Finite Group Databasebeta

← C2×#10592411 #11874338

Subgroups — C2×#10592411 #11874338

Order 1152.

2004 conjugacy classes of subgroups; only the 441 normal subgroups are shown.

normal subgroups only

This group has 2004 conjugacy classes of subgroups — too many to draw. Only its 441 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
1C22×#3745C212yesmaximal, complemented
2C22×#3744C212yesmaximal, complemented
3C2×#64084C211yesmaximal, characteristic, complemented
4C2×#64083C211yesmaximal, characteristic, complemented
5C2×C32×#97C211yesmaximal, characteristic, complemented
6#10592411C218yesmaximal, direct product factor
7C2×#4712—34nomaximal
8C22×C4⋊(C3⋊D3)—22no—
9C22×C4⋊(C3⋊D3)C2212yes—
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C22×C32×C8C2212yes—
13C2×C32×C42C2211yescharacteristic
14C2×#3752—22no—
15C2×#3745—28no—
16C2×#3745C2218yescomplemented
17C2×#3744—28no—
18C2×#3744C2218yescomplemented
19#64084—22no—
20#64084C2214yescomplemented
21#64083—22no—
22#64083C2214yescomplemented
23C32×#97C2214yescomplemented
24C22×D24—38no—
25C22×#204—38no—
26C2×#875—34no—
27C2×#874—34no—
28C2×C3×#97D314yescomplemented
29#4712—332no—
30C23×C3⋊D3—22no—
31C23×C3⋊D3—21no—
32C22×C32×C4D412yes—
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3—21no—
35C2×C4⋊(C3⋊D3)—24no—
36C2×C4⋊(C3⋊D3)—24no—
37C2×C4⋊(C3⋊D3)—24no—
38C2×C4⋊(C3⋊D3)—22no—
39C2×C4⋊(C3⋊D3)—28no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—48no—
42C2×C4⋊(C3⋊D3)C2314yes—
43C2×C4⋊(C3⋊D3)C2312yes—
44C2×#634—24no—
45C2×#634—21no—
46C2×#634C2312yes—
47C2×C32×C8D418yescomplemented
48C2×C32×C8C2314yes—
49C32×C42D412yes—
50C32×C42C2312yes—
51#3752—28no—
52#3745—216no—
53#3744—216no—
54C2×#496—91noSylow
55C22×D12—38no—
56C22×D12—34no—
57C22×D12—68no—
58C22×Dic6—34no—
59C22×C3×C8C2×D318yes—
60C2×C3×C42C2×D314yes—
61C2×(C2×D3)⋊C4—68no—
62C2×D24—332no—
63C2×D24—632no—
64C2×#204—332no—
65C2×#204—632no—
66#875—316no—
67#875—68no—
68#874—316no—
69#874—68no—
70C3×#97C2×D3116yescomplemented
71C23×C32C2×D411yescharacteristic
72C22×C3⋊D3—22no—
73C22×C3⋊D3—24no—
74C22×C3⋊D3—44no—
75C22×C3⋊D3—42no—
76C22×C3⋊D3—44no—
77C22×C3⋊D3—48no—
78C2×C32×C4—24no—
79C2×C32×C4C2×D414yes—
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4C2×D414yes—
82C2×C32×C4C2411yescharacteristic
83C2×C3⋊Dic3—22no—
84C2×C3⋊Dic3—42no—
85C4⋊(C3⋊D3)—24no—
86C4⋊(C3⋊D3)—24no—
87C4⋊(C3⋊D3)—24no—
88C4⋊(C3⋊D3)—416no—
89C4⋊(C3⋊D3)—44no—
90C4⋊(C3⋊D3)—42no—
91#634—24no—
92#634—42no—
93C32×C8C2×D418yescomplemented
94C22×SD16—92no—
95C22×D8—92no—
96C2×#127—91no—
97C2×#124—91no—
98#496—98no—
99C2×#97C3⋊D311yescharacteristic, complemented
100C23×D3—64no—
101C23×D3—68no—
102C22×C3×C4D1218yes—
103C22×C3×C4C22×D314yes—
104C22×Dic3—64no—
105C2×D12—316no—
106C2×D12—38no—
107C2×D12—616no—
108C2×D12—616no—
109C2×D12—616no—
110C2×D12—632no—
111C2×D12—68no—
112C2×D12—64no—
113C2×D12—1232no—
114C2×Dic6—38no—
115C2×Dic6—616no—
116C2×Dic6—64no—
117C2×C3×C8D12132yescomplemented
118C2×C3×C8C22×D3116yes—
119C3×C42D1218yes—
120C3×C42C22×D318yes—
121(C2×D3)⋊C4—632no—
122D24—664no—
123#204—664no—
124C22×C32#12712yes—
125C22×C32AGL(1,ℤ/8)14yes—
126C22×C32C22×D411yescharacteristic
127C2×C3⋊D3—44no—
128C2×C3⋊D3—42no—
129C2×C3⋊D3—48no—
130C2×C3⋊D3—44no—
131C2×C3⋊D3—84no—
132C2×C3⋊D3—88no—
133C32×C4—24no—
134C32×C4#12712yes—
135C32×C4C22×D412yes—
136C3⋊Dic3—42no—
137C22×Q8—91no—
138C22×D4—91no—
139C22×D4—92no—
140C22×D4—182no—
141C2×SD16—98no—
142C2×SD16—188no—
143C2×D8—98no—
