Finite Group Databasebeta

← #11797452

Subgroups — #11797452

Order 1152.

377 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 377 conjugacy classes of subgroups — too many to draw. Only its 112 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
1C8×#625C211yesmaximal, characteristic
2C2×D3×C3⋊C16C212yesmaximal, complemented
3C16×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C3×(C2×D3)⋊C16C212yesmaximal, complemented
5#10589133C211yesmaximal, characteristic, complemented
6#67⋊C16—32nomaximal
7C2×C3×D3×C8C2212yes—
8C4×#625C411yescharacteristic
9C2×C32×C16C2211yescharacteristic
10C8×C3⋊Dic3C2211yescharacteristic
11C2×C3⋊(C3⋊C16)C2211yescharacteristic
12C2×C3×C3⋊C16C2212yes—
13#63572C411yescharacteristic
14(C2×D3)⋊(C3⋊C8)C412yes—
15D3×C3⋊C16—24no—
16C8×#67—32no—
17C22×C3⋊C16—32no—
18C2×D3×C16—32no—
19C3×C22⋊C16—32no—
20(C2×D3)⋊C16D312yescomplemented
21Dic3⋊C16—32no—
22Dic3×C16—32no—
23Dic3×C16—61no—
24C2×C3×C4×D3C2×C412yes—
25C2×#625C811yescharacteristic
26C2×C32×C8C2311yescharacteristic
27C4×C3⋊Dic3C2×C411yescharacteristic
28C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
29C2×C3×C3⋊C8C2×C412yes—
30C3×D3×C8—22no—
31C3×D3×C8—22no—
32#3724C811yescharacteristic
33(C2×D3)⋊Dic3C812yes—
34C32×C16—21no—
35C3⋊(C3⋊C16)D412yescomplemented
36C3×C3⋊C16—22no—
37D4×C16—91noSylow
38C22×C3×C8—32no—
39C4×#67—32no—
40C2×D3×C8C2×D312yes—
41C2×C3×C16—21no—
42C2×C3×C16—32no—
43C2×C3×C16C2×D312yes—
44#830—32no—
45(C2×D3)⋊C8—32no—
46Dic3⋊C8—32no—
47C8×Dic3—32no—
48C8×Dic3—61no—
49C2×C3⋊C16—32no—
50C2×C3⋊C16—61no—
51C2×C3⋊C16—64no—
52C2×C3⋊C16C2×D312yes—
53D3×C16—64no—
54C22×C3×D3C2×C812yes—
55C2×C32×C4C22×C411yescharacteristic
56C2×C3⋊Dic3C2×C811yescharacteristic
57C2×C3⋊Dic3C2×C811yescharacteristic
58C2×C3×Dic3C2×C812yes—
59C3×C4×D3—22no—
60C3×C4×D3—22no—
61#625C1614yescomplemented
62C32×C8C2×D411yescharacteristic
63C32×C8#4111yescharacteristic
64C3⋊(C3⋊C8)—21no—
65C3×C3⋊C8—22no—
66C22×C16—92no—
67C8×D4—91no—
68C4⋊C16—91no—
69C22⋊C16—32no—
70C4×C16—91no—
71C22×C3×C4—32no—
72C2×#67—32no—
73C2×C4×D3C4×D312yes—
74C2×C3×C8—21no—
75C2×C3×C8—32no—
76C2×C3×C8—62no—
77C2×C3×C8—62no—
78C2×C3×C8C22×D312yes—
79#217—32no—
80(C2×D3)⋊C4—32no—
81Dic3⋊C4—32no—
82C4×Dic3—32no—
83C4×Dic3—61no—
84C2×C3⋊C8—32no—
85C2×C3⋊C8—61no—
86C2×C3⋊C8C4×D312yes—
87D3×C8—22no—
88D3×C8—22no—
89C3×C16—22no—
90C3×C16—22no—
91C3×C16—62no—
92C3⋊C16—22no—
93C3⋊C16—34no—
94C3⋊C16—62no—
95C22×C32C22×C811yescharacteristic
96C2×C3×D3—22no—
97C2×C3×D3—22no—
98C2×C3×D3C2×C1614yescomplemented
99C32×C4C4×D411yescharacteristic
100C32×C4#13111yescharacteristic
101C3⋊Dic3—21no—
102C3⋊Dic3C2×C1612yescomplemented
103C3×Dic3—22no—
104C22×C8—32no—
