Finite Group Databasebeta

← #7626776

Subgroups — #7626776

Order 512.

7754 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3459C211yesmaximal, characteristic
2#34426C214yesmaximal, complemented
3#34425C214yesmaximal, complemented
4#34417C218yesmaximal, complemented
5#34416C218yesmaximal, complemented
6#34384C214yesmaximal, complemented
7#34382C212yesmaximal, complemented
8#34362C214yesmaximal, complemented
9#34360C212yesmaximal, complemented
10#34270C212yesmaximal, complemented
11#34264C214yesmaximal, complemented
12#34243C212yesmaximal, complemented
13#34241C214yesmaximal, complemented
14#34202C212yesmaximal, complemented
15#34200C214yesmaximal, complemented
16#34185C212yesmaximal, complemented
17#34181C211yesmaximal, characteristic, complemented
18C2×#2352C211yesmaximal, characteristic, complemented
19C2×D4×C4⋊C4C212yesmaximal, complemented
20C4×#534C212yesmaximal, complemented
21#3459C4132yescomplemented
22C2×#543C2211yescharacteristic
23C2×#539C2214yes—
24C2×#539C2212yes—
25C2×#538C2214yes—
26C2×#538C2212yes—
27C2×#534C2211yescharacteristic
28C2×#534C2212yes—
29C2×#529C2212yes—
30C2×#529C2214yes—
31C2×#525C2212yes—
32C2×#525C2214yes—
33C2×#520C2212yescomplemented
34C2×#518C2212yes—
35C22×C4×D4C2214yes—
36C22×C4×D4C2212yes—
37C22×C4×D4C2211yescharacteristic
38C22×#117C2211yescharacteristic, complemented
39C23×C4⋊C4C2211yescharacteristic
40C23×C4⋊C4C2212yescomplemented
41#2383C2218yescomplemented
42#2383C2218yescomplemented
43#2382C2214yescomplemented
44#2379C2214yescomplemented
45#2378C2218yescomplemented
46#2377C2218yescomplemented
47#2376C2218yescomplemented
48#2373C2218yescomplemented
49#2373C2218yescomplemented
50#2370C2214yescomplemented
51#2368C2218yescomplemented
52#2368C2218yescomplemented
53#2367C2214yescomplemented
54#2364C2218yes—
55#2364C2218yes—
56#2361C2218yes—
57#2361C2218yes—
58#2361C2218yescomplemented
59#2360C2218yescomplemented
60#2360C2218yescomplemented
61#2360C2218yescomplemented
62#2359C2218yescomplemented
63#2359C2218yescomplemented
64#2359C2218yescomplemented
65#2358C2218yescomplemented
66#2358C2218yescomplemented
67#2355C2214yescomplemented
68#2355C2212yescomplemented
69#2354C2212yescomplemented
70#2354C2214yescomplemented
71#2353C2218yescomplemented
72#2353C2218yescomplemented
73#2352C2214yescomplemented
74#2352C2214yescomplemented
75#2352C2214yescomplemented
76#2352C2214yescomplemented
77#2352C2214yescomplemented
78#2352C2218yescomplemented
79#2352C2214yescomplemented
80#2352C2214yescomplemented
81#2352C2214yescomplemented
82#2352C2214yescomplemented
83Q8×C4⋊C4C2212yescomplemented
84#2349C2218yescomplemented
85D4×C4⋊C4C2214yescomplemented
86D4×C4⋊C4C2214yescomplemented
87D4×C4⋊C4C2214yescomplemented
88D4×C4⋊C4C2214yescomplemented
89D4×C4⋊C4C2218yescomplemented
90D4×C4⋊C4C2218yescomplemented
91D4×C4⋊C4C2214yescomplemented
92D4×C4⋊C4C2214yescomplemented
93D4×C4⋊C4C2214yescomplemented
94D4×C4⋊C4C2212yescomplemented
95#2337C2218yescomplemented
96#2336C2218yescomplemented
97#2335C2218yescomplemented
98#2335C2218yescomplemented
99#2334C2218yescomplemented
100#2334C2218yescomplemented
101#2330C2218yescomplemented
102#2329C2214yescomplemented
103#2329C2214yescomplemented
104#2329C2214yescomplemented
105#2326C2218yescomplemented
106#2325C2214yes—
107#2325C2214yes—
108#2325C2214yescomplemented
109#2324C2214yescomplemented
