Finite Group Databasebeta

← #35567330

Subgroups — #35567330

Order 21248.

2630 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581775C211yesmaximal, characteristic
2#24910607C214yesmaximal, complemented
3#24910455C214yesmaximal, complemented
4#24910341C212yesmaximal, complemented
5#24910315C212yesmaximal, complemented
6#24910314C212yesmaximal, complemented
7#24910279C212yesmaximal
8#24910253C214yesmaximal, complemented
9#24910129C214yesmaximal, complemented
10#24910080C211yesmaximal, characteristic, complemented
11#24910076C211yesmaximal, characteristic, complemented
12#24910065C211yesmaximal, characteristic, complemented
13#24910060C211yesmaximal, characteristic, complemented
14C2×#19127561C211yesmaximal, characteristic, complemented
15C83×#2280C211yesmaximal, characteristic, complemented
16C23×C22⋊D83C2211yescharacteristic
17C2×#14581775C4116yescomplemented
18C2×#14581775C2212yes—
19C2×#14581775C2212yes—
20C2×#14581775C2212yes—
21C2×#14581775C2212yes—
22C2×(C22⋊D83)⋊C4C2214yes—
23C2×#14581748C2212yes—
24C22×C4⋊Dic83C2212yescomplemented
25C22×Dic83⋊C4C2211yescharacteristic
26C22×Dic83⋊C4C2211yescharacteristic
27C22×C22⋊Dic83C2212yes—
28C22×C22⋊Dic83C2211yescharacteristic
29C22×(C2×D83)⋊C4C2211yescharacteristic
30C22×(C2×D83)⋊C4C2211yescharacteristic
31C2×C22⋊C4×D83C2212yes—
32#19127601C2214yes—
33#19127598C2214yescomplemented
34#19127598C2214yescomplemented
35#19127596C2214yescomplemented
36#19127595C2214yescomplemented
37#19127593C2214yescomplemented
38#19127593C2214yescomplemented
39#19127592C2214yescomplemented
40#19127591C2214yescomplemented
41#19127589C2214yescomplemented
42#19127588C2214yescomplemented
43#19127588C2214yescomplemented
44#19127585C2214yescomplemented
45#19127582C2214yescomplemented
46#19127578C2214yes—
47#19127577C2214yes—
48#19127575C2214yescomplemented
49#19127575C2214yescomplemented
50#19127573C2214yescomplemented
51#19127572C2214yescomplemented
52#19127562C2212yes—
53#19127561C2211yescharacteristic
54#19127561C2212yes—
55#19127561C2211yescharacteristic
56#19127561C2212yescomplemented
57#19127561C2212yescomplemented
58#19127559C2212yes—
59#19127559C2212yes—
60#19127556C2212yes—
61C4×Dic83⋊C4C2214yescomplemented
62C22⋊C4×Dic83C2212yes—
63C22⋊C4×Dic83C2212yes—
64C22⋊C4×Dic83C2214yescomplemented
65C4×(C2×D83)⋊C4C2214yescomplemented
66C2×C83⋊#95C2212yescomplemented
67C24×C4×C83C2211yescharacteristic
68C2×#117×C83C2212yescomplemented
69#381×C83C2212yescomplemented
70#380×C83C2211yescharacteristic
71#380×C83C2211yescharacteristic
