Finite Group Databasebeta

← #7699609

Subgroups — #7699609

Order 512.

5834 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60003C214yesmaximal, complemented
2#59973C214yesmaximal, complemented
3#59581C214yesmaximal, complemented
4#59545C214yesmaximal, complemented
5#59466C211yesmaximal, characteristic, complemented
6#59272C214yesmaximal, complemented
7#59193C214yesmaximal, complemented
8#59143C211yesmaximal, characteristic, complemented
9#59070C211yesmaximal, characteristic, complemented
10#36340C214yesmaximal, complemented
11#36302C212yesmaximal, complemented
12#36300C212yesmaximal, complemented
13#36293C214yesmaximal, complemented
14#36253C214yesmaximal, complemented
15#36251C214yesmaximal, complemented
16#36193C212yesmaximal, complemented
17#36162C214yesmaximal, complemented
18#36121C211yesmaximal, characteristic
19C4×#559C211yesmaximal, characteristic, complemented
20C4×#552C212yesmaximal, complemented
21#34155C211yesmaximal, characteristic, complemented
22C2×#2366C211yesmaximal, characteristic, complemented
23D4×#117C214yesmaximal, complemented
24C2×#559C2211yescharacteristic
25C2×#552C2212yes—
26C2×#546C2212yes—
27C2×#532C2211yescharacteristic
28C22×#127C2211yescharacteristic
29C22×C4×D4C2214yes—
30C22×#117C2214yes—
31#2861C2214yescomplemented
32#2860C2214yescomplemented
33#2858C2211yescharacteristic
34#2857C2211yescharacteristic
35#2856C2211yescharacteristic
36#2855C2214yes—
37#2854C2214yescomplemented
38#2853C2214yescomplemented
39#2849C2214yes—
40#2761C2218yescomplemented
41#2753C2218yescomplemented
42#2748C2214yescomplemented
43#2741C2218yescomplemented
44#2717C2214yescomplemented
45#2709C2214yes—
46#2597C2218yescomplemented
47#2597C2218yescomplemented
48#2591C2214yescomplemented
49#2579C2214yescomplemented
50#2578C2218yescomplemented
51#2567C2212yescomplemented
52#2566C2214yescomplemented
53#2554C2218yescomplemented
54#2553C2218yescomplemented
55#2552C2212yescomplemented
56#2548C2212yes—
57#2544C2214yes—
58#2544C2212yes—
59#2531C2218yescomplemented
60#2531C2218yescomplemented
61#2526C2218yescomplemented
62#2521C2218yescomplemented
63#2520C2218yescomplemented
64#2518C2218yescomplemented
65#2513C2214yescomplemented
66#2513C2214yescomplemented
67#2512C2214yescomplemented
68#2511C2214yescomplemented
69#2508C2214yescomplemented
70#2507C2214yescomplemented
71#2500C2214yescomplemented
72#2490C2214yescomplemented
73#2482C2218yes—
74#2480C2218yes—
75#2479C2218yescomplemented
76#2476C2218yescomplemented
77#2476C2218yescomplemented
78#2474C2218yescomplemented
79#2470C2218yescomplemented
80#2467C2218yescomplemented
81#2467C2218yescomplemented
82#2460C2218yescomplemented
83#2460C2218yescomplemented
84#2454C2214yescomplemented
85#2454C2214yescomplemented
86#2454C2214yescomplemented
87#2448C2214yescomplemented
88#2447C2214yescomplemented
89#2445C2214yes—
90#2445C2214yes—
91#2442C2214yes—
92#2438C2218yes—
93#2435C2214yes—
94#2435C2212yes—
95#2431C2212yes—
96#2428C2214yes—
97#2427C2214yescomplemented
98#2427C2214yescomplemented
99#2422C2214yescomplemented
100#2413C2214yescomplemented
101#2412C2214yes—
102#2411C2218yes—
103#2408C2214yes—
104#2406C2214yescomplemented
