Finite Group Databasebeta

← #7630367

Subgroups — #7630367

Order 512.

8106 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3475C212yesmaximal, complemented
2#36645C211yesmaximal, characteristic, complemented
3#36631C212yesmaximal, complemented
4#36594C211yesmaximal, characteristic, complemented
5#36559C211yesmaximal, characteristic, complemented
6#36534C212yesmaximal, complemented
7#36468C214yesmaximal, complemented
8#36415C212yesmaximal, complemented
9#36386C214yesmaximal, complemented
10#36270C214yesmaximal, complemented
11#36262C218yesmaximal, complemented
12#36187C211yesmaximal, characteristic, complemented
13#36181C212yesmaximal, complemented
14#36127C211yesmaximal, characteristic, complemented
15#36121C212yesmaximal, complemented
16#34946C212yesmaximal, complemented
17#34935C214yesmaximal, complemented
18#34914C218yesmaximal, complemented
19#34910C214yesmaximal, complemented
20D4×#117C214yesmaximal, complemented
21C4×#532C212yesmaximal, complemented
22C2×C4×#127C211yesmaximal, characteristic, complemented
23C42×#41C211yesmaximal, characteristic, complemented
24#3475—232no—
25C2×#556C2212yescomplemented
26C2×#555C2212yescomplemented
27C2×#554C2212yescomplemented
28C2×#553C2214yescomplemented
29C2×#552C2214yes—
30C2×#552C2214yescomplemented
31C2×#551C2218yes—
32C2×#547C2212yescomplemented
33C2×#546C2214yes—
34C2×#533C2212yes—
35C2×#532C2212yes—
36C22×#127C2211yescharacteristic
37C2×#529C2214yescomplemented
38C2×#529C2218yescomplemented
39C2×#525C2214yes—
40C2×C4×#41C2212yes—
41C2×C4×#41C2211yescharacteristic
42C2×C4×#41C2214yescomplemented
43C22×C4×D4C2214yes—
44C22×C4×D4C2212yes—
45C22×#117C2214yes—
46#2868C2211yescharacteristic, complemented
47#2868C2211yescharacteristic, complemented
48#2862C2212yescomplemented
49#2861C2214yescomplemented
50#2860C2218yescomplemented
51#2859C2212yescomplemented
52#2859C2214yescomplemented
53#2858C2212yes—
54#2857C2212yes—
55#2857C2212yes—
56#2857C2214yes—
57#2857C2212yescomplemented
58#2856C2212yes—
59#2854C2218yescomplemented
60#2850C2214yescomplemented
61#2602C22116yescomplemented
62#2601C22116yescomplemented
63#2566C2214yescomplemented
64#2565C2214yescomplemented
65#2563C2212yescomplemented
66#2563C2212yescomplemented
67#2562C2218yescomplemented
68#2561C2218yes—
69#2560C22116yescomplemented
70#2559C22116yescomplemented
71#2558C22116yescomplemented
72#2557C22116yescomplemented
73#2547C2212yescomplemented
74#2547C2212yescomplemented
75#2545C2214yescomplemented
76#2544C2214yes—
77#2538C2214yescomplemented
78#2538C2214yescomplemented
79#2537C2214yescomplemented
80#2537C2214yescomplemented
81#2536C2218yescomplemented
82#2535C2218yescomplemented
83#2534C22116yes—
84#2512C2218yescomplemented
85#2506C2218yescomplemented
86#2503C2214yes—
87#2500C2214yescomplemented
88#2499C2214yescomplemented