72#380×C83C2212yescomplemented
73#379×C83C2212yes—
74C4×C22⋊C4×C83C2212yes—
75C4×C22⋊C4×C83C2212yescomplemented
76C24×D83C2311yescharacteristic
77C22×C22⋊D83—44no—
78C22×C22⋊D83C2×C418yes—
79C22×C22⋊D83C2312yes—
80C22×C22⋊D83C2312yes—
81C23×Dic83C2311yescharacteristic
82C23×Dic83C2314yes—
83C23×Dic83C2311yescharacteristic
84C23×Dic83C2311yescharacteristic
85C22×C4×D83C2314yes—
86#14581775C2×C4116yescomplemented
87#14581775C2×C4116yescomplemented
88#14581775C2×C4116yescomplemented
89#14581775C2×C4116yescomplemented
90(C22⋊D83)⋊C4—48no—
91#14581748—44no—
92C2×C4⋊Dic83—44no—
93C2×C4⋊Dic83C2312yes—
94C2×C4⋊Dic83C2314yes—
95C2×C4⋊Dic83C2312yes—
96C2×Dic83⋊C4C2×C418yescomplemented
97C2×Dic83⋊C4C2×C418yescomplemented
98C2×Dic83⋊C4C2314yes—
99C2×Dic83⋊C4C2314yes—
100C2×Dic83⋊C4C2314yes—
101C2×Dic83⋊C4C2312yes—
102C2×Dic83⋊C4C2312yes—
103C2×Dic83⋊C4C2312yes—
104C2×Dic83⋊C4C2312yes—
105C2×C22⋊Dic83—44no—
106C2×C22⋊Dic83C2×C418yescomplemented
107C2×C22⋊Dic83C2312yes—
108C2×C22⋊Dic83C2312yes—
109C2×C22⋊Dic83C2314yes—
110C2×C22⋊Dic83C2312yes—
111C2×C22⋊Dic83C2312yes—
112C2×(C2×D83)⋊C4C2×C418yescomplemented
113C2×(C2×D83)⋊C4C2×C418yescomplemented
114C2×(C2×D83)⋊C4C2314yes—
115C2×(C2×D83)⋊C4C2314yes—
116C2×(C2×D83)⋊C4C2314yes—
117C2×(C2×D83)⋊C4C2312yes—
118C2×(C2×D83)⋊C4C2312yes—
119C2×(C2×D83)⋊C4C2312yes—
120C2×(C2×D83)⋊C4C2312yes—
121C22⋊C4×D83—44no—
122C2×C4×Dic83C2314yes—
123C2×C4×Dic83C2314yes—
124C2×C4×Dic83C2314yes—
125C83⋊#95C2314yes—
126C83⋊#95C2314yes—
127C83⋊#95C2314yes—
128C83⋊#95C2312yes—
129C83⋊#95C2312yes—
130C83⋊#95C2314yes—
131C83⋊#95C2314yes—
132C83⋊#95C2314yes—
133C83⋊#95C2314yes—
134C25×C83C2311yescharacteristic
135C23×C4×C83—44no—
136C23×C4×C83C2×C418yescomplemented
137C23×C4×C83C2311yescharacteristic
138C23×C4×C83C2311yescharacteristic
139C23×C4×C83C2311yescharacteristic
140C23×C4×C83C2311yescharacteristic
141C23×C4×C83C2311yescharacteristic
142C23×C4×C83C2311yescharacteristic
143#117×C83—44no—
144C2×C4⋊C4×C83C2312yes—
145C2×C4⋊C4×C83C2312yes—
146C2×C22⋊C4×C83C2312yes—
147C2×C22⋊C4×C83C2312yes—
148C2×C22⋊C4×C83C2314yes—
149C2×C22⋊C4×C83C2314yes—
150C2×C42×C83C2314yes—
151#95×C83C2312yes—
152#95×C83C2314yes—
153#95×C83C2312yes—
154C23×D83—22no—
155C23×D83—22no—
156C23×D83—42no—
157C23×D83—42no—
158C23×D83C22×C414yes—
159C23×D83C2412yes—
160C2×C22⋊D83—28no—
161C2×C22⋊D83—44no—
162C2×C22⋊D83—416no—
163C2×C22⋊D83C22×C418yes—
164C2×C22⋊D83C22×C418yes—
165C22×Dic83—22no—
166C22×Dic83—22no—
167C22×Dic83—28no—
168C22×Dic83—42no—
169C22×Dic83—42no—
170C22×Dic83—44no—
171C22×Dic83—44no—
