Finite Group Databasebeta

← #7672210

Subgroups — #7672210

Order 512.

8210 conjugacy classes of subgroups.

The subgroup lattice has 1041 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3499C211yesmaximal, characteristic, complemented
2C22×#533C211yesmaximal, characteristic, complemented
3#59042C214yesmaximal, complemented
4#59040C214yesmaximal, complemented
5#59036C214yesmaximal, complemented
6#59034C214yesmaximal, complemented
7#38907C214yesmaximal, complemented
8#38905C214yesmaximal, complemented
9#37749C218yesmaximal, complemented
10#36624C211yesmaximal, characteristic, complemented
11#36426C214yesmaximal, complemented
12#36422C214yesmaximal, complemented
13#36150C214yesmaximal, complemented
14#36129C214yesmaximal, complemented
15#35661C212yesmaximal, complemented
16#35659C212yesmaximal, complemented
17#35289C211yesmaximal, characteristic, complemented
18#35279C211yesmaximal, characteristic, complemented
19#35182C212yesmaximal, complemented
20#34257C212yesmaximal, complemented
21#34209C211yesmaximal, characteristic, complemented
22C4×#525C211yesmaximal, characteristic, complemented
23C22×2−1+4C2212yes—
24#3499—216no—
25C2×D4×Q8C2212yescomplemented
26C2×D4×Q8C2212yescomplemented
27C2×#547C2214yes—
28C2×#547C2214yes—
29C2×#547C2212yescomplemented
30C2×#547C2212yescomplemented
31C2×#536C2212yes—
32C2×#536C2214yescomplemented
33C2×#533—216no—
34C2×#533C2214yes—
35C2×#533C2214yes—
36C2×#533C2214yes—
37C2×#533C2214yes—
38C2×#532C2211yescharacteristic
39C2×#532C2212yescomplemented
40C22×C4⋊Q8C2211yescharacteristic
41C22×C4⋊Q8C2211yescharacteristic
42C22×C4⋊Q8C2212yescomplemented
43C22×#125C2212yes—
44C2×#525C2211yescharacteristic
45C2×#525C2212yes—
46C22×C22⋊Q8C2212yes—
47C22×C22⋊Q8C2212yes—
48C2×#519C2212yes—
49C2×C4×#41C2211yescharacteristic
50C22×C4×Q8C2212yes—
51C22×C4×Q8C2212yes—
52C22×#117C2212yes—
53C23×C42C2211yescharacteristic
54#2862C2212yescomplemented
55#2858C2212yescomplemented
56#2857C2212yes—
57#2857C2214yescomplemented
58#2856C2212yes—
59#2854C2212yes—
60#2854C2212yes—
61#2853C2218yes—
62#2850C2214yes—
63#2847C2212yes—
64#2847C2212yes—
65#2696C22116yes—
66#2694C22116yescomplemented
67#2692C22116yes—
68#2690C22116yescomplemented
69#2640C2214yescomplemented
70#2628C2214yescomplemented
71#2623C2218yes—
72#2568C2212yescomplemented
73#2567C2212yescomplemented
74#2563C2212yescomplemented
75#2563C2214yescomplemented
76#2550C2218yescomplemented
77#2547C2214yescomplemented
78#2542C2212yescomplemented
79#2540C2218yes—
80#2538C2218yes—
81#2536C2218yes—
82#2504C2214yes—
83#2492C2218yes—
84#2490C2218yescomplemented
85#2487C2214yes—
86#2477C22116yes—
87#2471C22116yes—
88#2465C22116yescomplemented