89#2496C2218yescomplemented
90#2491C2218yescomplemented
91#2486C2218yes—
92#2452C2218yescomplemented
93#2445C2218yes—
94#2435C2214yes—
95#2432C2214yescomplemented
96#2431C2214yes—
97#2428C2218yes—
98#2422C2218yescomplemented
99#2408C2218yes—
100#2398C2218yescomplemented
101#2392C22116yescomplemented
102#2354C2214yescomplemented
103#2354C2214yescomplemented
104#2352C2218yescomplemented
105#2352C2218yescomplemented
106D4×C4⋊C4C2214yescomplemented
107D4×C4⋊C4C2214yescomplemented
108#2344C2218yes—
109#2342C22116yes—
110D4×C22⋊C4C2218yes—
111C4×C4⋊Q8C2212yescomplemented
112C4×C4⋊Q8C2212yescomplemented
113C4×C4⋊Q8C2214yescomplemented
114C4×C4⋊Q8C2212yescomplemented
115C4×#127C2211yescharacteristic
116C4×#127C2212yes—
117C4×#127C2211yescharacteristic
118C4×#127C2212yes—
119C4×#127C2211yescharacteristic
120C4×#127C2212yes—
121C4×#127C2214yes—
122C4×#127C2214yes—
123C4×#127C2211yescharacteristic
124C4×#124C2214yescomplemented
125C4×#124C2214yescomplemented
126C4×#124C2214yescomplemented
127C4×#121C2218yescomplemented
128C4×#121C2218yescomplemented
129C4×#121C2218yescomplemented
130#2297C2214yescomplemented
131#2293C2218yescomplemented
132#2293C2218yescomplemented
133C2×#390C2212yes—
134C2×#390C2214yes—
135#2290C22116yescomplemented
136#2285C2214yes—
137#2285C2212yescomplemented
138C2×#384C2211yescharacteristic
139#2280C2218yes—
140C42×Q8C2212yescomplemented
141C42×Q8C2211yescharacteristic, complemented
142C42×Q8C2211yescharacteristic, complemented
143C42×D4C2212yes—
144C42×D4C2212yes—
145C42×D4C2214yes—
146C42×D4C2211yescharacteristic, complemented
147C42×D4C2211yescharacteristic, complemented
148C42×D4C2218yescomplemented
149C42×D4C2212yescomplemented
150C4×#117C2212yes—
151C4×#117C2211yescharacteristic
152C4×#117C2212yescomplemented
153C4×#117C2214yescomplemented
154C2×C43C2211yescharacteristic
155C2×C43C2212yescomplemented
156C22×#41C2314yes—
157C22×#41C2311yescharacteristic
158C23×D4C2314yes—
159C23×D4C2312yes—
160C24×C4C2314yes—
161#556—216no—
162#555—216no—
163#554—216no—
164#553—232no—
165#552—232no—
166#552—232no—
167#551—264no—
168#547—216no—
169#546—232no—
170#533—216no—
171#532—216no—
172C2×C4⋊Q8C2312yes—
173C2×C4⋊Q8C2312yes—
174C2×C4⋊Q8C2312yes—
175C2×C4⋊Q8C2312yes—
176C2×C4⋊Q8C2314yes—
177C2×#127—28no—
178C2×#127C2311yescharacteristic
179C2×#127C2314yes—
180C2×#127C2312yes—
181C2×#127C2311yescharacteristic
182#529—264no—
183#529—232no—
184C2×#126C2318yes—
185C2×#126C2318yes—
186C2×#126C2318yes—
187C2×#125C2314yes—
188C2×#125C2314yes—
189C2×#125C2318yes—
190C2×#124C2314yes—
191C2×#124C2318yes—
192C2×#124C2314yes—
193C2×#124C2314yes—
194#525—232no—
195C2×#123C2318yes—
196C2×#123C2318yes—
197C2×#123C2318yes—
198C2×#123C2318yes—
199C2×C22⋊Q8C2318yes—
200C2×C22⋊Q8C2314yes—
201C2×C22⋊Q8C2314yes—
202C2×C22⋊Q8C2314yes—
203C2×C22⋊Q8C2314yes—
204C2×C22⋊Q8C2314yes—
