Finite Group Databasebeta

← #11776965

Subgroups — #11776965

Order 1152.

387 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 387 conjugacy classes of subgroups — too many to draw. Only its 106 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#10592534C211yesmaximal, characteristic
2#10590340C211yesmaximal, characteristic
3C4×#3712C211yesmaximal, characteristic
4C3×#4479C212yesmaximal, complemented
5#10589097C212yesmaximal, complemented
6#68571—32nomaximal
7C42×C3⋊D3C2211yescharacteristic
8C2×#3712—21no—
9C2×#3712C412yes—
10C32×C4⋊C8C2211yescharacteristic
11#63647—21no—
12#63642—21no—
13C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
14C3×C4⋊(C3⋊C8)C2212yes—
15C3×C4×C3⋊C8C2212yes—
16#63572—21no—
17#63555C411yescharacteristic
18#63555C411yescharacteristic
19#4837—32no—
20#4835—32no—
21#4835—61no—
22C4×ΓL(1,𝔽25)—32no—
23C3×#335—32no—
24#4480—32no—
25#4479D312yescomplemented
26#4457—32no—
27C2×C4×C3⋊D3C2×C411yescharacteristic
28C2×C4×C3⋊D3D411yescharacteristic
29C2×C4×C3⋊D3Q811yescharacteristic
30C2×C32×C8—21no—
31C32×C42C2311yescharacteristic
32C4×C3⋊Dic3C2×C411yescharacteristic
33C4×C3⋊Dic3D411yescharacteristic
34C4×C3⋊Dic3Q811yescharacteristic
35C2×C3⋊(C3⋊C8)—21no—
36C2×C3×C3⋊C8—22no—
37C2×C3×C3⋊C8C2×C412yes—
38C2×C3×C3⋊C8C2×C412yes—
39#3712—24no—
40#3712—42no—
41#1569—91noSylow
42C2×ΓL(1,𝔽25)—32no—
43C2×ΓL(1,𝔽25)—32no—
44C2×ΓL(1,𝔽25)—62no—
45C42×D3—32no—
46C42×D3—61no—
47C3×C4⋊C8—21no—
48C3×C4⋊C8—32no—
49C3×C4⋊C8C2×D312yes—
50C3×C4×C8—32no—
51(C2×D3)⋊C8—62no—
52(C2×D3)⋊C8—62no—
53#815—32no—
54#815—32no—
55#815—62no—
56#815—62no—
57Dic3⋊C8—62no—
58C4⋊(C3⋊C8)—32no—
59C4⋊(C3⋊C8)—61no—
60C4⋊(C3⋊C8)C2×D312yes—
61C4×C3⋊C8C2×D312yes—
62C22×C3⋊D3C4⋊C411yescharacteristic
63C2×C32×C4C22×C411yescharacteristic
64C2×C32×C4C2×D411yescharacteristic
65C2×C32×C4C2×Q811yescharacteristic
66C2×C3⋊Dic3C4⋊C411yescharacteristic
67C2×C3⋊Dic3C4⋊C411yescharacteristic
68C2×C3⋊Dic3C4⋊C411yescharacteristic
69C4×C3⋊D3—22no—
70C4×C3⋊D3—21no—
71C4×C3⋊D3—21no—
72C4×C3⋊D3—41no—
73C32×C8—41no—
74C3⋊(C3⋊C8)—41no—
75C3×C3⋊C8—22no—
76C3×C3⋊C8—42no—
77C3×C3⋊C8M1614yescomplemented
78#432—91no—
79#423—91no—
80C4×M16—91no—
81#335—32no—
82#334—92no—
83C2×C4×D3—32no—
84C2×C4×D3—32no—
85C2×C4×D3—32no—
86C2×C4×D3—61no—
87C2×C4×D3—61no—
88C2×C4×D3—61no—
89C2×C3×C8—22no—
90C2×C3×C8—22no—
91C2×C3×C8—32no—
92C2×C3×C8—32no—
93C2×C3×C8—62no—
94C3×C42—21no—
95C3×C42C22×D312yes—
96C4×Dic3—32no—
97C4×Dic3—32no—
98C4×Dic3—32no—
99C4×Dic3—61no—
100C4×Dic3—61no—
101C4×Dic3—61no—
102C2×C3⋊C8—22no—
103C2×C3⋊C8—62no—
104C2×C3⋊C8—62no—
105C2×C3⋊C8C4×D312yes—
106C2×C3⋊C8C4×D312yes—
107ΓL(1,𝔽25)—64no—
108ΓL(1,𝔽25)—64no—
109ΓL(1,𝔽25)—124no—
110C22×C32C2×C4⋊C411yescharacteristic
111C2×C3⋊D3—21no—
112C2×C3⋊D3—21no—
113C2×C3⋊D3—21no—
114C32×C4—21no—
115C32×C4C2×M1612yes—
116C32×C4AGL(1,ℤ/8)11yescharacteristic
117C32×C4#13711yescharacteristic
