Finite Group Databasebeta

← #7626933

Subgroups — #7626933

Order 512.

7442 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3508C211yesmaximal, characteristic
2#34498C212yesmaximal, complemented
3#34494C214yesmaximal, complemented
4#34492C218yesmaximal, complemented
5#34478C214yesmaximal, complemented
6#34442C218yesmaximal, complemented
7#34438C214yesmaximal, complemented
8#34402C212yesmaximal, complemented
9#34373C211yesmaximal, characteristic, complemented
10#34367C212yesmaximal, complemented
11#34364C211yesmaximal, characteristic, complemented
12#34331C212yesmaximal, complemented
13#34330C212yesmaximal, complemented
14#34329C214yesmaximal, complemented
15#34292C214yesmaximal, complemented
16#34261C214yesmaximal, complemented
17#34222C212yesmaximal, complemented
18#34210C211yesmaximal, characteristic, complemented
19#34193C211yesmaximal, characteristic, complemented
20C4×#550C212yesmaximal, complemented
21#34123C211yesmaximal, characteristic, complemented
22#34085C211yesmaximal, characteristic, complemented
23#34070C212yesmaximal, complemented
24#3508C4132yescomplemented
25C2×#559C2212yes—
26C2×#559C2212yes—
27C2×#550C2212yes—
28C2×#550C2212yes—
29C2×#546C2214yes—
30C2×#546C2214yes—
31C2×#540C2214yes—
32C2×#535C2212yes—
33C2×#533C2211yescharacteristic
34C2×#532C2212yes—
35C2×#532C2212yes—
36C22×#127C2211yescharacteristic
37C2×#518C2212yes—
38C2×#518C2212yes—
39C2×C4×#41C2211yescharacteristic
40C2×C4×#41C2214yescomplemented
41#2380C2214yes—
42#2378C2214yes—
43#2377C2218yescomplemented
44#2377C2218yescomplemented
45#2377C2218yescomplemented
46#2376C2218yescomplemented
47#2375C2218yes—
48#2374C2218yescomplemented
49#2372C2218yescomplemented
50#2367C2214yescomplemented
51#2367C2214yescomplemented
52#2367C2214yescomplemented
53#2367C2214yescomplemented
54#2366C2214yes—
55#2366C2212yes—
56#2366C2212yes—
57#2366C2214yes—
58#2366C2214yescomplemented
59#2366C2214yescomplemented
60#2364C2218yescomplemented
61#2364C2218yescomplemented
62#2363C2214yescomplemented
63#2363C2214yescomplemented
64#2363C2218yescomplemented
65#2362C2214yes—
66#2361C2218yescomplemented
67#2359C2218yescomplemented
68#2359C2218yescomplemented
69#2358C2218yes—
70#2357C2214yescomplemented
71#2356C2212yescomplemented
72#2355C2214yescomplemented
73#2355C2212yescomplemented
74#2354C2214yes—
75#2354C2214yescomplemented
76#2354C2212yescomplemented
77#2354C2214yescomplemented
78#2353C2214yes—
79#2353C2218yescomplemented
80#2353C2218yescomplemented
81#2352C2218yescomplemented
82Q8×C4⋊C4C2212yescomplemented
83Q8×C4⋊C4C2212yescomplemented
84#2349C2214yescomplemented
85#2349C2212yescomplemented
86D4×C4⋊C4C2214yescomplemented
87D4×C4⋊C4C2214yescomplemented
88#2347C2212yes—
89#2347C2214yescomplemented
90#2346C2212yes—
91#2343C2214yescomplemented
92#2342C2218yes—
93#2342C2218yes—
94#2341C2212yes—
95#2341C2214yescomplemented
96#2339C2212yes—
97#2339C2214yescomplemented
98#2339C2218yescomplemented