205C2×#121C2314yes—
206C2×#121C2318yes—
207C2×#121C2314yes—
208C2×#121C2314yes—
209C2×#121C2318yes—
210C2×#121C2318yes—
211C2×#120C2318yes—
212C4×#41—232no—
213C4×#41—216no—
214C4×#41D4116yescomplemented
215C2×C4×Q8C2314yes—
216C2×C4×Q8C2314yes—
217C2×C4×Q8C2314yes—
218C2×C4×Q8C2312yes—
219C2×C4×Q8C2312yes—
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×D4—216no—
223C2×C4×D4—232no—
224C2×C4×D4C2314yes—
225C2×C4×D4C2312yes—
226C2×C4×D4C2312yes—
227C2×C4×D4C2314yes—
228C2×C4×D4C2318yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2318yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2318yes—
238C2×C4×D4C2318yes—
239C2×C4×D4C2318yes—
240C2×C4×D4C2318yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2318yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×#117—232no—
251C2×#117C2318yes—
252C2×#117C2318yes—
253C2×#117C2314yes—
254C2×#117C2314yes—
255C2×#117C2314yes—
256C2×#117C2314yes—
257C2×#117C2318yes—
258C2×#117C2312yes—
259C2×#117C2314yes—
260C2×#117C2311yescharacteristic
261C2×#117C2312yes—
262C22×C4⋊C4C2314yes—
263C22×C4⋊C4C2314yes—
264C22×C4⋊C4C2314yes—
265C22×C4⋊C4C2312yes—
266C22×C22⋊C4C2314yes—
267C22×C22⋊C4C2318yes—
268C22×C22⋊C4C2318yes—
269C22×C42C2312yes—
270C22×C42C2311yescharacteristic
271C22×C42C2318yes—
272C22×C42C2314yes—
273C22×C42C2312yes—
274C22×C42C2314yes—
275C22×C42C2312yes—
276C22×C42C2311yescharacteristic
277C22×C42C2311yescharacteristic
278C22×C42C2312yes—
279C22×C42C2312yes—
280#400C23116yes—
281#398C23116yes—
282#397C2318yes—
283#397C2318yes—
284#397C23116yes—
285#396C23116yes—
286#396C23116yes—
287#394C23116yes—
288#394C23116yes—
289#394C23116yes—
290#394C23116yes—
291#393C2318yes—
292#393C2318yes—
293#392C23116yes—
294#391C2318yes—
295#391C2314yes—
296#391C2314yes—
297#391C2314yes—
298#391C2314yes—
299#390C2318yes—
300#390C2312yes—
301#390C2312yes—
302#390C2314yes—
303#390C2318yes—
304#390C2314yes—
305#390C2314yes—
306#390C2312yes—
307#390C2314yes—
308#390C2312yes—
309#390C2318yes—
310#390C2314yes—
311#390C2318yes—
312#390C2314yes—
313#390C2318yes—
314#390C2318yes—
315#390C2318yes—
316#389C2318yes—
317#389C2318yes—
318#389C2318yes—
319#389C2318yes—
320#389C2318yes—
321#389C2318yes—
322#389C2318yes—
323#389C2318yes—
324#388C23116yes—
325#388C23116yes—
326#388C23116yes—
327#388C23116yes—
328#388C23116yes—
329#388C23116yes—
330#388C23116yes—
331#388C23116yes—
332#387C23116yes—
333#387C23116yes—
334#386C23116yes—
335#386C23116yes—
336#386C23116yes—
337#386C23116yes—
338#385C23116yes—
339#385C23116yes—
340#384C2311yescharacteristic
341#384C2312yes—
342#384C2311yescharacteristic
343#384C2314yes—
344#384C2312yes—
345#384C2312yes—
346#384C2314yes—
347#384C2314yes—
348#384C2314yes—
349#382C2314yes—
350#382C2314yes—
351#382C2318yes—
352#381C23116yes—
353#380C2318yes—
354#380C2318yes—
355#380C2318yes—
