Finite Group Databasebeta

← #11795342

Subgroups — #11795342

Order 1152.

409 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 409 conjugacy classes of subgroups — too many to draw. Only its 118 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#10592698C211yesmaximal, characteristic
2C3×#4995C212yesmaximal
3C2×#63574C211yesmaximal, characteristic
4#10589167C212yesmaximal
5#10589165C211yesmaximal, characteristic
6#70671—32nomaximal
7C32×#117C2211yescharacteristic
8C2×#3748C2211yescharacteristic
9C22×C3⋊(C3⋊C8)C2211yescharacteristic
10C2×C3×C4⋊Dic3C2212yes—
11C2×C3×#208C2212yes—
12C4⋊(C3⋊(C3⋊C8))—22no—
13C3×#808—22no—
14C3×#807—22no—
15#63574—22no—
16C3×#428—32no—
17#4999—32no—
18#4999—61no—
19#4995D312yes—
20C2×#808—32no—
21#4558—32no—
22#4554—32no—
23#4530—32no—
24C22×C32×C4C2311yescharacteristic
25C22×C3×Dic3—22no—
26C32×C4⋊C4D412yes—
27C32×C22⋊C4—21no—
28C32×C42—21no—
29#3748—22no—
30C2×C3⋊(C3⋊C8)—22no—
31C2×C3⋊(C3⋊C8)—21no—
32C2×C3⋊(C3⋊C8)D412yes—
33C3×C4⋊Dic3—22no—
34C3×C4⋊Dic3—22no—
35C3×#208—22no—
36C3×#208Q814yes—
37C2×C3×C3⋊C8—22no—
38#2090—91noSylow
39C2×C3×M16—32no—
40C3×#117—21no—
41C3×#117C2×D312yes—
42C2×C3×C4⋊C4—32no—
43C2×C4⋊Dic3C2×D312yes—
44C2×#208—32no—
45C2×#208—61no—
46C2×#208C2×D312yes—
47C22×C3⋊C8—32no—
48C22×C3⋊C8—61no—
49C3×#107—62no—
50C3×#106—62no—
51#808—22no—
52#808—64no—
53#807—22no—
54C4⋊(C3⋊C8)—64no—
55C4⋊(C3⋊C8)—64no—
56C23×C32#4111yescharacteristic
57C2×C32×C4—22no—
58C2×C32×C4C2×D411yescharacteristic
59C2×C32×C4C2×D411yescharacteristic
60C2×C32×C4C2×Q812yes—
61C2×C32×C4#4112yes—
62C2×C3×Dic3—42no—
63C2×C3×Dic3—82no—
64C3⋊(C3⋊C8)—22no—
65C3⋊(C3⋊C8)—41no—
66C3×C3⋊C8—24no—
67#428—32no—
68C2×#106—91no—
69#424—91no—
70#343—92no—
71#341—91no—
72C22×C3×C4—21no—
73C22×C3×C4—62no—
74C22×C3×C4C22×D312yes—
75C22×Dic3—22no—
76C3×M16—34no—
77C3×M16—62no—
78C2×C3×C8—62no—
79C3×C4⋊C4—22no—
80C3×C4⋊C4—62no—
81C3×C4⋊C4—62no—
82C3×C4⋊C4#6712yes—
83C3×C4⋊C4#6712yes—
84C3×C22⋊C4—22no—
85C3×C22⋊C4—22no—
86C3×C42—22no—
87C3×C42—22no—
88C4⋊Dic3—22no—
89C4⋊Dic3—22no—
90#208—22no—
91#208—62no—
92#208—62no—
93#208—122no—
94#208Dic614yes—
95C2×C3⋊C8—22no—
96C2×C3⋊C8—34no—
97C2×C3⋊C8—62no—
98C2×C3⋊C8—62no—
99C2×C3⋊C8—62no—
100C2×C3⋊C8—62no—
101C2×C3⋊C8—62no—
102C2×C3⋊C8—122no—
103C22×C32—22no—
104C22×C32#12111yescharacteristic
105C22×C32#12512yes—
106C32×C4—42no—
107C32×C4C22⋊Q812yes—
108C32×C4#12311yescharacteristic