144C2×D8—188no—
145C22×C8C2×C3⋊D312yes—
146#127—94no—
147#127—182no—
148#124—94no—
149#124—182no—
150C2×C22⋊C4—182no—
151C2×C42C2×C3⋊D311yescharacteristic
152#97C2×C3⋊D314yescomplemented
153C23×C3C2×D1214yes—
154C22×D3—68no—
155C22×D3—616no—
156C22×D3—1216no—
157C22×D3—128no—
158C22×D3—1232no—
159C22×D3—1216no—
160C2×C3×C4—216no—
161C2×C3×C4C2×D12116yes—
162C2×C3×C4C2×D1214yes—
163C2×C3×C4C2×D12116yes—
164C2×C3×C4C23×D314yes—
165C2×Dic3—68no—
166C2×Dic3—128no—
167D12—616no—
168D12—616no—
169D12—616no—
170D12—1264no—
171D12—1216no—
172D12—128no—
173Dic6—616no—
174Dic6—128no—
175C3×C8C2×D12132yescomplemented
176C2×C32#49614yescomplemented
177C2×C32C2×#12711yescharacteristic
178C2×C32C2×AGL(1,ℤ/8)12yes—
179C3⋊D3—84no—
180C3⋊D3—82no—
181C24—181no—
182C24—182no—
183C2×Q8—92no—
184C2×Q8—181no—
185C2×Q8—184no—
186C2×D4—92no—
187C2×D4—94no—
188C2×D4—184no—
189C2×D4—184no—
190C2×D4—184no—
191C2×D4—181no—
192C2×D4—188no—
193C2×D4—182no—
194C2×D4—368no—
195C22×C4—181no—
196C22×C4C4⋊(C3⋊D3)12yes—
197C22×C4C22×C3⋊D311yescharacteristic
198SD16—1816no—
199D8—1816no—
200C2×C8C4⋊(C3⋊D3)18yescomplemented
201C2×C8C22×C3⋊D314yes—
202C22⋊C4—188no—
203C42C4⋊(C3⋊D3)12yes—
204C42C22×C3⋊D312yes—
205C22×C3#87418yes—
206C22×C3#908116yes—
207C22×C3C22×D1214yes—
208C2×D3—1216no—
209C2×D3—128no—
210C2×D3—1232no—
211C2×D3—1216no—
212C2×D3—2432no—
213C2×D3—2416no—
214C3×C4—216no—
215C3×C4#87418yes—
216C3×C4C22×D1218yes—
217Dic3—128no—
218C32C2×#49611yescharacteristic, complemented, Sylow
219C23—182no—
220C23—184no—
221C23—362no—
222C23—364no—
223C23—368no—
224C23—364no—
225C23C2×C4⋊(C3⋊D3)11yescharacteristic
226Q8—184no—
227Q8—362no—
228D4—184no—
229D4—184no—
230D4—184no—
231D4—3616no—
232D4—362no—
233D4—364no—
234C2×C4—24no—
235C2×C4—182no—
236C2×C4—362no—
237C2×C4C2×C4⋊(C3⋊D3)14yes—
238C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
239C2×C4C2×C4⋊(C3⋊D3)14yes—
240C2×C4C23×C3⋊D311yescharacteristic
241C8C2×C4⋊(C3⋊D3)18yescomplemented
242C2×C3#4712116yescomplemented
243C2×C3C2×#87414yes—
244C2×C3C2×#90818yes—
245D3—2416no—
246D3—248no—
247C22—362no—
248C22—364no—
249C22—368no—
250C22—364no—
251C22—728no—
252C22—724no—
253C22#6408312yes—
254C22#6411714yes—
255C22C22×C4⋊(C3⋊D3)11yescharacteristic
256C4—24no—
257C4—362no—
258C4#6408312yes—
259C4C22×C4⋊(C3⋊D3)12yes—
260C3C2×#471214yescomplemented
261C2—724no—
262C2—722no—
263C2#1059241114yesdirect product factor
264C2C2×#6408311yescharacteristic
265C2C2×#6411712yes—
subgroupG/H
centerC23C2×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#97C2
socleC23×C32C2×D4
hypercenterC2×#97C3⋊D3
hypocenterC32C2×#496
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
1. C22×#3745C2semidirect
2. C22×#3744C2semidirect
3. C2×#64084C2semidirect
4. C2×#64083C2semidirect
5. C2×C32×#97C2semidirect
6. #10592411C2direct (N × H)
16. C2×#3745C22semidirect
18. C2×#3744C22semidirect
20. #64084C22semidirect
22. #64083C22semidirect
23. C32×#97C22semidirect
28. C2×C3×#97D3semidirect
47. C2×C32×C8D4semidirect
70. C3×#97C2×D3semidirect
93. C32×C8C2×D4semidirect
99. C2×#97C3⋊D3semidirect
117. C2×C3×C8D12semidirect
152. #97C2×C3⋊D3semidirect
175. C3×C8C2×D12semidirect
176. C2×C32#496semidirect
200. C2×C8C4⋊(C3⋊D3)semidirect
218. C32C2×#496semidirect
241. C8C2×C4⋊(C3⋊D3)semidirect
242. C2×C3#4712semidirect
260. C3C2×#4712semidirect
263. C2#10592411direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37452
C22×#37442
C2×#640842
C2×#640832
C2×C32×#972
#105924112
C2×#47123