89#2458C22116yescomplemented
90#2454C2218yescomplemented
91#2451C2218yescomplemented
92#2448C2218yescomplemented
93#2446C2218yescomplemented
94#2442C2218yescomplemented
95#2439C2218yes—
96#2436C2214yes—
97#2429C2218yes—
98#2427C2218yes—
99#2426C2218yes—
100#2426C2218yescomplemented
101#2423C2218yescomplemented
102#2421C2218yescomplemented
103#2417C2218yes—
104#2414C2218yes—
105#2413C2218yes—
106#2411C2218yes—
107#2409C2218yes—
108#2409C2214yes—
109#2409C2218yes—
110#2407C2218yes—
111#2407C2218yes—
112#2406C2218yes—
113#2404C2218yes—
114#2367C2218yescomplemented
115#2365C2214yescomplemented
116#2365C2214yescomplemented
117#2363C2218yes—
118#2360C2218yescomplemented
119#2352C2218yes—
120#2344C2214yes—
121#2344C2214yes—
122#2341C2218yescomplemented
123#2341C2218yescomplemented
124Q8×C22⋊C4C2218yescomplemented
125Q8×C22⋊C4C2218yescomplemented
126#2327C2214yescomplemented
127#2317C2212yes—
128#2311C2212yes—
129#2311C2212yes—
130#2311C2212yes—
131#2311C2218yes—
132#2310C2212yes—
133C4×C4⋊Q8C2214yescomplemented
134C4×C22⋊Q8C2212yes—
135C4×C22⋊Q8C2212yes—
136C4×#123C2212yes—
137C4×#123C2212yes—
138C4×#121C2214yes—
139C4×#121C2214yes—
140C4×#121C2212yes—
141C4×#121C2212yes—
142C4×#120C2212yes—
143C4×#120C2212yes—
144#2297C2212yes—
145#2297C2218yes—
146#2297C2211yescharacteristic
147#2296C2211yescharacteristic
148#2290C2214yes—
149#2285C2211yescharacteristic
150#2280C2211yescharacteristic
151C42×D4C2214yes—
152C4×#117C2211yescharacteristic
153C2×2−1+4—216no—
154C2×2−1+4—216no—
155C2×2−1+4—48no—
156C22×#41C2312yes—
157C22×#41C2318yes—
158C22×#41C2314yes—
159C22×#41C2314yes—
160C22×#41C2311yescharacteristic
161C23×Q8C2314yes—
162C23×Q8C2314yes—
163C23×Q8C2312yes—
164C23×Q8C2312yes—
165C24×C4C2311yescharacteristic
166C24×C4C2311yescharacteristic
167C24×C4C2311yescharacteristic
168D4×Q8—216no—
169D4×Q8—216no—
170#547—216no—
171#547—216no—
172#547—232no—
173#547—232no—
174#536—216no—
175#536—232no—
176#533—232no—
177#533—232no—
178#533—232no—
179#533—232no—
180#532—216no—
181#532—28no—
182C2×C4⋊Q8—216no—
183C2×C4⋊Q8—28no—
184C2×C4⋊Q8D4116yescomplemented
185C2×C4⋊Q8C2312yes—
186C2×C4⋊Q8C2312yes—
187C2×C4⋊Q8C2311yescharacteristic
188C2×C4⋊Q8C2312yes—
189C2×C4⋊Q8C2312yes—
190C2×C4⋊Q8C2314yes—
191C2×C4⋊Q8C2314yes—
192C2×C4⋊Q8C2314yes—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×#127C2311yescharacteristic
198C2×#125—216no—
199C2×#125C2318yes—
200C2×#125C2318yes—
201C2×#124C2312yes—
202C2×#124C2314yes—
203C2×#124C2318yes—
204#525—28no—
205#525—48no—
206C2×#123C2318yes—
207C2×#123C2312yes—
208C2×#123C2318yes—
209C2×#123C2318yes—
210C2×#123C2314yes—
211C2×C22⋊Q8—216no—
212C2×C22⋊Q8—216no—
213C2×C22⋊Q8C2318yes—