110#2323C2214yescomplemented
111#2322C2218yescomplemented
112#2322C2218yescomplemented
113#2322C2218yescomplemented
114#2322C2218yescomplemented
115#2321C2218yescomplemented
116#2321C2218yescomplemented
117#2317C2214yescomplemented
118#2317C2212yescomplemented
119#2316C2212yescomplemented
120#2315C2212yes—
121#2315C2212yescomplemented
122#2314C2214yescomplemented
123#2314C2214yescomplemented
124#2314C2214yescomplemented
125#2313C2214yescomplemented
126#2312C2214yescomplemented
127#2311C2214yescomplemented
128#2311C2212yescomplemented
129#2308C2214yes—
130C4×C22⋊Q8C2214yescomplemented
131C4×C22⋊Q8C2214yescomplemented
132C4×#123C2218yescomplemented
133C4×#123C2218yescomplemented
134C4×#121C2214yes—
135C4×#121C2214yes—
136C4×#120C2218yescomplemented
137C4×#120C2218yescomplemented
138C2×#389C2214yescomplemented
139C2×#388C2212yescomplemented
140C2×#387C2212yescomplemented
141C2×#386C2212yes—
142C2×#385C2214yes—
143C2×#385C2214yescomplemented
144#2285C2212yescomplemented
145C2×#384C2212yescomplemented
146#2283C2214yescomplemented
147C2×#382C2211yescharacteristic, complemented
148#2280C2214yescomplemented
149C2×#380C2212yes—
150C2×#380C2211yescharacteristic
151C2×#380C2211yescharacteristic, complemented
152C2×#380C2212yescomplemented
153C2×#380C2212yescomplemented
154#2274C2214yescomplemented
155#2274C2212yescomplemented
156#2273C2214yes—
157C2×C4×C4⋊C4C2212yescomplemented
158C2×C4×C4⋊C4C2211yescharacteristic, complemented
159C2×C4×C22⋊C4C2212yes—
160C22×#41C2312yes—
161C23×D4C2312yes—
162C23×D4C2311yescharacteristic
163C24×C4C2312yes—
164C24×C4C2314yes—
165C24×C4C2311yescharacteristic
166C24×C4C2312yes—
167C24×C4C2311yescharacteristic
168#543C2×C4116yescomplemented
169#539C2×C4164yescomplemented
170#539C2×C4132yescomplemented
171#538C2×C4164yescomplemented
172#538C2×C4132yescomplemented
173#534C2×C4116yescomplemented
174#534C2×C4132yescomplemented
175#529C2×C4164yescomplemented
176#529C2×C4132yescomplemented
177C2×#126C2314yes—
178C2×#126C2314yes—
179C2×#126C2314yes—
180C2×#125C2314yes—
181C2×#125C2312yes—
182C2×#124C2314yes—
183C2×#124C2312yes—
184#525C2×C4164yescomplemented
185#525C2×C4132yescomplemented
186C2×#123C2314yes—
187C2×#123C2314yes—
188C2×#123C2314yes—
189C2×#123C2314yes—
190C2×#123C2314yes—
191C2×#123C2314yes—
192C2×C22⋊Q8C2312yes—
193C2×C22⋊Q8C2312yes—
194C2×C22⋊Q8C2312yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2314yes—
198C2×#121C2312yes—
199C2×#121C2312yes—
200C2×#121C2314yes—
201C2×#121C2314yes—
202C2×#121C2312yes—
203C2×#121C2314yes—
204C2×#120C2314yes—
205C2×#120C2314yes—
206C2×#120C2314yes—
207#520—48no—
208#518—48no—
209C2×C4×Q8C2314yes—
210C2×C4×Q8C2314yes—
211C2×C4×Q8C2312yes—
212C2×C4×D4—416no—
213C2×C4×D4C2×C4132yescomplemented
214C2×C4×D4C2×C4116yescomplemented
215C2×C4×D4C2318yes—
216C2×C4×D4C2318yes—
217C2×C4×D4C2314yes—
218C2×C4×D4C2318yes—
219C2×C4×D4C2318yes—
220C2×C4×D4C2318yes—
221C2×C4×D4C2318yes—
222C2×C4×D4C2318yes—
223C2×C4×D4C2318yes—
224C2×C4×D4C2314yes—
225C2×C4×D4C2314yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2314yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2312yes—
232C2×C4×D4C2314yes—
233C2×#117—44no—
234C2×#117C2312yes—
235C2×#117C2312yes—
236C2×#117C2314yes—
237C2×#117C2314yes—
238C2×#117C2314yes—
239C2×#117C2314yes—
240C2×#117C2312yes—
241C2×#117C2314yes—
242C22×C4⋊C4—44no—
