Finite Group Databasebeta

← #11797027

Subgroups — #11797027

Order 1152.

369 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 369 conjugacy classes of subgroups — too many to draw. Only its 110 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
1C2×C16×C3⋊D3C211yesmaximal, characteristic
2#10590700C211yesmaximal, characteristic
3C2×#63544C211yesmaximal, characteristic
4C3×Dic3⋊C16C212yesmaximal, complemented
5Dic3⋊(C3⋊C16)C212yesmaximal, complemented
6#69285—32nomaximal
7C2×C8×C3⋊D3C2211yescharacteristic
8#63874C411yescharacteristic
9C2×#3712C411yescharacteristic
10C2×C32×C16C2211yescharacteristic
11C2×C3⋊(C3⋊C16)C2211yescharacteristic
12C16×C3⋊D3—22no—
13C3×C8×Dic3C2212yes—
14C2×C3×C3⋊C16C2212yes—
15#63554C412yes—
16#63544—22no—
17C2×#798—32no—
18C2×D3×C16—32no—
19C2×D3×C16—61no—
20#4689—32no—
21C3×C4⋊C16—32no—
22Dic3⋊C16—32no—
23Dic3⋊C16D312yescomplemented
24C4⋊(C3⋊C16)—32no—
25C2×C4×C3⋊D3C2×C411yescharacteristic
26C2×C32×C8C2311yescharacteristic
27C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
28C8×C3⋊D3D412yes—
29C8×C3⋊D3Q812yes—
30C3×C4×Dic3C2×C412yes—
31C2×C3×C3⋊C8C2×C412yes—
32#3724C811yescharacteristic
33#3724C811yescharacteristic
34#3722C812yes—
35#3712—22no—
36C32×C16—21no—
37C3⋊(C3⋊C16)—21no—
38C3×C3⋊C16—22no—
39#2151—91noSylow
40C2×ΓL(1,𝔽25)—32no—
41C2×D3×C8—32no—
42C2×D3×C8—61no—
43#872—32no—
44C2×C3×C16—21no—
45C2×C3×C16—32no—
46C2×C3×C16C2×D312yes—
47C3×C4×C8—32no—
48#815—32no—
49C8×Dic3C2×D312yes—
50C2×C3⋊C16—32no—
51C2×C3⋊C16—61no—
52C2×C3⋊C16C2×D312yes—
53#803—32no—
54#798—64no—
55D3×C16—64no—
56D3×C16—64no—
57C22×C3⋊D3C2×C811yescharacteristic
58C2×C32×C4C22×C411yescharacteristic
59C2×C3⋊Dic3C2×C811yescharacteristic
60C4×C3⋊D3C4⋊C412yes—
61C4×C3⋊D3M1612yes—
62C2×C3×Dic3C2×C812yes—
63C2×C3×Dic3C2×C812yes—
64C32×C8C2×D411yescharacteristic
65C32×C8C2×Q811yescharacteristic
66C3⋊(C3⋊C8)C4⋊C412yes—
67C3×C3⋊C8—22no—
68C2×M32—91no—
69C22×C16—91no—
70#405—91no—
71C4⋊C16—32no—
72C4⋊C16—92no—
73C2×C4×D3—32no—
74C2×C4×D3—61no—
75C2×C3×C8—21no—
76C2×C3×C8—32no—
77C2×C3×C8C22×D312yes—
78C3×C42—32no—
79(C2×D3)⋊C4—32no—
80(C2×D3)⋊C4—32no—
81Dic3⋊C4—32no—
82Dic3⋊C4—32no—
83C4×Dic3C4×D312yes—
84C2×C3⋊C8—32no—
85C2×C3⋊C8—61no—
86C2×C3⋊C8C4×D312yes—
87ΓL(1,𝔽25)—64no—
88D3×C8—34no—
89D3×C8—34no—
90D3×C8—62no—
91D3×C8—62no—
92C3×C16—22no—
93C3×C16—22no—
94C3×C16—62no—
95C3⋊C16—22no—
96C3⋊C16—62no—
97C3⋊C16—62no—
98C22×C32C22×C811yescharacteristic
99C2×C3⋊D3—21no—
100C2×C3⋊D3—21no—
101C2×C3⋊D3C4⋊C812yes—
102C32×C4C2×C4⋊C411yescharacteristic
