Finite Group Databasebeta

← #7645638

Subgroups — #7645638

Order 512.

8260 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3505C211yesmaximal, characteristic, complemented
2C22×#547C211yesmaximal, characteristic, complemented
3#41413C218yesmaximal, complemented
4#41409C218yesmaximal, complemented
5#38082C214yesmaximal, complemented
6#38079C214yesmaximal, complemented
7#37864C214yesmaximal, complemented
8#37863C214yesmaximal, complemented
9#37632C212yesmaximal, complemented
10#37448C212yesmaximal, complemented
11#37118C214yesmaximal, complemented
12#36956C214yesmaximal, complemented
13#35447C214yesmaximal, complemented
14#35233C212yesmaximal, complemented
15#35227C212yesmaximal, complemented
16#35088C214yesmaximal, complemented
17#35019C211yesmaximal, characteristic, complemented
18#35001C211yesmaximal, characteristic, complemented
19C2×#2503C211yesmaximal, characteristic, complemented
20C2×#2501C211yesmaximal, characteristic, complemented
21#34057C211yesmaximal, characteristic, complemented
22C23×#41C2212yes—
23#3505—216no—
24C2×#553C2214yescomplemented
25C2×#553C2212yescomplemented
26C2×#552C2212yescomplemented
27C2×#551C2214yescomplemented
28C2×#548C2212yescomplemented
29C2×#547—216no—
30C2×#547C2214yes—
31C2×#547C2214yes—
32C2×#547C2214yescomplemented
33C2×#547C2214yescomplemented
34C2×#546C2212yescomplemented
35C2×#539C2212yes—
36C2×#538C2212yes—
37C2×#534C2212yes—
38C2×#534C2214yes—
39C22×C4⋊Q8C2211yescharacteristic, complemented
40C2×#529C2212yes—
41C2×#525C2212yes—
42C22×#123C2212yes—
43C22×#123C2214yes—
44C22×#123C2212yescomplemented
45C22×C22⋊Q8C2211yescharacteristic
46C22×C22⋊Q8C2212yescomplemented
47C22×#121C2211yescharacteristic
48C22×#121C2211yescharacteristic
49C22×#121C2211yescharacteristic, complemented
50C2×#518C2212yes—
51C22×C4×D4C2211yescharacteristic
52C22×C4×D4C2211yescharacteristic, complemented
53C23×C4⋊C4C2211yescharacteristic
54C23×C4⋊C4C2211yescharacteristic, complemented
55#2856C2214yescomplemented
56#2850C2214yescomplemented
57#2849C2218yescomplemented
58#2849C2218yescomplemented
59#2821C2218yescomplemented
60#2813C2218yescomplemented
61#2723C22116yescomplemented
62#2720C22116yescomplemented
63#2718C22116yescomplemented
64#2710C22116yescomplemented
65#2706C22116yescomplemented
66#2703C22116yescomplemented
67#2696C22116yescomplemented
68#2692C22116yescomplemented
69#2660C2214yescomplemented
70#2656C2214yescomplemented
71#2640C2214yescomplemented
72#2639C2214yescomplemented
73#2636C2218yescomplemented
74#2635C2218yescomplemented
75#2628C2218yescomplemented
76#2623C2218yescomplemented
77#2620C2214yescomplemented
78#2619C2214yescomplemented
79#2614C2218yescomplemented
80#2613C2218yescomplemented
81#2598C2218yescomplemented
82#2591C2214yescomplemented
83#2567C2214yescomplemented
84#2566C2214yescomplemented
85#2563C2214yescomplemented
86#2561C2214yescomplemented
