Finite Group Databasebeta

← #11778809

Subgroups — #11778809

Order 1152.

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

normal subgroups only

This group has 303 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#10588724C211yesmaximal, characteristic
3#10588402C211yesmaximal, characteristic
4#10588339C211yesmaximal, characteristic
5C9×#328C211yesmaximal, characteristic
6#10588145C211yesmaximal, characteristic
7#10588128C211yesmaximal, characteristic
8#68331—31nomaximal
9C9×C22⋊Q8C2211yescharacteristic
10#63506—21no—
11C2×C4⋊Dic9C2211yescharacteristic
12#63486C2211yescharacteristic
13C2×Dic9⋊C4C2211yescharacteristic
14#63451—21no—
15#63451—21no—
16#63450—21no—
17#63440—21no—
18#63439—21no—
19C9×C22⋊C8C2211yescharacteristic
20C9×#95C2211yescharacteristic
21#63395—21no—
22C9⋊#95—21no—
23C9⋊#95—21no—
24#63389C2211yescharacteristic
25#63378—21no—
26#63376—21no—
27#63366—21no—
28#5623—31no—
29#5044—31no—
30#4722—31no—
31#4659—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⋊Dic9D411yescharacteristic
52Dic9⋊C4—21no—
53Dic9⋊C4—21no—
54Dic9⋊C4—21no—
55Dic9⋊C4—21no—
56Dic9⋊C4—21no—
57Dic9⋊C4—21no—
58Dic9⋊C4—21no—
59C4×Dic9—21no—
60C4×Dic9—21no—
61C2×C9⋊C8—21no—
62#1617—91noSylow
63C3×C22⋊Q8C2×D311yescharacteristic
64#944—61no—
65C2×C4⋊Dic3—31no—
66#924—31no—
67C2×Dic3⋊C4—31no—
68#889—61no—
69#889—61no—
70#888—61no—
71#878—61no—
72#877—61no—
73C3×C22⋊C8C2×D311yescharacteristic
74C3×#95C2×D311yescharacteristic
75#835—61no—
76C3⋊#95—61no—
77C3⋊#95—61no—
78#830—31no—
79#818—61no—
80#816—61no—
81#807—61no—
82C23×C9C2×D411yescharacteristic
83Q8×C9—41no—
84C2×C4×C9—21no—
85C2×C4×C9—21no—
86C2×C4×C9—41no—
87C2×C4×C9—41no—
88C2×C4×C9—41no—
89C2×C4×C9—41no—
90C2×C4×C9C2×D411yescharacteristic
91C2×C4×C9C2×D411yescharacteristic
92C2×Dic9—21no—
93C2×Dic9—21no—
94C2×Dic9—21no—
95C2×Dic9—21no—
96C2×Dic9—21no—
97C2×Dic9—41no—
98C2×Dic9—42no—
99C2×Dic9—41no—
100C2×Dic9Q1612yes—
101Dic18—41no—
102Dic18—81no—
103C8×C9—41no—
104C9⋊C8—41no—
105#544—91no—
106#484—91no—
107#484—91no—
108#400—91no—
109#328—91no—
110#328D911yescharacteristic
111#324—91no—
112C2×C3×Q8D1211yescharacteristic
113C22×C3×C4—21no—
114C22×C3×C4C22×D311yescharacteristic
115C22×Dic3—31no—
116C22×Dic3—31no—
117C22×Dic3—61no—
118C2×Dic6—31no—
119C2×Dic6—61no—
120C2×C3×C8—21no—
121C3×C4⋊C4—21no—
122C3×C4⋊C4D1211yescharacteristic
123C3×C22⋊C4—21no—
124#217—61no—
125C4⋊Dic3—31no—
126C4⋊Dic3—61no—
127C4⋊Dic3—61no—
128C4⋊Dic3—61no—
129Dic3⋊C4—61no—
130Dic3⋊C4—61no—
131Dic3⋊C4—61no—
132Dic3⋊C4—61no—
133Dic3⋊C4—61no—
134Dic3⋊C4—61no—
135Dic3⋊C4—61no—
136C4×Dic3—61no—
137C4×Dic3—61no—
138C2×C3⋊C8—61no—
139C22×C9—21no—
140C22×C9—21no—
141C22×C9#12011yescharacteristic
142C22×C9C2×Q1611yescharacteristic
143C22×C9#13711yescharacteristic
144C4×C9—21no—
145C4×C9—21no—
146C4×C9—41no—
147C4×C9—41no—
148C4×C9—81no—
149Dic9—22no—
150Dic9—41no—
151Dic9—41no—
152Dic9—41no—
153Dic9—81no—
154C4⋊Q8—181no—
155C4⋊Q8—181no—
156#125—181no—
157#125—181no—
158C22⋊Q8—91no—
