Finite Group Databasebeta

← #11772088

Subgroups — #11772088

Order 1152.

184 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 35 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#10590905C211yesmaximal, characteristic
2#10590171C211yesmaximal, characteristic
3#10589133C211yesmaximal, characteristic
4C2×C3×Dic12—21no—
5#63873—21no—
6C2×#3718C412yes—
7C4⋊#622—21no—
8C8×C3⋊Dic3C2211yescharacteristic
9C2×C3×C3⋊C16—21no—
10#5183—61no—
11Dic3⋊C16—61no—
12C2×C3×Dic6—22no—
13C2×#622—41no—
14C2×C32×C8D411yescharacteristic
15C4×C3⋊Dic3D411yescharacteristic
16C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
17C3×Dic12—41no—
18C3×Dic12—41no—
19#3724—41no—
20#3724—41no—
21#3718—42no—
22C3×C3⋊C16—41no—
23#1362—91nomaximal, Sylow
24C2×C3×Q16—61no—
25#944—62no—
26C2×#216—62no—
27C2×Dic12—21no—
28C2×C3×C16—61no—
29C8×Dic3—61no—
30C8×Dic3—61no—
31C2×C3⋊C16—21no—
32C2×C32×C4C22⋊C411yescharacteristic
33C2×C3⋊Dic3D811yescharacteristic
34C2×C3⋊Dic3SD1611yescharacteristic
35C2×C3×Dic3—42no—
36C3×Dic6—42no—
37C3×Dic6—42no—
38#622—81no—
39C32×C8D811yescharacteristic
40C32×C8SD1611yescharacteristic
41C3⋊(C3⋊C8)—21no—
42#494—91no—
43C4⋊C16—91no—
44#335—91no—
45C2×C3×Q8—62no—
46C2×Dic6—22no—
47C3×Q16—121no—
48C3×Q16—121no—
49C2×C3×C8—21no—
50C2×C3×C8—21no—
51#216—124no—
52Dic3⋊C4—122no—
53Dic3⋊C4—122no—
54C4×Dic3—61no—
55C4×Dic3—61no—
56C2×C3⋊C8—61no—
57C2×C3⋊C8—61no—
58Dic12—41no—
59Dic12—41no—
60C3×C16—121no—
61C3⋊C16—41no—
62C22×C32#10211yescharacteristic
63C32×C4#10011yescharacteristic
64C32×C4#10211yescharacteristic
65C3⋊Dic3—21no—
66C3⋊Dic3SD3211yescharacteristic
67C3⋊Dic3Q3211yescharacteristic
68C3×Dic3—82no—
69C2×Q16—61no—
70C2×Q16—92no—
71C4⋊Q8—181no—
72C2×C16—61no—
73C4⋊C8—181no—
74C4×C8—91no—
75C3×Q8—122no—
76C3×Q8—122no—
77C2×C3×C4—21no—
78C2×C3×C4—21no—
79C2×C3×C4—122no—
80C2×Dic3—42no—
81C2×Dic3—61no—
82C2×Dic3—61no—
83C2×Dic3—61no—
84C2×Dic3—61no—
85Dic6—42no—
86Dic6—42no—
87C3×C8—21no—
88C3×C8—21no—
89C3×C8—21no—
90C3×C8—21no—
91C3⋊C8—62no—
92C3⋊C8—121no—
93C2×C32#33111yescharacteristic
94C2×C32#35811yescharacteristic
95C2×C32#36211yescharacteristic
96C2×Q8—62no—
97Q16—121no—
98Q16—121no—
99Q16—362no—
100C2×C8—91no—
101C2×C8—361no—
102C2×C8GO+(4,𝔽2)11yescharacteristic
103C4⋊C4—361no—
104C4⋊C4—361no—
105C42—91no—
106C16—121no—
107C22×C3—21no—
108C22×C3—21no—
109C3×C4—21no—
110C3×C4—21no—
111C3×C4—21no—
112C3×C4—21no—
113C3×C4—242no—
114Dic3—61no—
115Dic3—61no—
116Dic3—61no—
117Dic3—61no—
118Dic3—62no—
119Dic3—82no—
120Dic3—121no—
121C32#136211yescharacteristic, complemented, Sylow
122Q8—122no—
123Q8—122no—
124C2×C4—91no—
125C2×C4—91no—
126C2×C4—122no—
127C2×C4D32⋊C411yescharacteristic
128C8—181no—
129C8—721no—
130C8#377411yescharacteristic
131C8#377511yescharacteristic
132C2×C3—21no—
133C2×C3—21no—
134C2×C3—21no—
135C2×C3—21no—
136C2×C3—21no—
137C2×C3—21no—
138C22#6372911yescharacteristic
139C4—91no—
140C4—91no—
141C4—181no—
142C4—242no—
143C4#6372711yescharacteristic
144C4#6373911yescharacteristic
145C3—21no—
146C3—21no—
147C2#1059001711yescharacteristic
148C2#1059002111yescharacteristic
149C2#1059003711yescharacteristic
subgroupG/H
centerC22#63729
commutatorC2×C3⋊(C3⋊C8)C2×C4
Frattini, hypercenterC2×C8GO+(4,𝔽2)
FittingC2×C32×C8D4
socle, prime radicalC22×C32#102
cosocleC8×C3⋊Dic3C22
hypocenterC32#1362
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
121. C32#1362semidirect

Maximal subgroups

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

subgroupindex
#105909052
#105901712
#105891332
#13629