Finite Group Databasebeta

← #7674837

Subgroups — #7674837

Order 512.

7394 conjugacy classes of subgroups.

The subgroup lattice has 1086 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3501C212yesmaximal, complemented
2#59113C214yesmaximal, complemented
3#59096C214yesmaximal, complemented
4#59016C214yesmaximal, complemented
5#58998C214yesmaximal, complemented
6#43909C218yesmaximal, complemented
7#43025C218yesmaximal, complemented
8#39615C212yesmaximal, complemented
9#39614C214yesmaximal, complemented
10#39614C212yesmaximal, complemented
11#39610C214yesmaximal, complemented
12#36561C212yesmaximal, complemented
13Q8×#121C212yesmaximal, complemented
14#35359C214yesmaximal, complemented
15#35011C211yesmaximal, characteristic, complemented
16#35002C212yesmaximal, complemented
17C2×#2417C212yesmaximal, complemented
18#34273C212yesmaximal
19C2×#2360C211yesmaximal, characteristic, complemented
20C4×#534C211yesmaximal, characteristic
21#3501—232no—
22C2×#554C2218yes—
23C2×#554C2214yes—
24C2×#554C2218yescomplemented
25C2×#554C2214yescomplemented
26C2×D4×Q8C2214yes—
27C2×D4×Q8C2214yescomplemented
28C2×D4×Q8C2212yescomplemented
29C2×#544C2214yescomplemented
30C2×#543C2214yes—
31C2×#543C2214yescomplemented
32C2×#534C2211yescharacteristic
33C2×#533C2214yescomplemented
34C22×C22⋊Q8C2212yes—
35C22×C22⋊Q8C2211yescharacteristic
36C22×C22⋊Q8C2214yescomplemented
37C22×C22⋊Q8C2212yescomplemented
38C2×#518C2214yes—
39C22×C4×Q8C2211yescharacteristic, complemented
40C22×C4×D4C2212yes—
41C23×C4⋊C4C2211yescharacteristic
42#2857C2214yescomplemented
43#2857C2214yescomplemented
44#2857C2212yescomplemented
45#2857C2212yescomplemented
46#2734C2214yescomplemented
47#2732C2214yescomplemented
48#2729C2218yescomplemented
49#2726C2214yescomplemented
50#2726C2218yescomplemented
51#2720C2218yescomplemented
52#2713C2218yescomplemented
53#2704C2218yescomplemented
54#2704C2218yescomplemented
55#2704C2218yescomplemented
56#2692C2218yescomplemented
57#2683C2214yescomplemented
58#2683C2218yescomplemented
59#2677C2218yescomplemented
60#2659C2214yescomplemented
61#2659C2214yescomplemented
62#2659C2212yescomplemented
63#2659C2212yescomplemented
64#2583C2218yescomplemented
65#2564C2218yescomplemented
66#2564C2218yescomplemented
67#2556C2218yescomplemented
68#2551C2212yescomplemented
69#2549C2218yescomplemented
70#2549C2218yescomplemented
71#2546C2214yescomplemented
72#2546C2212yescomplemented
73#2542C2212yescomplemented
74#2538C2214yescomplemented
75#2538C2212yescomplemented
76#2506C2214yescomplemented
77#2502C2214yescomplemented
78#2492C2214yescomplemented
79#2473C2218yescomplemented
80#2465C2218yescomplemented
81#2462C2218yescomplemented
82#2452C2214yescomplemented
83#2451C2218yescomplemented
84#2451C2214yescomplemented
85#2450C2218yes—
86#2450C2218yes—
87#2449C2218yes—
88#2449C2218yes—
89#2449C2218yescomplemented
90#2446C2214yescomplemented
91#2440C2218yescomplemented
