Finite Group Databasebeta

← #11787859

Subgroups — #11787859

Order 1152.

666 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 666 conjugacy classes of subgroups — too many to draw. Only its 122 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
1C2×#63502C211yesmaximal, characteristic
2#10589900C211yesmaximal, characteristic, complemented
3C2×C9×#100C211yesmaximal, characteristic, complemented
4#10588813C212yesmaximal, complemented
5#10588235C212yesmaximal, complemented
6#70070—31nomaximal
7C22×D4×C9C2211yescharacteristic
8C22×#611—22no—
9C22×D36C2211yescharacteristic
10C2×C9×M16C2212yes—
11C2×#3676—22no—
12#63502—22no—
13#63502C414yescomplemented
14D4×Dic9—24no—
15#63488C2212yes—
16C2×C4×Dic9C2211yescharacteristic
17C9×#100—22no—
18#63380—24no—
19C2×#940—31no—
20#5798—31no—
21C2×C3×#100D311yescharacteristic
22#5131—32no—
23#4555—32no—
24C24×C9D412yes—
25C23×D9—21no—
26C2×D4×C9—22no—
27C2×D4×C9—22no—
28C2×D4×C9C2×C412yes—
29C2×D4×C9D412yes—
30C22×C4×C9C2311yescharacteristic
31C2×#611—28no—
32C2×#611—48no—
33C22×Dic9—21no—
34C22×Dic9—24no—
35C2×D36—22no—
36C2×D36—22no—
37C2×D36—21no—
38C2×D36C2×C412yescomplemented
39C9×M16—22no—
40C9×M16—22no—
41C2×C8×C9—22no—
42#3676—24no—
43#3676—22no—
44C4⋊Dic9D414yescomplemented
45C4×Dic9—22no—
46C4×Dic9—21no—
47C4×Dic9C2×C412yescomplemented
48#1887—91noSylow
49C22×C3×D4C2×D311yescharacteristic
50C22×#67—62no—
51C22×D12—31no—
52C2×C3×M16C2×D312yes—
53C2×#217—62no—
54#940—34no—
55#940—62no—
56D4×Dic3—64no—
57#926—32no—
58C2×C4×Dic3—31no—
59C3×#100—22no—
60#821—64no—
61C23×C9—22no—
62C23×C9—22no—
63C23×C9—44no—
64C23×C9C22⋊C414yes—
65C23×C9C2×D411yescharacteristic
66C22×D9—22no—
67C22×D9—44no—
68C22×D9—41no—
69C22×D9—41no—
70D4×C9—24no—
71D4×C9—24no—
72C2×C4×C9C22×C411yescharacteristic
73C2×C4×C9C2×D412yes—
74C2×C4×C9C2×D411yescharacteristic
75C2×C4×C9#4112yes—
76#611—416no—
77C2×Dic9—24no—
78C2×Dic9—22no—
79C2×Dic9—24no—
80C2×Dic9—84no—
81D36—24no—
82D36—42no—
83C8×C9—42no—
84C2×#127—91no—
85#518—91no—
86#418—92no—
87C2×#100D911yescharacteristic, complemented
88#339—92no—
89C24×C3D1212yes—
90C23×D3—61no—
91C2×C3×D4—22no—
92C2×C3×D4—22no—
93C2×C3×D4C4×D312yes—
94C2×C3×D4#6712yes—
95C22×C3×C4C22×D311yescharacteristic
96C2×#67—68no—
97C2×#67—128no—
98C22×Dic3—61no—
99C22×Dic3—64no—
100C2×D12—32no—
101C2×D12—62no—
102C2×D12—62no—
103C2×D12—61no—
104C3×M16—22no—
105C3×M16—22no—
106C2×C3×C8—22no—
107#217—64no—
108#217—62no—
109C4⋊Dic3—34no—
110C4×Dic3—32no—
111C4×Dic3—62no—
112C4×Dic3—61no—
113C22×C9—22no—
114C22×C9—24no—
115C22×C9—44no—
116C22×C9—44no—
117C22×C9—82no—
118C22×C9C2×C22⋊C411yescharacteristic
119C22×C9#12011yescharacteristic
120C22×C9#12311yescharacteristic
121C2×D9—44no—
122C2×D9—42no—
123C2×D9—82no—
124C2×D9—82no—
125C4×C9C4×D412yes—
126C4×C9#12112yes—
127Dic9—24no—
128Dic9—44no—
129C22×D4—91no—
130C22×D4—182no—
131C22×D4C2×D911yescharacteristic
132C2×M16C2×D912yes—
133#127—94no—
134#127—182no—
135C4×D4—184no—
136#117—92no—
137C2×C22⋊C4—182no—
