Finite Group Databasebeta

← C2×#10589696 #11910207

Subgroups — C2×#10589696 #11910207

Order 1152.

2112 conjugacy classes of subgroups; only the 550 normal subgroups are shown.

normal subgroups only

This group has 2112 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×#120C211yesmaximal, characteristic, complemented
2C2×#63515C212yesmaximal, complemented
3C2×#63499C213yesmaximal, complemented
4C2×#63498C213yesmaximal, complemented
5#10589696C2116yesmaximal, direct product factor
6C2×#63447C216yesmaximal, complemented
7C2×#5594—31nomaximal
8C25×C9C2211yescharacteristic, complemented
9C24×D9C2211yescharacteristic, complemented
10C22×D4×C9C2213yes—
11C22×#611C2216yes—
12C22×Dic18C2213yescomplemented
13C9×#120C2218yescomplemented
14C2×C9×C22⋊C4C2213yescomplemented
15#63515C22116yescomplemented
16C2×#3676C2216yescomplemented
17C2×#3676C2213yescomplemented
18#63499C22124yescomplemented
19#63498C22124yescomplemented
20C2×(C2×D9)⋊C4C2216yescomplemented
21C2×C4×Dic9C2213yescomplemented
22#63447C22148yescomplemented
23C2×C3×#120D311yescharacteristic
24C2×#953—32no—
25C2×#937—33no—
26C2×#936—33no—
27#5594—316no—
28C2×#885—36no—
29C24×C9—46no—
30C24×C9C2311yescharacteristic
31C24×C9C2313yes—
32C24×C9C2314yescomplemented
33C23×D9—46no—
34C23×D9C2312yes—
35C23×D9C2314yescomplemented
36C2×D4×C9—46no—
37C2×D4×C9C23112yes—
38C22×C4×C9C2313yes—
39C2×#611—412no—
40C2×#611C23124yes—
41C22×Dic9C2316yes—
42C2×Dic18—46no—
43C2×Dic18C23112yescomplemented
44C9×C22⋊C4C23112yescomplemented
45#3676C23112yescomplemented
46#3676C23124yescomplemented
47(C2×D9)⋊C4C23124yescomplemented
48C4×Dic9C23112yescomplemented
49C2×H(3,𝔽4)—91noSylow
50C25×C3C2×D311yescharacteristic
51C24×D3—31no—
52C22×C3×D4C2×D313yes—
53C22×#67—36no—
54C22×Dic6—33no—
55C3×#120C2×D318yes—
56C2×C3×C22⋊C4C2×D313yes—
57#953—316no—
58C2×#217—36no—
59C2×#217—33no—
60#937—324no—
61#936—324no—
62C2×(C2×D3)⋊C4—36no—
63C2×C4×Dic3—33no—
64#885—348no—
65C23×C9—212no—
66C23×C9—26no—
67C23×C9—26no—
68C23×C9—412no—
69C23×C9—416no—
70C23×C9C2412yes—
71C23×C9C2416yes—
72C23×C9C2411yescharacteristic
73C22×D9—212no—
74C22×D9—412no—
75C22×D9—416no—
76C22×D9C2414yes—
77D4×C9—412no—
78C2×C4×C9—26no—
79C2×C4×C9C2416yes—
80#611—424no—
81C2×Dic9—212no—
82C2×Dic9C24112yes—
83Dic18—412no—
84H(3,𝔽4)—916no—
85C2×#124—93no—
86C2×#124—96no—
87C2×#120—92no—
88C2×#120—93no—
89C2×#120D911yescharacteristic, complemented
90C24×C3—46no—
91C24×C3C22×D313yes—
92C24×C3C22×D311yescharacteristic
93C24×C3C22×D314yes—
94C23×D3—32no—
95C23×D3—34no—
96C23×D3—126no—
97C2×C3×D4—46no—
98C2×C3×D4C22×D3112yes—
99C22×C3×C4C22×D313yes—
100C2×#67—324no—
101C2×#67—1212no—
102C22×Dic3—36no—
103C2×Dic6—312no—
104C2×Dic6—126no—
105C3×C22⋊C4C22×D3112yes—
106#217—324no—
107#217—312no—
108(C2×D3)⋊C4—324no—
109C4×Dic3—312no—
110C22×C9—212no—
111C22×C9—26no—
112C22×C9—26no—
113C22×C9—416no—
114C22×C9—44no—
115C22×C9—412no—
116C22×C9H(5,𝔽2)16yes—
117C22×C9C2511yescharacteristic
118C2×D9—212no—
119C2×D9—416no—
120C2×D9—48no—
121C4×C9—26no—
122Dic9—212no—
123C25—91no—
124C25C2×D911yescharacteristic, complemented
125C22×Q8—93no—
126C22×D4—96no—
127C22×D4C2×D913yes—
128#124—924no—
129#124—948no—
130#120—916no—
131#120—924no—
132#120C2×D918yescomplemented
