Finite Group Databasebeta

← #11797037

Subgroups — #11797037

Order 1152.

254 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 69 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#10593765C211yesmaximal, characteristic
2#10590625C211yesmaximal, characteristic
3C2×#63542C211yesmaximal, characteristic
4#10590022C214yesmaximal, complemented
5#64286C411yescharacteristic
6#64283C411yescharacteristic
7C2×C8×C3⋊D3C2211yescharacteristic
8#63767C412yes—
9C8×#157C2212yes—
10C3×#812—21no—
11C2×C3×C3⋊C16—21no—
12#63544—21no—
13#63542—21no—
14#63542C2212yes—
15#63542C2212yes—
16D3×M32—61no—
17C2×D3×C16—61no—
18C2×C4×C3⋊D3C2×C411yescharacteristic
19C22⋊#157C812yes—
20#3792—21no—
21C4⋊#157C812yes—
22C4×#157C2×C412yes—
23#3788—21no—
24#3787C2×C412yes—
25C2×C32×C8D411yescharacteristic
26C2×C3⋊(C3⋊C8)Q811yescharacteristic
27C8×C3⋊D3C2×C411yescharacteristic
28C8×C3⋊D3D411yescharacteristic
29C8×C3⋊D3Q811yescharacteristic
30C8×C3⋊D3C2311yescharacteristic
31C3×C3⋊C16—22no—
32C3×C3⋊C16—22no—
33#2151—91nomaximal, Sylow
34C2×D3×C8—61no—
35C2×D3×C8—61no—
36C3×M32—61no—
37C2×C3×C16—61no—
38#812—21no—
39C2×C3⋊C16—21no—
40#798—62no—
41D3×C16—62no—
42D3×C16—62no—
43D3×C16—62no—
44C22×C3⋊D3C2×C811yescharacteristic
45C2×#157C2×C814yes—
46C2×C32×C4C4⋊C411yescharacteristic
47C2×C3⋊Dic3M1611yescharacteristic
48C4×C3⋊D3C4⋊C411yescharacteristic
49C4×C3⋊D3C2×C811yescharacteristic
50C4×C3⋊D3M1611yescharacteristic
51C4×C3⋊D3C22×C411yescharacteristic
52#622—22no—
53C32×C8C4⋊C411yescharacteristic
54C32×C8C2×D411yescharacteristic
55C3⋊(C3⋊C8)C4⋊C411yescharacteristic
56C3⋊(C3⋊C8)C2×Q811yescharacteristic
57C2×M32—91no—
58C22×C16—91no—
59#405—91no—
60C4⋊C16—94no—
61C2×C4×D3—61no—
62C2×C4×D3—61no—
63C2×C3×C8—21no—
64C2×C3×C8—21no—
65C2×C3⋊C8—61no—
66C2×C3⋊C8—61no—
67D3×C8—61no—
68D3×C8—61no—
69D3×C8—61no—
70D3×C8—61no—
71D3×C8—61no—
72D3×C8—61no—
73D3×C8—61no—
74D3×C8—61no—
75C3×C16—62no—
76C3×C16—62no—
77C3⋊C16—22no—
78C3⋊C16—22no—
79C22×C32C4⋊C811yescharacteristic
80C2×C3⋊D3—22no—
81C2×C3⋊D3C4⋊C811yescharacteristic
82C2×C3⋊D3C22×C811yescharacteristic
83#157—24no—
84C32×C4C4⋊C811yescharacteristic
85C32×C4C2×C4⋊C411yescharacteristic
86C3⋊Dic3C4⋊C811yescharacteristic
87C3⋊Dic3C2×M1611yescharacteristic
88C2×M16—91no—
89C22×C8—91no—
90#117—91no—
91M32—61no—
92M32—181no—
93C2×C16—61no—
94C2×C16—92no—
95C2×C16—92no—
96C2×C16—181no—
97#97—92no—
98C4×C8—92no—
99C22×D3—61no—
100C22×D3—61no—
101C2×C3×C4—21no—
102C2×C3×C4—21no—
103C2×Dic3—61no—
104C2×Dic3—61no—
105C4×D3—61no—
106C4×D3—61no—
107C4×D3—61no—
108C4×D3—61no—
109C4×D3—61no—
110C4×D3—61no—
111C4×D3—61no—
112C4×D3—61no—
113C3×C8—21no—
114C3×C8—21no—
115C3×C8—21no—
116C3×C8—21no—
117C3⋊C8—61no—
118C3⋊C8—61no—
119C3⋊C8—61no—
120C3⋊C8—61no—
121C2×C32—21no—
122C2×C32C2×C4⋊C811yescharacteristic
123C3⋊D3—21no—
124C3⋊D3#50412yes—
125C22×C4—91no—
126M16—181no—
127M16—181no—
128C2×C8—91no—
129C2×C8—91no—
130C2×C8—91no—
131C2×C8—91no—
132C2×C8—91no—
133C2×C8—92no—
134C2×C8GO+(4,𝔽2)11yescharacteristic
135C4⋊C4—92no—
136C22⋊C4—92no—
137C42—92no—
138C16—62no—
139C16—62no—
140C22×C3—21no—
141C22×C3—21no—
142C2×D3—61no—
143C2×D3—61no—
144C2×D3—61no—
145C2×D3—61no—
146C2×D3—64no—
147C2×D3—122no—
148C3×C4—21no—
149C3×C4—21no—
150C3×C4—21no—
151C3×C4—21no—
152Dic3—61no—
153Dic3—61no—
154Dic3—61no—
155Dic3—61no—
156C32#215111yescharacteristic, complemented, Sylow
157C23—91no—
158C2×C4—91no—
159C2×C4—91no—
160C2×C4—91no—
161C2×C4—91no—
162C2×C4—91no—
163C2×C4—94no—
164C2×C4#377311yescharacteristic
165C8—91no—
166C8—91no—
167C8—182no—
168C8#377311yescharacteristic
169C8C2×GO+(4,𝔽2)11yescharacteristic
170C2×C3—22no—
171C2×C3—21no—
172C2×C3—21no—
173C2×C3—41no—
174D3—62no—
175D3—62no—
176D3—62no—
177D3—121no—
178C22—91no—
179C22—91no—
180C22—182no—
181C22#6373211yescharacteristic
182C4—91no—
183C4—91no—
184C4—184no—
185C4#6373211yescharacteristic
186C4C2×#377311yescharacteristic
187C3—21no—
188C3—21no—
189C2—21no—
190C2—92no—
191C2—181no—
192C2C2×#6373211yescharacteristic
subgroupG/H
center, FrattiniC8C2×GO+(4,𝔽2)
commutatorC2×C3⋊D3C22×C8
FittingC2×C32×C8D4
socleC2×C32C2×C4⋊C8
prime radicalC22×C3⋊D3C2×C8
cosocleC8×C3⋊D3C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2151
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C8 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
4. #10590022C2semidirect
156. C32#2151semidirect

Maximal subgroups

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

subgroupindex
#105937652
#105906252
C2×#635422
#105900222
#21519