109C32×C4C4⋊Q811yescharacteristic
110C3×Dic3—82no—
111C2×M16—32no—
112C2×M16—91no—
113C22×C8—91no—
114#117D3211yescharacteristic
115C2×C4⋊C4—32no—
116#107—62no—
117#106—62no—
118#106—182no—
119C4⋊C8—182no—
120C23×C3—21no—
121C23×C3#23712yes—
122C2×C3×C4—24no—
123C2×C3×C4—22no—
124C2×C3×C4—22no—
125C2×C3×C4—22no—
126C2×C3×C4—22no—
127C2×C3×C4—21no—
128C2×C3×C4—21no—
129C2×C3×C4—122no—
130C2×C3×C4—242no—
131C2×C3×C4C2×Dic612yes—
132C2×C3×C4#23512yes—
133C2×C3×C4D3×D412yes—
134C2×C3×C4D3×Q812yes—
135C2×C3×C4#23912yes—
136C2×C3×C4C2×#6712yes—
137C2×Dic3—42no—
138C2×Dic3—82no—
139C3×C8—64no—
140C3⋊C8—24no—
141C3⋊C8—64no—
142C3⋊C8—122no—
143C3⋊C8—122no—
144C3⋊C8—122no—
145C2×C32—22no—
146C2×C32#39811yescharacteristic
147C2×C32#47112yes—
148C22×C4—62no—
149C22×C4C2×D3211yescharacteristic
150M16—34no—
151M16—62no—
152M16—182no—
153C2×C8—62no—
154C2×C8—92no—
155C2×C8—182no—
156C2×C8—181no—
157C4⋊C4—62no—
158C4⋊C4—62no—
159C4⋊C4#62512yes—
160C22⋊C4—21no—
161C42—21no—
162C22×C3—22no—
163C22×C3—22no—
164C22×C3—22no—
165C22×C3—21no—
166C22×C3—42no—
167C22×C3#88912yes—
168C22×C3#89012yes—
169C22×C3#93912yes—
170C3×C4—21no—
171C3×C4—22no—
172C3×C4—21no—
173C3×C4—44no—
174C3×C4—42no—
175C3×C4—42no—
176C3×C4—242no—
177C3×C4#88812yes—
178C3×C4#89412yes—
179C3×C4#92412yes—
180C3×C4#94612yes—
181Dic3—82no—
182C32#209011yescharacteristic, complemented, Sylow
183C23#380511yescharacteristic
184C2×C4—22no—
185C2×C4—122no—
186C2×C4—242no—
187C2×C4D3×Dic612yes—
188C2×C4#379912yes—
189C2×C4C2×#62511yescharacteristic
190C2×C4#381111yescharacteristic
191C8—64no—
192C8—182no—
193C8—361no—
194C2×C3—22no—
195C2×C3—22no—
196C2×C3—22no—
197C2×C3—21no—
198C2×C3—42no—
199C2×C3#498212yes—
200C2×C3#520012yes—
201C2×C3#520312yes—
202C22—22no—
203C22#6384512yes—
204C22#6398011yescharacteristic
205C4—42no—
206C4—242no—
207C4#6384011yescharacteristic
208C4#6385612yes—
209C4#6389711yescharacteristic
210C3—21no—
211C3#7067112yescomplemented
212C2—22no—
213C2#1059121511yescharacteristic
214C2#1059168112yes—
subgroupG/H
centerC22#63980
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32#121
prime radicalC23×C32#41
hypercenter#117D32
hypocenterC32#2090
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
182. C32#2090semidirect
211. C3#70671semidirect

Maximal subgroups

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

subgroupindex
#105926982
C3×#49952
C2×#635742
#105891672
#105891652
#706713