Finite Group Databasebeta

← #11775315

Subgroups — #11775315

Order 1152.

411 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 411 conjugacy classes of subgroups — too many to draw. Only its 100 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×#63486C211yesmaximal, characteristic
2C9×#381C211yesmaximal, characteristic
3#10588887C211yesmaximal, characteristic
4#10588128C214yesmaximal, complemented
5#69533—31nomaximal
6C23×C4×C9C2211yescharacteristic
7C22×Dic18C411yescharacteristic, complemented
8C2×C9×C22⋊C4—21no—
9C2×#3676—21no—
10C2×C4⋊Dic9C411yescharacteristic, complemented
11#63486—21no—
12#63486—21no—
13#63486C412yescomplemented
14#63486C2212yes—
15C2×Dic9⋊C4—21no—
16C2×#3667—21no—
17C9×#95—21no—
18C9×#95C2212yes—
19#63389—21no—
20#63389C2212yes—
21C2×#924—31no—
22C3×#381D311yescharacteristic
23#5207—31no—
24#4452—34no—
25C24×C9D411yescharacteristic
26C22×C4×C9—22no—
27C22×C4×C9—42no—
28C22×C4×C9C2×C411yescharacteristic
29C22×C4×C9C2×C411yescharacteristic
30C22×C4×C9D411yescharacteristic
31C22×C4×C9D411yescharacteristic
32C22×C4×C9D411yescharacteristic
33C22×C4×C9C2311yescharacteristic
34C22×Dic9—21no—
35C22×Dic9—21no—
36C2×Dic18—21no—
37C2×Dic18—42no—
38C2×Dic18C2×C412yes—
39C9×C22⋊C4—42no—
40#3676—22no—
41#3676—22no—
42C4⋊Dic9—21no—
43C4⋊Dic9C2×C412yes—
44Dic9⋊C4—22no—
45Dic9⋊C4—22no—
46#3667—42no—
47C2×C9⋊C8—22no—
48#1511—91noSylow
49C23×C3×C4C2×D311yescharacteristic
50C22×Dic6—31no—
51C2×C3×C22⋊C4—21no—
52C2×#217—61no—
53C2×C4⋊Dic3—31no—
54#924—32no—
55#924—32no—
56#924—61no—
57#924—61no—
58C2×Dic3⋊C4—61no—
59C2×#208—61no—
60C3×#95—21no—
61C3×#95C2×D312yes—
62#830—32no—
63#830—61no—
64C23×C9—22no—
65C23×C9—22no—
66C23×C9—41no—
67C23×C9C22⋊C411yescharacteristic
68C23×C9C22⋊C411yescharacteristic
69C23×C9C2×D411yescharacteristic
70C2×C4×C9—22no—
71C2×C4×C9—22no—
72C2×C4×C9—41no—
73C2×C4×C9—41no—
74C2×C4×C9—41no—
75C2×C4×C9—41no—
76C2×C4×C9—42no—
77C2×C4×C9—42no—
78C2×C4×C9—42no—
79C2×C4×C9C22⋊C411yescharacteristic
80C2×C4×C9C22⋊C411yescharacteristic
81C2×C4×C9C22×C411yescharacteristic
82C2×C4×C9C2×D411yescharacteristic
83C2×Dic9—22no—
84C2×Dic9—22no—
85C2×Dic9—42no—
86C2×Dic9—42no—
87Dic18—42no—
88Dic18—42no—
89C9⋊C8—42no—
90C2×C22⋊Q8—91no—
91#407—91no—
92#381D911yescharacteristic
93#328—94no—
94C24×C3#6711yescharacteristic
95C22×C3×C4—22no—
96C22×C3×C4—42no—
97C22×C3×C4C4×D311yescharacteristic
98C22×C3×C4C4×D311yescharacteristic
99C22×C3×C4D1211yescharacteristic
100C22×C3×C4D1211yescharacteristic
101C22×C3×C4#6711yescharacteristic
102C22×C3×C4C22×D311yescharacteristic
103C22×Dic3—61no—
104C22×Dic3—61no—
105C2×Dic6—32no—
106C2×Dic6—61no—
107C2×Dic6—122no—
108C3×C22⋊C4—42no—
109#217—62no—
110#217—62no—
111C4⋊Dic3—32no—
112C4⋊Dic3—61no—
113Dic3⋊C4—62no—
114Dic3⋊C4—62no—
115#208—122no—
116C2×C3⋊C8—62no—
117C22×C9—21no—
118C22×C9—21no—
119C22×C9—21no—
120C22×C9—21no—
121C22×C9—21no—
122C22×C9—21no—
123C22×C9—21no—
124C22×C9—44no—
125C22×C9#9912yes—
126C22×C9C2×C22⋊C411yescharacteristic
127C22×C9#13712yes—
128C4×C9—21no—
129C4×C9—21no—
130C4×C9—21no—
131C4×C9—21no—
132C4×C9—82no—
133Dic9—42no—
134Dic9—42no—
135C22×Q8—91no—
136C23×C4C2×D911yescharacteristic
137C2×M16—181no—
138C22⋊Q8—92no—
139C22⋊Q8—92no—
140C22⋊Q8—181no—
141C22⋊Q8—181no—
142C2×C4⋊C4—91no—
