Finite Group Databasebeta

← #11773911

Subgroups — #11773911

Order 1152.

474 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 88 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×#611⋊C4C211yesmaximal, characteristic
2#10588408C212yesmaximal, complemented
3C9×#323C211yesmaximal, characteristic, complemented
4#10588202C211yesmaximal, characteristic, complemented
5#10588145C212yesmaximal, complemented
6#68121—31nomaximal
7C22×#611C411yescharacteristic
8C23×Dic9C411yescharacteristic
9C22×C4×D9C2211yescharacteristic
10C2×C9×C22⋊C4C2211yescharacteristic
11C2×(C2×D9)⋊C4C411yescharacteristic
12C2×Dic9⋊C4C2211yescharacteristic
13C2×C4×Dic9C411yescharacteristic
14C2×#3663—22no—
15#611⋊C4—22no—
16#611⋊C4—22no—
17C9×C22⋊C8C2212yes—
18#63389C2212yes—
19(C2×D9)⋊C8—22no—
20C2×#67⋊C4—31no—
21#4726—32no—
22C3×#323D311yescharacteristic
23#4525—31no—
24#4469—32no—
25C24×C9C2×C411yescharacteristic
26C23×D9C2×C411yescharacteristic
27C22×C4×C9C2×C411yescharacteristic
28C22×C4×C9C2311yescharacteristic
29C2×#611—22no—
30C2×#611—22no—
31C2×#611—22no—
32C22×Dic9—21no—
33C22×Dic9—21no—
34C22×Dic9—42no—
35C22×Dic9C2×C411yescharacteristic
36C22×Dic9C2×C411yescharacteristic
37C22×Dic9C2×C411yescharacteristic
38C2×C4×D9—42no—
39C2×C4×D9D412yes—
40C2×C4×D9D412yes—
41C2×C8×C9—22no—
42C9×C22⋊C4—22no—
43(C2×D9)⋊C4—22no—
44Dic9⋊C4—22no—
45C4×Dic9—21no—
46C4×Dic9—21no—
47C2×C9⋊C8—22no—
48#3663—44no—
49#1465—91noSylow
50C22×#67—31no—
51C23×Dic3—31no—
52C22×C4×D3—31no—
53C2×C3×C22⋊C4C2×D311yescharacteristic
54C2×(C2×D3)⋊C4—31no—
55C2×Dic3⋊C4—31no—
56C2×C4×Dic3—31no—
57C2×ΓL(1,𝔽25)—62no—
58#67⋊C4—62no—
59#67⋊C4—62no—
60C3×C22⋊C8C2×D312yes—
61#830—32no—
62(C2×D3)⋊C8—62no—
63C23×C9—21no—
64C23×C9—21no—
65C23×C9—41no—
66C23×C9—41no—
67C23×C9M1612yescomplemented
68C23×C9C22×C411yescharacteristic
69C22×D9—21no—
70C22×D9—21no—
71C22×D9—41no—
72C22×D9—41no—
73C22×D9C22⋊C412yes—
74C2×C4×C9—21no—
75C2×C4×C9—41no—
76C2×C4×C9—41no—
77C2×C4×C9C2×D412yes—
78#611—28no—
79C2×Dic9—21no—
80C2×Dic9—21no—
81C2×Dic9—22no—
82C2×Dic9—21no—
83C2×Dic9—42no—
84C2×Dic9—42no—
85C2×Dic9—41no—
86C2×Dic9C22⋊C411yescharacteristic
87C2×Dic9C22⋊C411yescharacteristic
88C2×Dic9M1612yescomplemented
89C4×D9—24no—
90C4×D9—42no—
91C8×C9—42no—
92C9⋊C8—42no—
93C2×C4×D4—91no—
94#407—92no—
95#324—92no—
96#323—91no—
97#323D911yescharacteristic, complemented
98C24×C3C4×D311yescharacteristic
99C23×D3—31no—
100C22×C3×C4C4×D311yescharacteristic
101C22×C3×C4C22×D311yescharacteristic
102C2×#67—62no—
103C2×#67—62no—
104C2×#67—62no—
105C22×Dic3—31no—
106C22×Dic3—31no—
107C22×Dic3—31no—
108C22×Dic3—61no—
109C22×Dic3—61no—
110C22×Dic3—122no—
111C2×C4×D3—32no—
112C2×C4×D3—32no—
113C2×C4×D3—122no—
114C2×C3×C8—22no—
115C3×C22⋊C4—22no—
116(C2×D3)⋊C4—62no—
117Dic3⋊C4—62no—
118C4×Dic3—61no—
119C4×Dic3—61no—
120C2×C3⋊C8—62no—
121ΓL(1,𝔽25)—124no—
122C22×C9—21no—
123C22×C9—21no—
124C22×C9—22no—
125C22×C9—42no—
126C22×C9—42no—
127C22×C9—41no—
128C22×C9—41no—
129C22×C9C2×C22⋊C411yescharacteristic
130C22×C9C2×M1611yescharacteristic
131C22×C9C2×M1611yescharacteristic
132C2×D9—22no—
133C2×D9—22no—
134C2×D9—22no—
135C2×D9—42no—
136C2×D9—42no—
137C4×C9—22no—
138C4×C9—41no—
139Dic9—22no—
140Dic9—21no—
141Dic9—41no—
142Dic9#9912yes—
143C22×D4—91no—
144C23×C4—91no—
145C23×C4—91no—
146C2×M16—182no—
147C4×D4—182no—
148C4×D4—182no—
149C2×C4⋊C4—91no—
150C2×C22⋊C4—91no—
151C2×C22⋊C4C2×D911yescharacteristic
152C2×C42—91no—
153C22⋊C8—92no—