356#380C2318yes—
357#380C2318yes—
358#380C2318yes—
359#380C2318yes—
360#380C2318yes—
361#379C23116yes—
362C4×C4⋊C4C2314yes—
363C4×C4⋊C4C2312yes—
364C4×C4⋊C4C2318yes—
365C4×C4⋊C4C2318yes—
366C4×C4⋊C4C2318yes—
367C4×C4⋊C4C2311yescharacteristic
368C4×C4⋊C4C2311yescharacteristic
369C4×C4⋊C4C2312yes—
370C4×C4⋊C4C2312yes—
371C4×C4⋊C4C2318yes—
372C4×C4⋊C4C2314yes—
373C4×C4⋊C4C2312yes—
374C4×C4⋊C4C2312yes—
375C4×C4⋊C4C2312yes—
376C4×C4⋊C4C2312yes—
377C4×C4⋊C4C2314yes—
378C4×C4⋊C4C2314yes—
379C4×C4⋊C4C2314yes—
380C4×C22⋊C4C23116yes—
381C4×C22⋊C4C2312yes—
382C4×C22⋊C4C2314yes—
383C4×C22⋊C4C2314yes—
384C4×C22⋊C4C23116yes—
385C4×C22⋊C4C2314yes—
386C4×C22⋊C4C23116yes—
387C4×C22⋊C4C23116yes—
388C4×C22⋊C4C2314yes—
389C4×C22⋊C4C2314yes—
390C4×C22⋊C4C2312yes—
391C4×C22⋊C4C2312yes—
392C4×C22⋊C4C2312yes—
393C4×C22⋊C4C2314yes—
394C4×C22⋊C4C2314yes—
395#376C2312yes—
396#376C2314yes—
397C43C2311yescharacteristic
398C43C2312yes—
399C43C2311yescharacteristic
400C43C2312yes—
401C43C2311yescharacteristic
402C43C2311yescharacteristic
403C43C2312yes—
404C43C2314yes—
405C43C2312yes—
406C43C2314yes—
407C43C2312yes—
408C25C2414yes—
409C2×#41—216no—
410C2×#41—216no—
411C2×#41—28no—
412C2×#41—48no—
413C2×#41C2×D418yes—
414C22×Q8C2414yes—
415C22×Q8C2411yescharacteristic
416C22×Q8C2414yes—
417C22×D4—216no—
418C22×D4—28no—
419C22×D4—28no—
420C22×D4—216no—
421C22×D4—48no—
422C22×D4—44no—
423C22×D4C2412yes—
424C22×D4C2414yes—
425C22×D4C2418yes—
426C22×D4C2414yes—
427C22×D4C2418yes—
428C22×D4C2412yes—
429C22×D4C2411yescharacteristic
430C22×D4C2414yes—
431C22×D4C2412yes—
432C22×D4C2418yes—
433C23×C4—216no—
434C23×C4—232no—
435C23×C4C2414yes—
436C23×C4C2414yes—
437C23×C4C2414yes—
438C23×C4C2414yes—
439C23×C4C2414yes—
440C23×C4C2414yes—
441C23×C4C2418yes—
442C23×C4C2411yescharacteristic
443C23×C4C2412yes—
444C23×C4C2412yes—
445C23×C4C2412yes—
446C23×C4C2418yes—
447C23×C4C2414yes—
448C23×C4C2411yescharacteristic
449C23×C4C2412yes—
450C23×C4C2412yes—
451C23×C4C2411yescharacteristic
452C4⋊Q8—28no—
453C4⋊Q8—28no—
454C4⋊Q8—28no—
455C4⋊Q8—48no—
456C4⋊Q8—44no—
457#127—216no—
458#127—28no—
459#127—24no—
460#127#4118yescomplemented
461#126—232no—
462#126—232no—
463#126—232no—
464#125—232no—
465#125—216no—
466#125—216no—
467#124—216no—
468#124—232no—
469#124—216no—
470#124—48no—
471#123—232no—
472#123—232no—
473#123—232no—
474#123—232no—
475C22⋊Q8—216no—
476C22⋊Q8—216no—
477C22⋊Q8—216no—
478C22⋊Q8—216no—
479C22⋊Q8—216no—
480C22⋊Q8—232no—
481#121—216no—
482#121—216no—
483#121—232no—
484#121—216no—
485#121—232no—
486#121—416no—
487#120—232no—
488C4×Q8—216no—
489C4×Q8—216no—
490C4×Q8—216no—
491C4×Q8—28no—
492C4×Q8—28no—
493C4×Q8C2×D418yescomplemented
494C4×Q8C2×D418yescomplemented
495C4×D4—232no—
496C4×D4—232no—
497C4×D4—232no—
498C4×D4—232no—
499C4×D4—216no—
500C4×D4—216no—
501C4×D4—28no—
502C4×D4—28no—
