Finite Group Databasebeta

← C2×#10592892 #11899539

Subgroups — C2×#10592892 #11899539

Order 1152.

1200 conjugacy classes of subgroups; only the 297 normal subgroups are shown.

normal subgroups only

This group has 1200 conjugacy classes of subgroups — too many to draw. Only its 297 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×#135C211yesmaximal, characteristic, complemented
2C22×#3745C211yesmaximal, characteristic, complemented
3#10592892C218yesmaximal, direct product factor
4C2×#63655C212yesmaximal, complemented
5C2×#63653C212yesmaximal, complemented
6C2×#63639C211yesmaximal, characteristic, complemented
7C2×#5193—34nomaximal
8C2×C32×#41—21no—
9C22×C4⋊(C3⋊D3)—21no—
10C32×#135—22no—
11C32×#135C2214yescomplemented
12C2×C32×Q16C2211yescharacteristic, complemented
13C2×C32×SD16—21no—
14C2×C32×D8C2211yescharacteristic, complemented
15C22×C32×C8C2211yescharacteristic
16C2×#3745—22no—
17C2×#3745—21no—
18C2×#3745C2212yes—
19C2×#3745C2214yescomplemented
20#63655C2218yescomplemented
21#63653C2218yescomplemented
22#63639C2214yescomplemented
23C2×C3⋊(C3⋊C16)C2212yescomplemented
24C2×C3×#135D314yescomplemented
25C22×D24—34no—
26#5193—332no—
27C2×#828—38no—
28C2×#826—38no—
29C2×#812—34no—
30C23×C3⋊D3—41no—
31C32×#41—24no—
32C32×#41—42no—
33C2×C32×Q8—21no—
34C2×C32×D4—21no—
35C2×C32×D4—41no—
36C22×C32×C4—41no—
37C22×C32×C4D411yescharacteristic
38C2×C4⋊(C3⋊D3)—22no—
39C2×C4⋊(C3⋊D3)—24no—
40C2×C4⋊(C3⋊D3)—41no—
41C2×C4⋊(C3⋊D3)—42no—
42C32×Q16—21no—
43C32×Q16C2312yescomplemented
44C32×SD16—24no—
45C32×D8—21no—
46C32×D8C2312yescomplemented
47C2×C32×C8D411yescharacteristic
48C2×C32×C8D412yes—
49C2×C32×C8C2311yescharacteristic
50C2×C32×C8C2312yes—
51#3745—22no—
52#3745—24no—
53#3745C2314yes—
54C3⋊(C3⋊C16)C2314yescomplemented
55C2×#509—91noSylow
56C2×C3×#41—24no—
57C22×D12—64no—
58C3×#135—28no—
59C3×#135C2×D3116yescomplemented
60C2×C3×Q16C2×D314yescomplemented
61C2×C3×SD16—24no—
62C2×C3×D8C2×D314yescomplemented
63C22×C3×C8C2×D314yes—
64C2×D24—38no—
65C2×D24—316no—
66C2×D24—64no—
67C2×D24—68no—
68#828—332no—
69#826—332no—
70#812—316no—
71C2×C3⋊C16—38no—
72C23×C32—41no—
73C23×C32D811yescharacteristic
74C22×C3⋊D3—44no—
75C22×C3⋊D3—42no—
76C22×C3⋊D3—84no—
77C32×Q8—22no—
78C32×Q8—41no—
79C32×D4—22no—
80C32×D4—44no—
81C32×D4—41no—
82C2×C32×C4—41no—
83C2×C32×C4—44no—
84C2×C32×C4D811yescharacteristic
85C2×C32×C4D812yes—
86C2×C32×C4C2×D411yescharacteristic
87C2×C32×C4C2×D412yes—
88C4⋊(C3⋊D3)—24no—
89C4⋊(C3⋊D3)—44no—
90C4⋊(C3⋊D3)—42no—
91C32×C8C2×D411yescharacteristic
92C32×C8C2×D412yes—
93C32×C8C2411yescharacteristic
94C2×#135C3⋊D311yescharacteristic, complemented
95C22×D8—91no—
96#509—98no—
97C2×SD32—92no—
98C2×D16—92no—
99C2×M32—91no—
100C23×D3—124no—
101C3×#41—216no—
102C3×#41—48no—
103C2×C3×Q8—24no—
104C2×C3×D4—24no—
105C2×C3×D4—44no—
106C22×C3×C4—44no—
107C22×C3×C4#6714yes—
108C2×D12—68no—
109C2×D12—616no—
110C2×D12—124no—
111C2×D12—128no—
112C3×Q16—24no—
113C3×Q16C22×D318yescomplemented
114C3×SD16—216no—
115C3×D8—24no—
116C3×D8C22×D318yescomplemented
117C2×C3×C8#6714yes—
118C2×C3×C8#6718yes—
119C2×C3×C8C22×D314yes—
120C2×C3×C8C22×D318yes—
121D24—316no—
122D24—68no—
123D24—616no—
124C3⋊C16—316no—
125C22×C32—22no—
126C22×C32—42no—
127C22×C32—82no—
128C22×C32C2×D812yes—
129C22×C32C2×D811yescharacteristic
130C2×C3⋊D3—44no—
131C2×C3⋊D3—88no—
132C2×C3⋊D3—84no—
133C32×C4—42no—
134C32×C4C2×D812yes—
135C32×C4C2×D811yescharacteristic
136C32×C4C22×D411yescharacteristic
137C2×#41—21no—
138C22×D4—181no—
139#135—22no—
140#135C2×C3⋊D314yescomplemented
141C2×Q16C2×C3⋊D311yescharacteristic, complemented
142C2×SD16—21no—
143C2×D8—92no—