159C22⋊Q8—181no—
160C22⋊Q8C2×D911yescharacteristic
161#117—181no—
162C2×C4⋊C4—91no—
163C2×C4⋊C4—91no—
164#107—181no—
165#107—181no—
166#103—181no—
167#103—181no—
168C22⋊C8—91no—
169C22⋊C8C2×D911yescharacteristic
170#95—181no—
171#95—181no—
172#95C2×D911yescharacteristic
173C23×C3D3×D411yescharacteristic
174C3×Q8—41no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—41no—
178C2×C3×C4—41no—
179C2×C3×C4—41no—
180C2×C3×C4—41no—
181C2×C3×C4C2×D1211yescharacteristic
182C2×C3×C4D3×D411yescharacteristic
183C2×Dic3—32no—
184C2×Dic3—61no—
185C2×Dic3—61no—
186C2×Dic3—61no—
187C2×Dic3—61no—
188C2×Dic3—61no—
189C2×Dic3—121no—
190C2×Dic3—122no—
191C2×Dic3—121no—
192Dic6—121no—
193Dic6—241no—
194C3×C8—41no—
195C3⋊C8—121no—
196C2×C9—21no—
197C2×C9—21no—
198C2×C9#45111yescharacteristic
199C2×C9#45411yescharacteristic
200C2×C9#45811yescharacteristic
201C2×Q8—91no—
202C2×Q8—181no—
203C2×Q8D3611yescharacteristic
204C22×C4—21no—
205C22×C4—91no—
206C22×C4—91no—
207C22×C4—181no—
208C22×C4C22×D911yescharacteristic
209C2×C8—21no—
210C2×C8—181no—
211C4⋊C4—21no—
212C4⋊C4—91no—
213C4⋊C4—181no—
214C4⋊C4—181no—
215C4⋊C4—181no—
216C4⋊C4—181no—
217C4⋊C4—181no—
218C4⋊C4—181no—
219C4⋊C4—181no—
220C4⋊C4—181no—
221C4⋊C4—181no—
222C4⋊C4—181no—
223C4⋊C4D3611yescharacteristic
224C22⋊C4—21no—
225C22⋊C4—181no—
226C42—181no—
227C42—181no—
228C22×C3—21no—
229C22×C3—21no—
230C22×C3#88211yescharacteristic
231C22×C3#91511yescharacteristic
232C22×C3D3×Q1611yescharacteristic
233C3×C4—21no—
234C3×C4—21no—
235C3×C4—41no—
236C3×C4—41no—
237C3×C4—81no—
238Dic3—62no—
239Dic3—121no—
240Dic3—121no—
241Dic3—121no—
242Dic3—241no—
243C9#161711yescharacteristic, complemented, Sylow
244C23D4×D911yescharacteristic
245Q8—41no—
246Q8—361no—
247Q8—721no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—92no—
255C2×C4—181no—
256C2×C4—181no—
257C2×C4—181no—
258C2×C4—181no—
259C2×C4—181no—
260C2×C4—361no—
261C2×C4—362no—
262C2×C4—361no—
263C2×C4C2×D3611yescharacteristic
264C2×C4D4×D911yescharacteristic
265C8—41no—
266C8—361no—
267C2×C3—21no—
268C2×C3—21no—
269C2×C3#474211yescharacteristic
270C2×C3#480911yescharacteristic
271C2×C3#482711yescharacteristic
272C22—21no—
273C22—21no—
274C22#6344411yescharacteristic
275C22#6347711yescharacteristic
276C22Q16×D911yescharacteristic
277C4—21no—
278C4—21no—
279C4—41no—
280C4—41no—
281C4—81no—
282C4—182no—
283C4—361no—
284C4—361no—
285C4—361no—
286C4—721no—
287C3#6833111yescharacteristic
288C2—21no—
289C2—21no—
290C2#1058842211yescharacteristic
291C2#1058848911yescharacteristic
292C2#1058850711yescharacteristic
subgroupG/H
centerC22#63444
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#328C2
socleC22×C3#882
prime radicalC23×C3D3×D4
hypercenter#328D9
hypocenterC9#1617
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
243. C9#1617semidirect

Maximal subgroups

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

subgroupindex
#105897252
#105887242
#105884022
#105883392
C9×#3282
#105881452
#105881282
#683313