Finite Group Databasebeta

← #7645640

Subgroups — #7645640

Order 512.

5266 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
1#41429C218yesmaximal, complemented
2#41395C214yesmaximal, complemented
3#41389C214yesmaximal, complemented
4#38112C214yesmaximal, complemented
5#38067C214yesmaximal, complemented
6#37883C214yesmaximal, complemented
7#37851C214yesmaximal, complemented
8#37502C214yesmaximal, complemented
9#37000C218yesmaximal, complemented
10#35448C212yesmaximal, complemented
11#35447C212yesmaximal, complemented
12#35229C214yesmaximal, complemented
13#35097C212yesmaximal, complemented
14#35089C212yesmaximal, complemented
15#35020C211yesmaximal, characteristic, complemented
16#35000C211yesmaximal, characteristic
17C2×#2501C211yesmaximal, characteristic, complemented
18C2×#2486C211yesmaximal, characteristic, complemented
19#34205C211yesmaximal, characteristic, complemented
20C2×#2344C211yesmaximal, characteristic, complemented
21#34057C211yesmaximal, characteristic, complemented
22C2×#534C2212yes—
23C22×#123C2212yes—
24C22×#123C2212yes—
25C22×#123C2212yes—
26C22×#121C2211yescharacteristic
27C2×#518C2212yes—
28C22×C4×D4C2211yescharacteristic
29C22×#117C2212yes—
30C23×C4⋊C4C2211yescharacteristic
31#2854C2212yes—
32#2854C2218yescomplemented
33#2853C2218yescomplemented
34#2851C2214yescomplemented
35#2847C2212yes—
36#2837C2218yescomplemented
37#2836C2218yescomplemented
38#2797C2218yescomplemented
39#2793C2218yescomplemented
40#2793C2218yescomplemented
41#2791C2218yescomplemented
42#2791C2218yescomplemented
43#2786C2218yescomplemented
44#2777C2218yescomplemented
45#2773C2218yescomplemented
46#2768C2218yescomplemented
47#2752C2218yescomplemented
48#2748C2218yescomplemented
49#2743C2218yescomplemented
50#2741C2218yescomplemented
51#2740C2218yescomplemented
52#2740C2218yescomplemented
53#2738C2218yescomplemented
54#2667C2218yescomplemented
55#2654C2218yescomplemented
56#2651C2218yescomplemented
57#2649C2218yescomplemented
58#2647C2214yescomplemented
59#2646C2214yescomplemented
60#2644C2214yescomplemented
61#2629C2214yescomplemented
62#2624C2214yescomplemented
63#2623C2218yescomplemented
64#2618C2212yes—
65#2618C2218yescomplemented
66#2617C2212yes—
67#2569C2214yescomplemented
68#2569C2214yescomplemented
69#2543C2214yes—
70#2534C2214yes—
71#2534C2218yescomplemented
72#2522C2218yescomplemented
73#2516C2218yescomplemented
74#2513C2214yescomplemented
75#2507C2214yescomplemented
76#2507C2214yescomplemented
77#2501C2214yes—
78#2501C2214yes—
79#2501C2212yescomplemented
80#2501C2214yescomplemented
81#2501C2212yescomplemented
82#2498C2218yescomplemented
83#2498C2218yescomplemented
84#2497C2214yescomplemented
85#2497C2214yescomplemented
86#2490C2214yescomplemented
87#2486C2212yes—
88#2486C2214yes—
89#2486C2214yes—
90#2486C2218yescomplemented
91#2486C2212yescomplemented
92#2486C2214yescomplemented
93#2486C2212yescomplemented
94#2484C2218yescomplemented
95#2484C2218yescomplemented
96#2483C2218yescomplemented
97#2482C2218yescomplemented
98#2454C2214yescomplemented
99#2442C2214yescomplemented
100#2442C2214yescomplemented
