Finite Group Databasebeta

← #7672736

Subgroups — #7672736

Order 512.

6944 conjugacy classes of subgroups.

The subgroup lattice has 1029 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3509C211yesmaximal, characteristic, complemented
2C2×#3503C211yesmaximal, characteristic, complemented
3#59651C218yesmaximal, complemented
4#59317C218yesmaximal, complemented
5#39427C218yesmaximal, complemented
6#39173C212yesmaximal, complemented
7#39172C212yesmaximal, complemented
8#39170C212yesmaximal, complemented
9#39167C212yesmaximal, complemented
10C2×#2862C211yesmaximal, characteristic, complemented
11#36534C212yesmaximal, complemented
12#36508C212yesmaximal, complemented
13#36474C212yesmaximal, complemented
14#36446C212yesmaximal, complemented
15#36151C214yesmaximal, complemented
16#36129C214yesmaximal, complemented
17#35668C212yesmaximal, complemented
18#35621C212yesmaximal
19#35316C211yesmaximal, characteristic, complemented
20#35312C212yesmaximal, complemented
21#35279C211yesmaximal, characteristic, complemented
22#34276C212yesmaximal, complemented
23C4×#533C211yesmaximal, characteristic, complemented
24C4×#532C211yesmaximal, characteristic
25#3509—216no—
26#3503—216no—
27C2×Q82C2212yes—
28C2×#557C2212yes—
29C2×#557C2212yes—
30C2×#557C2212yes—
31C2×#556C2212yes—
32C2×#556C2212yes—
33C2×#554C2212yes—
34C2×#554C2214yes—
35C2×#552C2214yes—
36C2×#552C2214yes—
37C2×D4×Q8C2214yes—
38C2×D4×Q8C2212yes—
39C2×#544C2214yes—
40C2×#544C2212yes—
41C2×#541C2214yes—
42C2×#536C2212yes—
43C2×#536C2212yes—
44C2×#533C2212yes—
45C2×#533C2212yes—
46C2×#533C2212yes—
47C2×#533C2211yescharacteristic
48C2×#532C2211yescharacteristic
49C22×C4⋊Q8C2211yescharacteristic
50C22×C4⋊Q8C2211yescharacteristic
51C22×C4⋊Q8C2212yes—
52C2×#520C2212yes—
53C2×#519C2212yes—
54C2×C4×#41C2211yescharacteristic
55C2×C4×#41C2211yescharacteristic
56#2862C2212yes—
57#2862C2214yes—
58#2862C2212yes—
59#2862C2214yes—
60#2862C2212yes—
61#2862C2212yes—
62#2862C2214yes—
63#2861C2214yes—
64#2857C2214yes—
65#2857C2214yes—
66#2723C22116yes—
67#2719C22116yes—
68#2716C22116yes—
69#2690C22116yes—
70#2642C2214yes—
71#2640C2214yes—
72#2628C2214yes—
73#2621C2214yes—
74#2568C2212yes—
75#2568C2214yes—
76#2567C2212yes—
77#2567C2214yes—
78#2565C2214yes—
79#2565C2214yes—
80#2563C2212yes—
81#2560C22116yes—
82#2550C22116yes—
83#2550C2218yes—
84#2547C2214yes—
85#2547C2212yes—
86#2547C2212yes—
87#2546C2214yes—
88#2546C2212yes—
89#2546C2212yes—
90#2545C2214yes—
91#2544C2214yes—
92#2542C2212yes—
93#2536C2218yes—
94#2519C22116yes—
95#2492C2218yes—
96#2489C2218yes—
97#2489C22116yes—
98#2489C2218yes—
99#2488C22116yes—
100#2487C2214yes—
101#2486C2214yes—
102#2486C2214yes—
103#2453C2218yes—
104#2453C2218yes—
105#2451C2218yes—
106#2446C2218yes—
107#2442C2218yes—
108#2439C2218yes—