92#2440C2218yescomplemented
93#2440C2218yescomplemented
94#2440C2214yescomplemented
95#2438C2218yescomplemented
96#2438C2218yescomplemented
97#2437C2218yescomplemented
98#2437C2218yescomplemented
99#2434C2214yescomplemented
100#2434C2214yescomplemented
101#2429C2218yescomplemented
102#2429C2218yescomplemented
103#2429C2214yescomplemented
104#2429C2214yescomplemented
105#2423C2214yescomplemented
106#2417C2218yes—
107#2417C2214yes—
108#2417C2214yes—
109#2417C2218yescomplemented
110#2417C2218yescomplemented
111#2417C2218yescomplemented
112#2417C2214yescomplemented
113#2417C2218yescomplemented
114#2417C2214yescomplemented
115#2417C2214yescomplemented
116#2409C2214yescomplemented
117C2×#398C2214yescomplemented
118C2×#396C2214yescomplemented
119#2365C2212yescomplemented
120#2360C2218yescomplemented
121#2360C2214yescomplemented
122#2360C2214yescomplemented
123#2360C2214yescomplemented
124#2359C2218yes—
125#2359C2218yes—
126#2358C2218yes—
127#2358C2218yes—
128Q8×C4⋊C4C2212yescomplemented
129D4×C4⋊C4C2212yescomplemented
130Q8×C22⋊C4C2214yescomplemented
131#2325C2212yes—
132#2325C2212yes—
133#2325C2214yes—
134#2325C2214yes—
135#2322C2214yes—
136#2321C2214yes—
137#2315C2212yes—
138#2315C2211yescharacteristic
139#2315C2212yes—
140#2308C2212yes—
141C4×#123C2214yes—
142C4×#121C2212yes—
143C4×#121C2212yes—
144C4×#121C2214yes—
145C4×#121C2214yes—
146C4×#120C2214yes—
147C2×#391C2211yescharacteristic, complemented
148C2×#391C2212yescomplemented
149C2×#389C2212yescomplemented
150C2×#389C2211yescharacteristic, complemented
151C2×#389C2212yescomplemented
152C2×#387C2212yescomplemented
153C2×#386C2214yes—
154C2×#385C2212yes—
155C2×#380C2214yes—
156C2×#380C2212yescomplemented
157C2×C4×C4⋊C4C2211yescharacteristic, complemented
158C2×C4×C22⋊C4C2211yescharacteristic
159C2×C4×C22⋊C4C2212yes—
160C23×Q8C2314yes—
161C23×Q8C2312yes—
162C23×Q8C2311yescharacteristic
163C23×D4C2312yes—
164C24×C4C2312yes—
165C24×C4C2312yes—
166C24×C4C2311yescharacteristic
167#554—232no—
168#554—264no—
169#554—232no—
170#554—264no—
171D4×Q8—232no—
172D4×Q8—232no—
173D4×Q8—48no—
174#544—232no—
175#543—232no—
176#543—232no—
177#534Q8116yescomplemented
178#533—232no—
179C2×C4⋊Q8C2314yes—
180C2×C4⋊Q8C2314yes—
181C2×C4⋊Q8C2318yes—
182C2×C4⋊Q8C2318yes—
183C2×C4⋊Q8C2312yes—
184C2×C4⋊Q8C2314yes—
185C2×C4⋊Q8C2312yes—
186C2×C4⋊Q8C2314yes—
187C2×#125C2318yes—
188C2×#125C2318yes—
189C2×#125C2318yes—
190C2×#123C2314yes—
191C2×C22⋊Q8—216no—
192C2×C22⋊Q8—232no—
193C2×C22⋊Q8—48no—
194C2×C22⋊Q8D4116yescomplemented
195C2×C22⋊Q8C2318yes—
196C2×C22⋊Q8C2318yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2314yes—
199C2×C22⋊Q8C2314yes—
200C2×C22⋊Q8C2314yes—
201C2×C22⋊Q8C2314yes—
202C2×C22⋊Q8C2314yes—
203C2×C22⋊Q8C2314yes—
204C2×C22⋊Q8C2318yes—
205C2×C22⋊Q8C2318yes—
206C2×C22⋊Q8C2318yes—
207C2×C22⋊Q8C2318yes—
208C2×C22⋊Q8C2318yes—
209C2×C22⋊Q8C2318yes—
210C2×C22⋊Q8C2318yes—
211C2×C22⋊Q8C2318yes—
