Finite Group Databasebeta

← #11774042

Subgroups — #11774042

Order 1152.

306 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 80 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×#63451C211yesmaximal, characteristic
2#10588399C211yesmaximal, characteristic
3#10588398C211yesmaximal, characteristic
4C9×#324C211yesmaximal, characteristic
5#10588205C211yesmaximal, characteristic
6#10588145C211yesmaximal, characteristic
7#10588145C211yesmaximal, characteristic
8#68128—31nomaximal
9C2×C9×C4⋊C4C2211yescharacteristic
10C2×C4⋊Dic9C411yescharacteristic
11C2×Dic9⋊C4C411yescharacteristic
12C2×Dic9⋊C4C411yescharacteristic
13C2×Dic9⋊C4C411yescharacteristic
14C2×Dic9⋊C4C2211yescharacteristic
15C2×C4×Dic9C2211yescharacteristic
16#63451—21no—
17#63451—21no—
18#63451—21no—
19#63451—21no—
20C9×C22⋊C8C2211yescharacteristic
21C9×C22⋊C8C2211yescharacteristic
22#63389C2211yescharacteristic
23#63389C2211yescharacteristic
24#63375—21no—
25Dic9⋊C8—21no—
26Dic9⋊C8—21no—
27C8×Dic9—21no—
28C2×#889—31no—
29#4719—31no—
30#4718—31no—
31C3×#324D311yescharacteristic
32#4528—31no—
33#4469—31no—
34#4469—31no—
35C22×C4×C9C2×C411yescharacteristic
36C22×C4×C9C2×C411yescharacteristic
37C22×C4×C9C2311yescharacteristic
38C22×Dic9C2×C411yescharacteristic
39C22×Dic9C2×C411yescharacteristic
40C22×Dic9C2×C411yescharacteristic
41C22×Dic9C2×C411yescharacteristic
42C2×C8×C9—21no—
43C2×C8×C9—21no—
44C9×C4⋊C4—21no—
45C9×C4⋊C4—21no—
46C4⋊Dic9—21no—
47C4⋊Dic9—21no—
48Dic9⋊C4—21no—
49Dic9⋊C4—21no—
50Dic9⋊C4—21no—
51Dic9⋊C4—21no—
52Dic9⋊C4—21no—
53Dic9⋊C4—21no—
54Dic9⋊C4—21no—
55Dic9⋊C4—21no—
56C4×Dic9D411yescharacteristic
57C4×Dic9D411yescharacteristic
58C4×Dic9D411yescharacteristic
59C4×Dic9D411yescharacteristic
60C2×C9⋊C8—21no—
61C2×C9⋊C8—21no—
62#1470—91noSylow
63C2×C3×C4⋊C4C2×D311yescharacteristic
64C2×C4⋊Dic3—31no—
65C2×Dic3⋊C4—31no—
66C2×Dic3⋊C4—31no—
67C2×Dic3⋊C4—31no—
68C2×Dic3⋊C4—31no—
69C2×C4×Dic3—31no—
70#889—61no—
71#889—61no—
72#889—61no—
73#889—61no—
74C3×C22⋊C8C2×D311yescharacteristic
75C3×C22⋊C8C2×D311yescharacteristic
76#830—31no—
77#830—31no—
78#815—61no—
79Dic3⋊C8—61no—
80Dic3⋊C8—61no—
81C8×Dic3—61no—
82C23×C9C22×C411yescharacteristic
83C2×C4×C9—21no—
84C2×C4×C9—21no—
85C2×C4×C9—21no—
86C2×C4×C9—21no—
87C2×C4×C9—41no—
88C2×C4×C9—41no—
89C2×C4×C9C2×D411yescharacteristic
90C2×C4×C9C2×D411yescharacteristic
91C2×Dic9—21no—
92C2×Dic9—21no—
93C2×Dic9—22no—
94C2×Dic9—21no—
95C2×Dic9—21no—
96C2×Dic9—21no—
97C2×Dic9—21no—
98C2×Dic9—41no—
99C2×Dic9C22⋊C411yescharacteristic
100C2×Dic9C22⋊C411yescharacteristic
101C2×Dic9C22⋊C411yescharacteristic
102C2×Dic9C22⋊C411yescharacteristic
103C8×C9—41no—
104C8×C9—41no—
105C9⋊C8—41no—
106C9⋊C8—41no—
107C2×#125—91no—
108#432—91no—
109#431—91no—
110#324—91no—
111#324—91no—
112#324—91no—
113#324D911yescharacteristic
114C22×C3×C4C4×D311yescharacteristic
115C22×C3×C4C4×D311yescharacteristic
116C22×C3×C4C22×D311yescharacteristic
117C22×Dic3—31no—
118C22×Dic3—31no—
119C22×Dic3—31no—
120C22×Dic3—31no—
121C2×C3×C8—21no—
122C2×C3×C8—21no—
123C3×C4⋊C4—21no—
124C3×C4⋊C4—21no—
125C4⋊Dic3—61no—
126C4⋊Dic3—61no—
127Dic3⋊C4—61no—
128Dic3⋊C4—61no—
129Dic3⋊C4—61no—
130Dic3⋊C4—61no—
131Dic3⋊C4—61no—
132Dic3⋊C4—61no—
133Dic3⋊C4—61no—
134Dic3⋊C4—61no—
135C4×Dic3—31no—
136C4×Dic3—31no—
137C4×Dic3—31no—
138C4×Dic3—31no—
139C2×C3⋊C8—61no—
140C2×C3⋊C8—61no—
141C22×C9—21no—
142C22×C9—21no—
143C22×C9C2×C22⋊C411yescharacteristic
