Finite Group Databasebeta

← #35567851

Subgroups — #35567851

Order 21248.

2766 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128265C211yesmaximal, characteristic
2#24910638C212yesmaximal, complemented
3#24910600C212yesmaximal, complemented
4#24910526C212yesmaximal, complemented
5#24910501C212yesmaximal, complemented
6#24910479C212yesmaximal, complemented
7#24910444C212yesmaximal, complemented
8#24910358C212yesmaximal, complemented
9#24910283C212yesmaximal, complemented
10#24910275C214yesmaximal, complemented
11#24910152C212yesmaximal, complemented
12#24910119C214yesmaximal, complemented
13#24909969C212yesmaximal, complemented
14#24909954C211yesmaximal, characteristic, complemented
15C83×#2311C211yesmaximal, characteristic, complemented
16C23×D332C2211yescharacteristic
17#19128265C4116yescomplemented
18C2×#14581788C2212yes—
19C2×#14581781C2212yes—
20C2×#14581766C2212yes—
21C2×#14581766C2212yes—
22C2×#14581760C2212yes—
23C2×#14581760C2212yes—
24C2×#14581754C2212yes—
25C2×#14581754C2212yes—
26C2×C4×C22⋊D83C2214yescomplemented
27C2×(C22⋊D83)⋊C4C2214yescomplemented
28C2×#14581751C2211yescharacteristic
29C2×#14581751C2211yescharacteristic, complemented
30C2×C22⋊C4×D83C2214yes—
31C22×C4×Dic83C2211yescharacteristic, complemented
32#19127608C2212yescomplemented
33#19127604C2212yes—
34#19127602C2212yes—
35#19127602C2212yes—
36#19127601C2214yescomplemented
37#19127601C2214yescomplemented
38#19127597C2212yescomplemented
39#19127597C2212yescomplemented
40#19127593C2214yescomplemented
41#19127592C2214yescomplemented
42#19127591C2214yescomplemented
43#19127590C2214yescomplemented
44#19127589C2214yes—
45#19127589C2214yes—
46#19127581C2211yescharacteristic
47#19127581C2211yescharacteristic
48#19127581C2211yescharacteristic, complemented
49#19127581C2211yescharacteristic, complemented
50#19127580C2214yescomplemented
51#19127579C2214yes—
52#19127579C2214yes—
53#19127578C2214yescomplemented
54#19127577C2214yescomplemented
55#19127577C2214yescomplemented
56#19127575C2214yescomplemented
57#19127572C2214yescomplemented
58#19127568C2214yescomplemented
59#19127556C2214yes—
60C4⋊C4×Dic83C2212yescomplemented
61C4⋊C4×Dic83C2212yescomplemented
62#19127552C2214yescomplemented
63C4×(C2×D83)⋊C4C2214yescomplemented
64C4×C22⋊Dic83C2212yes—
65C4×C22⋊Dic83C2212yescomplemented
66#19127548C2214yescomplemented
67C22×#41×C83C2211yescharacteristic
68C2×#117×C83C2211yescharacteristic, complemented
69C22×C4⋊C4×C83C2211yescharacteristic, complemented
70#391×C83C2212yescomplemented
71#390×C83C2212yes—
72#386×C83C2212yes—
73#386×C83C2212yescomplemented
74#380×C83C2212yes—