503C4×D4—216no—
504C4×D4—28no—
505C4×D4—216no—
506C4×D4—28no—
507C4×D4—216no—
508C4×D4—216no—
509C4×D4—216no—
510C4×D4—232no—
511C4×D4—216no—
512C4×D4—232no—
513C4×D4—216no—
514C4×D4—28no—
515C4×D4—28no—
516C4×D4—416no—
517C4×D4C2×D4116yes—
518C4×D4C2×D4116yes—
519C4×D4C2×D418yescomplemented
520C4×D4C2×D418yescomplemented
521#117—216no—
522#117—216no—
523#117—28no—
524#117—216no—
525#117—216no—
526#117—232no—
527#117—232no—
528#117—232no—
529#117—216no—
530#117C2×D418yes—
531#117C2×D4116yescomplemented
532C2×C4⋊C4—28no—
533C2×C4⋊C4—216no—
534C2×C4⋊C4—216no—
535C2×C4⋊C4—216no—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2411yescharacteristic
561C2×C4⋊C4C2411yescharacteristic
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2412yes—
564C2×C22⋊C4—216no—
565C2×C22⋊C4—232no—
566C2×C22⋊C4—232no—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2418yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C24116yes—
586C2×C22⋊C4C24116yes—
587C2×C22⋊C4C24116yes—
588C2×C22⋊C4C24116yes—
589C2×C22⋊C4C2412yes—
590C2×C22⋊C4C2412yes—
591C2×C22⋊C4C2412yes—
592C2×C42—232no—
593C2×C42—216no—
594C2×C42—24no—
595C2×C42—28no—
596C2×C42—48no—
597C2×C42—44no—
598C2×C42—42no—
599C2×C42—44no—
600C2×C42C2×D418yes—
601C2×C42C2×D4116yescomplemented
602C2×C42#41116yescomplemented
603C2×C42C2418yes—
604C2×C42C2418yes—
605C2×C42C2414yes—
606C2×C42C2414yes—
607C2×C42C2414yes—
608C2×C42C2414yes—
609C2×C42C2412yes—
610C2×C42C2412yes—
611C2×C42C2412yes—
612C2×C42C2411yescharacteristic
613C2×C42C2412yes—
614C2×C42C2411yescharacteristic
615C2×C42C2412yes—
616C2×C42C2411yescharacteristic
617C2×C42C2418yes—
618C2×C42C2414yes—
619C2×C42C2414yes—
620C2×C42C2414yes—
621C2×C42C2414yes—
622C2×C42C2412yes—
623C2×C42C2412yes—
624C2×C42C2412yes—
625C2×C42C2412yes—
626C2×C42C2411yescharacteristic
627C2×C42C2411yescharacteristic
628C2×C42C2412yes—
629C2×C42C2412yes—
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632C2×C42C2412yes—
633C2×C42C2412yes—
634C2×C42C2411yescharacteristic
635C2×C42C2412yes—
636C2×C42C2412yes—
637#95C2414yes—
638#95C2414yes—
639#95C2414yes—
640#95C2414yes—
641#95C2412yes—
642#95C2412yes—
643#95C2414yes—
644#95C24116yes—
645#95C24116yes—
646#95C24116yes—
647#95C24116yes—
648#95C24116yes—
649#95C24116yes—
650C24—28no—
651C24—28no—
652C24—216no—
653C24—48no—
654C24—44no—
655C24C2514yes—
656C24C2512yes—
657C24C2514yes—
658C24C2511yescharacteristic
659#41—232no—
660#41—464no—
661C2×Q8—28no—
662C2×Q8—28no—
663C2×Q8—24no—
664C2×Q8—28no—
665C2×Q8—28no—
666C2×Q8—48no—
667C2×Q8C22×D414yes—
668C2×D4—28no—
669C2×D4—216no—
670C2×D4—216no—
671C2×D4—28no—
672C2×D4—216no—
673C2×D4—216no—
674C2×D4—24no—
675C2×D4—28no—
676C2×D4—24no—
677C2×D4—28no—
678C2×D4—24no—
679C2×D4—216no—
680C2×D4—28no—
681C2×D4—24no—
682C2×D4—28no—
683C2×D4—28no—
684C2×D4—24no—
685C2×D4—28no—
