Finite Group Databasebeta

← #11796748

Subgroups — #11796748

Order 1152.

406 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C2×#63802C211yesmaximal, characteristic
2C2×#63765C211yesmaximal, characteristic
3#10590712C211yesmaximal, characteristic
4#10590062C214yesmaximal, complemented
5C2×#3797—21no—
6C2×C8×C3⋊D3C2211yescharacteristic
7C2×C3×Dic12—21no—
8#63849—21no—
9C2×#3718C2212yes—
10#63802—22no—
11#63802C414yescomplemented
12C2×#3708C2212yes—
13#63765—22no—
14C3×#817—21no—
15#63576C2212yes—
16C2×D3×Q16—61no—
17#4860—61no—
18C2×C4×C3⋊D3D411yescharacteristic
19C2×C3×Dic6—22no—
20C2×#627—41no—
21C2×#624—41no—
22#3797—24no—
23#3797—42no—
24C2×C32×C8D411yescharacteristic
25C2×C3⋊(C3⋊C8)C2311yescharacteristic
26C8×C3⋊D3C2×C412yes—
27C8×C3⋊D3D412yes—
28C3×C4⋊Dic3—22no—
29C3×Dic12—24no—
30#3722—41no—
31Dic32—41no—
32#3718—22no—
33#3718C2×C414yes—
34#3708—22no—
35#2141—91nomaximal, Sylow
36C2×D3×Q8—62no—
37C2×C3×Q16—61no—
38C2×#216—62no—
39D3×Q16—64no—
40D3×Q16—64no—
41C2×Dic12—21no—
42C2×D3×C8—61no—
43C2×D3×C8—61no—
44#892—62no—
45C3×#106—61no—
46#817—21no—
47#807—62no—
48C22×C3⋊D3D811yescharacteristic
49C2×C32×C4C2×D411yescharacteristic
50C2×C3⋊Dic3D811yescharacteristic
51C4×C3⋊D3C22⋊C412yes—
52C4×C3⋊D3SD1612yes—
53C2×C3×Dic3—42no—
54C2×C3×Dic3—42no—
55C3×Dic6—24no—
56C3×Dic6—42no—
57#627—44no—
58#624—44no—
59C32×C8C22⋊C412yes—
60C3⋊(C3⋊C8)C22×C411yescharacteristic
61C3⋊(C3⋊C8)C2×D411yescharacteristic
62C22×Q16—91no—
63C2×M32—91no—
64#427—91no—
65#358—94no—
66C2×C3×Q8—62no—
67D3×Q8—68no—
68D3×Q8—124no—
69C2×C4×D3—61no—
70C2×C4×D3—61no—
71C2×C4×D3—122no—
72C2×Dic6—22no—
73C2×Dic6—122no—
74C3×Q16—64no—
75C2×C3×C8—21no—
76C2×C3×C8—21no—
77C3×C4⋊C4—62no—
78#216—64no—
79#216—64no—
80(C2×D3)⋊C4—122no—
81C4⋊Dic3—22no—
82C4×Dic3—122no—
83C2×C3⋊C8—61no—
84C2×C3⋊C8—61no—
85Dic12—24no—
86D3×C8—62no—
87D3×C8—62no—
88D3×C8—62no—
89D3×C8—62no—
90C22×C32C2×D811yescharacteristic
91C2×C3⋊D3—22no—
92C2×C3⋊D3#10212yes—
93C32×C4C2×C22⋊C411yescharacteristic
94C32×C4C2×SD1611yescharacteristic
95C3⋊Dic3#10212yes—
96C3×Dic3—44no—
97C3×Dic3—82no—
98C22×Q8—181no—
99C2×Q16—61no—
100C2×Q16—94no—
101C2×Q16—92no—
102C2×Q16—182no—
103C22×C8—91no—
104#117—181no—
105M32—182no—
106C2×C16—92no—
107#107—92no—
108#106—61no—
109C22×D3—61no—
110C22×D3—61no—
111C3×Q8—64no—
112C3×Q8—122no—
113C2×C3×C4—21no—
114C2×C3×C4—21no—
115C2×C3×C4—122no—
116C2×C3×C4—122no—
117C2×Dic3—42no—
118C2×Dic3—42no—
119C2×Dic3—61no—
120C2×Dic3—61no—
121C4×D3—62no—
122C4×D3—62no—
123C4×D3—62no—
124C4×D3—62no—
125C4×D3—128no—
126Dic6—24no—
127Dic6—42no—
128Dic6—128no—
129C3×C8—22no—
130C3×C8—22no—
131C3⋊C8—61no—
132C3⋊C8—61no—
133C3⋊C8—61no—
134C3⋊C8—61no—
135C2×C32C2×#10211yescharacteristic
136C2×C32#51012yes—
137C3⋊D3—22no—
138C2×Q8—62no—
139C2×Q8—184no—
140C2×Q8—361no—
141C2×Q8—362no—
142C22×C4—91no—
143C22×C4—361no—
144Q16—64no—
145Q16—94no—
146Q16—182no—
147C2×C8—91no—
148C2×C8—92no—
149C2×C8—92no—
150C2×C8GO+(4,𝔽2)11yescharacteristic
151C4⋊C4—62no—
152C22⋊C4—361no—
153C42—361no—
154C16—182no—
155C22×C3—21no—
156C22×C3—21no—
157C2×D3—62no—
158C2×D3—62no—
159C2×D3—64no—
160C2×D3—122no—
161C3×C4—21no—
162C3×C4—21no—
163C3×C4—21no—
164C3×C4—21no—
165C3×C4—124no—
166C3×C4—242no—
167Dic3—44no—
168Dic3—62no—
169Dic3—62no—
170Dic3—82no—
171C32#214111yescharacteristic, complemented, Sylow
172C23—91no—
173Q8—64no—
174Q8—122no—
175Q8—364no—
176C2×C4—91no—
177C2×C4—92no—
178C2×C4—92no—
179C2×C4—122no—
180C2×C4—122no—
181C2×C4—364no—
182C2×C4C2×GO+(4,𝔽2)11yescharacteristic
183C8—91no—
184C8—91no—
185C8D32⋊C412yes—
186C2×C3—21no—
187C2×C3—21no—
188C2×C3—22no—
189C2×C3—22no—
190D3—64no—
191D3—122no—
192C22—92no—
193C22—182no—
194C22#6422511yescharacteristic
195C4—92no—
196C4—124no—
197C4—242no—
198C4#6422711yescharacteristic
199C4C2×D32⋊C411yescharacteristic
200C3—21no—
201C3—21no—
202C2—182no—
203C2#1059327912yes—
204C2#1059336511yescharacteristic
subgroupG/H
centerC22#64225
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32C2×D8
prime radicalC22×C3⋊D3D8
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2141
LCSG ▷ C3⋊(C3⋊C8) ▷ 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
4. #10590062C2semidirect
11. #63802C4semidirect
171. C32#2141semidirect

Maximal subgroups

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

subgroupindex
C2×#638022
C2×#637652
#105907122
#105900622
#21419