144C2×D8—94no—
145C2×D8—181no—
146C2×D8—182no—
147C2×D8C2×C3⋊D311yescharacteristic, complemented
148C22×C8C2×C3⋊D311yescharacteristic
149SD32—98no—
150D16—98no—
151M32—94no—
152C2×C16—92no—
153C23×C3—44no—
154C23×C3#21314yes—
155C22×D3—1216no—
156C22×D3—128no—
157C22×D3—2416no—
158C3×Q8—28no—
159C3×Q8—44no—
160C3×D4—28no—
161C3×D4—416no—
162C3×D4—44no—
163C2×C3×C4—44no—
164C2×C3×C4—416no—
165C2×C3×C4#21314yes—
166C2×C3×C4#21318yes—
167C2×C3×C4C2×#6714yes—
168C2×C3×C4C2×#6718yes—
169D12—616no—
170D12—1216no—
171D12—128no—
172C3×C8C2×#6714yes—
173C3×C8C2×#6718yes—
174C3×C8C23×D314yes—
175C2×C32—22no—
176C2×C32—82no—
177C2×C32#50912yescomplemented
178C2×C32C22×D811yescharacteristic
179C3⋊D3—84no—
180C24—361no—
181#41—24no—
182#41—42no—
183C2×Q8—21no—
184C2×D4—21no—
185C2×D4—41no—
186C2×D4—184no—
187C2×D4—182no—
188C2×D4—362no—
189C2×D4—361no—
190C22×C4—41no—
191C22×C4#63811yescharacteristic
192Q16—21no—
193Q16C22×C3⋊D312yescomplemented
194SD16—24no—
195D8—21no—
196D8—94no—
197D8—182no—
198D8—184no—
199D8C22×C3⋊D312yescomplemented
200C2×C8#63811yescharacteristic
201C2×C8#63812yes—
202C2×C8C22×C3⋊D311yescharacteristic
203C2×C8C22×C3⋊D312yes—
204C16—94no—
205C22×C3—28no—
206C22×C3—48no—
207C22×C3—88no—
208C22×C3C2×#21318yes—
209C22×C3C2×#21314yes—
210C2×D3—1216no—
211C2×D3—2432no—
212C2×D3—2416no—
213C3×C4—48no—
214C3×C4C2×#21318yes—
215C3×C4C2×#21314yes—
216C3×C4C22×#6714yes—
217C32C2×#50911yescharacteristic, complemented, Sylow
218C23—41no—
219C23—364no—
220C23—362no—
221C23—724no—
222C23#375311yescharacteristic
223Q8—22no—
224Q8—41no—
225D4—22no—
226D4—44no—
227D4—41no—
228D4—184no—
229D4—364no—
230D4—362no—
231C2×C4—41no—
232C2×C4—44no—
233C2×C4#375312yes—
234C2×C4#375311yescharacteristic
235C2×C4C2×#63812yes—
236C2×C4C2×#63811yescharacteristic
237C8C2×#63811yescharacteristic
238C8C2×#63812yes—
239C8C23×C3⋊D311yescharacteristic
240C2×C3—28no—
241C2×C3—88no—
242C2×C3#519318yescomplemented
243C2×C3C22×#21314yes—
244D3—2416no—
245C22—22no—
246C22—42no—
247C22—82no—
248C22—364no—
249C22—728no—
250C22—724no—
251C22C2×#375312yes—
252C22C2×#375311yescharacteristic
253C4—42no—
254C4C2×#375312yes—
255C4C2×#375311yescharacteristic
256C4C22×#63811yescharacteristic
257C3C2×#519314yescomplemented
258C2—22no—
259C2—82no—
260C2—724no—
261C2#1059289212yesdirect product factor
262C2C22×#375311yescharacteristic
subgroupG/H
centerC22C2×#3753
commutator, cosocleC32×C8C24
FrattiniC8C23×C3⋊D3
FittingC2×C32×#135C2
socleC22×C32C2×D8
hypercenterC2×#135C3⋊D3
hypocenterC32C2×#509
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×C32×#135C2semidirect
2. C22×#3745C2semidirect
3. #10592892C2direct (N × H)
4. C2×#63655C2semidirect
5. C2×#63653C2semidirect
6. C2×#63639C2semidirect
11. C32×#135C22semidirect
12. C2×C32×Q16C22semidirect
14. C2×C32×D8C22semidirect
19. C2×#3745C22semidirect
20. #63655C22semidirect
21. #63653C22semidirect
22. #63639C22semidirect
23. C2×C3⋊(C3⋊C16)C22semidirect
24. C2×C3×#135D3semidirect
43. C32×Q16C23semidirect
46. C32×D8C23semidirect
54. C3⋊(C3⋊C16)C23semidirect
59. C3×#135C2×D3semidirect
60. C2×C3×Q16C2×D3semidirect
62. C2×C3×D8C2×D3semidirect
94. C2×#135C3⋊D3semidirect
113. C3×Q16C22×D3semidirect
116. C3×D8C22×D3semidirect
140. #135C2×C3⋊D3semidirect
141. C2×Q16C2×C3⋊D3semidirect
147. C2×D8C2×C3⋊D3semidirect
177. C2×C32#509semidirect
193. Q16C22×C3⋊D3semidirect
199. D8C22×C3⋊D3semidirect
217. C32C2×#509semidirect
242. C2×C3#5193semidirect
257. C3C2×#5193semidirect
261. C2#10592892direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1352
C22×#37452
#105928922
C2×#636552
C2×#636532
C2×#636392
C2×#51933