99D4×C22⋊C4C2214yes—
100D4×C22⋊C4C2214yes—
101D4×C22⋊C4C2214yes—
102D4×C22⋊C4C2214yes—
103#2337C2218yescomplemented
104#2336C2214yescomplemented
105#2336C2214yescomplemented
106#2335C2218yescomplemented
107#2335C2218yescomplemented
108#2333C2218yescomplemented
109#2333C2218yescomplemented
110#2332C2214yes—
111#2331C2211yescharacteristic, complemented
112#2331C2211yescharacteristic, complemented
113#2331C2212yescomplemented
114#2328C2212yes—
115#2328C2212yes—
116#2328C2214yes—
117#2328C2212yes—
118#2328C2212yes—
119#2328C2214yescomplemented
120#2327C2211yescharacteristic, complemented
121#2327C2212yescomplemented
122#2327C2211yescharacteristic, complemented
123#2326C2214yescomplemented
124#2326C2214yescomplemented
125#2326C2214yescomplemented
126#2325C2218yescomplemented
127#2325C2218yescomplemented
128#2325C2218yescomplemented
129#2324C2218yescomplemented
130#2323C2212yes—
131#2323C2212yes—
132#2322C2218yescomplemented
133#2321C2218yes—
134#2321C2218yes—
135#2319C2214yes—
136#2319C2212yescomplemented
137#2319C2214yescomplemented
138#2319C2214yescomplemented
139#2318C2218yescomplemented
140#2314C2214yes—
141#2312C2218yes—
142#2311C2218yescomplemented
143#2309C2212yes—
144#2308C2214yes—
145C4×#127C2212yes—
146C4×#127C2212yes—
147C4×#127C2214yescomplemented
148C4×#124C2214yescomplemented
149C4×#123C2218yescomplemented
150C4×#121C2214yescomplemented
151C4×#121C2218yescomplemented
152C4×#121C2214yescomplemented
153#2298C2214yes—
154#2297C2214yescomplemented
155#2295C2214yescomplemented
156#2295C2212yescomplemented
157#2295C2211yescharacteristic, complemented
158#2295C2211yescharacteristic, complemented
159#2293C2214yescomplemented
160#2290C2212yes—
161#2290C2212yes—
162#2290C2218yescomplemented
163#2290C2218yescomplemented
164C2×#388C2218yes—
165#2285C2211yescharacteristic
166#2285C2212yescomplemented
167#2283C2211yescharacteristic
168#2283C2211yescharacteristic
169#2283C2212yescomplemented
170#2283C2212yescomplemented
171#2276C2212yescomplemented
172#2275C2214yescomplemented
173#2275C2214yescomplemented
174C42×Q8C2212yescomplemented
175C42×D4C2214yescomplemented
176C42×D4C2211yescharacteristic, complemented
177C42×D4C2211yescharacteristic, complemented
178C4×#117C2211yescharacteristic
179C2×#376C2212yescomplemented
180C22×#41C2311yescharacteristic
181C22×#41C2314yes—
182C22×#41C2314yes—
183C23×D4C2312yes—
184C23×D4C2312yes—
185C23×D4C2312yes—
186#559C2×C4132yescomplemented
187#559C2×C4132yescomplemented
188#550C2×C4132yescomplemented
189#550C2×C4132yescomplemented
190#546C2×C4164yescomplemented
191#546C2×C4164yescomplemented
192#540C2×C4164yescomplemented
193#535C2×C4132yescomplemented
194#533C2×C4116yescomplemented
195#532C2×C4132yescomplemented
196#532C2×C4132yescomplemented
197C2×C4⋊Q8C2311yescharacteristic
198C2×C4⋊Q8C2311yescharacteristic
199C2×#127C2×C4116yescomplemented
200C2×#127C2312yes—
201C2×#127C2314yes—
202C2×#127C2312yes—
203C2×#127C2312yes—