172C22×Dic83C22×C414yes—
173C22×Dic83C22×C414yes—
174C22×Dic83C22×C414yes—
175C22×Dic83C2414yes—
176C22×Dic83C2414yes—
177C22×Dic83C2412yes—
178C22×Dic83C2412yes—
179C22×Dic83C2412yes—
180C2×C4×D83—44no—
181C2×C4×D83—44no—
182C2×C4×D83—44no—
183C4⋊Dic83—42no—
184C4⋊Dic83—44no—
185C4⋊Dic83—42no—
186Dic83⋊C4—44no—
187Dic83⋊C4—44no—
188Dic83⋊C4—44no—
189Dic83⋊C4C22×C418yes—
190Dic83⋊C4C22×C418yes—
191Dic83⋊C4C22×C418yes—
192Dic83⋊C4C22×C418yes—
193C22⋊Dic83—24no—
194C22⋊Dic83—24no—
195C22⋊Dic83—44no—
196C22⋊Dic83C22×C418yes—
197C22⋊Dic83C22×C418yes—
198(C2×D83)⋊C4—44no—
199(C2×D83)⋊C4—44no—
200(C2×D83)⋊C4—44no—
201(C2×D83)⋊C4C22×C418yes—
202(C2×D83)⋊C4C22×C418yes—
203(C2×D83)⋊C4C22×C418yes—
204(C2×D83)⋊C4C22×C418yes—
205C4×Dic83—44no—
206C4×Dic83—44no—
207C4×Dic83—44no—
208C24×C83—24no—
209C24×C83—22no—
210C24×C83—22no—
211C24×C83—42no—
212C24×C83C22×C414yes—
213C24×C83C2411yescharacteristic
214C24×C83C2411yescharacteristic
215C24×C83C2411yescharacteristic
216C22×C4×C83—24no—
217C22×C4×C83—24no—
218C22×C4×C83—416no—
219C22×C4×C83—42no—
220C22×C4×C83—42no—
221C22×C4×C83—42no—
222C22×C4×C83—42no—
223C22×C4×C83C22×C414yes—
224C22×C4×C83C22×C414yes—
225C22×C4×C83C22×C414yes—
226C22×C4×C83C22×C414yes—
227C22×C4×C83C22×C414yes—
228C22×C4×C83C22×C414yes—
229C22×C4×C83C2414yes—
230C22×C4×C83C2414yes—
231C22×C4×C83C2411yescharacteristic
232C22×C4×C83C2411yescharacteristic
233C22×C4×C83C2411yescharacteristic
234C22×C4×C83C2411yescharacteristic
235C4⋊C4×C83—42no—
236C4⋊C4×C83—42no—
237C22⋊C4×C83—28no—
238C22⋊C4×C83—24no—
239C22⋊C4×C83—24no—
240C22⋊C4×C83—44no—
241C42×C83—44no—
242C23×C83—22no—
243C23×C83—21no—
244C23×C83—21no—
245C23×C83—22no—
246C23×C83—22no—
247C23×C83—28no—
248C23×C83—28no—
249C23×C83—22no—
250C23×C83—21no—
251C23×C83—21no—
252C23×C83—22no—
253C23×C83—44no—
254C23×C83—48no—
255C23×C83—48no—
256C23×C83C23×C412yes—
257C23×C83C23×C412yes—
258C23×C83C23×C412yes—
259C23×C83H(5,𝔽2)14yes—
260C23×C83H(5,𝔽2)12yes—
261C23×C832−1+412yes—
262C23×C83C2511yescharacteristic
263C22×D83—22no—
264C22×D83—24no—
265C22×D83—22no—
266C22×D83—24no—
267C22×D83—28no—
268C22×D83—44no—
269C22×D83—44no—
270C22×D83—84no—
271C22×D83—84no—
272C22×D83C23×C414yes—
273C2×C4×C83—28no—
274C2×C4×C83—28no—
275C2×C4×C83—22no—
276C2×C4×C83—22no—
277C2×C4×C83—22no—
278C2×C4×C83—22no—
279C2×C4×C83—24no—
280C2×C4×C83—24no—
281C2×C4×C83—24no—
282C2×C4×C83—24no—
283C2×C4×C83—24no—
284C2×C4×C83—24no—
285C2×C4×C83—44no—
286C2×C4×C83—44no—
287C2×C4×C83—44no—
288C2×C4×C83—44no—
289C2×C4×C83C23×C412yes—
