Finite Group Databasebeta

← #11778582

Subgroups — #11778582

Order 1152.

315 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 315 conjugacy classes of subgroups — too many to draw. Only its 68 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#10589725C211yesmaximal, characteristic
2#10588723C211yesmaximal, characteristic
3#10588401C211yesmaximal, characteristic
4#10588341C211yesmaximal, characteristic
5C9×#328C211yesmaximal, characteristic
6#10588145C211yesmaximal, characteristic
7#10588128C211yesmaximal, characteristic
8#68329—31nomaximal
9C9×C22⋊Q8C2211yescharacteristic
10#63506—21no—
11C2×C4⋊Dic9—21no—
12C2×C4⋊Dic9C2211yescharacteristic
13#63486C2211yescharacteristic
14C2×Dic9⋊C4C2211yescharacteristic
15#63451—21no—
16#63451—21no—
17#63450—21no—
18#63440—21no—
19#63439—21no—
20C9×C22⋊C8C2211yescharacteristic
21C9×#95C2211yescharacteristic
22#63395—21no—
23C9⋊#95—21no—
24#63389C2211yescharacteristic
25#63377—21no—
26#63376—21no—
27#63367—21no—
28#5623—31no—
29#5043—31no—
30#4721—31no—
31#4661—31no—
32C3×#328D311yescharacteristic
33#4469—31no—
34#4452—31no—
35C2×Q8×C9D411yescharacteristic
36C22×C4×C9—21no—
37C22×C4×C9C2311yescharacteristic
38C22×Dic9—21no—
39C22×Dic9D411yescharacteristic
40C22×Dic9D411yescharacteristic
41C2×Dic18—21no—
42C2×Dic18D411yescharacteristic
43C2×C8×C9—21no—
44C9×C4⋊C4—21no—
45C9×C4⋊C4D411yescharacteristic
46C9×C22⋊C4—21no—
47#3676—21no—
48C4⋊Dic9—21no—
49C4⋊Dic9—21no—
50C4⋊Dic9—21no—
51C4⋊Dic9—42no—
52C4⋊Dic9D411yescharacteristic
53Dic9⋊C4—21no—
54Dic9⋊C4—21no—
55Dic9⋊C4—21no—
56Dic9⋊C4—21no—
57Dic9⋊C4—21no—
58Dic9⋊C4—21no—
59Dic9⋊C4—21no—
60C4×Dic9—21no—
61C4×Dic9—21no—
62C2×C9⋊C8—21no—
63#1611—91noSylow
64C3×C22⋊Q8C2×D311yescharacteristic
65#944—61no—
66C2×C4⋊Dic3—31no—
67C2×C4⋊Dic3—61no—
68#924—31no—
69C2×Dic3⋊C4—31no—
70#889—61no—
71#889—61no—
72#888—61no—
73#878—61no—
74#877—61no—
75C3×C22⋊C8C2×D311yescharacteristic
76C3×#95C2×D311yescharacteristic
77#835—61no—
78C3⋊#95—61no—
79#830—31no—
80#817—61no—
81#816—61no—
82#808—61no—
83C23×C9C2×D411yescharacteristic
84Q8×C9—41no—
85C2×C4×C9—22no—
86C2×C4×C9—21no—
87C2×C4×C9—21no—
88C2×C4×C9—41no—
89C2×C4×C9—41no—
90C2×C4×C9—41no—
91C2×C4×C9C2×D411yescharacteristic
92C2×C4×C9C2×D411yescharacteristic
93C2×Dic9—21no—
94C2×Dic9—21no—
95C2×Dic9—21no—
96C2×Dic9—21no—
97C2×Dic9—21no—
98C2×Dic9—41no—
99C2×Dic9—41no—
100C2×Dic9—41no—
101C2×Dic9—41no—
102C2×Dic9SD1612yes—
103Dic18—41no—
104Dic18—81no—
105C8×C9—41no—
106C9⋊C8—41no—
107#544—91no—
108#483—91no—
109#483—91no—
110#398—91no—
111#328—91no—
112#328D911yescharacteristic
113#324—91no—
114C2×C3×Q8D1211yescharacteristic
115C22×C3×C4—21no—
116C22×C3×C4C22×D311yescharacteristic
117C22×Dic3—31no—
118C22×Dic3—31no—
119C22×Dic3—61no—
120C2×Dic6—31no—
121C2×Dic6—61no—
122C2×C3×C8—21no—
123C3×C4⋊C4—21no—
124C3×C4⋊C4D1211yescharacteristic
125C3×C22⋊C4—21no—
126#217—61no—
127C4⋊Dic3—31no—
128C4⋊Dic3—61no—
129C4⋊Dic3—61no—
130C4⋊Dic3—61no—
131C4⋊Dic3—122no—
132Dic3⋊C4—61no—
133Dic3⋊C4—61no—
134Dic3⋊C4—61no—
135Dic3⋊C4—61no—
136Dic3⋊C4—61no—
137Dic3⋊C4—61no—
138Dic3⋊C4—61no—
139C4×Dic3—61no—
140C4×Dic3—61no—
141C2×C3⋊C8—61no—
142C22×C9—21no—
143C22×C9—21no—
144C22×C9#12011yescharacteristic
145C22×C9C2×SD1611yescharacteristic