144C22×C9#13111yescharacteristic
145C22×C9#13111yescharacteristic
146C4×C9—21no—
147C4×C9—21no—
148C4×C9—41no—
149C4×C9—41no—
150Dic9—21no—
151Dic9—21no—
152Dic9—21no—
153Dic9—41no—
154Dic9—41no—
155Dic9#10112yes—
156#125—181no—
157#125—181no—
158#125—181no—
159#125—181no—
160C2×C4⋊C4—91no—
161C2×C4⋊C4—91no—
162C2×C4⋊C4—91no—
163C2×C4⋊C4—91no—
164C2×C4⋊C4—91no—
165C2×C4⋊C4C2×D911yescharacteristic
166C2×C42—91no—
167C4⋊C8—181no—
168C4⋊C8—181no—
169C22⋊C8—91no—
170C22⋊C8—91no—
171C22⋊C8C2×D911yescharacteristic
172C22⋊C8C2×D911yescharacteristic
173#97—181no—
174C4×C8—181no—
175C23×C3C2×C4×D311yescharacteristic
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—41no—
181C2×C3×C4—41no—
182C2×C3×C4D3×D411yescharacteristic
183C2×C3×C4D3×D411yescharacteristic
184C2×Dic3—31no—
185C2×Dic3—31no—
186C2×Dic3—31no—
187C2×Dic3—31no—
188C2×Dic3—62no—
189C2×Dic3—61no—
190C2×Dic3—61no—
191C2×Dic3—61no—
192C2×Dic3—61no—
193C2×Dic3—61no—
194C2×Dic3—61no—
195C2×Dic3—121no—
196C3×C8—41no—
197C3×C8—41no—
198C3⋊C8—121no—
199C3⋊C8—121no—
200C2×C9—21no—
201C2×C9—21no—
202C2×C9#40811yescharacteristic
203C2×C9#41011yescharacteristic
204C2×C9C2×#10111yescharacteristic
205C22×C4—91no—
206C22×C4—91no—
207C22×C4—91no—
208C22×C4—91no—
209C22×C4C4×D911yescharacteristic
210C22×C4C4×D911yescharacteristic
211C22×C4C22×D911yescharacteristic
212C2×C8—21no—
213C2×C8—21no—
214C2×C8—181no—
215C2×C8—181no—
216C4⋊C4—21no—
217C4⋊C4—21no—
218C4⋊C4—181no—
219C4⋊C4—181no—
220C4⋊C4—181no—
221C4⋊C4—181no—
222C4⋊C4—181no—
223C4⋊C4—181no—
224C4⋊C4—181no—
225C4⋊C4—181no—
226C4⋊C4—181no—
227C4⋊C4—181no—
228C42—91no—
229C42—91no—
230C42—91no—
231C42—91no—
232C22×C3—21no—
233C22×C3—21no—
234C22×C3D3×C22⋊C411yescharacteristic
235C22×C3#90111yescharacteristic
236C22×C3#90711yescharacteristic
237C3×C4—21no—
238C3×C4—21no—
239C3×C4—41no—
240C3×C4—41no—
241Dic3—32no—
242Dic3—61no—
243Dic3—61no—
244Dic3—61no—
245Dic3—121no—
246Dic3—121no—
247C9#147011yescharacteristic, complemented, Sylow
248C23C2×C4×D911yescharacteristic
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—91no—
256C2×C4—91no—
257C2×C4—91no—
258C2×C4—91no—
259C2×C4—182no—
260C2×C4—181no—
261C2×C4—181no—
262C2×C4—181no—
263C2×C4—181no—
264C2×C4—181no—
265C2×C4—181no—
266C2×C4—361no—
267C2×C4D4×D911yescharacteristic
268C2×C4D4×D911yescharacteristic
269C8—41no—
270C8—41no—
271C8—361no—
272C8—361no—
273C2×C3—21no—
274C2×C3—21no—
275C2×C3#472711yescharacteristic
276C2×C3#474011yescharacteristic
277C2×C3D3×#10111yescharacteristic
278C22—21no—
279C22—21no—
280C22C22⋊C4×D911yescharacteristic
281C22#6346411yescharacteristic
282C22#6346911yescharacteristic
283C4—21no—
284C4—21no—
285C4—41no—
286C4—41no—
287C4—92no—
288C4—181no—
289C4—181no—
290C4—181no—
291C4—361no—
292C4—361no—
293C3#6812811yescharacteristic
294C2—21no—
295C2—21no—
296C2#1058840911yescharacteristic
297C2#1058842011yescharacteristic
298C2D9×#10111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D9
commutatorC23×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC9×#324C2
socleC22×C3D3×C22⋊C4
prime radicalC23×C3C2×C4×D3
cosocleC22×C4×C9C23
hypercenter#324D9
hypocenterC9#1470
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
247. C9#1470semidirect

Maximal subgroups

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

subgroupindex
C2×#634512
#105883992
#105883982
C9×#3242
#105882052
#105881452
#681283