87#2544C2214yescomplemented
88#2539C2214yes—
89#2539C2214yescomplemented
90#2534C2218yescomplemented
91#2534C2218yescomplemented
92#2504C2214yescomplemented
93#2504C2212yescomplemented
94#2503C2212yescomplemented
95#2503C2212yescomplemented
96#2503C2214yescomplemented
97#2503C2212yescomplemented
98#2503C2214yescomplemented
99#2503C2214yescomplemented
100#2502C2214yescomplemented
101#2501C2212yes—
102#2501C2212yes—
103#2501C2214yes—
104#2501C2212yes—
105#2501C2212yescomplemented
106#2501C2214yescomplemented
107#2501C2214yescomplemented
108#2500C2214yescomplemented
109#2487C2218yescomplemented
110#2486C2218yescomplemented
111#2486C2218yescomplemented
112#2436C2212yescomplemented
113#2435C2212yescomplemented
114#2433C2212yes—
115#2433C2212yescomplemented
116#2431C2214yescomplemented
117#2430C22116yescomplemented
118#2430C22116yescomplemented
119#2425C22116yescomplemented
120#2425C22116yescomplemented
121#2413C22116yescomplemented
122#2412C22116yescomplemented
123#2406C22116yescomplemented
124#2404C22116yescomplemented
125C2×#400C2214yescomplemented
126C2×#399C2214yescomplemented
127#2328C2214yescomplemented
128#2326C2214yescomplemented
129#2318C2214yescomplemented
130#2318C2214yescomplemented
131#2317C2214yescomplemented
132#2315C2212yes—
133#2313C2212yescomplemented
134#2312C2212yescomplemented
135#2311C2214yescomplemented
136#2308C2212yes—
137#2308C2214yes—
138C2×#391C2212yescomplemented
139C2×#390C2212yescomplemented
140#2290C2214yescomplemented
141#2290C2214yescomplemented
142C2×#384C2212yescomplemented
143#2283C2212yescomplemented
144C2×#382C2212yescomplemented
145#2280C2212yescomplemented
146C2×#381C2214yes—
147C2×C4×C22⋊C4C2211yescharacteristic
148C2×C4×C22⋊C4C2211yescharacteristic
149C22×#41—216no—
150C22×#41—416no—
151C22×#41C2318yes—
152C22×#41C2318yes—
153C22×#41C2312yes—
154C23×Q8C2312yes—
155C23×Q8C2311yescharacteristic
156C23×D4C2312yes—
157C23×D4C2312yes—
158C23×D4C2311yescharacteristic
159C23×D4C2312yes—
160C23×D4C2311yescharacteristic
161C23×D4C2311yescharacteristic
162C24×C4C2312yes—
163C24×C4C2312yes—
164C24×C4C2312yes—
165C24×C4C2311yescharacteristic
166C24×C4C2311yescharacteristic
167#553—216no—
168#553—232no—
169#552—216no—
170#551—232no—
171#548—216no—
172#547—232no—
173#547—232no—
174#547—232no—
175#547—232no—
176#546—216no—
177#539—216no—
178#538—216no—
179#534—216no—
180#534—416no—
181C2×C4⋊Q8—28no—
182C2×C4⋊Q8C2314yes—
183C2×C4⋊Q8C2314yes—
184C2×#127C2314yes—
185#529—216no—
186C2×#126C2314yes—
187C2×#126C2314yes—
188C2×#126C2314yes—
189C2×#125C2312yes—
190C2×#125C2314yes—
191C2×#124C2312yes—
192C2×#124C2314yes—
193C2×#124C2314yes—
194#525—216no—
195C2×#123—216no—
196C2×#123—216no—
197C2×#123—416no—
198C2×#123C2314yes—
199C2×#123C2314yes—
200C2×#123C2314yes—
201C2×#123C2318yes—
202C2×#123C2318yes—
203C2×#123C2318yes—
204C2×#123C2318yes—
205C2×#123C2314yes—
