yes—
848C4⋊C4C22×D4124yes—
849C22⋊C4—212no—
850C22⋊C4—212no—
851C22⋊C4—212no—
852C22⋊C4—212no—
853C22⋊C4—24no—
854C22⋊C4—224no—
855C22⋊C4—212no—
856C22⋊C4—24no—
857C22⋊C4—22no—
858C22⋊C4—22no—
859C22⋊C4—26no—
860C22⋊C4—26no—
861C22⋊C4—24no—
862C22⋊C4—43no—
863C22⋊C4—43no—
864C22⋊C4—43no—
865C22⋊C4—43no—
866C22⋊C4—46no—
867C22⋊C4—46no—
868C22⋊C4—46no—
869C22⋊C4—42no—
870C22⋊C4—46no—
871C22⋊C4C23×C4124yes—
872C22⋊C4C23×C4148yes—
873C22⋊C4C23×C4124yes—
874C22⋊C4C23×C418yes—
875C22⋊C4C23×C4124yes—
876C22⋊C4C23×C4124yes—
877C22⋊C4C22×D4124yes—
878C42—212no—
879C42—24no—
880C42—212no—
881C42—26no—
882C42—22no—
883C42—224no—
884C42—212no—
885C42—224no—
886C42—212no—
887C42—26no—
888C42—26no—
889C42—22no—
890C42—26no—
891C42—26no—
892C42—26no—
893C42—212no—
894C42—412no—
895C42—46no—
896C42—42no—
897C42—46no—
898C42C23×C4124yes—
899C42C22×D4124yes—
900C23—23no—
901C23—23no—
902C23—23no—
903C23—23no—
904C23—21no—
905C23—22no—
906C23—23no—
907C23—21no—
908C23—22no—
909C23—23no—
910C23—21no—
911C23—21no—
912C23—23no—
913C23—23no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—23no—
918C23—23no—
919C23—22no—
920C23—21no—
921C23—21no—
922C23—224no—
923C23—412no—
924C23—412no—
925C23—86no—
926C23—86no—
927C23—86no—
928C23—86no—
929C23C24×C412yes—
930C23C24×C416yes—
931C23C24×C414yes—
932C23C24×C416yes—
933C23C23×D416yes—
934C23C22×#4116yes—
935C23C2611yescharacteristic
936Q8—224no—
937Q8—248no—
938Q8—224no—
939Q8C2×C4×D4116yes—
940D4—248no—
941D4—248no—
942D4—224no—
943D4—28no—
944D4—424no—
945D4—48no—
946D4C2×C4×D4148yes—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—23no—
950C2×C4—26no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—23no—
954C2×C4—26no—
955C2×C4—26no—
956C2×C4—26no—
957C2×C4—22no—
958C2×C4—26no—
959C2×C4—22no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—26no—
963C2×C4—22no—
964C2×C4—21no—
965C2×C4—224no—
966C2×C4—248no—
967C2×C4—28no—
968C2×C4—224no—
969C2×C4—224no—
970C2×C4—224no—
971C2×C4—248no—
972C2×C4—23no—
973C2×C4—22no—
974C2×C4—26no—
975C2×C4—23no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—23no—
979C2×C4—23no—
980C2×C4—23no—
981C2×C4—23no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—23no—
985C2×C4—22no—
986C2×C4—23no—
987C2×C4—26no—
988C2×C4—23no—
989C2×C4—23no—
990C2×C4—23no—
991C2×C4—23no—
992C2×C4—21no—
993C2×C4—22no—
994C2×C4—26no—
995C2×C4—21no—
996C2×C4—424no—
997C2×C4—424no—
998C2×C4—48no—
999C2×C4—412no—
1000C2×C4—412no—
1001C2×C4—812no—
1002C2×C4—812no—
1003C2×C4—812no—
1004C2×C4—86no—
1005C2×C4—812no—
1006C2×C4—86no—
1007C2×C4C2×C4×D4148yes—
1008C2×C4C24×C414yes—
1009C2×C4C24×C4112yes—
1010C2×C4C24×C4112yes—
1011C2×C4C24×C412yes—
1012C2×C4C24×C416yes—
1013C2×C4C24×C416yes—
1014C2×C4C24×C412yes—
1015C2×C4C23×D4112yes—
1016C2×C4C23×D414yes—
1017C2×C4C23×D416yes—
1018C2×C4C23×D412yes—
1019C2×C4C22×#4112yes—
1020C2×C4C22×#4116yes—
1021C2×C4#58512yes—
1022C2×C4#58512yes—
1023C22—26no—
1024C22—26no—
1025C22—26no—
1026C22—26no—
1027C22—26no—
1028C22—26no—
1029C22—22no—
1030C22—24no—
1031C22—26no—
1032C22—24no—
1033C22—26no—
1034C22—22no—
1035C22—22no—
1036C22—24no—
1037C22—26no—
1038C22—42no—
1039C22—43no—
1040C22—41no—
1041C22—42no—
1042C22—43no—
1043C22—41no—
1044C22—42no—
1045C22—43no—
1046C22—41no—
1047C22—42no—
1048C22—43no—
1049C22—41no—
1050C22—824no—
1051C22C22×C4×D4112yes—
1052C22C25×C411yescharacteristic
1053C22C24×D411yescharacteristic
1054C22C23×#4111yescharacteristic
1055C22C2×#58511yescharacteristic
1056C22C2×#58511yescharacteristic
1057C222−1+611yescharacteristic
1058C222−1+611yescharacteristic
1059C4—212no—
1060C4—22no—
1061C4—22no—
1062C4—24no—
1063C4—22no—
1064C4—26no—
1065C4—212no—