101#2425C2218yescomplemented
102#2425C2218yescomplemented
103#2420C2214yescomplemented
104#2419C2218yescomplemented
105#2419C2218yescomplemented
106#2419C2218yescomplemented
107#2419C2218yescomplemented
108#2416C2214yes—
109#2413C2218yes—
110#2413C2218yes—
111#2413C2218yescomplemented
112#2412C2218yes—
113#2411C2218yes—
114#2411C2218yescomplemented
115#2408C2212yes—
116C2×#399C2214yescomplemented
117C2×#398C2212yescomplemented
118C2×#397C2212yescomplemented
119#2364C2214yes—
120#2361C2214yes—
121#2344C2214yescomplemented
122#2344C2214yescomplemented
123#2344C2214yescomplemented
124#2344C2214yescomplemented
125#2344C2212yescomplemented
126#2342C2214yescomplemented
127D4×C22⋊C4C2212yescomplemented
128#2330C2214yescomplemented
129#2325C2214yescomplemented
130#2324C2214yescomplemented
131#2319C2214yescomplemented
132#2318C2214yes—
133#2318C2214yescomplemented
134#2315C2211yescharacteristic
135#2315C2211yescharacteristic
136#2315C2212yes—
137#2315C2212yes—
138#2314C2214yescomplemented
139#2313C2212yescomplemented
140#2312C2212yescomplemented
141#2308C2211yescharacteristic
142#2308C2211yescharacteristic
143#2308C2212yes—
144#2308C2212yes—
145C4×#121C2214yescomplemented
146C2×#390C2212yescomplemented
147C2×#389C2212yescomplemented
148C2×#389C2212yescomplemented
149#2290C2214yes—
150#2290C2214yescomplemented
151C2×#387C2214yescomplemented
152C2×#384C2212yescomplemented
153#2283C2212yescomplemented
154#2280C2212yescomplemented
155C2×#381C2212yes—
156C2×#381C2212yes—
157C2×#380C2211yescharacteristic
158C2×#380C2211yescharacteristic
159C2×#380C2212yescomplemented
160C2×C4×C4⋊C4C2212yescomplemented
161C2×C4×C22⋊C4C2211yescharacteristic
162C2×C4×C22⋊C4C2211yescharacteristic
163C23×D4C2311yescharacteristic
164C23×D4C2312yes—
165C23×D4C2311yescharacteristic
166C24×C4C2312yes—
167C24×C4C2311yescharacteristic
168C24×C4C2311yescharacteristic
169#534—48no—
170C2×#125C2314yes—
171C2×#123—48no—
172C2×#123—48no—
173C2×#123—48no—
174C2×#123C2314yes—
175C2×#123C2314yes—
176C2×#123C2314yes—
177C2×#123C2314yes—
178C2×#123C2314yes—
179C2×#123C2314yes—
180C2×#123C2314yes—
181C2×#123C2318yes—
182C2×#123C2318yes—
183C2×#123C2318yes—
184C2×#123C2314yes—
185C2×#121—28no—
186C2×#121C2312yes—
187C2×#121C2312yes—
188C2×#121C2312yes—
189C2×#121C2312yes—
190C2×#121C2314yes—
191C2×#121C2318yes—
192C2×#120C2314yes—
193C2×#120C2314yes—
194#518—48no—
195C2×C4×D4—28no—
196C2×C4×D4C2312yes—
197C2×C4×D4C2312yes—
198C2×C4×D4C2312yes—
199C2×C4×D4C2312yes—
200C2×C4×D4C2314yes—
201C2×C4×D4C2318yes—
202C2×C4×D4C2318yes—
203C2×#117—48no—
204C2×#117C2314yes—
205C2×#117C2314yes—
206C2×#117C2318yes—
207C2×#117C2318yes—
208C22×C4⋊C4—28no—
209C22×C4⋊C4C2311yescharacteristic
210C22×C4⋊C4C2312yes—
211C22×C4⋊C4C2312yes—
212C22×C4⋊C4C2312yes—
213C22×C4⋊C4C2312yes—
214C22×C4⋊C4C2311yescharacteristic
215C22×C4⋊C4C2311yescharacteristic
216C22×C4⋊C4C2312yes—
217C22×C4⋊C4C2311yescharacteristic
218C22×C4⋊C4C2312yes—
219C22×C4⋊C4C2314yes—
220C22×C4⋊C4C2314yes—
221C22×C4⋊C4C2314yes—
222C22×C4⋊C4C2314yes—
223C22×C4⋊C4C2312yes—
224C22×C22⋊C4C2311yescharacteristic
225C22×C22⋊C4C2311yescharacteristic