686C2×D4—24no—
687C2×D4—432no—
688C2×D4—464no—
689C2×D4—48no—
690C2×D4—44no—
691C2×D4—48no—
692C2×D4—416no—
693C2×D4C22×D418yes—
694C2×D4C22×D414yes—
695C2×D4C2×#41116yes—
696C2×D4C2×#4118yes—
697C22×C4—28no—
698C22×C4—22no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—22no—
702C22×C4—24no—
703C22×C4—24no—
704C22×C4—28no—
705C22×C4—216no—
706C22×C4—216no—
707C22×C4—28no—
708C22×C4—216no—
709C22×C4—28no—
710C22×C4—28no—
711C22×C4—28no—
712C22×C4—28no—
713C22×C4—28no—
714C22×C4—28no—
715C22×C4—216no—
716C22×C4—216no—
717C22×C4—216no—
718C22×C4—216no—
719C22×C4—28no—
720C22×C4—216no—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—44no—
724C22×C4—42no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—48no—
728C22×C4—416no—
729C22×C4—464no—
730C22×C4C22×D414yes—
731C22×C4C22×D418yes—
732C22×C4C22×D418yes—
733C22×C4C22×D414yes—
734C22×C4C22×D418yes—
735C22×C4C22×D414yes—
736C22×C4C2×#4118yes—
737C22×C4C2×#4118yes—
738C22×C4C2×#4118yes—
739C22×C4C2514yes—
740C22×C4C2514yes—
741C22×C4C2514yes—
742C22×C4C2518yes—
743C22×C4C2518yes—
744C22×C4C2514yes—
745C22×C4C2512yes—
746C22×C4C2512yes—
747C22×C4C2511yescharacteristic
748C22×C4C2511yescharacteristic
749C22×C4C2511yescharacteristic
750C22×C4C2512yes—
751C22×C4C2512yes—
752C22×C4C2512yes—
753C22×C4C2512yes—
754C22×C4C2511yescharacteristic
755C22×C4C2511yescharacteristic
756C22×C4C2512yes—
757C22×C4C2511yescharacteristic
758C4⋊C4—24no—
759C4⋊C4—28no—
760C4⋊C4—28no—
761C4⋊C4—216no—
762C4⋊C4—216no—
763C4⋊C4—24no—
764C4⋊C4—28no—
765C4⋊C4—28no—
766C4⋊C4—216no—
767C4⋊C4—216no—
768C4⋊C4—216no—
769C4⋊C4—216no—
770C4⋊C4—28no—
771C4⋊C4—216no—
772C4⋊C4—28no—
773C4⋊C4—28no—
774C4⋊C4—28no—
775C4⋊C4—28no—
776C4⋊C4—24no—
777C4⋊C4—24no—
778C4⋊C4—216no—
779C4⋊C4—216no—
780C4⋊C4—48no—
781C4⋊C4—48no—
782C4⋊C4C22×D414yes—
783C4⋊C4C22×D414yes—
784C4⋊C4C22×D418yes—
785C4⋊C4C22×D418yes—
786C22⋊C4—216no—
787C22⋊C4—216no—
788C22⋊C4—216no—
789C22⋊C4—28no—
790C22⋊C4—232no—
791C22⋊C4—28no—
792C22⋊C4—216no—
793C22⋊C4—216no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—216no—
798C22⋊C4—216no—
799C22⋊C4—216no—
800C22⋊C4—216no—
801C22⋊C4—216no—
802C22⋊C4—216no—
803C22⋊C4—28no—
804C22⋊C4—28no—
805C22⋊C4—416no—
806C22⋊C4—416no—
807C22⋊C4—416no—
808C22⋊C4C22×D418yes—
809C22⋊C4C22×D418yes—
810C22⋊C4C22×D418yes—
811C42—216no—
812C42—216no—
813C42—216no—
814C42—28no—
815C42—28no—
816C42—28no—
817C42—28no—
818C42—24no—
819C42—22no—
820C42—24no—
821C42—22no—
822C42—24no—
823C42—28no—
824C42—24no—
825C42—22no—
826C42—24no—
827C42—42no—
828C42—42no—
829C42—44no—
830C42—42no—
831C42—44no—
832C42—44no—
833C42C22×D418yes—
834C42C22×D414yes—
835C42C22×D414yes—
836C42C22×D414yes—
837C42C22×D414yes—
838C42C22×D418yes—
839C42C22×D418yes—
840C42C2×#4114yes—
841C42C2×#4118yes—
842C42C2×#4118yes—
843C42C2×#4118yes—
844C42C2×#4118yes—