146C22×C9#13711yescharacteristic
147C4×C9—21no—
148C4×C9—21no—
149C4×C9—42no—
150C4×C9—41no—
151C4×C9—41no—
152Dic9—22no—
153Dic9—41no—
154Dic9—41no—
155Dic9—41no—
156Dic9—81no—
157C4⋊Q8—181no—
158C4⋊Q8—181no—
159#125—181no—
160#125—181no—
161C22⋊Q8—91no—
162C22⋊Q8—181no—
163C22⋊Q8C2×D911yescharacteristic
164#117—181no—
165C2×C4⋊C4—91no—
166C2×C4⋊C4—91no—
167C2×C4⋊C4—181no—
168#106—181no—
169#106—181no—
170#103—181no—
171#103—181no—
172C22⋊C8—91no—
173C22⋊C8C2×D911yescharacteristic
174#95—181no—
175#95C2×D911yescharacteristic
176C23×C3D3×D411yescharacteristic
177C3×Q8—41no—
178C2×C3×C4—22no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—41no—
182C2×C3×C4—41no—
183C2×C3×C4—41no—
184C2×C3×C4C2×D1211yescharacteristic
185C2×C3×C4D3×D411yescharacteristic
186C2×Dic3—32no—
187C2×Dic3—61no—
188C2×Dic3—61no—
189C2×Dic3—61no—
190C2×Dic3—61no—
191C2×Dic3—61no—
192C2×Dic3—121no—
193C2×Dic3—121no—
194C2×Dic3—121no—
195C2×Dic3—121no—
196Dic6—121no—
197Dic6—241no—
198C3×C8—41no—
199C3⋊C8—121no—
200C2×C9—21no—
201C2×C9—21no—
202C2×C9#44811yescharacteristic
203C2×C9#45611yescharacteristic
204C2×C9#45811yescharacteristic
205C2×Q8—91no—
206C2×Q8—181no—
207C2×Q8D3611yescharacteristic
208C22×C4—21no—
209C22×C4—91no—
210C22×C4—91no—
211C22×C4—181no—
212C22×C4C22×D911yescharacteristic
213C2×C8—21no—
214C2×C8—181no—
215C4⋊C4—21no—
216C4⋊C4—91no—
217C4⋊C4—181no—
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—362no—
228C4⋊C4D3611yescharacteristic
229C22⋊C4—21no—
230C22⋊C4—181no—
231C42—181no—
232C42—181no—
233C22×C3—21no—
234C22×C3—21no—
235C22×C3#88211yescharacteristic
236C22×C3D3×SD1611yescharacteristic
237C22×C3#91811yescharacteristic
238C3×C4—21no—
239C3×C4—21no—
240C3×C4—42no—
241C3×C4—41no—
242C3×C4—41no—
243Dic3—62no—
244Dic3—121no—
245Dic3—121no—
246Dic3—121no—
247Dic3—241no—
248C9#161111yescharacteristic, complemented, Sylow
249C23D4×D911yescharacteristic
250Q8—41no—
251Q8—361no—
252Q8—721no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—92no—
260C2×C4—181no—
261C2×C4—181no—
262C2×C4—181no—
263C2×C4—181no—
264C2×C4—181no—
265C2×C4—361no—
266C2×C4—361no—
267C2×C4—361no—
268C2×C4—361no—
269C2×C4C2×D3611yescharacteristic
270C2×C4D4×D911yescharacteristic
271C8—41no—
272C8—361no—
273C2×C3—21no—
274C2×C3—21no—
275C2×C3#474211yescharacteristic
276C2×C3#480611yescharacteristic
277C2×C3#482611yescharacteristic
278C22—21no—
279C22—21no—
280C22#6344411yescharacteristic
281C22SD16×D911yescharacteristic
282C22#6348011yescharacteristic
283C4—21no—
284C4—21no—
285C4—42no—
286C4—41no—
287C4—41no—
288C4—182no—
289C4—361no—
290C4—361no—
291C4—361no—
292C4—721no—
293C3#6832911yescharacteristic
294C2—21no—
295C2—21no—
296C2#1058842211yescharacteristic
297C2#1058848611yescharacteristic
298C2#1058850611yescharacteristic
subgroupG/H
centerC22#63444
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#328C2
socleC22×C3#882
prime radicalC23×C3D3×D4
hypercenter#328D9
hypocenterC9#1611
LCSG ▷ C22×C4×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
248. C9#1611semidirect

Maximal subgroups

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

subgroupindex
#105897252
#105887232
#105884012
#105883412
C9×#3282
#105881452
#105881282
#683293