243C22×C4⋊C4—48no—
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2314yes—
246C22×C4⋊C4C2312yes—
247C22×C4⋊C4C2314yes—
248C22×C4⋊C4C2312yes—
249C22×C4⋊C4C2312yes—
250C22×C4⋊C4C2314yes—
251C22×C4⋊C4C2318yes—
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2312yes—
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2314yes—
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2314yes—
261C22×C4⋊C4C2314yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2311yescharacteristic
264C22×C22⋊C4C2312yes—
265C22×C22⋊C4C2314yes—
266C22×C22⋊C4C2314yes—
267C22×C22⋊C4C2314yes—
268C22×C22⋊C4C2312yes—
269C22×C22⋊C4C2312yes—
270C22×C22⋊C4C2311yescharacteristic
271C22×C22⋊C4C2312yes—
272C22×C22⋊C4C2312yes—
273C22×C22⋊C4C2311yescharacteristic
274C22×C42C2312yes—
275C22×C42C2314yes—
276C22×C42C2312yes—
277C22×C42C2311yescharacteristic
278C22×C42C2312yes—
279#391C2314yes—
280#391C2318yes—
281#391C2318yes—
282#391C2314yes—
283#390C2314yes—
284#390C2318yes—
285#390C2314yes—
286#390C2318yes—
287#389C2318yes—
288#389C2318yes—
289#389C2314yes—
290#389C2318yes—
291#389C2314yes—
292#389C2318yes—
293#389C2314yes—
294#389C2314yes—
295#389C2318yes—
296#389C2318yes—
297#389C2318yes—
298#389C2318yes—
299#389C2318yes—
300#389C2318yes—
301#388C2318yes—
302#388C2318yes—
303#388C2318yes—
304#388C2318yes—
305#388C2318yes—
306#388C2318yes—
307#388C2318yes—
308#388C2318yes—
309#388C2318yes—
310#388C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#387C2318yes—
320#387C2318yes—
321#387C2318yes—
322#387C2318yes—
323#387C2318yes—
324#387C2318yes—
325#387C2318yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#386C2318yes—
338#386C2318yes—
339#386C2318yes—
340#386C2318yes—
341#386C2318yes—
342#386C2318yes—
343#386C2318yes—
344#386C2318yes—
345#386C2318yes—
346#386C2318yes—
347#386C2318yes—
348#386C2318yes—
349#385C2318yes—
350#385C2318yes—
351#385C2318yes—
352#385C2318yes—
353#385C2318yes—
354#385C2318yes—
355#385C2318yes—
356#385C2318yes—
357#385C2318yes—
358#385C2318yes—
359#385C2318yes—
360#385C2318yes—
361#385C2318yes—
362#385C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2318yes—
367#384C2312yes—
368#384C2314yes—
369#384C2314yes—
370#384C2312yes—
371#384C2318yes—
372#383C2318yes—
373#382C2314yes—
374#382C2314yes—
375#382C2314yes—
376#382C2314yes—
377#382C2314yes—
378#381C2318yes—
379#381C2318yes—
380#380C2314yes—
381#380C2314yes—
382#380C2314yes—
383#380C2314yes—
384#380C2314yes—
385#380C2314yes—
386#380C2314yes—
387#380C2314yes—
388#380C2314yes—
389#380C2314yes—
390#380C2314yes—
391#380C2314yes—
392#380C2314yes—
393#380C2318yes—
394#380C2314yes—
395#380C2314yes—
396#380C2314yes—
397#379C2318yes—
398C4×C4⋊C4C2314yes—
399C4×C4⋊C4C2312yes—
400C4×C4⋊C4C2314yes—
401C4×C4⋊C4C2314yes—
402C4×C4⋊C4C2314yes—
403C4×C4⋊C4C2314yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2318yes—
406C4×C4⋊C4C2318yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2318yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2318yes—
412C4×C4⋊C4C2318yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2312yes—
415C4×C4⋊C4C2314yes—
416C4×C22⋊C4C2318yes—
417C4×C22⋊C4C2318yes—
418C4×C22⋊C4C2318yes—
419C4×C22⋊C4C2318yes—
420C4×C22⋊C4C2318yes—
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2318yes—
423C4×C22⋊C4C2318yes—
424C4×C22⋊C4C2318yes—
425C4×C22⋊C4C2318yes—
426C4×C22⋊C4C2318yes—
