Finite Group Databasebeta

← #11771272

Subgroups — #11771272

Order 1152.

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

normal subgroups only

This group has 232 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#10593731C211yesmaximal, characteristic
2#10590299C211yesmaximal, characteristic
3#10590260C211yesmaximal, characteristic
4C42×C3⋊D3C2211yescharacteristic
5#63779—21no—
6#63778C412yes—
7#63777—21no—
8C3×C4⋊(C3⋊C8)—21no—
9C3×#803—21no—
10#63572—21no—
11#63557C412yes—
12#63557C412yes—
13#63555—21no—
14#4835—61no—
15#4705—61no—
16C2×C4×C3⋊D3C2×C411yescharacteristic
17C2×C4×C3⋊D3C2×C411yescharacteristic
18C2×C4×C3⋊D3C2×C411yescharacteristic
19C2×#622—22no—
20C32×C42D411yescharacteristic
21C4×C3⋊Dic3D411yescharacteristic
22C4×C3⋊Dic3D411yescharacteristic
23C4×C3⋊Dic3Q811yescharacteristic
24C2×C3×C3⋊C8—22no—
25C2×C3×C3⋊C8—22no—
26#1308—91nomaximal, Sylow
27C42×D3—61no—
28C42×D3—61no—
29C3×C4⋊C8—61no—
30C3×#97—61no—
31(C2×D3)⋊C8—62no—
32(C2×D3)⋊C8—62no—
33#815—62no—
34Dic3⋊C8—62no—
35C4⋊(C3⋊C8)—21no—
36#803—21no—
37C22×C3⋊D3C4211yescharacteristic
38C2×C32×C4C22⋊C411yescharacteristic
39C2×C32×C4C22⋊C411yescharacteristic
40C2×C32×C4C4⋊C411yescharacteristic
41C2×C3⋊Dic3C22⋊C411yescharacteristic
42C2×C3⋊Dic3C4⋊C411yescharacteristic
43C2×C3⋊Dic3C4⋊C411yescharacteristic
44C4×C3⋊D3—41no—
45C4×C3⋊D3—41no—
46C4×C3⋊D3—41no—
47#622—42no—
48C3×C3⋊C8—42no—
49C3×C3⋊C8—42no—
50#432—91no—
51#432—91no—
52#432—91no—
53C2×C4×D3—61no—
54C2×C4×D3—61no—
55C2×C4×D3—61no—
56C2×C4×D3—61no—
57C2×C4×D3—61no—
58C2×C4×D3—61no—
59C2×C3×C8—62no—
60C2×C3×C8—62no—
61C3×C42—21no—
62C3×C42—21no—
63C4×Dic3—61no—
64C4×Dic3—61no—
65C4×Dic3—61no—
66C4×Dic3—61no—
67C4×Dic3—61no—
68C4×Dic3—61no—
69C2×C3⋊C8—22no—
70C2×C3⋊C8—22no—
71C22×C32#9511yescharacteristic
72C2×C3⋊D3—21no—
73C2×C3⋊D3—21no—
74C2×C3⋊D3—21no—
75C32×C4—21no—
76C32×C4—21no—
77C32×C4—21no—
78C3⋊Dic3—21no—
79C3⋊Dic3—21no—
80C3⋊Dic3—21no—
81C2×C42—91no—
82C4⋊C8—61no—
83C4⋊C8—181no—
84C4⋊C8—181no—
85C22⋊C8—92no—
86C22⋊C8—92no—
87C22⋊C8—92no—
88#97—61no—
89#97—181no—
90#97—181no—
91C22×D3—61no—
92C22×D3—61no—
93C2×C3×C4—21no—
94C2×C3×C4—21no—
95C2×C3×C4—21no—
96C2×C3×C4—21no—
97C2×C3×C4—21no—
98C2×C3×C4—21no—
99C2×Dic3—61no—
100C2×Dic3—61no—
101C2×Dic3—61no—
102C2×Dic3—61no—
103C2×Dic3—61no—
104C2×Dic3—61no—
105C4×D3—122no—
106C4×D3—121no—
107C4×D3—122no—
108C4×D3—121no—
109C4×D3—122no—
110C4×D3—122no—
111C4×D3—122no—
112C3×C8—122no—
113C3×C8—122no—
114C3⋊C8—42no—
115C3⋊C8—42no—
116C2×C32#34411yescharacteristic
117C2×C32#34411yescharacteristic
118C2×C32#34411yescharacteristic
119C3⋊D3—41no—
120C22×C4—91no—
121C22×C4—91no—
122C22×C4—91no—
123C2×C8—62no—
124C2×C8—62no—
125C2×C8—182no—
126C42—91no—
127C42—91no—
128C42—91no—
129C42GO+(4,𝔽2)11yescharacteristic
130C22×C3—21no—
131C22×C3—21no—
132C2×D3—62no—
133C2×D3—62no—
134C2×D3—121no—
135C2×D3—121no—
136C2×D3—121no—
137C2×D3—121no—
138C3×C4—21no—
139C3×C4—22no—
140C3×C4—21no—
141C3×C4—22no—
142C3×C4—41no—
143C3×C4—41no—
144C3×C4—41no—
145Dic3—62no—
146Dic3—121no—
147Dic3—121no—
148Dic3—121no—
149Dic3—121no—
150Dic3—121no—
151C32#130811yescharacteristic, complemented, Sylow
152C23—91no—
153C2×C4—91no—
154C2×C4—91no—
155C2×C4—91no—
156C2×C4—361no—
157C2×C4—361no—
158C2×C4—361no—
159C2×C4D32⋊C411yescharacteristic
160C2×C4D32⋊C411yescharacteristic
161C2×C4#377311yescharacteristic
162C8—122no—
163C8—122no—
164C8—362no—
165C2×C3—21no—
166C2×C3—21no—
167C2×C3—21no—
168C2×C3—21no—
169C2×C3—21no—
170C2×C3—21no—
171D3—122no—
172D3—122no—
173C22—181no—
174C22—181no—
175C22—181no—
176C22#6373711yescharacteristic
177C4—21no—
178C4—21no—
179C4—21no—
180C4—181no—
181C4—181no—
182C4—181no—
183C3—21no—
184C3—21no—
185C2—361no—
186C2#1059005411yescharacteristic
187C2#1059005511yescharacteristic
188C2#1059005611yescharacteristic
subgroupG/H
centerC22#63737
commutator, prime radicalC22×C3⋊D3C42
Frattini, hypercenterC42GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32#95
cosocleC42×C3⋊D3C22
hypocenterC32#1308
LCSG ▷ C22×C3⋊D3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
151. C32#1308semidirect

Maximal subgroups

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

subgroupindex
#105937312
#105902992
#105902602
#13089