226C22×C22⋊C4C2311yescharacteristic
227C22×C22⋊C4C2311yescharacteristic
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2311yescharacteristic
231C22×C22⋊C4C2311yescharacteristic
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2314yes—
234C22×C22⋊C4C2314yes—
235C22×C22⋊C4C2314yes—
236C22×C22⋊C4C2314yes—
237C22×C42C2311yescharacteristic
238C22×C42C2312yes—
239C22×C42C2314yes—
240C22×C42C2312yes—
241#400C2318yes—
242#400C2318yes—
243#400C2318yes—
244#400C2318yes—
245#400C2318yes—
246#400C2318yes—
247#399C2318yes—
248#399C2318yes—
249#399C2318yes—
250#399C2318yes—
251#399C2318yes—
252#399C2318yes—
253#398C2318yes—
254#398C2318yes—
255#398C2314yes—
256#398C2318yes—
257#398C2318yes—
258#398C2318yes—
259#398C2318yes—
260#398C2314yes—
261#398C2318yes—
262#398C2318yes—
263#398C2314yes—
264#398C2318yes—
265#398C2318yes—
266#398C2318yes—
267#397C2318yes—
268#397C2318yes—
269#397C2318yes—
270#397C2314yes—
271#397C2318yes—
272#397C2314yes—
273#397C2318yes—
274#397C2314yes—
275#397C2318yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#396C2318yes—
280#396C2318yes—
281#396C2318yes—
282#396C2318yes—
283#396C2318yes—
284#396C2318yes—
285#396C2318yes—
286#394C2318yes—
287#394C2318yes—
288#394C2318yes—
289#394C2314yes—
290#394C2318yes—
291#394C2318yes—
292#392C2314yes—
293#390C2314yes—
294#390C2314yes—
295#390C2318yes—
296#390C2314yes—
297#390C2318yes—
298#390C2314yes—
299#390C2318yes—
300#389C2314yes—
301#389C2314yes—
302#389C2314yes—
303#389C2318yes—
304#389C2314yes—
305#389C2318yes—
306#389C2318yes—
307#389C2318yes—
308#389C2314yes—
309#389C2314yes—
310#389C2314yes—
311#389C2314yes—
312#389C2318yes—
313#389C2318yes—
314#388C2314yes—
315#388C2314yes—
316#388C2314yes—
317#388C2314yes—
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#387C2314yes—
332#387C2314yes—
333#387C2314yes—
334#387C2314yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#386C2314yes—
351#386C2314yes—
352#386C2314yes—
353#386C2314yes—
354#386C2318yes—
355#386C2314yes—
356#386C2318yes—
357#386C2314yes—
358#386C2318yes—
359#386C2318yes—
360#386C2318yes—
361#386C2318yes—
362#386C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2314yes—
366#385C2314yes—
367#385C2314yes—
368#385C2314yes—
369#385C2318yes—
370#385C2318yes—
371#385C2318yes—
372#385C2318yes—
373#385C2318yes—
374#384C2314yes—
375#384C2314yes—
376#384C2318yes—
377#383C2314yes—
378#382C2314yes—
379#382C2314yes—
380#381C2312yes—
381#381C2312yes—
382#381C2314yes—
383#381C2314yes—
384#381C2314yes—
385#381C2318yes—
386#381C2314yes—
387#381C2318yes—
388#381C2318yes—
389#381C2314yes—
390#381C2318yes—
391#381C2318yes—
392#380C2312yes—
393#380C2312yes—
394#380C2312yes—
395#380C2312yes—
396#380C2312yes—
397#380C2312yes—
398#380C2318yes—
399#380C2318yes—
400#380C2314yes—
401#380C2314yes—
402#380C2314yes—
403#380C2318yes—
404#380C2312yes—
405#380C2312yes—
406#380C2312yes—
407#380C2312yes—
408#380C2312yes—
409#380C2314yes—
410#380C2318yes—
411#380C2312yes—
412#380C2318yes—
413#379C2312yes—
414#379C2312yes—
415#379C2314yes—
416#379C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2318yes—
421C4×C4⋊C4C2314yes—
