Finite Group Databasebeta

← #11771922

Subgroups — #11771922

Order 1152.

486 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 95 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#10592646C211yesmaximal, characteristic
2C32×#323C211yesmaximal, characteristic
3#10589392C211yesmaximal, characteristic
4#67449—34nomaximal
5C22×#634C411yescharacteristic, complemented
6C2×C32×C22⋊C4C2211yescharacteristic
7C2×#3757—21no—
8C2×#3757—21no—
9C32×C22⋊C8—21no—
10#63658—21no—
11#63658C411yescharacteristic, complemented
12#4947—34no—
13C3×#323D314yes—
14#4526—34no—
15C24×C32D411yescharacteristic
16C22×C32×C4C2×C411yescharacteristic
17C22×C32×C4D411yescharacteristic
18C22×C3⋊Dic3—21no—
19C22×C3⋊Dic3—21no—
20C22×C3⋊Dic3—41no—
21C2×#634—41no—
22C2×#634—42no—
23C2×C32×C8—41no—
24C32×C22⋊C4—41no—
25#3757—22no—
26#3757—42no—
27#3757—41no—
28#1351—91noSylow
29C22×Dic6—34no—
30C2×C3×C22⋊C4C2×D314yes—
31C2×#217—64no—
32C2×#217—64no—
33C3×C22⋊C8—24no—
34C3⋊#95—34no—
35C3⋊#95—64no—
36C23×C32—21no—
37C23×C32—21no—
38C23×C32—41no—
39C23×C32—41no—
40C23×C32C22⋊C411yescharacteristic
41C23×C32SD1611yescharacteristic
42C23×C32Q1611yescharacteristic
43C2×C32×C4—21no—
44C2×C32×C4—21no—
45C2×C32×C4—41no—
46C2×C32×C4—41no—
47C2×C3⋊Dic3—22no—
48C2×C3⋊Dic3—41no—
49C2×C3⋊Dic3—41no—
50C2×C3⋊Dic3—42no—
51C2×C3⋊Dic3—41no—
52C2×C3⋊Dic3—41no—
53C2×C3⋊Dic3—41no—
54C2×C3⋊Dic3—81no—
55C2×C3⋊Dic3—81no—
56#634—42no—
57#634—42no—
58C32×C8—81no—
59#393—91no—
60#342—91no—
61#323C3⋊D311yescharacteristic
62C24×C3D1214yes—
63C22×C3×C4C4×D314yes—
64C22×C3×C4#6714yes—
65C22×Dic3—64no—
66C22×Dic3—64no—
67C22×Dic3—124no—
68C2×Dic6—124no—
69C2×Dic6—128no—
70C2×C3×C8—44no—
71C3×C22⋊C4—44no—
72#217—68no—
73#217—128no—
74#217—124no—
75C22×C32—21no—
76C22×C32—21no—
77C22×C32—21no—
78C22×C32—21no—
79C22×C32—41no—
80C22×C32—41no—
81C22×C32—41no—
82C22×C32—41no—
83C22×C32—81no—
84C22×C32#9911yescharacteristic
85C22×C32#10311yescharacteristic
86C22×C32#10411yescharacteristic
87C32×C4—41no—
88C32×C4—41no—
89C3⋊Dic3—42no—
90C3⋊Dic3—81no—
91C3⋊Dic3—82no—
92C22×Q8—91no—
93C2×C22⋊C4—181no—
94C2×C22⋊C4—181no—
95C2×C22⋊C4C2×C3⋊D311yescharacteristic
96C22⋊C8—21no—
97#95—91no—
98#95—181no—
99C23×C3—24no—
100C23×C3—24no—
101C23×C3—44no—
102C23×C3—44no—
103C23×C3#20414yes—
104C23×C3Dic1214yes—
105C23×C3(C2×D3)⋊C414yes—
106C2×C3×C4—24no—
107C2×C3×C4—24no—
108C2×C3×C4—44no—
109C2×C3×C4—44no—
110C2×Dic3—68no—
111C2×Dic3—124no—
112C2×Dic3—124no—
113C2×Dic3—128no—
114C2×Dic3—124no—
115C2×Dic3—124no—
116C2×Dic3—124no—
117C2×Dic3—244no—
118C2×Dic3—244no—
119Dic6—128no—
120Dic6—128no—
121C3×C8—84no—
122C2×C32—21no—
123C2×C32—21no—
124C2×C32—41no—
125C2×C32—41no—
126C2×C32#32811yescharacteristic
127C2×C32AΣL(1,𝔽16)11yescharacteristic
128C2×C32#35411yescharacteristic
129C24C4⋊(C3⋊D3)11yescharacteristic
130C2×Q8—361no—
131C2×Q8—362no—
132C22×C4—181no—
133C22×C4—181no—
134C22×C4—361no—
135C22×C4C4×C3⋊D311yescharacteristic
136C22×C4#63811yescharacteristic
137C2×C8—41no—
138C22⋊C4—41no—
139C22⋊C4—182no—
140C22⋊C4—362no—
141C22⋊C4—361no—
142C22×C3—24no—
143C22×C3—24no—
144C22×C3—24no—
145C22×C3—24no—
146C22×C3—44no—
147C22×C3—44no—
148C22×C3—44no—
149C22×C3—44no—
150C22×C3—84no—
151C22×C3#80614yes—
152C22×C3#81614yes—
153C22×C3#82514yes—
154C3×C4—44no—
155C3×C4—44no—
156Dic3—128no—
157Dic3—244no—
158Dic3—248no—
159C32#135111yescharacteristic, complemented, Sylow
160C23—21no—
161C23—21no—
162C23—41no—
163C23—41no—
164C23#374411yescharacteristic
165C23#374611yescharacteristic
166C23#375211yescharacteristic
167Q8—362no—
168Q8—362no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—182no—
174C2×C4—361no—
175C2×C4—361no—
176C2×C4—362no—
177C2×C4—361no—
178C2×C4—361no—
179C2×C4—361no—
180C2×C4—721no—
181C2×C4—721no—
182C8—81no—
183C2×C3—24no—
184C2×C3—24no—
185C2×C3—44no—
186C2×C3—44no—
187C2×C3#446714yes—
188C2×C3#447314yes—
189C2×C3#447514yes—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—41no—
195C22—41no—
196C22—41no—
197C22—41no—
198C22—81no—
199C22#6363311yescharacteristic
200C22#6364311yescharacteristic
201C22#6365211yescharacteristic
202C4—41no—
203C4—41no—
204C4—362no—
205C4—721no—
206C4—722no—
207C3#6744914yescomplemented
208C2—21no—
209C2—21no—
210C2—41no—
211C2—41no—
212C2#1058933311yescharacteristic
213C2#1058933911yescharacteristic
214C2#1058934111yescharacteristic
subgroupG/H
centerC22#63633
commutatorC22×C32×C4C2×C4
FrattiniC2×C22⋊C4C2×C3⋊D3
FittingC32×#323C2
socleC22×C32#99
prime radicalC24×C32D4
cosocleC2×C32×C22⋊C4C22
hypercenter#323C3⋊D3
hypocenterC32#1351
LCSG ▷ C22×C32×C4 ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #323

Complements

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

NH ≅ G/Ntype
5. C22×#634C4semidirect
11. #63658C4semidirect
159. C32#1351semidirect
207. C3#67449semidirect

Maximal subgroups

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

subgroupindex
#105926462
C32×#3232
#105893922
#674493