105#2405C2214yes—
106#2374C2214yescomplemented
107#2373C2214yescomplemented
108#2372C2214yescomplemented
109#2371C2214yescomplemented
110#2370C2214yescomplemented
111#2370C2212yescomplemented
112#2369C2212yescomplemented
113#2367C2214yescomplemented
114#2367C2214yescomplemented
115#2366C2211yescharacteristic
116#2366C2214yes—
117#2366C2211yescharacteristic
118#2366C2211yescharacteristic
119#2366C2214yes—
120#2366C2214yes—
121#2366C2212yes—
122#2363C2214yescomplemented
123#2363C2214yescomplemented
124#2363C2214yescomplemented
125#2362C2212yescomplemented
126#2360C2212yes—
127#2359C2214yes—
128#2357C2214yescomplemented
129#2356C2212yescomplemented
130#2355C2212yescomplemented
131#2354C2214yescomplemented
132#2354C2214yescomplemented
133#2352C2212yes—
134#2352C2218yescomplemented
135#2352C2218yescomplemented
136D4×C4⋊C4C2214yescomplemented
137D4×C4⋊C4C2214yescomplemented
138#2346C2212yescomplemented
139#2344C2214yes—
140#2344C2212yes—
141#2343C2214yes—
142#2342C2218yes—
143#2342C2218yes—
144#2342C2214yes—
145D4×C22⋊C4C2214yes—
146D4×C22⋊C4C2214yes—
147C4×#127C2211yescharacteristic
148C4×#125C2212yescomplemented
149C4×#125C2214yescomplemented
150C4×#126C2214yescomplemented
151C4×#124C2214yescomplemented
152C4×C22⋊Q8C2212yes—
153C4×C22⋊Q8C2212yescomplemented
154C4×#123C2214yes—
155C4×#123C2214yescomplemented
156#2297C2214yescomplemented
157#2293C2214yescomplemented
158#2293C2214yescomplemented
159#2293C2214yescomplemented
160C2×#390C2214yes—
161#2290C2218yescomplemented
162#2290C2218yescomplemented
163C2×#386C2214yes—
164#2285C2214yes—
165#2280C2218yes—
166C42×Q8C2212yescomplemented
167C42×D4C2211yescharacteristic
168C42×D4C2214yescomplemented
169C42×D4C2214yescomplemented
170C4×#117C2214yes—
171C4×#117C2212yescomplemented
172C2×C4×C4⋊C4C2212yes—
173C22×#41C2312yes—
174C23×D4C2314yes—
175C23×D4C2312yes—
176C24×C4C2314yes—
177#559—28no—
178#552—216no—
179#546—48no—
180#532—28no—
181C2×C4⋊Q8C2311yescharacteristic
182C2×#127—28no—
183C2×#127C2311yescharacteristic
184C2×#127C2314yes—
185C2×#127C2312yes—
186C2×#127C2311yescharacteristic
187C2×#126C2314yes—
188C2×#126C2318yes—
189C2×#125C2312yes—
190C2×#125C2314yes—
191C2×#125C2314yes—
192C2×#124C2314yes—
193C2×#124C2312yes—
194C2×#124C2312yes—
195C2×#124C2314yes—
196C2×#124C2312yes—
197C2×#123C2314yes—
198C2×#123C2314yes—
199C2×#123C2314yes—
200C2×#123C2314yes—
201C2×#123C2314yes—
202C2×C22⋊Q8C2312yes—
203C2×C22⋊Q8C2312yes—
204C2×C22⋊Q8C2312yes—
205C2×#121C2314yes—
206C2×#121C2314yes—
207C2×#121C2314yes—
208C2×#121C2312yes—
209C2×#120C2314yes—
210C2×C4×Q8C2312yes—
211C2×C4×Q8C2312yes—
212C2×C4×Q8C2312yes—
213C2×C4×D4—232no—
214C2×C4×D4C2314yes—
215C2×C4×D4C2314yes—
216C2×C4×D4C2314yes—
217C2×C4×D4C2312yes—
218C2×C4×D4C2318yes—
219C2×C4×D4C2314yes—
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2314yes—
222C2×C4×D4C2314yes—
223C2×C4×D4C2318yes—
224C2×C4×D4C2312yes—
225C2×C4×D4C2314yes—
226C2×C4×D4C2314yes—
227C2×#117—416no—
228C2×#117C2314yes—
229C2×#117C2314yes—
230C2×#117C2312yes—
231C2×#117C2318yes—
232C2×#117C2312yes—
233C2×#117C2318yes—
234C2×#117C2318yes—
235C2×#117C2314yes—
236C22×C4⋊C4C2314yes—