212C2×C22⋊Q8C2318yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2318yes—
215C2×C22⋊Q8C2318yes—
216C2×C22⋊Q8C2318yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2314yes—
219C2×#121C2312yes—
220C2×#121C2312yes—
221C2×#120C2314yes—
222#518—232no—
223C2×C4×Q8—44no—
224C2×C4×Q8C2314yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2318yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2314yes—
230C2×C4×D4—216no—
231C2×C4×D4C2318yes—
232C2×C4×D4C2318yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2318yes—
236C2×C4×D4C2318yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2314yes—
243C2×#117C2318yes—
244C22×C4⋊C4—44no—
245C22×C4⋊C4C2312yes—
246C22×C4⋊C4C2314yes—
247C22×C4⋊C4C2314yes—
248C22×C4⋊C4C2312yes—
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2318yes—
252C22×C4⋊C4C2314yes—
253C22×C4⋊C4C2312yes—
254C22×C4⋊C4C2314yes—
255C22×C4⋊C4C2312yes—
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2314yes—
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2312yes—
262C22×C22⋊C4C2311yescharacteristic
263C22×C22⋊C4C2312yes—
264C22×C22⋊C4C2314yes—
265C22×C22⋊C4C2312yes—
266C22×C22⋊C4C2318yes—
267C22×C22⋊C4C2314yes—
268C22×C22⋊C4C2314yes—
269C22×C22⋊C4C2312yes—
270C22×C22⋊C4C2311yescharacteristic
271C22×C42C2312yes—
272C22×C42C2312yes—
273C22×C42C2311yescharacteristic
274C22×C42C2311yescharacteristic
275C22×C42C2312yes—
276#400C2318yes—
277#400C2318yes—
278#399C2318yes—
279#399C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#396C2318yes—
295#396C2318yes—
296#396C2318yes—
297#396C2318yes—
298#396C2318yes—
299#396C2318yes—
300#396C2318yes—
301#396C2318yes—
302#395C2318yes—
303#395C2318yes—
304#395C2318yes—
305#395C2318yes—
306#395C2318yes—
307#395C2318yes—
308#395C2318yes—
309#395C2318yes—
310#393C2318yes—
311#393C2318yes—
312#391C2314yes—
313#391C2318yes—
314#391C2314yes—
315#391C2318yes—
316#391C2314yes—
317#391C2318yes—
318#391C2314yes—
319#391C2314yes—
320#391C2314yes—
321#391C2318yes—
322#391C2318yes—
323#390C2312yes—
324#390C2312yes—
325#390C2314yes—
326#390C2314yes—
327#389C2312yes—
328#389C2312yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2314yes—
334#389C2318yes—
335#389C2314yes—
336#389C2318yes—
337#389C2314yes—
338#389C2314yes—
339#389C2314yes—
340#389C2318yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2318yes—
345#389C2318yes—
346#389C2314yes—
347#389C2314yes—
348#389C2318yes—
349#389C2318yes—
350#388C2314yes—
351#388C2314yes—
352#388C2314yes—
353#388C2314yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2314yes—
363#387C2314yes—
364#387C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#386C2314yes—
369#386C2314yes—
370#386C2314yes—
371#386C2314yes—
372#386C2318yes—
373#386C2318yes—
374#386C2314yes—
375#386C2314yes—
376#386C2318yes—
377#386C2318yes—
378#386C2318yes—
379#386C2318yes—
380#385C2318yes—
381#385C2318yes—
382#385C2318yes—
383#385C2318yes—
384#385C2314yes—
385#385C2314yes—
386#385C2318yes—
