Finite Group Databasebeta

← #35315083

Subgroups — #35315083

Order 21248.

402 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24913229C211yesmaximal, characteristic
2#24907540C211yesmaximal, characteristic
3#24905464C214yesmaximal
4C83×#1464C211yesmaximal, characteristic
5C2×#14581792C411yescharacteristic, complemented
6C2×#14581771—21no—
7#19127631—21no—
8#19127631C412yescomplemented
9#19127626—21no—
10#19127626C2212yes—
11#19127607—21no—
12#19127567C411yescharacteristic, complemented
13#19127564—21no—
14#19127468—21no—
15#19127468C2212yes—
16C2×#117×C83C2211yescharacteristic
17#432×C83—21no—
18#324×C83—21no—
19#323×C83C2212yes—
20C22×Dic166—21no—
21#14581792—41no—
22#14581792—41no—
23#14581771—44no—
24C2×C4⋊Dic83—21no—
25C2×C4⋊Dic83—21no—
26C2×C4⋊Dic83C2×C412yes—
27C2×Dic83⋊C4—22no—
28C2×C22⋊Dic83—22no—
29C2×C22⋊Dic83—22no—
30C83⋊#95—21no—
31C83⋊#95—22no—
32C83⋊#95—22no—
33C83⋊#95—41no—
34C83⋊#95—41no—
35C83⋊#95C2×C412yes—
36C23×C4×C83D411yescharacteristic
37#117×C83—41no—
38#117×C83—41no—
39C2×C4⋊C4×C83C2×C411yescharacteristic
40C2×C4⋊C4×C83D411yescharacteristic
41C2×C22⋊C4×C83D411yescharacteristic
42C2×C22⋊C4×C83C2311yescharacteristic
43C2×C42×C83C2×C411yescharacteristic
44C2×C42×C83D411yescharacteristic
45C4⋊C8×C83—41no—
46C22⋊C8×C83—22no—
47#97×C83—41no—
48C2×Dic166—42no—
49C2×Dic166—42no—
50C2×Dic166—41no—
51C2×Dic166—41no—
52C22×Dic83—22no—
53C22×Dic83—22no—
54C22×Dic83—42no—
55C4⋊Dic83—42no—
56C4⋊Dic83—42no—
57C4⋊Dic83—42no—
58Dic83⋊C4—44no—
59C22⋊Dic83—44no—
60C22⋊Dic83—42no—
61C22⋊Dic83—42no—
62C24×C83C2×D411yescharacteristic
63C22×C4×C83—22no—
64C22×C4×C83—21no—
65C22×C4×C83—21no—
66C22×C4×C83—41no—
67C22×C4×C83C22⋊C411yescharacteristic
68C22×C4×C83C22⋊C411yescharacteristic
69C22×C4×C83C22⋊C411yescharacteristic
70C22×C4×C83C22⋊C411yescharacteristic
71C22×C4×C83C22×C411yescharacteristic
72C22×C4×C83C2×D411yescharacteristic
73C2×C8×C83—42no—
74C4⋊C4×C83—41no—
75C4⋊C4×C83—41no—
76C22⋊C4×C83—41no—
77C22⋊C4×C83—41no—
78C42×C83—21no—
79C42×C83—21no—
80C42×C83—21no—
81C42×C83—21no—
82C23×C83—21no—
83C23×C83—21no—
84C23×C83—41no—
85C23×C83—41no—
86C23×C83C2×C22⋊C411yescharacteristic
87C23×C83AGL(1,ℤ/8)12yes—
88C2×C4×C83—21no—
89C2×C4×C83—21no—
90C2×C4×C83—21no—
91C2×C4×C83—21no—
92C2×C4×C83—21no—
93C2×C4×C83—21no—
94C2×C4×C83—21no—
95C2×C4×C83—21no—
96C2×C4×C83—21no—
97C2×C4×C83—42no—
98C2×C4×C83—42no—
99C2×C4×C83—41no—
100C2×C4×C83—41no—
101C2×C4×C83—41no—
102C2×C4×C83—41no—
103C2×C4×C83#9911yescharacteristic
104C2×C4×C83#9911yescharacteristic
105C2×Dic83—42no—
106C2×Dic83—42no—
107C2×Dic83—42no—
108C2×Dic83—42no—
109C2×Dic83—42no—
110C2×Dic83—42no—
111C2×Dic83—82no—
112C2×Dic83—82no—
113C2×Dic83—82no—
114Dic166—82no—
115Dic166—82no—
116C8×C83—82no—
117C22×C83—21no—
118C22×C83—21no—
119C22×C83—22no—
120C22×C83—42no—
121C22×C83—41no—
122C22×C83—41no—
123C22×C83—81no—
124C22×C83C2×#9911yescharacteristic
125C22×C83#41811yescharacteristic
126C22×C83#42111yescharacteristic
127C4×C83—21no—
128C4×C83—21no—
129C4×C83—41no—
130C4×C83—41no—
131C4×C83—41no—
132C4×C83—41no—
133C4×C83—41no—
134Dic83—82no—
135Dic83—82no—
136Dic83—162no—
137#11801—831nomaximal, Sylow
138C2×C83—21no—
139C2×C83—21no—
140C2×C83—42no—
141C2×C83#151011yescharacteristic