237C22×C4⋊C4C2314yes—
238C22×C4⋊C4C2312yes—
239C22×C4⋊C4C2312yes—
240C22×C22⋊C4C2314yes—
241C22×C22⋊C4C2318yes—
242C22×C22⋊C4C2314yes—
243C22×C22⋊C4C2314yes—
244C22×C42C2314yes—
245C22×C42C2311yescharacteristic
246C22×C42C2311yescharacteristic
247C22×C42C2314yes—
248C22×C42C2314yes—
249#400C2318yes—
250#400C2318yes—
251#399C2318yes—
252#399C2318yes—
253#398C2318yes—
254#398C2318yes—
255#398C2318yes—
256#397C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#396C2318yes—
263#396C2318yes—
264#396C2318yes—
265#395C2318yes—
266#394C2318yes—
267#394C2318yes—
268#394C2318yes—
269#394C2318yes—
270#394C2318yes—
271#394C2318yes—
272#394C2318yes—
273#394C2318yes—
274#394C2318yes—
275#392C2318yes—
276#391C2314yes—
277#391C2314yes—
278#391C2312yes—
279#391C2312yes—
280#391C2312yes—
281#391C2318yes—
282#390C2314yes—
283#390C2312yes—
284#390C2314yes—
285#390C2314yes—
286#390C2314yes—
287#390C2314yes—
288#390C2314yes—
289#390C2318yes—
290#390C2318yes—
291#390C2318yes—
292#390C2312yes—
293#390C2314yes—
294#390C2314yes—
295#390C2314yes—
296#390C2314yes—
297#390C2318yes—
298#390C2314yes—
299#390C2314yes—
300#389C2312yes—
301#389C2312yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#389C2318yes—
307#389C2314yes—
308#389C2314yes—
309#389C2312yes—
310#389C2314yes—
311#389C2314yes—
312#389C2312yes—
313#389C2314yes—
314#388C2314yes—
315#388C2314yes—
316#388C2314yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C2318yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
332#388C2314yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2314yes—
337#388C2318yes—
338#387C2314yes—
339#387C2314yes—
340#387C2314yes—
341#387C2314yes—
342#387C2314yes—
343#387C2314yes—
344#387C2314yes—
345#387C2314yes—
346#387C2314yes—
347#387C2318yes—
348#387C2314yes—
349#387C2318yes—
350#387C2314yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2314yes—
356#387C2314yes—
357#386C2314yes—
358#386C2318yes—
359#386C2314yes—
360#386C2314yes—
361#386C2314yes—
362#386C2314yes—
363#386C2314yes—
364#386C2314yes—
365#386C2318yes—
366#386C2318yes—
367#386C2318yes—
368#386C2318yes—
369#386C2318yes—
370#386C2314yes—
371#386C2314yes—
372#386C2314yes—
373#386C2318yes—
374#385C2314yes—
375#385C2318yes—
376#385C2314yes—
377#385C2318yes—
378#385C2314yes—
379#385C2318yes—
380#385C2318yes—
381#385C2318yes—
382#385C2318yes—
383#385C2314yes—
384#385C2314yes—
385#385C2314yes—
386#384C2311yescharacteristic
387#384C2314yes—
388#384C2314yes—
389#383C2314yes—
390#382C2312yes—
391#382C2314yes—
392#382C2318yes—
393#382C2314yes—
394#381C2318yes—
395#381C2314yes—
396#381C2314yes—
397#381C2314yes—
398#380C2318yes—
399#380C2314yes—
400#380C2312yes—
401#380C2314yes—
402#380C2318yes—
403#380C2312yes—
404#380C2318yes—
405#380C2318yes—
406#380C2318yes—
407#379C2314yes—
408#379C2318yes—
409#379C2318yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2312yes—
415C4×C4⋊C4C2312yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2312yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2318yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2312yes—
427C4×C4⋊C4C2312yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2312yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2312yes—