204C2×#127C2312yes—
205C2×#125C2312yes—
206C2×#124C2314yes—
207C2×#124C2314yes—
208C2×#124C2314yes—
209C2×#123C2318yes—
210C2×#123C2318yes—
211C2×C22⋊Q8C2312yes—
212C2×C22⋊Q8C2312yes—
213C2×#121C2318yes—
214C2×#121C2314yes—
215C2×#121C2314yes—
216C2×#121C2318yes—
217C2×#121C2314yes—
218C2×#121C2314yes—
219C2×#120C2318yes—
220#518—48no—
221#518C2×C4132yescomplemented
222C4×#41—416no—
223C4×#41C2×C4116yescomplemented
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×D4C2314yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2318yes—
238C2×C4×D4C2318yes—
239C2×C4×D4C2318yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2318yes—
248C2×C4×D4C2318yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2312yes—
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2314yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2314yes—
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2312yes—
262C2×#117C2318yes—
263C2×#117C2314yes—
264C2×#117C2318yes—
265C2×#117C2312yes—
266C2×#117C2312yes—
267C2×#117C2311yescharacteristic
268C22×C4⋊C4C2318yes—
269C22×C22⋊C4C2318yes—
270C22×C22⋊C4C2318yes—
271C22×C22⋊C4C2318yes—
272C22×C42C2312yes—
273C22×C42C2318yes—
274C22×C42C2312yes—
275C22×C42C2311yescharacteristic
276C22×C42C2312yes—
277#391C2314yes—
278#391C2318yes—
279#391C2312yes—
280#391C2312yes—
281#391C2312yes—
282#391C2314yes—
283#391C2314yes—
284#391C2312yes—
285#390C2314yes—
286#390C2314yes—
287#390C2314yes—
288#390C2314yes—
289#390C2314yes—
290#390C2314yes—
291#390C2318yes—
292#390C2314yes—
293#390C2314yes—
294#390C2318yes—
295#390C2318yes—
296#390C2318yes—
297#390C2318yes—
298#390C2314yes—
299#390C2318yes—
300#390C2314yes—
301#390C2314yes—
302#389C2318yes—
303#389C2312yes—
304#389C2312yes—
305#389C2314yes—
306#389C2314yes—
307#389C2318yes—
308#389C2314yes—
309#389C2312yes—
310#389C2314yes—
311#389C2312yes—
312#388C2314yes—
313#388C2314yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2314yes—
327#388C2318yes—
328#388C2318yes—
329#388C2318yes—
330#388C2314yes—
331#388C2314yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2314yes—
338#388C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2314yes—
342#387C2314yes—
343#387C2314yes—
344#387C2314yes—
345#387C2314yes—
346#387C2314yes—
347#387C2314yes—
348#387C2318yes—
349#387C2318yes—
350#387C2314yes—
351#387C2314yes—
352#387C2314yes—
353#387C2314yes—
354#387C2318yes—
355#387C2314yes—
356#387C2314yes—
357#387C2314yes—
358#386C2318yes—
359#386C2318yes—
360#386C2318yes—
361#386C2318yes—
362#386C2318yes—
363#386C2318yes—
364#386C2318yes—
365#386C2318yes—
366#386C2318yes—
367#386C2314yes—
368#386C2314yes—
369#386C2318yes—
370#386C2318yes—
371#386C2318yes—
372#386C2318yes—
373#386C2318yes—
374#386C2318yes—
375#386C2318yes—
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#384C2312yes—
391#384C2314yes—
392#384C2314yes—
393#383C2314yes—
394#383C2312yes—
395#383C2312yes—
396#383C2314yes—
397#382C2314yes—
398#382C2314yes—