206C2×#123C2314yes—
207C2×#123C2318yes—
208C2×#123C2318yes—
209C2×#123C2318yes—
210C2×#123C2318yes—
211C2×#123C23116yes—
212C2×C22⋊Q8—28no—
213C2×C22⋊Q8—216no—
214C2×C22⋊Q8C2312yes—
215C2×C22⋊Q8C2312yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2312yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2318yes—
220C2×C22⋊Q8C2318yes—
221C2×C22⋊Q8C2314yes—
222C2×#121—28no—
223C2×#121—28no—
224C2×#121—28no—
225C2×#121C2312yes—
226C2×#121C2312yes—
227C2×#121C2312yes—
228C2×#121C2312yes—
229C2×#121C2312yes—
230C2×#121C2314yes—
231C2×#121C2314yes—
232C2×#121C2312yes—
233C2×#121C2312yes—
234C2×#121C2312yes—
235C2×#121C2312yes—
236C2×#121C2314yes—
237C2×#121C2314yes—
238C2×#121C2314yes—
239C2×#121C23116yes—
240C2×#120C2314yes—
241C2×#120C2314yes—
242C2×#120C2318yes—
243C2×#120C2318yes—
244#518—216no—
245C2×C4×Q8C2312yes—
246C2×C4×D4—28no—
247C2×C4×D4D4116yescomplemented
248C2×C4×D4C2312yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2312yes—
260C2×#117C2312yes—
261C2×#117C2314yes—
262C2×#117C2314yes—
263C2×#117C2314yes—
264C22×C4⋊C4—28no—
265C22×C4⋊C4—28no—
266C22×C4⋊C4C2314yes—
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2314yes—
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2312yes—
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2311yescharacteristic
273C22×C4⋊C4C2312yes—
274C22×C4⋊C4C2312yes—
275C22×C4⋊C4C2312yes—
276C22×C4⋊C4C2311yescharacteristic
277C22×C4⋊C4C2312yes—
278C22×C4⋊C4C2311yescharacteristic
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2312yes—
281C22×C4⋊C4C2318yes—
282C22×C4⋊C4C2311yescharacteristic
283C22×C22⋊C4C2312yes—
284C22×C22⋊C4C2312yes—
285C22×C22⋊C4C2312yes—
286C22×C22⋊C4C2312yes—
287C22×C22⋊C4C2312yes—
288C22×C22⋊C4C2312yes—
289C22×C22⋊C4C2314yes—
290C22×C22⋊C4C2312yes—
291C22×C22⋊C4C2318yes—
292C22×C22⋊C4C2311yescharacteristic
293C22×C22⋊C4C2311yescharacteristic
294C22×C42C2312yes—
295C22×C42C2312yes—
296C22×C42C2311yescharacteristic
297#400C2318yes—
298#400C2318yes—
299#400C2318yes—
300#400C23116yes—
301#399C2318yes—
302#399C2318yes—
303#399C2318yes—
304#399C23116yes—
305#399C2318yes—
306#398C23116yes—
307#398C23116yes—
308#397C2318yes—
309#397C23116yes—
310#397C23116yes—
311#396C23116yes—
312#396C23116yes—
313#395C23116yes—
314#395C23116yes—
315#394C2318yes—
316#394C23116yes—
317#394C23116yes—
318#394C23116yes—
319#394C23116yes—
320#393C2318yes—
321#393C23116yes—
322#393C23116yes—
323#392C2318yes—
324#392C23116yes—
325#392C23116yes—
326#392C2318yes—
327#391C2314yes—
328#391C2314yes—
329#391C2314yes—
330#391C2318yes—
331#390C2314yes—
332#390C2314yes—
333#390C2314yes—
334#390C2314yes—
335#390C2314yes—
336#390C23116yes—
337#390C2318yes—
338#389C23116yes—
339#389C23116yes—
340#388C23116yes—
341#388C2318yes—
342#388C2318yes—
343#388C23116yes—
344#388C23116yes—
345#387C2318yes—
346#387C2318yes—
347#386C2318yes—
348#386C2318yes—
349#386C2318yes—
