Finite Group Databasebeta

← #44483240

Subgroups — #44483240

Order 30592.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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#29505320C211yesmaximal, characteristic
2#29504828C211yesmaximal, characteristic, complemented
3C4⋊C8×D239C211yesmaximal, characteristic, complemented
4#29504520C211yesmaximal, characteristic, complemented
5#29504520C211yesmaximal, characteristic, complemented
6#29504516C211yesmaximal, characteristic, complemented
7#331×C239C211yesmaximal, characteristic, complemented
8C2×#16838547C412yes—
9C2×C8×D239—21no—
10#21439960C2211yescharacteristic
11#21439947C412yes—
12#21439931—21no—
13#21439931—21no—
14D4×Dic239—21no—
15D4×Dic239—21no—
16C42×D239C2211yescharacteristic
17C4⋊(C239⋊C8)C2211yescharacteristic
18C4⋊(C239⋊C8)C2211yescharacteristic
19Dic239⋊C8—21no—
20(C2×D239)⋊C8—21no—
21#21439870—21no—
22#127×C239C2211yescharacteristic
23C4⋊C8×C239C2211yescharacteristic
24C4⋊C8×C239C2211yescharacteristic
25#16838547—44no—
26C2×Dic478C2×C412yes—
27C2×C22⋊D239—22no—
28C22×Dic239—22no—
29C2×C4×D239C2×C411yescharacteristic
30C2×C4×D239D411yescharacteristic
31C2×C4×D239D411yescharacteristic
32C2×C239⋊C8—21no—
33C2×C239⋊C8—21no—
34C8×D239—42no—
35C4⋊Dic239—21no—
36C4⋊Dic239—21no—
37C22⋊Dic239—22no—
38C22⋊Dic239—22no—
39C4×Dic239C2×C411yescharacteristic
40C4×Dic239D411yescharacteristic
41C4×Dic239D411yescharacteristic
42C2×D4×C239—21no—
43C2×D4×C239—21no—
44C2×D4×C239C2×C412yes—
45C2×C8×C239—21no—
46C2×C8×C239—21no—
47C42×C239C2311yescharacteristic
48C22×D239C22⋊C411yescharacteristic
49Dic478—42no—
50C22⋊D239—44no—
51C2×Dic239—22no—
52C2×Dic239—44no—
53C2×Dic239C22⋊C411yescharacteristic
54C2×Dic239C22⋊C411yescharacteristic
55C2×Dic239C22⋊C411yescharacteristic
56C4×D239—22no—
57C4×D239—21no—
58C4×D239—21no—
59C4×D239—21no—
60C4×D239—21no—
61C239⋊C8—41no—
62C239⋊C8—41no—
63C23×C239—22no—
64D4×C239—42no—
65D4×C239—41no—
66D4×C239—41no—
67D4×C239—41no—
68D4×C239—41no—
69C2×C4×C239C22×C411yescharacteristic
70C2×C4×C239C2×D411yescharacteristic
71C2×C4×C239C2×D411yescharacteristic
72C8×C239—41no—
73C8×C239—41no—
74C22×C239—42no—
75C22×C239—42no—
76C22×C239—42no—
77C22×C239C2×C22⋊C411yescharacteristic
78C2×D239—21no—
79C2×D239—21no—
80C2×D239#10012yes—
81C4×C239—21no—
82C4×C239#13511yescharacteristic
83C4×C239#13511yescharacteristic
84C4×C239AGL(1,ℤ/8)11yescharacteristic
85C4×C239#13711yescharacteristic
86Dic239—21no—
87Dic239—21no—
88Dic239—21no—
89Dic239—42no—
90C2×C239—82no—
91C2×C239C2×#10011yescharacteristic
92C2×C239#41611yescharacteristic
93C2×C239#41711yescharacteristic
94D239—22no—
95C239#155111yescharacteristic, complemented, Sylow
96#1551—2391nomaximal, Sylow
97#532—2391no—
98#432—2391no—
99C2×C4⋊C8—2391no—
100#333—2391no—
101#333—2391no—
102#331—2391no—
103#331D23911yescharacteristic, complemented
104C2×#41—2392no—
105C22×C8—4781no—
106C4⋊Q8—2391no—
107#127C2×D23911yescharacteristic
108#124—2392no—
109#121—4781no—
110#121—4781no—
111C4×D4—4781no—
112C4×D4—4781no—
113C2×C42—2391no—
114C4⋊C8—4781no—
115C4⋊C8—2391no—
116C4⋊C8—2391no—
117C4⋊C8C2×D23911yescharacteristic
118C4⋊C8C2×D23911yescharacteristic
119C22⋊C8—4781no—
120#97—4781no—
121#41—9564no—
122C2×Q8—2392no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—4782no—
126C2×D4C4×D23912yes—
127C22×C4—4782no—
128C22×C4—2391no—
129C22×C4—2391no—
130C22×C4—2391no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—9562no—
134C2×C8—4781no—
135C2×C8—4781no—
136C4⋊C4—4781no—
137C4⋊C4—4781no—
138C22⋊C4—4782no—
139C22⋊C4—4782no—
140C42—2391no—
141C42—2391no—
142C42—2391no—
143C42C22×D23911yescharacteristic
144C23—22no—
145C23—2391no—
146Q8—9562no—
147D4—42no—
148D4—41no—
149D4—41no—
150D4—41no—
151D4—41no—
152D4—9564no—
153C2×C4—9564no—
154C2×C4—4782no—
155C2×C4—4782no—
156C2×C4—4781no—
157C2×C4—4781no—
158C2×C4—4781no—
159C2×C4—4781no—
160C2×C4—2391no—
161C2×C4—2391no—
162C2×C4—2391no—
163C2×C4C2×C4×D23911yescharacteristic
164C2×C4D4×D23911yescharacteristic
165C2×C4D4×D23911yescharacteristic
166C8—41no—
167C8—41no—
168C8—9561no—
169C8—9561no—
170C22—42no—
171C22—42no—
172C22—42no—
173C22—4781no—
174C22—4781no—
175C22—2392no—
176C22C22⋊C4×D23911yescharacteristic
177C4—21no—
178C4—9562no—
179C4—4781no—
180C4—4781no—
181C4—4781no—
182C4#2143997911yescharacteristic
183C4#2143998111yescharacteristic
184C4#2143998411yescharacteristic
185C4#2143998911yescharacteristic
186C2—82no—
187C2—4782no—
188C2#100×D23911yescharacteristic
189C2#2950476511yescharacteristic
190C2#2950477011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D239
commutatorC2×C4×C239C22×C4
FrattiniC42C22×D239
Fitting#331×C239C2
socleC22×C239C2×C22⋊C4
prime radical#29505320C2
cosocleC42×C239C23
hypercenter#331D239
hypocenterC239#1551
LCSG ▷ C2×C4×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #29504828C2semidirect
3. C4⋊C8×D239C2semidirect
4. #29504520C2semidirect
5. #29504520C2semidirect
6. #29504516C2semidirect
7. #331×C239C2semidirect
95. C239#1551semidirect
103. #331D239semidirect

Maximal subgroups

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

subgroupindex
#295053202
#295048282
C4⋊C8×D2392
#295045202
#295045162
#331×C2392
#1551239