214C2×C22⋊Q8C2318yes—
215C2×C22⋊Q8C2312yes—
216C2×C22⋊Q8C2318yes—
217C2×C22⋊Q8C2318yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2318yes—
221C2×C22⋊Q8C2318yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2318yes—
224C2×#121C2312yes—
225C2×#121C2312yes—
226C2×#121C2314yes—
227C2×#121C2312yes—
228C2×#121C2314yes—
229C2×#121C2314yes—
230C2×#121C2314yes—
231C2×#121C2314yes—
232C2×#120C2312yes—
233C2×#120C2314yes—
234#519—48no—
235C4×#41—28no—
236C2×C4×Q8—216no—
237C2×C4×Q8—216no—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2318yes—
241C2×C4×Q8C2318yes—
242C2×C4×Q8C2318yes—
243C2×C4×Q8C2318yes—
244C2×C4×Q8C2318yes—
245C2×C4×Q8C2318yes—
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2312yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2314yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2318yes—
257C2×C4×D4C2314yes—
258C2×#117—216no—
259C2×#117C2311yescharacteristic
260C2×#117C2312yes—
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C2×#117C2318yes—
264C2×#117C2312yes—
265C2×#117C2318yes—
266C2×#117C2318yes—
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2314yes—
269C22×C4⋊C4C2314yes—
270C22×C4⋊C4C2314yes—
271C22×C4⋊C4C2312yes—
272C22×C4⋊C4C2314yes—
273C22×C4⋊C4C2312yes—
274C22×C4⋊C4C2312yes—
275C22×C22⋊C4C2314yes—
276C22×C42—28no—
277C22×C42C2312yes—
278C22×C42C2314yes—
279C22×C42C2311yescharacteristic
280C22×C42C2311yescharacteristic
281C22×C42C2312yes—
282C22×C42C2312yes—
283C22×C42C2311yescharacteristic
284C22×C42C2312yes—
285C22×C42C2312yes—
286C22×C42C2311yescharacteristic
287#400C2318yes—
288#400C23116yes—
289#399C23116yes—
290#399C2318yes—
291#398C23116yes—
292#398C23116yes—
293#397C23116yes—
294#397C23116yes—
295#396C23116yes—
296#396C23116yes—
297#395C2318yes—
298#395C23116yes—
299#394C23116yes—
300#394C23116yes—
301#393C2318yes—
302#393C23116yes—
303#393C23116yes—
304#392C23116yes—
305#391C2318yes—
306#391C2318yes—
307#391C2314yes—
308#391C2314yes—
309#391C23116yes—
310#391C2314yes—
311#391C2318yes—
312#391C2314yes—
313#391C2312yes—
314#391C23116yes—
315#391C2318yes—
316#390C2314yes—
317#390C2318yes—
318#390C2314yes—
319#390C23116yes—
320#390C2314yes—
321#390C2314yes—
322#390C2312yes—
323#390C23116yes—
324#390C2314yes—
325#390C2314yes—
326#390C23116yes—
327#389C2318yes—
328#389C2318yes—
329#389C2318yes—
330#389C2318yes—
331#389C2314yes—
332#389C2314yes—
333#389C23116yes—
334#389C2312yes—
335#389C2312yes—
336#388C2318yes—
337#388C2318yes—
338#388C23116yes—
339#388C23116yes—
340#388C23116yes—
341#388C23116yes—
342#388C2314yes—
343#388C2314yes—
344#387C23116yes—
345#387C23116yes—
346#387C23116yes—
347#387C23116yes—
348#387C2314yes—
349#387C2314yes—
350#386C2312yes—
