Finite Group Databasebeta

← #35309166

Subgroups — #35309166

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#24908399C211yesmaximal, characteristic
2#24907465C211yesmaximal, characteristic
3#24907465C211yesmaximal, characteristic
4#24905346C211yesmaximal, characteristic
5#24905346C211yesmaximal, characteristic
6#24905298C211yesmaximal, characteristic
7C83×#1834C211yesmaximal, characteristic
8C2×C4×Dic166C2211yescharacteristic
9C2×C4⋊(C83⋊C8)C2211yescharacteristic
10C2×C4⋊(C83⋊C8)C2211yescharacteristic
11C2×C4⋊(C83⋊C8)C2211yescharacteristic
12C2×#14581715—21no—
13C2×#14581715—21no—
14#19127463—21no—
15#19127463—21no—
16#19127455—21no—
17#19127455—21no—
18C2×C4×C8×C83C2211yescharacteristic
19#384×C83C2211yescharacteristic
20#384×C83C2211yescharacteristic
21#340×C83—21no—
22#340×C83—21no—
23C22×Dic166D411yescharacteristic
24C22×C83⋊C8—21no—
25C22×C83⋊C8—21no—
26C22×C83⋊C8—21no—
27C4×Dic166—21no—
28C4×Dic166—21no—
29C4×Dic166—21no—
30C4×Dic166—21no—
31C2×C4⋊Dic83D411yescharacteristic
32C2×Dic83⋊C4—21no—
33C2×C4×Dic83—21no—
34C4⋊(C83⋊C8)—21no—
35C4⋊(C83⋊C8)—21no—
36C4⋊(C83⋊C8)—21no—
37C4⋊(C83⋊C8)—21no—
38C4⋊(C83⋊C8)—21no—
39C4⋊(C83⋊C8)—21no—
40#14581715—42no—
41#14581715—42no—
42C22×C8×C83D411yescharacteristic
43C22×C8×C83D411yescharacteristic
44C2×C4⋊C4×C83—21no—
45C2×C4⋊C4×C83—21no—
46C2×C4⋊C4×C83—21no—
47C2×C4⋊C4×C83—21no—
48C2×C4⋊C4×C83—21no—
49C2×C4⋊C4×C83—21no—
50C2×C42×C83C2311yescharacteristic
51C4×C8×C83—21no—
52C4×C8×C83—21no—
53C2×Dic166—21no—
54C2×Dic166—21no—
55C2×Dic166—21no—
56C2×Dic166—21no—
57C2×Dic166—21no—
58C2×Dic166SD1612yes—
59C22×Dic83—21no—
60C22×Dic83—21no—
61C2×C83⋊C8—41no—
62C2×C83⋊C8—41no—
63C2×C83⋊C8—41no—
64C2×C83⋊C8—41no—
65C2×C83⋊C8—41no—
66C2×C83⋊C8—41no—
67C2×C83⋊C8—41no—
68C2×C83⋊C8—41no—
69C2×C83⋊C8—41no—
70C4⋊Dic83—21no—
71C4⋊Dic83—21no—
72Dic83⋊C4—41no—
73Dic83⋊C4—41no—
74C4×Dic83—41no—
75C4×Dic83—41no—
76C22×C4×C83—41no—
77C22×C4×C83—41no—
78C22×C4×C83C2×D411yescharacteristic
79C22×C4×C83C2×D411yescharacteristic
80C22×C4×C83#4111yescharacteristic
81C2×C8×C83—21no—
82C2×C8×C83—21no—
83C2×C8×C83—21no—
84C2×C8×C83—21no—
85C2×C8×C83—21no—
86C2×C8×C83—21no—
87C4⋊C4×C83—41no—
88C4⋊C4×C83—41no—
89C4⋊C4×C83—41no—
90C4⋊C4×C83—41no—
91C4⋊C4×C83—41no—
92C4⋊C4×C83—41no—
93C4⋊C4×C83—41no—
94C4⋊C4×C83—41no—
95C4⋊C4×C83—81no—
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—81no—
108C2×C4×C83—81no—
109C2×C4×C83—81no—
110C2×C4×C83#12311yescharacteristic
111C2×C4×C83#12311yescharacteristic
112C2×C4×C83#12311yescharacteristic
113C2×C4×C83#12411yescharacteristic
114C2×C4×C83#12611yescharacteristic
115C2×C4×C83#12611yescharacteristic
116C2×C4×C83C2×SD1611yescharacteristic
117C2×C4×C83#13511yescharacteristic
118C2×C4×C83#13511yescharacteristic
119C2×C4×C83#13511yescharacteristic
120C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C83#13711yescharacteristic
122C2×C4×C83#13711yescharacteristic
123C2×C4×C83#13711yescharacteristic
124C2×Dic83—22no—
125C2×Dic83—41no—
126C2×Dic83—41no—
127C2×Dic83—41no—
128C2×Dic83—41no—
129C2×Dic83—41no—
130Dic166—22no—
131Dic166—22no—
132Dic166—41no—
133Dic166—41no—
134C8×C83—41no—
135C8×C83—41no—
136C83⋊C8—81no—
137C83⋊C8—81no—
138C83⋊C8—81no—
139C22×C83#39711yescharacteristic
140C22×C83#46411yescharacteristic
141C22×C83#46411yescharacteristic
142C22×C83#46511yescharacteristic
143C22×C83#46811yescharacteristic
144C22×C83#47211yescharacteristic
145C22×C83#47311yescharacteristic
146C4×C83—21no—
147C4×C83—21no—
148C4×C83—161no—
149C4×C83—161no—
150C4×C83#48111yescharacteristic
151C4×C83#48211yescharacteristic
152C4×C83#48311yescharacteristic
153C4×C83#48511yescharacteristic
154C4×C83#48511yescharacteristic
155C4×C83#48511yescharacteristic
156C4×C83#48811yescharacteristic
157C4×C83#49111yescharacteristic
158Dic83—42no—
159Dic83—81no—
160#10626—831nomaximal, Sylow
161C2×C83#167811yescharacteristic
162C2×C83#168011yescharacteristic
163C2×C83#169811yescharacteristic
164C2×C83#170011yescharacteristic
