Finite Group Databasebeta

← C2×#10596065 #11910208

Subgroups — C2×#10596065 #11910208

Order 1152.

4224 conjugacy classes of subgroups; only the 793 normal subgroups are shown.

normal subgroups only

This group has 4224 conjugacy classes of subgroups — too many to draw. Only its 793 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×C32×#120C211yesmaximal, characteristic, complemented
2C2×#64162C212yesmaximal, complemented
3C2×#64146C213yesmaximal, complemented
4C2×#64145C213yesmaximal, complemented
5#10596065C2116yesmaximal, direct product factor
6C2×#64094C216yesmaximal, complemented
7C2×#5594—34nomaximal
8C25×C32C2211yescharacteristic, complemented
9C24×C3⋊D3C2211yescharacteristic, complemented
10C22×C32×D4C2213yes—
11C22×#638C2216yes—
12C22×#634C2213yescomplemented
13C32×#120C2218yescomplemented
14C2×C32×C22⋊C4C2213yescomplemented
15#64162C22116yescomplemented
16C2×#3757C2216yescomplemented
17C2×#3757C2213yescomplemented
18#64146C22124yescomplemented
19#64145C22124yescomplemented
20C2×#3752C2216yescomplemented
21C2×C4×C3⋊Dic3C2213yescomplemented
22#64094C22148yescomplemented
23C2×C3×#120D314yescomplemented
24C2×#953—38no—
25C2×#937—312no—
26C2×#936—312no—
27#5594—364no—
28C2×#885—324no—
29C24×C32—46no—
30C24×C32C2313yes—
31C24×C32C2311yescharacteristic
32C24×C32C2314yescomplemented
33C23×C3⋊D3—46no—
34C23×C3⋊D3C2312yes—
35C23×C3⋊D3C2314yescomplemented
36C2×C32×D4—46no—
37C2×C32×D4C23112yes—
38C22×C32×C4C2313yes—
39C2×#638—412no—
40C2×#638C23124yes—
41C22×C3⋊Dic3C2316yes—
42C2×#634—46no—
43C2×#634C23112yescomplemented
44C32×C22⋊C4C23112yescomplemented
45#3757C23124yescomplemented
46#3757C23112yescomplemented
47#3752C23124yescomplemented
48C4×C3⋊Dic3C23112yescomplemented
49C2×H(3,𝔽4)—91noSylow
50C25×C3C2×D314yescomplemented
51C24×D3—34no—
52C22×C3×D4C2×D3112yes—
53C22×#67—324no—
54C22×Dic6—312no—
55C3×#120C2×D3132yescomplemented
56C2×C3×C22⋊C4C2×D3112yescomplemented
57#953—364no—
58C2×#217—324no—
59C2×#217—312no—
60#937—396no—
61#936—396no—
62C2×(C2×D3)⋊C4—324no—
63C2×C4×Dic3—312no—
64#885—3192no—
65C23×C32—26no—
66C23×C32—212no—
67C23×C32—26no—
68C23×C32—412no—
69C23×C32—416no—
70C23×C32C2412yes—
71C23×C32C2416yes—
72C23×C32C2411yescharacteristic
73C22×C3⋊D3—212no—
74C22×C3⋊D3—412no—
75C22×C3⋊D3—416no—
76C22×C3⋊D3C2414yes—
77C32×D4—412no—
78C2×C32×C4—26no—
79C2×C32×C4C2416yes—
80#638—424no—
81C2×C3⋊Dic3—212no—
82C2×C3⋊Dic3C24112yes—
83#634—412no—
84H(3,𝔽4)—916no—
85C2×#124—93no—
86C2×#124—96no—
87C2×#120—92no—
88C2×#120—93no—
89C2×#120C3⋊D311yescharacteristic, complemented
90C24×C3—424no—
91C24×C3C22×D3112yes—
92C24×C3C22×D314yes—
93C24×C3C22×D3116yescomplemented
94C23×D3—38no—
95C23×D3—316no—
96C23×D3—1224no—
97C2×C3×D4—424no—
98C2×C3×D4C22×D3148yes—
99C22×C3×C4C22×D3112yes—
100C2×#67—396no—
101C2×#67—1248no—
102C22×Dic3—324no—
103C2×Dic6—348no—
104C2×Dic6—1224no—
105C3×C22⋊C4C22×D3148yescomplemented
106#217—396no—
107#217—348no—
108(C2×D3)⋊C4—396no—
109C4×Dic3—348no—
110C22×C32—212no—
111C22×C32—26no—
112C22×C32—26no—
113C22×C32—416no—
114C22×C32—44no—
115C22×C32—412no—
116C22×C32H(5,𝔽2)16yes—
117C22×C32C2511yescharacteristic
118C2×C3⋊D3—212no—
119C2×C3⋊D3—416no—
120C2×C3⋊D3—48no—
121C32×C4—26no—
122C3⋊Dic3—212no—
123C25—91no—
124C25C2×C3⋊D311yescharacteristic, complemented
125C22×Q8—93no—
126C22×D4—96no—
127C22×D4C2×C3⋊D313yes—
128#124—924no—
129#124—948no—
130#120—916no—
131#120—924no—
132#120C2×C3⋊D318yescomplemented