290C2×C4×C83C23×C412yes—
291C2×C4×C83C23×C412yes—
292C2×C4×C83C23×C412yes—
293C22⋊D83—216no—
294C22⋊D83—48no—
295C2×Dic83—28no—
296C2×Dic83—22no—
297C2×Dic83—24no—
298C2×Dic83—22no—
299C2×Dic83—24no—
300C2×Dic83—24no—
301C2×Dic83—24no—
302C2×Dic83—24no—
303C2×Dic83—24no—
304C2×Dic83—24no—
305C2×Dic83—24no—
306C2×Dic83—44no—
307C2×Dic83—44no—
308C2×Dic83—88no—
309C2×Dic83C23×C414yes—
310C2×Dic83C23×C414yes—
311C2×Dic83C23×C414yes—
312C4×D83—88no—
313C22×C83—22no—
314C22×C83—22no—
315C22×C83—22no—
316C22×C83—22no—
317C22×C83—24no—
318C22×C83—24no—
319C22×C83—24no—
320C22×C83—24no—
321C22×C83—22no—
322C22×C83—22no—
323C22×C83—22no—
324C22×C83—416no—
325C22×C83—42no—
326C22×C83—42no—
327C22×C83#51814yes—
328C22×C83#52014yes—
329C22×C83C24×C411yescharacteristic
330C22×C83C2×H(5,𝔽2)12yes—
331C22×C83C2×H(5,𝔽2)11yescharacteristic
332C22×C83C2×2−1+411yescharacteristic
333C22×C83#58512yes—
334C2×D83—24no—
335C2×D83—24no—
336C2×D83—24no—
337C2×D83—44no—
338C2×D83—44no—
339C2×D83—88no—
340C4×C83—22no—
341C4×C83—22no—
342C4×C83—22no—
343C4×C83—22no—
344C4×C83—44no—
345C4×C83—44no—
346Dic83—24no—
347Dic83—24no—
348Dic83—24no—
349Dic83—44no—
350Dic83—44no—
351#34376—831nomaximal, Sylow
352C2×C83—24no—
353C2×C83—24no—
354C2×C83—42no—
355C2×C83C2×#51811yescharacteristic
356C2×C83C2×#52011yescharacteristic
357C2×C83#342811yescharacteristic
358C2×C83#353412yes—
359C2×C83#353512yes—
360D83—44no—
361C22×#123—831no—
362#2376—834no—
363#2359—834no—
364#2345—832no—
365#2342—832no—
366#2342—832no—
367D4×C22⋊C4—832no—
368#2335—834no—
369#2322—834no—
370#2316—831no—
371#2315—831no—
372#2313—831no—
373#2312—831no—
374#2280D8311yescharacteristic, complemented
375C2×#380—831no—
376C83#3437611yescharacteristic, complemented, Sylow
377C23×D4—831no—
378C24×C4C2×D8311yescharacteristic
379C2×#123—8316no—
380C2×#123—832no—
381C2×#123—832no—
382C2×#123—832no—
383C2×#123—832no—
384C2×C4×D4—834no—
385C2×#117—832no—
386C2×#117C2×D8312yescomplemented
387C22×C4⋊C4—832no—
388C22×C4⋊C4—831no—
389C22×C4⋊C4—831no—
390C22×C22⋊C4—832no—
391C22×C22⋊C4—832no—
392C22×C22⋊C4—831no—
393C22×C22⋊C4—831no—
394C22×C22⋊C4—831no—
395#390—834no—
396#389—834no—
397#389—834no—
398#389—834no—
399#388—834no—
400#388—834no—
401#388—834no—
402#388—834no—
403#388—834no—
404#388—834no—
405#387—834no—
406#387—834no—
407#387—834no—
408#387—834no—
409#386—834no—
410#386—834no—
411#385—834no—
412#385—834no—
413#385—834no—
414#385—834no—
415#381—832no—
416#381C2×D8312yescomplemented
417#380—831no—
418#380—831no—
419#380—832no—
420#380—832no—