133C2×C22⋊C4—93no—
134C2×C22⋊C4—96no—
135C2×C22⋊C4—96no—
136C2×C22⋊C4C2×D913yescomplemented
137C2×C42—93no—
138C23×C3—212no—
139C23×C3—26no—
140C23×C3—26no—
141C23×C3—412no—
142C23×C3—416no—
143C23×C3C23×D312yes—
144C23×C3C23×D316yes—
145C23×C3C23×D311yescharacteristic
146C22×D3—34no—
147C22×D3—612no—
148C22×D3—1212no—
149C22×D3—1216no—
150C3×D4—412no—
151C2×C3×C4—26no—
152C2×C3×C4C23×D316yes—
153#67—1224no—
154C2×Dic3—312no—
155C2×Dic3—612no—
156Dic6—1212no—
157C2×C9—42no—
158C2×C9—46no—
159C2×C9H(3,𝔽4)14yescomplemented
160C2×C9C2×H(5,𝔽2)13yes—
161D9—44no—
162C24—46no—
163C24—92no—
164C24—94no—
165C24—366no—
166C24C22×D911yescharacteristic
167C24C22×D913yes—
168C24C22×D914yescomplemented
169C2×Q8—912no—
170C2×Q8—366no—
171C2×D4—46no—
172C2×D4—924no—
173C2×D4—3612no—
174C2×D4C22×D9112yes—
175C22×C4—96no—
176C22×C4C22×D913yes—
177C22⋊C4—912no—
178C22⋊C4—924no—
179C22⋊C4—924no—
180C22⋊C4C22×D9112yescomplemented
181C42—912no—
182C22×C3—212no—
183C22×C3—26no—
184C22×C3—26no—
185C22×C3—416no—
186C22×C3—44no—
187C22×C3—412no—
188C22×C3#100416yes—
189C22×C3C24×D311yescharacteristic
190C2×D3—612no—
191C2×D3—1216no—
192C2×D3—128no—
193C3×C4—26no—
194Dic3—612no—
195C9C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
196C23—26no—
197C23—26no—
198C23—212no—
199C23—412no—
200C23—416no—
201C23—94no—
202C23—1812no—
203C23—3612no—
204C23—3616no—
205C23C23×D912yes—
206C23C23×D916yes—
207C23C23×D911yescharacteristic
208Q8—3612no—
209D4—412no—
210D4—3624no—
211C2×C4—26no—
212C2×C4—912no—
213C2×C4—1812no—
214C2×C4C23×D916yes—
215C2×C3—42no—
216C2×C3—46no—
217C2×C3#559414yes—
218C2×C3C2×#100413yes—
219D3—124no—
220C22—26no—
221C22—26no—
222C22—212no—
223C22—416no—
224C22—412no—
225C22—44no—
226C22—1812no—
227C22—3616no—
228C22—368no—
229C22#6371016yes—
230C22C24×D911yescharacteristic
231C4—26no—
232C4—1812no—
233C3C2×#559411yescharacteristic
234C2—46no—
235C2—42no—
236C2—364no—
237C2#1058969614yesdirect product factor
238C2C2×#6371013yes—
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C9×#120C2
socleC23×C3C23×D3
hypercenterC2×#120D9
hypocenterC9C2×H(3,𝔽4)
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×C9×#120C2semidirect
2. C2×#63515C2semidirect
3. C2×#63499C2semidirect
4. C2×#63498C2semidirect
5. #10589696C2direct (N × H)
6. C2×#63447C2semidirect
8. C25×C9C22semidirect
9. C24×D9C22semidirect
12. C22×Dic18C22semidirect
13. C9×#120C22semidirect
14. C2×C9×C22⋊C4C22semidirect
15. #63515C22semidirect
16. C2×#3676C22semidirect
17. C2×#3676C22semidirect
18. #63499C22semidirect
19. #63498C22semidirect
20. C2×(C2×D9)⋊C4C22semidirect
21. C2×C4×Dic9C22semidirect
22. #63447C22semidirect
32. C24×C9C23semidirect
35. C23×D9C23semidirect
43. C2×Dic18C23semidirect
44. C9×C22⋊C4C23semidirect
45. #3676C23semidirect
46. #3676C23semidirect
47. (C2×D9)⋊C4C23semidirect
48. C4×Dic9C23semidirect
89. C2×#120D9semidirect
124. C25C2×D9semidirect
132. #120C2×D9semidirect
136. C2×C22⋊C4C2×D9semidirect
159. C2×C9H(3,𝔽4)semidirect
168. C24C22×D9semidirect
180. C22⋊C4C22×D9semidirect
195. C9C2×H(3,𝔽4)semidirect
237. C2#10589696direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C9×#1202
C2×#635152
C2×#634992
C2×#634982
#105896962
C2×#634472
C2×#55943