Finite Group Databasebeta

← #11775890

Subgroups — #11775890

Order 1152.

318 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 76 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
1#10589790C211yesmaximal, characteristic
2#10588386C211yesmaximal, characteristic
3D9×#97C211yesmaximal, characteristic
4C9×#330C211yesmaximal, characteristic, complemented
5#10588220C211yesmaximal, characteristic, complemented
6#10588141C211yesmaximal, characteristic, complemented
7#10588141C211yesmaximal, characteristic, complemented
8#68365—31nomaximal
9C9×#125C2211yescharacteristic
10C2×C8×D9—21no—
11#63458—21no—
12#63458—21no—
13#63454C411yescharacteristic
14#63454C411yescharacteristic
15#63450C411yescharacteristic
16#63450C411yescharacteristic
17#63449—21no—
18#63449—21no—
19C42×D9C2211yescharacteristic
20#63432C2211yescharacteristic
21C9×#97C2211yescharacteristic
22C9×#97C2211yescharacteristic
23(C2×D9)⋊C8—21no—
24#63375—21no—
25Dic9⋊C8—21no—
26#63362C2211yescharacteristic
27#63362C2211yescharacteristic
28#5688—31no—
29#4705—31no—
30D3×#97—31no—
31C3×#330D311yescharacteristic
32#4543—31no—
33#4465—31no—
34#4465—31no—
35C2×C4×D9C2×C411yescharacteristic
36C2×C4×D9D411yescharacteristic
37C2×C4×D9D411yescharacteristic
38C2×Dic18—21no—
39C2×Dic18—21no—
40C2×C8×C9—21no—
41C2×C8×C9—21no—
42C9×C4⋊C4—21no—
43C9×C4⋊C4—21no—
44C9×C4⋊C4C2×C411yescharacteristic
45C9×C4⋊C4C2×C411yescharacteristic
46C42×C9C2311yescharacteristic
47(C2×D9)⋊C4—21no—
48(C2×D9)⋊C4—21no—
49C4⋊Dic9C2×C411yescharacteristic
50C4⋊Dic9C2×C411yescharacteristic
51Dic9⋊C4—21no—
52Dic9⋊C4—21no—
53Dic9⋊C4—21no—
54Dic9⋊C4—21no—
55C4×Dic9—21no—
56C4×Dic9—21no—
57C4×Dic9C2×C411yescharacteristic
58C4×Dic9D411yescharacteristic
59C4×Dic9D411yescharacteristic
60C2×C9⋊C8—21no—
61C2×C9⋊C8—21no—
62C8×D9—24no—
63#1531—91noSylow
64C3×#125C2×D311yescharacteristic
65C2×D3×C8—61no—
66#896—61no—
67#896—61no—
68#892—31no—
69#892—31no—
70#888—31no—
71#888—31no—
72#887—61no—
73#887—61no—
74C42×D3—31no—
75#870—31no—
76C3×#97C2×D311yescharacteristic
77C3×#97C2×D311yescharacteristic
78(C2×D3)⋊C8—61no—
79#815—61no—
80Dic3⋊C8—61no—
81#803—31no—
82#803—31no—
83C22×D9C22⋊C411yescharacteristic
84C2×C4×C9—21no—
85C2×C4×C9—21no—
86C2×C4×C9C22×C411yescharacteristic
87C2×C4×C9C2×D411yescharacteristic
88C2×C4×C9C2×D411yescharacteristic
89C2×Dic9—21no—
90C2×Dic9—21no—
91C2×Dic9C22⋊C411yescharacteristic
92C2×Dic9C22⋊C411yescharacteristic
93C2×Dic9C22⋊C411yescharacteristic
94C4×D9—22no—
95C4×D9—22no—
96C4×D9—41no—
97Dic18—42no—
98Dic18—42no—
99C8×C9—22no—
100C8×C9—41no—
101C9⋊C8—22no—
102C9⋊C8—41no—
103#533—91no—
104#432—91no—
105C2×#97—91no—
106#330—91no—
107#330—91no—
108#330—91no—
109#330D911yescharacteristic, complemented
110C2×C4×D3—31no—
111C2×C4×D3—31no—
112C2×C4×D3—31no—
113C2×Dic6—61no—
114C2×Dic6—61no—
115C2×C3×C8—21no—
116C2×C3×C8—21no—
117C3×C4⋊C4—21no—
118C3×C4⋊C4—21no—
119C3×C4⋊C4C4×D311yescharacteristic
120C3×C4⋊C4C4×D311yescharacteristic
121C3×C42C22×D311yescharacteristic
122(C2×D3)⋊C4—61no—
123(C2×D3)⋊C4—61no—
124C4⋊Dic3—31no—
125C4⋊Dic3—31no—
126Dic3⋊C4—61no—
127Dic3⋊C4—61no—
128Dic3⋊C4—61no—
129Dic3⋊C4—61no—
130C4×Dic3—31no—
131C4×Dic3—31no—
132C4×Dic3—31no—
133C4×Dic3—61no—
134C4×Dic3—61no—
135C2×C3⋊C8—61no—
136C2×C3⋊C8—61no—
137D3×C8—64no—
