Finite Group Databasebeta

← #35309152

Subgroups — #35309152

Order 21248.

350 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24908398C211yesmaximal, characteristic
2#24907590C211yesmaximal, characteristic
3#24907469C211yesmaximal, characteristic
4#24907465C211yesmaximal, characteristic
5#24905347C211yesmaximal, characteristic
6#24905297C211yesmaximal, characteristic
7C83×#1296C211yesmaximal, characteristic
8C2×C4×Dic166C2211yescharacteristic
9C2×C4⋊(C83⋊C8)C2211yescharacteristic
10C2×#14581717—21no—
11C2×#14581715—21no—
12C2×C4×C83⋊C8C2211yescharacteristic
13#19127571C2211yescharacteristic
14#19127464—21no—
15#19127463—21no—
16#19127463—21no—
17#19127463—21no—
18#19127455—21no—
19#19127455—21no—
20C2×C4⋊C8×C83C2211yescharacteristic
21C2×C4⋊C8×C83C2211yescharacteristic
22#384×C83C2211yescharacteristic
23C22×Dic166D411yescharacteristic
24C22×C83⋊C8—21no—
25C22×C83⋊C8D411yescharacteristic
26C22×C83⋊C8D411yescharacteristic
27C4×Dic166—21no—
28C4×Dic166—21no—
29C4×Dic166—21no—
30C4×Dic166—21no—
31C2×C4⋊Dic83—21no—
32C2×C4⋊Dic83—21no—
33C2×C4⋊Dic83—21no—
34C2×C4⋊Dic83D411yescharacteristic
35C2×Dic83⋊C4—21no—
36C2×C4×Dic83—21no—
37C4⋊(C83⋊C8)—21no—
38C4⋊(C83⋊C8)—21no—
39#14581717—42no—
40#14581715—42no—
41C4×C83⋊C8—21no—
42C4×C83⋊C8—21no—
43C22×C8×C83—21no—
44C22×C8×C83—21no—
45C2×C4⋊C4×C83—21no—
46C2×C4⋊C4×C83—21no—
47C2×C4⋊C4×C83—21no—
48C2×C42×C83C2311yescharacteristic
49C4⋊C8×C83—21no—
50C4⋊C8×C83—21no—
51C4⋊C8×C83—21no—
52C4⋊C8×C83—21no—
53C2×Dic166—21no—
54C2×Dic166—21no—
55C2×Dic166—21no—
56C2×Dic166—21no—
57C2×Dic166—21no—
58C2×Dic166D812yes—
59C22×Dic83—21no—
60C22×Dic83—21no—
61C22×Dic83—41no—
62C2×C83⋊C8—21no—
63C2×C83⋊C8—21no—
64C2×C83⋊C8—21no—
65C2×C83⋊C8—21no—
66C2×C83⋊C8—21no—
67C2×C83⋊C8—21no—
68C2×C83⋊C8—41no—
69C2×C83⋊C8—41no—
70C2×C83⋊C8—41no—
71C4⋊Dic83—21no—
72C4⋊Dic83—21no—
73C4⋊Dic83—41no—
74C4⋊Dic83—41no—
75C4⋊Dic83—41no—
76C4⋊Dic83—41no—
77C4⋊Dic83—81no—
78Dic83⋊C4—41no—
79Dic83⋊C4—41no—
80C4×Dic83—41no—
81C4×Dic83—41no—
82C22×C4×C83—41no—
83C22×C4×C83C2×D411yescharacteristic
84C22×C4×C83C2×D411yescharacteristic
85C22×C4×C83#4111yescharacteristic
86C2×C8×C83—41no—
87C2×C8×C83—41no—
88C2×C8×C83—41no—
89C2×C8×C83—41no—
90C2×C8×C83—41no—
91C2×C8×C83—41no—
92C4⋊C4×C83—41no—
93C4⋊C4×C83—41no—
94C4⋊C4×C83—41no—
95C4⋊C4×C83—41no—
96C4⋊C4×C83—81no—
97C42×C83#4111yescharacteristic
98C42×C83#4111yescharacteristic
99C42×C83#4111yescharacteristic
100C42×C83#4111yescharacteristic
101C23×C83#12111yescharacteristic
102C2×C4×C83—21no—
103C2×C4×C83—21no—
104C2×C4×C83—81no—
105C2×C4×C83—81no—
106C2×C4×C83—81no—
107C2×C4×C83#12311yescharacteristic
108C2×C4×C83#12311yescharacteristic
109C2×C4×C83#12311yescharacteristic
110C2×C4×C83#12411yescharacteristic
111C2×C4×C83#12611yescharacteristic