165C2×C83#207411yescharacteristic
166C2×C83#207711yescharacteristic
167C2×C83#207811yescharacteristic
168#1984—831no—
169#1834D8311yescharacteristic
170#1803—831no—
171#1803—831no—
172#1296—831no—
173#1296—831no—
174#1277—831no—
175C83#1062611yescharacteristic, complemented, Sylow
176C2×C4×Q8—831no—
177C2×C4⋊C8—831no—
178C2×C4⋊C8—831no—
179C2×C4⋊C8—831no—
180C2×#103—1661no—
181C2×#103—1661no—
182C2×C4×C8C2×D8311yescharacteristic
183#384C2×D8311yescharacteristic
184#384C2×D8311yescharacteristic
185#340—21no—
186#340—21no—
187#340—1661no—
188#340—1661no—
189#336—1661no—
190#336—1661no—
191C22×Q8—831no—
192C22×C8—1661no—
193C22×C8—1661no—
194C22×C8—1661no—
195C22×C8C22⋊D8311yescharacteristic
196C22×C8C22⋊D8311yescharacteristic
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—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—831no—
208C2×C4⋊C4—1661no—
209C2×C42—1661no—
210C2×C42C22×D8311yescharacteristic
211C4⋊C8—1661no—
212C4⋊C8—1661no—
213C4⋊C8—1661no—
214C4⋊C8—1661no—
215C4⋊C8—1661no—
216C4⋊C8—1661no—
217#103—3322no—
218#103—3322no—
219C4×C8—21no—
220C4×C8—21no—
221C2×Q8—832no—
222C2×Q8—1661no—
223C2×Q8—1661no—
224C2×Q8—1661no—
225C2×Q8—1661no—
226C2×Q8—1661no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—1661no—
230C22×C4—1661no—
231C22×C4D4×D8311yescharacteristic
232C22×C4C2×C22⋊D8311yescharacteristic
233C22×C4#1305058911yescharacteristic
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—3321no—
241C2×C8—3321no—
242C2×C8—3321no—
243C2×C8—3321no—
244C2×C8—3321no—
245C2×C8—3321no—
246C2×C8—3321no—
247C2×C8—3321no—
248C2×C8—3321no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—81no—
258C4⋊C4—81no—
259C4⋊C4—3321no—
260C4⋊C4—3321no—
261C4⋊C4—1661no—
262C4⋊C4—1661no—
263C42—3321no—
264C42—3321no—
265C42#1305059011yescharacteristic
266C42#1305059011yescharacteristic
267C42#1305059111yescharacteristic
268C42#1305059111yescharacteristic
269C23#1458176311yescharacteristic
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—81no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—3321no—
283C2×C4—3321no—
284C2×C4—3321no—
285C2×C4—3321no—
286C2×C4—3321no—
287C2×C4—1662no—
288C2×C4#1458177511yescharacteristic
289C2×C4#1458177711yescharacteristic
290C2×C4#1458177711yescharacteristic
291C2×C4#1458178111yescharacteristic
292C2×C4#1458178711yescharacteristic
293C2×C4#1458178711yescharacteristic
294C2×C4SD16×D8311yescharacteristic
295C2×C4#1458181211yescharacteristic
296C2×C4#1458181211yescharacteristic
297C2×C4#1458181311yescharacteristic
298C2×C4#1458181911yescharacteristic
299C2×C4#1458182111yescharacteristic
300C2×C4#1458182211yescharacteristic
301C2×C4#1458182211yescharacteristic
302C8—41no—
303C8—41no—
304C8—6641no—
305C8—6641no—
306C8—6641no—
307C22#1912762711yescharacteristic
308C22#1912792011yescharacteristic
309C22#1912792011yescharacteristic
310C22#1912792711yescharacteristic
311C22#1912794411yescharacteristic
312C22#1912796811yescharacteristic
313C22#1912797311yescharacteristic
314C4—21no—
315C4—21no—
316C4—161no—
317C4—161no—
318C4—3322no—
319C4—6641no—
320C4#1912802111yescharacteristic
321C4#1912802711yescharacteristic
322C4#1912803311yescharacteristic
323C4#1912804211yescharacteristic
324C4#1912804211yescharacteristic
325C4#1912804511yescharacteristic
326C4#1912805811yescharacteristic
327C4#1912807111yescharacteristic
328C2#2490687611yescharacteristic
329C2#2490689011yescharacteristic
330C2#2490700011yescharacteristic
331C2#2490701411yescharacteristic
332C2#2490888211yescharacteristic
333C2#2490889711yescharacteristic
334C2#2490890411yescharacteristic
subgroupG/H
centerC23#14581763
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1834C2
socle, prime radicalC23×C83#121
hypercenter#1834D83
hypocenterC83#10626
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
175. C83#10626semidirect

Maximal subgroups

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

subgroupindex
#249083992
#249074652
#249053462
#249052982
C83×#18342
#1062683