Finite Group Databasebeta

← C2×#5832 #87261

Subgroups — C2×#5832 #87261

Order 384.

1728 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#41C211yesmaximal, characteristic, complemented
2C22×#235C211yesmaximal, characteristic, complemented
3#5832C2116yesmaximal, direct product factor
4C2×#947C211yesmaximal, characteristic, complemented
5C2×#944C211yesmaximal, characteristic, complemented
6C2×#940C211yesmaximal, characteristic, complemented
7C2×#939C214yesmaximal, complemented
8C2×#936C211yesmaximal, characteristic, complemented
9C2×C4×#67C214yesmaximal, complemented
10C22×C4×Dic3C211yesmaximal, characteristic, complemented
11C2×#532—31nomaximal, Sylow
12C2×C3×#41—28no—
13C2×C3×#41C2218yescomplemented
14C22×C3×Q8C2211yescharacteristic
15C22×C3×D4C2211yescharacteristic
16C22×C3×D4C2212yes—
17C23×C3×C4C2212yes—
18C23×C3×C4C2211yescharacteristic
19C22×#67C2212yes—
20C22×#67C2214yes—
21C23×Dic3C2212yes—
22C2×#235—28no—
23C2×#235C2218yescomplemented
24C22×D12C2211yescharacteristic
25C22×C4×D3C2212yes—
26C22×Dic6C2211yescharacteristic
27C2×#217C2214yes—
28#947C2218yescomplemented
29#944C2218yescomplemented
30#940C2218yescomplemented
31#939C22132yescomplemented
32#936C2218yescomplemented
33C4×#67C22132yescomplemented
34C2×(C2×D3)⋊C4C2214yes—
35C2×Dic3⋊C4C2214yes—
36C2×C4×Dic3C2212yes—
37C2×C4×Dic3C2211yescharacteristic
38C2×C4×Dic3C2211yescharacteristic
39C2×C4×Dic3C2218yescomplemented
40C22×#41—31no—
41C22×#41D311yescharacteristic, complemented
42#532—316no—
43C2×C4⋊Q8—31no—
44C2×#127—31no—
45C2×#124—31no—
46C2×#124—31no—
47C2×#121—34no—
48C2×C4×D4—34no—
49C22×C42—31no—
50C24×C3C2312yes—
51C24×C3C2311yescharacteristic
52C23×D3C2312yes—
53C3×#41—232no—
54C2×C3×Q8—24no—
55C2×C3×Q8C2314yes—
56C2×C3×D4—28no—
57C2×C3×D4—24no—
58C2×C3×D4C2314yes—
59C2×C3×D4C2318yes—
60C22×C3×C4—28no—
61C22×C3×C4D418yescomplemented
62C22×C3×C4C2312yes—
63C22×C3×C4C2318yes—
64C22×C3×C4C2311yescharacteristic
65C22×C3×C4C2314yes—
66C22×C3×C4C2311yescharacteristic
67C2×#67—28no—
68C2×#67—216no—
69C2×#67C23116yes—
70C2×#67C2318yes—
71C22×Dic3—28no—
72C22×Dic3C2312yes—
73C22×Dic3C2318yes—
74C22×Dic3C2312yes—
75C22×Dic3C2312yes—
76#235—232no—
77C2×D12—24no—
78C2×D12C2314yes—
79C2×C4×D3—28no—
80C2×C4×D3C2318yes—
81C2×Dic6—24no—
82C2×Dic6C2314yes—
83#217C23116yes—
84(C2×D3)⋊C4C23116yes—
85Dic3⋊C4C23116yes—
86C4×Dic3C2318yes—
87C4×Dic3C2314yes—
88C4×Dic3C2314yes—
89C2×#41—28no—
90C2×#41—38no—
91C2×#41—68no—
92C2×#41C2×D318yescomplemented
93C22×Q8—31no—
94C22×Q8C2×D311yescharacteristic
95C22×D4—34no—
96C22×D4—32no—
97C22×D4—31no—
98C22×D4C2×D312yes—
99C22×D4C2×D311yescharacteristic
100C23×C4—32no—
101C23×C4—32no—
102C23×C4C2×D312yes—
103C23×C4C2×D311yescharacteristic
104C4⋊Q8—38no—
105#127—38no—
106#124—38no—
107#124—38no—
108#121—332no—
109C4×D4—332no—
110C2×C4⋊C4—34no—
111C2×C22⋊C4—34no—
112C2×C22⋊C4—34no—
113C2×C42—31no—
114C2×C42—31no—
115C2×C42—38no—
116C2×C42—32no—
117C23×C3—24no—
118C23×C3—24no—
119C23×C3—28no—
120C23×C3C2×D414yes—
