Finite Group Databasebeta

← #11773676

Subgroups — #11773676

Order 1152.

534 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 189 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#10592384C211yesmaximal, characteristic
2#10592384C211yesmaximal, characteristic
3#10592384C211yesmaximal, characteristic
4C32×#322C211yesmaximal, characteristic, complemented
5#10589321C211yesmaximal, characteristic, complemented
6#10589320C211yesmaximal, characteristic, complemented
7C8×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#68074—34nomaximal
9C42×C3⋊D3C2211yescharacteristic
10C32×C4×C8C2211yescharacteristic
11C32×C4×C8C2211yescharacteristic
12C32×C4×C8C2211yescharacteristic
13#63647C412yes—
14#63647C412yes—
15#63647C412yes—
16#63641C412yes—
17#63641C412yes—
18#63641C412yes—
19C4×C3⋊(C3⋊C8)C2211yescharacteristic
20C4×C3⋊(C3⋊C8)C2211yescharacteristic
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22#4685—34no—
23#4685—34no—
24#4685—34no—
25C3×#322D314yescomplemented
26#4455—34no—
27#4454—34no—
28C8×C3⋊C8—34no—
29C2×C4×C3⋊D3C2×C411yescharacteristic
30C2×C4×C3⋊D3C2×C411yescharacteristic
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C32×C8C2×C412yes—
33C2×C32×C8C2×C412yes—
34C2×C32×C8C2×C412yes—
35C32×C42C2311yescharacteristic
36C4×C3⋊Dic3C2×C411yescharacteristic
37C4×C3⋊Dic3C2×C411yescharacteristic
38C4×C3⋊Dic3C2×C411yescharacteristic
39C2×C3⋊(C3⋊C8)C2×C412yes—
40C2×C3⋊(C3⋊C8)C2×C412yes—
41C2×C3⋊(C3⋊C8)C2×C412yes—
42#1454—91noSylow
43C42×D3—34no—
44C3×C4×C8C2×D314yes—
45C3×C4×C8C2×D314yes—
46C3×C4×C8C2×D314yes—
47(C2×D3)⋊C8—38no—
48(C2×D3)⋊C8—38no—
49(C2×D3)⋊C8—38no—
50Dic3⋊C8—38no—
51Dic3⋊C8—38no—
52Dic3⋊C8—38no—
53C4×C3⋊C8—34no—
54C4×C3⋊C8—34no—
55C4×C3⋊C8—34no—
56C22×C3⋊D3C4211yescharacteristic
57C2×C32×C4C22×C411yescharacteristic
58C2×C32×C4C22×C411yescharacteristic
59C2×C32×C4C22×C411yescharacteristic
60C2×C3⋊Dic3C4211yescharacteristic
61C2×C3⋊Dic3C4211yescharacteristic
62C2×C3⋊Dic3C4211yescharacteristic
63C4×C3⋊D3—22no—
64C4×C3⋊D3—22no—
65C4×C3⋊D3—22no—
66C32×C8—22no—
67C32×C8—22no—
68C32×C8—22no—
69C3⋊(C3⋊C8)—22no—
70C3⋊(C3⋊C8)—22no—
71C3⋊(C3⋊C8)—22no—
72#431—91no—
73#431—91no—
74#431—91no—
75#322—91no—
76#322—91no—
77#322C3⋊D311yescharacteristic, complemented
78C82—91no—
79C2×C4×D3—34no—
80C2×C4×D3—34no—
81C2×C4×D3—34no—
82C2×C3×C8C4×D318yes—
83C2×C3×C8C4×D318yes—
84C2×C3×C8C4×D318yes—
85C3×C42C22×D314yes—
86C4×Dic3—34no—
87C4×Dic3—34no—
88C4×Dic3—34no—
89C2×C3⋊C8—38no—
90C2×C3⋊C8—38no—
91C2×C3⋊C8—38no—
92C22×C32C2×C4211yescharacteristic
93C2×C3⋊D3—21no—
94C2×C3⋊D3—21no—
95C2×C3⋊D3—21no—
96C32×C4#13112yes—