387#385C2318yes—
388#385C2318yes—
389#385C2318yes—
390#385C2314yes—
391#385C2314yes—
392#385C2318yes—
393#385C2318yes—
394#385C2318yes—
395#385C2318yes—
396#384C2312yes—
397#384C2314yes—
398#384C2312yes—
399#384C2314yes—
400#381C2314yes—
401#380C2314yes—
402#380C2318yes—
403#380C2318yes—
404#380C2312yes—
405#380C2314yes—
406#380C2314yes—
407#380C2312yes—
408#380C2314yes—
409#380C2314yes—
410#380C2318yes—
411#380C2314yes—
412#380C2318yes—
413#380C2318yes—
414#380C2318yes—
415#380C2318yes—
416#379C2314yes—
417C4×C4⋊C4C2312yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2312yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2312yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2312yes—
424C4×C22⋊C4C2314yes—
425C4×C22⋊C4C2318yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2318yes—
428C4×C22⋊C4C2318yes—
429C4×C22⋊C4C2318yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432C2×#95C2312yes—
433C2×#95C2312yes—
434C2×#95C2311yescharacteristic
435C2×#95C2312yes—
436C2×#95C2311yescharacteristic
437C2×#95C2312yes—
438C2×#95C2314yes—
439C2×#95C2314yes—
440C2×#95C2314yes—
441C2×#95C2314yes—
442C25C2412yes—
443C25C2411yescharacteristic
444C22×Q8—216no—
445C22×Q8—28no—
446C22×Q8—42no—
447C22×Q8—42no—
448C22×Q8—44no—
449C22×Q8—48no—
450C22×Q8—44no—
451C22×Q8—48no—
452C22×Q8C2×D418yes—
453C22×Q8C2414yes—
454C22×Q8C2412yes—
455C22×Q8C2418yes—
456C22×Q8C2414yes—
457C22×Q8C2418yes—
458C22×Q8C2412yes—
459C22×D4—28no—
460C22×D4—28no—
461C22×D4C2×Q8116yescomplemented
462C22×D4C2414yes—
463C22×D4C2414yes—
464C22×D4C2412yes—
465C22×D4C2412yes—
466C23×C4—28no—
467C23×C4—28no—
468C23×C4—42no—
469C23×C4—42no—
470C23×C4—44no—
471C23×C4—44no—
472C23×C4—44no—
473C23×C4—82no—
474C23×C4C2×D418yes—
475C23×C4C2414yes—
476C23×C4C2414yes—
477C23×C4C2412yes—
478C23×C4C2411yescharacteristic
479C23×C4C2412yes—
480C23×C4C2412yes—
481C23×C4C2414yes—
482C23×C4C2414yes—
483C23×C4C2412yes—
484C23×C4C2411yescharacteristic
485C23×C4C2412yes—
486C23×C4C2418yes—
487C23×C4C2414yes—
488C23×C4C2418yes—
489C23×C4C2411yescharacteristic
490C23×C4C2412yes—
491C23×C4C2414yes—
492C23×C4C2412yes—
493C23×C4C2412yes—
494C23×C4C2412yes—
495C23×C4C2411yescharacteristic
496C23×C4C2411yescharacteristic
497C23×C4C2411yescharacteristic
498C4⋊Q8—216no—
499C4⋊Q8—232no—
500C4⋊Q8—216no—
501C4⋊Q8—232no—
502C4⋊Q8—48no—
503C4⋊Q8—44no—
504C4⋊Q8—44no—
505C4⋊Q8—84no—
506#125—232no—
507#125—232no—
508#125—232no—
509#123C2×Q8132yescomplemented
510C22⋊Q8—216no—
511C22⋊Q8—232no—
512C22⋊Q8—216no—
513C22⋊Q8—216no—
514C22⋊Q8—216no—
515C22⋊Q8—216no—
516C22⋊Q8—232no—
517C22⋊Q8—232no—
518C22⋊Q8—216no—
519C22⋊Q8—232no—
520C22⋊Q8—232no—
521C22⋊Q8—232no—
522C22⋊Q8—232no—
523C22⋊Q8—216no—
524C22⋊Q8—232no—
525C22⋊Q8—232no—
526C22⋊Q8—232no—
527C22⋊Q8—232no—
528C22⋊Q8—416no—
529C22⋊Q8—416no—
530C22⋊Q8—48no—
531C22⋊Q8—88no—
532C22⋊Q8C2×D4132yes—
533C22⋊Q8C2×D4132yes—
534#121C2×Q8116yescomplemented
535#121C2×Q8116yescomplemented
