Finite Group Databasebeta

← #11797364

Subgroups — #11797364

Order 1152.

341 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 341 conjugacy classes of subgroups — too many to draw. Only its 102 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#10592800C211yesmaximal, characteristic
2C3×#4549C212yesmaximal
3#10589133C212yesmaximal, complemented
4#10589104C211yesmaximal, characteristic, complemented
5#10589102C211yesmaximal, characteristic, complemented
6#69094—32nomaximal
7C22×C32×C8C2211yescharacteristic
8#64135C411yescharacteristic
9C2×#3748C411yescharacteristic
10#63642C411yescharacteristic
11#63642C411yescharacteristic
12C8×C3⋊Dic3C2211yescharacteristic
13C8×C3⋊Dic3C2211yescharacteristic
14C2×C3×C3⋊C16C2212yes—
15C2×C3×C3⋊C16C2212yes—
16#5101—32no—
17#5101—61no—
18C3×C22⋊C16—32no—
19#4549D312yes—
20#4502—32no—
21Dic3⋊C16—32no—
22Dic3⋊C16—32no—
23Dic3×C16—32no—
24C22×C32×C4C2×C411yescharacteristic
25C2×C32×C8—22no—
26C2×C32×C8C2×C411yescharacteristic
27C2×C32×C8C2311yescharacteristic
28#3757C812yes—
29C4⋊(C3⋊Dic3)C812yes—
30C4×C3⋊Dic3C2×C411yescharacteristic
31C4×C3⋊Dic3C2×C411yescharacteristic
32#3748—22no—
33C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
34C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
35C3×C3⋊C16—22no—
36C3×C3⋊C16—22no—
37#2164—91noSylow
38C22×C3×C8—21no—
39C22×C3×C8C2×D312yes—
40#926—32no—
41#926—61no—
42C2×#208—32no—
43C2×#208—61no—
44C2×C3×C16—32no—
45C2×C3×C16—32no—
46#815—32no—
47#815—32no—
48#815—61no—
49#815—61no—
50C8×Dic3—32no—
51C8×Dic3—32no—
52C8×Dic3—61no—
53C8×Dic3—61no—
54C2×C3⋊C16C2×D312yes—
55C2×C3⋊C16C2×D312yes—
56C23×C32C2×C811yescharacteristic
57C2×C32×C4—21no—
58C2×C32×C4—21no—
59C2×C32×C4C2×C811yescharacteristic
60C2×C32×C4C22×C411yescharacteristic
61C2×C3⋊Dic3C2×C812yes—
62C2×C3⋊Dic3C2×C812yes—
63C32×C8—21no—
64C32×C8#4112yes—
65C3⋊(C3⋊C8)—21no—
66C3⋊(C3⋊C8)M1612yes—
67#405—91no—
68C4⋊C16—92no—
69C22⋊C16—32no—
70#346—91no—
71C4×C16—91no—
72C22×C3×C4—21no—
73C22×C3×C4C4×D312yes—
74C2×C3×C8—24no—
75C2×C3×C8—22no—
76C2×C3×C8—22no—
77C2×C3×C8—21no—
78C2×C3×C8—21no—
79C2×C3×C8C4×D312yes—
80C2×C3×C8C22×D312yes—
81#217—32no—
82#217—32no—
83#217—62no—
84C4⋊Dic3—32no—
85C4⋊Dic3—32no—
86C4⋊Dic3—62no—
87C4×Dic3—32no—
88C4×Dic3—32no—
89C4×Dic3—61no—
90C4×Dic3—61no—
91#208—64no—
92#208—64no—
93C2×C3⋊C8—32no—
94C2×C3⋊C8—32no—
95C2×C3⋊C8—61no—
96C2×C3⋊C8—61no—
97C3×C16—62no—
98C3×C16—62no—
99C3⋊C16—22no—
100C3⋊C16—22no—
101C22×C32—21no—
102C22×C32—22no—
103C22×C32C22×C811yescharacteristic
104C32×C4—21no—
105C32×C4#11711yescharacteristic
106C32×C4C2×M1611yescharacteristic
107C3⋊Dic3—22no—
108C3⋊Dic3—22no—
109C2×M16—91no—
110C22×C8D3211yescharacteristic
111#117—91no—
112C2×C16—32no—
113C2×C16—32no—
114#97—91no—
115#97—91no—
116C4×C8—91no—
117C4×C8—91no—
118C23×C3—21no—
119C23×C3D3×C812yes—
120C2×C3×C4—22no—
121C2×C3×C4—22no—
122C2×C3×C4—22no—
123C2×C3×C4—22no—
124C2×C3×C4—21no—
125C2×C3×C4—21no—
126C2×C3×C4D3×C812yes—
127C2×C3×C4C2×C4×D312yes—
128C2×Dic3—32no—
129C2×Dic3—32no—
130C2×Dic3—32no—
131C2×Dic3—32no—
132C2×Dic3—62no—
133C2×Dic3—62no—
134C3×C8—22no—
135C3×C8—22no—
136C3×C8—22no—
137C3×C8#23712yes—
138C3×C8#23712yes—
139C3⋊C8—34no—
140C3⋊C8—62no—
141C3⋊C8—62no—
142C3⋊C8—62no—
143C2×C32—41no—
144C2×C32#43111yescharacteristic
145C2×C32#50412yes—
146C22×C4#62411yescharacteristic
147M16—182no—
148C2×C8—22no—
149C2×C8—91no—
150C2×C8—91no—
151C2×C8#62411yescharacteristic
152C2×C8C2×D3211yescharacteristic
153C4⋊C4—92no—
154C22⋊C4—92no—
155C42—91no—
156C42—91no—
157C16—62no—
158C16—62no—
159C22×C3—22no—
160C22×C3—22no—
161C22×C3—22no—
162C22×C3—22no—
163C22×C3—21no—
164C22×C3—42no—
165C22×C3C2×D3×C812yes—
166C3×C4—22no—
167C3×C4—22no—
168C3×C4—21no—
169C3×C4—21no—
170C3×C4#87712yes—
171C3×C4D3×M1612yes—
172Dic3—62no—
173Dic3—62no—
174Dic3—62no—
175Dic3—62no—
176Dic3—122no—
177Dic3—122no—
178C32#216411yescharacteristic, complemented, Sylow
179C23#371011yescharacteristic
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—92no—
183C2×C4—92no—
184C2×C4#371011yescharacteristic
185C2×C4C2×#62411yescharacteristic
186C8—21no—
187C8—92no—
188C8—181no—
189C8#380512yes—
190C2×C3—21no—
191C2×C3—22no—
192C2×C3—42no—
193C2×C3—42no—
194C2×C3#471812yes—
195C2×C3#490112yes—
196C2×C3#490712yes—
197C22—21no—
198C22—22no—
199C22C2×#371011yescharacteristic
200C4—21no—
201C4—182no—
202C4—182no—
203C4#6381811yescharacteristic
204C4#6395711yescharacteristic
205C3—21no—
206C3#6909412yescomplemented
207C2—41no—
208C2#1059062412yes—
209C2#1059106111yescharacteristic
subgroupG/H
center, FrattiniC2×C8C2×D32
commutator, socleC22×C32C22×C8
FittingC22×C32×C8C22
prime radicalC23×C32C2×C8
cosocleC2×C32×C8C23
hypercenterC22×C8D32
hypocenterC32#2164
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
5. #10589102C2semidirect
178. C32#2164semidirect
206. C3#69094semidirect

Maximal subgroups

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

subgroupindex
#105928002
C3×#45492
#105891332
#105891042
#105891022
#690943