75#380×C83C2212yescomplemented
76C24×D83C2312yes—
77C22×D332—42no—
78C22×D332—42no—
79C22×D332C2×C418yescomplemented
80C22×D332C2312yes—
81C22×D332C2312yes—
82C22×C22⋊D83C2314yes—
83C22×C22⋊D83C2314yes—
84C23×Dic83C2311yescharacteristic
85C23×Dic83C2311yescharacteristic
86C22×C4×D83C2314yes—
87C22×C4×D83C2314yes—
88#14581788C2×C4116yescomplemented
89#14581781C2×C4116yescomplemented
90#14581766C2×C4116yescomplemented
91#14581766C2×C4116yescomplemented
92#14581760C2×C4116yescomplemented
93#14581760C2×C4116yescomplemented
94#14581754—44no—
95#14581754—44no—
96C4×C22⋊D83—48no—
97(C22⋊D83)⋊C4—48no—
98#14581751—42no—
99#14581751C2×C418yescomplemented
100C2×C4⋊Dic83C2312yes—
101C2×C4⋊Dic83C2312yes—
102C2×Dic83⋊C4C2314yes—
103C2×Dic83⋊C4C2314yes—
104C2×C22⋊Dic83C2312yes—
105C2×C22⋊Dic83C2312yes—
106C2×C22⋊Dic83C2312yes—
107C2×C22⋊Dic83C2311yescharacteristic
108C2×C22⋊Dic83C2312yes—
109C2×C22⋊Dic83C2311yescharacteristic
110C2×C22⋊Dic83C2312yes—
111C2×(C2×D83)⋊C4C2314yes—
112C2×(C2×D83)⋊C4C2314yes—
113C2×(C2×D83)⋊C4C2314yes—
114C2×(C2×D83)⋊C4C2314yes—
115C2×(C2×D83)⋊C4C2314yes—
116C2×(C2×D83)⋊C4C2314yes—
117C2×(C2×D83)⋊C4C2314yes—
118C2×(C2×D83)⋊C4C2314yes—
119C22⋊C4×D83—48no—
120C2×C4×Dic83—42no—
121C2×C4×Dic83C2312yes—
122C2×C4×Dic83C2312yes—
123C2×C4×Dic83C2314yes—
124C2×C4×Dic83C2314yes—
125C2×C4×Dic83C2312yes—
126C2×C4×Dic83C2312yes—
127C83⋊#95C2312yes—
128C83⋊#95C2314yes—
129C83⋊#95C2314yes—
130C83⋊#95C2312yes—
131C83⋊#95C2314yes—
132C83⋊#95C2314yes—
133C83⋊#95C2312yes—
134C83⋊#95C2312yes—
135C2×#41×C83—42no—
136C2×#41×C83—42no—
137C2×#41×C83C2×C418yescomplemented
138C22×Q8×C83C2311yescharacteristic
139C22×D4×C83C2311yescharacteristic
140C22×D4×C83C2311yescharacteristic
141C22×D4×C83C2311yescharacteristic
142C23×C4×C83C2311yescharacteristic
143C23×C4×C83C2311yescharacteristic
144C23×C4×C83C2311yescharacteristic
145C23×C4×C83C2312yes—
146#117×C83—42no—
147C2×C4⋊C4×C83—42no—
148C2×C4⋊C4×C83C2312yes—
149C2×C4⋊C4×C83C2312yes—
150C2×C4⋊C4×C83C2312yes—
151C2×C22⋊C4×C83C2314yes—
152C2×C22⋊C4×C83C2312yes—
153C2×C22⋊C4×C83C2314yes—
154C2×C42×C83C2312yes—
155#95×C83C2314yes—
156#95×C83C2314yes—
157C23×D83—42no—
158C23×D83—42no—
159C23×D83—44no—
160C23×D83—44no—
161C23×D83C22×C418yes—
162C23×D83C2414yes—
163C2×D332—24no—
164C2×D332—24no—
165C2×D332—416no—
166C2×D332—42no—
167C2×D332—42no—
168C2×D332C22×C418yes—
169C2×D332C22×C418yes—
170C2×C22⋊D83—44no—
171C2×C22⋊D83—44no—
172C2×C22⋊D83—44no—
173C2×C22⋊D83—44no—
174C2×C22⋊D83C22×C4116yes—
175C2×C22⋊D83C22×C4116yes—
176C22×Dic83—24no—
177C22×Dic83—42no—
178C22×Dic83—41no—
179C22×Dic83—41no—
180C22×Dic83C2412yes—
