Finite Group Databasebeta

← #35313833

Subgroups — #35313833

Order 21248.

330 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 69 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#24916092C211yesmaximal, characteristic
2#24909272C212yesmaximal, complemented
3#24905413C212yesmaximal, complemented
4#24905399C211yesmaximal, characteristic
5C83×#1320C211yesmaximal, characteristic
6C22×C4×Dic83C411yescharacteristic
7#19127755—22no—
8#19127751—22no—
9#19127724C411yescharacteristic
10#19127724C2211yescharacteristic
11#19127665C411yescharacteristic
12M16×Dic83C411yescharacteristic
13M16×Dic83C2211yescharacteristic
14#19127521—22no—
15#19127483C2212yes—
16#19127478—22no—
17#407×C83C2211yescharacteristic
18#349×C83C2212yes—
19C23×Dic83—21no—
20C2×#13050574C2×C411yescharacteristic
21C2×#13050574C2×C411yescharacteristic
22C2×C4×Dic83—21no—
23C2×C4×Dic83—21no—
24C2×C4×Dic83—21no—
25C2×C4×Dic83—21no—
26C2×C4×Dic83—21no—
27C2×C4×Dic83C2×C411yescharacteristic
28C2×C4×Dic83C2×C411yescharacteristic
29#14581732—22no—
30Dic83⋊C8—22no—
31Dic83⋊C8—22no—
32C22⋊(C83⋊C8)—22no—
33#14581702—21no—
34#14581702D412yes—
35C8×Dic83—21no—
36C8×Dic83D412yes—
37C23×C4×C83C2×C411yescharacteristic
38C2×M16×C83C2×C411yescharacteristic
39C2×M16×C83C2311yescharacteristic
40M32×C83—22no—
41C22⋊C8×C83—22no—
42C22×Dic83—21no—
43C22×Dic83—21no—
44C22×Dic83—21no—
45C22×Dic83—21no—
46C22×Dic83—21no—
47C22×Dic83—21no—
48C22×Dic83—44no—
49#13050574—41no—
50#13050574—41no—
51C2×C83⋊C8—21no—
52C2×C83⋊C8C22⋊C412yes—
53C4×Dic83—21no—
54C4×Dic83—21no—
55C4×Dic83—21no—
56C4×Dic83—21no—
57C4×Dic83—21no—
58C4×Dic83—21no—
59C4×Dic83C22⋊C411yescharacteristic
60C4×Dic83C22⋊C411yescharacteristic
61C4×Dic83M1611yescharacteristic
62C4×Dic83M1611yescharacteristic
63C83⋊C16—42no—
64C24×C83M1611yescharacteristic
65C22×C4×C83—21no—
66C22×C4×C83—21no—
67C22×C4×C83—41no—
68C22×C4×C83—41no—
69C22×C4×C83M1611yescharacteristic
70C22×C4×C83C22×C411yescharacteristic
71M16×C83—41no—
72M16×C83—41no—
73C2×C8×C83—21no—
74C2×C8×C83C2×D412yes—
75C16×C83—42no—
76C23×C83—21no—
77C23×C83—41no—
78C23×C83—42no—
79C23×C83C2×M1611yescharacteristic
80C2×C4×C83—21no—
81C2×C4×C83—21no—
82C2×C4×C83—21no—
83C2×C4×C83—42no—
84C2×C4×C83—41no—
85C2×C4×C83—41no—
86C2×C4×C83—41no—
87C2×C4×C83C2×C22⋊C411yescharacteristic
88C2×C4×C83C2×M1611yescharacteristic
89C2×Dic83—24no—
90C2×Dic83—21no—
91C2×Dic83—21no—
92C2×Dic83—21no—
93C2×Dic83—21no—
94C2×Dic83—42no—
95C2×Dic83—42no—
96C2×Dic83—42no—
97C2×Dic83—42no—
98C2×Dic83—42no—
99C8×C83—22no—
100C8×C83—41no—
101C83⋊C8—22no—
102C83⋊C8—41no—
103C22×C83—22no—
104C22×C83—21no—
105C22×C83—41no—
106C22×C83—41no—
107C22×C83—42no—
108C22×C83—42no—
109C22×C83—41no—
110C22×C83#40711yescharacteristic
111C4×C83—21no—
112C4×C83—41no—
113C4×C83#41011yescharacteristic
114C4×C83#41311yescharacteristic
115Dic83—22no—
116Dic83—22no—
117Dic83—41no—