351#386C2314yes—
352#386C2318yes—
353#386C2318yes—
354#386C2318yes—
355#386C2318yes—
356#386C2318yes—
357#386C2314yes—
358#386C23116yes—
359#386C23116yes—
360#386C2314yes—
361#386C2314yes—
362#386C2312yes—
363#385C2318yes—
364#385C2312yes—
365#385C23116yes—
366#385C23116yes—
367#385C2312yes—
368#385C2314yes—
369#385C2314yes—
370#384C2312yes—
371#384C2314yes—
372#382C2314yes—
373#382C2318yes—
374#382C2312yes—
375#381C2318yes—
376#381C2312yes—
377#380C2318yes—
378#380C2318yes—
379#380C2318yes—
380#380C2318yes—
381#380C23116yes—
382#380C23116yes—
383#380C2312yes—
384#380C2312yes—
385#380C2314yes—
386#380C2314yes—
387#380C2312yes—
388#380C2312yes—
389#379C2312yes—
390C4×C4⋊C4C2318yes—
391C4×C4⋊C4C2318yes—
392C4×C4⋊C4C2312yes—
393C4×C4⋊C4C2312yes—
394C4×C4⋊C4C2312yes—
395C4×C4⋊C4C2312yes—
396C4×C4⋊C4C2314yes—
397C4×C4⋊C4C2314yes—
398C4×C4⋊C4C2314yes—
399C4×C22⋊C4C2314yes—
400C4×C22⋊C4C23116yes—
401C4×C22⋊C4C23116yes—
402C4×C22⋊C4C2318yes—
403C4×C22⋊C4C2312yes—
404C4×C22⋊C4C2312yes—
405C4×C22⋊C4C2314yes—
406C4×C22⋊C4C2314yes—
407C4×C22⋊C4C2314yes—
408C4×C22⋊C4C2314yes—
409C4×C22⋊C4C2314yes—
410#376C2312yes—
411C43C2312yes—
412C25C2411yescharacteristic
4132−1+4—4128no—
414C2×#41—216no—
415C2×#41—216no—
416C2×#41—232no—
417C2×#41—216no—
418C2×#41—24no—
419C2×#41—28no—
420C2×#41—232no—
421C2×#41—216no—
422C2×#41—28no—
423C2×#41—24no—
424C2×#41—28no—
425C2×#41—416no—
426C2×#41—48no—
427C2×#41—48no—
428C2×#41#4118yes—
429C22×Q8—216no—
430C22×Q8—216no—
431C22×Q8—216no—
432C22×Q8—28no—
433C22×Q8—28no—
434C22×Q8—216no—
435C22×Q8—28no—
436C22×Q8—48no—
437C22×Q8—48no—
438C22×Q8—48no—
439C22×Q8C2×D4116yes—
440C22×Q8C2414yes—
441C22×Q8C2412yes—
442C22×Q8C2418yes—
443C22×Q8C2414yes—
444C22×Q8C2414yes—
445C22×Q8C2411yescharacteristic
446C22×Q8C2414yes—
447C22×D4C2412yes—
448C22×D4C2412yes—
449C22×D4C2414yes—
450C22×D4C2412yes—
451C22×D4C2414yes—
452C22×D4C2418yes—
453C22×D4C2412yes—
454C22×D4C2411yescharacteristic
455C22×D4C2418yes—
456C23×C4—24no—
457C23×C4—28no—
458C23×C4—24no—
459C23×C4—24no—
460C23×C4—24no—
461C23×C4—24no—
462C23×C4—44no—
463C23×C4C2411yescharacteristic
464C23×C4C2412yes—
465C23×C4C2412yes—
466C23×C4C2412yes—
467C23×C4C2412yes—
468C23×C4C2414yes—
469C23×C4C2412yes—
470C23×C4C2412yes—
471C23×C4C2411yescharacteristic
472C23×C4C2418yes—
473C23×C4C2418yes—
474C23×C4C2414yes—
475C23×C4C2411yescharacteristic
476C23×C4C2411yescharacteristic
477C23×C4C2412yes—
478C23×C4C2412yes—
479C23×C4C2414yes—
480C23×C4C2411yescharacteristic
481C23×C4C2412yes—
482C23×C4C2411yescharacteristic
483C4⋊Q8—216no—
484C4⋊Q8—216no—
485C4⋊Q8—216no—
486C4⋊Q8—24no—
487C4⋊Q8—28no—
488C4⋊Q8—28no—
489C4⋊Q8—28no—
490C4⋊Q8—28no—
491C4⋊Q8C2×D4116yes—