105C4×D4—91no—
106C2×C16—32no—
107C2×C16—91no—
108C2×C16—184no—
109C2×C16D3211yescharacteristic
110C4⋊C8—91no—
111C22⋊C8—92no—
112C4×C8—91no—
113C23×C3—32no—
114C22×D3D3×C812yes—
115C2×C3×C4—21no—
116C2×C3×C4—32no—
117C2×C3×C4—62no—
118C2×C3×C4—62no—
119C2×C3×C4C2×C4×D312yes—
120#67—38no—
121C2×Dic3—32no—
122C2×Dic3—32no—
123C2×Dic3—61no—
124C2×Dic3—61no—
125C2×Dic3D3×C812yes—
126C4×D3—22no—
127C4×D3—22no—
128C3×C8—21no—
129C3×C8—21no—
130C3×C8—62no—
131C3×C8D3×D412yes—
132C3×C8#23712yes—
133C3⋊C8—22no—
134C3⋊C8—62no—
135C3⋊C8—62no—
136C2×C32C8×D411yescharacteristic
137C2×C32C22×C1611yescharacteristic
138C2×C32#50411yescharacteristic
139C3×D3—24no—
140C2×D4—91no—
141C22×C4—32no—
142C2×C8—32no—
143C2×C8—62no—
144C2×C8—62no—
145C2×C8—91no—
146C2×C8C2×D3211yescharacteristic
147C4⋊C4—91no—
148C22⋊C4—92no—
149C42—91no—
150C16—21no—
151C16—62no—
152C16—92no—
153C22×C3—21no—
154C22×C3—34no—
155C22×C3—62no—
156C22×C3—62no—
157C22×C3C2×D3×C812yes—
158C2×D3—22no—
159C2×D3—22no—
160C2×D3D3×C1614yescomplemented
161C3×C4—21no—
162C3×C4—21no—
163C3×C4—62no—
164C3×C4#67⋊C412yes—
165C3×C4#90712yes—
166Dic3—22no—
167Dic3—34no—
168Dic3—62no—
169Dic3—62no—
170Dic3—62no—
171C32D4×C1611yescharacteristic, complemented, Sylow
172C23—32no—
173D4—94no—
174C2×C4—32no—
175C2×C4—62no—
176C2×C4—62no—
177C2×C4—91no—
178C2×C4—91no—
179C2×C4C4×D3211yescharacteristic
180C8—62no—
181C8—181no—
182C8#380211yescharacteristic
183C8#380511yescharacteristic
184C2×C3—21no—
185C2×C3—21no—
186C2×C3—21no—
187C2×C3—64no—
188C2×C3#67⋊C812yes—
189C2×C3C2×D3×C1612yes—
190C2×C3#490712yes—
191D3—24no—
192C22—34no—
193C22—62no—
194C22—62no—
195C22D32×C811yescharacteristic
196C4—62no—
197C4—92no—
198C4—181no—
199C4#6380511yescharacteristic
200C4#6390211yescharacteristic
201C3—21no—
202C3#67⋊C1612yescomplemented
203C2—64no—
204C2D32×C1611yescharacteristic
205C2#1059022911yescharacteristic
206C2#1059071811yescharacteristic
subgroupG/H
center, FrattiniC2×C8C2×D32
commutatorC2×C32C22×C16
FittingC2×C32×C16C22
socleC22×C32C22×C8
prime radicalC2×#625C8
cosocleC2×C32×C8C23
hypercenterC2×C16D32
hypocenterC32D4×C16
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
2. C2×D3×C3⋊C16C2semidirect
3. C16×C3⋊Dic3C2semidirect
4. C3×(C2×D3)⋊C16C2semidirect
5. #10589133C2semidirect
20. (C2×D3)⋊C16D3semidirect
35. C3⋊(C3⋊C16)D4semidirect
61. #625C16semidirect
98. C2×C3×D3C2×C16semidirect
102. C3⋊Dic3C2×C16semidirect
160. C2×D3D3×C16semidirect
171. C32D4×C16semidirect
202. C3#67⋊C16semidirect

Maximal subgroups

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

subgroupindex
C8×#6252
C2×D3×C3⋊C162
C16×C3⋊Dic32
C3×(C2×D3)⋊C162
#105891332
#67⋊C163