133C2×C22⋊C4—93no—
134C2×C22⋊C4—96no—
135C2×C22⋊C4—96no—
136C2×C22⋊C4C2×C3⋊D313yescomplemented
137C2×C42—93no—
138C23×C3—248no—
139C23×C3—224no—
140C23×C3—224no—
141C23×C3—448no—
142C23×C3—464no—
143C23×C3C23×D318yes—
144C23×C3C23×D3124yes—
145C23×C3C23×D314yes—
146C22×D3—316no—
147C22×D3—648no—
148C22×D3—1248no—
149C22×D3—1264no—
150C3×D4—448no—
151C2×C3×C4—224no—
152C2×C3×C4C23×D3124yes—
153#67—1296no—
154C2×Dic3—348no—
155C2×Dic3—648no—
156Dic6—1248no—
157C2×C32—42no—
158C2×C32—46no—
159C2×C32H(3,𝔽4)14yescomplemented
160C2×C32C2×H(5,𝔽2)13yes—
161C3⋊D3—44no—
162C24—46no—
163C24—92no—
164C24—94no—
165C24—366no—
166C24C22×C3⋊D311yescharacteristic
167C24C22×C3⋊D313yes—
168C24C22×C3⋊D314yescomplemented
169C2×Q8—912no—
170C2×Q8—366no—
171C2×D4—46no—
172C2×D4—924no—
173C2×D4—3612no—
174C2×D4C22×C3⋊D3112yes—
175C22×C4—96no—
176C22×C4C22×C3⋊D313yes—
177C22⋊C4—912no—
178C22⋊C4—924no—
179C22⋊C4—924no—
180C22⋊C4C22×C3⋊D3112yescomplemented
181C42—912no—
182C22×C3—248no—
183C22×C3—224no—
184C22×C3—224no—
185C22×C3—464no—
186C22×C3—416no—
187C22×C3—448no—
188C22×C3#1004124yes—
189C22×C3C24×D314yes—
190C2×D3—648no—
191C2×D3—1264no—
192C2×D3—1232no—
193C3×C4—224no—
194Dic3—648no—
195C32C2×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×C3⋊D312yes—
206C23C23×C3⋊D316yes—
207C23C23×C3⋊D311yescharacteristic
208Q8—3612no—
209D4—412no—
210D4—3624no—
211C2×C4—26no—
212C2×C4—912no—
213C2×C4—1812no—
214C2×C4C23×C3⋊D316yes—
215C2×C3—48no—
216C2×C3—424no—
217C2×C3#5594116yescomplemented
218C2×C3C2×#1004112yes—
219D3—1216no—
220C22—26no—
221C22—26no—
222C22—212no—
223C22—416no—
224C22—412no—
225C22—44no—
226C22—1812no—
227C22—3616no—
228C22—368no—
229C22#6436116yes—
230C22C24×C3⋊D311yescharacteristic
231C4—26no—
232C4—1812no—
233C3C2×#559414yescomplemented
234C2—46no—
235C2—42no—
236C2—364no—
237C2#1059606514yesdirect product factor
238C2C2×#6436113yes—
subgroupG/H
centerC23C23×C3⋊D3
commutator, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC2×C32×#120C2
socleC23×C32C24
hypercenterC2×#120C3⋊D3
hypocenterC32C2×H(3,𝔽4)
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×C32×#120C2semidirect
2. C2×#64162C2semidirect
3. C2×#64146C2semidirect
4. C2×#64145C2semidirect
5. #10596065C2direct (N × H)
6. C2×#64094C2semidirect
8. C25×C32C22semidirect
9. C24×C3⋊D3C22semidirect
12. C22×#634C22semidirect
13. C32×#120C22semidirect
14. C2×C32×C22⋊C4C22semidirect
15. #64162C22semidirect
16. C2×#3757C22semidirect
17. C2×#3757C22semidirect
18. #64146C22semidirect
19. #64145C22semidirect
20. C2×#3752C22semidirect
21. C2×C4×C3⋊Dic3C22semidirect
22. #64094C22semidirect
23. C2×C3×#120D3semidirect
32. C24×C32C23semidirect
35. C23×C3⋊D3C23semidirect
43. C2×#634C23semidirect
44. C32×C22⋊C4C23semidirect
45. #3757C23semidirect
46. #3757C23semidirect
47. #3752C23semidirect
48. C4×C3⋊Dic3C23semidirect
50. C25×C3C2×D3semidirect
55. C3×#120C2×D3semidirect
56. C2×C3×C22⋊C4C2×D3semidirect
89. C2×#120C3⋊D3semidirect
93. C24×C3C22×D3semidirect
105. C3×C22⋊C4C22×D3semidirect
124. C25C2×C3⋊D3semidirect
132. #120C2×C3⋊D3semidirect
136. C2×C22⋊C4C2×C3⋊D3semidirect
159. C2×C32H(3,𝔽4)semidirect
168. C24C22×C3⋊D3semidirect
180. C22⋊C4C22×C3⋊D3semidirect
195. C32C2×H(3,𝔽4)semidirect
217. C2×C3#5594semidirect
233. C3C2×#5594semidirect
237. C2#10596065direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1202
C2×#641622
C2×#641462
C2×#641452
#105960652
C2×#640942
C2×#55943