427C4×C22⋊C4C2318yes—
428C4×C22⋊C4C2318yes—
429C4×C22⋊C4C2318yes—
430C4×C22⋊C4C2318yes—
431#376C2318yes—
432C2×#95C2312yes—
433C2×#95C2312yes—
434C2×#95C2314yes—
435C2×#95C2314yes—
436C2×#95C2312yes—
437C2×#95C2312yes—
438C2×#95C2312yes—
439C2×#95C2314yes—
440C2×#95C2314yes—
441C25C2411yescharacteristic
442C25C2412yes—
443C25C2411yescharacteristic
444C2×#41—44no—
445C2×#41—44no—
446C2×#41C22×C4116yescomplemented
447C22×Q8C2412yes—
448C22×Q8C2412yes—
449C22×D4—28no—
450C22×D4—24no—
451C22×D4—28no—
452C22×D4—24no—
453C22×D4C22×C4116yes—
454C22×D4C22×C418yes—
455C22×D4C2414yes—
456C22×D4C2414yes—
457C22×D4C2414yes—
458C22×D4C2412yes—
459C22×D4C2414yes—
460C22×D4C2412yes—
461C22×D4C2414yes—
462C23×C4—28no—
463C23×C4—42no—
464C23×C4—44no—
465C23×C4—42no—
466C23×C4—42no—
467C23×C4—42no—
468C23×C4—44no—
469C23×C4—44no—
470C23×C4—48no—
471C23×C4—48no—
472C23×C4—82no—
473C23×C4—84no—
474C23×C4C22×C418yes—
475C23×C4C22×C4116yescomplemented
476C23×C4C22×C418yescomplemented
477C23×C4C2412yes—
478C23×C4C2414yes—
479C23×C4C2412yes—
480C23×C4C2411yescharacteristic
481C23×C4C2412yes—
482C23×C4C2414yes—
483C23×C4C2412yes—
484C23×C4C2411yescharacteristic
485C23×C4C2414yes—
486C23×C4C2412yes—
487C23×C4C2412yes—
488C23×C4C2414yes—
489C23×C4C2414yes—
490C23×C4C2412yes—
491C23×C4C2418yes—
492C23×C4C2414yes—
493C23×C4C2414yes—
494C23×C4C2418yes—
495C23×C4C2412yes—
496C23×C4C2411yescharacteristic
497C23×C4C2412yes—
498C23×C4C2411yescharacteristic
499C23×C4C2412yes—
500C23×C4C2411yescharacteristic
501C23×C4C2414yes—
502C23×C4C2412yes—
503#126C22×C4132yescomplemented
504#126C22×C4132yescomplemented
505#126C22×C4132yescomplemented
506#125C22×C4132yescomplemented
507#125C22×C4116yescomplemented
508#124C22×C4132yescomplemented
509#124C22×C4116yescomplemented
510#123C22×C4132yes—
511#123C22×C4132yescomplemented
512#123C22×C4132yescomplemented
513#123C22×C4132yescomplemented
514#123C22×C4132yescomplemented
515#123C22×C4132yescomplemented
516C22⋊Q8C22×C4132yescomplemented
517C22⋊Q8C22×C4116yescomplemented
518C22⋊Q8C22×C4132yescomplemented
519C22⋊Q8C22×C4116yescomplemented
520C22⋊Q8C22×C4132yescomplemented
521C22⋊Q8C22×C4116yescomplemented
522#121C22×C4116yes—
523#121C22×C4132yes—
524#121C22×C4116yes—
525#121C22×C4132yes—
526#121C22×C4116yescomplemented
527#121C22×C4132yescomplemented
528#120C22×C4132yes—
529#120C22×C4132yescomplemented
530#120C22×C4132yescomplemented
531C4×Q8—48no—
532C4×Q8—84no—
533C4×Q8C22×C4116yescomplemented
534C4×D4—48no—
535C4×D4—416no—
536C4×D4—416no—
537C4×D4—416no—
538C4×D4—416no—
539C4×D4—416no—
540C4×D4—416no—
541C4×D4—416no—
542C4×D4—84no—
543C4×D4—88no—
544C4×D4C22×C4132yes—
545C4×D4C22×C4132yes—
546C4×D4C22×C4132yescomplemented
547C4×D4C22×C4132yescomplemented
548C4×D4C22×C4132yescomplemented
549C4×D4C22×C4132yescomplemented
550C4×D4C22×C4132yescomplemented
551C4×D4C22×C4116yescomplemented
552#117—28no—
553#117—48no—
554#117—48no—
555#117—44no—
556#117—48no—
557#117—48no—
558#117C22×C4116yescomplemented
559#117C22×C4132yescomplemented
560C2×C4⋊C4—28no—
561C2×C4⋊C4—24no—
562C2×C4⋊C4—216no—
563C2×C4⋊C4—42no—
564C2×C4⋊C4—44no—
565C2×C4⋊C4—48no—
566C2×C4⋊C4—44no—
567C2×C4⋊C4—48no—
568C2×C4⋊C4—416no—
569C2×C4⋊C4—44no—
570C2×C4⋊C4—48no—
571C2×C4⋊C4—44no—
572C2×C4⋊C4—44no—
573C2×C4⋊C4—42no—
574C2×C4⋊C4—42no—
575C2×C4⋊C4—44no—
576C2×C4⋊C4—48no—
577C2×C4⋊C4—84no—