845C23—21no—
846C23—22no—
847C23—21no—
848C23—24no—
849C23—24no—
850C23—28no—
851C23—22no—
852C23—28no—
853C23—24no—
854C23—22no—
855C23—24no—
856C23—24no—
857C23—28no—
858C23—24no—
859C23—24no—
860C23—28no—
861C23—416no—
862C23—432no—
863C23—416no—
864C23—88no—
865C23—816no—
866C23C23×D414yes—
867C23C23×D412yes—
868C23C22×#4118yes—
869C23C22×#4114yes—
870C23C2611yescharacteristic
871Q8—28no—
872Q8—416no—
873Q8—88no—
874D4—216no—
875D4—28no—
876D4—216no—
877D4—232no—
878D4—416no—
879D4—432no—
880D4—432no—
881D4—48no—
882D4—416no—
883D4—816no—
884C2×C4—24no—
885C2×C4—22no—
886C2×C4—21no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—24no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—21no—
897C2×C4—22no—
898C2×C4—216no—
899C2×C4—28no—
900C2×C4—216no—
901C2×C4—216no—
902C2×C4—24no—
903C2×C4—28no—
904C2×C4—28no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—24no—
909C2×C4—28no—
910C2×C4—28no—
911C2×C4—28no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—216no—
916C2×C4—28no—
917C2×C4—48no—
918C2×C4—44no—
919C2×C4—48no—
920C2×C4—432no—
921C2×C4—416no—
922C2×C4—416no—
923C2×C4—416no—
924C2×C4—416no—
925C2×C4—416no—
926C2×C4—416no—
927C2×C4—416no—
928C2×C4—816no—
929C2×C4#532116yescomplemented
930C2×C4C23×D414yes—
931C2×C4C23×D414yes—
932C2×C4C23×D412yes—
933C2×C4C23×D412yes—
934C2×C4C23×D414yes—
935C2×C4C23×D412yes—
936C2×C4C23×D412yes—
937C2×C4C23×D412yes—
938C2×C4C23×D412yes—
939C2×C4C22×#4114yes—
940C2×C4C22×#4114yes—
941C2×C4C22×#4114yes—
942C2×C4C22×#4114yes—
943C2×C4C22×#4114yes—
944C2×C4C22×#4112yes—
945C2×C4C22×#4114yes—
946C2×C4C22×#4114yes—
947C2×C4#58512yes—
948C2×C4#58514yes—
949C22—22no—
950C22—24no—
951C22—22no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—24no—
956C22—28no—
957C22—216no—
958C22—44no—
959C22—44no—
960C22—48no—
961C22—44no—
962C22—44no—
963C22—44no—
964C22—48no—
965C22—44no—
966C22—44no—
967C22—48no—
968C22—832no—
969C22C2×#53214yes—
970C22C24×D411yescharacteristic
971C22C23×#4112yes—
972C22C23×#4111yescharacteristic
973C22C2×#58512yes—
974C22C2×#58511yescharacteristic
975C4—22no—
976C4—24no—
977C4—22no—
978C4—24no—
979C4—24no—
980C4—24no—
981C4—24no—
982C4—22no—
983C4—24no—
984C4—48no—
985C4—44no—
986C4—44no—
987C4—44no—
988C4—48no—
989C4—44no—
990C4C2×#53214yes—
991C4C2×#53214yes—
992C4D4×#4114yes—
993C4#347518yescomplemented
994C2—24no—
995C2—44no—
996C2—48no—
997C2—84no—
998C2C22×#53211yescharacteristic
999C2C2×D4×#4111yescharacteristic
1000C2C2×#347512yes—
1001C2#6281211yescharacteristic
1002C2#6281512yes—
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3475C2semidirect
2. #36645C2semidirect
3. #36631C2semidirect
4. #36594C2semidirect
5. #36559C2semidirect
6. #36534C2semidirect
7. #36468C2semidirect
8. #36415C2semidirect
9. #36386C2semidirect
10. #36270C2semidirect
11. #36262C2semidirect
