Finite Group Databasebeta

← #11773864

Subgroups — #11773864

Order 1152.

468 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 90 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×C4⋊C4×D9C211yesmaximal, characteristic
2#10588408C212yesmaximal
3C9×#324C211yesmaximal, characteristic, complemented
4#10588205C211yesmaximal, characteristic, complemented
5#10588145C212yesmaximal, complemented
6#68144—31nomaximal
7C22×C4×D9C411yescharacteristic
8C22×C4×D9C411yescharacteristic
9C22×C4×D9C2211yescharacteristic
10C2×C9×C4⋊C4C2211yescharacteristic
11C2×C4⋊Dic9C411yescharacteristic
12C2×Dic9⋊C4C411yescharacteristic
13C2×Dic9⋊C4C2211yescharacteristic
14C2×#3663—22no—
15C4⋊C4×D9—22no—
16C4⋊C4×D9—22no—
17C9×C22⋊C8C2212yes—
18#63389C2212yes—
19(C2×D9)⋊C8—22no—
20C2×D3×C4⋊C4—31no—
21#4726—32no—
22C3×#324D311yescharacteristic
23#4528—31no—
24#4469—32no—
25C23×D9C2×C411yescharacteristic
26C22×C4×C9C2×C411yescharacteristic
27C22×C4×C9C2×C411yescharacteristic
28C22×C4×C9C2311yescharacteristic
29C22×Dic9C2×C411yescharacteristic
30C22×Dic9C2×C411yescharacteristic
31C22×Dic9C2×C411yescharacteristic
32C2×C4×D9—21no—
33C2×C4×D9—21no—
34C2×C4×D9—22no—
35C2×C4×D9—22no—
36C2×C4×D9—21no—
37C2×C4×D9—21no—
38C2×C4×D9—42no—
39C2×C4×D9—42no—
40C2×C4×D9D412yes—
41C2×C4×D9D412yes—
42C2×C8×C9—22no—
43C9×C4⋊C4—22no—
44C4⋊Dic9—22no—
45Dic9⋊C4—22no—
46Dic9⋊C4—22no—
47C2×C9⋊C8—22no—
48#3663—44no—
49#1463—91noSylow
50C22×C4×D3—31no—
51C22×C4×D3—31no—
52C22×C4×D3—31no—
53C2×C3×C4⋊C4C2×D311yescharacteristic
54C2×C4⋊Dic3—31no—
55C2×Dic3⋊C4—31no—
56C2×Dic3⋊C4—31no—
57C2×ΓL(1,𝔽25)—62no—
58D3×C4⋊C4—62no—
59D3×C4⋊C4—62no—
60C3×C22⋊C8C2×D312yes—
61#830—32no—
62(C2×D3)⋊C8—62no—
63C23×C9C22×C411yescharacteristic
64C22×D9—21no—
65C22×D9—21no—
66C22×D9—22no—
67C22×D9—22no—
68C22×D9C22⋊C411yescharacteristic
69C22×D9C22⋊C411yescharacteristic
70C2×C4×C9—21no—
71C2×C4×C9—21no—
72C2×C4×C9—21no—
73C2×C4×C9—41no—
74C2×C4×C9—41no—
75C2×C4×C9M1612yescomplemented
76C2×C4×C9C2×D412yes—
77C2×Dic9—21no—
78C2×Dic9—21no—
79C2×Dic9—21no—
80C2×Dic9—41no—
81C2×Dic9—41no—
82C2×Dic9C22⋊C412yes—
83C2×Dic9M1612yescomplemented
84C4×D9—24no—
85C4×D9—24no—
86C4×D9—24no—
87C4×D9—42no—
88C4×D9—42no—
89C4×D9—42no—
90C8×C9—42no—
91C9⋊C8—42no—
92C22×C4⋊C4—91no—
93#407—92no—
94#324—91no—
95#324—92no—
96#324D911yescharacteristic, complemented
97C23×D3—31no—
98C22×C3×C4C4×D311yescharacteristic
99C22×C3×C4C4×D311yescharacteristic
100C22×C3×C4C22×D311yescharacteristic
101C22×Dic3—31no—
102C22×Dic3—31no—
103C22×Dic3—31no—
104C2×C4×D3—32no—
105C2×C4×D3—32no—
106C2×C4×D3—62no—
107C2×C4×D3—61no—
108C2×C4×D3—61no—
109C2×C4×D3—62no—
110C2×C4×D3—61no—
111C2×C4×D3—61no—
112C2×C4×D3—122no—
113C2×C4×D3—122no—
114C2×C3×C8—22no—
115C3×C4⋊C4—22no—
116C4⋊Dic3—62no—
117Dic3⋊C4—62no—
118Dic3⋊C4—62no—
119C2×C3⋊C8—62no—
120ΓL(1,𝔽25)—124no—
121C22×C9—21no—
122C22×C9—21no—
123C22×C9C2×C22⋊C411yescharacteristic
124C22×C9C2×M1611yescharacteristic
125C22×C9C2×M1611yescharacteristic
126C2×D9—24no—
127C2×D9—24no—
128C2×D9—21no—
129C2×D9—21no—
130C2×D9—21no—
131C2×D9—21no—
132C2×D9#9912yes—
133C2×D9#10112yes—
134C4×C9—22no—
135C4×C9—22no—
136C4×C9—41no—
137Dic9—22no—
138Dic9—22no—
139Dic9—41no—
140C23×C4—91no—
141C23×C4—91no—
142C23×C4—91no—
143C2×M16—182no—
144C2×C4⋊C4—91no—
145C2×C4⋊C4—91no—
146C2×C4⋊C4—91no—
147C2×C4⋊C4—182no—