109#2438C22116yes—
110#2429C2218yes—
111#2425C22116yes—
112#2421C2218yes—
113#2421C2218yes—
114#2417C2218yes—
115#2415C2218yes—
116#2415C2218yes—
117#2409C2214yes—
118#2409C2218yes—
119#2362C2218yes—
120#2362C2218yes—
121#2360C2218yes—
122#2359C22116yes—
123#2352C2218yes—
124#2351C2218yes—
125Q8×C22⋊C4C2218yes—
126#2327C2214yes—
127#2326C2214yes—
128#2317C2212yes—
129#2311C2212yes—
130#2310C2212yes—
131C4×C4⋊Q8C2211yescharacteristic
132C4×C4⋊Q8C2212yes—
133C4×C4⋊Q8C2212yes—
134C4×C4⋊Q8C2211yescharacteristic
135C4×C4⋊Q8C2214yes—
136C4×#127C2211yescharacteristic
137C4×#127C2211yescharacteristic
138C4×#125C2214yes—
139C4×#124C2211yescharacteristic
140C4×#124C2211yescharacteristic
141C4×#124C2211yescharacteristic
142C4×#124C2214yes—
143C4×#124C2211yescharacteristic
144C4×C22⋊Q8C2214yes—
145C4×C22⋊Q8C2214yes—
146C4×#121C2214yes—
147C4×#121C2214yes—
148#2297C2211yescharacteristic
149#2297C2211yescharacteristic
150#2296C2212yes—
151#2295C2212yes—
152#2295C2212yes—
153C2×#391C2214yes—
154C2×#391C2212yes—
155C2×#391C2212yes—
156#2293C2214yes—
157#2285C2211yescharacteristic
158#2285C2211yescharacteristic
159C2×#382C2214yes—
160C42×Q8C2212yes—
161C42×Q8C2212yes—
162C42×D4C2214yes—
163C4×#117C2212yes—
164C2×C43C2211yescharacteristic
165C22×#41C2311yescharacteristic
166C22×#41C2311yescharacteristic
167C23×Q8C2312yes—
168C23×Q8C2314yes—
169C23×Q8C2312yes—
170Q82—216no—
171#557—216no—
172#557—216no—
173#557—216no—
174#556—216no—
175#556—216no—
176#554—232no—
177#554—216no—
178#552—232no—
179#552—232no—
180D4×Q8—232no—
181D4×Q8—216no—
182#544—232no—
183#544—216no—
184#541—232no—
185#536—216no—
186#536—216no—
187#533—216no—
188#533—216no—
189#533—216no—
190#533D4116yescomplemented
191#532—28no—
192C2×C4⋊Q8—216no—
193C2×C4⋊Q8—28no—
194C2×C4⋊Q8—28no—
195C2×C4⋊Q8C2311yescharacteristic
196C2×C4⋊Q8C2314yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2314yes—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2314yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2318yes—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#126C2318yes—
215C2×#126C2318yes—
216C2×#125C2314yes—
217C2×#125C2314yes—
218C2×#125C2314yes—
219C2×#125C2314yes—
220C2×#125C2318yes—
221C2×#125C2318yes—
222C2×#125C2318yes—
223C2×#125C2312yes—
224C2×#124C2314yes—
225C2×#124C2314yes—
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#123C2318yes—
229C2×#123C2318yes—
230C2×C22⋊Q8C2318yes—
231C2×C22⋊Q8C2318yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2318yes—
239C2×C22⋊Q8C2318yes—
240C2×C22⋊Q8C2318yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2312yes—
243C2×#121C2314yes—
244#520—216no—
245#519—216no—
246C4×#41—28no—
247C4×#41—28no—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2314yes—
256C2×C4×Q8C2314yes—
257C2×C4×Q8C2314yes—
