Finite Group Databasebeta

← C2×#10589822 #11910153

Subgroups — C2×#10589822 #11910153

Order 1152.

2016 conjugacy classes of subgroups; only the 550 normal subgroups are shown.

normal subgroups only

This group has 2016 conjugacy classes of subgroups — too many to draw. Only its 550 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×C9×#127C211yesmaximal, characteristic, complemented
2C2×#63501C216yesmaximal, complemented
3C2×#63499C213yesmaximal, complemented
4C2×#63497C213yesmaximal, complemented
5#10589822C2116yesmaximal, direct product factor
6C2×#63438C212yesmaximal, complemented
7C2×#5720—31nomaximal
8C24×D9C2211yescharacteristic
9C22×D4×C9C2213yes—
10C22×D4×C9C2213yescomplemented
11C22×#611C2216yes—
12C23×Dic9C2213yescomplemented
13C9×#127C2218yescomplemented
14C2×C42×C9C2211yescharacteristic, complemented
15C2×#3676C2213yes—
16C2×#3676C2213yescomplemented
17#63501C22148yescomplemented
18#63499C22124yescomplemented
19#63497C22124yescomplemented
20C2×(C2×D9)⋊C4C2216yes—
21C2×Dic9⋊C4C2216yescomplemented
22#63438C22116yescomplemented
23C2×C3×#127D311yescharacteristic
24C2×#939—36no—
25C2×#937—33no—
26C2×#935—33no—
27#5720—316no—
28C2×#876—32no—
29C24×C9C2311yescharacteristic
30C24×C9C2313yes—
31C23×D9—46no—
32C23×D9C2312yes—
33C23×D9C2314yes—
34C2×D4×C9—46no—
35C2×D4×C9—46no—
36C2×D4×C9C23112yes—
37C2×D4×C9C23112yescomplemented
38C22×C4×C9C2313yes—
39C2×#611—412no—
40C2×#611C23124yes—
41C22×Dic9—46no—
42C22×Dic9C2316yes—
43C22×Dic9C23112yescomplemented
44C42×C9C2314yescomplemented
45#3676C23112yes—
46#3676C23112yescomplemented
47(C2×D9)⋊C4C23124yes—
48Dic9⋊C4C23124yescomplemented
49C2×#560—91noSylow
50C24×D3—31no—
51C22×C3×D4C2×D313yes—
52C22×C3×D4C2×D313yes—
53C22×#67—36no—
54C23×Dic3—33no—
55C3×#127C2×D318yes—
56C2×C3×C42C2×D311yescharacteristic
57C2×#217—33no—
58C2×#217—33no—
59#939—348no—
60#937—324no—
61#935—324no—
62C2×(C2×D3)⋊C4—36no—
63C2×Dic3⋊C4—36no—
64#876—316no—
65C23×C9—26no—
66C23×C9—212no—
67C23×C9—26no—
68C23×C9C2412yes—
69C23×C9C2416yes—
70C23×C9C2411yescharacteristic
71C22×D9—212no—
72C22×D9—412no—
73C22×D9—416no—
74C22×D9C2414yes—
75D4×C9—412no—
76D4×C9—412no—
77C2×C4×C9—26no—
78C2×C4×C9C2416yes—
79#611—424no—
80C2×Dic9—212no—
81C2×Dic9—412no—
82C2×Dic9C24112yes—
83#560—916no—
84C2×#127D911yescharacteristic, complemented
85C2×#126—92no—
86C2×#123—93no—
87C2×#121—96no—
88C2×#120—93no—
89C24×C3C22×D311yescharacteristic
90C24×C3C22×D313yes—
91C23×D3—32no—
92C23×D3—34no—
93C23×D3—126no—
94C2×C3×D4—46no—
95C2×C3×D4—46no—
96C2×C3×D4C22×D3112yes—
97C2×C3×D4C22×D3112yes—
98C22×C3×C4C22×D313yes—
99C2×#67—324no—
100C2×#67—1212no—
101C22×Dic3—36no—
102C22×Dic3—312no—
103C22×Dic3—126no—
104C3×C42C22×D314yes—
105#217—312no—
106#217—312no—
107(C2×D3)⋊C4—324no—
108Dic3⋊C4—324no—
109C22×C9—26no—
110C22×C9—212no—
111C22×C9—26no—
112C22×C9—44no—
113C22×C9—412no—
114C22×C9H(5,𝔽2)16yes—
115C22×C9C2511yescharacteristic
116C2×D9—212no—
117C2×D9—416no—
118C2×D9—48no—
119C4×C9—26no—
120Dic9—212no—
121C25—91no—
122C22×D4—96no—
123C22×D4C2×D913yes—
124C22×D4C2×D913yescomplemented
125C23×C4—93no—