97C32×C4#13112yes—
98C32×C4#13112yes—
99C3⋊Dic3—21no—
100C3⋊Dic3—21no—
101C3⋊Dic3—21no—
102C2×C42—91no—
103C4⋊C8—92no—
104C4⋊C8—92no—
105C4⋊C8—92no—
106C22⋊C8—92no—
107C22⋊C8—92no—
108C22⋊C8—92no—
109C4×C8—91no—
110C4×C8—91no—
111C4×C8—91no—
112C4×C8C2×C3⋊D311yescharacteristic
113C4×C8C2×C3⋊D311yescharacteristic
114C4×C8C2×C3⋊D311yescharacteristic
115C22×D3—34no—
116C2×C3×C4C2×C4×D314yes—
117C2×C3×C4C2×C4×D314yes—
118C2×C3×C4C2×C4×D314yes—
119C2×Dic3—34no—
120C2×Dic3—34no—
121C2×Dic3—34no—
122C4×D3—68no—
123C4×D3—68no—
124C4×D3—68no—
125C3×C8—28no—
126C3×C8—28no—
127C3×C8—28no—
128C3⋊C8—68no—
129C3⋊C8—68no—
130C3⋊C8—68no—
131C2×C32#40511yescharacteristic
132C2×C32#40511yescharacteristic
133C2×C32#40511yescharacteristic
134C3⋊D3—41no—
135C22×C4—91no—
136C22×C4—91no—
137C22×C4—91no—
138C2×C8—92no—
139C2×C8—92no—
140C2×C8—92no—
141C2×C8C4×C3⋊D312yes—
142C2×C8C4×C3⋊D312yes—
143C2×C8C4×C3⋊D312yes—
144C42—91no—
145C42—91no—
146C42—91no—
147C42C22×C3⋊D311yescharacteristic
148C22×C3C42×D314yes—
149C2×D3—64no—
150C2×D3—64no—
151C2×D3—64no—
152C3×C4#90118yes—
153C3×C4#90718yes—
154C3×C4#90718yes—
155Dic3—64no—
156Dic3—64no—
157Dic3—64no—
158C32#145411yescharacteristic, complemented, Sylow
159C23—91no—
160C2×C4—91no—
161C2×C4—91no—
162C2×C4—91no—
163C2×C4—182no—
164C2×C4—182no—
165C2×C4—182no—
166C2×C4C2×C4×C3⋊D311yescharacteristic
167C2×C4C2×C4×C3⋊D311yescharacteristic
168C2×C4C2×C4×C3⋊D311yescharacteristic
169C8—22no—
170C8—22no—
171C8—22no—
172C8—182no—
173C8—182no—
174C8—182no—
175C2×C3#468914yes—
176C2×C3#470814yes—
177C2×C3#470814yes—
178D3—124no—
179C22—181no—
180C22—181no—
181C22—181no—
182C22C42×C3⋊D311yescharacteristic
183C4—181no—
184C4—181no—
185C4—181no—
186C4#6411012yes—
187C4#6411612yes—
188C4#6411612yes—
189C3#6807414yescomplemented
190C2—361no—
191C2#1059238811yescharacteristic
192C2#1059240711yescharacteristic
193C2#1059240711yescharacteristic
subgroupG/H
center, FrattiniC42C22×C3⋊D3
commutator, socleC22×C32C2×C42
FittingC32×#322C2
prime radicalC22×C3⋊D3C42
cosocleC32×C42C23
hypercenter#322C3⋊D3
hypocenterC32#1454
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C42 ◁ #322

Complements

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

NH ≅ G/Ntype
4. C32×#322C2semidirect
5. #10589321C2semidirect
6. #10589320C2semidirect
7. C8×C3⋊(C3⋊C8)C2semidirect
25. C3×#322D3semidirect
77. #322C3⋊D3semidirect
158. C32#1454semidirect
189. C3#68074semidirect

Maximal subgroups

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

subgroupindex
#105923842
C32×#3222
#105893212
#105893202
C8×C3⋊(C3⋊C8)2
#680743