258C2×C4×Q8C2314yes—
259C2×C4×Q8C2314yes—
260C2×C4×Q8C2314yes—
261C2×C4×Q8C2314yes—
262C2×C4×Q8C2314yes—
263C2×C4×Q8C2312yes—
264C2×C4×Q8C2312yes—
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2314yes—
267C2×C4×D4C2311yescharacteristic
268C2×C4×D4C2311yescharacteristic
269C2×C4×D4C2311yescharacteristic
270C2×C4×D4C2314yes—
271C2×C4×D4C2318yes—
272C2×C4×D4C2312yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2312yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×#117C2311yescharacteristic
279C2×#117C2312yes—
280C2×#117C2311yescharacteristic
281C2×#117C2314yes—
282C2×#117C2318yes—
283C2×#117C2314yes—
284C2×#117C2314yes—
285C2×#117C2312yes—
286C2×#117C2312yes—
287C2×#117C2312yes—
288C22×C4⋊C4C2312yes—
289C22×C4⋊C4C2314yes—
290C22×C4⋊C4C2314yes—
291C22×C4⋊C4C2312yes—
292C22×C4⋊C4C2312yes—
293C22×C4⋊C4C2312yes—
294C22×C42C2312yes—
295C22×C42C2312yes—
296C22×C42C2311yescharacteristic
297C22×C42C2311yescharacteristic
298C22×C42C2312yes—
299C22×C42C2312yes—
300C22×C42C2311yescharacteristic
301#400C2318yes—
302#400C23116yes—
303#400C23116yes—
304#400C23116yes—
305#399C2318yes—
306#398C23116yes—
307#398C23116yes—
308#398C2318yes—
309#398C2318yes—
310#398C23116yes—
311#397C2318yes—
312#397C2318yes—
313#397C23116yes—
314#397C23116yes—
315#396C23116yes—
316#395C2318yes—
317#395C23116yes—
318#394C23116yes—
319#393C2318yes—
320#393C23116yes—
321#391C2318yes—
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#391C2314yes—
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#391C2314yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2314yes—
333#391C2318yes—
334#391C2314yes—
335#391C2318yes—
336#391C23116yes—
337#391C2314yes—
338#391C2318yes—
339#391C23116yes—
340#391C2318yes—
341#391C2318yes—
342#391C2318yes—
343#391C2318yes—
344#390C2314yes—
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2314yes—
349#390C2311yescharacteristic
350#390C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C23116yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2318yes—
359#389C23116yes—
360#389C2318yes—
361#389C2318yes—
362#389C2318yes—
363#389C23116yes—
364#388C23116yes—
365#388C23116yes—
366#388C23116yes—
367#388C23116yes—
368#388C23116yes—
369#388C2314yes—
370#388C2314yes—
371#388C2314yes—
372#388C2314yes—
373#387C23116yes—
374#387C2318yes—
375#387C2318yes—
376#387C23116yes—
377#387C23116yes—
378#387C23116yes—
379#386C23116yes—
380#386C2318yes—
381#386C2314yes—
382#386C2314yes—
383#385C2318yes—
384#385C23116yes—
385#385C2318yes—
386#384C2311yescharacteristic
387#384C2311yescharacteristic
388#384C2312yes—
389#384C2314yes—
390#382C2312yes—
391#382C2314yes—
392#382C2311yescharacteristic
393#382C2311yescharacteristic
394#382C2318yes—
395#382C2318yes—
396#382C2318yes—
397#382C2318yes—
