Finite Group Databasebeta

← #11783265

Subgroups — #11783265

Order 1152.

754 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 754 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C22×#3787C211yesmaximal, characteristic
2C2×#63874C212yesmaximal
3#10590075C214yesmaximal, complemented
4C22×C4×C3⋊D3C2211yescharacteristic
5C22×#622C2212yes—
6C2×#3787—24no—
7C2×#3787C414yescomplemented
8C2×C3×C4×Dic3—22no—
9C2×#3724C2214yes—
10C2×#3722—22no—
11#63874—24no—
12#63874C418yescomplemented
13C2×#872—62no—
14C23×C3⋊D3D411yescharacteristic
15C22×C32×C4D411yescharacteristic
16C22×C3⋊Dic3C2311yescharacteristic
17C2×C4×C3⋊D3C2×C412yes—
18C2×C4×C3⋊D3C2×C414yes—
19C2×C4×C3⋊D3D414yes—
20C2×C4×C3⋊D3Q812yes—
21C22×C3×Dic3—24no—
22C2×#622—24no—
23C2×#622C2×C414yes—
24#3787—28no—
25C3×C4×Dic3—28no—
26#3724—24no—
27#3724C2×C418yes—
28#3722—28no—
29#1735—91nomaximal, Sylow
30C22×C4×D3—62no—
31C2×C3×C42—62no—
32C2×(C2×D3)⋊C4—64no—
33C2×Dic3⋊C4—64no—
34C2×C4×Dic3—22no—
35#872—68no—
36#872—68no—
37C23×C32C2×D411yescharacteristic
38C22×C3⋊D3—24no—
39C22×C3⋊D3C22⋊C414yes—
40C22×C3⋊D3C4⋊C412yes—
41C2×C32×C4C22⋊C414yes—
42C2×C32×C4C4⋊C412yes—
43C2×C3⋊Dic3C22×C411yescharacteristic
44C2×C3⋊Dic3C22×C412yes—
45C2×C3⋊Dic3C2×D412yes—
46C2×C3⋊Dic3C2×Q811yescharacteristic
47C4×C3⋊D3C4214yes—
48C4×C3⋊D3C22⋊C414yes—
49C4×C3⋊D3C4⋊C418yes—
50C2×C3×Dic3—28no—
51C2×C3×Dic3—48no—
52#622—24no—
53C23×C8—91no—
54C2×#117—92no—
55#340—94no—
56C23×D3—62no—
57C22×C3×C4—22no—
58C22×C3×C4—64no—
59C22×Dic3—24no—
60C22×Dic3—62no—
61C2×C4×D3—64no—
62C2×C4×D3—64no—
63C2×C4×D3—64no—
64C2×C4×D3—64no—
65C2×C4×D3—64no—
66C2×C4×D3—64no—
67C3×C42—68no—
68(C2×D3)⋊C4—616no—
69Dic3⋊C4—68no—
70Dic3⋊C4—68no—
71C4×Dic3—28no—
72C22×C32C2×C22⋊C412yes—
73C22×C32C2×C4⋊C411yescharacteristic
74C22×C32#13514yes—
75C2×C3⋊D3—28no—
76C2×C3⋊D3—24no—
77C2×C3⋊D3#9514yes—
78C32×C4#9514yes—
79C3⋊Dic3C2×C4211yescharacteristic
80C3⋊Dic3C2×C22⋊C411yescharacteristic
81C3⋊Dic3C2×C4⋊C412yes—
82C3×Dic3—48no—
83C23×C4—91no—
84C22×C8—94no—
85C22×C8—92no—
86C22×C8—184no—
87#117—98no—
88#117—184no—
89C2×C4⋊C4—94no—
90C2×C22⋊C4—182no—
91C2×C42—62no—
92C23×C3—22no—
93C22×D3—64no—
94C22×D3—64no—
95C22×D3—64no—
96C22×D3—128no—
97C2×C3×C4—24no—
98C2×C3×C4—24no—
99C2×C3×C4—24no—
100C2×C3×C4—68no—
101C2×C3×C4—128no—
102C2×Dic3—28no—
103C2×Dic3—48no—
104C2×Dic3—62no—
105C2×Dic3—62no—
106C2×Dic3—62no—
107C2×Dic3—62no—
108C2×Dic3—62no—
109C2×Dic3—62no—
110C4×D3—68no—
111C4×D3—68no—
112C4×D3—68no—
113C4×D3—68no—
114C2×C32C2×#9511yescharacteristic
115C2×C32#41614yes—
116C2×C32#42712yes—
117C3⋊D3—24no—
118C24—91no—
119C22×C4—64no—
120C22×C4—91no—
121C22×C4—94no—
122C22×C4—94no—
123C22×C4—92no—
124C22×C4—92no—
125C22×C4GO+(4,𝔽2)11yescharacteristic
126C2×C8—94no—
127C2×C8—188no—
128C2×C8—184no—
129C4⋊C4—98no—
130C4⋊C4—184no—
131C22⋊C4—188no—
132C42—68no—
133C22×C3—28no—
134C22×C3—22no—
135C22×C3—22no—
136C22×C3—22no—
137C2×D3—68no—
138C2×D3—128no—
139C2×D3—128no—
140C2×D3—128no—
141C3×C4—28no—
142C3×C4—128no—
143Dic3—48no—
144Dic3—62no—
145Dic3—62no—
146Dic3—62no—
147Dic3—62no—
148C32#173511yescharacteristic, complemented, Sylow
149C23—94no—
150C23—92no—
151C23—184no—
152C23C2×GO+(4,𝔽2)11yescharacteristic
153C2×C4—68no—
154C2×C4—92no—
155C2×C4—92no—
156C2×C4—91no—
157C2×C4—91no—
158C2×C4—94no—
159C2×C4—94no—
160C2×C4—98no—
161C2×C4—128no—
162C2×C4D32⋊C414yes—
163C2×C4#377312yes—
164C8—184no—
165C2×C3—24no—
166C2×C3—24no—
167C2×C3—24no—
168C2×C3—22no—
169D3—128no—
170C22—94no—
171C22—188no—
172C22—184no—
173C22#6422314yes—
174C22C2×D32⋊C412yes—
175C22C2×#377311yescharacteristic
176C4—91no—
177C4—91no—
178C4—92no—
179C4—128no—
180C4#6373714yes—
181C3—22no—
182C2—184no—
183C2#1059334914yes—
184C2#1059338912yes—
185C2C2×#6373711yescharacteristic
subgroupG/H
center, hypercenterC22×C4GO+(4,𝔽2)
commutatorC3⋊Dic3C2×C42
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C3⋊Dic3C23
hypocenterC32#1735
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. #10590075C2semidirect
7. C2×#3787C4semidirect
12. #63874C4semidirect
148. C32#1735semidirect

Maximal subgroups

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

subgroupindex
C22×#37872
C2×#638742
#105900752
#17359