492C4⋊Q8C2×D4116yes—
493C4⋊Q8C2×D4116yes—
494C4⋊Q8C2×D4116yes—
495#127—24no—
496#125—232no—
497#125—232no—
498#124—216no—
499#124—28no—
500#124—416no—
501#123—28no—
502#123—232no—
503#123—232no—
504#123—232no—
505#123—48no—
506C22⋊Q8—232no—
507C22⋊Q8—232no—
508C22⋊Q8—216no—
509C22⋊Q8—216no—
510C22⋊Q8—28no—
511C22⋊Q8—232no—
512C22⋊Q8—232no—
513C22⋊Q8—232no—
514C22⋊Q8—232no—
515C22⋊Q8—416no—
516C22⋊Q8—48no—
517#121—28no—
518#121—28no—
519#121—28no—
520#121—216no—
521#121—216no—
522#121—216no—
523#121—48no—
524#121—48no—
525#120—28no—
526#120—48no—
527C4×Q8—232no—
528C4×Q8—232no—
529C4×Q8—232no—
530C4×Q8—232no—
531C4×Q8—24no—
532C4×Q8—24no—
533C4×Q8—416no—
534C4×Q8—416no—
535C4×D4—28no—
536C4×D4—28no—
537C4×D4—216no—
538C4×D4—216no—
539C4×D4—216no—
540C4×D4—216no—
541C4×D4—24no—
542C4×D4—24no—
543C4×D4—28no—
544C4×D4—28no—
545C4×D4—48no—
546C4×D4—416no—
547#117—24no—
548#117—24no—
549#117—24no—
550#117—28no—
551#117—232no—
552#117—232no—
553#117—28no—
554#117—416no—
555C2×C4⋊C4—28no—
556C2×C4⋊C4—216no—
557C2×C4⋊C4—216no—
558C2×C4⋊C4—28no—
559C2×C4⋊C4—216no—
560C2×C4⋊C4—216no—
561C2×C4⋊C4C2×D4116yes—
562C2×C4⋊C4C2×D4116yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C24116yes—
568C2×C4⋊C4C24116yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C24116yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C24116yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C22⋊C4—216no—
593C2×C22⋊C4C24116yes—
594C2×C22⋊C4C2412yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2412yes—
597C2×C22⋊C4C2412yes—
598C2×C22⋊C4C2412yes—
599C2×C22⋊C4C2412yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C24116yes—
615C2×C22⋊C4C24116yes—
616C2×C22⋊C4C24116yes—
617C2×C42—216no—
618C2×C42—24no—
619C2×C42—24no—
620C2×C42—24no—
621C2×C42—28no—
622C2×C42—28no—
623C2×C42—28no—
624C2×C42—28no—
625C2×C42—28no—
626C2×C42C2×D418yes—
627C2×C42C24116yes—
628C2×C42C2412yes—
629C2×C42C2414yes—
630C2×C42C2412yes—
631C2×C42C2412yes—
632C2×C42C2412yes—
633C2×C42C2412yes—
634C2×C42C2414yes—
635C2×C42C2414yes—
636C2×C42C2412yes—
637C2×C42C2412yes—
638C2×C42C2412yes—
639C2×C42C2412yes—
640C2×C42C2412yes—
641C2×C42C2412yes—
642C2×C42C24116yes—
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645C2×C42C2411yescharacteristic
646C2×C42C2411yescharacteristic
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2418yes—
651#95C2414yes—
652#95C2414yes—
653#95C2414yes—
654#95C2414yes—
655#95C2414yes—
656#95C2418yes—
657#95C24116yes—
658#95C24116yes—
659#95C2414yes—
660#95C2414yes—
661#95C24116yes—
662#95C24116yes—
663#95C24116yes—
664#95C24116yes—
665C24—22no—
666C24—24no—
667C24—22no—
668C24—22no—
669C24—42no—
670C24C2514yes—