398#382C23116yes—
399#381C2318yes—
400#380C2318yes—
401#380C2318yes—
402#380C2318yes—
403#380C23116yes—
404#380C2318yes—
405#380C2312yes—
406#380C2314yes—
407#380C2312yes—
408C4×C4⋊C4C2318yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2318yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C23116yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2312yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2312yes—
421C4×C4⋊C4C2314yes—
422C4×C22⋊C4C23116yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2318yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2314yes—
430#376C2314yes—
431C2×#95C2318yes—
432C2×#95C2318yes—
433C43C2312yes—
434C43C2311yescharacteristic
435C43C2311yescharacteristic
436C43C2312yes—
437C43C2314yes—
438C43C2311yescharacteristic
439C43C2311yescharacteristic
440C2×#41—24no—
441C2×#41—24no—
442C2×#41—24no—
443C2×#41—24no—
444C2×#41—24no—
445C2×#41#4118yes—
446C22×Q8—216no—
447C22×Q8—28no—
448C22×Q8—28no—
449C22×Q8—28no—
450C22×Q8—28no—
451C22×Q8—48no—
452C22×Q8—416no—
453C22×Q8C2414yes—
454C22×Q8C2414yes—
455C22×Q8C2411yescharacteristic
456C22×Q8C2414yes—
457C22×Q8C2412yes—
458C22×Q8C2412yes—
459C22×Q8C2411yescharacteristic
460C22×Q8C2418yes—
461C22×Q8C2414yes—
462C22×D4C2412yes—
463C22×D4C2411yescharacteristic
464C22×D4C2414yes—
465C22×D4C2412yes—
466C22×D4C2411yescharacteristic
467C23×C4C2414yes—
468C23×C4C2412yes—
469C23×C4C2412yes—
470C23×C4C2412yes—
471C23×C4C2412yes—
472C23×C4C2412yes—
473C23×C4C2412yes—
474C23×C4C2412yes—
475C23×C4C2411yescharacteristic
476C23×C4C2411yescharacteristic
477C23×C4C2412yes—
478C23×C4C2414yes—
479C23×C4C2418yes—
480C23×C4C2411yescharacteristic
481C4⋊Q8—216no—
482C4⋊Q8—24no—
483C4⋊Q8—216no—
484C4⋊Q8—216no—
485C4⋊Q8—216no—
486C4⋊Q8—232no—
487C4⋊Q8—28no—
488C4⋊Q8—28no—
489C4⋊Q8—28no—
490C4⋊Q8—28no—
491C4⋊Q8—28no—
492C4⋊Q8—28no—
493C4⋊Q8—28no—
494C4⋊Q8—28no—
495C4⋊Q8—216no—
496C4⋊Q8—216no—
497C4⋊Q8C2×D418yes—
498C4⋊Q8C2×D418yes—
499#127—24no—
500#126—232no—
501#126—232no—
502#125—216no—
503#125—216no—
504#125—216no—
505#125—232no—
506#125—232no—
507#125—232no—
508#125—216no—
509#125C2×D4116yes—
510#124—24no—
511#124—24no—
512#124—216no—
513#124—216no—
514#123—232no—
515#123—232no—
516C22⋊Q8—216no—
517C22⋊Q8—216no—
518C22⋊Q8—216no—
519C22⋊Q8—232no—
520C22⋊Q8—216no—
521C22⋊Q8—216no—
522C22⋊Q8—216no—
523C22⋊Q8—232no—
524C22⋊Q8—232no—
525C22⋊Q8—232no—
526C22⋊Q8—416no—
527C22⋊Q8C2×D4116yes—
528C22⋊Q8C2×D4116yes—
529#121—216no—
530C4×Q8—216no—
531C4×Q8—216no—
532C4×Q8—216no—
533C4×Q8—216no—
534C4×Q8—216no—
535C4×Q8—216no—
536C4×Q8—24no—
537C4×Q8—24no—
538C4×Q8—24no—
539C4×Q8—24no—
540C4×Q8—216no—
541C4×Q8—216no—
542C4×Q8—216no—
543C4×Q8—216no—
544C4×Q8—48no—
545C4×Q8C2×D4116yes—
546C4×Q8C2×D4116yes—
547C4×D4—28no—
548C4×D4—28no—
549C4×D4—28no—
