Finite Group Databasebeta

← #11770846

Subgroups — #11770846

Order 1152.

294 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 53 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×C22⋊AGL(1,𝔽9)C211yesmaximal, characteristic
2C2×C22⋊AGL(1,𝔽9)C211yesmaximal, characteristic
3C22⋊C4×#157C211yesmaximal, characteristic
4C23×#157C2211yescharacteristic
5C22×AGL(1,𝔽9)—21no—
6C22×AGL(1,𝔽9)C412yescomplemented
7C2×C22⋊#157C411yescharacteristic
8C2×C4×#157—21no—
9C22⋊AGL(1,𝔽9)—21no—
10C22⋊AGL(1,𝔽9)—21no—
11C22⋊AGL(1,𝔽9)—21no—
12C22⋊AGL(1,𝔽9)C412yescomplemented
13C22⋊C4×C3⋊D3C411yescharacteristic
14#63781—21no—
15C23×C3⋊D3C2×C411yescharacteristic
16C22×#157—21no—
17C22×#157—42no—
18C22×#157C2×C411yescharacteristic
19C22×#157C2×C411yescharacteristic
20C22×#157D411yescharacteristic
21C22×#157D411yescharacteristic
22C22×#157D411yescharacteristic
23C22×#157Q811yescharacteristic
24C2×AGL(1,𝔽9)—22no—
25C2×AGL(1,𝔽9)—22no—
26C2×AGL(1,𝔽9)—42no—
27C2×AGL(1,𝔽9)—42no—
28C2×C4×C3⋊D3—21no—
29C22⋊#157—21no—
30C22⋊#157C812yescomplemented
31C4×#157—42no—
32C32×C22⋊C4C811yescharacteristic, complemented
33#3757C811yescharacteristic, complemented
34#3752—21no—
35#1282—91nomaximal, Sylow
36D3×C22⋊C4—121no—
37C23×C32C2×C811yescharacteristic
38C22×C3⋊D3—41no—
39C22×C3⋊D3—41no—
40C22×C3⋊D3C4211yescharacteristic
41C22×C3⋊D3C22⋊C411yescharacteristic
42C22×C3⋊D3C4⋊C411yescharacteristic
43C22×C3⋊D3C2×C811yescharacteristic
44C22×C3⋊D3M1611yescharacteristic
45C22×C3⋊D3M1611yescharacteristic
46C2×#157—22no—
47C2×#157—22no—
48C2×#157—22no—
49C2×#157—22no—
50C2×#157—41no—
51C2×#157—41no—
52C2×#157—41no—
53C2×#157—41no—
54C2×#157—41no—
55C2×#157C22⋊C411yescharacteristic
56C2×#157C22⋊C411yescharacteristic
57C2×#157C4⋊C411yescharacteristic
58C2×#157C4⋊C411yescharacteristic
59AGL(1,𝔽9)—42no—
60AGL(1,𝔽9)—42no—
61C2×C32×C4—21no—
62C2×C3⋊Dic3—21no—
63C4×C3⋊D3—41no—
64C4×C3⋊D3—41no—
65C2×C22⋊C8—91no—
66C2×C22⋊C8—91no—
67C4×C22⋊C4—91no—
68C23×D3—121no—
69C2×C4×D3—122no—
70C3×C22⋊C4—41no—
71#217—121no—
72(C2×D3)⋊C4—122no—
73C22×C32—41no—
74C22×C32C4×C811yescharacteristic
75C22×C32C22⋊C811yescharacteristic
76C22×C32C4⋊C811yescharacteristic
77C2×C3⋊D3—21no—
78C2×C3⋊D3—21no—
79C2×C3⋊D3—21no—
80C2×C3⋊D3—21no—
81C2×C3⋊D3—21no—
82C2×C3⋊D3—21no—
83C2×C3⋊D3—41no—
84C2×C3⋊D3—41no—
85C2×C3⋊D3—41no—
86C2×C3⋊D3#9511yescharacteristic
87C2×C3⋊D3#9711yescharacteristic
88C2×C3⋊D3C22⋊C811yescharacteristic
89C2×C3⋊D3C4⋊C811yescharacteristic
90#157—21no—
91#157—21no—
92#157—21no—
93#157—42no—
94#157#9912yes—
95C32×C4—41no—
96C3⋊Dic3—41no—
97C23×C4—91no—
98C22×C8—92no—
99C22×C8—181no—
100C2×C22⋊C4—91no—
101C2×C22⋊C4—91no—
102C2×C42—181no—
103C22⋊C8—92no—
104C22⋊C8—181no—
105C22⋊C8—181no—
106C22⋊C8—181no—
107#95—181no—
108C23×C3—41no—
109C22×D3—121no—
110C22×D3—121no—
