Finite Group Databasebeta

← #11773884

Subgroups — #11773884

Order 1152.

378 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 86 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×#63439C211yesmaximal, characteristic
2#10588399C212yesmaximal, complemented
3C9×#323C211yesmaximal, characteristic
4#10588202C211yesmaximal, characteristic
5#10588145C212yesmaximal, complemented
6#68102—31nomaximal
7C23×Dic9C411yescharacteristic
8C2×C9×C22⋊C4C2211yescharacteristic
9C2×#3676C411yescharacteristic
10C2×Dic9⋊C4C411yescharacteristic
11C2×Dic9⋊C4C2211yescharacteristic
12C2×C4×Dic9C411yescharacteristic
13C2×C4×Dic9C2211yescharacteristic
14#63439—22no—
15#63439—22no—
16C9×C22⋊C8C2212yes—
17#63389C2212yes—
18#63375—22no—
19Dic9⋊C8—22no—
20C2×#877—31no—
21#4719—32no—
22C3×#323D311yescharacteristic
23#4525—31no—
24#4469—32no—
25C24×C9C2×C411yescharacteristic
26C22×C4×C9C2×C411yescharacteristic
27C22×C4×C9C2311yescharacteristic
28C22×Dic9—22no—
29C22×Dic9—21no—
30C22×Dic9—21no—
31C22×Dic9—22no—
32C22×Dic9C2×C411yescharacteristic
33C22×Dic9C2×C411yescharacteristic
34C22×Dic9C2×C411yescharacteristic
35C22×Dic9C2×C411yescharacteristic
36C2×C8×C9—22no—
37C9×C22⋊C4—22no—
38#3676—22no—
39Dic9⋊C4—22no—
40Dic9⋊C4—22no—
41C4×Dic9—21no—
42C4×Dic9—21no—
43C4×Dic9D412yes—
44C4×Dic9D412yes—
45C2×C9⋊C8—22no—
46#1464—91noSylow
47C23×Dic3—31no—
48C2×C3×C22⋊C4C2×D311yescharacteristic
49C2×#217—31no—
50C2×Dic3⋊C4—31no—
51C2×Dic3⋊C4—31no—
52C2×C4×Dic3—31no—
53C2×C4×Dic3—31no—
54#877—62no—
55#877—62no—
56C3×C22⋊C8C2×D312yes—
57#830—32no—
58#815—62no—
59Dic3⋊C8—62no—
60C23×C9—21no—
61C23×C9—21no—
62C23×C9—41no—
63C23×C9—41no—
64C23×C9M1612yes—
65C23×C9C22×C411yescharacteristic
66C2×C4×C9—21no—
67C2×C4×C9—41no—
68C2×C4×C9—41no—
69C2×C4×C9C2×D412yes—
70C2×Dic9—24no—
71C2×Dic9—24no—
72C2×Dic9—21no—
73C2×Dic9—21no—
74C2×Dic9—21no—
75C2×Dic9—21no—
76C2×Dic9—21no—
77C2×Dic9—41no—
78C2×Dic9—41no—
79C2×Dic9C22⋊C411yescharacteristic
80C2×Dic9C22⋊C411yescharacteristic
81C2×Dic9C22⋊C412yes—
82C2×Dic9M1612yes—
83C8×C9—42no—
84C9⋊C8—42no—
85C2×#117—91no—
86#432—92no—
87#324—92no—
88#323—91no—
89#323D911yescharacteristic
90C24×C3C4×D311yescharacteristic
91C22×C3×C4C4×D311yescharacteristic
92C22×C3×C4C22×D311yescharacteristic
93C22×Dic3—31no—
94C22×Dic3—31no—
95C22×Dic3—31no—
96C22×Dic3—31no—
97C22×Dic3—61no—
98C22×Dic3—61no—
99C22×Dic3—62no—
100C22×Dic3—62no—
101C2×C3×C8—22no—
102C3×C22⋊C4—22no—
103#217—62no—
104Dic3⋊C4—62no—
105Dic3⋊C4—62no—
106C4×Dic3—32no—
107C4×Dic3—32no—
108C4×Dic3—61no—
109C4×Dic3—61no—
110C2×C3⋊C8—62no—
111C22×C9—21no—
112C22×C9—21no—
113C22×C9—22no—
114C22×C9—42no—
115C22×C9—42no—
116C22×C9—41no—
117C22×C9—41no—
118C22×C9C2×C22⋊C411yescharacteristic
119C22×C9C2×M1611yescharacteristic
120C22×C9C2×M1611yescharacteristic
121C4×C9—22no—
122C4×C9—41no—
123Dic9—21no—
124Dic9—21no—
125Dic9—22no—
126Dic9—22no—
127Dic9—41no—
128C23×C4—91no—
129#117—182no—
130#117—182no—
131C2×C4⋊C4—91no—
132C2×C4⋊C4—91no—
133C2×C22⋊C4—91no—
