Finite Group Databasebeta

← #11785720

Subgroups — #11785720

Order 1152.

948 conjugacy classes of subgroups; only the 281 normal subgroups are shown.

normal subgroups only

This group has 948 conjugacy classes of subgroups — too many to draw. Only its 281 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
1C22×C32×C4⋊C4C211yesmaximal, characteristic
2#10592906C212yesmaximal
3#10589396C214yesmaximal, complemented
4#71562—34nomaximal
5C23×C32×C4C412yes—
6C23×C32×C4C2211yescharacteristic
7C2×C32×C4⋊C4—22no—
8C2×C32×C4⋊C4—22no—
9C2×C32×C4⋊C4C412yes—
10C2×C32×C4⋊C4C2212yes—
11C2×#3748C2214yes—
12#63657—22no—
13#63657—22no—
14C22×C3×C4⋊C4D314yes—
15#5207—38no—
16#4530—316no—
17C24×C32C2×C411yescharacteristic
18C22×C32×C4—24no—
19C22×C32×C4—22no—
20C22×C32×C4—22no—
21C22×C32×C4—44no—
22C22×C32×C4C2×C411yescharacteristic
23C22×C32×C4C2×C414yes—
24C22×C32×C4D412yes—
25C22×C32×C4D412yes—
26C22×C32×C4C2311yescharacteristic
27C32×C4⋊C4—24no—
28C32×C4⋊C4—24no—
29#3748—28no—
30C2×C3⋊(C3⋊C8)—24no—
31#1821—91noSylow
32C23×C3×C4Dic318yes—
33C23×C3×C4C2×D314yes—
34C2×C3×C4⋊C4—28no—
35C2×C3×C4⋊C4—28no—
36C2×C3×C4⋊C4Dic318yes—
37C2×C3×C4⋊C4C2×D318yes—
38C2×#208—316no—
39#830—68no—
40#830—68no—
41C23×C32—22no—
42C23×C32—22no—
43C23×C32—22no—
44C23×C32C22⋊C411yescharacteristic
45C23×C32C22⋊C411yescharacteristic
46C23×C32C22×C411yescharacteristic
47C2×C32×C4—22no—
48C2×C32×C4—24no—
49C2×C32×C4—24no—
50C2×C32×C4—24no—
51C2×C32×C4—44no—
52C2×C32×C4—44no—
53C2×C32×C4—44no—
54C2×C32×C4C22⋊C412yes—
55C2×C32×C4C2×D412yes—
56C2×C32×C4#4114yes—
57C3⋊(C3⋊C8)—44no—
58C22×C4⋊C4C3⋊D311yescharacteristic
59#407—92no—
60#343—94no—
61C24×C3C2×Dic314yes—
62C22×C3×C4—216no—
63C22×C3×C4—28no—
64C22×C3×C4—28no—
65C22×C3×C4—416no—
66C22×C3×C4C2×Dic314yes—
67C22×C3×C4C2×Dic3116yes—
68C22×C3×C4#6718yes—
69C22×C3×C4#6718yes—
70C22×C3×C4C22×D314yes—
71C3×C4⋊C4—216no—
72C3×C4⋊C4—216no—
73#208—632no—
74C2×C3⋊C8—616no—
75C22×C32—28no—
76C22×C32—21no—
77C22×C32—21no—
78C22×C32—21no—
79C22×C32—21no—
80C22×C32—21no—
81C22×C32—21no—
82C22×C32#10012yes—
83C22×C32#10112yes—
84C22×C32C2×C22⋊C411yescharacteristic
85C22×C32#11712yes—
86C32×C4—22no—
87C32×C4—44no—
88C32×C4#12314yes—
89C23×C4C3⋊Dic312yes—
90C23×C4C2×C3⋊D311yescharacteristic
91C2×M16—94no—
92C2×C4⋊C4—22no—
93C2×C4⋊C4—22no—
94C2×C4⋊C4C3⋊Dic312yes—
95C2×C4⋊C4C2×C3⋊D312yes—
96C22⋊C8—182no—
97C22⋊C8—182no—
98C23×C3—28no—
99C23×C3—28no—
100C23×C3—28no—
101C23×C3#21714yes—
102C23×C3#21714yes—
103C23×C3C22×Dic314yes—
104C2×C3×C4—28no—
105C2×C3×C4—216no—
106C2×C3×C4—216no—
107C2×C3×C4—216no—
108C2×C3×C4—416no—
109C2×C3×C4—416no—
110C2×C3×C4—416no—
111C2×C3×C4#21718yes—
112C2×C3×C4#235116yes—
113C2×C3×C4C2×#6718yes—
114C3⋊C8—1216no—
115C2×C32—22no—
116C2×C32—22no—
117C2×C32—22no—
118C2×C32#38111yescharacteristic
119C2×C32C2×#10011yescharacteristic
120C2×C32C2×#10111yescharacteristic
121C24C2×C3⋊Dic311yescharacteristic
122C22×C4—24no—
123C22×C4—22no—
124C22×C4—22no—
125C22×C4—44no—
126C22×C4C2×C3⋊Dic311yescharacteristic
127C22×C4C2×C3⋊Dic314yes—
128C22×C4#63812yes—
129C22×C4#63812yes—
130C22×C4C22×C3⋊D311yescharacteristic
131M16—188no—
132C2×C8—184no—
133C4⋊C4—24no—
134C4⋊C4—24no—
135C22×C3—232no—
136C22×C3—24no—
137C22×C3—24no—
138C22×C3—24no—
139C22×C3—24no—
140C22×C3—24no—
141C22×C3—24no—
142C22×C3#83318yes—
143C22×C3#83618yes—
144C22×C3#92618yes—
145C22×C3C2×#21714yes—
146C3×C4—28no—
147C3×C4—416no—
148C3×C4#929116yes—
149C32#182111yescharacteristic, complemented, Sylow
150C23—22no—
151C23—22no—
152C23—22no—
153C23#375711yescharacteristic
154C23#375711yescharacteristic
155C23C22×C3⋊Dic311yescharacteristic
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—44no—
161C2×C4—44no—
162C2×C4—44no—
163C2×C4#375712yes—
164C2×C4#382814yes—
165C2×C4C2×#63812yes—
166C8—364no—
167C2×C3—28no—
168C2×C3—28no—
169C2×C3—28no—
170C2×C3#521114yes—
171C2×C3C2×#83314yes—
172C2×C3C2×#83614yes—
173C22—28no—
174C22—21no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—21no—
179C22—21no—
180C22#6366012yes—
181C22#6366312yes—
182C22#6413512yes—
183C22C2×#375711yescharacteristic
184C4—22no—
185C4—44no—
186C4#6413814yes—
187C3#7156214yescomplemented
188C2—22no—
189C2—22no—
190C2—22no—
191C2#1059291011yescharacteristic
192C2C2×#6366011yescharacteristic
193C2C2×#6366311yescharacteristic
subgroupG/H
centerC22C2×#3757
commutatorC23×C32C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC22×C32×C4⋊C4C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C32×C4C23
hypercenterC22×C4⋊C4C3⋊D3
hypocenterC32#1821
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #10589396C2semidirect
149. C32#1821semidirect
187. C3#71562semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C4⋊C42
#105929062
#105893962
#715623