Finite Group Databasebeta

← #11797332

Subgroups — #11797332

Order 1152.

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

normal subgroups only

This group has 385 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
1C2×C8×C3⋊Dic3C211yesmaximal, characteristic
2C3×#4549C212yesmaximal
3#10589133C212yesmaximal, complemented
4#10589104C212yesmaximal, complemented
5#69093—32nomaximal
6C22×C32×C8C2211yescharacteristic
7C2×C4×C3⋊Dic3C411yescharacteristic
8C22×C3⋊(C3⋊C8)C411yescharacteristic
9C8×C3⋊Dic3C411yescharacteristic
10C8×C3⋊Dic3C411yescharacteristic
11C8×C3⋊Dic3C2211yescharacteristic
12C8×C3⋊Dic3C2211yescharacteristic
13C2×C3×C3⋊C16C2214yes—
14C2×C8×Dic3—32no—
15C2×C8×Dic3—61no—
16C3×C22⋊C16—32no—
17#4549D312yes—
18#4502—34no—
19Dic3⋊C16—34no—
20C22×C32×C4C2×C411yescharacteristic
21C22×C3⋊Dic3C811yescharacteristic
22C22×C3⋊Dic3C811yescharacteristic
23C2×C32×C8—22no—
24C2×C32×C8C2×C411yescharacteristic
25C2×C32×C8C2311yescharacteristic
26C4×C3⋊Dic3C811yescharacteristic
27C4×C3⋊Dic3C811yescharacteristic
28C4×C3⋊Dic3C2×C411yescharacteristic
29C4×C3⋊Dic3C2×C411yescharacteristic
30C2×C3⋊(C3⋊C8)—22no—
31C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
32C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
33C3×C3⋊C16—24no—
34#2163—91noSylow
35C22×C3×C8—21no—
36C22×C3×C8C2×D312yes—
37C2×C4×Dic3—32no—
38C2×C4×Dic3—61no—
39C22×C3⋊C8—32no—
40C22×C3⋊C8—61no—
41C2×C3×C16—34no—
42C8×Dic3—32no—
43C8×Dic3—32no—
44C8×Dic3—32no—
45C8×Dic3—32no—
46C8×Dic3—61no—
47C8×Dic3—61no—
48C8×Dic3—61no—
49C8×Dic3—61no—
50C2×C3⋊C16C2×D314yes—
51C23×C32C2×C811yescharacteristic
52C2×C32×C4—21no—
53C2×C32×C4—21no—
54C2×C32×C4C2×C811yescharacteristic
55C2×C32×C4C22×C411yescharacteristic
56C2×C3⋊Dic3—22no—
57C2×C3⋊Dic3—22no—
58C2×C3⋊Dic3C2×C811yescharacteristic
59C2×C3⋊Dic3C2×C811yescharacteristic
60C2×C3⋊Dic3C2×C811yescharacteristic
61C2×C3⋊Dic3C2×C811yescharacteristic
62C32×C8—21no—
63C32×C8#4112yes—
64C3⋊(C3⋊C8)—21no—
65C3⋊(C3⋊C8)M1612yes—
66C2×C4×C8—91no—
67C4⋊C16—92no—
68C22⋊C16—32no—
69#346—92no—
70C22×C3×C4—21no—
71C22×C3×C4C4×D312yes—
72C22×Dic3—32no—
73C22×Dic3—32no—
74C22×Dic3—61no—
75C22×Dic3—61no—
76C2×C3×C8—24no—
77C2×C3×C8—24no—
78C2×C3×C8—21no—
79C2×C3×C8—21no—
80C2×C3×C8C4×D312yes—
81C2×C3×C8C22×D312yes—
82C4×Dic3—32no—
83C4×Dic3—32no—
84C4×Dic3—32no—
85C4×Dic3—32no—
86C4×Dic3—61no—
87C4×Dic3—61no—
88C4×Dic3—61no—
89C4×Dic3—61no—
90C2×C3⋊C8—32no—
91C2×C3⋊C8—32no—
92C2×C3⋊C8—61no—
93C2×C3⋊C8—61no—
94C2×C3⋊C8—64no—
95C2×C3⋊C8—64no—
96C3×C16—64no—
97C3⋊C16—24no—
98C22×C32—21no—
99C22×C32—21no—
100C22×C32M3212yes—
101C22×C32C22×C811yescharacteristic
102C32×C4—21no—
103C32×C4#11711yescharacteristic
104C32×C4C2×M1611yescharacteristic
105C3⋊Dic3—21no—
106C3⋊Dic3—21no—
107C3⋊Dic3—21no—