112C2×C4×C83#12611yescharacteristic
113C2×C4×C83C2×D811yescharacteristic
114C2×C4×C83#13511yescharacteristic
115C2×C4×C83#13511yescharacteristic
116C2×C4×C83#13511yescharacteristic
117C2×C4×C83#13711yescharacteristic
118C2×C4×C83#13711yescharacteristic
119C2×C4×C83#13711yescharacteristic
120C2×C4×C83#13711yescharacteristic
121C2×Dic83—22no—
122C2×Dic83—41no—
123C2×Dic83—41no—
124C2×Dic83—41no—
125C2×Dic83—41no—
126C2×Dic83—41no—
127C2×Dic83—81no—
128C2×Dic83—81no—
129C2×Dic83—81no—
130Dic166—22no—
131Dic166—22no—
132Dic166—41no—
133Dic166—41no—
134C8×C83—81no—
135C8×C83—81no—
136C83⋊C8—41no—
137C83⋊C8—41no—
138C83⋊C8—81no—
139C22×C83#39711yescharacteristic
140C22×C83#46411yescharacteristic
141C22×C83#46411yescharacteristic
142C22×C83#46611yescharacteristic
143C22×C83#47011yescharacteristic
144C22×C83#47111yescharacteristic
145C22×C83#47111yescharacteristic
146C4×C83—21no—
147C4×C83—21no—
148C4×C83—161no—
149C4×C83#48011yescharacteristic
150C4×C83#48011yescharacteristic
151C4×C83#48511yescharacteristic
152C4×C83#48511yescharacteristic
153C4×C83#48511yescharacteristic
154C4×C83#48511yescharacteristic
155C4×C83#48811yescharacteristic
156C4×C83#49111yescharacteristic
157Dic83—42no—
158Dic83—81no—
159Dic83—161no—
160#10623—831nomaximal, Sylow
161C2×C83#168211yescharacteristic
162C2×C83#168211yescharacteristic
163C2×C83#170411yescharacteristic
164C2×C83#170411yescharacteristic
165C2×C83#207411yescharacteristic
166C2×C83#207511yescharacteristic
167C2×C83#207911yescharacteristic
168#1984—831no—
169#1834—831no—
170#1803—831no—
171#1803—831no—
172#1296—831no—
173#1296D8311yescharacteristic
174#1277—831no—
175C83#1062311yescharacteristic, complemented, Sylow
176C2×C4×Q8—831no—
177C2×C4⋊C8—831no—
178C2×C4⋊C8C2×D8311yescharacteristic
179C2×C4⋊C8C2×D8311yescharacteristic
180C2×#103—1661no—
181C2×#103—1661no—
182C2×C4×C8—831no—
183#384—831no—
184#384C2×D8311yescharacteristic
185#340—1661no—
186#340—1661no—
187#340—1661no—
188#340—1661no—
189#336—1661no—
190#336—1661no—
191C22×Q8—831no—
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—831no—
195C22×C8—831no—
196C22×C8—1661no—
197C4×Q8—1661no—
198C4×Q8—1661no—
199C4×Q8—1661no—
200C4×Q8—1661no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—831no—
205C2×C4⋊C4—1661no—
206C2×C4⋊C4—1661no—
207C2×C4⋊C4—1661no—
208C2×C4⋊C4—1661no—
209C2×C42—1661no—
210C2×C42C22×D8311yescharacteristic
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—1661no—
216C4⋊C8—1661no—
217#103—3322no—
218#103—3322no—
219C4×C8—1661no—
220C4×C8—1661no—
221C2×Q8—832no—
222C2×Q8—1661no—
223C2×Q8—1661no—
224C2×Q8—1661no—
225C2×Q8—1661no—
226C2×Q8—1661no—
227C22×C4—41no—
228C22×C4—3321no—
229C22×C4—1661no—
230C22×C4—1661no—
231C22×C4D4×D8311yescharacteristic
232C22×C4D4×D8311yescharacteristic