350#386C2318yes—
351#386C23116yes—
352#386C23116yes—
353#386C23116yes—
354#386C23116yes—
355#386C23116yes—
356#386C23116yes—
357#386C23116yes—
358#385C23116yes—
359#385C2318yes—
360#385C2318yes—
361#385C23116yes—
362#385C23116yes—
363#385C23116yes—
364#384C2314yes—
365#384C2314yes—
366#384C2314yes—
367#384C2318yes—
368#383C2314yes—
369#382C2314yes—
370#382C2314yes—
371#382C2314yes—
372#382C2314yes—
373#382C2318yes—
374#381C2318yes—
375#381C2314yes—
376#381C2314yes—
377#381C2318yes—
378#381C2318yes—
379#381C23116yes—
380#380C23116yes—
381#380C23116yes—
382#380C2314yes—
383#380C2314yes—
384#380C2314yes—
385#379C2318yes—
386#379C2314yes—
387C4×C4⋊C4C2314yes—
388C4×C22⋊C4C2312yes—
389C4×C22⋊C4C2312yes—
390C4×C22⋊C4C2312yes—
391C4×C22⋊C4C2312yes—
392C4×C22⋊C4C2314yes—
393C4×C22⋊C4C2312yes—
394C4×C22⋊C4C2312yes—
395C4×C22⋊C4C2312yes—
396C4×C22⋊C4C2312yes—
397#376C2314yes—
398C2×#95C2312yes—
399C2×#95C2312yes—
400C2×#95C2318yes—
401C2×#95C2318yes—
402C25C2412yes—
403C25C2412yes—
404C25C2411yescharacteristic
405C25C2411yescharacteristic
406C2×#41—232no—
407C2×#41—232no—
408C2×#41—28no—
409C2×#41—432no—
410C2×#41—432no—
411C2×#41—48no—
412C2×#41—4128no—
413C22×Q8—28no—
414C22×Q8—24no—
415C22×Q8—48no—
416C22×Q8—44no—
417C22×Q8C2412yes—
418C22×Q8C2412yes—
419C22×Q8C2418yes—
420C22×D4—28no—
421C22×D4—28no—
422C22×D4—28no—
423C22×D4—28no—
424C22×D4—216no—
425C22×D4—216no—
426C22×D4—24no—
427C22×D4—24no—
428C22×D4—44no—
429C22×D4—44no—
430C22×D4—48no—
431C22×D4C2×D418yes—
432C22×D4C2414yes—
433C22×D4C2414yes—
434C22×D4C2412yes—
435C22×D4C2412yes—
436C22×D4C2414yes—
437C22×D4C2414yes—
438C22×D4C2412yes—
439C22×D4C2412yes—
440C22×D4C2412yes—
441C22×D4C2414yes—
442C22×D4C2414yes—
443C22×D4C2412yes—
444C22×D4C2418yes—
445C22×D4C24116yes—
446C23×C4—28no—
447C23×C4—28no—
448C23×C4—216no—
449C23×C4—28no—
450C23×C4—44no—
451C23×C4—44no—
452C23×C4—48no—
453C23×C4—48no—
454C23×C4C2×D418yes—
455C23×C4C2×D418yes—
456C23×C4C2414yes—
457C23×C4C2412yes—
458C23×C4C2412yes—
459C23×C4C2412yes—
460C23×C4C2412yes—
461C23×C4C2414yes—
462C23×C4C2411yescharacteristic
463C23×C4C2411yescharacteristic
464C23×C4C2411yescharacteristic
465C23×C4C2412yes—
466C23×C4C2411yescharacteristic
467C23×C4C2414yes—
468C23×C4C2412yes—
469C23×C4C2412yes—
470C23×C4C2414yes—
471C23×C4C2414yes—
472C23×C4C2414yes—
473C23×C4C2418yes—
474C23×C4C2418yes—
475C23×C4C2411yescharacteristic
476C23×C4C2411yescharacteristic
477C23×C4C2411yescharacteristic
478C23×C4C2411yescharacteristic
479C23×C4C2411yescharacteristic
480C23×C4C2412yes—
481C4⋊Q8—216no—
482C4⋊Q8—216no—
483#127—48no—
484#126—216no—
485#126—216no—
486#126—216no—
487#125—216no—
488#125—28no—
489#124—216no—
490#124—28no—
491#124—48no—
492#123—216no—
493#123—216no—
494#123—216no—
495#123—216no—
496#123—232no—
497#123—232no—
498#123—232no—
499#123—232no—
500#123—216no—
501#123—416no—
502#123—416no—