399#382C2311yescharacteristic
400#382C2311yescharacteristic
401#382C2312yes—
402#382C2312yes—
403#381C2312yes—
404#381C2312yes—
405#381C2318yes—
406#381C2314yes—
407#381C2318yes—
408#381C2314yes—
409#380C2314yes—
410#380C2314yes—
411#380C2318yes—
412#380C2318yes—
413#380C2318yes—
414#380C2312yes—
415#380C2312yes—
416#380C2318yes—
417#380C2312yes—
418#380C2312yes—
419#380C2314yes—
420#380C2314yes—
421#379C2318yes—
422#379C2318yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2312yes—
428C4×C4⋊C4C2312yes—
429C4×C4⋊C4C2312yes—
430C4×C4⋊C4C2318yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2314yes—
434C4×C4⋊C4C2318yes—
435C4×C4⋊C4C2312yes—
436C4×C4⋊C4C2312yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2312yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2312yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2312yes—
448C4×C4⋊C4C2311yescharacteristic
449C4×C22⋊C4C2318yes—
450C4×C22⋊C4C2318yes—
451C4×C22⋊C4C2318yes—
452C4×C22⋊C4C2318yes—
453C4×C22⋊C4C2318yes—
454C4×C22⋊C4C2312yes—
455C4×C22⋊C4C2314yes—
456C4×C22⋊C4C2314yes—
457C4×C22⋊C4C2318yes—
458C4×C22⋊C4C2318yes—
459C4×C22⋊C4C2318yes—
460C4×C22⋊C4C2318yes—
461C4×C22⋊C4C2318yes—
462C4×C22⋊C4C2312yes—
463C4×C22⋊C4C2312yes—
464C4×C22⋊C4C2312yes—
465C4×C22⋊C4C2312yes—
466C4×C22⋊C4C2312yes—
467C4×C22⋊C4C2318yes—
468C4×C22⋊C4C2318yes—
469C4×C22⋊C4C2314yes—
470#376C2314yes—
471#376C2312yes—
472#376C2314yes—
473#376C2312yes—
474#376C2312yes—
475#376C2311yescharacteristic
476#376C2312yes—
477#376C2311yescharacteristic
478#376C2314yes—
479#376C2314yes—
480C2×#95C2318yes—
481C2×#95C2314yes—
482C2×#95C2314yes—
483C2×#95C2318yes—
484C43C2311yescharacteristic
485C43C2311yescharacteristic
486C43C2314yes—
487C25C2414yes—
488C2×#41—48no—
489C2×#41—48no—
490C2×#41—44no—
491C2×#41—88no—
492C2×#41C22×C418yes—
493C2×#41C22×C4132yes—
494C2×#41C22×C4132yes—
495C22×Q8C2411yescharacteristic
496C22×Q8C2412yes—
497C22×Q8C2412yes—
498C22×D4—44no—
499C22×D4—44no—
500C22×D4—48no—
501C22×D4—84no—
502C22×D4C22×C4116yes—
503C22×D4C22×C4116yes—
504C22×D4C22×C4116yes—
505C22×D4C2414yes—
506C22×D4C2411yescharacteristic
507C22×D4C2414yes—
508C22×D4C2412yes—
509C22×D4C2418yes—
510C22×D4C2418yes—
511C22×D4C2414yes—
512C22×D4C2414yes—
513C22×D4C2414yes—
514C22×D4C2414yes—
515C23×C4C2411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2412yes—
518C23×C4C2418yes—
519C23×C4C2414yes—
520C23×C4C2418yes—
521C23×C4C2418yes—
522C23×C4C2418yes—
523C23×C4C2414yes—
524C23×C4C2418yes—
525C23×C4C2418yes—
526C23×C4C2412yes—
527C23×C4C2412yes—
528C23×C4C2411yescharacteristic
529C4⋊Q8C22×C418yes—
530C4⋊Q8C22×C418yes—
531#127C22×C4116yes—
532#127C22×C4116yes—
533#127C22×C4116yes—
534#127C22×C4116yes—
535#127C22×C4132yes—
536#125C22×C4116yes—
537#124C22×C4132yes—
538#124C22×C4132yes—
539#124C22×C4132yes—
540#123C22×C4164yes—
541#123C22×C4164yes—
542C22⋊Q8C22×C4116yes—
543C22⋊Q8C22×C4116yes—
544#121C22×C4132yes—
545#121C22×C4132yes—