154C22⋊C8—182no—
155C22⋊C8C2×D912yes—
156C23×C3—21no—
157C23×C3—21no—
158C23×C3—41no—
159C23×C3—41no—
160C23×C3ΓL(1,𝔽25)12yes—
161C23×C3C2×C4×D311yescharacteristic
162C22×D3—32no—
163C22×D3—61no—
164C22×D3—61no—
165C22×D3—121no—
166C22×D3—121no—
167C2×C3×C4—21no—
168C2×C3×C4—41no—
169C2×C3×C4—41no—
170C2×C3×C4D3×D412yes—
171#67—68no—
172C2×Dic3—31no—
173C2×Dic3—31no—
174C2×Dic3—32no—
175C2×Dic3—62no—
176C2×Dic3—61no—
177C2×Dic3—61no—
178C2×Dic3—61no—
179C2×Dic3—122no—
180C2×Dic3—122no—
181C2×Dic3—121no—
182C4×D3—64no—
183C4×D3—122no—
184C3×C8—42no—
185C3⋊C8—122no—
186C2×C9—21no—
187C2×C9—21no—
188C2×C9—42no—
189C2×C9#40711yescharacteristic
190C2×C9C2×#9911yescharacteristic
191C2×C9#41311yescharacteristic
192D9—42no—
193C24—91no—
194C24C4×D911yescharacteristic
195C2×D4—182no—
196C2×D4—182no—
197C2×D4—182no—
198C22×C4—91no—
199C22×C4—91no—
200C22×C4—92no—
201C22×C4—92no—
202C22×C4—91no—
203C22×C4—181no—
204C22×C4—181no—
205C22×C4—362no—
206C22×C4—362no—
207C22×C4C4×D911yescharacteristic
208C22×C4C22×D911yescharacteristic
209M16—364no—
210C2×C8—22no—
211C2×C8—182no—
212C4⋊C4—182no—
213C22⋊C4—22no—
214C22⋊C4—182no—
215C42—181no—
216C42—181no—
217C22×C3—21no—
218C22×C3—21no—
219C22×C3—22no—
220C22×C3—42no—
221C22×C3—42no—
222C22×C3—41no—
223C22×C3—41no—
224C22×C3D3×C22⋊C411yescharacteristic
225C22×C3C2×ΓL(1,𝔽25)11yescharacteristic
226C22×C3D3×M1611yescharacteristic
227C2×D3—62no—
228C2×D3—62no—
229C2×D3—62no—
230C2×D3—122no—
231C2×D3—122no—
232C3×C4—22no—
233C3×C4—41no—
234Dic3—32no—
235Dic3—62no—
236Dic3—61no—
237Dic3—121no—
238C9#146511yescharacteristic, complemented, Sylow
239C23—21no—
240C23—21no—
241C23—41no—
242C23—41no—
243C23—92no—
244C23—181no—
245C23—181no—
246C23—361no—
247C23—361no—
248C23#366312yescomplemented
249C23C2×C4×D911yescharacteristic
250D4—188no—
251C2×C4—21no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—91no—
255C2×C4—91no—
256C2×C4—92no—
257C2×C4—184no—
258C2×C4—182no—
259C2×C4—181no—
260C2×C4—181no—
261C2×C4—181no—
262C2×C4—362no—
263C2×C4—362no—
264C2×C4—362no—
265C2×C4—361no—
266C2×C4D4×D912yes—
267C8—42no—
268C8—362no—
269C2×C3—21no—
270C2×C3—21no—
271C2×C3—42no—
272C2×C3#472611yescharacteristic
273C2×C3D3×#9911yescharacteristic
274C2×C3#474511yescharacteristic
275D3—122no—
276C22—21no—
277C22—21no—
278C22—22no—
279C22—42no—
280C22—42no—
281C22—41no—
282C22—41no—
283C22—182no—
284C22—182no—
285C22—182no—
286C22—362no—
287C22—362no—
288C22C22⋊C4×D911yescharacteristic
289C22C2×#366311yescharacteristic
290C22M16×D911yescharacteristic
291C4—22no—
292C4—41no—
293C4—92no—
294C4—181no—
295C4—182no—
296C4—361no—
297C3#6812111yescharacteristic
298C2—21no—
299C2—21no—
300C2—42no—
301C2—362no—
302C2#1058840811yescharacteristic
303C2D9×#9911yescharacteristic
304C2#1058842511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D9
commutatorC23×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC9×#323C2
socleC22×C3D3×C22⋊C4
prime radicalC22×#611C4
cosocleC22×C4×C9C23
hypercenter#323D9
hypocenterC9#1465
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. #10588408C2semidirect
3. C9×#323C2semidirect
4. #10588202C2semidirect
5. #10588145C2semidirect
67. C23×C9M16semidirect
88. C2×Dic9M16semidirect
97. #323D9semidirect
238. C9#1465semidirect
248. C23#3663semidirect

Maximal subgroups

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

subgroupindex
C2×#611⋊C42
#105884082
C9×#3232
#105882022
#105881452
#681213