181C22×Dic83C2412yes—
182C22×Dic83C2412yes—
183C22×Dic83C2414yes—
184C22×Dic83C2412yes—
185C2×C4×D83—28no—
186C2×C4×D83—44no—
187C2×C4×D83—44no—
188C2×C4×D83—44no—
189C2×C4×D83—44no—
190C2×C4×D83—44no—
191C4⋊Dic83—42no—
192C4⋊Dic83C22×C418yes—
193Dic83⋊C4—28no—
194Dic83⋊C4—44no—
195C22⋊Dic83—24no—
196C22⋊Dic83—24no—
197C22⋊Dic83—42no—
198C22⋊Dic83—42no—
199C22⋊Dic83—41no—
200C22⋊Dic83—41no—
201C22⋊Dic83C22×C418yes—
202(C2×D83)⋊C4—28no—
203(C2×D83)⋊C4—44no—
204(C2×D83)⋊C4—44no—
205(C2×D83)⋊C4—44no—
206(C2×D83)⋊C4—44no—
207(C2×D83)⋊C4—44no—
208(C2×D83)⋊C4C22×C4116yes—
209(C2×D83)⋊C4C22×C4116yes—
210C4×Dic83—24no—
211C4×Dic83—24no—
212C4×Dic83—42no—
213C4×Dic83—44no—
214C4×Dic83—44no—
215C4×Dic83C22×C418yes—
216C24×C83C2411yescharacteristic
217C24×C83C2411yescharacteristic
218C24×C83C2411yescharacteristic
219#41×C83—416no—
220C2×Q8×C83—41no—
221C2×Q8×C83—41no—
222C2×Q8×C83C22×C414yes—
223C2×D4×C83—41no—
224C2×D4×C83—41no—
225C2×D4×C83—41no—
226C2×D4×C83—41no—
227C2×D4×C83—41no—
228C2×D4×C83—41no—
229C2×D4×C83C22×C414yes—
230C2×D4×C83C22×C414yes—
231C2×D4×C83C22×C414yes—
232C22×C4×C83—22no—
233C22×C4×C83—22no—
234C22×C4×C83—22no—
235C22×C4×C83—22no—
236C22×C4×C83—22no—
237C22×C4×C83—22no—
238C22×C4×C83—42no—
239C22×C4×C83—44no—
240C22×C4×C83C22×C414yes—
241C22×C4×C83C22×C414yes—
242C22×C4×C83C22×C414yes—
243C22×C4×C83C2414yes—
244C22×C4×C83C2414yes—
245C22×C4×C83C2411yescharacteristic
246C22×C4×C83C2411yescharacteristic
247C22×C4×C83C2411yescharacteristic
248C22×C4×C83C2411yescharacteristic
249C4⋊C4×C83—24no—
250C4⋊C4×C83—24no—
251C4⋊C4×C83—42no—
252C22⋊C4×C83—42no—
253C22⋊C4×C83—44no—
254C22⋊C4×C83—44no—
255C42×C83—42no—
256C23×C83—21no—
257C23×C83—22no—
258C23×C83—22no—
259C23×C83—21no—
260C23×C83—21no—
261C23×C83—21no—
262C23×C83—21no—
263C23×C83—21no—
264C23×C83—22no—
265C23×C83—22no—
266C23×C83—22no—
267C23×C83—22no—
268C23×C83C23×C412yes—
269C23×C83C23×C412yes—
270C23×C83C23×C412yes—
271C23×C83C2511yescharacteristic
272C22×D83—24no—
273C22×D83—24no—
274C22×D83—24no—
275C22×D83—24no—
276C22×D83—24no—
277C22×D83—24no—
278C22×D83—48no—
279C22×D83—416no—
280C22×D83—84no—
281C22×D83—84no—
282C22×D83—88no—
283C22×D83C23×C418yes—
284Q8×C83—44no—
285D4×C83—44no—
286D4×C83—44no—
287D4×C83—44no—
288C2×C4×C83—21no—
289C2×C4×C83—21no—
290C2×C4×C83—21no—
291C2×C4×C83—21no—
292C2×C4×C83—21no—
293C2×C4×C83—21no—
294C2×C4×C83—28no—
295C2×C4×C83—28no—
296C2×C4×C83—28no—
297C2×C4×C83—24no—
298C2×C4×C83—24no—
299C2×C4×C83—24no—
300C2×C4×C83—24no—
301C2×C4×C83—24no—
302C2×C4×C83—24no—
303C2×C4×C83—84no—
304C2×C4×C83C23×C412yes—
305C2×C4×C83C23×C412yes—
306C2×C4×C83C23×C412yes—