546#121C22×C4132yes—
547#121C22×C4132yes—
548#121C22×C4164yes—
549#121C22×C4164yes—
550#120C22×C4164yes—
551C4×Q8—28no—
552C4×Q8—44no—
553C4×Q8—48no—
554C4×Q8—48no—
555C4×Q8C22×C418yes—
556C4×Q8C22×C418yes—
557C4×Q8C22×C4116yes—
558C4×Q8C22×C4116yes—
559C4×D4—216no—
560C4×D4—48no—
561C4×D4—44no—
562C4×D4—44no—
563C4×D4—48no—
564C4×D4—48no—
565C4×D4—48no—
566C4×D4—48no—
567C4×D4—48no—
568C4×D4—48no—
569C4×D4—416no—
570C4×D4—416no—
571C4×D4—416no—
572C4×D4—88no—
573C4×D4—88no—
574C4×D4—84no—
575C4×D4—84no—
576C4×D4C22×C4116yes—
577C4×D4C22×C4116yes—
578C4×D4C22×C418yes—
579C4×D4C22×C418yes—
580C4×D4C22×C4132yes—
581C4×D4C22×C4132yes—
582C4×D4C22×C4132yes—
583C4×D4C22×C4132yes—
584C4×D4C22×C4132yes—
585C4×D4C22×C4132yes—
586#117—24no—
587#117—42no—
588#117—416no—
589#117—48no—
590#117—44no—
591#117—88no—
592#117C22×C418yes—
593#117C22×C4116yes—
594#117C22×C4116yes—
595C2×C4⋊C4—88no—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C22⋊C4—416no—
626C2×C22⋊C4—88no—
627C2×C22⋊C4C22×C4164yes—
628C2×C22⋊C4C2412yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2412yes—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2418yes—
657C2×C42—28no—
658C2×C42—416no—
659C2×C42—44no—
660C2×C42C22×C418yes—
661C2×C42C22×C4116yes—
662C2×C42C2414yes—
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2414yes—
670C2×C42C2414yes—
671C2×C42C2412yes—
672C2×C42C2414yes—
673C2×C42C2418yes—
674C2×C42C2414yes—
675C2×C42C2418yes—
676C2×C42C2414yes—
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2418yes—
680C2×C42C2414yes—
681C2×C42C2418yes—
682C2×C42C2414yes—
683C2×C42C2412yes—
684C2×C42C2411yescharacteristic
685C2×C42C2414yes—
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692#95C2414yes—
693#95C2412yes—
694#95C2412yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2418yes—
704#95C2418yes—
705#95C2418yes—
706#95C2418yes—
707#95C2412yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2412yes—
712#95C2412yes—
713#95C2414yes—
714#95C2412yes—
715#95C2414yes—
716#95C2414yes—
717#95C2412yes—
718#95C2418yes—
719#95C2414yes—
720#95C2418yes—
721#95C2414yes—
722#95C2412yes—
723#95C2412yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2412yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731C24—44no—
732C24—48no—
733C24—44no—
734C24—48no—
735C24C23×C4116yes—
736C24C2511yescharacteristic
737C24C2518yes—
738C24C2512yes—
739#41—416no—
740#41—464no—
741#41—832no—
742C2×Q8—24no—
743C2×Q8—24no—
744C2×Q8—24no—
745C2×Q8—44no—
746C2×Q8C23×C414yes—
747C2×Q8C23×C418yes—
748C2×Q8C23×C418yes—
749C2×D4—28no—
750C2×D4—28no—
751C2×D4—28no—
752C2×D4—24no—
753C2×D4—28no—
754C2×D4—432no—
755C2×D4—432no—
756C2×D4—44no—
757C2×D4—48no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—48no—
761C2×D4—48no—
762C2×D4—44no—
763C2×D4—48no—
764C2×D4—48no—
765C2×D4—44no—
766C2×D4—48no—
767C2×D4—816no—
768C2×D4C23×C4116yes—
769C2×D4C23×C414yes—
770C2×D4C23×C4116yes—
771C2×D4C23×C418yes—
