Finite Group Databasebeta

← #11856259

Subgroups — #11856259

Order 1152.

1653 conjugacy classes of subgroups; only the 262 normal subgroups are shown.

normal subgroups only

This group has 1653 conjugacy classes of subgroups — too many to draw. Only its 262 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
1C24×Dic9C211yesmaximal, characteristic, complemented
2C2×#63515C211yesmaximal, characteristic
3C2×#63448C212yesmaximal, complemented
4C9×#379C211yesmaximal, characteristic, complemented
5#10588638C214yesmaximal, complemented
6#10588630C214yesmaximal, complemented
7#10588623C212yesmaximal, complemented
8#73847—31nomaximal
9C25×C9C2211yescharacteristic
10C22×#611C2211yescharacteristic
11C22×#611C2212yes—
12C23×Dic9—24no—
13C23×Dic9—28no—
14C23×Dic9C2214yes—
15C23×Dic9C2212yes—
16C2×C9×C22⋊C4C2212yes—
17C2×C9×C22⋊C4C2214yes—
18#63515—24no—
19C2×#3676C2211yescharacteristic
20C2×#3676C2212yes—
21C2×(C2×D9)⋊C4C2214yescomplemented
22C2×C4⋊Dic9C2214yescomplemented
23#63448—28no—
24C9⋊#95C2218yescomplemented
25C24×Dic3—31no—
26C2×#953—31no—
27C2×#886—32no—
28C3×#379D311yescharacteristic
29#4958—34no—
30#4950—34no—
31#4943—32no—
32C24×C9—24no—
33C24×C9—28no—
34C24×C9D414yes—
35C24×C9C2311yescharacteristic
36C24×C9C2312yes—
37C23×D9C2311yescharacteristic
38C22×C4×C9C2314yes—
39C2×#611—22no—
40C2×#611—24no—
41C2×#611—24no—
42C2×#611—28no—
43C22×Dic9—232no—
44C22×Dic9—28no—
45C22×Dic9—24no—
46C22×Dic9—24no—
47C22×Dic9—216no—
48C22×Dic9D418yescomplemented
49C22×Dic9C2312yes—
50C22×Dic9C2311yescharacteristic
51C22×Dic9C2314yes—
52C9×C22⋊C4—24no—
53C9×C22⋊C4—28no—
54#3676—22no—
55#3676—24no—
56(C2×D9)⋊C4—28no—
57C4⋊Dic9—28no—
58#2849—91noSylow
59C25×C3C2×D311yescharacteristic
60C22×#67—32no—
61C22×#67—31no—
62C23×Dic3—32no—
63C23×Dic3—34no—
64C23×Dic3—68no—
65C23×Dic3—64no—
66C2×C3×C22⋊C4C2×D312yes—
67C2×C3×C22⋊C4C2×D314yes—
68#953—64no—
69C2×#217—31no—
70C2×#217—32no—
71C2×(C2×D3)⋊C4—34no—
72C2×C4⋊Dic3—34no—
73#886—68no—
74C3⋊#95—38no—
75C23×C9—232no—
76C23×C9—28no—
77C23×C9—216no—
78C23×C9—24no—
79C23×C9—24no—
80C23×C9—24no—
81C23×C9C2×D412yes—
82C23×C9C2×D414yes—
83C23×C9C2×D414yes—
84C23×C9#4118yes—
85C23×C9C2411yescharacteristic
86C22×D9—22no—
87C22×D9—21no—
88C22×D9—24no—
89C2×C4×C9—24no—
90C2×C4×C9—28no—
91#611—44no—
92#611—48no—
93C2×Dic9—232no—
94C2×Dic9—216no—
95C2×Dic9—24no—
96C2×Dic9—24no—
97C2×Dic9—22no—
98C2×Dic9—21no—
99C2×Dic9—22no—
100C2×Dic9—24no—
101C2×Dic9C2×D418yes—
102C24×C4—91no—
103C2×#123—92no—
104C2×#120—91no—
105#386—94no—
106#385—94no—
107#381—92no—
108#379D911yescharacteristic, complemented
109C24×C3—24no—
110C24×C3—28no—
111C24×C3D1214yes—
112C24×C3C22×D311yescharacteristic
113C24×C3C22×D312yes—
114C23×D3—31no—
115C22×C3×C4C22×D314yes—
116C2×#67—62no—
117C2×#67—64no—
118C2×#67—64no—
119C2×#67—68no—
120C22×Dic3—38no—
121C22×Dic3—34no—
122C22×Dic3—32no—
123C22×Dic3—31no—
124C22×Dic3—616no—
125C22×Dic3—632no—
126C22×Dic3—68no—
127C22×Dic3—64no—
128C22×Dic3—64no—
129C3×C22⋊C4—24no—
130C3×C22⋊C4—28no—
131#217—62no—
132#217—64no—
133(C2×D3)⋊C4—68no—
134C4⋊Dic3—68no—
135C22×C9—232no—
136C22×C9—24no—
137C22×C9—24no—
138C22×C9—24no—
139C22×C9—28no—
140C22×C9—216no—
141C22×C9#12014yes—
142C22×C9#12318yescomplemented
143C22×C9C22×D411yescharacteristic
144C22×C9C22×D412yes—
145C22×C9C2×#4114yes—
146C2×D9—41no—
147C2×D9—42no—
148C2×D9—44no—
149C4×C9—44no—
150Dic9—28no—
151Dic9—41no—
152Dic9—42no—
153C25C2×D911yescharacteristic