307C2×C4×C83C23×C412yes—
308C2×C4×C83H(5,𝔽2)12yes—
309C2×C4×C83H(5,𝔽2)12yes—
310C22⋊D83—416no—
311C22⋊D83—416no—
312C2×Dic83—22no—
313C2×Dic83—24no—
314C2×Dic83—22no—
315C2×Dic83—24no—
316C2×Dic83—22no—
317C2×Dic83—22no—
318C2×Dic83—22no—
319C2×Dic83—22no—
320C2×Dic83—22no—
321C2×Dic83—22no—
322C2×Dic83—22no—
323C2×Dic83—22no—
324C2×Dic83—22no—
325C2×Dic83—44no—
326C2×Dic83—44no—
327C2×Dic83C23×C418yes—
328C2×Dic83H(5,𝔽2)14yes—
329D332—216no—
330D332—48no—
331C4×D83—88no—
332C4×D83—88no—
333C22×C83—22no—
334C22×C83—22no—
335C22×C83—22no—
336C22×C83—24no—
337C22×C83—24no—
338C22×C83—24no—
339C22×C83—41no—
340C22×C83—41no—
341C22×C83—41no—
342C22×C83—41no—
343C22×C83—41no—
344C22×C83—41no—
345C22×C83—42no—
346C22×C83—42no—
347C22×C83—42no—
348C22×C83C24×C411yescharacteristic
349C22×C83C2×H(5,𝔽2)12yes—
350C22×C83C2×H(5,𝔽2)11yescharacteristic
351C22×C83C2×H(5,𝔽2)11yescharacteristic
352C22×C83#58512yes—
353C2×D83—28no—
354C2×D83—28no—
355C2×D83—28no—
356C2×D83—44no—
357C2×D83—44no—
358C2×D83—44no—
359C2×D83—44no—
360C2×D83—816no—
361C4×C83—22no—
362C4×C83—22no—
363C4×C83—22no—
364C4×C83—44no—
365C4×C83—44no—
366C4×C83#51814yes—
367Dic83—28no—
368Dic83—24no—
369Dic83—42no—
370Dic83—42no—
371Dic83—42no—
372#34411—831nomaximal, Sylow
373C2×C83—42no—
374C2×C83—42no—
375C2×C83—42no—
376C2×C83C2×#51811yescharacteristic
377C2×C83C4×H(5,𝔽2)12yes—
378C2×C83#353711yescharacteristic
379C2×C83#354011yescharacteristic
380C2×C83#354612yes—
381D83—48no—
382C2×#535—831no—
383#2380—832no—
384#2375—832no—
385#2366—832no—
386#2363—832no—
387#2361—832no—
388#2358—832no—
389#2347—832no—
390D4×C22⋊C4—832no—
391#2337—834no—
392#2324—832no—
393#2321—834no—
394#2311D8311yescharacteristic, complemented
395C4×#121—832no—
396#2297—831no—
397C83#3441111yescharacteristic, complemented, Sylow
398C22×#41C2×D8311yescharacteristic
399C23×D4—831no—
400#535—8316no—
401C2×#127—832no—
402C2×#124—832no—
403C2×#121—832no—
404C2×#121—832no—
405C2×#120—832no—
406C2×#120—832no—
407C2×C4×D4—834no—
408C2×C4×D4—832no—
409C2×C4×D4—832no—
410C2×C4×D4—834no—
411C2×#117—831no—
412C2×#117—831no—
413C2×#117C2×D8311yescharacteristic, complemented
414C22×C4⋊C4C2×D8311yescharacteristic, complemented
415C22×C22⋊C4—834no—
416C22×C42—831no—
417#391—832no—
418#391C2×D8312yescomplemented
419#390—832no—
420#390—832no—
421#390—832no—
422#390—834no—
423#390—834no—
424#390C2×D8312yes—
425#389—832no—
426#389—832no—
427#388—834no—
428#388—834no—
429#388—834no—
430#388—834no—
431#388—834no—
432#388—834no—
433#386—831no—
434#386—831no—
435#386—831no—
436#386—831no—
437#386—834no—
438#386—834no—
439#386—834no—