233C22×C4#1305059011yescharacteristic
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—3321no—
241C2×C8—3321no—
242C2×C8—3321no—
243C2×C8—1661no—
244C2×C8—1661no—
245C2×C8—1661no—
246C2×C8—1661no—
247C2×C8—1661no—
248C2×C8—1661no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—81no—
254C4⋊C4—3321no—
255C4⋊C4—3321no—
256C4⋊C4—3321no—
257C4⋊C4—3321no—
258C4⋊C4—3321no—
259C4⋊C4—3321no—
260C4⋊C4—6641no—
261C4⋊C4—1661no—
262C4⋊C4—1661no—
263C42—3321no—
264C42—3321no—
265C42#1305058911yescharacteristic
266C42#1305059011yescharacteristic
267C42#1305059011yescharacteristic
268C42#1305059111yescharacteristic
269C23#1458176511yescharacteristic
270Q8—3321no—
271Q8—3321no—
272Q8—1662no—
273Q8—1662no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—3321no—
280C2×C4—3321no—
281C2×C4—3321no—
282C2×C4—3321no—
283C2×C4—3321no—
284C2×C4—6641no—
285C2×C4—6641no—
286C2×C4—6641no—
287C2×C4—1662no—
288C2×C4#1458177411yescharacteristic
289C2×C4#1458177711yescharacteristic
290C2×C4#1458177711yescharacteristic
291C2×C4#1458177811yescharacteristic
292C2×C4#1458178611yescharacteristic
293C2×C4#1458178711yescharacteristic
294C2×C4D8×D8311yescharacteristic
295C2×C4#1458181111yescharacteristic
296C2×C4#1458181311yescharacteristic
297C2×C4#1458181311yescharacteristic
298C2×C4#1458182111yescharacteristic
299C2×C4#1458182111yescharacteristic
300C2×C4#1458182411yescharacteristic
301C2×C4#1458182411yescharacteristic
302C8—81no—
303C8—81no—
304C8—3321no—
305C8—3321no—
306C8—6641no—
307C22#1912763011yescharacteristic
308C22#1912792211yescharacteristic
309C22#1912792611yescharacteristic
310C22#1912793611yescharacteristic
311C22#1912795811yescharacteristic
312C22#1912796311yescharacteristic
313C22#1912796711yescharacteristic
314C4—21no—
315C4—21no—
316C4—161no—
317C4—13281no—
318C4—3322no—
319C4—6641no—
320C4#1912801311yescharacteristic
321C4#1912801611yescharacteristic
322C4#1912804011yescharacteristic
323C4#1912804411yescharacteristic
324C4#1912804511yescharacteristic
325C4#1912804511yescharacteristic
326C4#1912805411yescharacteristic
327C4#1912806811yescharacteristic
328C2#2490690611yescharacteristic
329C2#2490691011yescharacteristic
330C2#2490704411yescharacteristic
331C2#2490704811yescharacteristic
332C2#2490888511yescharacteristic
333C2#2490889011yescharacteristic
334C2#2490891211yescharacteristic
subgroupG/H
centerC23#14581765
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1296C2
socle, prime radicalC23×C83#121
hypercenter#1296D83
hypocenterC83#10623
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
175. C83#10623semidirect

Maximal subgroups

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

subgroupindex
#249083982
#249075902
#249074692
#249074652
#249053472
#249052972
C83×#12962
#1062383