Finite Group Databasebeta

← #11785454

Subgroups — #11785454

Order 1152.

816 conjugacy classes of subgroups; only the 225 normal subgroups are shown.

normal subgroups only

This group has 816 conjugacy classes of subgroups — too many to draw. Only its 225 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×#3748C211yesmaximal, characteristic
2C32×#407C211yesmaximal, characteristic
3#10592906C211yesmaximal, characteristic
4C2×#63649C212yesmaximal, complemented
5#10589424C212yesmaximal, complemented
6#69983—34nomaximal
7C23×C32×C4C2211yescharacteristic
8C2×C32×M16C2212yes—
9C2×#3748—24no—
10C2×#3748C414yes—
11C2×#3748C2212yes—
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C32×C22⋊C8—22no—
15#63657—22no—
16#63649—24no—
17C22×#208—34no—
18C3×#407D314yes—
19#5207—34no—
20C2×#822—38no—
21#4558—38no—
22C24×C32Q811yescharacteristic
23C22×C32×C4—22no—
24C22×C32×C4—22no—
25C22×C32×C4C2×C412yes—
26C22×C32×C4D412yes—
27C22×C32×C4Q811yescharacteristic
28C22×C32×C4C2311yescharacteristic
29C32×M16—22no—
30C32×M16—22no—
31C2×C32×C8—22no—
32#3748—28no—
33#3748—22no—
34#3748—22no—
35C2×C3⋊(C3⋊C8)—22no—
36C2×C3⋊(C3⋊C8)—22no—
37C2×C3⋊(C3⋊C8)C2×C412yes—
38C2×C3⋊(C3⋊C8)C2×C412yes—
39C2×C3⋊(C3⋊C8)D414yes—
40#1811—91noSylow
41C23×C3×C4C2×D314yes—
42C2×C3×M16C2×D318yes—
43C2×#208—316no—
44C2×#208—38no—
45C2×#208—616no—
46C22×C3⋊C8—34no—
47C22×C3⋊C8—34no—
48C3×C22⋊C8—28no—
49#830—68no—
50#822—616no—
51C23×C32—22no—
52C23×C32—42no—
53C23×C32C4⋊C412yes—
54C23×C32C2×Q811yescharacteristic
55C2×C32×C4—22no—
56C2×C32×C4—22no—
57C2×C32×C4—22no—
58C2×C32×C4—24no—
59C2×C32×C4C4⋊C412yes—
60C2×C32×C4C22×C411yescharacteristic
61C2×C32×C4C2×D412yes—
62C2×C32×C4C2×D411yescharacteristic
63C2×C32×C4#4112yes—
64C32×C8—42no—
65C3⋊(C3⋊C8)—22no—
66C3⋊(C3⋊C8)—42no—
67C3⋊(C3⋊C8)C22⋊C414yes—
68C22×M16—91no—
69C2×#108—92no—
70#407—91no—
71#407C3⋊D311yescharacteristic
72#341—92no—
73C24×C3Dic614yes—
74C22×C3×C4—28no—
75C22×C3×C4—28no—
76C22×C3×C4Dic614yes—
77C22×C3×C4C4×D318yes—
78C22×C3×C4#6718yes—
79C22×C3×C4C22×D314yes—
80C3×M16—28no—
81C3×M16—28no—
82C2×C3×C8—28no—
83#208—632no—
84#208—68no—
85#208—68no—
86C2×C3⋊C8—38no—
87C2×C3⋊C8—316no—
88C2×C3⋊C8—38no—
89C2×C3⋊C8—68no—
90C2×C3⋊C8—68no—
91C22×C32—22no—
92C22×C32—22no—
93C22×C32—24no—
94C22×C32—44no—
95C22×C32C2×C4⋊C411yescharacteristic
96C22×C32C22⋊Q812yes—
97C32×C4—22no—
98C32×C4C2×C22⋊C411yescharacteristic
99C32×C4#11711yescharacteristic
100C32×C4#12112yes—
101C23×C4C2×C3⋊D311yescharacteristic
102C2×M16—94no—
103C2×M16—92no—
104C2×M16—184no—
105C2×M16C2×C3⋊D312yes—
106C22×C8—91no—
107C22×C8—91no—
108#108—184no—
109C22⋊C8—22no—
110C22⋊C8—182no—
111C23×C3—28no—
112C23×C3—48no—
113C23×C3Dic3⋊C418yes—
114C23×C3C2×Dic614yes—
115C2×C3×C4—28no—
116C2×C3×C4—28no—
117C2×C3×C4—28no—
118C2×C3×C4—216no—
119C2×C3×C4Dic3⋊C418yes—
120C2×C3×C4C2×C4×D314yes—
121C2×C3×C4D3×D418yes—
122C2×C3×C4#23718yes—
123C2×C3×C4C2×#6714yes—
124C3×C8—48no—
125C3⋊C8—316no—
126C3⋊C8—68no—
127C3⋊C8—128no—
128C2×C32—22no—
129C2×C32—42no—
130C2×C32#38011yescharacteristic
131C2×C32#43012yes—
132C24#63411yescharacteristic
133C22×C4—22no—
134C22×C4—22no—
135C22×C4#63411yescharacteristic
136C22×C4C4×C3⋊D312yes—
137C22×C4#63812yes—
138C22×C4C22×C3⋊D311yescharacteristic
139M16—22no—
140M16—22no—
141M16—188no—
142M16—182no—
143M16—182no—
144C2×C8—22no—
145C2×C8—92no—
146C2×C8—94no—
147C2×C8—92no—
148C2×C8—182no—
149C2×C8—182no—
150C22×C3—28no—
151C22×C3—216no—
152C22×C3—28no—
153C22×C3—416no—
154C22×C3#87818yes—
155C22×C3C2×Dic3⋊C414yes—
156C3×C4—28no—
157C3×C4#87714yes—
158C3×C4D3×C22⋊C414yes—
159C3×C4#93918yes—
160C32#181111yescharacteristic, complemented, Sylow
161C23—22no—
162C23—42no—
163C23#375012yes—
164C23C2×#63411yescharacteristic
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—24no—
169C2×C4#375012yes—
170C2×C4C2×C4×C3⋊D311yescharacteristic
171C2×C4D4×C3⋊D312yes—
172C2×C4#383012yes—
173C2×C4C2×#63811yescharacteristic
174C8—42no—
175C8—94no—
176C8—182no—
177C8—362no—
178C2×C3—28no—
179C2×C3—48no—
180C2×C3#494214yes—
181C2×C3#512418yes—
182C22—22no—
183C22—24no—
184C22—22no—
185C22—44no—
186C22#6408712yes—
187C22C2×#375011yescharacteristic
188C4—22no—
189C4#6408611yescharacteristic
190C4C22⋊C4×C3⋊D311yescharacteristic
191C4#6414812yes—
192C3#6998314yescomplemented
193C2—22no—
194C2—42no—
195C2#1059264111yescharacteristic
196C2#1059282312yes—
subgroupG/H
centerC2×C4C2×#638
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#407C2
socleC22×C32C2×C4⋊C4
prime radicalC24×C32Q8
cosocleC22×C32×C4C23
hypercenter#407C3⋊D3
hypocenterC32#1811
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
4. C2×#63649C2semidirect
5. #10589424C2semidirect
160. C32#1811semidirect
192. C3#69983semidirect

Maximal subgroups

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

subgroupindex
C22×#37482
C32×#4072
#105929062
C2×#636492
#105894242
#699833