103C32×C4C2×M1611yescharacteristic
104C3⋊Dic3C4⋊C812yes—
105C3×Dic3—22no—
106C3×Dic3—22no—
107C2×M16—91no—
108C22×C8—91no—
109#117—91no—
110M32—182no—
111C2×C16—32no—
112C2×C16—91no—
113C2×C16—182no—
114C2×C16D3211yescharacteristic
115#97—92no—
116C4×C8—32no—
117C22×D3—32no—
118C22×D3—61no—
119C2×C3×C4—21no—
120C2×C3×C4—32no—
121C2×C3×C4—32no—
122C2×C3×C4C2×C4×D312yes—
123C2×Dic3—32no—
124C2×Dic3—61no—
125C2×Dic3D3×C812yes—
126C2×Dic3D3×C812yes—
127C4×D3—34no—
128C4×D3—34no—
129C4×D3—62no—
130C4×D3—62no—
131C3×C8—21no—
132C3×C8—21no—
133C3×C8—62no—
134C3×C8D3×D412yes—
135C3×C8D3×Q812yes—
136C3⋊C8—22no—
137C3⋊C8—34no—
138C3⋊C8—62no—
139C2×C32C2×C4⋊C811yescharacteristic
140C2×C32#50411yescharacteristic
141C2×C32#50411yescharacteristic
142C3⋊D3—22no—
143C22×C4—91no—
144M16—182no—
145C2×C8—32no—
146C2×C8—91no—
147C2×C8—92no—
148C2×C8—92no—
149C2×C8C2×D3211yescharacteristic
150C4⋊C4—91no—
151C4⋊C4—91no—
152C22⋊C4—92no—
153C42—32no—
154C16—21no—
155C16—62no—
156C16—181no—
157C22×C3—21no—
158C22×C3C2×D3×C812yes—
159C2×D3—34no—
160C2×D3—62no—
161C2×D3—62no—
162C2×D3—62no—
163C2×D3—62no—
164C2×D3—62no—
165C3×C4—21no—
166C3×C4—21no—
167C3×C4—62no—
168C3×C4—62no—
169C3×C4D3×C4⋊C412yes—
170C3×C4D3×M1612yes—
171Dic3—22no—
172Dic3—22no—
173Dic3—34no—
174Dic3—62no—
175C32#215111yescharacteristic, complemented, Sylow
176C23—91no—
177C2×C4—32no—
178C2×C4—32no—
179C2×C4—91no—
180C2×C4—92no—
181C2×C4—92no—
182C2×C4C4×D3211yescharacteristic
183C8—62no—
184C8—92no—
185C8#379711yescharacteristic
186C8#381111yescharacteristic
187C2×C3—21no—
188C2×C3—21no—
189C2×C3—21no—
190C2×C3D3×C4⋊C812yes—
191C2×C3#490112yes—
192C2×C3#490712yes—
193D3—64no—
194D3—64no—
195C22—92no—
196C22—181no—
197C22—181no—
198C22D32×C811yescharacteristic
199C4—62no—
200C4—62no—
201C4—92no—
202C4#6379111yescharacteristic
203C4#6388311yescharacteristic
204C3—21no—
205C3#6928512yescomplemented
206C2—182no—
207C2#1059022711yescharacteristic
208C2#1059022911yescharacteristic
209C2#1059065811yescharacteristic
subgroupG/H
center, FrattiniC2×C8C2×D32
commutator, socleC22×C32C22×C8
FittingC2×C32×C16C22
prime radicalC22×C3⋊D3C2×C8
cosocleC2×C32×C8C23
hypercenterC2×C16D32
hypocenterC32#2151
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
4. C3×Dic3⋊C16C2semidirect
5. Dic3⋊(C3⋊C16)C2semidirect
23. Dic3⋊C16D3semidirect
175. C32#2151semidirect
205. C3#69285semidirect

Maximal subgroups

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

subgroupindex
C2×C16×C3⋊D32
#105907002
C2×#635442
C3×Dic3⋊C162
Dic3⋊(C3⋊C16)2
#692853