503#123—432no—
504#123—416no—
505#123—416no—
506C22⋊Q8—28no—
507C22⋊Q8—28no—
508C22⋊Q8—28no—
509C22⋊Q8—28no—
510C22⋊Q8—28no—
511C22⋊Q8—232no—
512C22⋊Q8—232no—
513C22⋊Q8—216no—
514#121—216no—
515#121—216no—
516#121—28no—
517#121—28no—
518#121—28no—
519#121—28no—
520#121—216no—
521#121—28no—
522#121—28no—
523#121—216no—
524#121—28no—
525#121—28no—
526#121—28no—
527#121—216no—
528#121—432no—
529#120—216no—
530#120—216no—
531#120—416no—
532#120—416no—
533C4×Q8—28no—
534C4×D4—216no—
535C4×D4—216no—
536C4×D4—216no—
537C4×D4—216no—
538C4×D4—216no—
539C4×D4—216no—
540C4×D4—216no—
541C4×D4—28no—
542C4×D4C2×D4116yes—
543C4×D4C2×D4116yes—
544C4×D4C2×D4116yes—
545C4×D4C2×D4116yes—
546#117—28no—
547#117—216no—
548#117—216no—
549#117—48no—
550C2×C4⋊C4—24no—
551C2×C4⋊C4—24no—
552C2×C4⋊C4—24no—
553C2×C4⋊C4—28no—
554C2×C4⋊C4—28no—
555C2×C4⋊C4—28no—
556C2×C4⋊C4—28no—
557C2×C4⋊C4—216no—
558C2×C4⋊C4—28no—
559C2×C4⋊C4—28no—
560C2×C4⋊C4—216no—
561C2×C4⋊C4—24no—
562C2×C4⋊C4—24no—
563C2×C4⋊C4—28no—
564C2×C4⋊C4—28no—
565C2×C4⋊C4—416no—
566C2×C4⋊C4C2×D418yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2412yes—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C24116yes—
588C2×C4⋊C4C24116yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C24116yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C22⋊C4—28no—
595C2×C22⋊C4—28no—
596C2×C22⋊C4—28no—
597C2×C22⋊C4—28no—
598C2×C22⋊C4—28no—
599C2×C22⋊C4—28no—
600C2×C22⋊C4—28no—
601C2×C22⋊C4—216no—
602C2×C22⋊C4—416no—
603C2×C22⋊C4C2×D418yes—
604C2×C22⋊C4C2×D418yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C24116yes—
624C2×C22⋊C4C24116yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C24116yes—
627C2×C22⋊C4C24116yes—
628C2×C22⋊C4C24116yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C24116yes—
631C2×C22⋊C4C2412yes—
632C2×C22⋊C4C2412yes—
633C2×C22⋊C4C2412yes—
634C2×C22⋊C4C2412yes—
635C2×C42—44no—
636C2×C42—44no—
637C2×C42C2×D418yes—
638C2×C42C2414yes—
639C2×C42C2414yes—
640C2×C42C2414yes—
641C2×C42C2414yes—
642C2×C42C2414yes—
643C2×C42C2414yes—
644C2×C42C2412yes—
645C2×C42C2412yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C24116yes—
651#95C24116yes—
652#95C24116yes—
653#95C24116yes—
654#95C2418yes—
655#95C2418yes—
656#95C2418yes—
657#95C2418yes—
658#95C24116yes—
659#95C24116yes—
660C24—24no—
661C24—24no—
662C24—24no—
663C24—28no—
664C24—28no—
665C24—42no—
666C24—42no—
667C24—42no—
668C24—42no—
669C24—44no—
670C24—44no—
671C24—44no—
672C24—44no—
673C24C22×D414yes—
674C24C22×D414yes—
675C24H(5,𝔽2)18yes—
676C24C2514yes—
677C24C2514yes—
678C24C2512yes—
679C24C2511yescharacteristic
680C24C2511yescharacteristic
681C24C2511yescharacteristic
682#41—4128no—
683#41—4128no—
684#41—816no—
685C2×Q8—24no—
686C2×Q8—216no—
687C2×Q8—24no—
688C2×Q8—28no—
689C2×Q8—416no—
690C2×Q8—44no—
691C2×Q8—432no—
692C2×Q8—88no—
693C2×D4—232no—
694C2×D4—28no—