671C24C2512yes—
672C24C2512yes—
673C24C2511yescharacteristic
674#41—232no—
675#41—4128no—
676#41—464no—
677#41—464no—
678#41—432no—
679C2×Q8—264no—
680C2×Q8—22no—
681C2×Q8—28no—
682C2×Q8—28no—
683C2×Q8—216no—
684C2×Q8—24no—
685C2×Q8—28no—
686C2×Q8—28no—
687C2×Q8—216no—
688C2×Q8—24no—
689C2×Q8—28no—
690C2×Q8—28no—
691C2×Q8—22no—
692C2×Q8—24no—
693C2×Q8—216no—
694C2×Q8—48no—
695C2×Q8—48no—
696C2×Q8—464no—
697C2×Q8—432no—
698C2×Q8—464no—
699C2×Q8C22×D4116yes—
700C2×Q8C22×D4116yes—
701C2×Q8C2×#4114yes—
702C2×D4—24no—
703C2×D4—24no—
704C2×D4—28no—
705C2×D4—28no—
706C2×D4—216no—
707C2×D4—28no—
708C2×D4—28no—
709C2×D4—28no—
710C2×D4—216no—
711C2×D4—22no—
712C2×D4—24no—
713C2×D4—24no—
714C2×D4—216no—
715C2×D4—24no—
716C2×D4—24no—
717C2×D4—22no—
718C2×D4—24no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—44no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4C2×#4118yes—
726C2×D4C2×#4114yes—
727C22×C4—232no—
728C22×C4—22no—
729C22×C4—28no—
730C22×C4—28no—
731C22×C4—24no—
732C22×C4—24no—
733C22×C4—24no—
734C22×C4—24no—
735C22×C4—24no—
736C22×C4—24no—
737C22×C4—24no—
738C22×C4—24no—
739C22×C4—24no—
740C22×C4—24no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—28no—
744C22×C4—22no—
745C22×C4—216no—
746C22×C4—22no—
747C22×C4—24no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—24no—
751C22×C4—24no—
752C22×C4—24no—
753C22×C4—216no—
754C22×C4—216no—
755C22×C4—28no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—216no—
759C22×C4—28no—
760C22×C4—24no—
761C22×C4—28no—
762C22×C4—24no—
763C22×C4—28no—
764C22×C4—24no—
765C22×C4—28no—
766C22×C4—24no—
767C22×C4—42no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4—48no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4—416no—
774C22×C4—416no—
775C22×C4C22×D414yes—
776C22×C4C22×D414yes—
777C22×C4C22×D4116yes—
778C22×C4C22×D414yes—
779C22×C4C2×#4118yes—
780C22×C4C2×#4114yes—
781C22×C4H(5,𝔽2)14yes—
782C22×C42−1+418yescomplemented
783C22×C4C2514yes—
784C22×C4C2518yes—
785C22×C4C2512yes—
786C22×C4C2514yes—
787C22×C4C2514yes—
788C22×C4C2512yes—
789C22×C4C2518yes—
790C22×C4C2512yes—
791C22×C4C2512yes—
792C22×C4C2511yescharacteristic
793C22×C4C2511yescharacteristic
794C22×C4C2518yes—
795C22×C4C2512yes—
796C22×C4C2512yes—
797C22×C4C2511yescharacteristic
798C22×C4C2511yescharacteristic
799C22×C4C2511yescharacteristic
800C22×C4C2511yescharacteristic
801C4⋊C4—24no—
802C4⋊C4—24no—
803C4⋊C4—28no—
804C4⋊C4—28no—
805C4⋊C4—232no—
806C4⋊C4—232no—
807C4⋊C4—28no—
808C4⋊C4—28no—
809C4⋊C4—216no—
810C4⋊C4—216no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—22no—
814C4⋊C4—22no—
815C4⋊C4—24no—
816C4⋊C4—28no—
817C4⋊C4—24no—
818C4⋊C4—28no—
819C4⋊C4—28no—
820C4⋊C4—28no—