111C22×D3—121no—
112C22×D3—121no—
113C22×D3—121no—
114C22×D3—121no—
115C22×D3—242no—
116C22×D3—242no—
117C2×C3×C4—42no—
118C2×Dic3—122no—
119C4×D3—242no—
120C4×D3—242no—
121C2×C32—21no—
122C2×C32—21no—
123C2×C32—21no—
124C2×C32#33611yescharacteristic
125C3⋊D3—21no—
126C3⋊D3—21no—
127C3⋊D3—21no—
128C3⋊D3#34211yescharacteristic
129C3⋊D3#34411yescharacteristic
130C24—91no—
131C22×C4—91no—
132C22×C4—91no—
133C22×C4—91no—
134C22×C4—91no—
135C22×C4—91no—
136C22×C4—91no—
137C22×C4—181no—
138C22×C4—181no—
139C22×C4—362no—
140C2×C8—182no—
141C2×C8—182no—
142C2×C8—362no—
143C2×C8—362no—
144C22⋊C4—92no—
145C22⋊C4—91no—
146C22⋊C4—181no—
147C22⋊C4—181no—
148C22⋊C4AGL(1,𝔽9)11yescharacteristic, complemented
149C42—362no—
150C22×C3—41no—
151C22×C3—41no—
152C22×C3—41no—
153C22×C3—82no—
154C2×D3—121no—
155C2×D3—121no—
156C2×D3—121no—
157C2×D3—121no—
158C2×D3—122no—
159C2×D3—122no—
160C2×D3—241no—
161C2×D3—241no—
162C2×D3—241no—
163C2×D3—241no—
164C2×D3—242no—
165C2×D3—242no—
166C2×D3—242no—
167C3×C4—82no—
168Dic3—242no—
169C32#128211yescharacteristic, complemented, Sylow
170C23—91no—
171C23—91no—
172C23—91no—
173C23—91no—
174C23—91no—
175C23—91no—
176C23—361no—
177C23—361no—
178C23C2×AGL(1,𝔽9)11yescharacteristic
179C2×C4—21no—
180C2×C4—91no—
181C2×C4—91no—
182C2×C4—91no—
183C2×C4—91no—
184C2×C4—182no—
185C2×C4—182no—
186C2×C4—182no—
187C2×C4—182no—
188C2×C4—181no—
189C2×C4—361no—
190C2×C4—361no—
191C2×C4—361no—
192C2×C4—361no—
193C2×C4—361no—
194C2×C4—361no—
195C2×C4—361no—
196C8—362no—
197C8—362no—
198C2×C3—42no—
199C2×C3—41no—
200C2×C3—81no—
201C2×C3—81no—
202D3—121no—
203D3—121no—
204D3—122no—
205D3—241no—
206D3—241no—
207C22—41no—
208C22—91no—
209C22—91no—
210C22—91no—
211C22—91no—
212C22—181no—
213C22—181no—
214C22—181no—
215C22—181no—
216C22—181no—
217C22—181no—
218C22—361no—
219C22—361no—
220C22—361no—
221C22C4×AGL(1,𝔽9)11yescharacteristic
222C22C4⋊AGL(1,𝔽9)11yescharacteristic
223C22C22⋊AGL(1,𝔽9)11yescharacteristic
224C4—41no—
225C4—92no—
226C4—181no—
227C4—181no—
228C4—181no—
229C4—361no—
230C4—362no—
231C3—41no—
232C2—21no—
233C2—21no—
234C2—21no—
235C2—91no—
236C2—91no—
237C2—181no—
238C2—181no—
239C2—181no—
240C2#1059326711yescharacteristic
subgroupG/H
centerC2#10593267
commutatorC22×C32C4×C8
FrattiniC23C2×AGL(1,𝔽9)
FittingC32×C22⋊C4C8
socleC2×C32#336
prime radicalC23×C3⋊D3C2×C4
cosocleC23×#157C22
hypercenterC22⋊C4AGL(1,𝔽9)
hypocenterC32#1282
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C23 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
6. C22×AGL(1,𝔽9)C4semidirect
12. C22⋊AGL(1,𝔽9)C4semidirect
30. C22⋊#157C8semidirect
32. C32×C22⋊C4C8semidirect
33. #3757C8semidirect
148. C22⋊C4AGL(1,𝔽9)semidirect
169. C32#1282semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊AGL(1,𝔽9)2
C22⋊C4×#1572
#12829