578C2×C4⋊C4C22×C4116yescomplemented
579C2×C4⋊C4C22×C418yescomplemented
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2411yescharacteristic
618C2×C22⋊C4—216no—
619C2×C22⋊C4—28no—
620C2×C22⋊C4—44no—
621C2×C22⋊C4—48no—
622C2×C22⋊C4—48no—
623C2×C22⋊C4—82no—
624C2×C22⋊C4C22×C4116yes—
625C2×C22⋊C4C22×C418yes—
626C2×C22⋊C4C22×C4116yescomplemented
627C2×C22⋊C4C22×C418yescomplemented
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C42—44no—
654C2×C42—48no—
655C2×C42—82no—
656C2×C42C22×C4116yescomplemented
657C2×C42C22×C418yescomplemented
658C2×C42C2414yes—
659C2×C42C2414yes—
660C2×C42C2418yes—
661C2×C42C2418yes—
662C2×C42C2418yes—
663C2×C42C2418yes—
664C2×C42C2418yes—
665C2×C42C2418yes—
666C2×C42C2414yes—
667C2×C42C2414yes—
668C2×C42C2418yes—
669C2×C42C2414yes—
670C2×C42C2412yes—
671C2×C42C2414yes—
672C2×C42C2412yes—
673#95C2418yes—
674#95C2418yes—
675#95C2418yes—
676#95C2418yes—
677#95C2414yes—
678#95C2418yes—
679#95C2418yes—
680#95C2418yes—
681#95C2418yes—
682#95C2418yes—
683#95C2418yes—
684#95C2418yes—
685#95C2414yes—
686#95C2418yes—
687#95C2418yes—
688#95C2418yes—
689#95C2418yes—
690#95C2418yes—
691#95C2418yes—
692#95C2418yes—
693#95C2418yes—
694#95C2418yes—
695C24—24no—
696C24—24no—
697C24—22no—
698C24—22no—
699C24—41no—
700C24—42no—
701C24—41no—
702C24—42no—
703C24—41no—
704C24—42no—
705C24—41no—
706C24—42no—
707C24—41no—
708C24—41no—
709C24—41no—
710C24—41no—
711C24C23×C418yes—
712C24C23×C414yes—
713C24C23×C414yes—
714C24H(5,𝔽2)14yes—
715C242−1+414yes—
716C24C2512yes—
717C24C2514yes—
718C24C2511yescharacteristic
719C24C2512yes—
720#41—432no—
721C2×Q8—42no—
722C2×Q8—42no—
723C2×Q8—42no—
724C2×Q8—42no—
725C2×Q8C23×C418yes—
726C2×Q8C23×C418yes—
727C2×D4—264no—
728C2×D4—232no—
729C2×D4—28no—
730C2×D4—28no—
731C2×D4—28no—
732C2×D4—28no—
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—42no—
736C2×D4—44no—
737C2×D4—42no—
738C2×D4—44no—
739C2×D4—44no—
740C2×D4—42no—
741C2×D4—44no—
742C2×D4—42no—
743C2×D4C23×C4116yes—
744C2×D4C23×C4116yes—
745C2×D4C23×C4116yes—
746C2×D4C23×C418yes—
747C2×D4C23×C4116yes—
748C2×D4C23×C418yes—
749C2×D4C23×C4116yes—
750C22×C4—24no—
751C22×C4—22no—
752C22×C4—24no—
753C22×C4—22no—
754C22×C4—24no—
755C22×C4—22no—
756C22×C4—28no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—22no—
760C22×C4—24no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—24no—
764C22×C4—28no—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—24no—
771C22×C4—28no—
772C22×C4—216no—
773C22×C4—416no—
774C22×C4—432no—
775C22×C4—416no—
776C22×C4—41no—
777C22×C4—41no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—44no—
781C22×C4—41no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—44no—
787C22×C4—42no—
788C22×C4—41no—
789C22×C4—42no—
790C22×C4—41no—
791C22×C4—44no—
792C22×C4—42no—
793C22×C4—41no—
794C22×C4—42no—
795C22×C4—42no—
796C22×C4—42no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—48no—
800C22×C4—42no—
801C22×C4—42no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—44no—
805C22×C4—48no—
806C22×C4—48no—
807C22×C4—48no—
808C22×C4—48no—
809C22×C4—42no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—816no—
818C22×C4—832no—
819C22×C4C23×C418yes—
820C22×C4C23×C414yes—
821C22×C4C23×C418yes—
822C22×C4C23×C414yes—
823C22×C4C23×C4116yes—
824C22×C4C23×C418yes—
825C22×C4C23×C418yes—
826C22×C4C23×C414yes—