118C3⋊Dic3—21no—
119C3⋊Dic3—21no—
120C3⋊Dic3—21no—
121C2×M16—92no—
122C2×M16—181no—
123C2×C42—91no—
124C4⋊C8—32no—
125C4⋊C8—91no—
126C4⋊C8—181no—
127C4⋊C8D3211yescharacteristic
128C22⋊C8—181no—
129#97—91no—
130#97—91no—
131#97—181no—
132C4×C8—32no—
133C22×D3—32no—
134C22×D3—61no—
135C2×C3×C4—21no—
136C2×C3×C4—21no—
137C2×C3×C4—21no—
138C2×C3×C4C2×C4×D312yes—
139C2×C3×C4D3×D412yes—
140C2×C3×C4D3×Q812yes—
141C2×Dic3—32no—
142C2×Dic3—32no—
143C2×Dic3—32no—
144C2×Dic3—61no—
145C2×Dic3—61no—
146C2×Dic3—61no—
147C4×D3—62no—
148C4×D3—62no—
149C4×D3—62no—
150C4×D3—62no—
151C4×D3—122no—
152C4×D3—121no—
153C4×D3—121no—
154C4×D3—122no—
155C4×D3—122no—
156C3×C8—34no—
157C3×C8—42no—
158C3×C8—42no—
159C3×C8—62no—
160C3×C8—122no—
161C3⋊C8—22no—
162C3⋊C8—42no—
163C3⋊C8—122no—
164C3⋊C8—122no—
165C3⋊C8ΓL(1,𝔽25)14yescomplemented
166C2×C32#42311yescharacteristic
167C2×C32#42811yescharacteristic
168C2×C32#43011yescharacteristic
169C3⋊D3—41no—
170C22×C4—91no—
171C22×C4—91no—
172C22×C4—91no—
173M16—184no—
174M16—362no—
175C2×C8—21no—
176C2×C8—32no—
177C2×C8—32no—
178C2×C8—62no—
179C2×C8—181no—
180C42—91no—
181C42—91no—
182C42—91no—
183C42C2×D3211yescharacteristic
184C22×C3—21no—
185C22×C3D3×C4⋊C412yes—
186C2×D3—62no—
187C2×D3—62no—
188C2×D3—62no—
189C2×D3—62no—
190C2×D3—121no—
191C2×D3—121no—
192C3×C4—22no—
193C3×C4—22no—
194C3×C4—21no—
195C3×C4—21no—
196C3×C4—41no—
197C3×C4C2×ΓL(1,𝔽25)12yes—
198C3×C4D3×M1612yes—
199C3×C4#91112yes—
200C3×C4#91812yes—
201Dic3—62no—
202Dic3—62no—
203Dic3—62no—
204Dic3—121no—
205Dic3—121no—
206Dic3—121no—
207C32#156911yescharacteristic, complemented, Sylow
208C23—91no—
209C2×C4—91no—
210C2×C4—91no—
211C2×C4—91no—
212C2×C4—182no—
213C2×C4—181no—
214C2×C4—181no—
215C2×C4—361no—
216C2×C4#379711yescharacteristic
217C2×C4C4×D3211yescharacteristic
218C2×C4#381111yescharacteristic
219C8—34no—
220C8—41no—
221C8—62no—
222C8—122no—
223C8—361no—
224C2×C3—21no—
225C2×C3—21no—
226C2×C3—21no—
227C2×C3#483712yes—
228C2×C3#488112yes—
229C2×C3#489312yes—
230D3—122no—
231D3—122no—
232C22—181no—
233C22—181no—
234C22—181no—
235C22#6388311yescharacteristic
236C4—21no—
237C4—181no—
238C4—181no—
239C4—181no—
240C4D3×ΓL(1,𝔽25)12yes—
241C4#6392711yescharacteristic
242C4#6394511yescharacteristic
243C3—21no—
244C3#6857112yescomplemented
245C2—361no—
246C2#1059058211yescharacteristic
247C2#1059066611yescharacteristic
248C2#1059097411yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C4⋊C4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1569
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. C3×#4479C2semidirect
5. #10589097C2semidirect
25. #4479D3semidirect
77. C3×C3⋊C8M16semidirect
165. C3⋊C8ΓL(1,𝔽25)semidirect
207. C32#1569semidirect
244. C3#68571semidirect

Maximal subgroups

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

subgroupindex
#105925342
#105903402
C4×#37122
C3×#44792
#105890972
#685713