821C4⋊C4—28no—
822C4⋊C4—416no—
823C4⋊C4—44no—
824C4⋊C4—48no—
825C4⋊C4—416no—
826C4⋊C4C22×D4116yes—
827C4⋊C4C22×D4116yes—
828C4⋊C4C22×D4116yes—
829C4⋊C4C22×D4116yes—
830C22⋊C4—24no—
831C22⋊C4—24no—
832C22⋊C4—28no—
833C22⋊C4—24no—
834C22⋊C4—28no—
835C22⋊C4—28no—
836C22⋊C4—232no—
837C22⋊C4—24no—
838C22⋊C4—24no—
839C22⋊C4—216no—
840C22⋊C4—216no—
841C22⋊C4—28no—
842C22⋊C4—28no—
843C22⋊C4—28no—
844C22⋊C4—28no—
845C22⋊C4—216no—
846C22⋊C4—44no—
847C22⋊C4—44no—
848C22⋊C4—48no—
849C22⋊C4—48no—
850C22⋊C4—48no—
851C22⋊C4—416no—
852C22⋊C4—416no—
853C22⋊C4—416no—
854C42—24no—
855C42—24no—
856C42—24no—
857C42—24no—
858C42—24no—
859C42—24no—
860C42—232no—
861C42—24no—
862C42—24no—
863C42—24no—
864C42—24no—
865C42—28no—
866C42—24no—
867C42—28no—
868C42—28no—
869C42—416no—
870C42C22×D414yes—
871C42C22×D414yes—
872C42C22×D414yes—
873C42C22×D414yes—
874C23—22no—
875C23—22no—
876C23—28no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—24no—
883C23—22no—
884C23—24no—
885C23—22no—
886C23—22no—
887C23—24no—
888C23—24no—
889C23—24no—
890C23—28no—
891C23—28no—
892C23—48no—
893C23—48no—
894C23—44no—
895C23—44no—
896C23C23×D412yes—
897C23C22×#4114yes—
898C23C22×#4112yes—
899C23C2×H(5,𝔽2)12yes—
900C23C2×2−1+414yes—
901C23C2611yescharacteristic
902Q8—232no—
903Q8—232no—
904Q8—28no—
905Q8—432no—
906Q8—416no—
907Q8—48no—
908Q8—416no—
909D4—216no—
910D4—28no—
911D4—432no—
912D4—416no—
913D4—416no—
914D4—48no—
915D4—48no—
916D4—48no—
917D4—816no—
918C2×C4—216no—
919C2×C4—28no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—28no—
923C2×C4—28no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—232no—
929C2×C4—216no—
930C2×C4—28no—
931C2×C4—216no—
932C2×C4—28no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—28no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—28no—
944C2×C4—22no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—28no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—22no—
953C2×C4—28no—
954C2×C4—216no—
955C2×C4—22no—
956C2×C4—24no—
957C2×C4—432no—
958C2×C4—432no—
959C2×C4—48no—
960C2×C4—44no—
961C2×C4—416no—
962C2×C4—44no—
963C2×C4—48no—
964C2×C4—48no—
965C2×C4—416no—
966C2×C4—48no—
967C2×C4—48no—
968C2×C4—48no—
969C2×C4#546116yes—
970C2×C4C23×D412yes—
971C2×C4C23×D412yes—
972C2×C4C23×D4116yes—
973C2×C4C23×D412yes—
974C2×C4C23×D412yes—
975C2×C4C23×D412yes—
976C2×C4C23×D412yes—
977C2×C4C22×#4114yes—
978C2×C4C22×#4112yes—
979C2×C4C22×#4112yes—
980C2×C4C2×H(5,𝔽2)12yes—
981C2×C4C2×H(5,𝔽2)12yes—
982C2×C4C2×2−1+414yes—
983C2×C4C2×2−1+414yes—
984C2×C4#58514yes—
985C22—22no—
986C22—22no—
987C22—24no—
988C22—24no—
989C22—24no—
990C22—24no—
991C22—28no—
992C22—24no—
993C22—24no—
994C22—416no—
995C22—42no—