536#120C2×Q8132yescomplemented
537C4×Q8—216no—
538C4×Q8—216no—
539C4×Q8—232no—
540C4×Q8—28no—
541C4×Q8—48no—
542C4×Q8—44no—
543C4×D4—216no—
544C4×D4—216no—
545C4×D4—216no—
546C4×D4—216no—
547C4×D4—232no—
548C4×D4—232no—
549C4×D4—232no—
550C4×D4—232no—
551C4×D4—48no—
552C4×D4—44no—
553C4×D4—44no—
554C4×D4—84no—
555#117—232no—
556C2×C4⋊C4—28no—
557C2×C4⋊C4—216no—
558C2×C4⋊C4—28no—
559C2×C4⋊C4—232no—
560C2×C4⋊C4—216no—
561C2×C4⋊C4—24no—
562C2×C4⋊C4—28no—
563C2×C4⋊C4—44no—
564C2×C4⋊C4—48no—
565C2×C4⋊C4—42no—
566C2×C4⋊C4—44no—
567C2×C4⋊C4—44no—
568C2×C4⋊C4—48no—
569C2×C4⋊C4—82no—
570C2×C4⋊C4—84no—
571C2×C4⋊C4C2×D418yes—
572C2×C4⋊C4C2×D4116yes—
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2418yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2418yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2411yescharacteristic
618C2×C22⋊C4—28no—
619C2×C22⋊C4—216no—
620C2×C22⋊C4—24no—
621C2×C22⋊C4—28no—
622C2×C22⋊C4—232no—
623C2×C22⋊C4—48no—
624C2×C22⋊C4—84no—
625C2×C22⋊C4C2×D4116yes—
626C2×C22⋊C4C2×Q818yescomplemented
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C42—28no—
649C2×C42—42no—
650C2×C42—44no—
651C2×C42—42no—
652C2×C42—82no—
653C2×C42C2418yes—
654C2×C42C2418yes—
655C2×C42C2414yes—
656C2×C42C2414yes—
657C2×C42C2412yes—
658C2×C42C2414yes—
659C2×C42C2412yes—
660C2×C42C2414yes—
661C2×C42C2414yes—
662C2×C42C2412yes—
663C2×C42C2414yes—
664C2×C42C2412yes—
665#95C2414yes—
666#95C2418yes—
667#95C2414yes—
668#95C2418yes—
669#95C2418yes—
670#95C2418yes—
671#95C2414yes—
672#95C2414yes—
673#95C2418yes—
674#95C2418yes—
675#95C2418yes—
676#95C2418yes—
677#95C2418yes—
678#95C2418yes—
679#95C2418yes—
680#95C2414yes—
681#95C2414yes—
682#95C2418yes—
683#95C2418yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2418yes—
689#95C2418yes—
690C24—24no—
691C24—24no—
692C24—41no—
693C24—41no—
694C24—41no—
695C24—41no—
696C24—42no—
697C24—42no—
698C24—42no—
699C24—42no—
700C24C22×D414yes—
701C24C22×Q818yes—
702C24C22×Q814yes—
703C242−1+414yes—
704C24C2514yes—
705C24C2512yes—
706C24C2511yescharacteristic
707C2×Q8—28no—
708C2×Q8—216no—
709C2×Q8—28no—
710C2×Q8—216no—
711C2×Q8—24no—
712C2×Q8—28no—
713C2×Q8—24no—
714C2×Q8—28no—
715C2×Q8—42no—
716C2×Q8—42no—
717C2×Q8—44no—
718C2×Q8—48no—
719C2×Q8—48no—
720C2×Q8—44no—
721C2×Q8—48no—
722C2×Q8—48no—
723C2×Q8—416no—
724C2×Q8—816no—
725C2×Q8—832no—
726C2×Q8C22×D418yes—
727C2×Q8C22×D418yes—
728C2×D4—264no—
729C2×D4—28no—
730C2×D4—28no—
731C2×D4—28no—
732C2×D4—28no—
733C2×D4—42no—
734C2×D4—42no—
735C2×D4—42no—
736C2×D4—42no—
737C2×D4C22×Q8116yes—
738C2×D4C22×Q8116yes—
739C2×D4C22×Q818yes—
740C2×D4C22×Q818yes—
741C22×C4—24no—
742C22×C4—24no—
743C22×C4—22no—
744C22×C4—24no—
745C22×C4—22no—
746C22×C4—24no—
747C22×C4—28no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—28no—
751C22×C4—28no—
752C22×C4—24no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—28no—
756C22×C4—24no—
757C22×C4—28no—