421#380—832no—
422#380—832no—
423#380—832no—
424#380C2×D8311yescharacteristic
425#380C2×D8311yescharacteristic
426#380C2×D8312yescomplemented
427#379—832no—
428#379C2×D8312yes—
429C4×C4⋊C4—834no—
430C4×C22⋊C4—832no—
431C4×C22⋊C4—832no—
432C4×C22⋊C4—834no—
433C4×C22⋊C4—834no—
434C4×C22⋊C4C2×D8312yes—
435C4×C22⋊C4C2×D8312yescomplemented
436C2×#95—832no—
437C25—831no—
438C25C22×D8311yescharacteristic
439C22×D4—3324no—
440C22×D4—838no—
441C22×D4—832no—
442C22×D4—832no—
443C23×C4—44no—
444C23×C4—834no—
445C23×C4—831no—
446C23×C4—831no—
447C23×C4—834no—
448C23×C4—831no—
449C23×C4C4×D8318yescomplemented
450C23×C4C22×D8311yescharacteristic
451C23×C4C22×D8311yescharacteristic
452C23×C4C22×D8311yescharacteristic
453C23×C4C22×D8311yescharacteristic
454C23×C4C22×D8311yescharacteristic
455C23×C4C22×D8311yescharacteristic
456#123—8316no—
457#123—8316no—
458#123—8316no—
459#123—8316no—
460C4×D4—3328no—
461#117—44no—
462#117—3324no—
463C2×C4⋊C4—3324no—
464C2×C4⋊C4—832no—
465C2×C4⋊C4—834no—
466C2×C4⋊C4—832no—
467C2×C4⋊C4—834no—
468C2×C4⋊C4—834no—
469C2×C4⋊C4—834no—
470C2×C4⋊C4—838no—
471C2×C4⋊C4—838no—
472C2×C4⋊C4—832no—
473C2×C4⋊C4—832no—
474C2×C4⋊C4—832no—
475C2×C4⋊C4—832no—
476C2×C4⋊C4C22×D8312yes—
477C2×C4⋊C4C22×D8312yes—
478C2×C22⋊C4—3324no—
479C2×C22⋊C4—3324no—
480C2×C22⋊C4—834no—
481C2×C22⋊C4—834no—
482C2×C22⋊C4—834no—
483C2×C22⋊C4—834no—
484C2×C22⋊C4—838no—
485C2×C22⋊C4—832no—
486C2×C22⋊C4—832no—
487C2×C22⋊C4—838no—
488C2×C22⋊C4—838no—
489C2×C22⋊C4—832no—
490C2×C22⋊C4—832no—
491C2×C22⋊C4—832no—
492C2×C22⋊C4—832no—
493C2×C22⋊C4—832no—
494C2×C22⋊C4—832no—
495C2×C22⋊C4C22×D8312yes—
496C2×C22⋊C4C22×D8314yes—
497C2×C22⋊C4C22×D8312yes—
498C2×C22⋊C4C22×D8314yes—
499C2×C42—834no—
500C2×C42—834no—
501C2×C42—834no—
502C2×C42C22×D8314yes—
503#95—834no—
504#95—832no—
505#95—832no—
506#95—834no—
507#95—834no—
508#95—834no—
509#95—834no—
510#95—834no—
511#95—834no—
512#95C22×D8314yes—
513#95C22×D8312yes—
514#95C22×D8312yes—
515C24—24no—
516C24—22no—
517C24—22no—
518C24—42no—
519C24—3322no—
520C24—3322no—
521C24—834no—
522C24—832no—
523C24—1662no—
524C24—1662no—
525C24C2×C4×D8314yes—
526C24C23×D8311yescharacteristic
527C24C23×D8311yescharacteristic
528C24C23×D8311yescharacteristic
529C2×D4—33216no—
530C2×D4—3324no—
531C2×D4—838no—
532C2×D4—838no—
533C2×D4—1668no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—416no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—3324no—
542C22×C4—3324no—
543C22×C4—3324no—
544C22×C4—3322no—
545C22×C4—3322no—
546C22×C4—3324no—
547C22×C4—3324no—