827C22×C4C23×C418yes—
828C22×C4C23×C414yes—
829C22×C4C23×C418yes—
830C22×C4C23×C414yes—
831C22×C4C23×C4116yes—
832C22×C4C23×C418yes—
833C22×C4C2514yes—
834C22×C4C2514yes—
835C22×C4C2518yes—
836C22×C4C2514yes—
837C22×C4C2518yes—
838C22×C4C2512yes—
839C22×C4C2512yes—
840C22×C4C2514yes—
841C22×C4C2512yes—
842C22×C4C2514yes—
843C22×C4C2512yes—
844C22×C4C2514yes—
845C22×C4C2511yescharacteristic
846C22×C4C2512yes—
847C22×C4C2512yes—
848C22×C4C2511yescharacteristic
849C4⋊C4—28no—
850C4⋊C4—24no—
851C4⋊C4—28no—
852C4⋊C4—24no—
853C4⋊C4—22no—
854C4⋊C4—216no—
855C4⋊C4—24no—
856C4⋊C4—28no—
857C4⋊C4—24no—
858C4⋊C4—48no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—42no—
862C4⋊C4—42no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—42no—
866C4⋊C4—48no—
867C4⋊C4—48no—
868C4⋊C4—44no—
869C4⋊C4—48no—
870C4⋊C4—48no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C4⋊C4C23×C4116yes—
876C4⋊C4C23×C4116yes—
877C4⋊C4C23×C4116yes—
878C4⋊C4C23×C418yes—
879C4⋊C4C23×C4116yes—
880C4⋊C4C23×C418yes—
881C4⋊C4C23×C4116yes—
882C4⋊C4C23×C4116yes—
883C4⋊C4C23×C418yes—
884C4⋊C4C23×C418yes—
885C4⋊C4C23×C4116yes—
886C4⋊C4H(5,𝔽2)14yes—
887C22⋊C4—216no—
888C22⋊C4—216no—
889C22⋊C4—216no—
890C22⋊C4—28no—
891C22⋊C4—44no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—48no—
897C22⋊C4—48no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4C23×C4116yes—
901C22⋊C4C23×C4116yes—
902C22⋊C4C23×C4116yes—
903C22⋊C4C23×C4116yes—
904C22⋊C4C23×C4116yes—
905C22⋊C4C23×C4116yes—
906C22⋊C4C23×C4116yes—
907C22⋊C4C23×C4116yes—
908C22⋊C4C23×C4116yes—
909C22⋊C4C23×C4116yes—
910C22⋊C4C23×C4116yes—
911C22⋊C4C23×C4116yes—
912C42—28no—
913C42—44no—
914C42—48no—
915C42—48no—
916C42—44no—
917C42—44no—
918C42—48no—
919C42—48no—
920C42—48no—
921C42—48no—
922C42—48no—
923C42C23×C4116yes—
924C42C23×C418yes—
925C42C23×C4116yes—
926C42C23×C418yes—
927C23—22no—
928C23—21no—
929C23—22no—
930C23—21no—
931C23—22no—
932C23—21no—
933C23—21no—
934C23—22no—
935C23—22no—
936C23—24no—
937C23—22no—
938C23—24no—
939C23—24no—
940C23—22no—
941C23—24no—
942C23—22no—
943C23—22no—
944C23—24no—
945C23—24no—
946C23—22no—
947C23—216no—
948C23—28no—
949C23—44no—
950C23—48no—
951C23—44no—
952C23—44no—
953C23—48no—
954C23—44no—
955C23—44no—
956C23—44no—
957C23—44no—
958C23—44no—
959C23—48no—
960C23—48no—
961C23—48no—
962C23—48no—
963C23—82no—
964C23—82no—
965C23—82no—
966C23—82no—
967C23#520116yescomplemented
968C23C24×C418yes—
969C23C24×C414yes—
970C23C24×C414yes—
971C23C24×C412yes—
972C23C2×H(5,𝔽2)12yes—
973C23C2×H(5,𝔽2)14yes—
974C23C2×2−1+414yes—
975C23C2×2−1+412yes—
976C23C2611yescharacteristic
977Q8—48no—
978Q8—48no—
979D4—232no—
980D4—232no—
981D4—232no—
982D4—48no—
983D4—416no—
984D4—48no—
985D4—416no—
986C2×C4—22no—
987C2×C4—24no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—24no—
991C2×C4—22no—
992C2×C4—21no—
993C2×C4—24no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—21no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—22no—
1004C2×C4—216no—
1005C2×C4—28no—
1006C2×C4—216no—
1007C2×C4—28no—
1008C2×C4—232no—
1009C2×C4—216no—
1010C2×C4—24no—
1011C2×C4—28no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—28no—
1015C2×C4—28no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—28no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—28no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—28no—