433C4×C4⋊C4C2312yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2311yescharacteristic
437C4×C22⋊C4C2312yes—
438C4×C22⋊C4C2314yes—
439C4×C22⋊C4C2314yes—
440C4×C22⋊C4C2318yes—
441C4×C22⋊C4C2318yes—
442C4×C22⋊C4C2314yes—
443C4×C22⋊C4C2312yes—
444C4×C22⋊C4C2314yes—
445C4×C22⋊C4C2314yes—
446C4×C22⋊C4C2314yes—
447C4×C22⋊C4C2318yes—
448C4×C22⋊C4C2318yes—
449C4×C22⋊C4C2318yes—
450C4×C22⋊C4C2311yescharacteristic
451C4×C22⋊C4C2314yes—
452C4×C22⋊C4C2318yes—
453C4×C22⋊C4C2318yes—
454C4×C22⋊C4C2318yes—
455C4×C22⋊C4C2311yescharacteristic
456#376C2314yes—
457#376C2314yes—
458#376C2314yes—
459C2×#95C2314yes—
460C43C2314yes—
461C43C2311yescharacteristic
462C43C2314yes—
463C25C2414yes—
464C2×#41—28no—
465C2×#41—44no—
466C2×#41—82no—
467C22×Q8C2412yes—
468C22×Q8C2412yes—
469C22×D4—216no—
470C22×D4—28no—
471C22×D4—216no—
472C22×D4—48no—
473C22×D4—44no—
474C22×D4—82no—
475C22×D4C2411yescharacteristic
476C22×D4C2414yes—
477C22×D4C2418yes—
478C22×D4C2414yes—
479C22×D4C2414yes—
480C22×D4C2414yes—
481C22×D4C2412yes—
482C22×D4C2414yes—
483C22×D4C2412yes—
484C23×C4—232no—
485C23×C4—48no—
486C23×C4C2412yes—
487C23×C4C2414yes—
488C23×C4C2414yes—
489C23×C4C2418yes—
490C23×C4C2414yes—
491C23×C4C2411yescharacteristic
492C23×C4C2411yescharacteristic
493C23×C4C2414yes—
494C23×C4C2412yes—
495C23×C4C2414yes—
496C23×C4C2414yes—
497C23×C4C2414yes—
498C23×C4C2414yes—
499C4⋊Q8—24no—
500#127—28no—
501#127—216no—
502#127—24no—
503#127#4118yes—
504#126—216no—
505#126—88no—
506#125—216no—
507#125—28no—
508#125—48no—
509#124—28no—
510#124—216no—
511#124—44no—
512#124—48no—
513#124—82no—
514#123—216no—
515#123—216no—
516#123—48no—
517#123—84no—
518#123—84no—
519C22⋊Q8—28no—
520C22⋊Q8—28no—
521C22⋊Q8—44no—
522#121—216no—
523#121—44no—
524#121—48no—
525#121—48no—
526#120—48no—
527C4×Q8—28no—
528C4×Q8—28no—
529C4×Q8—44no—
530C4×D4—216no—
531C4×D4—216no—
532C4×D4—28no—
533C4×D4—216no—
534C4×D4—216no—
535C4×D4—216no—
536C4×D4—216no—
537C4×D4—232no—
538C4×D4—232no—
539C4×D4—24no—
540C4×D4—48no—
541C4×D4—48no—
542C4×D4—44no—
543#117—216no—
544#117—28no—
545#117—216no—
546#117—416no—
547#117—416no—
548#117—416no—
549#117—44no—
550#117—84no—
551C2×C4⋊C4—44no—
552C2×C4⋊C4—48no—
553C2×C4⋊C4—48no—
554C2×C4⋊C4#41116yescomplemented
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2411yescharacteristic
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2418yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2414yes—
587C2×C22⋊C4—232no—
588C2×C22⋊C4—216no—
589C2×C22⋊C4—48no—
590C2×C22⋊C4—84no—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2412yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2411yescharacteristic
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2412yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2411yescharacteristic
625C2×C42—216no—
626C2×C42—24no—
627C2×C42—24no—
628C2×C42—48no—
629C2×C42—48no—
630C2×C42C2414yes—
631C2×C42C2414yes—
632C2×C42C2414yes—
633C2×C42C2414yes—
634C2×C42C2411yescharacteristic
635C2×C42C2412yes—
636C2×C42C2412yes—
637C2×C42C2414yes—
638C2×C42C2414yes—
639C2×C42C2414yes—
640C2×C42C2414yes—
