Finite Group Databasebeta

← #11783385

Subgroups — #11783385

Order 1152.

538 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C2×#64286C212yesmaximal
2C2×#64286C211yesmaximal, characteristic
3#10590098C214yesmaximal
4C22×C4×C3⋊D3C2211yescharacteristic
5C2×C22⋊#157C2214yes—
6C2×C22⋊#157C2212yes—
7#64286—22no—
8#64286—22no—
9#64286—22no—
10#64286—22no—
11#64286C414yescomplemented
12#64286C414yescomplemented
13C2×C4⋊#157—22no—
14C2×C4⋊#157C412yescomplemented
15C2×C4×#157—22no—
16C2×C4×#157C412yescomplemented
17C23×C3⋊D3C2311yescharacteristic
18C22×#157—24no—
19C22×#157C2×C414yes—
20C22×C32×C4Q811yescharacteristic
21C22×C3⋊Dic3Q811yescharacteristic
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3C2×C411yescharacteristic
24C2×C4×C3⋊D3C2×C412yes—
25C2×C4×C3⋊D3C2×C412yes—
26C2×C4×C3⋊D3D412yes—
27C2×C4×C3⋊D3D412yes—
28C2×C4×C3⋊D3D411yescharacteristic
29C2×C4×C3⋊D3D411yescharacteristic
30C22⋊#157—24no—
31C22⋊#157—24no—
32C22⋊#157C2×C418yes—
33C4⋊#157—24no—
34C4⋊#157—24no—
35C4⋊#157—24no—
36C4×#157—24no—
37C4×#157—24no—
38C4×#157—22no—
39C4×#157—22no—
40#1740—91nomaximal, Sylow
41C22×C4×D3—121no—
42C23×C32C2×Q811yescharacteristic
43C22×C3⋊D3—42no—
44C22×C3⋊D3C22×C411yescharacteristic
45C22×C3⋊D3C22×C412yes—
46C22×C3⋊D3C2×D412yes—
47C22×C3⋊D3C2×D411yescharacteristic
48C2×#157—28no—
49C2×#157—24no—
50C2×#157—48no—
51C2×#157—44no—
52C2×C32×C4C4⋊C411yescharacteristic
53C2×C32×C4C4⋊C411yescharacteristic
54C2×C32×C4C4⋊C412yes—
55C2×C32×C4C4⋊C412yes—
56C2×C3⋊Dic3C4⋊C411yescharacteristic
57C2×C3⋊Dic3C4⋊C411yescharacteristic
58C2×C3⋊Dic3C4⋊C412yes—
59C2×C3⋊Dic3C4⋊C412yes—
60C4×C3⋊D3C4211yescharacteristic
61C4×C3⋊D3C4211yescharacteristic
62C4×C3⋊D3C4212yes—
63C4×C3⋊D3C22⋊C412yes—
64C4×C3⋊D3C22⋊C412yes—
65C4×C3⋊D3C22⋊C411yescharacteristic
66C4×C3⋊D3C22⋊C411yescharacteristic
67C4×C3⋊D3C22⋊C412yes—
68C4×C3⋊D3C22⋊C412yes—
69C4×C3⋊D3C22⋊C412yes—
70C2×#117—91no—
71C2×#117—92no—
72#342—94no—
73C23×D3—121no—
74C22×C3×C4—41no—
75C22×Dic3—121no—
76C2×C4×D3—121no—
77C2×C4×D3—121no—
78C2×C4×D3—122no—
79C2×C4×D3—122no—
80C2×C4×D3—122no—
81C2×C4×D3—122no—
82C2×C4×D3—121no—
83C2×C4×D3—121no—
84C22×C32—41no—
85C22×C32C2×C4⋊C411yescharacteristic
86C22×C32C2×C4⋊C412yes—
87C2×C3⋊D3—22no—
88C2×C3⋊D3—24no—
89C2×C3⋊D3—42no—
90C2×C3⋊D3—41no—
91C2×C3⋊D3C2×C4211yescharacteristic
92C2×C3⋊D3C2×C22⋊C412yes—
93C2×C3⋊D3C2×C22⋊C411yescharacteristic
94#157—48no—
95#157—44no—
96C32×C4#9511yescharacteristic
97C32×C4#9512yes—
98C32×C4#9511yescharacteristic
99C3⋊Dic3#9511yescharacteristic
100C3⋊Dic3#9511yescharacteristic
101C3⋊Dic3#9512yes—
102C23×C4—91no—
103#117—94no—
104#117—94no—
105#117—182no—
106#117—182no—
107#117—182no—
108#117—182no—
109C2×C4⋊C4—92no—
110C2×C4⋊C4—182no—
111C2×C22⋊C4—94no—
112C2×C22⋊C4—92no—