422C4×C22⋊C4C2312yes—
423C4×C22⋊C4C2312yes—
424C4×C22⋊C4C2312yes—
425C4×C22⋊C4C2312yes—
426C4×C22⋊C4C2312yes—
427C4×C22⋊C4C2318yes—
428C4×C22⋊C4C2312yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2312yes—
431C4×C22⋊C4C2312yes—
432#376C2314yes—
433C2×#95C2312yes—
434C2×#95C2312yes—
435C2×#95C2312yes—
436C2×#95C2312yes—
437C2×#95C2314yes—
438C2×#95C2314yes—
439C2×#95C2314yes—
440C2×#95C2314yes—
441C25C2412yes—
442C25C2411yescharacteristic
443C25C2411yescharacteristic
444C22×D4—24no—
445C22×D4—28no—
446C22×D4—28no—
447C22×D4—24no—
448C22×D4—28no—
449C22×D4—24no—
450C22×D4—24no—
451C22×D4—44no—
452C22×D4C2412yes—
453C22×D4C2414yes—
454C22×D4C2412yes—
455C22×D4C2414yes—
456C22×D4C2412yes—
457C22×D4C2412yes—
458C22×D4C2418yes—
459C23×C4—28no—
460C23×C4—28no—
461C23×C4—28no—
462C23×C4—24no—
463C23×C4—44no—
464C23×C4—44no—
465C23×C4#4118yes—
466C23×C4C2414yes—
467C23×C4C2412yes—
468C23×C4C2414yes—
469C23×C4C2411yescharacteristic
470C23×C4C2412yes—
471C23×C4C2412yes—
472C23×C4C2412yes—
473C23×C4C2411yescharacteristic
474C23×C4C2411yescharacteristic
475C23×C4C2411yescharacteristic
476C23×C4C2412yes—
477C23×C4C2412yes—
478C23×C4C2414yes—
479C23×C4C2411yescharacteristic
480C23×C4C2414yes—
481C23×C4C2412yes—
482C23×C4C2411yescharacteristic
483C23×C4C2412yes—
484C23×C4C2412yes—
485C23×C4C2418yes—
486C23×C4C2411yescharacteristic
487C23×C4C2411yescharacteristic
488C23×C4C2411yescharacteristic
489#125—48no—
490#123—416no—
491#123—48no—
492#123—48no—
493#123—48no—
494#123—416no—
495#123—48no—
496#123—416no—
497#123—48no—
498#123—48no—
499#123—48no—
500#123—48no—
501#121—28no—
502#121—28no—
503#121—28no—
504#121—28no—
505#121—48no—
506#121—416no—
507#120—48no—
508#120—48no—
509C4×D4—28no—
510C4×D4—28no—
511C4×D4—28no—
512C4×D4—28no—
513C4×D4—48no—
514C4×D4—416no—
515C4×D4—416no—
516#117—48no—
517#117—416no—
518#117—416no—
519#117—48no—
520C2×C4⋊C4—28no—
521C2×C4⋊C4—28no—
522C2×C4⋊C4—24no—
523C2×C4⋊C4—24no—
524C2×C4⋊C4—28no—
525C2×C4⋊C4—28no—
526C2×C4⋊C4—28no—
527C2×C4⋊C4—24no—
528C2×C4⋊C4—24no—
529C2×C4⋊C4—44no—
530C2×C4⋊C4—44no—
531C2×C4⋊C4—48no—
532C2×C4⋊C4—48no—
533C2×C4⋊C4—48no—
534C2×C4⋊C4—48no—
535C2×C4⋊C4C2412yes—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2412yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2418yes—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—28no—
570C2×C22⋊C4—24no—
571C2×C22⋊C4—28no—
572C2×C22⋊C4—24no—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4—28no—
576C2×C22⋊C4—48no—
577C2×C22⋊C4—48no—
578C2×C22⋊C4—48no—
579C2×C22⋊C4—48no—
580C2×C22⋊C4C2412yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2412yes—
583C2×C22⋊C4C2412yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2412yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2412yes—
589C2×C22⋊C4C2412yes—
590C2×C22⋊C4C2412yes—
591C2×C22⋊C4C2412yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2412yes—
595C2×C22⋊C4C2412yes—
596C2×C22⋊C4C2412yes—
597C2×C22⋊C4C2412yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C42—24no—
616C2×C42—44no—
617C2×C42—44no—
618C2×C42—48no—
619C2×C42C2414yes—
620C2×C42C2414yes—
