Finite Group Databasebeta

← #11778800

Subgroups — #11778800

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
2C9×#484C211yesmaximal, characteristic
3#10588665C211yesmaximal, characteristic
4#10588646C211yesmaximal, characteristic
5#10588215C211yesmaximal, characteristic
6#10588145C211yesmaximal, characteristic
7#10588144C211yesmaximal, characteristic
8#71179—31nomaximal
9C9×C22⋊Q8C2211yescharacteristic
10C2×C9×C4⋊C4C2211yescharacteristic
11#63506—21no—
12#63486C2211yescharacteristic
13C2×Dic9⋊C4C2211yescharacteristic
14#63451—21no—
15#63451—21no—
16#63450—21no—
17#63440—21no—
18#63439—21no—
19C9×#107—21no—
20C9×#103—21no—
21C9×C22⋊C8C2211yescharacteristic
22C9⋊#95—21no—
23C9⋊#95—21no—
24C9⋊#95C2211yescharacteristic
25#63389C2211yescharacteristic
26#63368—21no—
27#63366—21no—
28#5623—31no—
29C3×#484D311yescharacteristic
30#4985—31no—
31#4970—31no—
32#4538—31no—
33#4469—31no—
34#4467—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⋊C4—21no—
46C9×C4⋊C4—21no—
47C9×C4⋊C4D411yescharacteristic
48C9×C22⋊C4—21no—
49#3676—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
64C2×C3×C4⋊C4C2×D311yescharacteristic
65#944—61no—
66#924—31no—
67C2×Dic3⋊C4—31no—
68#889—61no—
69#889—61no—
70#888—61no—
71#878—61no—
72#877—61no—
73C3×#107—21no—
74C3×#103—21no—
75C3×C22⋊C8C2×D311yescharacteristic
76C3⋊#95—31no—
77C3⋊#95—61no—
78C3⋊#95—61no—
79#830—31no—
80#810—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—42no—
88C2×C4×C9—41no—
89C2×C4×C9C2×D411yescharacteristic
90C2×C4×C9C2×D411yescharacteristic
91C2×Dic9—21no—
92C2×Dic9—21no—
93C2×Dic9—21no—
94C2×Dic9—21no—
95C2×Dic9—21no—
96C2×Dic9—41no—
97C2×Dic9—41no—
98C2×Dic9—41no—
99C2×Dic9—41no—
100C2×Dic9Q1612yes—
101Dic18—41no—
102Dic18—81no—
103C8×C9—41no—
104C9⋊C8—41no—
105#544—91no—
106#484—91no—
107#484D911yescharacteristic
108#400—91no—
109#328—91no—
110#328—91no—
111#324—91no—
112C2×C3×Q8#6711yescharacteristic
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⋊C4—21no—
123C3×C4⋊C4—21no—
124C3×C4⋊C4#6711yescharacteristic
125C3×C22⋊C4—21no—
126#217—61no—
127C4⋊Dic3—31no—
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⋊C4C2×D911yescharacteristic
164#107—21no—
165#107—181no—
166#103—21no—
167#103—181no—
168C22⋊C8—91no—
169C22⋊C8C2×D911yescharacteristic
170#95—91no—
171#95—181no—
172#95—181no—
173C23×C3D3×D411yescharacteristic
174C3×Q8—41no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—41no—
178C2×C3×C4—42no—
179C2×C3×C4—41no—
180C2×C3×C4D3×D411yescharacteristic
181C2×C3×C4C2×#6711yescharacteristic
182C2×Dic3—32no—
183C2×Dic3—61no—
184C2×Dic3—61no—
185C2×Dic3—61no—
186C2×Dic3—61no—
187C2×Dic3—61no—
188C2×Dic3—121no—
189C2×Dic3—121no—
190C2×Dic3—121no—
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×Q8#61111yescharacteristic
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—21no—
213C4⋊C4—21no—
214C4⋊C4—91no—
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⋊C4#61111yescharacteristic
224C22⋊C4—21no—
225C22⋊C4—181no—
226C42—181no—
227C42—181no—
228C22×C3—21no—
229C22×C3—21no—
230C22×C3D3×Q1611yescharacteristic
231C22×C3#91811yescharacteristic
232C22×C3#93711yescharacteristic
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—42no—
252C2×C4—41no—
253C2×C4—92no—
254C2×C4—181no—
255C2×C4—181no—
256C2×C4—181no—
257C2×C4—181no—
258C2×C4—181no—
259C2×C4—361no—
260C2×C4—361no—
261C2×C4—361no—
262C2×C4—361no—
263C2×C4D4×D911yescharacteristic
264C2×C4C2×#61111yescharacteristic
265C8—41no—
266C8—361no—
267C2×C3—21no—
268C2×C3—21no—
269C2×C3#505311yescharacteristic
270C2×C3#518611yescharacteristic
271C2×C3#520111yescharacteristic
272C22—21no—
273C22—21no—
274C22Q16×D911yescharacteristic
275C22#6348011yescharacteristic
276C22#6349911yescharacteristic
277C4—21no—
278C4—21no—
279C4—41no—
280C4—41no—
281C4—81no—
282C4—182no—
283C4—361no—
284C4—361no—
285C4—361no—
286C4—721no—
287C3#7117911yescharacteristic
288C2—21no—
289C2—21no—
290C2#1058873311yescharacteristic
291C2#1058886611yescharacteristic
292C2#1058888111yescharacteristic
subgroupG/H
centerC22#63499
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#484C2
socleC22×C3#937
prime radicalC23×C3D3×D4
hypercenter#484D9
hypocenterC9#1617
LCSG ▷ C22×C4×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

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
C9×#4842
#105886652
#105886462
#105882152
#105881452
#105881442
#711793