Finite Group Databasebeta

← #11786115

Subgroups — #11786115

Order 1152.

423 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 423 conjugacy classes of subgroups — too many to draw. Only its 122 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#10592817C211yesmaximal, characteristic
2#10591120C211yesmaximal, characteristic
3C2×#63555C211yesmaximal, characteristic
4C3×#4558C212yesmaximal
5#10589166C212yesmaximal
6#68929—32nomaximal
7C2×C32×M16C2211yescharacteristic
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C2×#3748C2211yescharacteristic
10C2×C3×#208C2212yes—
11C22×C3×C3⋊C8C2212yes—
12#63641—22no—
13#63572—22no—
14#63555C412yes—
15#63555C412yes—
16#5118—32no—
17#5118—32no—
18#5118—61no—
19C2×#815—32no—
20C3×#341—32no—
21#4558—32no—
22#4558D312yes—
23#4552—32no—
24C22×C32×C4C2311yescharacteristic
25C22×C3⋊Dic3Q812yes—
26C32×M16—22no—
27C2×C32×C8—21no—
28C4×C3⋊Dic3C2×C411yescharacteristic
29C4×C3⋊Dic3C2×C411yescharacteristic
30C4×C3⋊Dic3D412yes—
31#3748—22no—
32C2×C3⋊(C3⋊C8)—21no—
33C3×#208—22no—
34C3×#208—22no—
35C2×C3×C3⋊C8—22no—
36C2×C3×C3⋊C8—22no—
37C2×C3×C3⋊C8—22no—
38C2×C3×C3⋊C8C2×C414yes—
39#1838—91noSylow
40C2×C3×M16—21no—
41C2×C3×M16—32no—
42C2×C3×M16C2×D312yes—
43C22×C3×C8—32no—
44C2×C4×Dic3—32no—
45C2×C4×Dic3—61no—
46C2×#208—32no—
47C2×#208—61no—
48C2×#208C2×D312yes—
49C22×C3⋊C8C2×D312yes—
50#815—34no—
51#815—34no—
52Dic3⋊C8—64no—
53Dic3⋊C8—64no—
54Dic3⋊C8—64no—
55C23×C32C2×Q811yescharacteristic
56C2×C32×C4C22×C411yescharacteristic
57C2×C32×C4C2×D411yescharacteristic
58C2×C32×C4#4112yes—
59C2×C32×C4#4112yes—
60C2×C3⋊Dic3—42no—
61C2×C3⋊Dic3C4⋊C412yes—
62C2×C3⋊Dic3C4⋊C412yes—
63C32×C8—41no—
64C3⋊(C3⋊C8)—41no—
65C3×C3⋊C8—24no—
66C3×C3⋊C8—42no—
67#423—91no—
68#423—91no—
69C2×#97—91no—
70#341—32no—
71#341—92no—
72C22×C3×C4—21no—
73C22×C3×C4C22×D312yes—
74C22×Dic3—34no—
75C22×Dic3—62no—
76C3×M16—22no—
77C3×M16—22no—
78C3×M16—42no—
79C3×M16—62no—
80C3×M16—62no—
81C2×C3×C8—22no—
82C2×C3×C8—22no—
83C2×C3×C8—34no—
84C2×C3×C8—62no—
85C2×C3×C8—62no—
86C2×C3×C8—62no—
87C4×Dic3—32no—
88C4×Dic3—32no—
89C4×Dic3—34no—
90C4×Dic3—62no—
91C4×Dic3—61no—
92C4×Dic3—61no—
93#208—22no—
94#208—22no—
95#208—62no—
96#208—62no—
97#208—122no—
98C2×C3⋊C8—22no—
99C2×C3⋊C8—22no—
100C2×C3⋊C8—22no—
101C2×C3⋊C8—62no—
102C2×C3⋊C8—62no—
103C2×C3⋊C8C4×D314yes—
104C22×C32—22no—
105C22×C32C2×C4⋊C411yescharacteristic
106C22×C32#12512yes—
107C32×C4#11712yes—
108C32×C4#12411yescharacteristic
109C32×C4#12411yescharacteristic
110C3⋊Dic3—22no—
111C3⋊Dic3—22no—
112C2×M16—32no—
113C2×M16—91no—
114C2×M16D3211yescharacteristic
115C22×C8—32no—
116C2×C42—91no—
117C4⋊C8—182no—
118C4⋊C8—182no—
119#97—92no—
120#97—92no—
121C23×C3—21no—
122C23×C3D3×Q812yes—
123C2×C3×C4—22no—
124C2×C3×C4—21no—
125C2×C3×C4—22no—
126C2×C3×C4—21no—
127C2×C3×C4C2×C4×D312yes—
128C2×C3×C4#23512yes—
129C2×C3×C4#23512yes—
130C2×C3×C4D3×D412yes—
131C2×C3×C4#23712yes—
132C2×C3×C4#23712yes—
133C2×Dic3—34no—
134C2×Dic3—34no—
135C2×Dic3—62no—
136C2×Dic3—62no—
137C2×Dic3—124no—
138C2×Dic3—124no—
139C3×C8—42no—
140C3×C8—42no—
141C3×C8—64no—
142C3×C8—122no—
143C3⋊C8—24no—
144C3⋊C8—42no—
145C3⋊C8—122no—
146C3⋊C8—122no—
147C2×C32—22no—
148C2×C32#38211yescharacteristic
149C2×C32#43012yes—
150C22×C4—92no—
151C22×C4C2×D3211yescharacteristic
152M16—22no—
153M16—62no—
154M16—62no—
155M16—182no—
156C2×C8—21no—
157C2×C8—34no—
158C2×C8—62no—
159C2×C8—62no—
160C2×C8—62no—
161C2×C8—181no—
162C42—91no—
163C42—91no—
164C42—92no—
165C22×C3—24no—
166C22×C3—22no—
167C22×C3—21no—
168C22×C3—42no—
169C22×C3#88912yes—
170C22×C3#88912yes—
171C22×C3D3×C4⋊C412yes—
172C3×C4—22no—
173C3×C4—21no—
174C3×C4—21no—
175C3×C4#87212yes—
176C3×C4#87712yes—
177C3×C4#88512yes—
178C3×C4#88512yes—
179Dic3—64no—
180Dic3—64no—
181Dic3—64no—
182Dic3—122no—
183C32#183811yescharacteristic, complemented, Sylow
184C23#379711yescharacteristic
185C2×C4—92no—
186C2×C4—92no—
187C2×C4—362no—
188C2×C4#379512yes—
189C2×C4C4×D3211yescharacteristic
190C2×C4#380412yes—
191C2×C4#381111yescharacteristic
192C8—41no—
193C8—64no—
194C8—122no—
195C8—361no—
196C2×C3—22no—
197C2×C3—22no—
198C2×C3—21no—
199C2×C3—22no—
200C2×C3—42no—
201C2×C3#465012yes—
202C2×C3#489314yes—
203C22—22no—
204C22#6384712yes—
205C22#6388311yescharacteristic
206C4—182no—
207C4—182no—
208C4#6387712yes—
209C4#6391311yescharacteristic
210C4#6395311yescharacteristic
211C3—21no—
212C3#6892912yescomplemented
213C2—22no—
214C2#1059097412yes—
215C2#1059124711yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C4⋊C4
prime radicalC23×C32C2×Q8
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1838
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
183. C32#1838semidirect
212. C3#68929semidirect

Maximal subgroups

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

subgroupindex
#105928172
#105911202
C2×#635552
C3×#45582
#105891662
#689293