Finite Group Databasebeta

← #11777088

Subgroups — #11777088

Order 1152.

375 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 375 conjugacy classes of subgroups — too many to draw. Only its 100 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#10590331C211yesmaximal, characteristic
3#10590297C211yesmaximal, characteristic
4C3×#4480C212yesmaximal, complemented
5#10589099C212yesmaximal, complemented
6#68534—32nomaximal
7C42×C3⋊D3C2211yescharacteristic
8C2×#3710—21no—
9C32×C4⋊C8C2211yescharacteristic
10#63647—21no—
11#63642—21no—
12C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
13C3×C4⋊(C3⋊C8)C2212yes—
14C3×C4×C3⋊C8C2212yes—
15#63572—21no—
16#63572C412yes—
17#63557C411yescharacteristic
18#63557C411yescharacteristic
19#4835—32no—
20#4835—61no—
21D3×C4⋊C8—32no—
22#4685—32no—
23C3×#334—32no—
24#4480D312yescomplemented
25#4479—32no—
26#4458—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#3710—42no—
40#1573—91noSylow
41C2×D3×C8—62no—
42C42×D3—32no—
43C42×D3—61no—
44C3×C4⋊C8—21no—
45C3×C4⋊C8—32no—
46C3×C4⋊C8C2×D312yes—
47C3×C4×C8—32no—
48(C2×D3)⋊C8—32no—
49(C2×D3)⋊C8—32no—
50(C2×D3)⋊C8—62no—
51(C2×D3)⋊C8—62no—
52#815—62no—
53#815—62no—
54Dic3⋊C8—32no—
55Dic3⋊C8—32no—
56Dic3⋊C8—62no—
57C4⋊(C3⋊C8)—32no—
58C4⋊(C3⋊C8)—61no—
59C4⋊(C3⋊C8)C2×D312yes—
60C4×C3⋊C8C2×D312yes—
61C22×C3⋊D3C4⋊C411yescharacteristic
62C2×C32×C4C22×C411yescharacteristic
63C2×C32×C4C2×D411yescharacteristic
64C2×C32×C4C2×Q811yescharacteristic
65C2×C3⋊Dic3C4⋊C411yescharacteristic
66C2×C3⋊Dic3C4⋊C411yescharacteristic
67C2×C3⋊Dic3C4⋊C411yescharacteristic
68C4×C3⋊D3—22no—
69C4×C3⋊D3—22no—
70C4×C3⋊D3—21no—
71C4×C3⋊D3—21no—
72C32×C8—41no—
73C3⋊(C3⋊C8)—41no—
74C3×C3⋊C8—22no—
75C3×C3⋊C8—22no—
76C3×C3⋊C8—42no—
77#432—91no—
78#431—91no—
79C2×C4⋊C8—91no—
80#335—92no—
81#334—32no—
82C2×C4×D3—32no—
83C2×C4×D3—32no—
84C2×C4×D3—32no—
85C2×C4×D3—61no—
86C2×C4×D3—61no—
87C2×C4×D3—61no—
88C2×C3×C8—22no—
89C2×C3×C8—22no—
90C2×C3×C8—32no—
91C2×C3×C8—32no—
92C2×C3×C8—62no—
93C3×C42—21no—
94C3×C42C22×D312yes—
95C4×Dic3—32no—
96C4×Dic3—32no—
97C4×Dic3—32no—
98C4×Dic3—61no—
99C4×Dic3—61no—
100C4×Dic3—61no—
101C2×C3⋊C8—22no—
102C2×C3⋊C8—62no—
103C2×C3⋊C8—62no—
104C2×C3⋊C8C4×D312yes—
105C2×C3⋊C8C4×D312yes—
106D3×C8—124no—
107C22×C32C2×C4⋊C411yescharacteristic
108C2×C3⋊D3—21no—
109C2×C3⋊D3—21no—
110C2×C3⋊D3#10812yes—
111C32×C4—21no—
112C32×C4#13112yes—
113C32×C4AGL(1,ℤ/8)11yescharacteristic
114C32×C4#13711yescharacteristic
115C3⋊Dic3—21no—
116C3⋊Dic3—21no—
117C3⋊Dic3—21no—
118C22×C8—181no—
119C2×C42—91no—
120C4⋊C8—32no—
121C4⋊C8—92no—
122C4⋊C8—91no—
123C4⋊C8—181no—
