Finite Group Databasebeta

← #11771480

Subgroups — #11771480

Order 1152.

361 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 361 conjugacy classes of subgroups — too many to draw. Only its 66 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#10592674C211yesmaximal, characteristic
2C3×#4528C212yesmaximal
3#67453—32nomaximal
4C2×C32×C4⋊C4C2211yescharacteristic
5C2×C4⋊(C3⋊Dic3)C411yescharacteristic
6C2×#3750—22no—
7C2×C4×C3⋊Dic3C411yescharacteristic
8C3×#830—22no—
9#4975—32no—
10#4975—61no—
11C3×#324—32no—
12#4528D312yes—
13C22×C32×C4C2×C411yescharacteristic
14C22×C32×C4D412yes—
15C22×C3⋊Dic3—21no—
16C22×C3⋊Dic3—21no—
17C32×C4⋊C4—41no—
18C4⋊(C3⋊Dic3)—41no—
19#3750—44no—
20C4×C3⋊Dic3—21no—
21C4×C3⋊Dic3C812yescomplemented
22C2×C3×C3⋊C8—42no—
23#1325—91noSylow
24C2×C3×C4⋊C4—21no—
25C2×C3×C4⋊C4C2×D312yes—
26C2×C4⋊Dic3—32no—
27C2×C4⋊Dic3—61no—
28C2×Dic3⋊C4—64no—
29C2×Dic3⋊C4—62no—
30C2×Dic3⋊C4—62no—
31C2×C4×Dic3—32no—
32C2×C4×Dic3—61no—
33C3×C22⋊C8—62no—
34#830—22no—
35C23×C32C22⋊C411yescharacteristic
36C2×C32×C4—21no—
37C2×C32×C4—21no—
38C2×C32×C4—22no—
39C2×C32×C4—42no—
40C2×C32×C4C2×C811yescharacteristic
41C2×C32×C4M1611yescharacteristic
42C2×C3⋊Dic3—22no—
43C2×C3⋊Dic3—22no—
44C2×C3⋊Dic3—22no—
45C2×C3⋊Dic3—42no—
46C2×C3⋊Dic3—41no—
47C3×C3⋊C8—82no—
48#384—91no—
49#324—32no—
50C22×C3×C4—21no—
51C22×C3×C4—22no—
52C22×C3×C4C4×D312yes—
53C22×C3×C4D1212yes—
54C22×C3×C4#6712yes—
55C22×Dic3—62no—
56C22×Dic3—62no—
57C22×Dic3—62no—
58C22×Dic3—62no—
59C2×C3×C8—122no—
60C3×C4⋊C4—42no—
61C3×C4⋊C4—42no—
62C4⋊Dic3—122no—
63C4⋊Dic3—122no—
64Dic3⋊C4—124no—
65Dic3⋊C4—124no—
66Dic3⋊C4—128no—
67C4×Dic3—34no—
68C4×Dic3—62no—
69C4×Dic3—62no—
70C4×Dic3—62no—
71C2×C3⋊C8—42no—
72C22×C32—21no—
73C22×C32—21no—
74C22×C32C22⋊C811yescharacteristic
75C22×C32#9911yescharacteristic
76C22×C32#10111yescharacteristic
77C32×C4—21no—
78C32×C4—21no—
79C32×C4—42no—
80C3⋊Dic3—24no—
81C3⋊Dic3—81no—
82C2×C4⋊C4—91no—
83C2×C4⋊C4—182no—
84C2×C4⋊C4D3211yescharacteristic
85C2×C42—91no—
86C22⋊C8—62no—
87C23×C3—21no—
88C23×C3(C2×D3)⋊C412yes—
89C2×C3×C4—22no—
90C2×C3×C4—22no—
91C2×C3×C4—22no—
92C2×C3×C4—22no—
93C2×C3×C4—22no—
94C2×C3×C4—22no—
95C2×C3×C4—21no—
96C2×C3×C4—21no—
97C2×C3×C4—42no—
98C2×C3×C4—42no—
99C2×C3×C4—42no—
100C2×C3×C4—44no—
101C2×C3×C4D3×C812yes—
102C2×C3×C4ΓL(1,𝔽25)12yes—
103C2×Dic3—64no—
104C2×Dic3—64no—
105C2×Dic3—64no—
106C2×Dic3—64no—
107C2×Dic3—64no—
108C2×Dic3—64no—
109C2×Dic3—124no—
110C2×Dic3—122no—
111C2×Dic3—122no—
112C2×Dic3—122no—
113C2×Dic3—122no—
114C3×C8—242no—
115C3⋊C8—82no—
116C2×C32—21no—
117C2×C32—21no—
118C2×C32#32411yescharacteristic
119C2×C32#35311yescharacteristic
120C2×C32#35611yescharacteristic
121C22×C4—181no—
122C22×C4—181no—
123C22×C4#62411yescharacteristic
124C22×C4#62612yes—
125C2×C8—122no—
126C4⋊C4—41no—
127C4⋊C4—361no—
128C4⋊C4—364no—
129C42—92no—
130C42—181no—
131C22×C3—22no—
132C22×C3—22no—
133C22×C3—22no—
134C22×C3—22no—
135C22×C3—21no—
136C22×C3—21no—
137C22×C3—21no—
138C22×C3#80612yes—
139C22×C3(C2×D3)⋊C812yes—
140C22×C3#82412yes—
141C3×C4—22no—
142C3×C4—22no—
143C3×C4—22no—
144C3×C4—22no—
145C3×C4—42no—
146C3×C4—42no—
147C3×C4—82no—
148Dic3—68no—
149Dic3—68no—
150Dic3—242no—
151Dic3—242no—
152C32#132511yescharacteristic, complemented, Sylow
153C23#372211yescharacteristic
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—42no—
158C2×C4—182no—
159C2×C4—182no—
160C2×C4—182no—
161C2×C4—362no—
162C2×C4—361no—
163C2×C4#371011yescharacteristic
164C2×C4#371211yescharacteristic
165C8—242no—
166C2×C3—22no—
167C2×C3—22no—
168C2×C3—22no—
169C2×C3—22no—
170C2×C3—21no—
171C2×C3—21no—
172C2×C3—21no—
173C2×C3#446912yes—
174C2×C3#447412yes—
175C2×C3#447812yes—
176C22—21no—
177C22—21no—
178C22#6355711yescharacteristic
179C22#6356111yescharacteristic
180C22#6358111yescharacteristic
181C4—21no—
182C4—21no—
183C4—42no—
184C4—184no—
185C4—721no—
186C3—21no—
187C3#6745312yescomplemented
188C2—21no—
189C2—21no—
190C2#1058914811yescharacteristic
191C2#1058917911yescharacteristic
192C2#1058918511yescharacteristic
subgroupG/H
centerC22#63581
commutatorC2×C32×C4C2×C8
Frattini, hypercenterC2×C4⋊C4D32
Fitting, cosocleC2×C32×C4⋊C4C22
socleC22×C32#99
prime radicalC23×C32C22⋊C4
hypocenterC32#1325
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
21. C4×C3⋊Dic3C8semidirect
152. C32#1325semidirect
187. C3#67453semidirect

Maximal subgroups

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

subgroupindex
#105926742
C3×#45282
#674533