Finite Group Databasebeta

← #11773771

Subgroups — #11773771

Order 1152.

382 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 69 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×#64286C211yesmaximal, characteristic
2#10596484C212yesmaximal, complemented
3#10593272C212yesmaximal
4#10593260C212yesmaximal, complemented
5C22×C4×C3⋊D3C411yescharacteristic
6C2×C22⋊#157C411yescharacteristic
7C2×C22⋊#157C2211yescharacteristic
8#64286—22no—
9#64286—22no—
10C2×C4⋊#157C411yescharacteristic
11C2×C4⋊#157C2211yescharacteristic
12C2×C4×#157C411yescharacteristic
13C2×C4×#157C2211yescharacteristic
14C22⋊AGL(1,𝔽9)C2214yes—
15C4⋊AGL(1,𝔽9)—22no—
16C4×AGL(1,𝔽9)—22no—
17C23×C3⋊D3C2×C411yescharacteristic
18C22×#157C2×C411yescharacteristic
19C22×#157C2×C411yescharacteristic
20C22×#157C2×C411yescharacteristic
21C22×#157C2311yescharacteristic
22C2×AGL(1,𝔽9)—24no—
23C22×C32×C4C811yescharacteristic, complemented
24C22×C3⋊Dic3C811yescharacteristic, complemented
25C2×C4×C3⋊D3—21no—
26C2×C4×C3⋊D3—21no—
27C2×C4×C3⋊D3—21no—
28C2×C4×C3⋊D3—21no—
29C2×C4×C3⋊D3C811yescharacteristic, complemented
30C2×C4×C3⋊D3C811yescharacteristic, complemented
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3C2×C411yescharacteristic
33C22⋊#157—22no—
34C22⋊#157—22no—
35C4⋊#157—22no—
36C4⋊#157—22no—
37C4×#157—21no—
38C4×#157—21no—
39C4×#157D412yes—
40C4×#157D412yes—
41#1458—91nomaximal, Sylow
42C22×C4×D3—121no—
43C23×C32C2×C811yescharacteristic
44C22×C3⋊D3—21no—
45C22×C3⋊D3—21no—
46C22×C3⋊D3—41no—
47C22×C3⋊D3—41no—
48C22×C3⋊D3C2×C811yescharacteristic
49C22×C3⋊D3C22×C411yescharacteristic
50C2×#157—21no—
51C2×#157—21no—
52C2×#157—41no—
53C2×#157—41no—
54C2×#157—41no—
55C2×#157—41no—
56C2×#157C22⋊C412yes—
57C2×#157C2×D412yes—
58AGL(1,𝔽9)—44no—
59C2×C32×C4—21no—
60C2×C32×C4—21no—
61C2×C32×C4C2×C811yescharacteristic
62C2×C32×C4C2×C811yescharacteristic
63C2×C3⋊Dic3—21no—
64C2×C3⋊Dic3—21no—
65C2×C3⋊Dic3C2×C811yescharacteristic
66C2×C3⋊Dic3C2×C811yescharacteristic
67C4×C3⋊D3—21no—
68C4×C3⋊D3—21no—
69C4×C3⋊D3—21no—
70C4×C3⋊D3—21no—
71C4×C3⋊D3—21no—
72C4×C3⋊D3—21no—
73C4×C3⋊D3C22⋊C411yescharacteristic
74C4×C3⋊D3C22⋊C411yescharacteristic
75C4×C3⋊D3M1611yescharacteristic
76C4×C3⋊D3M1611yescharacteristic
77C2×#117—91no—
78#431—92no—
79#324—92no—
80#323—92no—
81C23×D3—121no—
82C22×C3×C4—41no—
83C22×Dic3—121no—
84C2×C4×D3—121no—
85C2×C4×D3—121no—
86C2×C4×D3—121no—
87C2×C4×D3—121no—
88C2×C4×D3—122no—
89C2×C4×D3—122no—
90C2×C4×D3—122no—
91C2×C4×D3—122no—
92C22×C32—21no—
93C22×C32—41no—
94C22×C32C22×C811yescharacteristic
95C2×C3⋊D3—21no—
96C2×C3⋊D3—21no—
97C2×C3⋊D3—21no—
98C2×C3⋊D3—42no—
99C2×C3⋊D3—41no—
100C2×C3⋊D3—41no—
101C2×C3⋊D3—41no—
102C2×C3⋊D3C2×C22⋊C411yescharacteristic
103C2×C3⋊D3C2×M1611yescharacteristic
104#157—22no—
105#157—22no—
106#157—41no—
107#157—41no—
108C32×C4—21no—
109C32×C4C22⋊C811yescharacteristic
110C32×C4C22⋊C811yescharacteristic
111C3⋊Dic3—21no—
112C3⋊Dic3C22⋊C811yescharacteristic
113C3⋊Dic3C22⋊C811yescharacteristic
114C23×C4—91no—
115#117—182no—
116#117—182no—
117C2×C4⋊C4—91no—
118C2×C4⋊C4—91no—
119C2×C22⋊C4—91no—
120C2×C22⋊C4—91no—
121C2×C42—91no—
122C2×C42—91no—
123C4⋊C8—182no—
124C22⋊C8—94no—
125C4×C8—182no—