695C2×D4—28no—
696C2×D4—28no—
697C2×D4—28no—
698C2×D4—216no—
699C2×D4—28no—
700C2×D4—28no—
701C2×D4—216no—
702C2×D4—216no—
703C2×D4—216no—
704C2×D4—216no—
705C2×D4—28no—
706C2×D4—28no—
707C2×D4—24no—
708C2×D4—24no—
709C2×D4—24no—
710C2×D4—24no—
711C2×D4—28no—
712C2×D4—28no—
713C2×D4—44no—
714C2×D4—416no—
715C2×D4—416no—
716C2×D4—44no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—416no—
720C2×D4—416no—
721C2×D4—416no—
722C2×D4—432no—
723C2×D4—432no—
724C2×D4—432no—
725C2×D4—88no—
726C2×D4C22×D418yes—
727C2×D4C22×D418yes—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—24no—
731C22×C4—28no—
732C22×C4—24no—
733C22×C4—24no—
734C22×C4—24no—
735C22×C4—24no—
736C22×C4—24no—
737C22×C4—216no—
738C22×C4—28no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—216no—
742C22×C4—28no—
743C22×C4—28no—
744C22×C4—28no—
745C22×C4—216no—
746C22×C4—28no—
747C22×C4—24no—
748C22×C4—24no—
749C22×C4—28no—
750C22×C4—216no—
751C22×C4—28no—
752C22×C4—28no—
753C22×C4—416no—
754C22×C4—416no—
755C22×C4—44no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—42no—
760C22×C4—44no—
761C22×C4—416no—
762C22×C4—416no—
763C22×C4—42no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—48no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—48no—
771C22×C4—432no—
772C22×C4—432no—
773C22×C4—432no—
774C22×C4C22×D414yes—
775C22×C4C22×D414yes—
776C22×C4C22×D414yes—
777C22×C4C22×D414yes—
778C22×C4C22×D418yes—
779C22×C4C22×D414yes—
780C22×C4C22×D414yes—
781C22×C4C22×D414yes—
782C22×C4C22×D414yes—
783C22×C4C22×D414yes—
784C22×C4C22×D418yes—
785C22×C4C2518yes—
786C22×C4C2514yes—
787C22×C4C2514yes—
788C22×C4C2518yes—
789C22×C4C2514yes—
790C22×C4C2514yes—
791C22×C4C2514yes—
792C22×C4C2514yes—
793C22×C4C2511yescharacteristic
794C22×C4C2512yes—
795C22×C4C2512yes—
796C22×C4C2511yescharacteristic
797C22×C4C2511yescharacteristic
798C22×C4C2512yes—
799C22×C4C2511yescharacteristic
800C4⋊C4—24no—
801C4⋊C4—24no—
802C4⋊C4—24no—
803C4⋊C4—24no—
804C4⋊C4—24no—
805C4⋊C4—24no—
806C4⋊C4—216no—
807C4⋊C4—28no—
808C4⋊C4—28no—
809C4⋊C4—24no—
810C4⋊C4—28no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—28no—
814C4⋊C4—24no—
815C4⋊C4—216no—
816C4⋊C4—28no—
817C4⋊C4—28no—
818C4⋊C4—28no—
819C4⋊C4—28no—
820C4⋊C4—416no—
821C4⋊C4—416no—
822C4⋊C4—48no—
823C4⋊C4—48no—
824C4⋊C4—416no—
825C4⋊C4C22×D418yes—
826C4⋊C4C22×D418yes—
827C22⋊C4—28no—
828C22⋊C4—28no—
829C22⋊C4—28no—
830C22⋊C4—28no—
831C22⋊C4—28no—
832C22⋊C4—28no—
833C22⋊C4—28no—
834C22⋊C4—28no—
835C22⋊C4—28no—
836C22⋊C4—28no—
837C22⋊C4—28no—
838C22⋊C4—216no—
839C22⋊C4—216no—
840C22⋊C4—28no—
841C22⋊C4—28no—
842C22⋊C4—28no—
843C22⋊C4—28no—
844C22⋊C4—28no—
845C22⋊C4—416no—
846C22⋊C4—416no—
847C22⋊C4—416no—
848C22⋊C4—48no—
849C22⋊C4—48no—
850C22⋊C4—416no—
851C22⋊C4—416no—
852C22⋊C4—416no—
853C22⋊C4C22×D418yes—
854C22⋊C4C22×D418yes—
855C22⋊C4C22×D418yes—
856C22⋊C4C22×D418yes—
857C42—28no—
858C42—28no—