772C2×D4C23×C4116yes—
773C2×D4C23×C4116yes—
774C2×D4C23×C4132yes—
775C2×D4C23×C4132yes—
776C2×D4C23×C4116yes—
777C2×D4C23×C4116yes—
778C22×C4—24no—
779C22×C4—22no—
780C22×C4—24no—
781C22×C4—22no—
782C22×C4—24no—
783C22×C4—28no—
784C22×C4—216no—
785C22×C4—48no—
786C22×C4—48no—
787C22×C4—48no—
788C22×C4—42no—
789C22×C4—44no—
790C22×C4—48no—
791C22×C4—44no—
792C22×C4—48no—
793C22×C4—44no—
794C22×C4—48no—
795C22×C4—48no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—48no—
799C22×C4—48no—
800C22×C4—44no—
801C22×C4—44no—
802C22×C4—48no—
803C22×C4—48no—
804C22×C4—48no—
805C22×C4—48no—
806C22×C4—48no—
807C22×C4—48no—
808C22×C4C23×C414yes—
809C22×C4C23×C418yes—
810C22×C4C23×C414yes—
811C22×C4C23×C418yes—
812C22×C4C23×C418yes—
813C22×C4C23×C414yes—
814C22×C4C23×C4132yes—
815C22×C4C23×C4132yes—
816C22×C4C2514yes—
817C22×C4C2514yes—
818C22×C4C2512yes—
819C22×C4C2512yes—
820C22×C4C2514yes—
821C22×C4C2512yes—
822C22×C4C2514yes—
823C22×C4C2518yes—
824C22×C4C2511yescharacteristic
825C22×C4C2511yescharacteristic
826C22×C4C2512yes—
827C22×C4C2512yes—
828C22×C4C2511yescharacteristic
829C22×C4C2511yescharacteristic
830C22×C4C2514yes—
831C22×C4C2514yes—
832C22×C4C2512yes—
833C22×C4C2512yes—
834C22×C4C2511yescharacteristic
835C22×C4C2511yescharacteristic
836C4⋊C4—24no—
837C4⋊C4—28no—
838C4⋊C4—28no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—28no—
843C4⋊C4—24no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—48no—
847C4⋊C4—48no—
848C4⋊C4—42no—
849C4⋊C4—48no—
850C4⋊C4—44no—
851C4⋊C4—44no—
852C4⋊C4—44no—
853C4⋊C4—48no—
854C4⋊C4—44no—
855C4⋊C4C23×C414yes—
856C4⋊C4C23×C414yes—
857C4⋊C4C23×C418yes—
858C4⋊C4C23×C418yes—
859C4⋊C4C23×C418yes—
860C4⋊C4C23×C418yes—
861C4⋊C4C23×C418yes—
862C4⋊C4C23×C418yes—
863C4⋊C4C23×C4116yes—
864C4⋊C4C23×C4116yes—
865C22⋊C4—24no—
866C22⋊C4—216no—
867C22⋊C4—44no—
868C22⋊C4—48no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4—42no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C22⋊C4—48no—
877C22⋊C4—48no—
878C22⋊C4—48no—
879C22⋊C4—48no—
880C22⋊C4—44no—
881C22⋊C4—48no—
882C22⋊C4—48no—
883C22⋊C4—44no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C22⋊C4C23×C418yes—
887C22⋊C4C23×C4116yes—
888C22⋊C4C23×C4132yes—
889C22⋊C4C23×C4132yes—
890C22⋊C4C23×C418yes—
891C22⋊C4C23×C418yes—
892C22⋊C4C23×C4132yes—
893C22⋊C4C23×C4132yes—
894C42—28no—
895C42—24no—
896C42—28no—
897C42—22no—
898C42—22no—
899C42—24no—
900C42—22no—
901C42—24no—
902C42—24no—
903C42—28no—
904C42—44no—
905C42—48no—
906C42—48no—
907C42—44no—
908C42—44no—
909C42—48no—
910C42—42no—
911C42—44no—
912C42—42no—
913C42—48no—
914C42—44no—
915C42C23×C414yes—
916C42C23×C418yes—
917C42C23×C414yes—
918C42C23×C418yes—
919C42C23×C418yes—
920C42C23×C414yes—
921C42C23×C414yes—
922C42C23×C4116yes—
923C42H(5,𝔽2)14yes—
924C23—21no—
925C23—28no—
926C23—22no—
927C23—21no—
928C23—24no—
929C23—28no—
930C23—28no—
931C23—28no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—28no—
936C23—24no—