621C2×C42C2412yes—
622C2×C42C2412yes—
623C2×C42C2418yes—
624C2×C42C2418yes—
625C2×C42C2418yes—
626C2×C42C2414yes—
627C2×C42C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2418yes—
634#95C2418yes—
635#95C2418yes—
636#95C2418yes—
637#95C2414yes—
638#95C2414yes—
639#95C2414yes—
640#95C2418yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644#95C2414yes—
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2414yes—
650#95C2418yes—
651#95C2414yes—
652#95C2414yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656#95C2418yes—
657#95C2418yes—
658#95C2418yes—
659#95C2418yes—
660C24—22no—
661C24—22no—
662C24—24no—
663C24—24no—
664C24—24no—
665C24—22no—
666C24—42no—
667C24—42no—
668C24—42no—
669C24—42no—
670C24—44no—
671C24—44no—
672C24C2×#4114yes—
673C24H(5,𝔽2)14yes—
674C24H(5,𝔽2)14yes—
675C24C2512yes—
676C24C2514yes—
677C24C2511yescharacteristic
678C24C2511yescharacteristic
679C24C2511yescharacteristic
680C2×D4—24no—
681C2×D4—24no—
682C2×D4—28no—
683C2×D4—28no—
684C2×D4—28no—
685C2×D4—28no—
686C2×D4—24no—
687C2×D4—28no—
688C2×D4—24no—
689C2×D4—28no—
690C2×D4—24no—
691C2×D4—24no—
692C2×D4—24no—
693C2×D4—24no—
694C2×D4—28no—
695C2×D4—44no—
696C2×D4—48no—
697C2×D4—48no—
698C2×D4—48no—
699C2×D4—416no—
700C2×D4—432no—
701C2×D4—88no—
702C22×C4—24no—
703C22×C4—24no—
704C22×C4—24no—
705C22×C4—22no—
706C22×C4—24no—
707C22×C4—28no—
708C22×C4—24no—
709C22×C4—24no—
710C22×C4—28no—
711C22×C4—24no—
712C22×C4—24no—
713C22×C4—24no—
714C22×C4—24no—
715C22×C4—28no—
716C22×C4—28no—
717C22×C4—28no—
718C22×C4—22no—
719C22×C4—24no—
720C22×C4—24no—
721C22×C4—24no—
722C22×C4—28no—
723C22×C4—24no—
724C22×C4—24no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—24no—
731C22×C4—24no—
732C22×C4—28no—
733C22×C4—24no—
734C22×C4—416no—
735C22×C4—42no—
736C22×C4—42no—
737C22×C4—42no—
738C22×C4—42no—
739C22×C4—42no—
740C22×C4—42no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—42no—
753C22×C4—48no—
754C22×C4—48no—
755C22×C4—48no—
756C22×C4—432no—
757C22×C4—88no—
758C22×C4C2×#4114yes—
759C22×C4C2×#4114yes—
760C22×C4C2×#4114yes—
761C22×C4C2×#4114yes—
762C22×C4C2×#4114yes—
763C22×C4C2×#4114yes—
764C22×C4C2512yes—
765C22×C4C2512yes—
766C22×C4C2514yes—
767C22×C4C2518yes—
768C22×C4C2518yes—
769C22×C4C2514yes—
770C22×C4C2514yes—
771C22×C4C2514yes—
772C22×C4C2514yes—
773C22×C4C2512yes—
774C22×C4C2514yes—
775C22×C4C2514yes—
776C22×C4C2511yescharacteristic
777C22×C4C2511yescharacteristic
778C22×C4C2511yescharacteristic
779C22×C4C2511yescharacteristic
780C4⋊C4—28no—
781C4⋊C4—24no—
782C4⋊C4—24no—
783C4⋊C4—28no—
784C4⋊C4—24no—
785C4⋊C4—24no—
786C4⋊C4—24no—
787C4⋊C4—24no—
788C4⋊C4—24no—
789C4⋊C4—24no—
790C4⋊C4—28no—
791C4⋊C4—28no—
792C4⋊C4—44no—
793C4⋊C4—44no—
794C4⋊C4—48no—
795C4⋊C4—48no—
796C4⋊C4—48no—
797C4⋊C4—48no—
798C4⋊C4—48no—
799C4⋊C4—48no—
800C4⋊C4—48no—
801C4⋊C4—48no—
802C4⋊C4—44no—
803C4⋊C4—44no—
804C4⋊C4—48no—
805C4⋊C4—48no—
806C4⋊C4—44no—
807C4⋊C4—44no—
808C4⋊C4—48no—
809C4⋊C4—48no—
810C4⋊C4—48no—
811C4⋊C4—48no—
812C22⋊C4—24no—
813C22⋊C4—24no—
814C22⋊C4—24no—
815C22⋊C4—28no—
816C22⋊C4—24no—
817C22⋊C4—24no—
818C22⋊C4—28no—
819C22⋊C4—28no—
