Finite Group Databasebeta

← #11773873

Subgroups — #11773873

Order 1152.

730 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 730 conjugacy classes of subgroups — too many to draw. Only its 74 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×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic
2#10593845C212yesmaximal
3#10590202C214yesmaximal, complemented
4C23×C32×C4C411yescharacteristic
5C23×C3⋊Dic3C411yescharacteristic
6C23×C3⋊Dic3C2211yescharacteristic
7C2×#3792—22no—
8C2×C4⋊(C3⋊Dic3)—22no—
9C2×C4⋊(C3⋊Dic3)—22no—
10C2×C4⋊(C3⋊Dic3)C412yes—
11C2×C4⋊(C3⋊Dic3)C2212yes—
12C22⋊#622—22no—
13C22⋊#622C2214yes—
14C22×C4⋊Dic3—62no—
15C24×C32C2×C411yescharacteristic
16C22×C32×C4—21no—
17C22×C32×C4—21no—
18C22×C32×C4—24no—
19C22×C32×C4C2×C412yes—
20C22×C3⋊Dic3—21no—
21C22×C3⋊Dic3—21no—
22C22×C3⋊Dic3—42no—
23C22×C3⋊Dic3—42no—
24C22×C3⋊Dic3C2×C412yes—
25C22×C3⋊Dic3C2×C411yescharacteristic
26C22×C3⋊Dic3D412yes—
27C22×C3⋊Dic3D412yes—
28C22×C3⋊Dic3C2311yescharacteristic
29#3792—44no—
30C2×#622—24no—
31C4⋊(C3⋊Dic3)—24no—
32C4⋊(C3⋊Dic3)—24no—
33#1463—91nomaximal, Sylow
34C23×C3×C4—22no—
35C23×Dic3—62no—
36C23×Dic3—62no—
37C2×C4⋊Dic3—64no—
38C2×C4⋊Dic3—64no—
39C2×C4⋊Dic3—68no—
40C2×C4⋊Dic3—68no—
41C23×C32—22no—
42C23×C32—22no—
43C23×C32—22no—
44C23×C32C22⋊C411yescharacteristic
45C23×C32C22⋊C411yescharacteristic
46C23×C32C22×C411yescharacteristic
47C2×C32×C4—24no—
48C2×C32×C4—24no—
49C2×C32×C4—22no—
50C2×C32×C4—22no—
51C2×C32×C4M1614yescomplemented
52C2×C3⋊Dic3—22no—
53C2×C3⋊Dic3—24no—
54C2×C3⋊Dic3—41no—
55C2×C3⋊Dic3—42no—
56C2×C3⋊Dic3—41no—
57C2×C3⋊Dic3—42no—
58C2×C3⋊Dic3—42no—
59C2×C3⋊Dic3—42no—
60C2×C3⋊Dic3C22⋊C412yes—
61C2×C3⋊Dic3C2×D412yes—
62#622—44no—
63C22×C4⋊C4—91no—
64#407—92no—
65#324—94no—
66C24×C3—22no—
67C22×C3×C4—24no—
68C22×C3×C4—24no—
69C22×C3×C4—216no—
70C22×C3×C4—24no—
71C22×Dic3—62no—
72C22×Dic3—64no—
73C22×Dic3—64no—
74C22×Dic3—64no—
75C22×Dic3—62no—
76C22×Dic3—64no—
77C22×Dic3—64no—
78C22×Dic3—128no—
79C22×Dic3—128no—
80C4⋊Dic3—616no—
81C4⋊Dic3—616no—
82C22×C32—28no—
83C22×C32—21no—
84C22×C32—21no—
85C22×C32—21no—
86C22×C32—21no—
87C22×C32—21no—
88C22×C32—21no—
89C22×C32#9912yes—
90C22×C32#10112yes—
91C22×C32C2×C22⋊C411yescharacteristic
92C22×C32C2×M1612yes—
93C32×C4—24no—
94C3⋊Dic3—22no—
95C3⋊Dic3—22no—
96C3⋊Dic3—42no—
97C23×C4—91no—
98C23×C4—91no—
99C23×C4#15711yescharacteristic
100C2×M16—182no—
101C2×C4⋊C4—92no—
102C2×C4⋊C4—92no—
103C2×C4⋊C4—182no—
104C2×C4⋊C4—182no—
105C22⋊C8—94no—
