Finite Group Databasebeta

← #11777016

Subgroups — #11777016

Order 1152.

395 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 395 conjugacy classes of subgroups — too many to draw. Only its 108 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#10592384C211yesmaximal, characteristic
2#10590340C211yesmaximal, characteristic
3#10590331C211yesmaximal, characteristic
4C3×#4458C212yesmaximal, complemented
5#10589100C212yesmaximal, complemented
6#68572—32nomaximal
7C42×C3⋊D3C2211yescharacteristic
8C2×#3712—21no—
9C2×#3710—21no—
10C32×C4×C8C2211yescharacteristic
11#63647C412yes—
12#63641C412yes—
13C4×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×C4⋊(C3⋊C8)C2212yes—
15C3×C4⋊(C3⋊C8)C2212yes—
16#63572—21no—
17#63572—21no—
18#4837—32no—
19D3×C4⋊C8—32no—
20#4685—32no—
21#4685—61no—
22C3×#335—32no—
23#4479—32no—
24#4479—32no—
25#4458D312yescomplemented
26C2×C4×C3⋊D3C2×C411yescharacteristic
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C4×C3⋊D3Q811yescharacteristic
29C2×C32×C8C2×C412yes—
30C32×C42C2311yescharacteristic
31C4×C3⋊Dic3C2×C411yescharacteristic
32C4×C3⋊Dic3D411yescharacteristic
33C4×C3⋊Dic3Q811yescharacteristic
34C2×C3⋊(C3⋊C8)C2×C412yes—
35C2×C3×C3⋊C8—22no—
36C2×C3×C3⋊C8—22no—
37#3712—42no—
38#3710—42no—
39#1571—91noSylow
40C2×ΓL(1,𝔽25)—62no—
41C2×D3×C8—62no—
42C42×D3—32no—
43C42×D3—61no—
44C3×C4⋊C8—32no—
45C3×C4⋊C8—32no—
46C3×C4×C8—21no—
47C3×C4×C8C2×D312yes—
48(C2×D3)⋊C8—32no—
49(C2×D3)⋊C8—32no—
50(C2×D3)⋊C8—62no—
51Dic3⋊C8—32no—
52Dic3⋊C8—32no—
53Dic3⋊C8—62no—
54Dic3⋊C8—62no—
55Dic3⋊C8—62no—
56C4⋊(C3⋊C8)C2×D312yes—
57C4⋊(C3⋊C8)C2×D312yes—
58C4×C3⋊C8—32no—
59C4×C3⋊C8—61no—
60C22×C3⋊D3C4⋊C411yescharacteristic
61C2×C32×C4C22×C411yescharacteristic
62C2×C32×C4C2×D411yescharacteristic
63C2×C32×C4C2×Q811yescharacteristic
64C2×C3⋊Dic3C4⋊C411yescharacteristic
65C2×C3⋊Dic3C4⋊C411yescharacteristic
66C2×C3⋊Dic3C4⋊C411yescharacteristic
67C4×C3⋊D3—22no—
68C4×C3⋊D3—41no—
69C4×C3⋊D3D812yes—
70C4×C3⋊D3Q1612yes—
71C32×C8—22no—
72C3⋊(C3⋊C8)—22no—
73C3×C3⋊C8—42no—
74C3×C3⋊C8—42no—
75#431—91no—
76#423—91no—
77C2×C4⋊C8—91no—
78#335—32no—
79#335—92no—
80C2×C4×D3—32no—
81C2×C4×D3—32no—
82C2×C4×D3—32no—
83C2×C4×D3—61no—
84C2×C4×D3—61no—
85C2×C4×D3—61no—
86C2×C3×C8—22no—
87C2×C3×C8—62no—
88C2×C3×C8—62no—
89C2×C3×C8C4×D312yes—
90C2×C3×C8C4×D312yes—
91C3×C42—21no—
92C3×C42C22×D312yes—
93C4×Dic3—32no—
94C4×Dic3—32no—
95C4×Dic3—32no—
96C4×Dic3—61no—
97C4×Dic3—61no—
98C4×Dic3—61no—
99C2×C3⋊C8—22no—
100C2×C3⋊C8—22no—
101C2×C3⋊C8—32no—
102C2×C3⋊C8—32no—
103C2×C3⋊C8—62no—
104ΓL(1,𝔽25)—124no—
105D3×C8—124no—
106C22×C32C2×C4⋊C411yescharacteristic
107C2×C3⋊D3—21no—
108C2×C3⋊D3—21no—
109C2×C3⋊D3#10712yes—
110C32×C4—21no—
111C32×C4#13112yes—
112C32×C4C2×D811yescharacteristic
113C32×C4C2×Q1611yescharacteristic