142C2×C83#212311yescharacteristic
143C2×C83#212911yescharacteristic
144#2621—831no—
145#1820—831no—
146#1464D8311yescharacteristic
147#1344—834no—
148C83#1180111yescharacteristic, complemented, Sylow
149C2×C4⋊Q8—831no—
150C2×C22⋊Q8—1661no—
151C2×#117C2×D8311yescharacteristic
152#432—21no—
153#398—832no—
154#398—1661no—
155#397—832no—
156#397—1661no—
157#391—1661no—
158#382—831no—
159#381—1661no—
160#342—832no—
161#342—1661no—
162#324—21no—
163#323C2×D8312yes—
164C22×Q8—1661no—
165C23×C4D33211yescharacteristic
166C4⋊Q8—3321no—
167C4⋊Q8—3321no—
168C22⋊Q8—3324no—
169#117—41no—
170#117—41no—
171C2×C4⋊C4—832no—
172C2×C4⋊C4—1662no—
173C2×C4⋊C4—1661no—
174C2×C4⋊C4—1661no—
175C2×C4⋊C4C4×D8311yescharacteristic
176C2×C4⋊C4C22⋊D8311yescharacteristic
177C2×C22⋊C4—1662no—
178C2×C22⋊C4—1662no—
179C2×C22⋊C4D33211yescharacteristic
180C2×C22⋊C4C22×D8311yescharacteristic
181C2×C42C4×D8311yescharacteristic
182C2×C42C22⋊D8311yescharacteristic
183C4⋊C8—41no—
184C22⋊C8—22no—
185#97—41no—
186#95—3321no—
187#95—3321no—
188#95—832no—
189#95—1661no—
190#95—1662no—
191#95—1662no—
192C24C2×D33211yescharacteristic
193C2×Q8—3322no—
194C2×Q8—3322no—
195C2×Q8—3321no—
196C2×Q8—3321no—
197C22×C4—22no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—41no—
201C22×C4—3322no—
202C22×C4—1662no—
203C22×C4—1662no—
204C22×C4(C2×D83)⋊C411yescharacteristic
205C22×C4(C2×D83)⋊C411yescharacteristic
206C22×C4(C2×D83)⋊C411yescharacteristic
207C22×C4(C2×D83)⋊C411yescharacteristic
208C22×C4C2×C4×D8311yescharacteristic
209C22×C4C2×C22⋊D8311yescharacteristic
210C2×C8—42no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—3322no—
214C4⋊C4—3324no—
215C4⋊C4—3322no—
216C4⋊C4—3322no—
217C22⋊C4—41no—
218C22⋊C4—41no—
219C22⋊C4—3324no—
220C22⋊C4—3322no—
221C22⋊C4—3322no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—21no—
226C23—21no—
227C23—21no—
228C23—41no—
229C23—41no—
230C23C2×(C2×D83)⋊C411yescharacteristic
231C23#1458182012yes—
232Q8—6642no—
233Q8—6642no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—3322no—
250C2×C4—3322no—
251C2×C4—3322no—
252C2×C4—3322no—
253C2×C4—3322no—
254C2×C4—3322no—
255C2×C4—6642no—
256C2×C4—6642no—
257C2×C4—6642no—
258C2×C4#1458170611yescharacteristic
259C2×C4#1458170611yescharacteristic
260C8—82no—
261C22—21no—
262C22—21no—
263C22—22no—
264C22—42no—
265C22—41no—
266C22—41no—
267C22—81no—
268C22C2×#1458170611yescharacteristic
269C22#1912770711yescharacteristic
270C22#1912771711yescharacteristic
271C4—21no—
272C4—21no—
273C4—41no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—41no—
278C4—13282no—
279C4—6642no—
280C4—6642no—
281C2—21no—
282C2—21no—
283C2—42no—
284C2#2490599311yescharacteristic
285C2#2490911811yescharacteristic
286C2#2490913711yescharacteristic
subgroupG/H
centerC22C2×#14581706
commutatorC22×C4×C83C22×C4
FrattiniC2×C22⋊C4C22×D83
FittingC83×#1464C2
socleC22×C83C2×#99
prime radicalC24×C83C2×D4
cosocleC2×C22⋊C4×C83C23
hypercenter#1464D83
hypocenterC83#11801
LCSG ▷ C22×C4×C83 ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
5. C2×#14581792C4semidirect
8. #19127631C4semidirect
12. #19127567C4semidirect
148. C83#11801semidirect

Maximal subgroups

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

subgroupindex
#249132292
#249075402
#249054642
C83×#14642
#1180183