859C42—28no—
860C42—28no—
861C42—44no—
862C42—44no—
863C42C22×D418yes—
864C42C22×D418yes—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—24no—
872C23—24no—
873C23—24no—
874C23—28no—
875C23—24no—
876C23—24no—
877C23—28no—
878C23—28no—
879C23—28no—
880C23—28no—
881C23—28no—
882C23—28no—
883C23—44no—
884C23—44no—
885C23—44no—
886C23—44no—
887C23—416no—
888C23—416no—
889C23—48no—
890C23—48no—
891C23—48no—
892C23—48no—
893C23—816no—
894C23—84no—
895C23—84no—
896C23—816no—
897C23#535116yes—
898C23C23×D414yes—
899C23C23×D412yes—
900C23C23×D412yes—
901C23C23×D412yes—
902C23C2×H(5,𝔽2)14yes—
903C23C2×H(5,𝔽2)14yes—
904C23C2×H(5,𝔽2)14yes—
905C23C2611yescharacteristic
906Q8—432no—
907Q8—48no—
908Q8—84no—
909D4—216no—
910D4—216no—
911D4—48no—
912D4—432no—
913D4—416no—
914D4—416no—
915D4—416no—
916D4—416no—
917D4—48no—
918D4—48no—
919D4—84no—
920D4—88no—
921D4—88no—
922D4—1616no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—22no—
928C2×C4—24no—
929C2×C4—28no—
930C2×C4—28no—
931C2×C4—28no—
932C2×C4—28no—
933C2×C4—216no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—28no—
941C2×C4—28no—
942C2×C4—28no—
943C2×C4—28no—
944C2×C4—28no—
945C2×C4—28no—
946C2×C4—28no—
947C2×C4—28no—
948C2×C4—28no—
949C2×C4—28no—
950C2×C4—28no—
951C2×C4—28no—
952C2×C4—48no—
953C2×C4—44no—
954C2×C4—44no—
955C2×C4—44no—
956C2×C4—44no—
957C2×C4—44no—
958C2×C4—432no—
959C2×C4—416no—
960C2×C4—432no—
961C2×C4—48no—
962C2×C4—48no—
963C2×C4—48no—
964C2×C4—416no—
965C2×C4—416no—
966C2×C4—48no—
967C2×C4—88no—
968C2×C4—88no—
969C2×C4—84no—
970C2×C4—88no—
971C2×C4—84no—
972C2×C4C23×D414yes—
973C2×C4C23×D414yes—
974C2×C4C23×D412yes—
975C2×C4C23×D414yes—
976C2×C4C23×D412yes—
977C2×C4C23×D412yes—
978C2×C4C23×D412yes—
979C2×C4#58514yes—
980C22—22no—
981C22—22no—
982C22—22no—
983C22—22no—
984C22—22no—
985C22—22no—
986C22—28no—
987C22—28no—
988C22—28no—
989C22—24no—
990C22—24no—
991C22—24no—
992C22—416no—
993C22—416no—
994C22—48no—
995C22—44no—
996C22—44no—
997C22—44no—
998C22—44no—
999C22—416no—
1000C22—416no—
1001C22—44no—
1002C22—44no—
1003C22—816no—
1004C22—168no—
1005C22C2×#53514yes—
1006C22C2×#53514yes—
1007C22C2×#53514yes—
1008C22C24×D411yescharacteristic
1009C22C22×H(5,𝔽2)12yes—
1010C22C2×#58512yes—
1011C222−1+612yes—
1012C4—22no—
1013C4—24no—
1014C4—22no—
1015C4—22no—
1016C4—24no—
1017C4—24no—
1018C4—44no—
1019C4—44no—
1020C4—48no—
1021C4—48no—
1022C4—44no—
1023C4—44no—
1024C4—44no—
1025C4—44no—
1026C4#348514yes—
1027C2—24no—
1028C2—24no—
1029C2—24no—
1030C2—44no—
1031C2—84no—
1032C2—84no—
1033C2C22×#53511yescharacteristic
1034C2C2×#348511yescharacteristic
1035C2#6285911yescharacteristic
1036C2#6290114yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3505C2semidirect
2. C22×#547C2semidirect
3. #41413C2semidirect
4. #41409C2semidirect
5. #38082C2semidirect
6. #38079C2semidirect
7. #37864C2semidirect
8. #37863C2semidirect