126C23×C3—41no—
127C22×D3—121no—
128C22×D3—121no—
129C22×D3—122no—
130C22×D3—122no—
131C22×D3—124no—
132C22×D3—124no—
133C2×C3×C4—42no—
134C2×C3×C4—42no—
135C2×C3×C4—41no—
136C2×C3×C4—41no—
137C2×Dic3—121no—
138C2×Dic3—121no—
139C2×Dic3—122no—
140C2×Dic3—122no—
141C4×D3—121no—
142C4×D3—121no—
143C4×D3—121no—
144C4×D3—121no—
145C4×D3—122no—
146C4×D3—122no—
147C4×D3—122no—
148C4×D3—122no—
149C4×D3—122no—
150C4×D3—122no—
151C2×C32—21no—
152C2×C32—41no—
153C2×C32C2×C22⋊C811yescharacteristic
154C3⋊D3—21no—
155C3⋊D3—41no—
156C3⋊D3#41011yescharacteristic
157C3⋊D3#41311yescharacteristic
158C24—91no—
159C22×C4—91no—
160C22×C4—91no—
161C22×C4—91no—
162C22×C4—91no—
163C22×C4—91no—
164C22×C4—91no—
165C22×C4—91no—
166C22×C4—91no—
167C22×C4—91no—
168C22×C4—181no—
169C22×C4—181no—
170C22×C4—181no—
171C22×C4—181no—
172C22×C4AGL(1,𝔽9)11yescharacteristic, complemented
173C2×C8—184no—
174C4⋊C4—182no—
175C4⋊C4—182no—
176C22⋊C4—182no—
177C22⋊C4—182no—
178C42—92no—
179C42—92no—
180C42—181no—
181C42—181no—
182C22×C3—42no—
183C22×C3—44no—
184C22×C3—41no—
185C2×D3—121no—
186C2×D3—121no—
187C2×D3—122no—
188C2×D3—122no—
189C2×D3—122no—
190C2×D3—124no—
191C2×D3—124no—
192C2×D3—124no—
193C2×D3—128no—
194C3×C4—42no—
195C3×C4—41no—
196C3×C4—41no—
197Dic3—121no—
198Dic3—121no—
199Dic3—122no—
200C32#145811yescharacteristic, complemented, Sylow
201C23—91no—
202C23—91no—
203C23—181no—
204C23—181no—
205C23—361no—
206C23—361no—
207C23C2×AGL(1,𝔽9)11yescharacteristic
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—91no—
211C2×C4—91no—
212C2×C4—91no—
213C2×C4—91no—
214C2×C4—91no—
215C2×C4—92no—
216C2×C4—92no—
217C2×C4—91no—
218C2×C4—181no—
219C2×C4—181no—
220C2×C4—181no—
221C2×C4—181no—
222C2×C4—181no—
223C2×C4—181no—
224C2×C4—181no—
225C2×C4—181no—
226C2×C4—181no—
227C2×C4—181no—
228C2×C4—361no—
229C2×C4—361no—
230C2×C4—361no—
231C2×C4—361no—
232C2×C4C2×AGL(1,𝔽9)11yescharacteristic
233C2×C4C2×AGL(1,𝔽9)11yescharacteristic
234C8—364no—
235C2×C3—42no—
236C2×C3—44no—
237C2×C3—41no—
238D3—121no—
239D3—121no—
240D3—122no—
241D3—124no—
242C22—21no—
243C22—41no—
244C22—91no—
245C22—91no—
246C22—181no—
247C22—181no—
248C22—181no—
249C22—361no—
250C22—361no—
251C22—361no—
252C22—362no—
253C22C22×AGL(1,𝔽9)11yescharacteristic
254C4—21no—
255C4—91no—
256C4—91no—
257C4—182no—
258C4—182no—
259C4—181no—
260C4—361no—
261C4—361no—
262C4C22⋊AGL(1,𝔽9)11yescharacteristic
263C4C22⋊AGL(1,𝔽9)11yescharacteristic
264C3—41no—
265C2—21no—
266C2—41no—
267C2—91no—
268C2—91no—
269C2—181no—
270C2—361no—
271C2C2×C22⋊AGL(1,𝔽9)11yescharacteristic
subgroupG/H
centerC4C22⋊AGL(1,𝔽9)
commutatorC22×C32C22×C8
FrattiniC22C22×AGL(1,𝔽9)
FittingC22×C32×C4C8
socleC2×C32C2×C22⋊C8
prime radicalC23×C3⋊D3C2×C4
cosocleC22×#157C23
hypercenterC22×C4AGL(1,𝔽9)
hypocenterC32#1458
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10596484C2semidirect
4. #10593260C2semidirect
23. C22×C32×C4C8semidirect
24. C22×C3⋊Dic3C8semidirect
29. C2×C4×C3⋊D3C8semidirect
30. C2×C4×C3⋊D3C8semidirect
172. C22×C4AGL(1,𝔽9)semidirect
200. C32#1458semidirect

Maximal subgroups

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

subgroupindex
C2×#642862
#105964842
#105932722
#105932602
#14589