1028C2×C4—48no—
1029C2×C4—44no—
1030C2×C4—416no—
1031C2×C4—48no—
1032C2×C4—44no—
1033C2×C4—48no—
1034C2×C4—44no—
1035C2×C4—48no—
1036C2×C4—48no—
1037C2×C4—416no—
1038C2×C4—816no—
1039C2×C4—84no—
1040C2×C4—88no—
1041C2×C4—84no—
1042C2×C4—88no—
1043C2×C4—84no—
1044C2×C4—88no—
1045C2×C4—816no—
1046C2×C4—164no—
1047C2×C4—164no—
1048C2×C4C24×C418yes—
1049C2×C4C24×C414yes—
1050C2×C4C24×C418yes—
1051C2×C4C24×C414yes—
1052C2×C4C24×C414yes—
1053C2×C4C24×C412yes—
1054C2×C4C24×C418yes—
1055C2×C4C24×C414yes—
1056C2×C4C24×C412yes—
1057C2×C4C2×H(5,𝔽2)14yes—
1058C2×C4C2×H(5,𝔽2)12yes—
1059C2×C4#58512yes—
1060C22—24no—
1061C22—22no—
1062C22—22no—
1063C22—24no—
1064C22—24no—
1065C22—22no—
1066C22—22no—
1067C22—24no—
1068C22—24no—
1069C22—22no—
1070C22—24no—
1071C22—22no—
1072C22—28no—
1073C22—24no—
1074C22—28no—
1075C22—24no—
1076C22—28no—
1077C22—24no—
1078C22—416no—
1079C22—432no—
1080C22—44no—
1081C22—42no—
1082C22—44no—
1083C22—42no—
1084C22—42no—
1085C22—44no—
1086C22—44no—
1087C22—42no—
1088C22—88no—
1089C22C2×#52018yes—
1090C22C2×#52014yes—
1091C22C25×C411yescharacteristic
1092C22C22×H(5,𝔽2)11yescharacteristic
1093C22C22×H(5,𝔽2)11yescharacteristic
1094C22C22×2−1+411yescharacteristic
1095C22C2×#58511yescharacteristic
1096C22H(7,𝔽2)11yescharacteristic
1097C222−1+611yescharacteristic
1098C4—24no—
1099C4—28no—
1100C4—24no—
1101C4—24no—
1102C4—22no—
1103C4—24no—
1104C4—28no—
1105C4—24no—
1106C4—28no—
1107C4—42no—
1108C4—44no—
1109C4—48no—
1110C4—44no—
1111C4—48no—
1112C4—44no—
1113C4C4×H(5,𝔽2)14yes—
1114C2—28no—
1115C2—24no—
1116C2—48no—
1117C2—44no—
1118C2C22×#52011yescharacteristic
1119C2C2×C4×H(5,𝔽2)11yescharacteristic
1120C2#6265411yescharacteristic
1121C2#6289211yescharacteristic
1122C2#6289311yescharacteristic
1123C2#6290111yescharacteristic
1124C2#6290211yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC2×#3459C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34426C2semidirect
3. #34425C2semidirect
4. #34417C2semidirect
5. #34416C2semidirect
6. #34384C2semidirect
7. #34382C2semidirect
8. #34362C2semidirect
9. #34360C2semidirect
10. #34270C2semidirect
11. #34264C2semidirect
12. #34243C2semidirect
13. #34241C2semidirect
14. #34202C2semidirect
15. #34200C2semidirect
16. #34185C2semidirect
17. #34181C2semidirect
18. C2×#2352C2semidirect
19. C2×D4×C4⋊C4C2semidirect
20. C4×#534C2semidirect
21. #3459C4semidirect
33. C2×#520C22semidirect
38. C22×#117C22semidirect
40. C23×C4⋊C4C22semidirect
41. #2383C22semidirect
42. #2383C22semidirect
43. #2382C22semidirect
44. #2379C22semidirect
45. #2378C22semidirect
46. #2377C22semidirect
47. #2376C22semidirect
48. #2373C22semidirect
49. #2373C22semidirect
50. #2370C22semidirect
51. #2368C22semidirect
52. #2368C22semidirect
53. #2367C22semidirect
58. #2361C22semidirect
59. #2360C22semidirect
60. #2360C22semidirect
61. #2360C22semidirect
62. #2359C22semidirect
63. #2359C22semidirect
64. #2359C22semidirect
65. #2358C22semidirect
66. #2358C22semidirect
67. #2355C22semidirect
68. #2355C22semidirect
69. #2354C22semidirect
70. #2354C22semidirect
71. #2353C22semidirect
72. #2353C22semidirect
73. #2352C22semidirect
74. #2352C22semidirect
75. #2352C22semidirect
76. #2352C22semidirect
77. #2352C22semidirect
78. #2352C22semidirect
79. #2352C22semidirect
80. #2352C22semidirect
81. #2352C22semidirect
82. #2352C22semidirect
83. Q8×C4⋊C4C22semidirect
