Finite Group Databasebeta

← #11772606

Subgroups — #11772606

Order 1152.

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

normal subgroups only

This group has 442 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#10593827C211yesmaximal, characteristic
2#10591527C212yesmaximal
3C2×D4×C3⋊D3C2211yescharacteristic
4C2×C22⋊#157—22no—
5C2×C4⋊#157C411yescharacteristic, complemented
6C2×C4×#157C411yescharacteristic, complemented
7#63974—22no—
8C3×#834—22no—
9#63581C414yescomplemented
10D3×#99—62no—
11C23×C3⋊D3D412yes—
12C22×#157—21no—
13C22×#157—21no—
14C2×C32×D4D411yescharacteristic
15C2×#638C2×C412yes—
16D4×C3⋊D3—41no—
17D4×C3⋊D3—41no—
18C2×C4⋊(C3⋊D3)Q811yescharacteristic
19C2×C4×C3⋊D3C2×C411yescharacteristic
20C2×#624—42no—
21C22⋊#157—44no—
22C4⋊#157—41no—
23C4×#157—41no—
24C3×#217—24no—
25#3722—42no—
26#1393—91nomaximal, Sylow
27C2×D3×D4—62no—
28D3×C22⋊C4—64no—
29C3×#99—62no—
30#834—22no—
31#806—64no—
32C23×C32C22⋊C412yes—
33C22×C3⋊D3—22no—
34C22×C3⋊D3—22no—
35C22×C3⋊D3—42no—
36C22×C3⋊D3—42no—
37C22×C3⋊D3C22⋊C411yescharacteristic
38C22×C3⋊D3C4⋊C412yes—
39C2×#157—22no—
40C2×#157—41no—
41C2×#157—41no—
42C2×#157—42no—
43C2×#157—41no—
44C32×D4—41no—
45C2×C32×C4C4⋊C411yescharacteristic
46#638—42no—
47C2×C3⋊Dic3C4211yescharacteristic
48C4⋊(C3⋊D3)—41no—
49C4×C3⋊D3—21no—
50C4×C3⋊D3—21no—
51C2×C3×Dic3—44no—
52#624—82no—
53#624—82no—
54C2×#99—92no—
55#390—91no—
56C23×D3—62no—
57C23×D3—62no—
58C2×C3×D4—22no—
59C2×#67—62no—
60C2×#67—62no—
61D3×D4—124no—
62D3×D4—124no—
63C2×D12—62no—
64C2×C4×D3—62no—
65C2×C4×D3—124no—
66C3×C22⋊C4—64no—
67#217—24no—
68(C2×D3)⋊C4—124no—
69C22×C32—22no—
70C22×C32—42no—
71C22×C32#9511yescharacteristic
72C2×C3⋊D3—22no—
73C2×C3⋊D3—21no—
74C2×C3⋊D3—21no—
75C2×C3⋊D3—42no—
76C2×C3⋊D3—42no—
77C2×C3⋊D3—42no—
78C2×C3⋊D3—82no—
79C2×C3⋊D3#9911yescharacteristic
80C2×C3⋊D3#9911yescharacteristic
81#157—42no—
82#157—81no—
83C32×C4—21no—
84C3⋊Dic3—21no—
85C3×Dic3—84no—
86C22×D4—91no—
87C2×C4⋊C4—91no—
88C2×C22⋊C4—182no—
89C2×C22⋊C4—182no—
90C2×C42—91no—
91#99—62no—
92#99—94no—
93C23×C3—22no—
94C23×C3—22no—
95C22×D3—62no—
96C22×D3—62no—
97C22×D3—62no—
98C22×D3—64no—
99C22×D3—64no—
100C22×D3—122no—
101C22×D3—122no—
102C22×D3—242no—
103C22×D3—242no—
104C22×D3—242no—
105C22×D3—242no—
106C3×D4—44no—
107C2×C3×C4—22no—
108C2×C3×C4—124no—
109#67—124no—
110#67—124no—
111C2×Dic3—44no—
112C2×Dic3—62no—
113D12—124no—
114C4×D3—122no—
115C4×D3—122no—
116C4×D3—244no—
117C4×D3—244no—
118C2×C32—21no—
119C2×C32—42no—
120C2×C32#34211yescharacteristic
121C3⋊D3—21no—
122C3⋊D3—42no—
123C3⋊D3#35311yescharacteristic
124C3⋊D3#35411yescharacteristic
125C24—92no—
126C2×D4—92no—
127C2×D4—91no—
128C2×D4—361no—
129C2×D4—361no—
130C2×D4GO+(4,𝔽2)11yescharacteristic
131C22×C4—91no—
132C22×C4—181no—
133C22×C4—181no—
134C22×C4—362no—
135C4⋊C4—361no—
136C22⋊C4—64no—
137C22⋊C4—362no—
138C22⋊C4—364no—
139C42—361no—
140C22×C3—24no—
141C22×C3—22no—
142C22×C3—42no—
143C22×C3—82no—
144C22×C3—82no—
145C2×D3—62no—
146C2×D3—62no—
147C2×D3—64no—
148C2×D3—122no—
149C2×D3—122no—
150C2×D3—122no—
151C2×D3—124no—
152C2×D3—124no—
153C2×D3—242no—
154C2×D3—242no—
155C2×D3—242no—
156C2×D3—242no—
157C2×D3—244no—
158C2×D3—244no—
159C3×C4—42no—
160C3×C4—244no—
161Dic3—84no—
162Dic3—122no—
163C32#139311yescharacteristic, complemented, Sylow
164C23—91no—
165C23—92no—
166C23—182no—
167C23—182no—
168C23—362no—
169C23—362no—
170C23D32⋊C412yes—
171D4—41no—
172D4—361no—
173D4—362no—
174C2×C4—91no—
175C2×C4—124no—
176C2×C4—181no—
177C2×C4—181no—
178C2×C4—182no—
179C2×C4—361no—
180C2×C4—361no—
181C2×C4—361no—
182C2×C4—362no—
183C2×C4—722no—
184C2×C4—722no—
185C2×C4#377311yescharacteristic
186C2×C3—22no—
187C2×C3—42no—
188C2×C3—44no—
189C2×C3—82no—
190D3—62no—
191D3—62no—
192D3—122no—
193D3—124no—
194D3—242no—
195C22—22no—
196C22—42no—
197C22—91no—
198C22—91no—
199C22—181no—
200C22—181no—
201C22—182no—
202C22—362no—
203C22—362no—
204C22—362no—
205C22—722no—
206C22#6373711yescharacteristic
207C4—21no—
208C4—181no—
209C4—244no—
210C4—362no—
211C4—721no—
212C3—22no—
213C2—21no—
214C2—42no—
215C2—91no—
216C2—91no—
217C2—181no—
218C2—362no—
219C2#1059007711yescharacteristic
subgroupG/H
centerC2#10590077
commutatorC2×C3⋊Dic3C42
Frattini, hypercenterC2×D4GO+(4,𝔽2)
FittingC2×C32×D4D4
socleC2×C32#342
prime radical, cosocleC2×D4×C3⋊D3C22
hypocenterC32#1393
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
5. C2×C4⋊#157C4semidirect
6. C2×C4×#157C4semidirect
9. #63581C4semidirect
163. C32#1393semidirect

Maximal subgroups

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

subgroupindex
#105938272
#105915272
#13939