134C2×C22⋊C4C2×D911yescharacteristic
135C2×C42—91no—
136C2×C42—91no—
137C4⋊C8—182no—
138C22⋊C8—92no—
139C22⋊C8C2×D912yes—
140#97—182no—
141C23×C3—21no—
142C23×C3—21no—
143C23×C3—41no—
144C23×C3—41no—
145C23×C3ΓL(1,𝔽25)12yes—
146C23×C3C2×C4×D311yescharacteristic
147C2×C3×C4—21no—
148C2×C3×C4—41no—
149C2×C3×C4—41no—
150C2×C3×C4D3×D412yes—
151C2×Dic3—31no—
152C2×Dic3—31no—
153C2×Dic3—32no—
154C2×Dic3—32no—
155C2×Dic3—64no—
156C2×Dic3—64no—
157C2×Dic3—61no—
158C2×Dic3—61no—
159C2×Dic3—61no—
160C2×Dic3—61no—
161C2×Dic3—61no—
162C2×Dic3—121no—
163C2×Dic3—121no—
164C3×C8—42no—
165C3⋊C8—122no—
166C2×C9—21no—
167C2×C9—21no—
168C2×C9—42no—
169C2×C9#40711yescharacteristic
170C2×C9#41011yescharacteristic
171C2×C9#41311yescharacteristic
172C24C4×D911yescharacteristic
173C22×C4—91no—
174C22×C4—91no—
175C22×C4—91no—
176C22×C4—91no—
177C22×C4—181no—
178C22×C4—181no—
179C22×C4—182no—
180C22×C4—182no—
181C22×C4C4×D911yescharacteristic
182C22×C4C22×D911yescharacteristic
183C2×C8—22no—
184C2×C8—182no—
185C4⋊C4—182no—
186C4⋊C4—182no—
187C22⋊C4—22no—
188C22⋊C4—182no—
189C42—92no—
190C42—92no—
191C42—181no—
192C42—181no—
193C22×C3—21no—
194C22×C3—21no—
195C22×C3—22no—
196C22×C3—42no—
197C22×C3—42no—
198C22×C3—41no—
199C22×C3—41no—
200C22×C3D3×C22⋊C411yescharacteristic
201C22×C3C2×ΓL(1,𝔽25)11yescharacteristic
202C22×C3D3×M1611yescharacteristic
203C3×C4—22no—
204C3×C4—41no—
205Dic3—61no—
206Dic3—61no—
207Dic3—62no—
208Dic3—62no—
209Dic3—121no—
210C9#146411yescharacteristic, complemented, Sylow
211C23—21no—
212C23—21no—
213C23—41no—
214C23—41no—
215C23#366312yes—
216C23C2×C4×D911yescharacteristic
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—91no—
221C2×C4—91no—
222C2×C4—92no—
223C2×C4—92no—
224C2×C4—184no—
225C2×C4—184no—
226C2×C4—181no—
227C2×C4—181no—
228C2×C4—181no—
229C2×C4—181no—
230C2×C4—181no—
231C2×C4—361no—
232C2×C4—361no—
233C2×C4D4×D912yes—
234C8—42no—
235C8—362no—
236C2×C3—21no—
237C2×C3—21no—
238C2×C3—42no—
239C2×C3#472611yescharacteristic
240C2×C3#474011yescharacteristic
241C2×C3#474511yescharacteristic
242C22—21no—
243C22—21no—
244C22—22no—
245C22—42no—
246C22—42no—
247C22—41no—
248C22—41no—
249C22C22⋊C4×D911yescharacteristic
250C22C2×#366311yescharacteristic
251C22M16×D911yescharacteristic
252C4—22no—
253C4—41no—
254C4—182no—
255C4—181no—
256C4—181no—
257C4—182no—
258C4—361no—
259C3#6810211yescharacteristic
260C2—21no—
261C2—21no—
262C2—42no—
263C2#1058840811yescharacteristic
264C2#1058842011yescharacteristic
265C2#1058842511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D9
commutatorC23×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC9×#323C2
socleC22×C3D3×C22⋊C4
prime radicalC24×C3C4×D3
cosocleC22×C4×C9C23
hypercenter#323D9
hypocenterC9#1464
LCSG ▷ C23×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #10588399C2semidirect
5. #10588145C2semidirect
210. C9#1464semidirect

Maximal subgroups

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

subgroupindex
C2×#634392
#105883992
C9×#3232
#105882022
#105881452
#681023