550C4×D4—28no—
551C4×D4—216no—
552C4×D4—232no—
553C4×D4—24no—
554C4×D4—24no—
555C4×D4—24no—
556C4×D4—24no—
557C4×D4—216no—
558C4×D4—216no—
559C4×D4—48no—
560#117—24no—
561#117—24no—
562#117—28no—
563#117—216no—
564#117—216no—
565#117—216no—
566#117—232no—
567#117—28no—
568#117—28no—
569#117C2×D4116yes—
570C2×C4⋊C4—28no—
571C2×C4⋊C4—28no—
572C2×C4⋊C4—28no—
573C2×C4⋊C4—28no—
574C2×C4⋊C4—216no—
575C2×C4⋊C4—216no—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C24116yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C24116yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C22⋊C4C2412yes—
617C2×C22⋊C4C2412yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2412yes—
620C2×C22⋊C4C2412yes—
621C2×C22⋊C4C2412yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C24116yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C24116yes—
634C2×C22⋊C4C2414yes—
635C2×C42—24no—
636C2×C42—24no—
637C2×C42—28no—
638C2×C42—28no—
639C2×C42—28no—
640C2×C42—44no—
641C2×C42C2×D418yes—
642C2×C42C2412yes—
643C2×C42C2418yes—
644C2×C42C2418yes—
645C2×C42C2412yes—
646C2×C42C2418yes—
647C2×C42C2414yes—
648C2×C42C2412yes—
649C2×C42C2412yes—
650C2×C42C2412yes—
651C2×C42C2412yes—
652C2×C42C2412yes—
653C2×C42C2412yes—
654C2×C42C2412yes—
655C2×C42C2418yes—
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2418yes—
665C2×C42C2412yes—
666C2×C42C2412yes—
667C2×C42C2411yescharacteristic
668C2×C42C2414yes—
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2412yes—
673#95C24116yes—
674#95C24116yes—
675#95C24116yes—
676#95C24116yes—
677#95C2418yes—
678#95C2418yes—
679#95C2414yes—
680#95C2414yes—
681#95C2414yes—
682#95C2414yes—
683#95C2414yes—
684#95C2414yes—
685#95C24116yes—
686#95C2414yes—
687#95C2414yes—
688#95C2418yes—
689#95C2418yes—
690#95C24116yes—
691#95C24116yes—
692#95C24116yes—
693C24C2512yes—
694C24C2512yes—
695C24C2511yescharacteristic
696#41—232no—
697#41—416no—
698C2×Q8—22no—
699C2×Q8—28no—
700C2×Q8—28no—
701C2×Q8—22no—
702C2×Q8—28no—
703C2×Q8—216no—
704C2×Q8—28no—
705C2×Q8—28no—
706C2×Q8—28no—
707C2×Q8—22no—
708C2×Q8—28no—
709C2×Q8—22no—
710C2×Q8—28no—
711C2×Q8—28no—
712C2×Q8—22no—
713C2×Q8—28no—
714C2×Q8—216no—
715C2×Q8—48no—
716C2×Q8—416no—
717C2×Q8—432no—
718C2×Q8—816no—
719C2×Q8—832no—
720C2×Q8C22×D418yes—
721C2×Q8C22×D418yes—
722C2×Q8C2×#4114yes—
723C2×D4—24no—
724C2×D4—24no—
725C2×D4—24no—
726C2×D4—28no—
727C2×D4—24no—
728C2×D4—24no—
729C2×D4—22no—
730C2×D4—22no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—28no—
734C2×D4—22no—
735C2×D4—44no—
736C2×D4C2×#4118yes—
737C2×D4C2×#4114yes—
738C22×C4—24no—
739C22×C4—24no—
740C22×C4—24no—
741C22×C4—24no—
742C22×C4—28no—
743C22×C4—24no—
744C22×C4—28no—
745C22×C4—24no—
746C22×C4—28no—
747C22×C4—28no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—24no—