440#386—834no—
441#386—834no—
442#386—834no—
443#386C2×D8312yes—
444#386C2×D8312yescomplemented
445#385—834no—
446#385—834no—
447#383—834no—
448#380C2×D8312yes—
449#380C2×D8312yescomplemented
450#379—834no—
451C4×C4⋊C4—832no—
452C4×C4⋊C4—832no—
453C4×C4⋊C4—834no—
454C4×C22⋊C4—832no—
455C4×C22⋊C4—832no—
456C4×C22⋊C4—834no—
457C4×C22⋊C4—834no—
458C25—832no—
459C2×#41—42no—
460C2×#41—42no—
461C2×#41C4×D8318yescomplemented
462C22×Q8C22×D8311yescharacteristic
463C22×D4—3322no—
464C22×D4—3322no—
465C22×D4—834no—
466C22×D4—834no—
467C22×D4—838no—
468C22×D4—832no—
469C22×D4—832no—
470C22×D4C22×D8311yescharacteristic
471C22×D4C22×D8311yescharacteristic
472C22×D4C22×D8311yescharacteristic
473C23×C4—831no—
474C23×C4—834no—
475C23×C4—834no—
476C23×C4—831no—
477C23×C4C22×D8311yescharacteristic
478C23×C4C22×D8311yescharacteristic
479C23×C4C22×D8311yescharacteristic
480C23×C4C22×D8312yes—
481#127—8316no—
482#124—8316no—
483#121—8316no—
484#121—8316no—
485#120—8316no—
486#120—8316no—
487C4×D4—3328no—
488C4×D4—3328no—
489C4×D4—3324no—
490C4×D4—3324no—
491#117—42no—
492#117—3322no—
493#117—838no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—832no—
496C2×C4⋊C4—834no—
497C2×C4⋊C4—832no—
498C2×C4⋊C4—834no—
499C2×C4⋊C4C22×D8312yes—
500C2×C4⋊C4C22×D8312yes—
501C2×C4⋊C4C22×D8312yes—
502C2×C22⋊C4—3328no—
503C2×C22⋊C4—831no—
504C2×C22⋊C4—831no—
505C2×C22⋊C4—832no—
506C2×C22⋊C4—832no—
507C2×C22⋊C4—834no—
508C2×C22⋊C4—834no—
509C2×C22⋊C4—834no—
510C2×C22⋊C4—834no—
511C2×C22⋊C4—834no—
512C2×C22⋊C4—832no—
513C2×C22⋊C4—834no—
514C2×C22⋊C4—834no—
515C2×C22⋊C4—832no—
516C2×C22⋊C4—832no—
517C2×C22⋊C4—834no—
518C2×C22⋊C4C22×D8314yes—
519C2×C22⋊C4C22×D8312yes—
520C2×C22⋊C4C22×D8314yes—
521C2×C42—3322no—
522C2×C42—834no—
523C2×C42—834no—
524C2×C42—832no—
525C2×C42—832no—
526C2×C42—832no—
527C2×C42—832no—
528C2×C42C22×D8312yes—
529#95—832no—
530#95—832no—
531#95—832no—
532#95—834no—
533#95—834no—
534#95—832no—
535#95—834no—
536#95—834no—
537#95C22×D8314yes—
538#95C22×D8314yes—
539C24—3324no—
540C24—3322no—
541C24—3322no—
542C24—3324no—
543C24—838no—
544C24—834no—
545C24C23×D8311yescharacteristic
546C24C23×D8311yescharacteristic
547C24C23×D8311yescharacteristic
548#41—416no—
549C2×Q8—41no—
550C2×Q8—41no—
551C2×Q8C2×C4×D8314yes—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—41no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—3322no—
559C2×D4—3322no—
560C2×D4—33216no—
561C2×D4—3324no—
562C2×D4—3324no—
563C2×D4—3324no—
564C2×D4—3324no—
565C2×D4—8316no—
566C2×D4—8316no—
567C2×D4—838no—
568C2×D4—838no—
569C2×D4—1664no—
570C2×D4—1664no—
571C2×D4C2×C4×D8314yes—
572C2×D4C2×C4×D8314yes—