84. #2349C22semidirect
85. D4×C4⋊C4C22semidirect
86. D4×C4⋊C4C22semidirect
87. D4×C4⋊C4C22semidirect
88. D4×C4⋊C4C22semidirect
89. D4×C4⋊C4C22semidirect
90. D4×C4⋊C4C22semidirect
91. D4×C4⋊C4C22semidirect
92. D4×C4⋊C4C22semidirect
93. D4×C4⋊C4C22semidirect
94. D4×C4⋊C4C22semidirect
95. #2337C22semidirect
96. #2336C22semidirect
97. #2335C22semidirect
98. #2335C22semidirect
99. #2334C22semidirect
100. #2334C22semidirect
101. #2330C22semidirect
102. #2329C22semidirect
103. #2329C22semidirect
104. #2329C22semidirect
105. #2326C22semidirect
108. #2325C22semidirect
109. #2324C22semidirect
110. #2323C22semidirect
111. #2322C22semidirect
112. #2322C22semidirect
113. #2322C22semidirect
114. #2322C22semidirect
115. #2321C22semidirect
116. #2321C22semidirect
117. #2317C22semidirect
118. #2317C22semidirect
119. #2316C22semidirect
121. #2315C22semidirect
122. #2314C22semidirect
123. #2314C22semidirect
124. #2314C22semidirect
125. #2313C22semidirect
126. #2312C22semidirect
127. #2311C22semidirect
128. #2311C22semidirect
130. C4×C22⋊Q8C22semidirect
131. C4×C22⋊Q8C22semidirect
132. C4×#123C22semidirect
133. C4×#123C22semidirect
136. C4×#120C22semidirect
137. C4×#120C22semidirect
138. C2×#389C22semidirect
139. C2×#388C22semidirect
140. C2×#387C22semidirect
143. C2×#385C22semidirect
144. #2285C22semidirect
145. C2×#384C22semidirect
146. #2283C22semidirect
147. C2×#382C22semidirect
148. #2280C22semidirect
151. C2×#380C22semidirect
152. C2×#380C22semidirect
153. C2×#380C22semidirect
154. #2274C22semidirect
155. #2274C22semidirect
157. C2×C4×C4⋊C4C22semidirect
158. C2×C4×C4⋊C4C22semidirect
168. #543C2×C4semidirect
169. #539C2×C4semidirect
170. #539C2×C4semidirect
171. #538C2×C4semidirect
172. #538C2×C4semidirect
173. #534C2×C4semidirect
174. #534C2×C4semidirect
175. #529C2×C4semidirect
176. #529C2×C4semidirect
184. #525C2×C4semidirect
185. #525C2×C4semidirect
213. C2×C4×D4C2×C4semidirect
214. C2×C4×D4C2×C4semidirect
446. C2×#41C22×C4semidirect
475. C23×C4C22×C4semidirect
476. C23×C4C22×C4semidirect
503. #126C22×C4semidirect
504. #126C22×C4semidirect
505. #126C22×C4semidirect
506. #125C22×C4semidirect
507. #125C22×C4semidirect
508. #124C22×C4semidirect
509. #124C22×C4semidirect
511. #123C22×C4semidirect
512. #123C22×C4semidirect
513. #123C22×C4semidirect
514. #123C22×C4semidirect
515. #123C22×C4semidirect
516. C22⋊Q8C22×C4semidirect
517. C22⋊Q8C22×C4semidirect
518. C22⋊Q8C22×C4semidirect
519. C22⋊Q8C22×C4semidirect
520. C22⋊Q8C22×C4semidirect
521. C22⋊Q8C22×C4semidirect
526. #121C22×C4semidirect
527. #121C22×C4semidirect
529. #120C22×C4semidirect
530. #120C22×C4semidirect
533. C4×Q8C22×C4semidirect
546. C4×D4C22×C4semidirect
547. C4×D4C22×C4semidirect
548. C4×D4C22×C4semidirect
549. C4×D4C22×C4semidirect
550. C4×D4C22×C4semidirect
551. C4×D4C22×C4semidirect
558. #117C22×C4semidirect
559. #117C22×C4semidirect
578. C2×C4⋊C4C22×C4semidirect
579. C2×C4⋊C4C22×C4semidirect
626. C2×C22⋊C4C22×C4semidirect
627. C2×C22⋊C4C22×C4semidirect
656. C2×C42C22×C4semidirect
657. C2×C42C22×C4semidirect
967. C23#520semidirect

Maximal subgroups

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

subgroupindex
C2×#34592
#344262
#344252
#344172
#344162
#343842
#343822
#343622
#343602
#342702
#342642
#342432
#342412
#342022
#342002
#341852
#341812
C2×#23522
C2×D4×C4⋊C42
C4×#5342