751C22×C4—24no—
752C22×C4—24no—
753C22×C4—24no—
754C22×C4—24no—
755C22×C4—24no—
756C22×C4—28no—
757C22×C4—28no—
758C22×C4—24no—
759C22×C4—28no—
760C22×C4—28no—
761C22×C4—216no—
762C22×C4—42no—
763C22×C4—42no—
764C22×C4—416no—
765C22×C4—48no—
766C22×C4C22×D414yes—
767C22×C4C22×D414yes—
768C22×C4C22×D414yes—
769C22×C4C2×#4118yes—
770C22×C4C2×#4114yes—
771C22×C42−1+414yes—
772C22×C4C2512yes—
773C22×C4C2512yes—
774C22×C4C2518yes—
775C22×C4C2512yes—
776C22×C4C2512yes—
777C22×C4C2518yes—
778C22×C4C2512yes—
779C22×C4C2512yes—
780C22×C4C2518yes—
781C22×C4C2512yes—
782C22×C4C2514yes—
783C22×C4C2511yescharacteristic
784C22×C4C2511yescharacteristic
785C22×C4C2514yes—
786C22×C4C2512yes—
787C22×C4C2512yes—
788C22×C4C2512yes—
789C22×C4C2511yescharacteristic
790C22×C4C2511yescharacteristic
791C22×C4C2511yescharacteristic
792C22×C4C2511yescharacteristic
793C4⋊C4—28no—
794C4⋊C4—28no—
795C4⋊C4—28no—
796C4⋊C4—28no—
797C4⋊C4—216no—
798C4⋊C4—28no—
799C4⋊C4—216no—
800C4⋊C4—28no—
801C4⋊C4—28no—
802C4⋊C4—28no—
803C4⋊C4—22no—
804C4⋊C4—22no—
805C4⋊C4—24no—
806C4⋊C4—24no—
807C4⋊C4—24no—
808C4⋊C4—22no—
809C4⋊C4—24no—
810C4⋊C4—22no—
811C4⋊C4—216no—
812C4⋊C4—216no—
813C4⋊C4—216no—
814C4⋊C4—216no—
815C4⋊C4—216no—
816C4⋊C4—216no—
817C4⋊C4—28no—
818C4⋊C4—28no—
819C4⋊C4—232no—
820C4⋊C4—28no—
821C4⋊C4—216no—
822C4⋊C4—28no—
823C4⋊C4—28no—
824C4⋊C4—44no—
825C4⋊C4—48no—
826C4⋊C4—416no—
827C4⋊C4C22×D418yes—
828C4⋊C4C22×D418yes—
829C4⋊C4C22×D418yes—
830C4⋊C4C22×D418yes—
831C4⋊C4C22×D4116yes—
832C4⋊C4C22×D4116yes—
833C22⋊C4—24no—
834C22⋊C4—24no—
835C22⋊C4—28no—
836C22⋊C4—28no—
837C22⋊C4—232no—
838C22⋊C4—24no—
839C22⋊C4—24no—
840C22⋊C4—216no—
841C22⋊C4—24no—
842C22⋊C4—24no—
843C22⋊C4—216no—
844C22⋊C4—216no—
845C22⋊C4—28no—
846C22⋊C4—28no—
847C22⋊C4—28no—
848C22⋊C4—44no—
849C22⋊C4—44no—
850C22⋊C4—416no—
851C22⋊C4C22×D4116yes—
852C42—24no—
853C42—24no—
854C42—24no—
855C42—24no—
856C42—24no—
857C42—24no—
858C42—216no—
859C42—216no—
860C42—216no—
861C42—24no—
862C42—22no—
863C42—22no—
864C42—28no—
865C42—22no—
866C42—24no—
867C42—24no—
868C42—24no—
869C42—22no—
870C42—24no—
871C42—216no—
872C42—24no—
873C42—24no—
874C42—42no—
875C42—42no—
876C42—48no—
877C42C22×D414yes—
878C42C22×D414yes—
879C42C22×D414yes—
880C42C22×D414yes—
881C42C22×D4116yes—
882C422−1+418yes—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—24no—
887C23—22no—
888C23—24no—
889C23—22no—
890C23—22no—
891C23—24no—
892C23—22no—
893C23—24no—
894C23C23×D412yes—
895C23C22×#4114yes—
896C23C22×#4112yes—
897C23C2×2−1+412yes—
898C23C2611yescharacteristic
899Q8—28no—
900Q8—216no—
901Q8—216no—
902Q8—416no—
903Q8—416no—
904Q8—44no—
905Q8—416no—
906Q8—88no—
907Q8—816no—
908D4—216no—
909D4—28no—
910D4—416no—
911D4—48no—
912D4—44no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—28no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—28no—