138C2×C42—91no—
139#102—184no—
140#100—22no—
141C23×C3—22no—
142C23×C3—22no—
143C23×C3—44no—
144C23×C3(C2×D3)⋊C414yes—
145C23×C3C2×D1211yescharacteristic
146C22×D3—62no—
147C22×D3—124no—
148C22×D3—121no—
149C22×D3—121no—
150C3×D4—24no—
151C3×D4—24no—
152C2×C3×C4C2×C4×D311yescharacteristic
153C2×C3×C4D3×D412yes—
154C2×C3×C4#23712yes—
155C2×C3×C4C2×#6711yescharacteristic
156#67—1216no—
157C2×Dic3—64no—
158C2×Dic3—62no—
159C2×Dic3—64no—
160C2×Dic3—244no—
161D12—64no—
162D12—122no—
163C3×C8—42no—
164C2×C9—21no—
165C2×C9—21no—
166C2×C9—44no—
167C2×C9#38611yescharacteristic
168C2×C9#45312yes—
169D9—82no—
170C24—181no—
171C24D3612yes—
172C2×D4—22no—
173C2×D4—22no—
174C2×D4—92no—
175C2×D4—188no—
176C2×D4—182no—
177C2×D4—182no—
178C2×D4—181no—
179C2×D4—368no—
180C2×D4C4×D912yes—
181C2×D4#61112yes—
182C22×C4—181no—
183C22×C4—184no—
184C22×C4C22×D911yescharacteristic
185M16—22no—
186M16—22no—
187C2×C8—22no—
188C4⋊C4—94no—
189C22⋊C4—184no—
190C22⋊C4—182no—
191C42—92no—
192C42—182no—
193C42—181no—
194C22×C3—22no—
195C22×C3—24no—
196C22×C3—44no—
197C22×C3—44no—
198C22×C3—82no—
199C22×C3#88211yescharacteristic
200C22×C3#88611yescharacteristic
201C22×C3C2×(C2×D3)⋊C411yescharacteristic
202C2×D3—124no—
203C2×D3—122no—
204C2×D3—242no—
205C2×D3—242no—
206C3×C4#67⋊C412yes—
207C3×C4#93912yes—
208Dic3—64no—
209Dic3—124no—
210C9#188711yescharacteristic, complemented, Sylow
211C23—22no—
212C23—22no—
213C23—44no—
214C23—182no—
215C23—364no—
216C23—361no—
217C23—361no—
218C23(C2×D9)⋊C414yes—
219C23C2×D3611yescharacteristic
220D4—24no—
221D4—24no—
222D4—184no—
223D4—3616no—
224D4—362no—
225C2×C4—184no—
226C2×C4—182no—
227C2×C4—184no—
228C2×C4—724no—
229C2×C4C2×C4×D911yescharacteristic
230C2×C4D4×D912yes—
231C2×C4#369912yes—
232C2×C4C2×#61111yescharacteristic
233C8—42no—
234C2×C3—21no—
235C2×C3—21no—
236C2×C3—44no—
237C2×C3#474712yes—
238C2×C3#495811yescharacteristic
239D3—242no—
240C22—22no—
241C22—24no—
242C22—44no—
243C22—44no—
244C22—82no—
245C22—364no—
246C22—362no—
247C22—722no—
248C22—722no—
249C22#6344411yescharacteristic
250C22#6344811yescharacteristic
251C22C2×(C2×D9)⋊C411yescharacteristic
252C4—184no—
253C4—364no—
254C4#611⋊C412yes—
255C4#6350112yes—
256C3#7007011yescharacteristic
257C2—21no—
258C2—21no—
259C2—44no—
260C2—722no—
261C2#1058842712yes—
262C2#1058863811yescharacteristic
subgroupG/H
centerC22#63444
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC2×C9×#100C2
socleC22×C3#882
prime radicalC2×#63502C2
cosocleC22×C4×C9C23
hypercenterC2×#100D9
hypocenterC9#1887
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. #10589900C2semidirect
3. C2×C9×#100C2semidirect
4. #10588813C2semidirect
5. #10588235C2semidirect
13. #63502C4semidirect
38. C2×D36C2×C4semidirect
44. C4⋊Dic9D4semidirect
47. C4×Dic9C2×C4semidirect
87. C2×#100D9semidirect
210. C9#1887semidirect

Maximal subgroups

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

subgroupindex
C2×#635022
#105899002
C2×C9×#1002
#105888132
#105882352
#700703