Finite Group Databasebeta

← #44483045

Subgroups — #44483045

Order 30592.

240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 71 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#29504822C211yesmaximal, characteristic
3#29504623C211yesmaximal, 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×Dic239⋊C4—21no—
18C2×C4×Dic239—21no—
19C2×C4×Dic239C2211yescharacteristic
20Dic239⋊C8—21no—
21C22⋊(C239⋊C8)C2211yescharacteristic
22C8×Dic239—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—24no—
36Dic239⋊C4—21no—
37Dic239⋊C4—21no—
38Dic239⋊C4—21no—
39Dic239⋊C4—21no—
40Dic239⋊C4—21no—
41C22⋊Dic239—21no—
42C4×Dic239—21no—
43C4×Dic239—21no—
44C4×Dic239—42no—
45C4×Dic239C2×C411yescharacteristic
46C4×Dic239C2×C411yescharacteristic
47C4×Dic239D411yescharacteristic
48C4×Dic239D411yescharacteristic
49C2×Q8×C239C2×C411yescharacteristic
50C22×C4×C239—21no—
51C22×C4×C239C2311yescharacteristic
52C2×C8×C239—21no—
53C4⋊C4×C239—21no—
54C4⋊C4×C239C2×C411yescharacteristic
55C22⋊C4×C239—21no—
56Dic478—42no—
57Dic478—41no—
58C2×Dic239—22no—
59C2×Dic239—22no—
60C2×Dic239—21no—
61C2×Dic239—21no—
62C2×Dic239—41no—
63C2×Dic239—41no—
64C2×Dic239C22⋊C411yescharacteristic
65C2×Dic239C22⋊C411yescharacteristic
66C2×Dic239C22⋊C411yescharacteristic
67C2×Dic239C22⋊C411yescharacteristic
68C2×Dic239SD1612yes—
69C2×Dic239Q1612yes—
70C239⋊C8—41no—
71C23×C239C2×D411yescharacteristic
72Q8×C239—41no—
73C2×C4×C239—22no—
74C2×C4×C239—21no—
75C2×C4×C239—21no—
76C2×C4×C239—41no—
77C2×C4×C239—41no—
78C2×C4×C239—41no—
79C2×C4×C239C22×C411yescharacteristic
80C2×C4×C239C2×D411yescharacteristic
81C8×C239—41no—
82C22×C239—21no—
83C22×C239—21no—
84C22×C239C2×C22⋊C411yescharacteristic
85C22×C239C2×SD1611yescharacteristic
86C22×C239C2×Q1611yescharacteristic
87C4×C239—21no—
88C4×C239—21no—
89C4×C239—42no—
90C4×C239—41no—
91C4×C239—41no—
92Dic239—21no—
93Dic239—42no—
94Dic239—41no—
95Dic239—41no—
96Dic239#10312yes—
97Dic239#10312yes—
98Dic239#10412yes—
99C2×C239—21no—
100C2×C239—21no—
101C2×C239#41011yescharacteristic
102C2×C239C2×#10311yescharacteristic
103C2×C239C2×#10411yescharacteristic
104C239#150311yescharacteristic, complemented, Sylow
105#1503—2391nomaximal, Sylow
106#533—2391no—
107#431—2391no—
108C4×C4⋊C4—2391no—
109#328—2391no—
110#328—2391no—
111#328—2391no—
112#328D23911yescharacteristic
113C4⋊Q8—2391no—
114C4⋊Q8—2391no—
115#125—4781no—
116C22⋊Q8—4781no—
117C22⋊Q8—2391no—
118C22⋊Q8C2×D23911yescharacteristic
119C4×Q8—4781no—
120C4×Q8—2391no—
121C4×Q8—2391no—
122#117—4781no—
123C2×C4⋊C4—4781no—
124C2×C42—4781no—
125C2×C42—2391no—
126C4⋊C8—4781no—
127C22⋊C8—2391no—
128C22⋊C8C2×D23911yescharacteristic
129C4×C8—4781no—
130#95—2391no—
131#95C2×D23911yescharacteristic
132C2×Q8—4781no—
133C2×Q8—2391no—
134C2×Q8C4×D23911yescharacteristic
135C22×C4—21no—
136C22×C4—4781no—
137C22×C4—2391no—
138C22×C4—2391no—
139C22×C4C22×D23911yescharacteristic
140C2×C8—21no—
141C2×C8—4781no—
142C4⋊C4—21no—
143C4⋊C4—4784no—
144C4⋊C4—4781no—
145C4⋊C4—4781no—
146C4⋊C4—4781no—
147C4⋊C4—4781no—
148C4⋊C4—4781no—
149C4⋊C4—4781no—
150C4⋊C4—2391no—
151C4⋊C4C4×D23911yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—4781no—
154C42—9562no—
155C42—4781no—
156C42—4781no—
157C42—2391no—
158C42—2391no—
159C42—2391no—
160C42—2391no—
161C23D4×D23911yescharacteristic
162Q8—41no—
163Q8—9561no—
164Q8—9562no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—9561no—
172C2×C4—9561no—
173C2×C4—4782no—
174C2×C4—4781no—
175C2×C4—4781no—
176C2×C4—4782no—
177C2×C4—2391no—
178C2×C4—2391no—
179C2×C4—2391no—
180C2×C4—2391no—
181C2×C4—2392no—
182C2×C4—2392no—
183C2×C4C2×C4×D23911yescharacteristic
184C2×C4D4×D23911yescharacteristic
185C8—41no—
186C8—9561no—
187C22—21no—
188C22—21no—
189C22C22⋊C4×D23911yescharacteristic
190C22SD16×D23911yescharacteristic
191C22Q16×D23911yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—41no—
196C4—41no—
197C4—9562no—
198C4—9561no—
199C4—9561no—
200C4—4781no—
201C4—2392no—
202C4—2392no—
203C4—2392no—
204C2—21no—
205C2—21no—
206C2#2950474411yescharacteristic
207C2#103×D23911yescharacteristic
208C2#104×D23911yescharacteristic
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#1503
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
104. C239#1503semidirect

Maximal subgroups

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

subgroupindex
#295053242
#295048222
#295046232
#295045102
#295045092
#295045082
#328×C2392
#1503239