573C2×D4C2×C4×D8314yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—42no—
581C22×C4—44no—
582C22×C4—3324no—
583C22×C4—3324no—
584C22×C4—3324no—
585C22×C4—3324no—
586C22×C4—3324no—
587C22×C4—3321no—
588C22×C4—3321no—
589C22×C4—3322no—
590C22×C4—834no—
591C22×C4—832no—
592C22×C4—832no—
593C22×C4—832no—
594C22×C4—832no—
595C22×C4—1668no—
596C22×C4—1664no—
597C22×C4C2×C4×D8314yes—
598C22×C4C2×C4×D8314yes—
599C22×C4C2×C4×D8314yes—
600C22×C4C23×D8314yes—
601C22×C4C23×D8314yes—
602C22×C4C23×D8311yescharacteristic
603C22×C4C23×D8311yescharacteristic
604C22×C4C23×D8311yescharacteristic
605C22×C4C23×D8311yescharacteristic
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—42no—
609C4⋊C4—3322no—
610C4⋊C4—3324no—
611C4⋊C4—838no—
612C4⋊C4—1668no—
613C22⋊C4—44no—
614C22⋊C4—42no—
615C22⋊C4—44no—
616C22⋊C4—3324no—
617C22⋊C4—3324no—
618C22⋊C4—3324no—
619C22⋊C4—3324no—
620C22⋊C4—3324no—
621C22⋊C4—3321no—
622C22⋊C4—3321no—
623C22⋊C4—3322no—
624C22⋊C4—3322no—
625C22⋊C4—838no—
626C22⋊C4—8316no—
627C22⋊C4—8316no—
628C22⋊C4—1668no—
629C22⋊C4—1664no—
630C22⋊C4—1664no—
631C42—42no—
632C42—3322no—
633C42—3324no—
634C42—3324no—
635C42—838no—
636C42—1664no—
637C42—1664no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—3328no—
651C23—33216no—
652C23—838no—
653C23—6644no—
654C23—6644no—
655C23—6648no—
656C23—1664no—
657C23—1664no—
658C23—1664no—
659C23—1664no—
660C23—1664no—
661C23—1664no—
662C23C22×C4×D8312yes—
663C23C22×C4×D8312yes—
664C23C22×C4×D8312yes—
665C23C24×D8311yescharacteristic
666Q8—44no—
667D4—44no—
668D4—44no—
669D4—44no—
670D4—3328no—
671D4—33216no—
672D4—33216no—
673D4—16616no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—28no—
681C2×C4—28no—
682C2×C4—28no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—84no—
690C2×C4—3324no—
691C2×C4—3324no—
692C2×C4—838no—
693C2×C4—834no—
694C2×C4—6648no—
695C2×C4—6648no—
696C2×C4—1662no—
697C2×C4—1662no—
698C2×C4—1662no—
699C2×C4—1662no—
700C2×C4—1662no—
701C2×C4—1662no—
702C2×C4—1662no—
703C2×C4—1662no—
704C2×C4—1662no—
705C2×C4—1664no—
706C2×C4—1662no—
707C2×C4—1662no—
708C2×C4—1664no—
709C2×C4C22×C4×D8312yes—
710C2×C4C22×C4×D8312yes—
711C2×C4C22×C4×D8312yes—
712C2×C4C22×C4×D8312yes—
713C2×C4#1458183712yes—
714C2×C4#1458183712yes—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—24no—
719C22—24no—
720C22—24no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—3324no—
731C22—3324no—
732C22—3324no—
733C22—3324no—
734C22—66416no—
735C22—1668no—
736C22—1668no—
737C22—1668no—
738C22C23×C4×D8311yescharacteristic
739C22H(5,𝔽2)×D8312yes—
740C22C2×#1458183711yescharacteristic