641C2×C42C2414yes—
642C2×C42C2412yes—
643C2×C42C2414yes—
644C2×C42C2411yescharacteristic
645C2×C42C2412yes—
646C2×C42C2411yescharacteristic
647C2×C42C2414yes—
648C2×C42C2418yes—
649C2×C42C2418yes—
650C2×C42C2414yes—
651C2×C42C2414yes—
652C2×C42C2411yescharacteristic
653C2×C42C2414yes—
654C2×C42C2411yescharacteristic
655#95C2414yes—
656#95C2414yes—
657#95C2414yes—
658#95C2414yes—
659#95C2412yes—
660#95C2412yes—
661#95C2414yes—
662#95C2414yes—
663#95C2414yes—
664#95C2414yes—
665#95C2414yes—
666#95C2414yes—
667#95C2414yes—
668#95C2414yes—
669#95C2414yes—
670#95C2414yes—
671#95C2414yes—
672#95C2414yes—
673#95C2418yes—
674#95C2418yes—
675#95C2418yes—
676#95C2418yes—
677#95C2412yes—
678#95C2418yes—
679#95C2418yes—
680#95C2418yes—
681#95C2414yes—
682#95C2414yes—
683#95C2414yes—
684#95C2418yes—
685#95C2414yes—
686#95C2414yes—
687#95C2418yes—
688C24—28no—
689C24—216no—
690C24—28no—
691C24—44no—
692C24—48no—
693C24C2514yes—
694C24C2511yescharacteristic
695C24C2514yes—
696C24C2511yescharacteristic
697#41—816no—
698C2×Q8—24no—
699C2×Q8—24no—
700C2×Q8—24no—
701C2×Q8—24no—
702C2×Q8—42no—
703C2×Q8—42no—
704C2×D4—24no—
705C2×D4—216no—
706C2×D4—22no—
707C2×D4—28no—
708C2×D4—28no—
709C2×D4—28no—
710C2×D4—216no—
711C2×D4—28no—
712C2×D4—28no—
713C2×D4—24no—
714C2×D4—28no—
715C2×D4—28no—
716C2×D4—464no—
717C2×D4—42no—
718C2×D4—48no—
719C2×D4—42no—
720C2×D4—44no—
721C2×D4—44no—
722C2×D4—42no—
723C2×D4—44no—
724C2×D4—44no—
725C2×D4—42no—
726C2×D4—44no—
727C2×D4—48no—
728C2×D4—816no—
729C2×D4C2×#41116yes—
730C2×D4C2×#4118yes—
731C22×C4—28no—
732C22×C4—28no—
733C22×C4—24no—
734C22×C4—24no—
735C22×C4—28no—
736C22×C4—22no—
737C22×C4—28no—
738C22×C4—28no—
739C22×C4—24no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—24no—
743C22×C4—216no—
744C22×C4—216no—
745C22×C4—216no—
746C22×C4—216no—
747C22×C4—28no—
748C22×C4—22no—
749C22×C4—24no—
750C22×C4—28no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—48no—
754C22×C4—44no—
755C22×C4—41no—
756C22×C4—41no—
757C22×C4—464no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4—48no—
763C22×C4—48no—
764C22×C4—44no—
765C22×C4C2×#4118yes—
766C22×C4C2×#41116yes—
767C22×C4C2511yescharacteristic
768C22×C4C2512yes—
769C22×C4C2514yes—
770C22×C4C2514yes—
771C22×C4C2514yes—
772C22×C4C2514yes—
773C22×C4C2514yes—
774C22×C4C2514yes—
775C22×C4C2512yes—
776C22×C4C2514yes—
777C22×C4C2514yes—
778C22×C4C2511yescharacteristic
779C22×C4C2512yes—
780C22×C4C2511yescharacteristic
781C22×C4C2514yes—
782C22×C4C2514yes—
783C22×C4C2511yescharacteristic
784C22×C4C2511yescharacteristic
785C22×C4C2512yes—
786C4⋊C4—28no—
787C4⋊C4—24no—
788C4⋊C4—28no—
789C4⋊C4—24no—
790C4⋊C4—28no—
791C4⋊C4—24no—
792C4⋊C4—28no—
793C4⋊C4—28no—
794C4⋊C4—28no—
795C4⋊C4—28no—
796C4⋊C4—28no—
797C4⋊C4—28no—
798C4⋊C4—22no—
799C4⋊C4—24no—
800C4⋊C4—24no—
801C4⋊C4—24no—
802C4⋊C4—28no—
803C4⋊C4—44no—
804C4⋊C4—48no—
805C4⋊C4—48no—
806C4⋊C4—48no—
807C4⋊C4—42no—
808C4⋊C4—44no—
809C4⋊C4—44no—
810C4⋊C4—44no—
811C4⋊C4—48no—
812C4⋊C4—48no—
813C4⋊C4—48no—
814C4⋊C4—44no—
815C4⋊C4C2×#4118yes—
816C4⋊C4C2×#4118yes—
817C4⋊C4C2×#41116yes—
818C22⋊C4—24no—
819C22⋊C4—28no—
820C22⋊C4—216no—
821C22⋊C4—216no—