126#127C2×D918yescomplemented
127#126—916no—
128#123—924no—
129#121—948no—
130#120—924no—
131C2×C4⋊C4—96no—
132C2×C22⋊C4—93no—
133C2×C22⋊C4—93no—
134C2×C22⋊C4—96no—
135C2×C42C2×D911yescharacteristic, complemented
136C23×C3—26no—
137C23×C3—212no—
138C23×C3—26no—
139C23×C3C23×D312yes—
140C23×C3C23×D316yes—
141C23×C3C23×D311yescharacteristic
142C22×D3—34no—
143C22×D3—612no—
144C22×D3—1212no—
145C22×D3—1216no—
146C3×D4—412no—
147C3×D4—412no—
148C2×C3×C4—26no—
149C2×C3×C4C23×D316yes—
150#67—1224no—
151C2×Dic3—312no—
152C2×Dic3—612no—
153C2×Dic3—1212no—
154C2×C9—42no—
155C2×C9—46no—
156C2×C9#56014yescomplemented
157C2×C9C2×H(5,𝔽2)13yes—
158D9—44no—
159C24—92no—
160C24—94no—
161C24—366no—
162C24C22×D911yescharacteristic
163C24C22×D913yes—
164C2×D4—46no—
165C2×D4—46no—
166C2×D4—924no—
167C2×D4—3612no—
168C2×D4C22×D9112yes—
169C2×D4C22×D9112yescomplemented
170C22×C4—96no—
171C22×C4—912no—
172C22×C4—366no—
173C22×C4C22×D913yes—
174C4⋊C4—924no—
175C22⋊C4—912no—
176C22⋊C4—912no—
177C22⋊C4—924no—
178C42C22×D914yescomplemented
179C22×C3—26no—
180C22×C3—212no—
181C22×C3—26no—
182C22×C3—44no—
183C22×C3—412no—
184C22×C3#100416yes—
185C22×C3C24×D311yescharacteristic
186C2×D3—612no—
187C2×D3—1216no—
188C2×D3—128no—
189C3×C4—26no—
190Dic3—612no—
191C9C2×#56011yescharacteristic, complemented, Sylow
192C23—26no—
193C23—212no—
194C23—26no—
195C23—94no—
196C23—1812no—
197C23—3612no—
198C23—3616no—
199C23C23×D912yes—
200C23C23×D916yes—
201C23C23×D911yescharacteristic
202D4—412no—
203D4—412no—
204D4—3624no—
205C2×C4—26no—
206C2×C4—912no—
207C2×C4—1812no—
208C2×C4—3612no—
209C2×C4C23×D916yes—
210C2×C3—42no—
211C2×C3—46no—
212C2×C3#572014yes—
213C2×C3C2×#100413yes—
214D3—124no—
215C22—26no—
216C22—212no—
217C22—26no—
218C22—44no—
219C22—412no—
220C22—1812no—
221C22—3616no—
222C22—368no—
223C22#6371016yes—
224C22C24×D911yescharacteristic
225C4—26no—
226C4—1812no—
227C3C2×#572011yescharacteristic
228C2—42no—
229C2—46no—
230C2—364no—
231C2#1058982214yesdirect product factor
232C2C2×#6371013yes—
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C9×#127C2
socleC23×C3C23×D3
hypercenterC2×#127D9
hypocenterC9C2×#560
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×C9×#127C2semidirect
2. C2×#63501C2semidirect
3. C2×#63499C2semidirect
4. C2×#63497C2semidirect
5. #10589822C2direct (N × H)
6. C2×#63438C2semidirect
10. C22×D4×C9C22semidirect
12. C23×Dic9C22semidirect
13. C9×#127C22semidirect
14. C2×C42×C9C22semidirect
16. C2×#3676C22semidirect
17. #63501C22semidirect
18. #63499C22semidirect
19. #63497C22semidirect
21. C2×Dic9⋊C4C22semidirect
22. #63438C22semidirect
37. C2×D4×C9C23semidirect
43. C22×Dic9C23semidirect
44. C42×C9C23semidirect
46. #3676C23semidirect
48. Dic9⋊C4C23semidirect
84. C2×#127D9semidirect
124. C22×D4C2×D9semidirect
126. #127C2×D9semidirect
135. C2×C42C2×D9semidirect
156. C2×C9#560semidirect
169. C2×D4C22×D9semidirect
178. C42C22×D9semidirect
191. C9C2×#560semidirect
231. C2#10589822direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9×#1272
C2×#635012
C2×#634992
C2×#634972
#105898222
C2×#634382
C2×#57203