Finite Group Databasebeta

← #44485007

Subgroups — #44485007

Order 30592.

378 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#21439919C211yesmaximal, characteristic, complemented
2C2×#21439875C212yesmaximal
3#29504635C211yesmaximal, characteristic, complemented
4#29504539C212yesmaximal, complemented
5C2×#123×C239C211yesmaximal, characteristic
6#21439919—24no—
7C2×C4⋊Dic239—21no—
8C2×C22⋊Dic239C2212yes—
9C2×C22⋊Dic239C2212yes—
10C2×C4×Dic239—21no—
11#21439875—24no—
12C239⋊#95—22no—
13C22×D4×C239C2211yescharacteristic
14C23×C4×C239C2211yescharacteristic
15#123×C239—22no—
16#123×C239—21no—
17#123×C239—21no—
18C2×C4⋊C4×C239C412yescomplemented
19C2×C22⋊C4×C239C412yescomplemented
20C2×C22⋊C4×C239C2211yescharacteristic
21C22×Dic239—22no—
22C22×Dic239—22no—
23C4⋊Dic239—24no—
24C22⋊Dic239—22no—
25C22⋊Dic239—22no—
26C22⋊Dic239—22no—
27C22⋊Dic239D414yes—
28C4×Dic239—24no—
29C24×C239C2×C411yescharacteristic
30C24×C239C2311yescharacteristic
31C2×D4×C239—21no—
32C2×D4×C239—21no—
33C2×D4×C239—22no—
34C2×D4×C239—22no—
35C22×C4×C239—22no—
36C22×C4×C239—22no—
37C22×C4×C239C2×C411yescharacteristic
38C22×C4×C239C2×C412yes—
39C22×C4×C239C2×C412yes—
40C22×C4×C239D412yes—
41C22×C4×C239D411yescharacteristic
42C22×C4×C239D411yescharacteristic
43C4⋊C4×C239—22no—
44C4⋊C4×C239—22no—
45C22⋊C4×C239—21no—
46C22⋊C4×C239—21no—
47C22⋊C4×C239—22no—
48C22⋊C4×C239—22no—
49C2×Dic239—24no—
50C2×Dic239—44no—
51C2×Dic239—44no—
52C2×Dic239—42no—
53C23×C239—21no—
54C23×C239—22no—
55C23×C239—42no—
56C23×C239—42no—
57C23×C239C22×C411yescharacteristic
58C23×C239C2×D411yescharacteristic
59C23×C239C2×D411yescharacteristic
60C23×C239C2×D412yes—
61C23×C239#4112yes—
62D4×C239—41no—
63D4×C239—42no—
64D4×C239—41no—
65C2×C4×C239—24no—
66C2×C4×C239—21no—
67C2×C4×C239—21no—
68C2×C4×C239—24no—
69C2×C4×C239—21no—
70C2×C4×C239—21no—
71C2×C4×C239—22no—
72C2×C4×C239—21no—
73C2×C4×C239—22no—
74C2×C4×C239—42no—
75C2×C4×C239C22⋊C412yes—
76C2×C4×C239C22⋊C412yes—
77C22×C239—22no—
78C22×C239—22no—
79C22×C239—22no—
80C22×C239—42no—
81C22×C239—42no—
82C22×C239—41no—
83C22×C239—42no—
84C22×C239—82no—
85C22×C239C2×C22⋊C411yescharacteristic
86C22×C239C4×D412yes—
87C22×C239#12011yescharacteristic
88C22×C239#12112yes—
89C22×C239#12311yescharacteristic
90C4×C239—22no—
91C4×C239—22no—
92C4×C239—41no—
93C4×C239—42no—
94Dic239—44no—
95Dic239—82no—
96C2×C239—21no—
97C2×C239—22no—
98C2×C239—22no—
99C2×C239—21no—
100C2×C239—81no—
101C2×C239#38611yescharacteristic
102C2×C239#41012yes—
103C239#189911yescharacteristic, complemented, Sylow
104#1899—2391nomaximal, Sylow
105C2×#123D23911yescharacteristic
106C2×#117—2391no—
107C2×#99—2392no—
108#381—2391no—
109#342—2392no—
110C22×D4C2×D23911yescharacteristic
111C23×C4C2×D23911yescharacteristic
112#123—22no—
113#123—21no—
114#123—21no—
115#117—4784no—
116C2×C4⋊C4—4781no—
117C2×C4⋊C4Dic23912yescomplemented
118C2×C22⋊C4—2392no—
119C2×C22⋊C4—2392no—
120C2×C22⋊C4Dic23912yescomplemented
121C2×C22⋊C4C2×D23911yescharacteristic
122C2×C42—4781no—
123#99—4784no—
124#95—4782no—
125C24C2×Dic23911yescharacteristic
126C24C22×D23911yescharacteristic
127C2×D4—22no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—22no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—4782no—
134C22×C4—4782no—
135C22×C4C2×Dic23911yescharacteristic
136C22×C4C2×Dic23912yes—
137C22×C4C2×Dic23912yes—
138C22×C4C22⋊D23912yes—
139C22×C4C22⋊D23911yescharacteristic
140C22×C4C22⋊D23911yescharacteristic
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—4784no—
144C22⋊C4—21no—
145C22⋊C4—21no—
146C22⋊C4—22no—
147C22⋊C4—22no—
148C22⋊C4—4782no—
149C22⋊C4—4782no—
150C22⋊C4—4782no—
151C22⋊C4—2394no—
152C42—4784no—
153C23—21no—
154C23—22no—
155C23—42no—
156C23—42no—
157C23C22×Dic23911yescharacteristic
158C23D4×D23912yes—
159C23C2×C22⋊D23911yescharacteristic
160C23C2×C22⋊D23911yescharacteristic
161C23#1683854712yes—
162D4—41no—
163D4—42no—
164D4—41no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—24no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—9564no—
176C2×C4—9562no—
177C2×C4—9564no—
178C2×C4—4784no—
179C2×C4C22⋊Dic23912yes—
180C2×C4C22⋊Dic23912yes—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—41no—
187C22—42no—
188C22—82no—
189C22C2×C22⋊Dic23911yescharacteristic
190C22D4×Dic23912yes—
191C22#2143992811yescharacteristic
192C22#2143993212yes—
193C22#2143994111yescharacteristic
194C4—22no—
195C4—22no—
196C4—41no—
197C4—42no—
198C4—19122no—
199C4—9564no—
200C2—22no—
201C2—21no—
202C2—22no—
203C2—21no—
204C2—81no—
205C2#2950465211yescharacteristic
206C2#2950474612yes—
subgroupG/H
centerC22C2×C22⋊Dic239
commutatorC23×C239C22×C4
FrattiniC24C22×D239
FittingC2×#123×C239C2
socleC22×C239C2×C22⋊C4
prime radicalC22×D4×C239C22
cosocleC24×C239C23
hypercenterC2×#123D239
hypocenterC239#1899
LCSG ▷ C23×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×#21439919C2semidirect
3. #29504635C2semidirect
4. #29504539C2semidirect
18. C2×C4⋊C4×C239C4semidirect
19. C2×C22⋊C4×C239C4semidirect
103. C239#1899semidirect
117. C2×C4⋊C4Dic239semidirect
120. C2×C22⋊C4Dic239semidirect

Maximal subgroups

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

subgroupindex
C2×#214399192
C2×#214398752
#295046352
#295045392
C2×#123×C2392
#1899239