822C22⋊C4—28no—
823C22⋊C4—28no—
824C22⋊C4—28no—
825C22⋊C4—216no—
826C22⋊C4—216no—
827C22⋊C4—216no—
828C22⋊C4—216no—
829C22⋊C4—28no—
830C22⋊C4—24no—
831C22⋊C4—28no—
832C22⋊C4—28no—
833C22⋊C4—28no—
834C22⋊C4—22no—
835C22⋊C4—48no—
836C22⋊C4—44no—
837C22⋊C4—44no—
838C22⋊C4—48no—
839C22⋊C4—44no—
840C22⋊C4—44no—
841C22⋊C4—48no—
842C22⋊C4—48no—
843C22⋊C4—44no—
844C22⋊C4—44no—
845C22⋊C4—48no—
846C22⋊C4—44no—
847C22⋊C4—48no—
848C22⋊C4—48no—
849C22⋊C4—48no—
850C22⋊C4—48no—
851C22⋊C4H(5,𝔽2)14yes—
852C42—28no—
853C42—28no—
854C42—28no—
855C42—28no—
856C42—24no—
857C42—22no—
858C42—22no—
859C42—24no—
860C42—28no—
861C42—28no—
862C42—28no—
863C42—24no—
864C42—28no—
865C42—28no—
866C42—22no—
867C42—24no—
868C42—28no—
869C42—48no—
870C42—48no—
871C42—44no—
872C42—44no—
873C42—44no—
874C42—41no—
875C42—44no—
876C42C2×#4114yes—
877C23—21no—
878C23—22no—
879C23—21no—
880C23—28no—
881C23—24no—
882C23—28no—
883C23—24no—
884C23—22no—
885C23—28no—
886C23—21no—
887C23—24no—
888C23—24no—
889C23—21no—
890C23—28no—
891C23—22no—
892C23—24no—
893C23—21no—
894C23—432no—
895C23—416no—
896C23—416no—
897C23—816no—
898C23—88no—
899C23C22×#4118yes—
900C23C22×#4114yes—
901C23C2×H(5,𝔽2)12yes—
902C23C2611yescharacteristic
903Q8—48no—
904Q8—84no—
905D4—232no—
906D4—48no—
907D4—432no—
908D4—44no—
909D4—416no—
910D4—84no—
911D4—88no—
912D4—88no—
913D4—164no—
914C2×C4—21no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—22no—
918C2×C4—24no—
919C2×C4—21no—
920C2×C4—24no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—232no—
926C2×C4—216no—
927C2×C4—22no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—21no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—21no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—21no—
945C2×C4—22no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—22no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—28no—
953C2×C4—24no—
954C2×C4—22no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—21no—
961C2×C4—416no—
962C2×C4—416no—
963C2×C4—432no—
964C2×C4—44no—
965C2×C4—44no—
966C2×C4—416no—
967C2×C4—48no—
968C2×C4—88no—
969C2×C4—88no—
970C2×C4—88no—
971C2×C4—88no—
972C2×C4C22×#4114yes—
973C2×C4C22×#4112yes—
974C2×C4C22×#4118yes—
975C2×C4C22×#4118yes—
976C2×C4C22×#4114yes—
977C2×C4C22×#4114yes—
978C2×C4C2×H(5,𝔽2)12yes—
979C2×C4C2×H(5,𝔽2)12yes—
980C2×C4#58514yes—
981C22—22no—
982C22—24no—
983C22—22no—
984C22—24no—
985C22—28no—
986C22—216no—
987C22—48no—
988C22—44no—
989C22—44no—
990C22—41no—
991C22—44no—
992C22—42no—
993C22—48no—
994C22—41no—
995C22—44no—
996C22—42no—
997C22—48no—
998C22—44no—
999C22—41no—
1000C22—832no—
1001C22#348114yes—
1002C22C23×#4111yescharacteristic
1003C22C23×#4112yes—
1004C22C22×H(5,𝔽2)11yescharacteristic
1005C22C2×#58512yes—
1006C22H(7,𝔽2)11yescharacteristic
1007C4—22no—
1008C4—22no—
1009C4—22no—
1010C4—24no—
1011C4—28no—
1012C4—28no—
1013C4—41no—
1014C4—44no—
1015C4—44no—
1016C4—42no—
1017C4—44no—
1018C4—44no—
1019C4—44no—
1020C4—44no—
1021C4—44no—
1022C4—42no—
1023C4—44no—
1024C4—41no—
1025C4#347518yes—
1026C2—24no—
1027C2—48no—
1028C2—81no—
1029C2—84no—
1030C2C2×#347512yes—
1031C2C2×#348111yescharacteristic
1032C2#6298311yescharacteristic
