Finite Group Databasebeta

← #11771806

Subgroups — #11771806

Order 1152.

316 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 30 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#10592373C211yesmaximal, characteristic
2#10590206C211yesmaximal, characteristic
3#10590204C211yesmaximal, characteristic
4C2×C22⋊#157—21no—
5C2×#3752—21no—
6C2×#3752C2211yescharacteristic
7C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
8C22⋊#622—21no—
9C32×#95C411yescharacteristic, complemented
10#63658—21no—
11#4674—62no—
12C23×C3⋊D3D411yescharacteristic
13C22×#157—41no—
14C22×C32×C4—21no—
15C22×C32×C4C2×C411yescharacteristic
16C22×C3⋊Dic3—21no—
17C22×C3⋊Dic3D411yescharacteristic
18C22⋊#157—22no—
19C22⋊#157—41no—
20C2×#622—41no—
21#3752—41no—
22#3752—41no—
23#3752—41no—
24C4⋊(C3⋊Dic3)—41no—
25#1344—91nomaximal, Sylow
26C2×(C2×D3)⋊C4—62no—
27C2×(C2×D3)⋊C4—64no—
28C2×C4⋊Dic3—62no—
29C3×#95—22no—
30C3⋊#95—64no—
31C23×C32C22⋊C411yescharacteristic
32C22×C3⋊D3—21no—
33C22×C3⋊D3—21no—
34C22×C3⋊D3—41no—
35C22×C3⋊D3—41no—
36C22×C3⋊D3D811yescharacteristic
37C22×C3⋊D3SD1611yescharacteristic
38C2×#157—42no—
39C2×#157—81no—
40C2×#157—81no—
41C2×C32×C4—21no—
42C2×C32×C4—41no—
43C2×C32×C4—41no—
44C2×C32×C4—41no—
45C2×C32×C4—41no—
46C2×C3⋊Dic3—21no—
47C2×C3⋊Dic3—41no—
48C2×C3⋊Dic3—41no—
49C2×C3⋊Dic3—41no—
50C2×C3⋊Dic3—41no—
51#622—81no—
52#397—91no—
53#342—91no—
54#323—91no—
55C23×D3—62no—
56C22×C3×C4—24no—
57C22×C3×C4—22no—
58C22×Dic3—62no—
59C22×Dic3—64no—
60(C2×D3)⋊C4—124no—
61(C2×D3)⋊C4—124no—
62(C2×D3)⋊C4—124no—
63C4⋊Dic3—124no—
64C22×C32—21no—
65C22×C32—21no—
66C22×C32#9911yescharacteristic
67C22×C32#10211yescharacteristic
68C22×C32#10411yescharacteristic
69C2×C3⋊D3—21no—
70C2×C3⋊D3—21no—
71C2×C3⋊D3—41no—
72C2×C3⋊D3—41no—
73C2×C3⋊D3—41no—
74C2×C3⋊D3—41no—
75C2×C3⋊D3—81no—
76#157—82no—
77C32×C4—41no—
78C32×C4—81no—
79C3⋊Dic3—41no—
80C3⋊Dic3—81no—
81C2×C4⋊C4—91no—
82C2×C22⋊C4—91no—
83C2×C22⋊C4—181no—
84C2×C22⋊C4—181no—
85C22⋊C8—181no—
86#95—181no—
87#95#15711yescharacteristic, complemented
88C23×C3—22no—
89C22×D3—62no—
90C22×D3—62no—
91C22×D3—122no—
92C22×D3—122no—
93C22×D3—124no—
94C22×D3—124no—
95C2×C3×C4—24no—
96C2×C3×C4—44no—
97C2×C3×C4—44no—
98C2×C3×C4—44no—
99C2×C3×C4—44no—
100C2×Dic3—122no—
101C2×Dic3—124no—
102C2×Dic3—124no—
103C2×Dic3—124no—
104C2×Dic3—124no—
105C2×C32—21no—
106C2×C32—21no—
107C2×C32#32711yescharacteristic
108C2×C32#35211yescharacteristic
109C2×C32#35411yescharacteristic
110C3⋊D3—41no—
111C3⋊D3—41no—
112C24—91no—
113C22×C4—21no—
114C22×C4—91no—
115C22×C4—181no—
116C22×C4—361no—
117C22×C4C2×#15711yescharacteristic
118C2×C8—361no—
119C4⋊C4—361no—
120C22⋊C4—182no—
121C22⋊C4—361no—
122C22⋊C4—361no—
123C22⋊C4—361no—
124C22⋊C4—361no—
125C22×C3—24no—
126C22×C3—24no—
127C22×C3—22no—
128C22×C3—22no—
129C22×C3—22no—
130C2×D3—122no—
131C2×D3—122no—
132C2×D3—124no—
133C2×D3—124no—
134C2×D3—242no—
135C2×D3—242no—
136C2×D3—244no—
137C3×C4—44no—
138C3×C4—84no—
139Dic3—242no—
140Dic3—244no—
141C32#134411yescharacteristic, complemented, Sylow
142C23—91no—
143C23—91no—
144C23—181no—
145C23—181no—
146C23—361no—
147C23—361no—
148C23C22⋊#15711yescharacteristic
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—181no—
155C2×C4—361no—
156C2×C4—362no—
157C2×C4—361no—
158C2×C4—361no—
159C2×C4—361no—
160C2×C4—721no—
161C2×C4—721no—
162C8—721no—
163C2×C3—24no—
164C2×C3—24no—
165C2×C3—22no—
166C2×C3—22no—
167C2×C3—22no—
168D3—242no—
169D3—242no—
170C22—21no—
171C22—21no—
172C22—181no—
173C22—181no—
174C22—361no—
175C22—361no—
176C22—361no—
177C22—361no—
178C22—721no—
179C22#6377411yescharacteristic
180C22#6378211yescharacteristic
181C22#6378511yescharacteristic
182C4—41no—
183C4—81no—
184C4—361no—
185C4—722no—
186C4—721no—
187C3—22no—
188C2—21no—
189C2—21no—
190C2—361no—
191C2—361no—
192C2#1059014311yescharacteristic
193C2#1059015411yescharacteristic
194C2#1059015711yescharacteristic
subgroupG/H
centerC22#63774
commutatorC22×C32×C4C2×C4
FrattiniC22×C4C2×#157
FittingC32×#95C4
socleC22×C32#99
prime radicalC23×C3⋊D3D4
cosocleC2×#3752C22
hypercenter#95#157
hypocenterC32#1344
LCSG ▷ C22×C32×C4 ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
7. C2×C4⋊(C3⋊Dic3)C4semidirect
9. C32×#95C4semidirect
87. #95#157semidirect
141. C32#1344semidirect

Maximal subgroups

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

subgroupindex
#105923732
#105902062
#105902042
#13449