Finite Group Databasebeta

← C2×#10596191 #11910154

Subgroups — C2×#10596191 #11910154

Order 1152.

4032 conjugacy classes of subgroups; only the 793 normal subgroups are shown.

normal subgroups only

This group has 4032 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×#127C211yesmaximal, characteristic, complemented
2C2×#64148C216yesmaximal, complemented
3C2×#64146C213yesmaximal, complemented
4C2×#64144C213yesmaximal, complemented
5#10596191C2116yesmaximal, direct product factor
6C2×#64085C212yesmaximal, complemented
7C2×#5720—34nomaximal
8C24×C3⋊D3C2211yescharacteristic
9C22×C32×D4C2213yes—
10C22×C32×D4C2213yescomplemented
11C22×#638C2216yes—
12C23×C3⋊Dic3C2213yescomplemented
13C32×#127C2218yescomplemented
14C2×C32×C42C2211yescharacteristic, complemented
15C2×#3757C2213yes—
16C2×#3757C2213yescomplemented
17#64148C22148yescomplemented
18#64146C22124yescomplemented
19#64144C22124yescomplemented
20C2×#3752C2216yes—
21C2×#3750C2216yescomplemented
22#64085C22116yescomplemented
23C2×C3×#127D314yescomplemented
24C2×#939—324no—
25C2×#937—312no—
26C2×#935—312no—
27#5720—364no—
28C2×#876—38no—
29C24×C32C2313yes—
30C24×C32C2311yescharacteristic
31C23×C3⋊D3—46no—
32C23×C3⋊D3C2312yes—
33C23×C3⋊D3C2314yes—
34C2×C32×D4—46no—
35C2×C32×D4—46no—
36C2×C32×D4C23112yes—
37C2×C32×D4C23112yescomplemented
38C22×C32×C4C2313yes—
39C2×#638—412no—
40C2×#638C23124yes—
41C22×C3⋊Dic3—46no—
42C22×C3⋊Dic3C2316yes—
43C22×C3⋊Dic3C23112yescomplemented
44C32×C42C2314yescomplemented
45#3757C23112yes—
46#3757C23112yescomplemented
47#3752C23124yes—
48#3750C23124yescomplemented
49C2×#560—91noSylow
50C24×D3—34no—
51C22×C3×D4C2×D3112yes—
52C22×C3×D4C2×D3112yescomplemented
53C22×#67—324no—
54C23×Dic3—312no—
55C3×#127C2×D3132yescomplemented
56C2×C3×C42C2×D314yescomplemented
57C2×#217—312no—
58C2×#217—312no—
59#939—3192no—
60#937—396no—
61#935—396no—
62C2×(C2×D3)⋊C4—324no—
63C2×Dic3⋊C4—324no—
64#876—364no—
65C23×C32—26no—
66C23×C32—26no—
67C23×C32—212no—
68C23×C32C2412yes—
69C23×C32C2416yes—
70C23×C32C2411yescharacteristic
71C22×C3⋊D3—212no—
72C22×C3⋊D3—412no—
73C22×C3⋊D3—416no—
74C22×C3⋊D3C2414yes—
75C32×D4—412no—
76C32×D4—412no—
77C2×C32×C4—26no—
78C2×C32×C4C2416yes—
79#638—424no—
80C2×C3⋊Dic3—212no—
81C2×C3⋊Dic3—412no—
82C2×C3⋊Dic3C24112yes—
83#560—916no—
84C2×#127C3⋊D311yescharacteristic, complemented
85C2×#126—92no—
86C2×#123—93no—
87C2×#121—96no—
88C2×#120—93no—
89C24×C3C22×D314yes—
90C24×C3C22×D3112yes—
91C23×D3—38no—
92C23×D3—316no—
93C23×D3—1224no—
94C2×C3×D4—424no—
95C2×C3×D4—424no—
96C2×C3×D4C22×D3148yes—
97C2×C3×D4C22×D3148yescomplemented
98C22×C3×C4C22×D3112yes—
99C2×#67—396no—
100C2×#67—1248no—
101C22×Dic3—324no—
102C22×Dic3—348no—
103C22×Dic3—1224no—
104C3×C42C22×D3116yescomplemented
105#217—348no—
106#217—348no—
107(C2×D3)⋊C4—396no—
108Dic3⋊C4—396no—
109C22×C32—26no—
110C22×C32—212no—
111C22×C32—26no—
112C22×C32—44no—
113C22×C32—412no—
114C22×C32H(5,𝔽2)16yes—
115C22×C32C2511yescharacteristic
116C2×C3⋊D3—212no—
117C2×C3⋊D3—416no—
118C2×C3⋊D3—48no—
119C32×C4—26no—
120C3⋊Dic3—212no—
121C25—91no—
122C22×D4—96no—
123C22×D4C2×C3⋊D313yes—
124C22×D4C2×C3⋊D313yescomplemented
125C23×C4—93no—
126#127C2×C3⋊D318yescomplemented
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×C3⋊D311yescharacteristic, complemented