548C22×C4—834no—
549C22×C4—834no—
550C22×C4—834no—
551C22×C4—832no—
552C22×C4—832no—
553C22×C4—832no—
554C22×C4—834no—
555C22×C4—834no—
556C22×C4—1668no—
557C22×C4—1662no—
558C22×C4—1662no—
559C22×C4C2×C4×D8314yes—
560C22×C4C2×C4×D8314yes—
561C22×C4C2×C4×D8314yes—
562C22×C4C2×C4×D8314yes—
563C22×C4C2×C4×D8314yes—
564C22×C4C2×C4×D8314yes—
565C22×C4C23×D8314yes—
566C22×C4C23×D8314yes—
567C22×C4C23×D8311yescharacteristic
568C22×C4C23×D8311yescharacteristic
569C22×C4C23×D8311yescharacteristic
570C22×C4C23×D8311yescharacteristic
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—3322no—
574C4⋊C4—3324no—
575C4⋊C4—3322no—
576C4⋊C4—3324no—
577C4⋊C4—3324no—
578C4⋊C4—3324no—
579C4⋊C4—838no—
580C4⋊C4—838no—
581C4⋊C4—838no—
582C4⋊C4—838no—
583C22⋊C4—28no—
584C22⋊C4—24no—
585C22⋊C4—24no—
586C22⋊C4—44no—
587C22⋊C4—3324no—
588C22⋊C4—3324no—
589C22⋊C4—3324no—
590C22⋊C4—3324no—
591C22⋊C4—838no—
592C22⋊C4—838no—
593C22⋊C4—838no—
594C22⋊C4—838no—
595C22⋊C4—838no—
596C22⋊C4—838no—
597C22⋊C4—1664no—
598C22⋊C4—1664no—
599C42—44no—
600C42—3324no—
601C42—3324no—
602C42—3324no—
603C23—22no—
604C23—21no—
605C23—21no—
606C23—22no—
607C23—22no—
608C23—28no—
609C23—28no—
610C23—22no—
611C23—21no—
612C23—21no—
613C23—22no—
614C23—44no—
615C23—48no—
616C23—48no—
617C23—3324no—
618C23—3324no—
619C23—834no—
620C23—6644no—
621C23—6644no—
622C23—1664no—
623C23—1662no—
624C23—1662no—
625C23—1664no—
626C23—1668no—
627C23C22×C4×D8312yes—
628C23C22×C4×D8312yes—
629C23C22×C4×D8312yes—
630C23#1458183714yes—
631C23#1458183812yes—
632C23#1458183912yes—
633C23C24×D8311yescharacteristic
634D4—3328no—
635D4—16616no—
636C2×C4—28no—
637C2×C4—28no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—44no—
649C2×C4—44no—
650C2×C4—44no—
651C2×C4—44no—
652C2×C4—3324no—
653C2×C4—3324no—
654C2×C4—834no—
655C2×C4—834no—
656C2×C4—834no—
657C2×C4—6648no—
658C2×C4—6648no—
659C2×C4—1664no—
660C2×C4—1664no—
661C2×C4—1664no—
662C2×C4—1664no—
663C2×C4—1664no—
664C2×C4—1664no—
665C2×C4—1668no—
666C2×C4—1664no—
667C2×C4—1662no—
668C2×C4—1662no—
669C2×C4—1664no—
670C2×C4C22×C4×D8312yes—
671C2×C4C22×C4×D8312yes—
672C2×C4C22×C4×D8312yes—
673C2×C4C22×C4×D8312yes—
674C22—24no—
675C22—24no—
676C22—24no—
677C22—24no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—416no—
686C22—42no—
687C22—42no—
688C22—3324no—
689C22—3324no—
690C22—6648no—
691C22—1664no—
692C22—1664no—
693C22—1664no—
694C22#1912817414yes—
695C22#1912818114yes—
696C22C23×C4×D8311yescharacteristic
697C22C2×#1458183712yes—
698C22C2×#1458183811yescharacteristic