108C3⋊Dic3M3212yes—
109C22×C8—91no—
110C22×C8D3211yescharacteristic
111C2×C42—91no—
112C2×C16—34no—
113C4×C8—91no—
114C4×C8—91no—
115C4×C8—91no—
116C4×C8—91no—
117C23×C3—21no—
118C23×C3D3×C812yes—
119C2×C3×C4—22no—
120C2×C3×C4—22no—
121C2×C3×C4—22no—
122C2×C3×C4—22no—
123C2×C3×C4—21no—
124C2×C3×C4—21no—
125C2×C3×C4D3×C812yes—
126C2×C3×C4C2×C4×D312yes—
127C2×Dic3—32no—
128C2×Dic3—32no—
129C2×Dic3—32no—
130C2×Dic3—32no—
131C2×Dic3—61no—
132C2×Dic3—61no—
133C2×Dic3—61no—
134C2×Dic3—61no—
135C2×Dic3—64no—
136C2×Dic3—64no—
137C2×Dic3—64no—
138C2×Dic3—64no—
139C3×C8—22no—
140C3×C8—22no—
141C3×C8—22no—
142C3×C8#23714yes—
143C3⋊C8—34no—
144C3⋊C8—62no—
145C3⋊C8—62no—
146C3⋊C8—62no—
147C2×C32—22no—
148C2×C32#43111yescharacteristic
149C2×C32C2×M3211yescharacteristic
150C2×C32C2×M3211yescharacteristic
151C22×C4—91no—
152C22×C4—91no—
153C22×C4#62411yescharacteristic
154C2×C8—22no—
155C2×C8—91no—
156C2×C8—91no—
157C2×C8—182no—
158C2×C8#62411yescharacteristic
159C2×C8C2×D3211yescharacteristic
160C42—91no—
161C42—91no—
162C42—91no—
163C42—91no—
164C16—64no—
165C22×C3—22no—
166C22×C3—22no—
167C22×C3—22no—
168C22×C3—22no—
169C22×C3—22no—
170C22×C3—21no—
171C22×C3#79814yes—
172C22×C3C2×D3×C812yes—
173C3×C4—22no—
174C3×C4—22no—
175C3×C4—21no—
176C3×C4—21no—
177C3×C4#87712yes—
178C3×C4D3×M1612yes—
179Dic3—34no—
180Dic3—62no—
181Dic3—62no—
182Dic3—62no—
183Dic3—62no—
184Dic3—62no—
185Dic3—62no—
186Dic3—62no—
187C32#216311yescharacteristic, complemented, Sylow
188C23#371011yescharacteristic
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—91no—
192C2×C4—91no—
193C2×C4—91no—
194C2×C4—91no—
195C2×C4—182no—
196C2×C4—182no—
197C2×C4#371011yescharacteristic
198C2×C4C2×#62411yescharacteristic
199C8—21no—
200C8—92no—
201C8—181no—
202C8#380512yes—
203C2×C3—24no—
204C2×C3—24no—
205C2×C3—21no—
206C2×C3—21no—
207C2×C3—21no—
208C2×C3#471812yes—
209C2×C3C2×#79812yes—
210C2×C3D3×M3212yes—
211C22—21no—
212C22—21no—
213C22#6354412yes—
214C22C2×#371011yescharacteristic
215C4—21no—
216C4—92no—
217C4—181no—
218C4—181no—
219C4—181no—
220C4#6381811yescharacteristic
221C4#6395711yescharacteristic
222C3—21no—
223C3#6909312yescomplemented
224C2—22no—
225C2#1059062511yescharacteristic
226C2C2×#6354411yescharacteristic
227C2#1059106111yescharacteristic
subgroupG/H
center, FrattiniC2×C8C2×D32
commutator, socleC22×C32C22×C8
FittingC22×C32×C8C22
prime radicalC23×C32C2×C8
cosocleC2×C32×C8C23
hypercenterC22×C8D32
hypocenterC32#2163
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. #10589133C2semidirect
4. #10589104C2semidirect
187. C32#2163semidirect
223. C3#69093semidirect

Maximal subgroups

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

subgroupindex
C2×C8×C3⋊Dic32
C3×#45492
#105891332
#105891042
#690933