114C3⋊Dic3—21no—
115C3⋊Dic3—21no—
116C3⋊Dic3#10712yes—
117C2×M16—181no—
118C22×C8—181no—
119C2×C42—91no—
120C4⋊C8—32no—
121C4⋊C8—32no—
122C4⋊C8—92no—
123C4⋊C8—181no—
124C4⋊C8—181no—
125C22⋊C8—92no—
126C4×C8—91no—
127C4×C8D3211yescharacteristic
128C22×D3—32no—
129C22×D3—61no—
130C2×C3×C4—21no—
131C2×C3×C4—21no—
132C2×C3×C4—21no—
133C2×C3×C4C2×C4×D312yes—
134C2×C3×C4D3×D412yes—
135C2×C3×C4D3×Q812yes—
136C2×Dic3—32no—
137C2×Dic3—32no—
138C2×Dic3—32no—
139C2×Dic3—61no—
140C2×Dic3—61no—
141C2×Dic3—61no—
142C4×D3—34no—
143C4×D3—34no—
144C4×D3—62no—
145C4×D3—62no—
146C4×D3—62no—
147C4×D3—62no—
148C4×D3—122no—
149C4×D3—122no—
150C4×D3—122no—
151C3×C8—22no—
152C3×C8—22no—
153C3×C8—42no—
154C3×C8—122no—
155C3×C8—122no—
156C3⋊C8—42no—
157C3⋊C8—42no—
158C3⋊C8—62no—
159C3⋊C8—62no—
160C3⋊C8—122no—
161C2×C32#42411yescharacteristic
162C2×C32C2×#10711yescharacteristic
163C2×C32#43011yescharacteristic
164C3⋊D3—22no—
165C22×C4—91no—
166C22×C4—91no—
167C22×C4—91no—
168M16—362no—
169C2×C8—62no—
170C2×C8—62no—
171C2×C8—92no—
172C2×C8—362no—
173C2×C8#62412yes—
174C42—91no—
175C42—91no—
176C42—91no—
177C42C2×D3211yescharacteristic
178C22×C3—21no—
179C22×C3D3×C4⋊C412yes—
180C2×D3—34no—
181C2×D3—62no—
182C2×D3—62no—
183C2×D3—62no—
184C2×D3—121no—
185C2×D3—121no—
186C3×C4—22no—
187C3×C4—22no—
188C3×C4—21no—
189C3×C4—21no—
190C3×C4—22no—
191C3×C4#90112yes—
192C3×C4#90712yes—
193C3×C4D3×D812yes—
194C3×C4D3×Q1612yes—
195Dic3—34no—
196Dic3—62no—
197Dic3—62no—
198Dic3—62no—
199Dic3—121no—
200Dic3—121no—
201C32#157111yescharacteristic, complemented, Sylow
202C23—91no—
203C2×C4—91no—
204C2×C4—92no—
205C2×C4—92no—
206C2×C4—91no—
207C2×C4—91no—
208C2×C4—182no—
209C2×C4—361no—
210C2×C4#379711yescharacteristic
211C2×C4#380211yescharacteristic
212C2×C4C2×#62411yescharacteristic
213C8—22no—
214C8—122no—
215C8—122no—
216C8—182no—
217C2×C3—21no—
218C2×C3—21no—
219C2×C3—21no—
220C2×C3#483912yes—
221C2×C3D3×#10712yes—
222C2×C3#489312yes—
223D3—64no—
224D3—122no—
225C22—92no—
226C22—181no—
227C22—181no—
228C22#6390011yescharacteristic
229C4—21no—
230C4—92no—
231C4—181no—
232C4—181no—
233C4#6379711yescharacteristic
234C4#6380211yescharacteristic
235C4#6381712yes—
236C3—21no—
237C3#6857212yescomplemented
238C2—182no—
239C2#1059033211yescharacteristic
240C2#1059068711yescharacteristic
241C2#1059091411yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C4⋊C4
cosocleC32×C42C23
hypercenterC4×C8D32
hypocenterC32#1571
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×#4458C2semidirect
5. #10589100C2semidirect
25. #4458D3semidirect
201. C32#1571semidirect
237. C3#68572semidirect

Maximal subgroups

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

subgroupindex
#105923842
#105903402
#105903312
C3×#44582
#105891002
#685723