699C22C2×#1458183911yescharacteristic
700C22#1912853712yes—
701C4—22no—
702C4—22no—
703C4—22no—
704C4—22no—
705C4—44no—
706C4—44no—
707C4—3324no—
708C4—3324no—
709C4—1664no—
710C4—1664no—
711C4—1664no—
712C2—24no—
713C2—24no—
714C2—42no—
715C2—3324no—
716C2C2×#1912817411yescharacteristic
717C2C2×#1912818111yescharacteristic
718C2#2492066411yescharacteristic
719C2#2492164712yes—
720C2#2492166612yes—
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2280C2
socle, cosocleC23×C83C25
prime radicalC23×C22⋊D83C22
hypercenter#2280D83
hypocenterC83#34376
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. #24910607C2semidirect
3. #24910455C2semidirect
4. #24910341C2semidirect
5. #24910315C2semidirect
6. #24910314C2semidirect
8. #24910253C2semidirect
9. #24910129C2semidirect
10. #24910080C2semidirect
11. #24910076C2semidirect
12. #24910065C2semidirect
13. #24910060C2semidirect
14. C2×#19127561C2semidirect
15. C83×#2280C2semidirect
17. C2×#14581775C4semidirect
24. C22×C4⋊Dic83C22semidirect
33. #19127598C22semidirect
34. #19127598C22semidirect
35. #19127596C22semidirect
36. #19127595C22semidirect
37. #19127593C22semidirect
38. #19127593C22semidirect
39. #19127592C22semidirect
40. #19127591C22semidirect
41. #19127589C22semidirect
42. #19127588C22semidirect
43. #19127588C22semidirect
44. #19127585C22semidirect
45. #19127582C22semidirect
48. #19127575C22semidirect
49. #19127575C22semidirect
50. #19127573C22semidirect
51. #19127572C22semidirect
56. #19127561C22semidirect
57. #19127561C22semidirect
61. C4×Dic83⋊C4C22semidirect
64. C22⋊C4×Dic83C22semidirect
65. C4×(C2×D83)⋊C4C22semidirect
66. C2×C83⋊#95C22semidirect
68. C2×#117×C83C22semidirect
69. #381×C83C22semidirect
72. #380×C83C22semidirect
75. C4×C22⋊C4×C83C22semidirect
86. #14581775C2×C4semidirect
87. #14581775C2×C4semidirect
88. #14581775C2×C4semidirect
89. #14581775C2×C4semidirect
96. C2×Dic83⋊C4C2×C4semidirect
97. C2×Dic83⋊C4C2×C4semidirect
106. C2×C22⋊Dic83C2×C4semidirect
112. C2×(C2×D83)⋊C4C2×C4semidirect
113. C2×(C2×D83)⋊C4C2×C4semidirect
136. C23×C4×C83C2×C4semidirect
374. #2280D83semidirect
376. C83#34376semidirect
386. C2×#117C2×D83semidirect
416. #381C2×D83semidirect
426. #380C2×D83semidirect
435. C4×C22⋊C4C2×D83semidirect
449. C23×C4C4×D83semidirect

Maximal subgroups

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

subgroupindex
C22×#145817752
#249106072
#249104552
#249103412
#249103152
#249103142
#249102792
#249102532
#249101292
#249100802
#249100762
#249100652
#249100602
C2×#191275612
C83×#22802
#3437683