1033C2#6300612yes—
1034C2#6302111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36121C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60003C2semidirect
2. #59973C2semidirect
3. #59581C2semidirect
4. #59545C2semidirect
5. #59466C2semidirect
6. #59272C2semidirect
7. #59193C2semidirect
8. #59143C2semidirect
9. #59070C2semidirect
10. #36340C2semidirect
11. #36302C2semidirect
12. #36300C2semidirect
13. #36293C2semidirect
14. #36253C2semidirect
15. #36251C2semidirect
16. #36193C2semidirect
17. #36162C2semidirect
19. C4×#559C2semidirect
20. C4×#552C2semidirect
21. #34155C2semidirect
22. C2×#2366C2semidirect
23. D4×#117C2semidirect
31. #2861C22semidirect
32. #2860C22semidirect
37. #2854C22semidirect
38. #2853C22semidirect
40. #2761C22semidirect
41. #2753C22semidirect
42. #2748C22semidirect
43. #2741C22semidirect
44. #2717C22semidirect
46. #2597C22semidirect
47. #2597C22semidirect
48. #2591C22semidirect
49. #2579C22semidirect
50. #2578C22semidirect
51. #2567C22semidirect
52. #2566C22semidirect
53. #2554C22semidirect
54. #2553C22semidirect
55. #2552C22semidirect
59. #2531C22semidirect
60. #2531C22semidirect
61. #2526C22semidirect
62. #2521C22semidirect
63. #2520C22semidirect
64. #2518C22semidirect
65. #2513C22semidirect
66. #2513C22semidirect
67. #2512C22semidirect
68. #2511C22semidirect
69. #2508C22semidirect
70. #2507C22semidirect
71. #2500C22semidirect
72. #2490C22semidirect
75. #2479C22semidirect
76. #2476C22semidirect
77. #2476C22semidirect
78. #2474C22semidirect
79. #2470C22semidirect
80. #2467C22semidirect
81. #2467C22semidirect
82. #2460C22semidirect
83. #2460C22semidirect
84. #2454C22semidirect
85. #2454C22semidirect
86. #2454C22semidirect
87. #2448C22semidirect
88. #2447C22semidirect
97. #2427C22semidirect
98. #2427C22semidirect
99. #2422C22semidirect
100. #2413C22semidirect
104. #2406C22semidirect
106. #2374C22semidirect
107. #2373C22semidirect
108. #2372C22semidirect
109. #2371C22semidirect
110. #2370C22semidirect
111. #2370C22semidirect
112. #2369C22semidirect
113. #2367C22semidirect
114. #2367C22semidirect
122. #2363C22semidirect
123. #2363C22semidirect
124. #2363C22semidirect
125. #2362C22semidirect
128. #2357C22semidirect
129. #2356C22semidirect
130. #2355C22semidirect
131. #2354C22semidirect
132. #2354C22semidirect
134. #2352C22semidirect
135. #2352C22semidirect
136. D4×C4⋊C4C22semidirect
137. D4×C4⋊C4C22semidirect
138. #2346C22semidirect
148. C4×#125C22semidirect
149. C4×#125C22semidirect
150. C4×#126C22semidirect
151. C4×#124C22semidirect
153. C4×C22⋊Q8C22semidirect
155. C4×#123C22semidirect
156. #2297C22semidirect
157. #2293C22semidirect
158. #2293C22semidirect
159. #2293C22semidirect
161. #2290C22semidirect
162. #2290C22semidirect
166. C42×Q8C22semidirect
168. C42×D4C22semidirect
169. C42×D4C22semidirect
171. C4×#117C22semidirect
554. C2×C4⋊C4#41semidirect

Maximal subgroups

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

subgroupindex
#600032
#599732
#595812
#595452
#594662
#592722
#591932
#591432
#590702
#363402
#363022
#363002
#362932
#362532
#362512
#361932
#361622
#361212
C4×#5592
C4×#5522
#341552
C2×#23662
D4×#1172