Finite Group Databasebeta

← #11788200

Subgroups — #11788200

Order 1152.

537 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 537 conjugacy classes of subgroups — too many to draw. Only its 138 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
1C9×#525C211yesmaximal, characteristic
2C2×#63488C211yesmaximal, characteristic, complemented
3C2×#63396C212yesmaximal, complemented
4#10588887C211yesmaximal, characteristic, complemented
5#10588208C212yesmaximal, complemented
6#71712—31nomaximal
7C2×C9×#41C2211yescharacteristic
8C23×C4×C9C2211yescharacteristic
9C9×#123—21no—
10C9×C22⋊Q8C412yescomplemented
11C9×#121C412yescomplemented
12C9×#120—21no—
13C4×D4×C9—22no—
14C9×#117C2211yescharacteristic
15C2×#3676—21no—
16#63488—24no—
17C2×C4⋊Dic9—21no—
18C2×C4×Dic9C2212yes—
19C2×#3667C2212yes—
20#63396—24no—
21#63389—22no—
22C3×#525D311yescharacteristic
23C2×#926—31no—
24C2×#837—32no—
25#5207—31no—
26#4532—32no—
27C24×C9D411yescharacteristic
28C9×#41—22no—
29C9×#41—22no—
30C2×Q8×C9C2×C411yescharacteristic
31C2×D4×C9—22no—
32C2×D4×C9—21no—
33C2×D4×C9C2×C411yescharacteristic
34C22×C4×C9—22no—
35C22×C4×C9—22no—
36C22×C4×C9—21no—
37C22×C4×C9C2×C412yes—
38C22×C4×C9D411yescharacteristic
39C22×C4×C9D412yes—
40C22×C4×C9C2311yescharacteristic
41C22×Dic9—22no—
42C9×C4⋊C4—22no—
43C9×C4⋊C4C2×C412yes—
44C9×C22⋊C4—22no—
45C9×C22⋊C4—21no—
46C9×C22⋊C4—22no—
47C42×C9—21no—
48#3676—24no—
49C4⋊Dic9—24no—
50C4×Dic9—22no—
51C4×Dic9D414yescomplemented
52#3667—22no—
53#3667—22no—
54C2×C9⋊C8—22no—
55#1897—91noSylow
56C2×C3×#41C2×D311yescharacteristic
57C23×C3×C4C2×D311yescharacteristic
58C3×#123—21no—
59C3×C22⋊Q8Dic312yes—
60C3×#121Dic312yes—
61C3×#120—21no—
62C3×C4×D4—22no—
63C3×#117C2×D311yescharacteristic
64C2×#217—61no—
65#926—64no—
66C2×C4⋊Dic3—61no—
67C2×C4×Dic3—32no—
68C2×#208—32no—
69#837—64no—
70#830—62no—
71C23×C9—21no—
72C23×C9—21no—
73C23×C9—21no—
74C23×C9—42no—
75C23×C9C22⋊C412yes—
76C23×C9C2×D411yescharacteristic
77Q8×C9—22no—
78D4×C9—22no—
79D4×C9—44no—
80D4×C9—41no—
81D4×C9—41no—
82C2×C4×C9—21no—
83C2×C4×C9—21no—
84C2×C4×C9—24no—
85C2×C4×C9—24no—
86C2×C4×C9—22no—
87C2×C4×C9—21no—
88C2×C4×C9—42no—
89C2×C4×C9C22⋊C412yes—
90C2×C4×C9C22×C411yescharacteristic
91C2×C4×C9C2×D412yes—
92C2×C4×C9C2×D411yescharacteristic
93C2×C4×C9#4112yes—
94C2×Dic9—24no—
95C2×Dic9—44no—
96C9⋊C8—42no—
97#525D911yescharacteristic
98C2×#117—91no—
99C2×#104—92no—
100#407—91no—
101#339—92no—
102C24×C3#6711yescharacteristic
103C3×#41—22no—
104C3×#41—22no—
105C2×C3×Q8C2×Dic311yescharacteristic
106C2×C3×D4—22no—
107C2×C3×D4—21no—
108C2×C3×D4C2×Dic311yescharacteristic
109C22×C3×C4—22no—
110C22×C3×C4—22no—
111C22×C3×C4—21no—
112C22×C3×C4C2×Dic312yes—
113C22×C3×C4#6711yescharacteristic
114C22×C3×C4#6712yes—
115C22×C3×C4C22×D311yescharacteristic
116C22×Dic3—62no—
117C3×C4⋊C4—22no—
118C3×C4⋊C4C2×Dic312yes—
119C3×C22⋊C4—22no—
120C3×C22⋊C4—21no—
121C3×C22⋊C4—22no—
122C3×C42—21no—
123#217—64no—
124C4⋊Dic3—64no—
125C4×Dic3—34no—
126C4×Dic3—62no—
127#208—62no—
128#208—62no—
129C2×C3⋊C8—62no—
130C22×C9—22no—
131C22×C9—22no—
132C22×C9—22no—
133C22×C9—22no—
134C22×C9—42no—
135C22×C9—42no—
136C22×C9—41no—
137C22×C9—42no—
138C22×C9C2×C22⋊C411yescharacteristic
139C22×C9#12011yescharacteristic
140C22×C9#12311yescharacteristic
141C4×C9—22no—
142C4×C9—41no—
143C4×C9—42no—
144C4×C9C4×D412yes—
145C4×C9#12112yes—
146Dic9—44no—
147C2×#41C2×D911yescharacteristic
148C23×C4C2×D911yescharacteristic
149C2×M16—92no—
150#123—21no—