996C22—42no—
997C22—42no—
998C22—42no—
999C22—44no—
1000C22—42no—
1001C22—42no—
1002C22—44no—
1003C22—44no—
1004C22—48no—
1005C22—48no—
1006C22—44no—
1007C22C2×#54614yes—
1008C22C24×D411yescharacteristic
1009C22C23×#4111yescharacteristic
1010C22C22×H(5,𝔽2)11yescharacteristic
1011C22C22×2−1+412yes—
1012C22C2×#58512yes—
1013C4—22no—
1014C4—24no—
1015C4—22no—
1016C4—24no—
1017C4—216no—
1018C4—42no—
1019C4—42no—
1020C4—42no—
1021C4—48no—
1022C4—44no—
1023C4—44no—
1024C4—48no—
1025C4—42no—
1026C4—44no—
1027C4C2×#54614yes—
1028C4C2×#54614yes—
1029C4#348614yes—
1030C4#348714yes—
1031C2—24no—
1032C2—44no—
1033C2—44no—
1034C2—84no—
1035C2C22×#54611yescharacteristic
1036C2C2×#348611yescharacteristic
1037C2C2×#348711yescharacteristic
1038C2#6280512yes—
1039C2#6283512yes—
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×#3499C2semidirect
2. C22×#533C2semidirect
3. #59042C2semidirect
4. #59040C2semidirect
5. #59036C2semidirect
6. #59034C2semidirect
7. #38907C2semidirect
8. #38905C2semidirect
9. #37749C2semidirect
10. #36624C2semidirect
11. #36426C2semidirect
12. #36422C2semidirect
13. #36150C2semidirect
14. #36129C2semidirect
15. #35661C2semidirect
16. #35659C2semidirect
17. #35289C2semidirect
18. #35279C2semidirect
19. #35182C2semidirect
20. #34257C2semidirect
21. #34209C2semidirect
22. C4×#525C2semidirect
25. C2×D4×Q8C22semidirect
26. C2×D4×Q8C22semidirect
29. C2×#547C22semidirect
30. C2×#547C22semidirect
32. C2×#536C22semidirect
39. C2×#532C22semidirect
42. C22×C4⋊Q8C22semidirect
54. #2862C22semidirect
55. #2858C22semidirect
57. #2857C22semidirect
66. #2694C22semidirect
68. #2690C22semidirect
69. #2640C22semidirect
70. #2628C22semidirect
72. #2568C22semidirect
73. #2567C22semidirect
74. #2563C22semidirect
75. #2563C22semidirect
76. #2550C22semidirect
77. #2547C22semidirect
78. #2542C22semidirect
84. #2490C22semidirect
88. #2465C22semidirect
89. #2458C22semidirect
90. #2454C22semidirect
91. #2451C22semidirect
92. #2448C22semidirect
93. #2446C22semidirect
94. #2442C22semidirect
100. #2426C22semidirect
101. #2423C22semidirect
102. #2421C22semidirect
114. #2367C22semidirect
115. #2365C22semidirect
116. #2365C22semidirect
118. #2360C22semidirect
122. #2341C22semidirect
123. #2341C22semidirect
124. Q8×C22⋊C4C22semidirect
125. Q8×C22⋊C4C22semidirect
126. #2327C22semidirect
133. C4×C4⋊Q8C22semidirect
184. C2×C4⋊Q8D4semidirect
782. C22×C42−1+4semidirect

Maximal subgroups

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

subgroupindex
C2×#34992
C22×#5332
#590422
#590402
#590362
#590342
#389072
#389052
#377492
#366242
#364262
#364222
#361502
#361292
#356612
#356592
#352892
#352792
#351822
#342572
#342092
C4×#5252