Finite Group Databasebeta

← #44483173

Subgroups — #44483173

Order 30592.

196 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 59 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#125×D239C211yesmaximal, characteristic
2#29504827C212yesmaximal
3#29504514C211yesmaximal, characteristic, complemented
4#29504513C212yesmaximal, complemented
5#330×C239C211yesmaximal, characteristic, complemented
6#21439952C2211yescharacteristic
7#21439951C412yes—
8#21439950—22no—
9C4⋊C4×D239—22no—
10C4⋊C4×D239C412yes—
11C42×D239C2211yescharacteristic
12Dic239⋊C8—22no—
13(C2×D239)⋊C8—22no—
14#21439871C2212yes—
15#125×C239C2211yescharacteristic
16#97×C239C2212yes—
17C2×C4×D239—22no—
18C2×C4×D239C2×C411yescharacteristic
19C2×C4×D239D412yes—
20C2×C239⋊C8—22no—
21C4⋊Dic239—22no—
22C4⋊Dic239C2×C412yes—
23Dic239⋊C4—22no—
24Dic239⋊C4—22no—
25Dic239⋊C4—22no—
26C4×Dic239C2×C411yescharacteristic
27C4×Dic239D412yes—
28C2×C8×C239—22no—
29C4⋊C4×C239—22no—
30C4⋊C4×C239C2×C412yes—
31C42×C239C2311yescharacteristic
32C22×D239C22⋊C411yescharacteristic
33C2×Dic239—22no—
34C2×Dic239C22⋊C412yes—
35C2×Dic239C22⋊C411yescharacteristic
36C4×D239—22no—
37C4×D239—42no—
38C4×D239—44no—
39C239⋊C8—42no—
40C2×C4×C239—22no—
41C2×C4×C239C22×C411yescharacteristic
42C2×C4×C239C2×D412yes—
43C8×C239—42no—
44C22×C239C2×C22⋊C411yescharacteristic
45C2×D239—22no—
46C2×D239#10112yes—
47C4×C239—21no—
48C4×C239—22no—
49C4×C239—42no—
50Dic239—21no—
51Dic239—22no—
52Dic239—42no—
53C2×C239C2×#10111yescharacteristic
54C2×C239#42112yes—
55D239—22no—
56C239#153411yescharacteristic, complemented, Sylow
57#1534—2391nomaximal, Sylow
58C2×#125—2391no—
59#432—2392no—
60#330—2391no—
61#330—2392no—
62#330D23911yescharacteristic, complemented
63#125—4782no—
64#125—2392no—
65#125—2391no—
66#125C2×D23911yescharacteristic
67C2×C4⋊C4—4782no—
68C2×C4⋊C4—2392no—
69C2×C42—2391no—
70C4⋊C8—4782no—
71C22⋊C8—4782no—
72#97—2392no—
73#97C2×D23912yes—
74C22×C4—4782no—
75C22×C4—2392no—
76C22×C4—2391no—
77C2×C8—22no—
78C2×C8—4782no—
79C4⋊C4—22no—
80C4⋊C4—4782no—
81C4⋊C4—4782no—
82C4⋊C4—4782no—
83C4⋊C4—4782no—
84C4⋊C4—2392no—
85C4⋊C4C4×D23912yes—
86C42—2391no—
87C42—2392no—
88C42C22×D23911yescharacteristic
89C23—2391no—
90C2×C4—22no—
91C2×C4—9562no—
92C2×C4—9564no—
93C2×C4—4782no—
94C2×C4—4782no—
95C2×C4—2392no—
96C2×C4—2391no—
97C2×C4C2×C4×D23911yescharacteristic
98C2×C4D4×D23912yes—
99C8—42no—
100C8—9562no—
101C22—4782no—
102C22—2392no—
103C22C22⋊C4×D23911yescharacteristic
104C4—22no—
105C4—21no—
106C4—42no—
107C4—9562no—
108C4—4782no—
109C4—4781no—
110C2—4782no—
111C2#101×D23911yescharacteristic
112C2#2950478712yes—
subgroupG/H
centerC22C22⋊C4×D239
commutatorC2×C4×C239C22×C4
FrattiniC42C22×D239
Fitting#330×C239C2
socleC22×C239C2×C22⋊C4
prime radicalC22×D239C22⋊C4
cosocleC42×C239C23
hypercenter#330D239
hypocenterC239#1534
LCSG ▷ C2×C4×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
3. #29504514C2semidirect
4. #29504513C2semidirect
5. #330×C239C2semidirect
56. C239#1534semidirect
62. #330D239semidirect

Maximal subgroups

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

subgroupindex
#125×D2392
#295048272
#295045142
#295045132
#330×C2392
#1534239