9. #37632C2semidirect
10. #37448C2semidirect
11. #37118C2semidirect
12. #36956C2semidirect
13. #35447C2semidirect
14. #35233C2semidirect
15. #35227C2semidirect
16. #35088C2semidirect
17. #35019C2semidirect
18. #35001C2semidirect
19. C2×#2503C2semidirect
20. C2×#2501C2semidirect
21. #34057C2semidirect
24. C2×#553C22semidirect
25. C2×#553C22semidirect
26. C2×#552C22semidirect
27. C2×#551C22semidirect
28. C2×#548C22semidirect
32. C2×#547C22semidirect
33. C2×#547C22semidirect
34. C2×#546C22semidirect
39. C22×C4⋊Q8C22semidirect
44. C22×#123C22semidirect
46. C22×C22⋊Q8C22semidirect
49. C22×#121C22semidirect
52. C22×C4×D4C22semidirect
54. C23×C4⋊C4C22semidirect
55. #2856C22semidirect
56. #2850C22semidirect
57. #2849C22semidirect
58. #2849C22semidirect
59. #2821C22semidirect
60. #2813C22semidirect
61. #2723C22semidirect
62. #2720C22semidirect
63. #2718C22semidirect
64. #2710C22semidirect
65. #2706C22semidirect
66. #2703C22semidirect
67. #2696C22semidirect
68. #2692C22semidirect
69. #2660C22semidirect
70. #2656C22semidirect
71. #2640C22semidirect
72. #2639C22semidirect
73. #2636C22semidirect
74. #2635C22semidirect
75. #2628C22semidirect
76. #2623C22semidirect
77. #2620C22semidirect
78. #2619C22semidirect
79. #2614C22semidirect
80. #2613C22semidirect
81. #2598C22semidirect
82. #2591C22semidirect
83. #2567C22semidirect
84. #2566C22semidirect
85. #2563C22semidirect
86. #2561C22semidirect
87. #2544C22semidirect
89. #2539C22semidirect
90. #2534C22semidirect
91. #2534C22semidirect
92. #2504C22semidirect
93. #2504C22semidirect
94. #2503C22semidirect
95. #2503C22semidirect
96. #2503C22semidirect
97. #2503C22semidirect
98. #2503C22semidirect
99. #2503C22semidirect
100. #2502C22semidirect
105. #2501C22semidirect
106. #2501C22semidirect
107. #2501C22semidirect
108. #2500C22semidirect
109. #2487C22semidirect
110. #2486C22semidirect
111. #2486C22semidirect
112. #2436C22semidirect
113. #2435C22semidirect
115. #2433C22semidirect
116. #2431C22semidirect
117. #2430C22semidirect
118. #2430C22semidirect
119. #2425C22semidirect
120. #2425C22semidirect
121. #2413C22semidirect
122. #2412C22semidirect
123. #2406C22semidirect
124. #2404C22semidirect
125. C2×#400C22semidirect
126. C2×#399C22semidirect
127. #2328C22semidirect
128. #2326C22semidirect
129. #2318C22semidirect
130. #2318C22semidirect
131. #2317C22semidirect
133. #2313C22semidirect
134. #2312C22semidirect
135. #2311C22semidirect
138. C2×#391C22semidirect
139. C2×#390C22semidirect
140. #2290C22semidirect
141. #2290C22semidirect
142. C2×#384C22semidirect
143. #2283C22semidirect
144. C2×#382C22semidirect
145. #2280C22semidirect
247. C2×C4×D4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35052
C22×#5472
#414132
#414092
#380822
#380792
#378642
#378632
#376322
#374482
#371182
#369562
#354472
#352332
#352272
#350882
#350192
#350012
C2×#25032
C2×#25012
#340572