154C22×D4—91no—
155C22×D4—92no—
156C23×C4—92no—
157C23×C4—94no—
158C23×C4—188no—
159C23×C4—184no—
160#123—188no—
161#120—184no—
162C2×C4⋊C4—94no—
163C2×C22⋊C4—91no—
164C2×C22⋊C4—92no—
165C2×C22⋊C4—94no—
166C2×C22⋊C4C2×D912yes—
167C2×C22⋊C4C2×D914yes—
168#95—98no—
169C23×C3—232no—
170C23×C3—28no—
171C23×C3—216no—
172C23×C3—24no—
173C23×C3—24no—
174C23×C3—24no—
175C23×C3C2×D1212yes—
176C23×C3C2×D1214yes—
177C23×C3D3×D414yes—
178C23×C3#23718yes—
179C23×C3C23×D311yescharacteristic
180C22×D3—61no—
181C22×D3—62no—
182C22×D3—64no—
183C2×C3×C4—24no—
184C2×C3×C4—28no—
185#67—124no—
186#67—128no—
187C2×Dic3—38no—
188C2×Dic3—632no—
189C2×Dic3—616no—
190C2×Dic3—64no—
191C2×Dic3—64no—
192C2×Dic3—61no—
193C2×Dic3—62no—
194C2×Dic3—62no—
195C2×Dic3—64no—
196C2×C9—24no—
197C2×C9—28no—
198C2×C9C2×#12011yescharacteristic
199C2×C9C2×#12312yes—
200C2×C9#52514yes—
201D9—81no—
202C24—24no—
203C24—28no—
204C24—91no—
205C24D3614yes—
206C24C22×D911yescharacteristic
207C24C22×D912yes—
208C2×D4—182no—
209C2×D4—184no—
210C2×D4—184no—
211C2×D4—188no—
212C22×C4—98no—
213C22×C4—94no—
214C22×C4—92no—
215C22×C4—91no—
216C22×C4—1816no—
217C22×C4—1832no—
218C22×C4—188no—
219C22×C4—184no—
220C22×C4—184no—
221C22×C4C22×D914yes—
222C4⋊C4—188no—
223C22⋊C4—24no—
224C22⋊C4—28no—
225C22⋊C4—188no—
226C22⋊C4—182no—
227C22⋊C4—184no—
228C22×C3—232no—
229C22×C3—24no—
230C22×C3—24no—
231C22×C3—24no—
232C22×C3—28no—
233C22×C3—216no—
234C22×C3#88214yes—
235C22×C3#88618yes—
236C22×C3C22×D1211yescharacteristic
237C22×C3C2×D3×D412yes—
238C22×C3C2×#23714yes—
239C2×D3—121no—
240C2×D3—122no—
241C2×D3—124no—
242C3×C4—44no—
243Dic3—68no—
244Dic3—121no—
245Dic3—122no—
246C9#284911yescharacteristic, complemented, Sylow
247C23—232no—
248C23—28no—
249C23—216no—
250C23—24no—
251C23—24no—
252C23—24no—
253C23—181no—
254C23—182no—
255C23—184no—
256C23C2×D3612yes—
257C23C2×D3614yes—
258C23D4×D914yes—
259C23#369918yes—
260C23C23×D911yescharacteristic
261D4—364no—
262D4—368no—
263C2×C4—24no—
264C2×C4—28no—
265C2×C4—98no—
266C2×C4—1832no—
267C2×C4—1816no—
268C2×C4—184no—
269C2×C4—184no—
270C2×C4—181no—
271C2×C4—182no—
272C2×C4—182no—
273C2×C4—184no—
274C2×C3—24no—
275C2×C3—28no—
276C2×C3C2×#88211yescharacteristic
277C2×C3C2×#88612yes—
278C2×C3#558614yes—
279D3—241no—
280C22—232no—
281C22—24no—
282C22—24no—
283C22—24no—
284C22—28no—
285C22—216no—
286C22—361no—
287C22—362no—
288C22—364no—
289C22#6344414yes—
290C22#6344818yescomplemented
291C22C22×D3611yescharacteristic
292C22C2×D4×D912yes—
293C22C2×#369914yes—
294C4—44no—
295C4—188no—
296C4—361no—
297C4—362no—
298C3#7384711yescharacteristic
299C2—24no—
300C2—28no—
301C2—721no—
302C2C2×#6344411yescharacteristic
303C2C2×#6344812yes—
304C2#1058968814yes—
subgroupG/H
centerC23C23×D9
commutator, cosocleC23×C9C24
Frattini, socleC23×C3C23×D3
FittingC9×#379C2
prime radicalC2×#63515C2
hypercenter#379D9
hypocenterC9#2849
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C24×Dic9C2semidirect
3. C2×#63448C2semidirect
4. C9×#379C2semidirect
5. #10588638C2semidirect
6. #10588630C2semidirect
7. #10588623C2semidirect
21. C2×(C2×D9)⋊C4C22semidirect
22. C2×C4⋊Dic9C22semidirect
24. C9⋊#95C22semidirect
48. C22×Dic9D4semidirect
108. #379D9semidirect
142. C22×C9#123semidirect
246. C9#2849semidirect
290. C22#63448semidirect

Maximal subgroups

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

subgroupindex
C24×Dic92
C2×#635152
C2×#634482
C9×#3792
#105886382
#105886302
#105886232
#738473