148C2×C4⋊C4—182no—
149C2×C4⋊C4C2×D911yescharacteristic
150C22⋊C8—92no—
151C22⋊C8—182no—
152C22⋊C8C2×D912yes—
153C23×C3C2×C4×D311yescharacteristic
154C22×D3—31no—
155C22×D3—31no—
156C22×D3—62no—
157C22×D3—62no—
158C22×D3—61no—
159C22×D3—61no—
160C2×C3×C4—21no—
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—41no—
164C2×C3×C4—41no—
165C2×C3×C4ΓL(1,𝔽25)12yes—
166C2×C3×C4D3×D412yes—
167C2×Dic3—32no—
168C2×Dic3—32no—
169C2×Dic3—61no—
170C2×Dic3—61no—
171C2×Dic3—61no—
172C2×Dic3—121no—
173C2×Dic3—121no—
174C4×D3—64no—
175C4×D3—64no—
176C4×D3—64no—
177C4×D3—122no—
178C4×D3—122no—
179C4×D3—122no—
180C3×C8—42no—
181C3⋊C8—122no—
182C2×C9—21no—
183C2×C9—21no—
184C2×C9#40711yescharacteristic
185C2×C9C2×#9911yescharacteristic
186C2×C9C2×#10111yescharacteristic
187D9—22no—
188D9—22no—
189C24—91no—
190C22×C4—91no—
191C22×C4—91no—
192C22×C4—92no—
193C22×C4—92no—
194C22×C4—91no—
195C22×C4—182no—
196C22×C4—181no—
197C22×C4—181no—
198C22×C4—181no—
199C22×C4—181no—
200C22×C4—182no—
201C22×C4—362no—
202C22×C4—362no—
203C22×C4C4×D911yescharacteristic
204C22×C4C4×D911yescharacteristic
205C22×C4C22×D911yescharacteristic
206M16—364no—
207C2×C8—22no—
208C2×C8—182no—
209C4⋊C4—22no—
210C4⋊C4—182no—
211C4⋊C4—182no—
212C4⋊C4—182no—
213C22×C3—21no—
214C22×C3—21no—
215C22×C3D3×C22⋊C411yescharacteristic
216C22×C3C2×ΓL(1,𝔽25)11yescharacteristic
217C22×C3D3×M1611yescharacteristic
218C2×D3—32no—
219C2×D3—32no—
220C2×D3—64no—
221C2×D3—64no—
222C2×D3—61no—
223C2×D3—61no—
224C2×D3—61no—
225C2×D3—61no—
226C3×C4—22no—
227C3×C4—22no—
228C3×C4—41no—
229Dic3—62no—
230Dic3—62no—
231Dic3—121no—
232C9#146311yescharacteristic, complemented, Sylow
233C23—91no—
234C23—91no—
235C23—182no—
236C23—182no—
237C23—181no—
238C23—181no—
239C23C2×C4×D911yescharacteristic
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—92no—
246C2×C4—92no—
247C2×C4—184no—
248C2×C4—184no—
249C2×C4—184no—
250C2×C4—181no—
251C2×C4—181no—
252C2×C4—181no—
253C2×C4—362no—
254C2×C4—362no—
255C2×C4—362no—
256C2×C4—361no—
257C2×C4—361no—
258C2×C4#366312yescomplemented
259C2×C4D4×D912yes—
260C8—42no—
261C8—362no—
262C2×C3—21no—
263C2×C3—21no—
264C2×C3#472611yescharacteristic
265C2×C3D3×#9911yescharacteristic
266C2×C3D3×#10111yescharacteristic
267D3—62no—
268D3—62no—
269C22—21no—
270C22—21no—
271C22—92no—
272C22—92no—
273C22—184no—
274C22—184no—
275C22—181no—
276C22—181no—
277C22—181no—
278C22—181no—
279C22C22⋊C4×D911yescharacteristic
280C22C2×#366311yescharacteristic
281C22M16×D911yescharacteristic
282C4—22no—
283C4—22no—
284C4—41no—
285C4—182no—
286C4—182no—
287C4—361no—
288C3#6814411yescharacteristic
289C2—21no—
290C2—21no—
291C2—182no—
292C2—182no—
293C2#1058840811yescharacteristic
294C2D9×#9911yescharacteristic
295C2D9×#10111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D9
commutatorC23×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC9×#324C2
socleC22×C3D3×C22⋊C4
prime radicalC23×D9C2×C4
cosocleC22×C4×C9C23
hypercenter#324D9
hypocenterC9#1463
LCSG ▷ C23×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
3. C9×#324C2semidirect
4. #10588205C2semidirect
5. #10588145C2semidirect
75. C2×C4×C9M16semidirect
83. C2×Dic9M16semidirect
96. #324D9semidirect
232. C9#1463semidirect
258. C2×C4#3663semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D92
#105884082
C9×#3242
#105882052
#105881452
#681443