Finite Group Databasebeta

← #11775177

Subgroups — #11775177

Order 1152.

450 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 60 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#10596199C211yesmaximal, characteristic
2#10593733C211yesmaximal, characteristic
3#10593730C211yesmaximal, characteristic
4#10590215C214yesmaximal
5C2×C4×#157—21no—
6C32×C4⋊Q8C411yescharacteristic, complemented
7#64155C2212yes—
8Q8×C3⋊Dic3C412yescomplemented
9#64106—21no—
10#64101—21no—
11#64099—21no—
12#64096—21no—
13C42×C3⋊D3C2211yescharacteristic
14#64078C411yescharacteristic, complemented
15#63781—21no—
16#63781C2212yes—
17#63778C2212yes—
18#63777—21no—
19C4⋊#622—21no—
20#5728—62no—
21C22×#157—22no—
22C2×C32×Q8C2×C412yes—
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C4×C3⋊D3C2311yescharacteristic
26C2×#634—21no—
27C2×#622—22no—
28C4×#157—24no—
29C32×C4⋊C4—21no—
30C32×C4⋊C4—21no—
31C32×C42C2×C411yescharacteristic
32#3752—22no—
33C4⋊(C3⋊Dic3)—21no—
34C4⋊(C3⋊Dic3)—22no—
35C4⋊(C3⋊Dic3)C2×C412yes—
36#3750—22no—
37C4×C3⋊Dic3—22no—
38C4×C3⋊Dic3C2×C411yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41#1506—91nomaximal, Sylow
42C3×C4⋊Q8—22no—
43#946—64no—
44Q8×Dic3—64no—
45#897—64no—
46#892—64no—
47#890—64no—
48#887—64no—
49C42×D3—62no—
50#869—62no—
51C22×C3⋊D3C2×D411yescharacteristic
52C2×#157—24no—
53C2×#157—42no—
54C2×#157—42no—
55C32×Q8—42no—
56C2×C32×C4—22no—
57C2×C32×C4C22⋊C411yescharacteristic
58C2×C32×C4C22⋊C411yescharacteristic
59C2×C32×C4C22×C411yescharacteristic
60C2×C3⋊Dic3—22no—
61C2×C3⋊Dic3C22⋊C411yescharacteristic
62C2×C3⋊Dic3C22⋊C411yescharacteristic
63C2×C3⋊Dic3C2×D411yescharacteristic
64C4×C3⋊D3—22no—
65C4×C3⋊D3—22no—
66C4×C3⋊D3—41no—
67#634—42no—
68#622—42no—
69#533—91no—
70#432—91no—
71#376—91no—
72#328—94no—
73C2×C3×Q8—24no—
74C2×C4×D3—62no—
75C2×C4×D3—62no—
76C2×C4×D3—62no—
77C2×Dic6—64no—
78C3×C4⋊C4—24no—
79C3×C4⋊C4—24no—
80C3×C42—22no—
81(C2×D3)⋊C4—68no—
82C4⋊Dic3—64no—
83C4⋊Dic3—64no—
84C4⋊Dic3—68no—
85Dic3⋊C4—68no—
86C4×Dic3—62no—
87C4×Dic3—62no—
88C4×Dic3—62no—
89C4×Dic3—68no—
90C22×C32C2×C22⋊C411yescharacteristic
91C2×C3⋊D3—21no—
92C2×C3⋊D3—21no—
93C2×C3⋊D3#13712yes—
94#157—44no—
95C32×C4—21no—
96C32×C4—21no—
97C32×C4—42no—
98C32×C4#10412yes—
99C3⋊Dic3—21no—
100C3⋊Dic3—21no—
101C3⋊Dic3—21no—
102C3⋊Dic3—42no—
103C4⋊Q8—91no—
104C4⋊Q8#15711yescharacteristic, complemented
105#125—181no—
106C22⋊Q8—92no—
107C22⋊Q8—181no—
108C4×Q8—92no—
109C4×Q8—181no—
110#117—181no—
111C2×C42—91no—
112C2×C42—181no—
113C4⋊C8—181no—
114C22⋊C8—92no—
115#97—181no—
116#95—92no—
117#95—181no—
118C22×D3—62no—
119C3×Q8—48no—
120C2×C3×C4—28no—
121C2×C3×C4—22no—
122C2×C3×C4—22no—
123C2×C3×C4—22no—
124C2×Dic3—62no—
125C2×Dic3—62no—
126C2×Dic3—62no—
127C2×Dic3—68no—
128C4×D3—68no—
129C4×D3—124no—
130C4×D3—124no—
131Dic6—128no—
132C2×C32#41011yescharacteristic
133C2×C32#41911yescharacteristic
134C2×C32C2×#10411yescharacteristic
135C3⋊D3—22no—
136C2×Q8—181no—
137C2×Q8C2×#15712yes—
138C22×C4—91no—
139C22×C4—91no—
140C22×C4—91no—
141C22×C4—182no—
142C2×C8—182no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—92no—
146C4⋊C4—182no—
147C4⋊C4—182no—
148C4⋊C4—181no—
149C22⋊C4—182no—
150C42—91no—
151C42—91no—
152C42—91no—
153C42—182no—
154C42—184no—
155C42C2×#15711yescharacteristic
156C22×C3—22no—
157C2×D3—64no—
158C2×D3—122no—
159C2×D3—122no—
160C3×C4—24no—
161C3×C4—24no—
162C3×C4—24no—
163C3×C4—48no—
164Dic3—64no—
165Dic3—122no—
166Dic3—122no—
167Dic3—128no—
168C32#150611yescharacteristic, complemented, Sylow
169C23—91no—
170Q8—42no—
171Q8—362no—
172C2×C4—22no—
173C2×C4—91no—
174C2×C4—91no—
175C2×C4—91no—
176C2×C4—182no—
177C2×C4—182no—
178C2×C4—184no—
179C2×C4—182no—
180C2×C4—361no—
181C2×C4—362no—
182C2×C4—362no—
183C2×C4C22⋊#15711yescharacteristic
184C2×C4C22⋊#15711yescharacteristic
185C2×C4C22×#15711yescharacteristic
186C8—362no—
187C2×C3—22no—
188C2×C3—22no—
189C2×C3—22no—
190D3—124no—
191C22—92no—
192C22—181no—
193C22—181no—
194C22C2×C22⋊#15711yescharacteristic
195C4—21no—
196C4—21no—
197C4—42no—
198C4—181no—
199C4—181no—
200C4—181no—
201C4—364no—
202C4—362no—
203C4#6378512yes—
204C3—22no—
205C2—182no—
206C2#1059381811yescharacteristic
207C2#1059382911yescharacteristic
208C2C2×#6378511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4⋊Q8C4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC4⋊Q8#157
hypocenterC32#1506
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
6. C32×C4⋊Q8C4semidirect
8. Q8×C3⋊Dic3C4semidirect
14. #64078C4semidirect
104. C4⋊Q8#157semidirect
168. C32#1506semidirect

Maximal subgroups

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

subgroupindex
#105961992
#105937332
#105937302
#105902152
#15069