741C22C2×#1458183711yescharacteristic
742C22#1912853812yes—
743C4—22no—
744C4—22no—
745C4—22no—
746C4—44no—
747C4—44no—
748C4—3322no—
749C4—3322no—
750C4—3322no—
751C4—1668no—
752C4—1664no—
753C4#1912817414yes—
754C2—42no—
755C2—42no—
756C2—42no—
757C2—3328no—
758C2C2×#1912817411yescharacteristic
759C2#2492066912yes—
760C2#2492169611yescharacteristic
761C2#2492174011yescharacteristic
762C2#2492182512yes—
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2311C2
socle, cosocleC23×C83C25
prime radicalC2×#19128265C2
hypercenter#2311D83
hypocenterC83#34411
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. #24910638C2semidirect
3. #24910600C2semidirect
4. #24910526C2semidirect
5. #24910501C2semidirect
6. #24910479C2semidirect
7. #24910444C2semidirect
8. #24910358C2semidirect
9. #24910283C2semidirect
10. #24910275C2semidirect
11. #24910152C2semidirect
12. #24910119C2semidirect
13. #24909969C2semidirect
14. #24909954C2semidirect
15. C83×#2311C2semidirect
17. #19128265C4semidirect
26. C2×C4×C22⋊D83C22semidirect
27. C2×(C22⋊D83)⋊C4C22semidirect
29. C2×#14581751C22semidirect
31. C22×C4×Dic83C22semidirect
32. #19127608C22semidirect
36. #19127601C22semidirect
37. #19127601C22semidirect
38. #19127597C22semidirect
39. #19127597C22semidirect
40. #19127593C22semidirect
41. #19127592C22semidirect
42. #19127591C22semidirect
43. #19127590C22semidirect
48. #19127581C22semidirect
49. #19127581C22semidirect
50. #19127580C22semidirect
53. #19127578C22semidirect
54. #19127577C22semidirect
55. #19127577C22semidirect
56. #19127575C22semidirect
57. #19127572C22semidirect
58. #19127568C22semidirect
60. C4⋊C4×Dic83C22semidirect
61. C4⋊C4×Dic83C22semidirect
62. #19127552C22semidirect
63. C4×(C2×D83)⋊C4C22semidirect
65. C4×C22⋊Dic83C22semidirect
66. #19127548C22semidirect
68. C2×#117×C83C22semidirect
69. C22×C4⋊C4×C83C22semidirect
70. #391×C83C22semidirect
73. #386×C83C22semidirect
75. #380×C83C22semidirect
79. C22×D332C2×C4semidirect
88. #14581788C2×C4semidirect
89. #14581781C2×C4semidirect
90. #14581766C2×C4semidirect
91. #14581766C2×C4semidirect
92. #14581760C2×C4semidirect
93. #14581760C2×C4semidirect
99. #14581751C2×C4semidirect
137. C2×#41×C83C2×C4semidirect
394. #2311D83semidirect
397. C83#34411semidirect
413. C2×#117C2×D83semidirect
414. C22×C4⋊C4C2×D83semidirect
418. #391C2×D83semidirect
444. #386C2×D83semidirect
449. #380C2×D83semidirect
461. C2×#41C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191282652
#249106382
#249106002
#249105262
#249105012
#249104792
#249104442
#249103582
#249102832
#249102752
#249101522
#249101192
#249099692
#249099542
C83×#23112
#3441183