124C4⋊C8D3211yescharacteristic
125C22⋊C8—91no—
126C22⋊C8—91no—
127C22⋊C8—181no—
128#97—181no—
129C4×C8—32no—
130C22×D3—32no—
131C22×D3—61no—
132C2×C3×C4—21no—
133C2×C3×C4—21no—
134C2×C3×C4—21no—
135C2×C3×C4C2×C4×D312yes—
136C2×C3×C4D3×D412yes—
137C2×C3×C4D3×Q812yes—
138C2×Dic3—32no—
139C2×Dic3—32no—
140C2×Dic3—32no—
141C2×Dic3—61no—
142C2×Dic3—61no—
143C2×Dic3—61no—
144C4×D3—64no—
145C4×D3—62no—
146C4×D3—62no—
147C4×D3—62no—
148C4×D3—62no—
149C4×D3—122no—
150C4×D3—121no—
151C4×D3—121no—
152C4×D3—122no—
153C3×C8—42no—
154C3×C8—42no—
155C3×C8—62no—
156C3×C8—62no—
157C3×C8—122no—
158C3⋊C8—22no—
159C3⋊C8—22no—
160C3⋊C8—42no—
161C3⋊C8—122no—
162C3⋊C8—122no—
163C2×C32#42411yescharacteristic
164C2×C32#42811yescharacteristic
165C2×C32C2×#10811yescharacteristic
166C3⋊D3—22no—
167C22×C4—91no—
168C22×C4—91no—
169C22×C4—91no—
170C2×C8—21no—
171C2×C8—32no—
172C2×C8—32no—
173C2×C8—62no—
174C2×C8—181no—
175C2×C8—362no—
176C42—91no—
177C42—91no—
178C42—91no—
179C42C2×D3211yescharacteristic
180C22×C3—21no—
181C22×C3D3×C4⋊C412yes—
182C2×D3—34no—
183C2×D3—62no—
184C2×D3—62no—
185C2×D3—62no—
186C2×D3—121no—
187C2×D3—121no—
188C3×C4—22no—
189C3×C4—22no—
190C3×C4—21no—
191C3×C4—21no—
192C3×C4—41no—
193C3×C4#90112yes—
194C3×C4#90712yes—
195C3×C4#91412yes—
196C3×C4#91512yes—
197Dic3—62no—
198Dic3—62no—
199Dic3—62no—
200Dic3—121no—
201Dic3—121no—
202Dic3—121no—
203C32#157311yescharacteristic, complemented, Sylow
204C23—91no—
205C2×C4—91no—
206C2×C4—91no—
207C2×C4—91no—
208C2×C4—182no—
209C2×C4—182no—
210C2×C4—181no—
211C2×C4—181no—
212C2×C4#379711yescharacteristic
213C2×C4C4×D3211yescharacteristic
214C2×C4#381111yescharacteristic
215C8—41no—
216C8—62no—
217C8—62no—
218C8—122no—
219C8—361no—
220C2×C3—21no—
221C2×C3—21no—
222C2×C3—21no—
223C2×C3#483912yes—
224C2×C3#486112yes—
225C2×C3D3×#10812yes—
226D3—64no—
227D3—122no—
228C22—92no—
229C22—181no—
230C22—181no—
231C22#6388311yescharacteristic
232C4—21no—
233C4—181no—
234C4—181no—
235C4—181no—
236C4#6380412yes—
237C4#6393111yescharacteristic
238C4#6394111yescharacteristic
239C3—21no—
240C3#6853412yescomplemented
241C2—182no—
242C2#1059058411yescharacteristic
243C2#1059070211yescharacteristic
244C2#1059097211yescharacteristic
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#1573
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×#4480C2semidirect
5. #10589099C2semidirect
24. #4480D3semidirect
203. C32#1573semidirect
240. C3#68534semidirect

Maximal subgroups

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

subgroupindex
#105925342
#105903312
#105902972
C3×#44802
#105890992
#685343