Finite Group Databasebeta

← #11783266

Subgroups — #11783266

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
1C23×#622C211yesmaximal, characteristic
2C2×#63957C212yesmaximal
3#10590075C214yesmaximal, complemented
4C23×C3⋊Dic3C2211yescharacteristic
5C22×#622—24no—
6C22×#622C414yescomplemented
7C22×#622C2212yes—
8C2×C3×#217—22no—
9C2×#3724C2214yes—
10#63957—24no—
11#63957C418yescomplemented
12C2×Dic32—22no—
13C2×#877—62no—
14C24×C32D411yescharacteristic
15C22×C3⋊Dic3C2×C412yes—
16C22×C3⋊Dic3C2×C414yes—
17C22×C3⋊Dic3D411yescharacteristic
18C22×C3⋊Dic3D414yes—
19C22×C3⋊Dic3Q812yes—
20C22×C3⋊Dic3C2311yescharacteristic
21C22×C3×Dic3—24no—
22C2×#622—28no—
23C2×#622—24no—
24C2×#622C2×C414yes—
25C3×#217—28no—
26#3724—24no—
27#3724C2×C418yes—
28Dic32—28no—
29#1735—91nomaximal, Sylow
30C23×Dic3—62no—
31C2×C3×C22⋊C4—62no—
32C2×#217—22no—
33C2×Dic3⋊C4—64no—
34C2×C4×Dic3—64no—
35#877—68no—
36#877—68no—
37C23×C32—24no—
38C23×C32C22⋊C414yes—
39C23×C32C4⋊C412yes—
40C23×C32C2×D411yescharacteristic
41C2×C3⋊Dic3C4214yes—
42C2×C3⋊Dic3C22⋊C414yes—
43C2×C3⋊Dic3C22⋊C414yes—
44C2×C3⋊Dic3C4⋊C412yes—
45C2×C3⋊Dic3C4⋊C418yes—
46C2×C3⋊Dic3C22×C411yescharacteristic
47C2×C3⋊Dic3C22×C412yes—
48C2×C3⋊Dic3C2×D412yes—
49C2×C3⋊Dic3C2×Q811yescharacteristic
50C2×C3×Dic3—28no—
51C2×C3×Dic3—48no—
52#622—24no—
53C23×C8—91no—
54C2×#117—92no—
55#340—94no—
56C24×C3—22no—
57C22×C3×C4—64no—
58C22×Dic3—24no—
59C22×Dic3—64no—
60C22×Dic3—64no—
61C22×Dic3—62no—
62C22×Dic3—62no—
63C22×Dic3—64no—
64C22×Dic3—64no—
65C22×Dic3—64no—
66C22×Dic3—64no—
67C3×C22⋊C4—68no—
68#217—28no—
69Dic3⋊C4—68no—
70Dic3⋊C4—68no—
71C4×Dic3—616no—
72C22×C32—28no—
73C22×C32—24no—
74C22×C32#9514yes—
75C22×C32C2×C22⋊C412yes—
76C22×C32C2×C4⋊C411yescharacteristic
77C22×C32#13514yes—
78C3⋊Dic3#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—62no—
91C2×C42—182no—
92C23×C3—22no—
93C23×C3—24no—
94C23×C3—24no—
95C23×C3—24no—
96C23×C3—48no—
97C2×C3×C4—68no—
98C2×C3×C4—128no—
99C2×Dic3—28no—
100C2×Dic3—48no—
101C2×Dic3—68no—
102C2×Dic3—64no—
103C2×Dic3—64no—
104C2×Dic3—68no—
105C2×Dic3—64no—
106C2×Dic3—68no—
107C2×Dic3—68no—
108C2×Dic3—62no—
109C2×Dic3—62no—
110C2×Dic3—62no—
111C2×Dic3—62no—
112C2×Dic3—62no—
113C2×Dic3—62no—
114C2×C32—24no—
115C2×C32C2×#9511yescharacteristic
116C2×C32#41614yes—
117C2×C32#42712yes—
118C24GO+(4,𝔽2)11yescharacteristic
119C22×C4—64no—
120C22×C4—91no—
121C22×C4—91no—
122C22×C4—94no—
123C22×C4—94no—
124C22×C4—92no—
125C22×C4—92no—
126C2×C8—94no—
127C2×C8—184no—
128C2×C8—188no—
129C4⋊C4—98no—
130C4⋊C4—184no—
131C22⋊C4—68no—
132C42—188no—
133C22×C3—22no—
134C22×C3—22no—
135C22×C3—22no—
136C22×C3—28no—
137C22×C3—28no—
138C22×C3—48no—
139C22×C3—48no—
140C22×C3—48no—
141C3×C4—128no—
142Dic3—48no—
143Dic3—68no—
144Dic3—62no—
145Dic3—62no—
146Dic3—62no—
147Dic3—62no—
148C32#173511yescharacteristic, complemented, Sylow
149C23—24no—
150C23D32⋊C414yes—
151C23#377312yes—
152C23C2×GO+(4,𝔽2)11yescharacteristic
153C2×C4—68no—
154C2×C4—94no—
155C2×C4—92no—
156C2×C4—92no—
157C2×C4—91no—
158C2×C4—92no—
159C2×C4—91no—
160C2×C4—94no—
161C2×C4—94no—
162C2×C4—98no—
163C2×C4—128no—
164C8—184no—
165C2×C3—22no—
166C2×C3—24no—
167C2×C3—24no—
168C2×C3—24no—
169C2×C3—48no—
170C22—28no—
171C22—24no—
172C22#6373714yes—
173C22C2×D32⋊C412yes—
174C22C2×#377311yescharacteristic
175C22#6423714yes—
176C4—91no—
177C4—94no—
178C4—91no—
179C4—92no—
180C4—128no—
181C3—22no—
182C2—24no—
183C2C2×#6373711yescharacteristic
184C2#1059349814yes—
185C2#1059351112yes—
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C2×C42
Fitting, prime radicalC24×C32D4
socleC23×C32C2×D4
cosocleC22×C3⋊Dic3C23
hypercenterC24GO+(4,𝔽2)
hypocenterC32#1735
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
3. #10590075C2semidirect
6. C22×#622C4semidirect
11. #63957C4semidirect
148. C32#1735semidirect

Maximal subgroups

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

subgroupindex
C23×#6222
C2×#639572
#105900752
#17359