Finite Group Databasebeta

← #44483097

Subgroups — #44483097

Order 30592.

208 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 61 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#29505324C211yesmaximal, characteristic
2#29504826C211yesmaximal, characteristic
3#29504639C211yesmaximal, characteristic
4#29504510C211yesmaximal, characteristic
5#29504509C211yesmaximal, characteristic
6#29504508C211yesmaximal, characteristic
7#328×C239C211yesmaximal, characteristic
8#21439959C411yescharacteristic, complemented
9#21439958C411yescharacteristic, complemented
10#21439950—21no—
11#21439939C2211yescharacteristic
12#21439937—21no—
13Q8×Dic239C411yescharacteristic, complemented
14#21439925—21no—
15#21439925C411yescharacteristic, complemented
16#21439916—21no—
17C2×C4×Dic239C2211yescharacteristic
18Dic239⋊C8—21no—
19C22⋊(C239⋊C8)C2211yescharacteristic
20#21439870—21no—
21C239⋊#95—21no—
22C239⋊#95—21no—
23C239⋊#95C2211yescharacteristic
24C22⋊Q8×C239C2211yescharacteristic
25C22⋊C8×C239C2211yescharacteristic
26#95×C239C2211yescharacteristic
27C2×Dic478—21no—
28C2×Dic478C2×C411yescharacteristic
29C22×Dic239—21no—
30C22×Dic239D411yescharacteristic
31C22×Dic239D411yescharacteristic
32C2×C239⋊C8—21no—
33C4⋊Dic239—21no—
34C4⋊Dic239C2×C411yescharacteristic
35Dic239⋊C4—21no—
36Dic239⋊C4—21no—
37Dic239⋊C4—21no—
38Dic239⋊C4—21no—
39Dic239⋊C4—21no—
40C22⋊Dic239—21no—
41C4×Dic239—21no—
42C4×Dic239—21no—
43C4×Dic239C2×C411yescharacteristic
44C4×Dic239C2×C411yescharacteristic
45C4×Dic239D411yescharacteristic
46C4×Dic239D411yescharacteristic
47C2×Q8×C239C2×C411yescharacteristic
48C22×C4×C239—21no—
49C22×C4×C239C2311yescharacteristic
50C2×C8×C239—21no—
51C4⋊C4×C239—21no—
52C4⋊C4×C239C2×C411yescharacteristic
53C22⋊C4×C239—21no—
54Dic478—42no—
55Dic478—41no—
56C2×Dic239—21no—
57C2×Dic239—21no—
58C2×Dic239—21no—
59C2×Dic239—21no—
60C2×Dic239—41no—
61C2×Dic239—41no—
62C2×Dic239—41no—
63C2×Dic239—41no—
64C2×Dic239C22⋊C411yescharacteristic
65C2×Dic239C22⋊C411yescharacteristic
66C2×Dic239C22⋊C411yescharacteristic
67C2×Dic239C22⋊C411yescharacteristic
68C239⋊C8—41no—
69C23×C239C2×D411yescharacteristic
70Q8×C239—41no—
71C2×C4×C239—21no—
72C2×C4×C239—21no—
73C2×C4×C239—41no—
74C2×C4×C239—41no—
75C2×C4×C239—41no—
76C2×C4×C239—41no—
77C2×C4×C239C22×C411yescharacteristic
78C2×C4×C239C2×D411yescharacteristic
79C8×C239—41no—
80C22×C239—21no—
81C22×C239—21no—
82C22×C239C2×C22⋊C411yescharacteristic
83C22×C239#13711yescharacteristic
84C22×C239#13711yescharacteristic
85C4×C239—21no—
86C4×C239—21no—
87C4×C239—41no—
88C4×C239—41no—
89C4×C239—81no—
90Dic239—21no—
91Dic239—21no—
92Dic239—21no—
93Dic239—21no—
94Dic239—41no—
95Dic239—41no—
96Dic239—81no—
97C2×C239—21no—
98C2×C239—21no—
99C2×C239#41011yescharacteristic
100C2×C239#41911yescharacteristic
101C2×C239#42111yescharacteristic
102C239#151511yescharacteristic, complemented, Sylow
103#1515—2391nomaximal, Sylow
104#533—2391no—
105#432—2391no—
106#383—2391no—
107#328—2391no—
108#328—2391no—
109#328—2391no—
110#328D23911yescharacteristic
111C4⋊Q8—2391no—
112C4⋊Q8—2391no—
113#125—4781no—
114C22⋊Q8—4781no—
115C22⋊Q8—2391no—
116C22⋊Q8C2×D23911yescharacteristic
117C4×Q8—4781no—
118C4×Q8—2391no—
119C4×Q8—2391no—
120#117—4781no—
121C2×C42—2391no—
122C4⋊C8—4781no—
123C22⋊C8—2391no—
124C22⋊C8C2×D23911yescharacteristic
125#97—4781no—
126#95—4781no—
127#95—4781no—
128#95—2391no—
129#95C2×D23911yescharacteristic
130C2×Q8—4781no—
131C2×Q8—2391no—
132C2×Q8C4×D23911yescharacteristic
133C22×C4—21no—
134C22×C4—4781no—
135C22×C4—2391no—
136C22×C4—2391no—
137C22×C4C22×D23911yescharacteristic
138C2×C8—21no—
139C2×C8—4781no—
140C4⋊C4—21no—
141C4⋊C4—4781no—
142C4⋊C4—4781no—
143C4⋊C4—4781no—
144C4⋊C4—4781no—
145C4⋊C4—4781no—
146C4⋊C4—4781no—
147C4⋊C4—2391no—
148C4⋊C4C4×D23911yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—4781no—
151C42—4781no—
152C42—4781no—
153C42—2391no—
154C42—2391no—
155C42—2391no—
156C42—2391no—
157C23D4×D23911yescharacteristic
158Q8—41no—
159Q8—9561no—
160Q8—9562no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—9561no—
168C2×C4—9561no—
169C2×C4—9561no—
170C2×C4—9561no—
171C2×C4—4781no—
172C2×C4—4781no—
173C2×C4—4781no—
174C2×C4—4781no—
175C2×C4—2391no—
176C2×C4—2391no—
177C2×C4—2391no—
178C2×C4—2391no—
179C2×C4C2×C4×D23911yescharacteristic
180C2×C4D4×D23911yescharacteristic
181C8—41no—
182C8—9561no—
183C22—21no—
184C22—21no—
185C22C22⋊C4×D23911yescharacteristic
186C22#2143998911yescharacteristic
187C22#2143999211yescharacteristic
188C4—21no—
189C4—21no—
190C4—41no—
191C4—41no—
192C4—81no—
193C4—19121no—
194C4—9561no—
195C4—9561no—
196C4—4781no—
197C4—4781no—
198C4—4781no—
199C4—4781no—
200C2—21no—
201C2—21no—
202C2#2950474411yescharacteristic
203C2#2950477911yescharacteristic
204C2#2950478711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D239
commutatorC2×C4×C239C22×C4
FrattiniC22×C4C22×D239
Fitting#328×C239C2
socleC22×C239C2×C22⋊C4
prime radicalC23×C239C2×D4
cosocleC22×C4×C239C23
hypercenter#328D239
hypocenterC239#1515
LCSG ▷ C2×C4×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
8. #21439959C4semidirect
9. #21439958C4semidirect
13. Q8×Dic239C4semidirect
15. #21439925C4semidirect
102. C239#1515semidirect

Maximal subgroups

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

subgroupindex
#295053242
#295048262
#295046392
#295045102
#295045092
#295045082
#328×C2392
#1515239