143C2×C4⋊C4—181no—
144C2×C22⋊C4—21no—
145C2×C22⋊C4—181no—
146C22⋊C8—92no—
147C22⋊C8—181no—
148#95—21no—
149#95C2×D912yes—
150C23×C3—22no—
151C23×C3—22no—
152C23×C3—41no—
153C23×C3(C2×D3)⋊C411yescharacteristic
154C23×C3(C2×D3)⋊C411yescharacteristic
155C23×C3C2×#6711yescharacteristic
156C2×C3×C4—22no—
157C2×C3×C4—22no—
158C2×C3×C4—41no—
159C2×C3×C4—41no—
160C2×C3×C4—41no—
161C2×C3×C4—41no—
162C2×C3×C4—42no—
163C2×C3×C4—42no—
164C2×C3×C4—42no—
165C2×C3×C4(C2×D3)⋊C411yescharacteristic
166C2×C3×C4(C2×D3)⋊C411yescharacteristic
167C2×C3×C4C2×C4×D311yescharacteristic
168C2×C3×C4C2×D1211yescharacteristic
169C2×Dic3—62no—
170C2×Dic3—62no—
171C2×Dic3—122no—
172C2×Dic3—122no—
173Dic6—122no—
174Dic6—122no—
175C3⋊C8—122no—
176C2×C9—22no—
177C2×C9—22no—
178C2×C9—41no—
179C2×C9C2×#9911yescharacteristic
180C2×C9#41911yescharacteristic
181C2×C9#42111yescharacteristic
182C24#61111yescharacteristic
183C2×Q8—92no—
184C2×Q8—181no—
185C2×Q8—362no—
186C22×C4—22no—
187C22×C4—42no—
188C22×C4—181no—
189C22×C4—181no—
190C22×C4C4×D911yescharacteristic
191C22×C4C4×D911yescharacteristic
192C22×C4D3611yescharacteristic
193C22×C4D3611yescharacteristic
194C22×C4#61111yescharacteristic
195C22×C4C22×D911yescharacteristic
196M16—362no—
197C2×C8—182no—
198C4⋊C4—92no—
199C4⋊C4—181no—
200C4⋊C4—182no—
201C4⋊C4—182no—
202C22⋊C4—42no—
203C22⋊C4—182no—
204C22⋊C4—182no—
205C22×C3—21no—
206C22×C3—21no—
207C22×C3—21no—
208C22×C3—21no—
209C22×C3—21no—
210C22×C3—21no—
211C22×C3—21no—
212C22×C3—44no—
213C22×C3#80612yes—
214C22×C3C2×(C2×D3)⋊C411yescharacteristic
215C22×C3#95112yes—
216C3×C4—21no—
217C3×C4—21no—
218C3×C4—21no—
219C3×C4—21no—
220C3×C4—82no—
221Dic3—122no—
222Dic3—122no—
223C9#151111yescharacteristic, complemented, Sylow
224C23—22no—
225C23—22no—
226C23—41no—
227C23(C2×D9)⋊C411yescharacteristic
228C23(C2×D9)⋊C411yescharacteristic
229C23C2×#61111yescharacteristic
230Q8—362no—
231Q8—362no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—182no—
242C2×C4—182no—
243C2×C4—362no—
244C2×C4—362no—
245C2×C4(C2×D9)⋊C411yescharacteristic
246C2×C4(C2×D9)⋊C411yescharacteristic
247C2×C4C2×C4×D911yescharacteristic
248C2×C4C2×D3611yescharacteristic
249C8—362no—
250C2×C3—22no—
251C2×C3—22no—
252C2×C3—41no—
253C2×C3C2×#80611yescharacteristic
254C2×C3#500411yescharacteristic
255C2×C3#500511yescharacteristic
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—44no—
264C22#6336512yes—
265C22C2×(C2×D9)⋊C411yescharacteristic
266C22#6351112yes—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—21no—
271C4—82no—
272C4—362no—
273C4—362no—
274C3#6953311yescharacteristic
275C2—22no—
276C2—22no—
277C2—41no—
278C2C2×#6336511yescharacteristic
279C2#1058868111yescharacteristic
280C2#1058868511yescharacteristic
subgroupG/H
centerC22C2×(C2×D9)⋊C4
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC9×#381C2
socleC22×C3C2×(C2×D3)⋊C4
prime radicalC24×C3#67
cosocleC22×C4×C9C23
hypercenter#381D9
hypocenterC9#1511
LCSG ▷ C2×C4×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
4. #10588128C2semidirect
7. C22×Dic18C4semidirect
10. C2×C4⋊Dic9C4semidirect
13. #63486C4semidirect
223. C9#1511semidirect

Maximal subgroups

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

subgroupindex
C2×#634862
C9×#3812
#105888872
#105881282
#695333