Finite Group Databasebeta

← #11785723

Subgroups — #11785723

Order 1152.

734 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 70 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×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
2#10593802C212yesmaximal
3#10590208C214yesmaximal, complemented
4C22×C4×C3⋊D3C412yes—
5C22×C4×C3⋊D3C2211yescharacteristic
6C2×#3792C2214yes—
7C2×C32×C4⋊C4C411yescharacteristic
8C2×C4⋊(C3⋊Dic3)C411yescharacteristic
9C2×#3750C2212yes—
10C4⋊C4×C3⋊D3—22no—
11C4⋊C4×C3⋊D3—22no—
12#63778—22no—
13#63778—22no—
14C2×D3×C4⋊C4—62no—
15C23×C3⋊D3C2×C411yescharacteristic
16C22×C32×C4C2×C411yescharacteristic
17C22×C32×C4C2×C412yes—
18C22×C3⋊Dic3C2×C412yes—
19C22×C3⋊Dic3C2311yescharacteristic
20C2×C4×C3⋊D3—24no—
21C2×C4×C3⋊D3—22no—
22C2×C4×C3⋊D3—22no—
23C2×C4×C3⋊D3—44no—
24C2×C4×C3⋊D3D412yes—
25C2×C4×C3⋊D3D412yes—
26#3792—28no—
27C2×#622—24no—
28C32×C4⋊C4—22no—
29C4⋊(C3⋊Dic3)—22no—
30#3750—24no—
31#1821—91nomaximal, Sylow
32C22×C4×D3—62no—
33C22×C4×D3—64no—
34C2×C3×C4⋊C4—22no—
35C2×C4⋊Dic3—62no—
36C2×Dic3⋊C4—64no—
37D3×C4⋊C4—68no—
38D3×C4⋊C4—68no—
39C23×C32C22×C411yescharacteristic
40C22×C3⋊D3—22no—
41C22×C3⋊D3—22no—
42C22×C3⋊D3—22no—
43C22×C3⋊D3C22⋊C411yescharacteristic
44C22×C3⋊D3C22⋊C411yescharacteristic
45C2×C32×C4—22no—
46C2×C32×C4—22no—
47C2×C32×C4—42no—
48C2×C32×C4C22⋊C412yes—
49C2×C3⋊Dic3—22no—
50C2×C3⋊Dic3—42no—
51C2×C3⋊Dic3C2×D412yes—
52C2×C3⋊Dic3#4114yes—
53C4×C3⋊D3—24no—
54C4×C3⋊D3—24no—
55C4×C3⋊D3—44no—
56C4×C3⋊D3—44no—
57#622—44no—
58C22×C4⋊C4—91no—
59#407—92no—
60#343—94no—
61C23×D3—62no—
62C22×C3×C4—24no—
63C22×C3×C4—22no—
64C22×Dic3—62no—
65C22×Dic3—64no—
66C2×C4×D3—64no—
67C2×C4×D3—64no—
68C2×C4×D3—616no—
69C2×C4×D3—68no—
70C2×C4×D3—68no—
71C2×C4×D3—1216no—
72C3×C4⋊C4—28no—
73C4⋊Dic3—68no—
74Dic3⋊C4—616no—
75C22×C32—21no—
76C22×C32—21no—
77C22×C32C2×C22⋊C411yescharacteristic
78C22×C32#11712yes—
79C2×C3⋊D3—28no—
80C2×C3⋊D3—21no—
81C2×C3⋊D3—21no—
82C2×C3⋊D3—21no—
83C2×C3⋊D3—21no—
84C2×C3⋊D3#10012yes—
85C2×C3⋊D3#10112yes—
86C32×C4—22no—
87C32×C4—42no—
88C3⋊Dic3—42no—
89C3⋊Dic3#12314yes—
90C23×C4—91no—
91C23×C4—92no—
92C2×M16—94no—
93C2×C4⋊C4—92no—
94C2×C4⋊C4—91no—
95C2×C4⋊C4—182no—
96C2×C4⋊C4—182no—
97C2×C4⋊C4#15711yescharacteristic
98C22⋊C8—182no—
99C22⋊C8—182no—
100C23×C3—22no—
101C22×D3—62no—
102C22×D3—62no—
103C22×D3—68no—
104C22×D3—68no—
105C22×D3—68no—
106C2×C3×C4—28no—
107C2×C3×C4—28no—
108C2×C3×C4—24no—
109C2×C3×C4—48no—
110C2×Dic3—64no—
111C2×Dic3—68no—
112C2×Dic3—68no—
113C2×Dic3—128no—
114C4×D3—616no—
115C4×D3—616no—
116C4×D3—1216no—
117C4×D3—1216no—
118C2×C32—22no—
119C2×C32#38111yescharacteristic
120C2×C32C2×#10011yescharacteristic
121C2×C32C2×#10111yescharacteristic
122C3⋊D3—22no—
123C3⋊D3—22no—
124C24—91no—
125C22×C4—91no—
126C22×C4—92no—
127C22×C4—92no—
128C22×C4—92no—
129C22×C4—184no—
130C22×C4—182no—
131C22×C4—182no—
132C22×C4—364no—
133C22×C4C2×#15712yes—
134C22×C4C2×#15711yescharacteristic
135M16—188no—
136C2×C8—184no—
137C4⋊C4—22no—
138C4⋊C4—184no—
139C4⋊C4—182no—
140C22×C3—24no—
141C22×C3—24no—
142C22×C3—24no—
143C22×C3—22no—
144C2×D3—64no—
145C2×D3—64no—
146C2×D3—64no—
147C2×D3—64no—
148C2×D3—64no—
149C2×D3—632no—
150C2×D3—64no—
151C3×C4—28no—
152C3×C4—48no—
153Dic3—68no—
154Dic3—128no—
155C32#182111yescharacteristic, complemented, Sylow
156C23—91no—
157C23—91no—
158C23—182no—
159C23—182no—
160C23—182no—
161C23C22×#15711yescharacteristic
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—42no—
165C2×C4—94no—
166C2×C4—92no—
167C2×C4—184no—
168C2×C4—184no—
169C2×C4—182no—
170C2×C4—364no—
171C2×C4—364no—
172C2×C4—362no—
173C2×C4C22⋊#15712yes—
174C8—364no—
175C2×C3—28no—
176C2×C3—22no—
177C2×C3—22no—
178C2×C3—22no—
179D3—68no—
180D3—68no—
181C22—21no—
182C22—21no—
183C22—92no—
184C22—92no—
185C22—188no—
186C22—181no—
187C22—181no—
188C22—181no—
189C22—181no—
190C22#6428612yes—
191C22C2×C22⋊#15711yescharacteristic
192C4—22no—
193C4—42no—
194C4—94no—
195C4—362no—
196C3—22no—
197C2—22no—
198C2—182no—
199C2—182no—
200C2#1059381111yescharacteristic
201C2#1059382511yescharacteristic
202C2#1059383611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC23×C32C22×C4
FrattiniC23C22×#157
FittingC2×C32×C4⋊C4C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1821
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #10590208C2semidirect
155. C32#1821semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
#105938022
#105902082
#18219