118Dic83—41no—
119#11521—831nomaximal, Sylow
120C2×C83—21no—
121C2×C83—42no—
122C2×C83—41no—
123C2×C83#146411yescharacteristic
124#2920—831no—
125#2165—832no—
126#1327—832no—
127#1320—831no—
128#1320D8311yescharacteristic
129C83#1152111yescharacteristic, complemented, Sylow
130C22×C42—831no—
131#432—1662no—
132#431—1662no—
133#423—831no—
134#423—831no—
135#407—831no—
136#407C2×D8311yescharacteristic
137C4×M16—831no—
138C4×M16—831no—
139#364—1662no—
140#349—832no—
141#349C2×D8312yes—
142#347—1662no—
143C23×C4—1661no—
144C23×C4C4×D8311yescharacteristic
145C2×M16—831no—
146C2×M16—831no—
147C2×M16C4×D8311yescharacteristic
148C2×M16C22×D8311yescharacteristic
149C2×C42—831no—
150C2×C42—831no—
151C2×C42—1661no—
152C2×C42—1661no—
153C2×C42—1661no—
154C2×C42—1661no—
155C2×C42—1661no—
156M32—22no—
157M32—1662no—
158C4⋊C8—1662no—
159C4⋊C8—1662no—
160C22⋊C8—22no—
161C22⋊C8—1662no—
162#97—832no—
163#97—1661no—
164C4×C8—832no—
165C4×C8—1661no—
166C24#1305057311yescharacteristic
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4—3324no—
172C22×C4—1661no—
173C22×C4—1661no—
174C22×C4—1661no—
175C22×C4—1661no—
176C22×C4—1661no—
177C22×C4—1661no—
178C22×C4#1305057311yescharacteristic
179C22×C4C2×C4×D8311yescharacteristic
180M16—41no—
181M16—41no—
182M16—3321no—
183M16—3321no—
184C2×C8—21no—
185C2×C8—832no—
186C2×C8—1661no—
187C2×C8D4×D8312yes—
188C42—831no—
189C42—831no—
190C42—831no—
191C42—831no—
192C42—1661no—
193C42—1661no—
194C42—1661no—
195C42—1661no—
196C42—1661no—
197C42—1661no—
198C16—42no—
199C16—3322no—
200C23—21no—
201C23—41no—
202C23—42no—
203C23C2×#1305057311yescharacteristic
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—3322no—
212C2×C4—3322no—
213C2×C4—3322no—
214C2×C4—3322no—
215C2×C4—3322no—
216C2×C4—1661no—
217C2×C4—1661no—
218C2×C4—1664no—
219C2×C4—1661no—
220C2×C4—1661no—
221C2×C4C22⋊C4×D8311yescharacteristic
222C2×C4M16×D8311yescharacteristic
223C8—22no—
224C8—41no—
225C8—3321no—
226C8—1662no—
227C22—22no—
228C22—21no—
229C22—41no—
230C22—41no—
231C22—42no—
232C22—42no—
233C22—41no—
234C22#1912766311yescharacteristic
235C4—21no—
236C4—41no—
237C4—3321no—
238C4—3321no—
239C4—1662no—
240C4—1662no—
241C4#1912767311yescharacteristic
242C4#1912768211yescharacteristic
243C2—21no—
244C2—42no—
245C2—41no—
246C2#2490579411yescharacteristic
subgroupG/H
centerC4#19127673
commutatorC22×C4×C83C22×C4
FrattiniC2×M16C22×D83
FittingC83×#1320C2
socleC2×C83#1464
prime radicalC24×C83M16
cosocleC2×M16×C83C23
hypercenter#1320D83
hypocenterC83#11521
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1320

Complements

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

NH ≅ G/Ntype
2. #24909272C2semidirect
3. #24905413C2semidirect
129. C83#11521semidirect

Maximal subgroups

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

subgroupindex
#249160922
#249092722
#249054132
#249053992
C83×#13202
#1152183