Finite Group Databasebeta

← #11772602

Subgroups — #11772602

Order 1152.

490 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 44 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×#63774C212yesmaximal
2#10592638C211yesmaximal, characteristic
3C22×C4⋊(C3⋊D3)C2211yescharacteristic
4C2×C22⋊#157—22no—
5C2×C32×C42C411yescharacteristic, complemented
6C2×#3752—22no—
7C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
8#63774—22no—
9#63774C414yescomplemented
10#4939—62no—
11C23×C3⋊D3D412yes—
12C22×#157—42no—
13C22×C32×C4—21no—
14C22×C32×C4C2×C411yescharacteristic
15C22×C3⋊Dic3—21no—
16C2×C4⋊(C3⋊D3)—41no—
17C2×C4⋊(C3⋊D3)—41no—
18C2×C4⋊(C3⋊D3)C2×C412yes—
19C2×C4⋊(C3⋊D3)D411yescharacteristic
20C2×C4⋊(C3⋊D3)Q811yescharacteristic
21C22⋊#157—24no—
22C22⋊#157—42no—
23C32×C42—41no—
24#3752—44no—
25C4⋊(C3⋊Dic3)—41no—
26#1393—91nomaximal, Sylow
27C22×D12—62no—
28C2×C3×C42—22no—
29C2×(C2×D3)⋊C4—68no—
30C2×C4⋊Dic3—62no—
31C23×C32C22⋊C411yescharacteristic
32C22×C3⋊D3—22no—
33C22×C3⋊D3—22no—
34C22×C3⋊D3—42no—
35C22×C3⋊D3—42no—
36C22×C3⋊D3C22⋊C412yes—
37C22×C3⋊D3C4⋊C412yes—
38C2×#157—44no—
39C2×#157—82no—
40C2×#157—82no—
41C2×C32×C4—21no—
42C2×C32×C4—21no—
43C2×C32×C4—22no—
44C2×C32×C4—41no—
45C2×C32×C4—41no—
46C2×C32×C4C4211yescharacteristic
47C2×C32×C4C4⋊C411yescharacteristic
48C2×C3⋊Dic3—42no—
49C2×C3⋊Dic3—41no—
50C4⋊(C3⋊D3)—42no—
51C4⋊(C3⋊D3)—41no—
52C4⋊(C3⋊D3)—41no—
53C2×#99—92no—
54#390—91no—
55C23×D3—64no—
56C22×C3×C4—24no—
57C22×C3×C4—22no—
58C22×Dic3—64no—
59C2×D12—64no—
60C2×D12—62no—
61C2×D12—62no—
62C2×D12—124no—
63C2×D12—124no—
64C3×C42—44no—
65(C2×D3)⋊C4—1216no—
66C4⋊Dic3—124no—
67C22×C32—21no—
68C22×C32—21no—
69C22×C32#9511yescharacteristic
70C22×C32#9911yescharacteristic
71C22×C32#9911yescharacteristic
72C2×C3⋊D3—22no—
73C2×C3⋊D3—22no—
74C2×C3⋊D3—42no—
75C2×C3⋊D3—42no—
76C2×C3⋊D3—42no—
77C2×C3⋊D3—42no—
78C2×C3⋊D3—82no—
79#157—84no—
80C32×C4—21no—
81C32×C4—21no—
82C32×C4—42no—
83C3⋊Dic3—81no—
84C22×D4—91no—
85C2×C4⋊C4—91no—
86C2×C22⋊C4—182no—
87C2×C22⋊C4—182no—
88C2×C42#15711yescharacteristic, complemented
89#99—94no—
90#99—182no—
91C23×C3—22no—
92C22×D3—64no—
93C22×D3—64no—
94C22×D3—124no—
95C22×D3—124no—
96C22×D3—128no—
97C22×D3—128no—
98C2×C3×C4—24no—
99C2×C3×C4—24no—
100C2×C3×C4—28no—
101C2×C3×C4—22no—
102C2×C3×C4—22no—
103C2×C3×C4—44no—
104C2×C3×C4—44no—
105C2×Dic3—124no—
106C2×Dic3—128no—
107D12—128no—
108D12—124no—
109D12—124no—
110C2×C32—21no—
111C2×C32—21no—
112C2×C32#34211yescharacteristic
113C2×C32#35311yescharacteristic
114C2×C32#35411yescharacteristic
115C3⋊D3—42no—
116C3⋊D3—42no—
117C24—92no—
118C2×D4—92no—
119C2×D4—91no—
120C2×D4—91no—
121C2×D4—361no—
122C2×D4—361no—
123C22×C4—21no—
124C22×C4—181no—
125C22×C4—362no—
126C22×C4C2×#15711yescharacteristic
127C4⋊C4—361no—
128C22⋊C4—184no—
129C22⋊C4—364no—
130C22⋊C4—362no—
131C42—41no—
132C22×C3—24no—
133C22×C3—24no—
134C22×C3—22no—
135C22×C3—22no—
136C22×C3—22no—
137C2×D3—124no—
138C2×D3—124no—
139C2×D3—128no—
140C2×D3—128no—
141C2×D3—244no—
142C2×D3—244no—
143C2×D3—248no—
144C3×C4—24no—
145C3×C4—24no—
146C3×C4—48no—
147Dic3—244no—
148C32#139311yescharacteristic, complemented, Sylow
149C23—92no—
150C23—92no—
151C23—182no—
152C23—182no—
153C23—362no—
154C23—362no—
155C23C22⋊#15711yescharacteristic
156D4—362no—
157D4—361no—
158D4—361no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—362no—
165C2×C4—364no—
166C2×C4—361no—
167C2×C4—722no—
168C2×C4—722no—
169C2×C4C4×#15711yescharacteristic
170C2×C4C4⋊#15711yescharacteristic
171C2×C3—24no—
172C2×C3—24no—
173C2×C3—22no—
174C2×C3—22no—
175C2×C3—22no—
176D3—244no—
177D3—244no—
178C22—21no—
179C22—21no—
180C22—182no—
181C22—182no—
182C22—362no—
183C22—362no—
184C22—362no—
185C22—362no—
186C22—722no—
187C22#6377411yescharacteristic
188C22#6378111yescharacteristic
189C22#6378611yescharacteristic
190C4—21no—
191C4—21no—
192C4—42no—
193C4—724no—
194C4—721no—
195C3—22no—
196C2—21no—
197C2—21no—
198C2—362no—
199C2—362no—
200C2#1059014211yescharacteristic
201C2#1059014311yescharacteristic
202C2#1059020611yescharacteristic
subgroupG/H
centerC22#63774
commutatorC2×C32×C4C42
FrattiniC22×C4C2×#157
FittingC2×C32×C42C4
socleC22×C32#99
prime radical, cosocleC22×C4⋊(C3⋊D3)C22
hypercenterC2×C42#157
hypocenterC32#1393
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
5. C2×C32×C42C4semidirect
7. C2×C4⋊(C3⋊Dic3)C4semidirect
9. #63774C4semidirect
88. C2×C42#157semidirect
148. C32#1393semidirect

Maximal subgroups

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

subgroupindex
C2×#637742
#105926382
#13939