937C23—28no—
938C23—416no—
939C23—416no—
940C23—416no—
941C23—168no—
942C23—168no—
943C23C24×C412yes—
944C23C24×C4116yes—
945C23C24×C414yes—
946C23C2611yescharacteristic
947Q8—28no—
948Q8—216no—
949Q8—48no—
950D4—232no—
951D4—28no—
952D4—232no—
953D4—416no—
954D4—416no—
955D4—416no—
956D4—416no—
957D4—48no—
958D4—432no—
959D4—432no—
960C2×C4—22no—
961C2×C4—24no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—24no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—24no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—22no—
975C2×C4—28no—
976C2×C4—28no—
977C2×C4—216no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—22no—
981C2×C4—28no—
982C2×C4—24no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—24no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—24no—
989C2×C4—22no—
990C2×C4—28no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—22no—
998C2×C4—24no—
999C2×C4—28no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—44no—
1003C2×C4—48no—
1004C2×C4—432no—
1005C2×C4—432no—
1006C2×C4—48no—
1007C2×C4—88no—
1008C2×C4—816no—
1009C2×C4—816no—
1010C2×C4—88no—
1011C2×C4—168no—
1012C2×C4—168no—
1013C2×C4C24×C412yes—
1014C2×C4C24×C412yes—
1015C2×C4C24×C414yes—
1016C2×C4C24×C414yes—
1017C2×C4C24×C414yes—
1018C2×C4C24×C412yes—
1019C2×C4C24×C412yes—
1020C2×C4C24×C418yes—
1021C2×C4C24×C418yes—
1022C2×C4C24×C412yes—
1023C2×C4C24×C412yes—
1024C2×C4C2×H(5,𝔽2)14yes—
1025C2×C4C2×H(5,𝔽2)12yes—
1026C2×C4#58514yes—
1027C2×C4#58512yes—
1028C22—22no—
1029C22—24no—
1030C22—216no—
1031C22—24no—
1032C22—22no—
1033C22—216no—
1034C22—24no—
1035C22—216no—
1036C22—22no—
1037C22—48no—
1038C22—44no—
1039C22—48no—
1040C22—42no—
1041C22—44no—
1042C22—48no—
1043C22—48no—
1044C22—42no—
1045C22—1616no—
1046C22C25×C411yescharacteristic
1047C22C22×H(5,𝔽2)11yescharacteristic
1048C22C2×#58512yes—
1049C22C2×#58511yescharacteristic
1050C22H(7,𝔽2)12yes—
1051C4—22no—
1052C4—24no—
1053C4—24no—
1054C4—22no—
1055C4—28no—
1056C4—24no—
1057C4—22no—
1058C4—28no—
1059C4—22no—
1060C4—24no—
1061C4—44no—
1062C4—44no—
1063C4—48no—
1064C4—42no—
1065C4—42no—
1066C4—42no—
1067C4—44no—
1068C4—44no—
1069C4#342814yes—
1070C4C4×H(5,𝔽2)14yes—
1071C2—44no—
1072C2—416no—
1073C2—42no—
1074C2C2×#342811yescharacteristic
1075C2C2×C4×H(5,𝔽2)11yescharacteristic
1076C2#6265211yescharacteristic
1077C2#6295512yes—
1078C2#6296612yes—
subgroupG/H
center, Frattini, socle, cosocleC23C26
commutatorC22C25×C4
prime radicalC2×#3508C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34498C2semidirect
3. #34494C2semidirect
4. #34492C2semidirect
5. #34478C2semidirect
6. #34442C2semidirect
7. #34438C2semidirect
8. #34402C2semidirect
9. #34373C2semidirect
10. #34367C2semidirect
11. #34364C2semidirect
12. #34331C2semidirect
13. #34330C2semidirect
14. #34329C2semidirect
15. #34292C2semidirect
16. #34261C2semidirect
17. #34222C2semidirect
18. #34210C2semidirect
19. #34193C2semidirect
20. C4×#550C2semidirect