923C2×C4—216no—
924C2×C4—28no—
925C2×C4—28no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—28no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—28no—
933C2×C4—22no—
934C2×C4—28no—
935C2×C4—22no—
936C2×C4—28no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—28no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—22no—
944C2×C4—28no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—28no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—216no—
951C2×C4—48no—
952C2×C4—48no—
953C2×C4—416no—
954C2×C4—48no—
955C2×C4—48no—
956C2×C4—48no—
957C2×C4—48no—
958C2×C4—48no—
959C2×C4—816no—
960C2×C4—88no—
961C2×C4#548116yes—
962C2×C4C23×D418yes—
963C2×C4C23×D418yes—
964C2×C4C23×D412yes—
965C2×C4C23×D412yes—
966C2×C4C23×D412yes—
967C2×C4C23×D412yes—
968C2×C4C23×D412yes—
969C2×C4C23×D412yes—
970C2×C4C22×#4114yes—
971C2×C4C22×#4112yes—
972C2×C4C22×#4112yes—
973C2×C4C2×2−1+414yes—
974C2×C4C2×2−1+414yes—
975C2×C4C2×2−1+412yes—
976C2×C4C2×2−1+412yes—
977C2×C4C2×2−1+414yes—
978C2×C4#58514yes—
979C22—22no—
980C22—24no—
981C22—22no—
982C22—24no—
983C22—28no—
984C22—24no—
985C22—42no—
986C22—42no—
987C22—44no—
988C22—42no—
989C22—44no—
990C22—42no—
991C22—44no—
992C22—42no—
993C22C2×#54814yes—
994C22C24×D411yescharacteristic
995C22C23×#4111yescharacteristic
996C22C22×2−1+412yes—
997C22C22×2−1+411yescharacteristic
998C22C2×#58512yes—
999C4—22no—
1000C4—28no—
1001C4—24no—
1002C4—22no—
1003C4—28no—
1004C4—24no—
1005C4—24no—
1006C4—42no—
1007C4—42no—
1008C4—48no—
1009C4—42no—
1010C4—42no—
1011C4—42no—
1012C4—48no—
1013C4—42no—
1014C4—42no—
1015C4—48no—
1016C4C2×#54814yes—
1017C4C2×#54814yes—
1018C4#349914yes—
1019C4#350014yes—
1020C2—24no—
1021C2—44no—
1022C2—82no—
1023C2C22×#54811yescharacteristic
1024C2C2×#349911yescharacteristic
1025C2#6280512yes—
1026C2C2×#350011yescharacteristic
1027C2#6283712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
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×#3509C2semidirect
2. C2×#3503C2semidirect
3. #59651C2semidirect
4. #59317C2semidirect
5. #39427C2semidirect
6. #39173C2semidirect
7. #39172C2semidirect
8. #39170C2semidirect
9. #39167C2semidirect
10. C2×#2862C2semidirect
11. #36534C2semidirect
12. #36508C2semidirect
13. #36474C2semidirect
14. #36446C2semidirect
15. #36151C2semidirect
16. #36129C2semidirect
17. #35668C2semidirect
19. #35316C2semidirect
20. #35312C2semidirect
21. #35279C2semidirect
22. #34276C2semidirect
23. C4×#533C2semidirect
190. #533D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35092
C2×#35032
#596512
#593172
#394272
#391732
#391722
#391702
#391672
C2×#28622
#365342
#365082
#364742
#364462
#361512
#361292
#356682
#356212
#353162
#353122
#352792
#342762
C4×#5332
C4×#5322