820C22⋊C4—24no—
821C22⋊C4—28no—
822C22⋊C4—24no—
823C22⋊C4—24no—
824C22⋊C4—24no—
825C22⋊C4—24no—
826C22⋊C4—24no—
827C22⋊C4—24no—
828C22⋊C4—28no—
829C22⋊C4—28no—
830C22⋊C4—48no—
831C22⋊C4—48no—
832C22⋊C4—48no—
833C22⋊C4—48no—
834C22⋊C4—48no—
835C22⋊C4—48no—
836C22⋊C4—48no—
837C22⋊C4—44no—
838C22⋊C4—48no—
839C22⋊C4—48no—
840C22⋊C4—44no—
841C22⋊C4—44no—
842C22⋊C4—44no—
843C22⋊C4—48no—
844C22⋊C4—48no—
845C22⋊C4—48no—
846C22⋊C4—48no—
847C42—24no—
848C42—24no—
849C42—28no—
850C42—28no—
851C42—44no—
852C42—44no—
853C42—48no—
854C42—48no—
855C42—48no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—24no—
864C23—22no—
865C23—24no—
866C23—24no—
867C23—22no—
868C23—24no—
869C23—28no—
870C23—28no—
871C23—24no—
872C23—44no—
873C23—44no—
874C23—48no—
875C23—48no—
876C23—48no—
877C23—44no—
878C23—48no—
879C23—82no—
880C23—82no—
881C23—84no—
882C23—84no—
883C23—84no—
884C23—88no—
885C23—88no—
886C23#540116yes—
887C23C22×#4112yes—
888C23C22×#4112yes—
889C23C22×#4112yes—
890C23C2×H(5,𝔽2)12yes—
891C23C2×H(5,𝔽2)12yes—
892C23C2×H(5,𝔽2)12yes—
893C23C2×H(5,𝔽2)12yes—
894C23C2×H(5,𝔽2)12yes—
895C23C2×H(5,𝔽2)12yes—
896C23C2611yescharacteristic
897D4—48no—
898D4—416no—
899D4—48no—
900D4—416no—
901D4—48no—
902D4—84no—
903D4—168no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—28no—
908C2×C4—28no—
909C2×C4—28no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—28no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—28no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—22no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—22no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—24no—
935C2×C4—28no—
936C2×C4—28no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—28no—
942C2×C4—28no—
943C2×C4—24no—
944C2×C4—44no—
945C2×C4—44no—
946C2×C4—44no—
947C2×C4—48no—
948C2×C4—48no—
949C2×C4—48no—
950C2×C4—416no—
951C2×C4—416no—
952C2×C4—48no—
953C2×C4—48no—
954C2×C4—48no—
955C2×C4—44no—
956C2×C4—48no—
957C2×C4—84no—
958C2×C4—82no—
959C2×C4—88no—
960C2×C4—84no—
961C2×C4—88no—
962C2×C4—82no—
963C2×C4—168no—
964C2×C4C22×#4112yes—
965C2×C4C22×#4112yes—
966C2×C4C22×#4112yes—
967C2×C4C22×#4112yes—
968C2×C4#58514yes—
969C22—22no—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—22no—
974C22—22no—
975C22—24no—
976C22—24no—
977C22—24no—
978C22—24no—
979C22—24no—
980C22—24no—
981C22—416no—
982C22—42no—
983C22—44no—
984C22—42no—
985C22—44no—
986C22—48no—
987C22—44no—
988C22—48no—
989C22—44no—
990C22—42no—
991C22—44no—
992C22—88no—
993C22—168no—
994C22C2×#54014yes—
995C22C2×#54014yes—
996C22C2×#54014yes—
997C22C23×#4111yescharacteristic
998C22C22×H(5,𝔽2)11yescharacteristic
999C22C22×H(5,𝔽2)11yescharacteristic
1000C22C2×#58512yes—
1001C222−1+612yes—
1002C4—22no—
1003C4—22no—
1004C4—22no—
1005C4—42no—
1006C4—42no—
1007C4—44no—
1008C4—44no—
1009C4—44no—
1010C4—48no—
1011C4—44no—
1012C4—48no—
1013C4—44no—
1014C4—44no—
1015C4—42no—
1016C4—44no—
1017C4#349114yes—
1018C2—24no—
1019C2—24no—
1020C2—24no—
1021C2—82no—
1022C2—84no—
1023C2C22×#54011yescharacteristic
1024C2C2×#349111yescharacteristic
1025C2#6286011yescharacteristic
1026C2#6290112yes—