21. #34123C2semidirect
22. #34085C2semidirect
23. #34070C2semidirect
24. #3508C4semidirect
40. C2×C4×#41C22semidirect
43. #2377C22semidirect
44. #2377C22semidirect
45. #2377C22semidirect
46. #2376C22semidirect
48. #2374C22semidirect
49. #2372C22semidirect
50. #2367C22semidirect
51. #2367C22semidirect
52. #2367C22semidirect
53. #2367C22semidirect
58. #2366C22semidirect
59. #2366C22semidirect
60. #2364C22semidirect
61. #2364C22semidirect
62. #2363C22semidirect
63. #2363C22semidirect
64. #2363C22semidirect
66. #2361C22semidirect
67. #2359C22semidirect
68. #2359C22semidirect
70. #2357C22semidirect
71. #2356C22semidirect
72. #2355C22semidirect
73. #2355C22semidirect
75. #2354C22semidirect
76. #2354C22semidirect
77. #2354C22semidirect
79. #2353C22semidirect
80. #2353C22semidirect
81. #2352C22semidirect
82. Q8×C4⋊C4C22semidirect
83. Q8×C4⋊C4C22semidirect
84. #2349C22semidirect
85. #2349C22semidirect
86. D4×C4⋊C4C22semidirect
87. D4×C4⋊C4C22semidirect
89. #2347C22semidirect
91. #2343C22semidirect
95. #2341C22semidirect
97. #2339C22semidirect
98. #2339C22semidirect
103. #2337C22semidirect
104. #2336C22semidirect
105. #2336C22semidirect
106. #2335C22semidirect
107. #2335C22semidirect
108. #2333C22semidirect
109. #2333C22semidirect
111. #2331C22semidirect
112. #2331C22semidirect
113. #2331C22semidirect
119. #2328C22semidirect
120. #2327C22semidirect
121. #2327C22semidirect
122. #2327C22semidirect
123. #2326C22semidirect
124. #2326C22semidirect
125. #2326C22semidirect
126. #2325C22semidirect
127. #2325C22semidirect
128. #2325C22semidirect
129. #2324C22semidirect
132. #2322C22semidirect
136. #2319C22semidirect
137. #2319C22semidirect
138. #2319C22semidirect
139. #2318C22semidirect
142. #2311C22semidirect
147. C4×#127C22semidirect
148. C4×#124C22semidirect
149. C4×#123C22semidirect
150. C4×#121C22semidirect
151. C4×#121C22semidirect
152. C4×#121C22semidirect
154. #2297C22semidirect
155. #2295C22semidirect
156. #2295C22semidirect
157. #2295C22semidirect
158. #2295C22semidirect
159. #2293C22semidirect
162. #2290C22semidirect
163. #2290C22semidirect
166. #2285C22semidirect
169. #2283C22semidirect
170. #2283C22semidirect
171. #2276C22semidirect
172. #2275C22semidirect
173. #2275C22semidirect
174. C42×Q8C22semidirect
175. C42×D4C22semidirect
176. C42×D4C22semidirect
177. C42×D4C22semidirect
179. C2×#376C22semidirect
186. #559C2×C4semidirect
187. #559C2×C4semidirect
188. #550C2×C4semidirect
189. #550C2×C4semidirect
190. #546C2×C4semidirect
191. #546C2×C4semidirect
192. #540C2×C4semidirect
193. #535C2×C4semidirect
194. #533C2×C4semidirect
195. #532C2×C4semidirect
196. #532C2×C4semidirect
199. C2×#127C2×C4semidirect
221. #518C2×C4semidirect
223. C4×#41C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#35082
#344982
#344942
#344922
#344782
#344422
#344382
#344022
#343732
#343672
#343642
#343312
#343302
#343292
#342922
#342612
#342222
#342102
#341932
C4×#5502
#341232
#340852
#340702