1066C4—212no—
1067C4—24no—
1068C4—42no—
1069C4—41no—
1070C4—43no—
1071C4—43no—
1072C4—43no—
1073C4—46no—
1074C4—43no—
1075C4—41no—
1076C4C22×C4×D414yes—
1077C4C22×C4×D4112yes—
1078C2—212no—
1079C2—44no—
1080C2—46no—
1081C2—42no—
1082C2C23×C4×D411yescharacteristic
1083C2C4×#58511yescharacteristic
1084C2#6265311yescharacteristic
1085C2#6298811yescharacteristic
1086C2#6299311yescharacteristic
1087C2#6300211yescharacteristic
1088C2#6300911yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC2×#3489C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×C4×2−1+4C2semidirect
3. C2×#3428C2semidirect
4. #34311C2semidirect
5. #34309C2semidirect
6. #34293C2semidirect
7. #34292C2semidirect
8. #34291C2semidirect
9. #34289C2semidirect
10. #34276C2semidirect
11. #34274C2semidirect
12. #34267C2semidirect
13. #34266C2semidirect
14. #34259C2semidirect
15. #34250C2semidirect
16. #34203C2semidirect
17. #34201C2semidirect
18. C4×#547C2semidirect
19. C4×#548C2semidirect
20. #34136C2semidirect
21. C2×#2362C2semidirect
22. C22⋊C4×#41C2semidirect
23. C4×#520C2semidirect
26. #3489C4semidirect
42. C2×#520C22semidirect
43. C2×#520C22semidirect
45. C2×#519C22semidirect
46. C2×#519C22semidirect
52. C2×C4×#41C22semidirect
53. C2×C4×#41C22semidirect
54. C22×C4×Q8C22semidirect
55. C22×C4×Q8C22semidirect
58. #2367C22semidirect
59. #2367C22semidirect
60. #2365C22semidirect
61. #2365C22semidirect
62. #2364C22semidirect
65. #2363C22semidirect
66. #2363C22semidirect
72. #2362C22semidirect
73. #2362C22semidirect
74. #2362C22semidirect
75. #2362C22semidirect
76. #2362C22semidirect
77. #2362C22semidirect
78. #2361C22semidirect
79. #2361C22semidirect
80. #2361C22semidirect
81. #2361C22semidirect
82. #2360C22semidirect
83. #2360C22semidirect
84. #2360C22semidirect
85. #2360C22semidirect
86. #2360C22semidirect
87. #2359C22semidirect
88. #2359C22semidirect
89. #2359C22semidirect
90. #2359C22semidirect
94. #2354C22semidirect
96. #2352C22semidirect
97. #2351C22semidirect
98. Q8×C4⋊C4C22semidirect
99. #2349C22semidirect
100. D4×C4⋊C4C22semidirect
101. #2344C22semidirect
107. Q8×C22⋊C4C22semidirect
108. Q8×C22⋊C4C22semidirect
111. #2339C22semidirect
112. #2339C22semidirect
115. #2327C22semidirect
116. #2326C22semidirect
117. #2325C22semidirect
118. #2324C22semidirect
121. #2323C22semidirect
122. #2322C22semidirect
124. #2317C22semidirect
125. #2316C22semidirect
126. #2311C22semidirect
127. #2310C22semidirect
128. C4×C4⋊Q8C22semidirect
129. C4×#124C22semidirect
130. C4×C22⋊Q8C22semidirect
131. C4×C22⋊Q8C22semidirect
132. C4×C22⋊Q8C22semidirect
133. C4×#123C22semidirect
134. C4×#123C22semidirect
135. C4×#121C22semidirect
136. C4×#121C22semidirect
139. #2297C22semidirect
140. #2296C22semidirect
141. C2×#391C22semidirect
143. C2×#389C22semidirect
145. #2290C22semidirect
148. C2×#387C22semidirect
150. #2276C22semidirect
151. #2275C22semidirect
152. #2274C22semidirect
153. #2274C22semidirect
154. C42×Q8C22semidirect
155. C42×D4C22semidirect
156. C42×D4C22semidirect
157. C4×#117C22semidirect
158. C2×C4×C4⋊C4C22semidirect
159. C2×C4×C4⋊C4C22semidirect
163. C2×2−1+4C2×C4semidirect
166. C22×#41C2×C4semidirect
178. D4×Q8C2×C4semidirect
179. #548C2×C4semidirect
180. #547C2×C4semidirect
181. #546C2×C4semidirect
182. #537C2×C4semidirect
183. #536C2×C4semidirect
186. #525C2×C4semidirect
189. C2×C22⋊Q8C2×C4semidirect
206. #520C2×C4semidirect
207. #520D4semidirect
708. #41C4×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34892
C2×C4×2−1+42
C2×#34282
#343112
#343092
#342932
#342922
#342912
#342892
#342762
#342742
#342672
#342662
#342592
#342502
#342032
#342012
C4×#5472
C4×#5482
#341362
C2×#23622
C22⋊C4×#412
C4×#5202