12. #36187C2semidirect
13. #36181C2semidirect
14. #36127C2semidirect
15. #36121C2semidirect
16. #34946C2semidirect
17. #34935C2semidirect
18. #34914C2semidirect
19. #34910C2semidirect
20. D4×#117C2semidirect
21. C4×#532C2semidirect
22. C2×C4×#127C2semidirect
23. C42×#41C2semidirect
25. C2×#556C22semidirect
26. C2×#555C22semidirect
27. C2×#554C22semidirect
28. C2×#553C22semidirect
30. C2×#552C22semidirect
32. C2×#547C22semidirect
37. C2×#529C22semidirect
38. C2×#529C22semidirect
42. C2×C4×#41C22semidirect
46. #2868C22semidirect
47. #2868C22semidirect
48. #2862C22semidirect
49. #2861C22semidirect
50. #2860C22semidirect
51. #2859C22semidirect
52. #2859C22semidirect
57. #2857C22semidirect
59. #2854C22semidirect
60. #2850C22semidirect
61. #2602C22semidirect
62. #2601C22semidirect
63. #2566C22semidirect
64. #2565C22semidirect
65. #2563C22semidirect
66. #2563C22semidirect
67. #2562C22semidirect
69. #2560C22semidirect
70. #2559C22semidirect
71. #2558C22semidirect
72. #2557C22semidirect
73. #2547C22semidirect
74. #2547C22semidirect
75. #2545C22semidirect
77. #2538C22semidirect
78. #2538C22semidirect
79. #2537C22semidirect
80. #2537C22semidirect
81. #2536C22semidirect
82. #2535C22semidirect
84. #2512C22semidirect
85. #2506C22semidirect
87. #2500C22semidirect
88. #2499C22semidirect
89. #2496C22semidirect
90. #2491C22semidirect
92. #2452C22semidirect
95. #2432C22semidirect
98. #2422C22semidirect
100. #2398C22semidirect
101. #2392C22semidirect
102. #2354C22semidirect
103. #2354C22semidirect
104. #2352C22semidirect
105. #2352C22semidirect
106. D4×C4⋊C4C22semidirect
107. D4×C4⋊C4C22semidirect
111. C4×C4⋊Q8C22semidirect
112. C4×C4⋊Q8C22semidirect
113. C4×C4⋊Q8C22semidirect
114. C4×C4⋊Q8C22semidirect
124. C4×#124C22semidirect
125. C4×#124C22semidirect
126. C4×#124C22semidirect
127. C4×#121C22semidirect
128. C4×#121C22semidirect
129. C4×#121C22semidirect
130. #2297C22semidirect
131. #2293C22semidirect
132. #2293C22semidirect
135. #2290C22semidirect
137. #2285C22semidirect
140. C42×Q8C22semidirect
141. C42×Q8C22semidirect
142. C42×Q8C22semidirect
146. C42×D4C22semidirect
147. C42×D4C22semidirect
148. C42×D4C22semidirect
149. C42×D4C22semidirect
152. C4×#117C22semidirect
153. C4×#117C22semidirect
155. C2×C43C22semidirect
214. C4×#41D4semidirect
460. #127#41semidirect
493. C4×Q8C2×D4semidirect
494. C4×Q8C2×D4semidirect
519. C4×D4C2×D4semidirect
520. C4×D4C2×D4semidirect
531. #117C2×D4semidirect
601. C2×C42C2×D4semidirect
602. C2×C42#41semidirect
929. C2×C4#532semidirect
993. C4#3475semidirect

Maximal subgroups

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

subgroupindex
C2×#34752
#366452
#366312
#365942
#365592
#365342
#364682
#364152
#363862
#362702
#362622
#361872
#361812
#361272
#361212
#349462
#349352
#349142
#349102
D4×#1172
C4×#5322
C2×C4×#1272
C42×#412