Finite Group Databasebeta

← #11771468

Subgroups — #11771468

Order 1152.

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

normal subgroups only

This group has 313 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#10592676C211yesmaximal, characteristic
2C3×#4528C212yesmaximal
3#67452—32nomaximal
4C2×C32×C4⋊C4C2211yescharacteristic
5C2×C4⋊(C3⋊Dic3)C411yescharacteristic
6C2×C4×C3⋊Dic3C411yescharacteristic
7#63658—22no—
8C3×#830—22no—
9#4977—32no—
10#4977—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—
19C4×C3⋊Dic3—21no—
20C4×C3⋊Dic3C812yescomplemented
21C2×C3×C3⋊C8—42no—
22#1324—91noSylow
23C2×C3×C4⋊C4—21no—
24C2×C3×C4⋊C4C2×D312yes—
25C2×C4⋊Dic3—32no—
26C2×C4⋊Dic3—61no—
27C2×C4×Dic3—32no—
28C2×C4×Dic3—61no—
29C3×C22⋊C8—62no—
30C3⋊#95—64no—
31C3⋊#95—62no—
32C3⋊#95—62no—
33#830—22no—
34C23×C32C22⋊C411yescharacteristic
35C2×C32×C4—21no—
36C2×C32×C4—21no—
37C2×C32×C4—22no—
38C2×C32×C4—42no—
39C2×C32×C4C2×C811yescharacteristic
40C2×C32×C4M1611yescharacteristic
41C2×C3⋊Dic3—22no—
42C2×C3⋊Dic3—41no—
43C2×C3⋊Dic3—41no—
44C2×C3⋊Dic3—42no—
45C2×C3⋊Dic3—41no—
46C3×C3⋊C8—82no—
47#382—91no—
48#324—32no—
49C22×C3×C4—21no—
50C22×C3×C4—22no—
51C22×C3×C4C4×D312yes—
52C22×C3×C4D1212yes—
53C22×C3×C4#6712yes—
54C22×Dic3—62no—
55C22×Dic3—62no—
56C22×Dic3—62no—
57C22×Dic3—62no—
58C2×C3×C8—122no—
59C3×C4⋊C4—42no—
60C3×C4⋊C4—42no—
61C4⋊Dic3—122no—
62C4⋊Dic3—122no—
63C4×Dic3—34no—
64C4×Dic3—62no—
65C4×Dic3—62no—
66C4×Dic3—62no—
67C2×C3⋊C8—42no—
68C22×C32—21no—
69C22×C32—21no—
70C22×C32C22⋊C811yescharacteristic
71C22×C32#9911yescharacteristic
72C22×C32#10111yescharacteristic
73C32×C4—21no—
74C32×C4—21no—
75C32×C4—42no—
76C3⋊Dic3—42no—
77C3⋊Dic3—81no—
78C2×C4⋊C4—91no—
79C2×C4⋊C4D3211yescharacteristic
80C2×C42—91no—
81C22⋊C8—62no—
82#95—182no—
83C23×C3—21no—
84C23×C3(C2×D3)⋊C412yes—
85C2×C3×C4—22no—
86C2×C3×C4—22no—
87C2×C3×C4—22no—
88C2×C3×C4—22no—
89C2×C3×C4—22no—
90C2×C3×C4—22no—
91C2×C3×C4—21no—
92C2×C3×C4—21no—
93C2×C3×C4—42no—
94C2×C3×C4—42no—
95C2×C3×C4—42no—
96C2×C3×C4—44no—
97C2×C3×C4D3×C812yes—
98C2×C3×C4ΓL(1,𝔽25)12yes—
99C2×Dic3—64no—
100C2×Dic3—64no—
101C2×Dic3—122no—
102C2×Dic3—122no—
103C2×Dic3—122no—
104C2×Dic3—122no—
105C2×Dic3—122no—
106C2×Dic3—124no—
107C2×Dic3—124no—
108C2×Dic3—122no—
109C3×C8—242no—
110C3⋊C8—82no—
111C2×C32—21no—
112C2×C32—21no—
113C2×C32#32411yescharacteristic
114C2×C32#35411yescharacteristic
115C2×C32#35511yescharacteristic
116C22×C4—181no—
117C22×C4—181no—
118C22×C4#62411yescharacteristic
119C22×C4#62612yes—
120C2×C8—122no—
121C4⋊C4—41no—
122C4⋊C4—361no—
123C42—92no—
124C42—181no—
125C22×C3—22no—
126C22×C3—22no—
127C22×C3—22no—
128C22×C3—22no—
129C22×C3—21no—
130C22×C3—21no—
131C22×C3—21no—
132C22×C3#80612yes—
133C22×C3(C2×D3)⋊C812yes—
134C22×C3#82412yes—
135C3×C4—22no—
136C3×C4—22no—
137C3×C4—22no—
138C3×C4—22no—
139C3×C4—42no—
140C3×C4—42no—
141C3×C4—82no—
142Dic3—124no—
143Dic3—124no—
144Dic3—242no—
145Dic3—242no—
146C32#132411yescharacteristic, complemented, Sylow
147C23#372211yescharacteristic
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—182no—
153C2×C4—361no—
154C2×C4—361no—
155C2×C4—362no—
156C2×C4—361no—
157C2×C4#371011yescharacteristic
158C2×C4#371211yescharacteristic
159C8—242no—
160C2×C3—22no—
161C2×C3—22no—
162C2×C3—22no—
163C2×C3—22no—
164C2×C3—21no—
165C2×C3—21no—
166C2×C3—21no—
167C2×C3#446912yes—
168C2×C3#447312yes—
169C2×C3#447712yes—
170C22—21no—
171C22—21no—
172C22#6355711yescharacteristic
173C22#6356111yescharacteristic
174C22#6358111yescharacteristic
175C4—21no—
176C4—21no—
177C4—42no—
178C4—362no—
179C4—721no—
180C3—21no—
181C3#6745212yescomplemented
182C2—21no—
183C2—21no—
184C2#1058914811yescharacteristic
185C2#1058918111yescharacteristic
186C2#1058918311yescharacteristic
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#1324
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
20. C4×C3⋊Dic3C8semidirect
146. C32#1324semidirect
181. C3#67452semidirect

Maximal subgroups

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

subgroupindex
#105926762
C3×#45282
#674523