136C23×C3—224no—
137C23×C3—248no—
138C23×C3—224no—
139C23×C3C23×D318yes—
140C23×C3C23×D3124yes—
141C23×C3C23×D314yes—
142C22×D3—316no—
143C22×D3—648no—
144C22×D3—1248no—
145C22×D3—1264no—
146C3×D4—448no—
147C3×D4—448no—
148C2×C3×C4—224no—
149C2×C3×C4C23×D3124yes—
150#67—1296no—
151C2×Dic3—348no—
152C2×Dic3—648no—
153C2×Dic3—1248no—
154C2×C32—42no—
155C2×C32—46no—
156C2×C32#56014yescomplemented
157C2×C32C2×H(5,𝔽2)13yes—
158C3⋊D3—44no—
159C24—92no—
160C24—94no—
161C24—366no—
162C24C22×C3⋊D311yescharacteristic
163C24C22×C3⋊D313yes—
164C2×D4—46no—
165C2×D4—46no—
166C2×D4—924no—
167C2×D4—3612no—
168C2×D4C22×C3⋊D3112yes—
169C2×D4C22×C3⋊D3112yescomplemented
170C22×C4—96no—
171C22×C4—912no—
172C22×C4—366no—
173C22×C4C22×C3⋊D313yes—
174C4⋊C4—924no—
175C22⋊C4—912no—
176C22⋊C4—912no—
177C22⋊C4—924no—
178C42C22×C3⋊D314yescomplemented
179C22×C3—224no—
180C22×C3—248no—
181C22×C3—224no—
182C22×C3—416no—
183C22×C3—448no—
184C22×C3#1004124yes—
185C22×C3C24×D314yes—
186C2×D3—648no—
187C2×D3—1264no—
188C2×D3—1232no—
189C3×C4—224no—
190Dic3—648no—
191C32C2×#56011yescharacteristic, complemented, Sylow
192C23—26no—
193C23—212no—
194C23—26no—
195C23—94no—
196C23—1812no—
197C23—3612no—
198C23—3616no—
199C23C23×C3⋊D312yes—
200C23C23×C3⋊D316yes—
201C23C23×C3⋊D311yescharacteristic
202D4—412no—
203D4—412no—
204D4—3624no—
205C2×C4—26no—
206C2×C4—912no—
207C2×C4—1812no—
208C2×C4—3612no—
209C2×C4C23×C3⋊D316yes—
210C2×C3—48no—
211C2×C3—424no—
212C2×C3#5720116yescomplemented
213C2×C3C2×#1004112yes—
214D3—1216no—
215C22—26no—
216C22—212no—
217C22—26no—
218C22—44no—
219C22—412no—
220C22—1812no—
221C22—3616no—
222C22—368no—
223C22#6436116yes—
224C22C24×C3⋊D311yescharacteristic
225C4—26no—
226C4—1812no—
227C3C2×#572014yescomplemented
228C2—42no—
229C2—46no—
230C2—364no—
231C2#1059619114yesdirect product factor
232C2C2×#6436113yes—
subgroupG/H
centerC23C23×C3⋊D3
commutator, cosocleC22×C32C25
FrattiniC22C24×C3⋊D3
FittingC2×C32×#127C2
socleC23×C32C24
hypercenterC2×#127C3⋊D3
hypocenterC32C2×#560
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×C32×#127C2semidirect
2. C2×#64148C2semidirect
3. C2×#64146C2semidirect
4. C2×#64144C2semidirect
5. #10596191C2direct (N × H)
6. C2×#64085C2semidirect
10. C22×C32×D4C22semidirect
12. C23×C3⋊Dic3C22semidirect
13. C32×#127C22semidirect
14. C2×C32×C42C22semidirect
16. C2×#3757C22semidirect
17. #64148C22semidirect
18. #64146C22semidirect
19. #64144C22semidirect
21. C2×#3750C22semidirect
22. #64085C22semidirect
23. C2×C3×#127D3semidirect
37. C2×C32×D4C23semidirect
43. C22×C3⋊Dic3C23semidirect
44. C32×C42C23semidirect
46. #3757C23semidirect
48. #3750C23semidirect
52. C22×C3×D4C2×D3semidirect
55. C3×#127C2×D3semidirect
56. C2×C3×C42C2×D3semidirect
84. C2×#127C3⋊D3semidirect
97. C2×C3×D4C22×D3semidirect
104. C3×C42C22×D3semidirect
124. C22×D4C2×C3⋊D3semidirect
126. #127C2×C3⋊D3semidirect
135. C2×C42C2×C3⋊D3semidirect
156. C2×C32#560semidirect
169. C2×D4C22×C3⋊D3semidirect
178. C42C22×C3⋊D3semidirect
191. C32C2×#560semidirect
212. C2×C3#5720semidirect
227. C3C2×#5720semidirect
231. C2#10596191direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1272
C2×#641482
C2×#641462
C2×#641442
#105961912
C2×#640852
C2×#57203