Finite Group Databasebeta

← #11773644

Subgroups — #11773644

Order 1152.

570 conjugacy classes of subgroups; only the 193 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 193 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
1C4×#3743C211yesmaximal, characteristic
2#10592384C211yesmaximal, characteristic
3#10592384C211yesmaximal, characteristic
4C32×#322C211yesmaximal, characteristic, complemented
5#10589320C211yesmaximal, characteristic, complemented
6#10589320C211yesmaximal, characteristic, complemented
7C8×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#68072—34nomaximal
9C2×#3743C412yes—
10C42×C3⋊D3C2211yescharacteristic
11C32×C4×C8C2211yescharacteristic
12C32×C4×C8C2211yescharacteristic
13C32×C4×C8C2211yescharacteristic
14#63647C412yes—
15#63647C412yes—
16#63642C412yes—
17#63641C412yes—
18#63641C412yes—
19C4×C3⋊(C3⋊C8)C2211yescharacteristic
20C4×C3⋊(C3⋊C8)C2211yescharacteristic
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C4×ΓL(1,𝔽25)—34no—
23#4685—34no—
24#4685—34no—
25C3×#322D314yescomplemented
26#4454—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#3743—24no—
43#1453—91noSylow
44C2×ΓL(1,𝔽25)—38no—
45C42×D3—34no—
46C3×C4×C8C2×D314yes—
47C3×C4×C8C2×D314yes—
48C3×C4×C8C2×D314yes—
49(C2×D3)⋊C8—38no—
50(C2×D3)⋊C8—38no—
51#815—38no—
52Dic3⋊C8—38no—
53Dic3⋊C8—38no—
54C4×C3⋊C8—34no—
55C4×C3⋊C8—34no—
56C4×C3⋊C8—34no—
57C22×C3⋊D3C4211yescharacteristic
58C2×C32×C4C22×C411yescharacteristic
59C2×C32×C4C22×C411yescharacteristic
60C2×C32×C4C22×C411yescharacteristic
61C2×C3⋊Dic3C4211yescharacteristic
62C2×C3⋊Dic3C4211yescharacteristic
63C2×C3⋊Dic3C4211yescharacteristic
64C4×C3⋊D3—22no—
65C4×C3⋊D3—22no—
66C4×C3⋊D3—22no—
67C32×C8—22no—
68C32×C8—22no—
69C32×C8—22no—
70C3⋊(C3⋊C8)—22no—
71C3⋊(C3⋊C8)—22no—
72C3⋊(C3⋊C8)M1614yes—
73#431—91no—
74#431—91no—
75C4×M16—91no—
76#322—91no—
77#322—91no—
78#322C3⋊D311yescharacteristic, complemented
79C82—91no—
80C2×C4×D3—34no—
81C2×C4×D3—34no—
82C2×C4×D3—34no—
83C2×C3×C8C4×D318yes—
84C2×C3×C8C4×D318yes—
85C2×C3×C8C4×D318yes—
86C3×C42C22×D314yes—
87C4×Dic3—34no—
88C4×Dic3—34no—
89C4×Dic3—34no—
90C2×C3⋊C8—38no—
91C2×C3⋊C8—38no—
92C2×C3⋊C8—38no—
93ΓL(1,𝔽25)—616no—
94C22×C32C2×C4211yescharacteristic
95C2×C3⋊D3—21no—
96C2×C3⋊D3—21no—
97C2×C3⋊D3—21no—
98C32×C4C2×M1612yes—
99C32×C4#13112yes—
100C32×C4#13112yes—
101C3⋊Dic3—21no—
102C3⋊Dic3—21no—
103C3⋊Dic3—21no—
104C2×M16—92no—
105C2×C42—91no—
106C4⋊C8—92no—
107C4⋊C8—92no—
108C22⋊C8—92no—
109C22⋊C8—92no—
110#97—92no—
111C4×C8—91no—
112C4×C8—91no—
113C4×C8—91no—
114C4×C8C2×C3⋊D311yescharacteristic
115C4×C8C2×C3⋊D311yescharacteristic
116C4×C8C2×C3⋊D311yescharacteristic
117C22×D3—34no—
118C2×C3×C4C2×C4×D314yes—
119C2×C3×C4C2×C4×D314yes—
120C2×C3×C4C2×C4×D314yes—
121C2×Dic3—34no—
122C2×Dic3—34no—
123C2×Dic3—34no—
124C4×D3—68no—
125C4×D3—68no—
126C4×D3—68no—
127C3×C8—28no—
128C3×C8—28no—
129C3×C8—28no—
130C3⋊C8—316no—
131C3⋊C8—68no—
132C3⋊C8—68no—
133C2×C32C4×M1611yescharacteristic
134C2×C32#40511yescharacteristic
135C2×C32#40511yescharacteristic
136C3⋊D3—41no—
137C22×C4—91no—
138C22×C4—91no—
139C22×C4—91no—
140M16—184no—
141C2×C8—92no—
142C2×C8—92no—
143C2×C8—92no—
144C2×C8C4×C3⋊D312yes—
145C2×C8C4×C3⋊D312yes—
146C2×C8C4×C3⋊D312yes—
147C42—91no—
148C42—91no—
149C42—91no—
150C42C22×C3⋊D311yescharacteristic
151C22×C3C42×D314yes—
152C2×D3—64no—
153C2×D3—64no—
154C2×D3—64no—
155C3×C4#90118yes—
156C3×C4D3×M1618yes—
157C3×C4#90718yes—
158Dic3—64no—
159Dic3—64no—
160Dic3—64no—
161C32#145311yescharacteristic, complemented, Sylow
162C23—91no—
163C2×C4—91no—
164C2×C4—91no—
165C2×C4—91no—
166C2×C4—182no—
167C2×C4—182no—
168C2×C4—182no—
169C2×C4C2×C4×C3⋊D311yescharacteristic
170C2×C4C2×C4×C3⋊D311yescharacteristic
171C2×C4C2×C4×C3⋊D311yescharacteristic
172C8—22no—
173C8—22no—
174C8—22no—
175C8—94no—
176C8—182no—
177C8—182no—
178C2×C3#468914yes—
179C2×C3#470714yes—
180C2×C3#470814yes—
181D3—124no—
182C22—181no—
183C22—181no—
184C22—181no—
185C22C42×C3⋊D311yescharacteristic
186C4—181no—
187C4—181no—
188C4—181no—
189C4#6411012yes—
190C4M16×C3⋊D312yes—
191C4#6411612yes—
192C3#6807214yescomplemented
193C2—361no—
194C2#1059238811yescharacteristic
195C2#1059240611yescharacteristic
196C2#1059240711yescharacteristic
subgroupG/H
center, FrattiniC42C22×C3⋊D3
commutator, socleC22×C32C2×C42
FittingC32×#322C2
prime radicalC22×C3⋊D3C42
cosocleC32×C42C23
hypercenter#322C3⋊D3
hypocenterC32#1453
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. #10589320C2semidirect
6. #10589320C2semidirect
7. C8×C3⋊(C3⋊C8)C2semidirect
25. C3×#322D3semidirect
78. #322C3⋊D3semidirect
161. C32#1453semidirect
192. C3#68072semidirect

Maximal subgroups

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

subgroupindex
C4×#37432
#105923842
C32×#3222
#105893202
C8×C3⋊(C3⋊C8)2
#680723