138C22×C9C2×C22⋊C411yescharacteristic
139C2×D9—21no—
140C2×D9—21no—
141C2×D9#10112yes—
142C4×C9—21no—
143C4×C9—21no—
144C4×C9—21no—
145C4×C9—41no—
146C4×C9—41no—
147Dic9—21no—
148Dic9—21no—
149Dic9—41no—
150Dic9—41no—
151Dic9#10412yes—
152C22×C8—181no—
153C4⋊Q8—91no—
154C4⋊Q8—91no—
155#125—91no—
156#125C2×D911yescharacteristic
157C22⋊Q8—181no—
158C22⋊Q8—181no—
159C4×Q8—181no—
160C4×Q8—181no—
161#117—91no—
162#117—91no—
163C2×C42—91no—
164C4⋊C8—181no—
165C22⋊C8—181no—
166#97—91no—
167#97—91no—
168#97—181no—
169#97C2×D911yescharacteristic
170#97C2×D911yescharacteristic
171C22×D3—31no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4C2×C4×D311yescharacteristic
175C2×C3×C4D3×D411yescharacteristic
176C2×C3×C4D3×D411yescharacteristic
177C2×Dic3—31no—
178C2×Dic3—31no—
179C2×Dic3—31no—
180C2×Dic3—61no—
181C2×Dic3—61no—
182C4×D3—62no—
183C4×D3—62no—
184C4×D3—121no—
185Dic6—122no—
186Dic6—122no—
187C3×C8—22no—
188C3×C8—41no—
189C3⋊C8—62no—
190C3⋊C8—121no—
191C2×C9C2×#10111yescharacteristic
192C2×C9C2×#10411yescharacteristic
193C2×C9#42111yescharacteristic
194D9—22no—
195C2×Q8—181no—
196C2×Q8—181no—
197C22×C4—91no—
198C22×C4—91no—
199C22×C4—91no—
200C2×C8—21no—
201C2×C8—21no—
202C2×C8—184no—
203C2×C8—181no—
204C2×C8—181no—
205C4⋊C4—21no—
206C4⋊C4—21no—
207C4⋊C4—91no—
208C4⋊C4—91no—
209C4⋊C4—181no—
210C4⋊C4—181no—
211C4⋊C4—181no—
212C4⋊C4—181no—
213C4⋊C4C4×D911yescharacteristic
214C4⋊C4C4×D911yescharacteristic
215C22⋊C4—181no—
216C22⋊C4—181no—
217C42—91no—
218C42—91no—
219C42—91no—
220C42—181no—
221C42—181no—
222C42C22×D911yescharacteristic
223C22×C3D3×C22⋊C411yescharacteristic
224C2×D3—32no—
225C2×D3—61no—
226C2×D3—61no—
227C3×C4—21no—
228C3×C4—21no—
229C3×C4—21no—
230C3×C4—41no—
231C3×C4—41no—
232Dic3—32no—
233Dic3—61no—
234Dic3—61no—
235Dic3—121no—
236Dic3—121no—
237C9#153111yescharacteristic, complemented, Sylow
238C23—91no—
239Q8—362no—
240Q8—362no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—91no—
244C2×C4—91no—
245C2×C4—91no—
246C2×C4—182no—
247C2×C4—182no—
248C2×C4—181no—
249C2×C4—181no—
250C2×C4—361no—
251C2×C4C2×C4×D911yescharacteristic
252C2×C4D4×D911yescharacteristic
253C2×C4D4×D911yescharacteristic
254C8—22no—
255C8—41no—
256C8—182no—
257C8—361no—
258C2×C3D3×#10111yescharacteristic
259C2×C3D3×#10411yescharacteristic
260C2×C3#482111yescharacteristic
261D3—62no—
262C22—92no—
263C22—181no—
264C22—181no—
265C22C22⋊C4×D911yescharacteristic
266C4—21no—
267C4—21no—
268C4—21no—
269C4—41no—
270C4—41no—
271C4—92no—
272C4—181no—
273C4—181no—
274C4—361no—
275C4—361no—
276C3#6836511yescharacteristic
277C2—182no—
278C2D9×#10111yescharacteristic
279C2D9×#10411yescharacteristic
280C2#1058850111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D9
commutatorC2×C4×C9C22×C4
FrattiniC3×C42C22×D3
FittingC9×#330C2
socleC22×C3D3×C22⋊C4
prime radicalC22×D9C22⋊C4
cosocleC42×C9C23
hypercenter#330D9
hypocenterC9#1531
LCSG ▷ C2×C4×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
4. C9×#330C2semidirect
5. #10588220C2semidirect
6. #10588141C2semidirect
7. #10588141C2semidirect
109. #330D9semidirect
237. C9#1531semidirect

Maximal subgroups

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

subgroupindex
#105897902
#105883862
D9×#972
C9×#3302
#105882202
#105881412
#683653