758C22×C4—24no—
759C22×C4—28no—
760C22×C4—28no—
761C22×C4—28no—
762C22×C4—216no—
763C22×C4—216no—
764C22×C4—28no—
765C22×C4—416no—
766C22×C4—41no—
767C22×C4—42no—
768C22×C4—41no—
769C22×C4—41no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—41no—
774C22×C4—44no—
775C22×C4—42no—
776C22×C4—41no—
777C22×C4—41no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—41no—
781C22×C4—41no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4—44no—
785C22×C4—44no—
786C22×C4—42no—
787C22×C4—42no—
788C22×C4—41no—
789C22×C4—42no—
790C22×C4—42no—
791C22×C4—48no—
792C22×C4—48no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—42no—
796C22×C4—48no—
797C22×C4—41no—
798C22×C4—42no—
799C22×C4—44no—
800C22×C4—48no—
801C22×C4—44no—
802C22×C4—816no—
803C22×C4—816no—
804C22×C4C22×D418yes—
805C22×C4C22×D414yes—
806C22×C4C22×D418yes—
807C22×C4C22×D418yes—
808C22×C4C22×D418yes—
809C22×C4C22×D414yes—
810C22×C4C22×Q818yes—
811C22×C4C22×Q814yes—
812C22×C4C22×Q814yes—
813C22×C4C2512yes—
814C22×C4C2512yes—
815C22×C4C2514yes—
816C22×C4C2512yes—
817C22×C4C2514yes—
818C22×C4C2518yes—
819C22×C4C2518yes—
820C22×C4C2514yes—
821C22×C4C2514yes—
822C22×C4C2514yes—
823C22×C4C2512yes—
824C22×C4C2511yescharacteristic
825C22×C4C2512yes—
826C22×C4C2512yes—
827C22×C4C2514yes—
828C22×C4C2512yes—
829C22×C4C2511yescharacteristic
830C4⋊C4—216no—
831C4⋊C4—28no—
832C4⋊C4—28no—
833C4⋊C4—28no—
834C4⋊C4—28no—
835C4⋊C4—216no—
836C4⋊C4—216no—
837C4⋊C4—216no—
838C4⋊C4—216no—
839C4⋊C4—216no—
840C4⋊C4—216no—
841C4⋊C4—216no—
842C4⋊C4—216no—
843C4⋊C4—216no—
844C4⋊C4—24no—
845C4⋊C4—22no—
846C4⋊C4—28no—
847C4⋊C4—24no—
848C4⋊C4—28no—
849C4⋊C4—216no—
850C4⋊C4—42no—
851C4⋊C4—44no—
852C4⋊C4—44no—
853C4⋊C4—48no—
854C4⋊C4—48no—
855C4⋊C4—48no—
856C4⋊C4—48no—
857C4⋊C4—42no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—42no—
861C4⋊C4—44no—
862C4⋊C4—42no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—44no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—42no—
869C4⋊C4C22×D418yes—
870C4⋊C4C22×D4132yes—
871C4⋊C4C22×D418yes—
872C4⋊C4C22×Q818yes—
873C4⋊C4C22×Q818yes—
874C4⋊C4H(5,𝔽2)14yes—
875C22⋊C4—216no—
876C22⋊C4—28no—
877C22⋊C4—28no—
878C22⋊C4—216no—
879C22⋊C4—28no—
880C22⋊C4—28no—
881C22⋊C4—28no—
882C22⋊C4—216no—
883C22⋊C4—216no—
884C22⋊C4—216no—
885C22⋊C4—48no—
886C22⋊C4—48no—
887C22⋊C4—48no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4C22×D4132yes—
893C22⋊C4C22×Q8116yes—
894C22⋊C4C22×Q8116yes—
895C22⋊C4C22×Q8116yes—
896C42—28no—
897C42—28no—
898C42—216no—
899C42—216no—
900C42—28no—
901C42—24no—
902C42—24no—
903C42—42no—
904C42—44no—
905C42—42no—
906C42—44no—
907C42—44no—
908C23—21no—
909C23—22no—
910C23—21no—
911C23—22no—
912C23—21no—
913C23—22no—
914C23—21no—
915C23—22no—
916C23—24no—
917C23—24no—
918C23—24no—
919C23—24no—
920C23—24no—
921C23—24no—
922C23—216no—
923C23—44no—
924C23—44no—
925C23—44no—
926C23—44no—
927C23—44no—
928C23—44no—
929C23—48no—
930C23—48no—
931C23—84no—
932C23—84no—