151C22⋊Q8Dic912yescomplemented
152#121Dic912yescomplemented
153#120—21no—
154C4×D4—22no—
155#117—184no—
156#117C2×D911yescharacteristic
157C2×C4⋊C4—181no—
158C2×C22⋊C4—181no—
159C2×C42—92no—
160#104—184no—
161C22⋊C8—182no—
162C23×C3—21no—
163C23×C3—21no—
164C23×C3—21no—
165C23×C3—42no—
166C23×C3#21712yes—
167C23×C3C2×#6711yescharacteristic
168C3×Q8—22no—
169C3×D4—22no—
170C3×D4—44no—
171C3×D4—41no—
172C3×D4—41no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—24no—
176C2×C3×C4—24no—
177C2×C3×C4—22no—
178C2×C3×C4—21no—
179C2×C3×C4—42no—
180C2×C3×C4#21712yes—
181C2×C3×C4D3×D412yes—
182C2×C3×C4#23712yes—
183C2×C3×C4C22×Dic311yescharacteristic
184C2×C3×C4C2×#6711yescharacteristic
185C2×Dic3—64no—
186C2×Dic3—124no—
187C3⋊C8—122no—
188C2×C9—21no—
189C2×C9—21no—
190C2×C9—42no—
191C2×C9—81no—
192C2×C9#38611yescharacteristic
193C2×C9#42112yes—
194C24#61111yescharacteristic
195#41—22no—
196#41—22no—
197C2×Q8C2×Dic911yescharacteristic
198C2×D4—22no—
199C2×D4—21no—
200C2×D4C2×Dic911yescharacteristic
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—21no—
204C22×C4—182no—
205C22×C4C2×Dic912yes—
206C22×C4#61111yescharacteristic
207C22×C4#61112yes—
208C22×C4C22×D911yescharacteristic
209M16—182no—
210M16—182no—
211C2×C8—182no—
212C4⋊C4—22no—
213C4⋊C4—184no—
214C4⋊C4C2×Dic912yes—
215C22⋊C4—22no—
216C22⋊C4—21no—
217C22⋊C4—22no—
218C22⋊C4—184no—
219C42—21no—
220C42—94no—
221C42—182no—
222C22×C3—22no—
223C22×C3—22no—
224C22×C3—22no—
225C22×C3—22no—
226C22×C3—42no—
227C22×C3—42no—
228C22×C3—41no—
229C22×C3—42no—
230C22×C3#93511yescharacteristic
231C22×C3#93711yescharacteristic
232C22×C3C2×#21711yescharacteristic
233C3×C4—22no—
234C3×C4—41no—
235C3×C4—42no—
236C3×C4D4×Dic312yes—
237C3×C4#93912yes—
238Dic3—124no—
239C9#189711yescharacteristic, complemented, Sylow
240C23—21no—
241C23—21no—
242C23—21no—
243C23—42no—
244C23#367612yes—
245C23C2×#61111yescharacteristic
246Q8—22no—
247D4—22no—
248D4—44no—
249D4—41no—
250D4—41no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—24no—
254C2×C4—24no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—42no—
258C2×C4—184no—
259C2×C4—364no—
260C2×C4#367612yes—
261C2×C4D4×D912yes—
262C2×C4#369912yes—
263C2×C4C22×Dic911yescharacteristic
264C2×C4C2×#61111yescharacteristic
265C8—362no—
266C2×C3—21no—
267C2×C3—21no—
268C2×C3—42no—
269C2×C3—81no—
270C2×C3#522011yescharacteristic
271C2×C3#523612yes—
272C22—22no—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—42no—
277C22—42no—
278C22—41no—
279C22—42no—
280C22#6349711yescharacteristic
281C22#6349911yescharacteristic
282C22C2×#367611yescharacteristic
283C4—22no—
284C4—41no—
285C4—42no—
286C4—364no—
287C4D4×Dic912yes—
288C4#6350112yes—
289C3#7171211yescharacteristic
290C2—21no—
291C2—21no—
292C2—42no—
293C2—81no—
294C2#1058890011yescharacteristic
295C2#1058891412yes—
subgroupG/H
centerC2×C4C2×#611
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC9×#525C2
socleC22×C3C2×#217
prime radicalC3×#525D3
cosocleC22×C4×C9C23
hypercenter#525D9
hypocenterC9#1897
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
2. C2×#63488C2semidirect
3. C2×#63396C2semidirect
4. #10588887C2semidirect
5. #10588208C2semidirect
10. C9×C22⋊Q8C4semidirect
11. C9×#121C4semidirect
51. C4×Dic9D4semidirect
151. C22⋊Q8Dic9semidirect
152. #121Dic9semidirect
239. C9#1897semidirect

Maximal subgroups

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

subgroupindex
C9×#5252
C2×#634882
C2×#633962
#105888872
#105882082
#717123