Finite Group Databasebeta

← #2275⋊C9 #11919401

Subgroups — #2275⋊C9 #11919401

Order 1152.

309 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 309 conjugacy classes of subgroups — too many to draw. Only its 39 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#376⋊C9C211yesmaximal, characteristic, complemented
2C2×#95⋊C9C212yesmaximal, complemented
3C3×#2275C311yesmaximal, characteristic
4D4×C22⋊C9—41nomaximal
5#95⋊C9C2211yescharacteristic
6C2×C3×C4×D4—31no—
7C3×C4×C4⋊C4—31no—
8C3×C4×C22⋊C4—32no—
9C3×#376C2×C311yescharacteristic
10C2×C3×#95C2×C312yes—
11C22×C22⋊C9—42no—
12C4×C22⋊C9—41no—
13#2275C911yescharacteristic, complemented, Sylow
14C22×C3×D4A411yescharacteristic
15C23×C3×C4—32no—
16C3×C4×D4—32no—
17C3×C4×D4—32no—
18C3×C4×D4—34no—
19C2×C3×C4⋊C4—31no—
20C2×C3×C22⋊C4—32no—
21C2×C3×C42—31no—
22C2×C3×C42—32no—
23C3×#95—32no—
24C3×#95—31no—
25C3×#95C22×C311yescharacteristic
26C2×C22⋊C9—41no—
27C2×C22⋊C9—82no—
28D4×C9—161no—
29C2×C4×D4—31no—
30C4×C4⋊C4—31no—
31C4×C22⋊C4—32no—
32#376C2×C911yescharacteristic, complemented
33C2×#95C2×C912yescomplemented
34C24×C3C2×A412yes—
35C2×C3×D4—31no—
36C2×C3×D4—31no—
37C2×C3×D4—32no—
38C22×C3×C4—31no—
39C22×C3×C4—31no—
40C22×C3×C4—32no—
41C22×C3×C4—34no—
42C22×C3×C4—34no—
43C22×C3×C4—124no—
44C22×C3×C4C2×A411yescharacteristic
45C3×C4⋊C4—32no—
46C3×C4⋊C4—32no—
47C3×C22⋊C4—34no—
48C3×C22⋊C4—34no—
49C3×C42—32no—
50C3×C42—32no—
51C3×C42—122no—
52C22×C9—162no—
53C22⋊C9—41no—
54C4×C9—161no—
55C22×D4C22⋊C911yescharacteristic
56C23×C4—32no—
57C4×D4—32no—
58C4×D4—32no—
59C4×D4—34no—
60C2×C4⋊C4—31no—
61C2×C22⋊C4—32no—
62C2×C42—31no—
63C2×C42—32no—
64#95—32no—
65#95—31no—
66#95C22×C911yescharacteristic
67C23×C3—22no—
68C23×C3—32no—
69C23×C3—32no—
70C23×C3—62no—
71C23×C3C22×A411yescharacteristic
72C3×D4—32no—
73C3×D4—32no—
74C3×D4—31no—
75C3×D4C42⋊C311yescharacteristic
76C2×C3×C4—31no—
77C2×C3×C4—31no—
78C2×C3×C4—32no—
79C2×C3×C4—32no—
80C2×C3×C4—34no—
81C2×C3×C4—61no—
82C2×C3×C4—64no—
83C2×C3×C4—62no—
84C2×C3×C4—61no—
85C2×C3×C4—124no—
86C2×C3×C4—124no—
87C2×C9—161no—
88C2×C9—322no—
89C24C2×C22⋊C912yes—
90C2×D4—31no—
91C2×D4—31no—
92C2×D4—32no—
93C22×C4—31no—
94C22×C4—31no—
95C22×C4—32no—
96C22×C4—34no—
97C22×C4—34no—
98C22×C4—124no—
99C22×C4C2×C22⋊C911yescharacteristic
100C4⋊C4—32no—
101C4⋊C4—32no—
102C22⋊C4—34no—
103C22⋊C4—34no—
104C42—32no—
105C42—32no—
106C42—122no—
107C22×C3—31no—
108C22×C3—31no—
109C22×C3—32no—
110C22×C3—62no—
111C22×C3—62no—
112C22×C3—62no—
113C22×C3—62no—
114C22×C3C2×C42⋊C312yes—
115C22×C32−1+4⋊C311yescharacteristic
116C3×C4—31no—
117C3×C4—62no—
118C3×C4—64no—
119C3×C4—62no—
120C3×C4C2×C42⋊C311yescharacteristic
121C9—161noSylow
122C23—22no—
123C23—32no—
124C23—32no—
125C23—62no—
126C23C22×C22⋊C911yescharacteristic
127D4—32no—
128D4—32no—
129D4—31no—
130D4C42⋊C911yescharacteristic
131C2×C4—31no—
132C2×C4—31no—
133C2×C4—32no—
134C2×C4—32no—
135C2×C4—34no—
136C2×C4—61no—
137C2×C4—64no—
138C2×C4—62no—
139C2×C4—61no—
140C2×C4—124no—
141C2×C4—124no—
142C2×C3—22no—
143C2×C3—31no—
144C2×C3—31no—
145C2×C3—62no—
146C2×C3C22×C42⋊C311yescharacteristic
147C22—31no—
148C22—31no—
149C22—32no—
150C22—62no—
151C22—62no—
152C22—62no—
153C22—62no—
154C22C2×C42⋊C912yes—
155C222−1+4⋊C911yescharacteristic
156C4—31no—
157C4—62no—
158C4—64no—
159C4—62no—
160C4C2×C42⋊C911yescharacteristic
161C3#2275⋊C311yescharacteristic
162C2—22no—
163C2—31no—
164C2—31no—
165C2—62no—
166C2C22×C42⋊C911yescharacteristic
subgroupG/H
centerC2×C3C22×C42⋊C3
commutator, hypocenter#95C22×C9
Frattini, socleC23×C3C22×A4
FittingC3×#2275C3
prime radicalC22×C3×D4A4
cosocleC3×#95C22×C3
hypercenterC3×D4C42⋊C3
LCSG ▷ #95
UCSC1 ◁ C2×C3 ◁ C3×D4

Complements

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

NH ≅ G/Ntype
1. #376⋊C9C2semidirect
2. C2×#95⋊C9C2semidirect
13. #2275C9semidirect
32. #376C2×C9semidirect
33. C2×#95C2×C9semidirect

Maximal subgroups

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

subgroupindex
#376⋊C92
C2×#95⋊C92
C3×#22753
D4×C22⋊C94