933C23—84no—
934C23—84no—
935C23D4×Q8116yescomplemented
936C23C23×D412yes—
937C23C23×D414yes—
938C23C23×Q818yes—
939C23C23×Q814yes—
940C23C23×Q812yes—
941C23C2×2−1+414yes—
942C23C2×2−1+412yes—
943C23C2611yescharacteristic
944Q8—216no—
945Q8—48no—
946Q8—416no—
947Q8—816no—
948Q8—88no—
949Q8—816no—
950D4—232no—
951D4—232no—
952D4—48no—
953D4—48no—
954C2×C4—24no—
955C2×C4—22no—
956C2×C4—24no—
957C2×C4—21no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—24no—
968C2×C4—22no—
969C2×C4—24no—
970C2×C4—216no—
971C2×C4—216no—
972C2×C4—28no—
973C2×C4—24no—
974C2×C4—28no—
975C2×C4—28no—
976C2×C4—24no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—28no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—24no—
986C2×C4—22no—
987C2×C4—24no—
988C2×C4—28no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—24no—
992C2×C4—28no—
993C2×C4—24no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—28no—
997C2×C4—44no—
998C2×C4—48no—
999C2×C4—48no—
1000C2×C4—48no—
1001C2×C4—44no—
1002C2×C4—44no—
1003C2×C4—48no—
1004C2×C4—416no—
1005C2×C4—416no—
1006C2×C4—816no—
1007C2×C4—88no—
1008C2×C4—816no—
1009C2×C4—88no—
1010C2×C4—84no—
1011C2×C4—82no—
1012C2×C4—82no—
1013C2×C4—84no—
1014C2×C4—84no—
1015C2×C4—88no—
1016C2×C4—88no—
1017C2×C4C23×D418yes—
1018C2×C4C23×D418yes—
1019C2×C4C23×D414yes—
1020C2×C4C23×D412yes—
1021C2×C4C23×D412yes—
1022C2×C4C23×Q814yes—
1023C2×C4C23×Q814yes—
1024C2×C4C23×Q818yes—
1025C2×C4C2×H(5,𝔽2)14yes—
1026C2×C4C2×H(5,𝔽2)12yes—
1027C2×C4#58512yes—
1028C22—22no—
1029C22—24no—
1030C22—22no—
1031C22—24no—
1032C22—22no—
1033C22—24no—
1034C22—22no—
1035C22—24no—
1036C22—22no—
1037C22—24no—
1038C22—22no—
1039C22—24no—
1040C22—28no—
1041C22—28no—
1042C22—28no—
1043C22—416no—
1044C22—44no—
1045C22—44no—
1046C22—44no—
1047C22—44no—
1048C22—816no—
1049C22C2×D4×Q818yes—
1050C22C2×D4×Q814yes—
1051C22C24×D411yescharacteristic
1052C22C24×Q811yescharacteristic
1053C22C22×H(5,𝔽2)11yescharacteristic
1054C22C22×2−1+411yescharacteristic
1055C22C2×#58511yescharacteristic
1056C22H(7,𝔽2)11yescharacteristic
1057C222−1+611yescharacteristic
1058C4—24no—
1059C4—24no—
1060C4—24no—
1061C4—22no—
1062C4—28no—
1063C4—28no—
1064C4—24no—
1065C4—28no—
1066C4—44no—
1067C4—48no—
1068C4—48no—
1069C4—44no—
1070C4—42no—
1071C4—44no—
1072C4—42no—
1073C4—42no—
1074C4#349614yes—
1075C2—28no—
1076C2—24no—
1077C2—48no—
1078C2C22×D4×Q811yescharacteristic
1079C2C2×#349611yescharacteristic
1080C2#6285311yescharacteristic
1081C2#6289411yescharacteristic
1082C2#6290411yescharacteristic
1083C2Q8×H(5,𝔽2)11yescharacteristic
1084C2#6298911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#534C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3501C2semidirect
2. #59113C2semidirect
3. #59096C2semidirect
4. #59016C2semidirect
5. #58998C2semidirect
6. #43909C2semidirect
7. #43025C2semidirect
8. #39615C2semidirect
9. #39614C2semidirect
10. #39614C2semidirect
11. #39610C2semidirect