113C2×C42—92no—
114C2×C42—182no—
115C23×C3—41no—
116C22×D3—121no—
117C22×D3—122no—
118C22×D3—122no—
119C22×D3—121no—
120C22×D3—128no—
121C2×C3×C4—41no—
122C2×C3×C4—42no—
123C2×C3×C4—41no—
124C2×C3×C4—42no—
125C2×Dic3—121no—
126C2×Dic3—122no—
127C2×Dic3—121no—
128C2×Dic3—122no—
129C4×D3—121no—
130C4×D3—122no—
131C4×D3—121no—
132C4×D3—121no—
133C4×D3—122no—
134C4×D3—122no—
135C4×D3—122no—
136C4×D3—122no—
137C4×D3—121no—
138C4×D3—122no—
139C2×C32—21no—
140C2×C32—22no—
141C2×C32C2×#9511yescharacteristic
142C3⋊D3—22no—
143C3⋊D3—21no—
144C3⋊D3#41012yes—
145C24—91no—
146C22×C4—91no—
147C22×C4—91no—
148C22×C4—92no—
149C22×C4—91no—
150C22×C4—92no—
151C22×C4—92no—
152C22×C4—92no—
153C22×C4—91no—
154C22×C4—91no—
155C22×C4—94no—
156C22×C4—184no—
157C22×C4PSU(3,𝔽2)11yescharacteristic
158C4⋊C4—184no—
159C4⋊C4—184no—
160C4⋊C4—184no—
161C22⋊C4—98no—
162C22⋊C4—184no—
163C22⋊C4—184no—
164C42—182no—
165C42—182no—
166C42—184no—
167C42—184no—
168C22×C3—44no—
169C22×C3—42no—
170C22×C3—41no—
171C2×D3—121no—
172C2×D3—121no—
173C2×D3—122no—
174C2×D3—124no—
175C2×D3—128no—
176C2×D3—128no—
177C2×D3—124no—
178C3×C4—41no—
179C3×C4—42no—
180C3×C4—41no—
181Dic3—121no—
182Dic3—121no—
183Dic3—122no—
184C32#174011yescharacteristic, complemented, Sylow
185C23—92no—
186C23—91no—
187C23—92no—
188C23—91no—
189C23—362no—
190C23C2×PSU(3,𝔽2)11yescharacteristic
191C2×C4—91no—
192C2×C4—92no—
193C2×C4—91no—
194C2×C4—92no—
195C2×C4—91no—
196C2×C4—92no—
197C2×C4—92no—
198C2×C4—92no—
199C2×C4—92no—
200C2×C4—91no—
201C2×C4—92no—
202C2×C4—91no—
203C2×C4—92no—
204C2×C4—91no—
205C2×C4—188no—
206C2×C4—184no—
207C2×C4—368no—
208C2×C4—364no—
209C2×C4#377711yescharacteristic
210C2×C4#377712yes—
211C2×C4#377711yescharacteristic
212C2×C4#377712yes—
213C2×C3—42no—
214C2×C3—44no—
215C2×C3—41no—
216D3—122no—
217D3—124no—
218D3—122no—
219C22—41no—
220C22—91no—
221C22—92no—
222C22—91no—
223C22—184no—
224C22—182no—
225C22—361no—
226C22—362no—
227C22C2×#377712yes—
228C22C2×#377711yescharacteristic
229C4—91no—
230C4—91no—
231C4—92no—
232C4—364no—
233C4—368no—
234C4#6374711yescharacteristic
235C4#6374712yes—
236C4#6374711yescharacteristic
237C3—41no—
238C2—22no—
239C2—21no—
240C2—92no—
241C2—182no—
242C2—181no—
243C2C2×#6374711yescharacteristic
subgroupG/H
centerC4#63747
commutatorC2×C3⋊D3C2×C42
FrattiniC23C2×PSU(3,𝔽2)
FittingC22×C32×C4Q8
socleC2×C32C2×#95
prime radical, cosocleC23×C3⋊D3C23
hypercenterC22×C4PSU(3,𝔽2)
hypocenterC32#1740
LCSG ▷ C2×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
11. #64286C4semidirect
12. #64286C4semidirect
14. C2×C4⋊#157C4semidirect
16. C2×C4×#157C4semidirect
184. C32#1740semidirect

Maximal subgroups

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

subgroupindex
C2×#642862
#105900982
#17409