106C22⋊C8—182no—
107C23×C3—28no—
108C23×C3—28no—
109C23×C3—28no—
110C23×C3—22no—
111C23×C3—22no—
112C23×C3—22no—
113C2×C3×C4—28no—
114C2×C3×C4—216no—
115C2×C3×C4—216no—
116C2×C3×C4—28no—
117C2×C3×C4—28no—
118C2×Dic3—64no—
119C2×Dic3—64no—
120C2×Dic3—68no—
121C2×Dic3—128no—
122C2×Dic3—124no—
123C2×Dic3—128no—
124C2×Dic3—124no—
125C2×Dic3—128no—
126C2×Dic3—128no—
127C2×Dic3—128no—
128C2×C32—22no—
129C2×C32—22no—
130C2×C32—22no—
131C2×C32#40711yescharacteristic
132C2×C32C2×#9911yescharacteristic
133C2×C32C2×#10111yescharacteristic
134C24C2×#15711yescharacteristic
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—24no—
138C22×C4—92no—
139C22×C4—91no—
140C22×C4—91no—
141C22×C4—92no—
142C22×C4—92no—
143C22×C4—181no—
144C22×C4—181no—
145C22×C4—362no—
146C22×C4—362no—
147C22×C4C2×#15712yes—
148M16—364no—
149C2×C8—184no—
150C4⋊C4—184no—
151C4⋊C4—184no—
152C22×C3—24no—
153C22×C3—24no—
154C22×C3—24no—
155C22×C3—24no—
156C22×C3—232no—
157C22×C3—24no—
158C22×C3—24no—
159C22×C3—24no—
160C22×C3—24no—
161C22×C3—24no—
162C22×C3—22no—
163C3×C4—216no—
164Dic3—124no—
165Dic3—124no—
166Dic3—128no—
167C32#146311yescharacteristic, complemented, Sylow
168C23—22no—
169C23—22no—
170C23—22no—
171C23C22⋊#15711yescharacteristic
172C23C22⋊#15711yescharacteristic
173C23C22×#15711yescharacteristic
174C2×C4—24no—
175C2×C4—24no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—92no—
179C2×C4—92no—
180C2×C4—184no—
181C2×C4—182no—
182C2×C4—361no—
183C2×C4—362no—
184C2×C4—361no—
185C2×C4—362no—
186C2×C4—362no—
187C2×C4—362no—
188C2×C4#379214yescomplemented
189C8—364no—
190C2×C3—28no—
191C2×C3—28no—
192C2×C3—28no—
193C2×C3—22no—
194C2×C3—22no—
195C2×C3—22no—
196C22—28no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22#6377412yes—
204C22#6378012yes—
205C22C2×#379212yes—
206C22C2×C22⋊#15711yescharacteristic
207C4—24no—
208C4—182no—
209C4—182no—
210C4—362no—
211C3—22no—
212C2—22no—
213C2—22no—
214C2—22no—
215C2C2×#6377411yescharacteristic
216C2C2×#6378011yescharacteristic
217C2#1059384511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC23×C32C22×C4
FrattiniC23C22×#157
FittingC23×C32×C4C4
socleC22×C32C2×C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C3⋊Dic3C23
hypercenterC23×C4#157
hypocenterC32#1463
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. #10590202C2semidirect
51. C2×C32×C4M16semidirect
167. C32#1463semidirect
188. C2×C4#3792semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊(C3⋊Dic3)2
#105938452
#105902022
#14639