12. #36561C2semidirect
13. Q8×#121C2semidirect
14. #35359C2semidirect
15. #35011C2semidirect
16. #35002C2semidirect
17. C2×#2417C2semidirect
19. C2×#2360C2semidirect
24. C2×#554C22semidirect
25. C2×#554C22semidirect
27. C2×D4×Q8C22semidirect
28. C2×D4×Q8C22semidirect
29. C2×#544C22semidirect
31. C2×#543C22semidirect
33. C2×#533C22semidirect
36. C22×C22⋊Q8C22semidirect
37. C22×C22⋊Q8C22semidirect
39. C22×C4×Q8C22semidirect
42. #2857C22semidirect
43. #2857C22semidirect
44. #2857C22semidirect
45. #2857C22semidirect
46. #2734C22semidirect
47. #2732C22semidirect
48. #2729C22semidirect
49. #2726C22semidirect
50. #2726C22semidirect
51. #2720C22semidirect
52. #2713C22semidirect
53. #2704C22semidirect
54. #2704C22semidirect
55. #2704C22semidirect
56. #2692C22semidirect
57. #2683C22semidirect
58. #2683C22semidirect
59. #2677C22semidirect
60. #2659C22semidirect
61. #2659C22semidirect
62. #2659C22semidirect
63. #2659C22semidirect
64. #2583C22semidirect
65. #2564C22semidirect
66. #2564C22semidirect
67. #2556C22semidirect
68. #2551C22semidirect
69. #2549C22semidirect
70. #2549C22semidirect
71. #2546C22semidirect
72. #2546C22semidirect
73. #2542C22semidirect
74. #2538C22semidirect
75. #2538C22semidirect
76. #2506C22semidirect
77. #2502C22semidirect
78. #2492C22semidirect
79. #2473C22semidirect
80. #2465C22semidirect
81. #2462C22semidirect
82. #2452C22semidirect
83. #2451C22semidirect
84. #2451C22semidirect
89. #2449C22semidirect
90. #2446C22semidirect
91. #2440C22semidirect
92. #2440C22semidirect
93. #2440C22semidirect
94. #2440C22semidirect
95. #2438C22semidirect
96. #2438C22semidirect
97. #2437C22semidirect
98. #2437C22semidirect
99. #2434C22semidirect
100. #2434C22semidirect
101. #2429C22semidirect
102. #2429C22semidirect
103. #2429C22semidirect
104. #2429C22semidirect
105. #2423C22semidirect
109. #2417C22semidirect
110. #2417C22semidirect
111. #2417C22semidirect
112. #2417C22semidirect
113. #2417C22semidirect
114. #2417C22semidirect
115. #2417C22semidirect
116. #2409C22semidirect
117. C2×#398C22semidirect
118. C2×#396C22semidirect
119. #2365C22semidirect
120. #2360C22semidirect
121. #2360C22semidirect
122. #2360C22semidirect
123. #2360C22semidirect
128. Q8×C4⋊C4C22semidirect
129. D4×C4⋊C4C22semidirect
130. Q8×C22⋊C4C22semidirect
147. C2×#391C22semidirect
148. C2×#391C22semidirect
149. C2×#389C22semidirect
150. C2×#389C22semidirect
151. C2×#389C22semidirect
152. C2×#387C22semidirect
156. C2×#380C22semidirect
157. C2×C4×C4⋊C4C22semidirect
177. #534Q8semidirect
194. C2×C22⋊Q8D4semidirect
461. C22×D4C2×Q8semidirect
509. #123C2×Q8semidirect
534. #121C2×Q8semidirect
535. #121C2×Q8semidirect
536. #120C2×Q8semidirect
626. C2×C22⋊C4C2×Q8semidirect
935. C23D4×Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#35012
#591132
#590962
#590162
#589982
#439092
#430252
#396152
#396142
#396102
#365612
Q8×#1212
#353592
#350112
#350022
C2×#24172
#342732
C2×#23602
C4×#5342