1027C2#6290112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35000C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #41429C2semidirect
2. #41395C2semidirect
3. #41389C2semidirect
4. #38112C2semidirect
5. #38067C2semidirect
6. #37883C2semidirect
7. #37851C2semidirect
8. #37502C2semidirect
9. #37000C2semidirect
10. #35448C2semidirect
11. #35447C2semidirect
12. #35229C2semidirect
13. #35097C2semidirect
14. #35089C2semidirect
15. #35020C2semidirect
17. C2×#2501C2semidirect
18. C2×#2486C2semidirect
19. #34205C2semidirect
20. C2×#2344C2semidirect
21. #34057C2semidirect
32. #2854C22semidirect
33. #2853C22semidirect
34. #2851C22semidirect
36. #2837C22semidirect
37. #2836C22semidirect
38. #2797C22semidirect
39. #2793C22semidirect
40. #2793C22semidirect
41. #2791C22semidirect
42. #2791C22semidirect
43. #2786C22semidirect
44. #2777C22semidirect
45. #2773C22semidirect
46. #2768C22semidirect
47. #2752C22semidirect
48. #2748C22semidirect
49. #2743C22semidirect
50. #2741C22semidirect
51. #2740C22semidirect
52. #2740C22semidirect
53. #2738C22semidirect
54. #2667C22semidirect
55. #2654C22semidirect
56. #2651C22semidirect
57. #2649C22semidirect
58. #2647C22semidirect
59. #2646C22semidirect
60. #2644C22semidirect
61. #2629C22semidirect
62. #2624C22semidirect
63. #2623C22semidirect
65. #2618C22semidirect
67. #2569C22semidirect
68. #2569C22semidirect
71. #2534C22semidirect
72. #2522C22semidirect
73. #2516C22semidirect
74. #2513C22semidirect
75. #2507C22semidirect
76. #2507C22semidirect
79. #2501C22semidirect
80. #2501C22semidirect
81. #2501C22semidirect
82. #2498C22semidirect
83. #2498C22semidirect
84. #2497C22semidirect
85. #2497C22semidirect
86. #2490C22semidirect
90. #2486C22semidirect
91. #2486C22semidirect
92. #2486C22semidirect
93. #2486C22semidirect
94. #2484C22semidirect
95. #2484C22semidirect
96. #2483C22semidirect
97. #2482C22semidirect
98. #2454C22semidirect
99. #2442C22semidirect
100. #2442C22semidirect
101. #2425C22semidirect
102. #2425C22semidirect
103. #2420C22semidirect
104. #2419C22semidirect
105. #2419C22semidirect
106. #2419C22semidirect
107. #2419C22semidirect
111. #2413C22semidirect
114. #2411C22semidirect
116. C2×#399C22semidirect
117. C2×#398C22semidirect
118. C2×#397C22semidirect
121. #2344C22semidirect
122. #2344C22semidirect
123. #2344C22semidirect
124. #2344C22semidirect
125. #2344C22semidirect
126. #2342C22semidirect
127. D4×C22⋊C4C22semidirect
128. #2330C22semidirect
129. #2325C22semidirect
130. #2324C22semidirect
131. #2319C22semidirect
133. #2318C22semidirect
138. #2314C22semidirect
139. #2313C22semidirect
140. #2312C22semidirect
145. C4×#121C22semidirect
146. C2×#390C22semidirect
147. C2×#389C22semidirect
148. C2×#389C22semidirect
150. #2290C22semidirect
151. C2×#387C22semidirect
152. C2×#384C22semidirect
153. #2283C22semidirect
154. #2280C22semidirect
159. C2×#380C22semidirect
160. C2×C4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#414292
#413952
#413892
#381122
#380672
#378832
#378512
#375022
#370002
#354482
#354472
#352292
#350972
#350892
#350202
#350002
C2×#25012
C2×#24862
#342052
C2×#23442
#340572