Finite Group Databasebeta

← #11771970

Subgroups — #11771970

Order 1152.

420 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 105 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
1C32×#395C211yesmaximal, characteristic
2#10589396C211yesmaximal, characteristic
3#10589394C211yesmaximal, characteristic
4#67648—34nomaximal
5C22×C32×Q8C411yescharacteristic
6C2×C32×C4⋊C4—21no—
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×#3748—21no—
9C32×#95—21no—
10C32×#95C411yescharacteristic
11#63657—21no—
12C3×#395D314yes—
13#4530—34no—
14#4528—34no—
15C2×C32×Q8—42no—
16C2×C32×Q8—41no—
17C22×C32×C4—21no—
18C22×C32×C4—21no—
19C22×C32×C4C2×C411yescharacteristic
20C22×C32×C4D411yescharacteristic
21C22×C32×C4D411yescharacteristic
22C32×C4⋊C4—41no—
23C32×C4⋊C4—42no—
24#3748—22no—
25#3748—41no—
26C2×C3⋊(C3⋊C8)—41no—
27C2×C3⋊(C3⋊C8)—41no—
28#1354—91noSylow
29C22×C3×Q8Dic314yes—
30C2×C3×C4⋊C4—24no—
31C2×C3×C4⋊C4C2×D314yes—
32C2×#208—64no—
33C3×#95—24no—
34C3×#95Dic314yes—
35#830—64no—
36C23×C32C22⋊C411yescharacteristic
37C32×Q8—42no—
38C32×Q8—42no—
39C2×C32×C4—21no—
40C2×C32×C4—21no—
41C2×C32×C4—22no—
42C2×C32×C4—22no—
43C2×C32×C4—21no—
44C2×C32×C4—21no—
45C2×C32×C4—41no—
46C2×C32×C4—41no—
47C2×C32×C4—41no—
48C2×C32×C4—41no—
49C2×C32×C4—41no—
50C2×C32×C4—41no—
51C2×C32×C4SD1611yescharacteristic
52C2×C32×C4Q1611yescharacteristic
53C3⋊(C3⋊C8)—42no—
54C3⋊(C3⋊C8)—81no—
55#395C3⋊D311yescharacteristic
56#343—91no—
57#324—91no—
58C2×C3×Q8—48no—
59C2×C3×Q8—44no—
60C22×C3×C4—24no—
61C22×C3×C4—24no—
62C22×C3×C4C2×Dic314yes—
63C22×C3×C4#6714yes—
64C22×C3×C4#6714yes—
65C3×C4⋊C4—44no—
66C3×C4⋊C4—48no—
67#208—68no—
68#208—124no—
69C2×C3⋊C8—124no—
70C2×C3⋊C8—124no—
71C22×C32—21no—
72C22×C32—21no—
73C22×C32#9911yescharacteristic
74C22×C32#10311yescharacteristic
75C22×C32#10411yescharacteristic
76C32×C4—21no—
77C32×C4—21no—
78C32×C4—42no—
79C32×C4—41no—
80C32×C4—42no—
81C32×C4—41no—
82C22×Q8C3⋊Dic311yescharacteristic
83C2×M16—181no—
84C2×C4⋊C4—21no—
85C2×C4⋊C4C2×C3⋊D311yescharacteristic
86C22⋊C8—181no—
87#95—21no—
88#95C3⋊Dic311yescharacteristic
89C23×C3#21714yes—
90C3×Q8—48no—
91C3×Q8—48no—
92C2×C3×C4—24no—
93C2×C3×C4—24no—
94C2×C3×C4—28no—
95C2×C3×C4—28no—
96C2×C3×C4—24no—
97C2×C3×C4—24no—
98C2×C3×C4—44no—
99C2×C3×C4—44no—
100C2×C3×C4—44no—
101C2×C3×C4—44no—
102C2×C3×C4—44no—
103C2×C3×C4—44no—
104C2×C3×C4#21514yes—
105C2×C3×C4#21614yes—
106C3⋊C8—128no—
107C3⋊C8—244no—
108C2×C32—21no—
109C2×C32—21no—
110C2×C32#32811yescharacteristic
111C2×C32AΣL(1,𝔽16)11yescharacteristic
112C2×C32#35611yescharacteristic
113C2×Q8—42no—
114C2×Q8—41no—
115C22×C4—21no—
116C22×C4—21no—
117C22×C4C2×C3⋊Dic311yescharacteristic
118C22×C4#63811yescharacteristic
119C22×C4#63811yescharacteristic
120M16—182no—
121M16—361no—
122C2×C8—361no—
123C2×C8—361no—
124C4⋊C4—41no—
125C4⋊C4—42no—
126C22×C3—24no—
127C22×C3—24no—
128C22×C3#83414yes—
129C22×C3#83514yes—
130C22×C3#83714yes—
131C3×C4—24no—
132C3×C4—24no—
133C3×C4—48no—
134C3×C4—44no—
135C3×C4—48no—
136C3×C4—44no—
137C32#135411yescharacteristic, complemented, Sylow
138C23#375711yescharacteristic
139Q8—42no—
140Q8—42no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4#375511yescharacteristic
154C2×C4#375611yescharacteristic
155C8—362no—
156C8—721no—
157C2×C3—24no—
158C2×C3—24no—
159C2×C3#453614yes—
160C2×C3#453814yes—
161C2×C3#454814yes—
162C22—21no—
163C22—21no—
164C22#6366111yescharacteristic
165C22#6366211yescharacteristic
166C22#6366411yescharacteristic
167C4—21no—
168C4—21no—
169C4—42no—
170C4—41no—
171C4—42no—
172C4—41no—
173C3#6764814yescomplemented
174C2—21no—
175C2—21no—
176C2#1058940211yescharacteristic
177C2#1058940411yescharacteristic
178C2#1058941411yescharacteristic
subgroupG/H
centerC22#63661
commutatorC22×C32×C4C2×C4
FrattiniC2×C4⋊C4C2×C3⋊D3
FittingC32×#395C2
socleC22×C32#99
prime radicalC23×C32C22⋊C4
cosocleC2×C32×C4⋊C4C22
hypercenter#395C3⋊D3
hypocenterC32#1354
LCSG ▷ C22×C32×C4 ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #395

Complements

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

NH ≅ G/Ntype
137. C32#1354semidirect
173. C3#67648semidirect

Maximal subgroups

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

subgroupindex
C32×#3952
#105893962
#105893942
#676483