121C23×C3C2414yes—
122C23×C3C2412yes—
123C23×C3C2411yescharacteristic
124C22×D3—24no—
125C22×D3—28no—
126C22×D3C2414yes—
127C3×Q8—28no—
128C3×D4—216no—
129C3×D4—28no—
130C2×C3×C4—24no—
131C2×C3×C4—216no—
132C2×C3×C4C2×D414yes—
133C2×C3×C4C2×D414yes—
134C2×C3×C4C2×D4116yescomplemented
135C2×C3×C4C2414yes—
136C2×C3×C4C2412yes—
137C2×C3×C4C2412yes—
138#67—216no—
139#67—232no—
140C2×Dic3—24no—
141C2×Dic3—24no—
142C2×Dic3—216no—
143C2×Dic3#4118yescomplemented
144C2×Dic3C2414yes—
145C2×Dic3C2414yes—
146C2×Dic3C2414yes—
147D12—28no—
148C4×D3—216no—
149Dic6—28no—
150C24—32no—
151C24C22×D312yes—
152C24C22×D311yescharacteristic
153#41—232no—
154#41—632no—
155C2×Q8—24no—
156C2×Q8—34no—
157C2×Q8—64no—
158C2×Q8C22×D314yes—
159C2×D4—28no—
160C2×D4—24no—
161C2×D4—316no—
162C2×D4—38no—
163C2×D4—34no—
164C2×D4—616no—
165C2×D4—68no—
166C2×D4—64no—
167C2×D4C22×D318yes—
168C2×D4C22×D314yes—
169C22×C4—28no—
170C22×C4—32no—
171C22×C4—32no—
172C22×C4—38no—
173C22×C4—32no—
174C22×C4—38no—
175C22×C4—68no—
176C22×C4—68no—
177C22×C4#6718yescomplemented
178C22×C4C22×D312yes—
179C22×C4C22×D318yes—
180C22×C4C22×D311yescharacteristic
181C22×C4C22×D314yes—
182C22×C4C22×D311yescharacteristic
183C4⋊C4—316no—
184C22⋊C4—316no—
185C22⋊C4—316no—
186C42—38no—
187C42—34no—
188C42—34no—
189C22×C3—28no—
190C22×C3—24no—
191C22×C3—24no—
192C22×C3—28no—
193C22×C3—48no—
194C22×C3C22×D414yes—
195C22×C3C22×D412yes—
196C22×C3C2×#4114yes—
197C22×C3C2511yescharacteristic
198C2×D3—24no—
199C2×D3—28no—
200C2×D3—48no—
201C3×C4—24no—
202C3×C4C22×D414yes—
203C3×C4C22×D414yes—
204Dic3—24no—
205Dic3—24no—
206Dic3C2×#4118yescomplemented
207C23—24no—
208C23—28no—
209C23—24no—
210C23—34no—
211C23—68no—
212C23—64no—
213C23C2×#6714yes—
214C23C23×D314yes—
215C23C23×D312yes—
216C23C23×D311yescharacteristic
217Q8—28no—
218Q8—68no—
219D4—216no—
220D4—28no—
221D4—632no—
222D4—616no—
223D4—68no—
224C2×C4—24no—
225C2×C4—216no—
226C2×C4—38no—
227C2×C4—34no—
228C2×C4—34no—
229C2×C4—34no—
230C2×C4—616no—
231C2×C4—64no—
232C2×C4—64no—
233C2×C4—616no—
234C2×C4C2×#6714yes—
235C2×C4C2×#6714yes—
236C2×C4C2×#67116yescomplemented
237C2×C4C23×D314yes—
238C2×C4C23×D312yes—
239C2×C4C23×D312yes—
240C2×C3—24no—
241C2×C3—44no—
242C2×C3#53214yescomplemented
243C2×C3C23×D411yescharacteristic
244C2×C3C22×#4112yes—
245D3—44no—
246C22—24no—
247C22—28no—
248C22—28no—
249C22—24no—
250C22—48no—
251C22—68no—
252C22—64no—
253C22—128no—
254C22D3×#4114yes—
255C22C22×#6714yes—
256C22C22×#6712yes—
257C22C24×D311yescharacteristic
258C4—24no—
259C4—38no—
260C4—64no—
261C4—64no—
262C4C22×#6714yes—
263C4C22×#6714yes—
264C3C2×#53211yescharacteristic, complemented, Sylow
265C2—24no—
266C2—44no—
267C2—124no—
268C2#583214yesdirect product factor
269C2C2×D3×#4112yes—
270C2C23×#6711yescharacteristic
subgroupG/H
centerC22×C4C22×D3
commutator, cosocleC22×C3C25
FrattiniC22C24×D3
FittingC22×C3×#41C2
socleC23×C3C24
hypercenterC22×#41D3
hypocenterC3C2×#532
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×C3×#41C2semidirect
2. C22×#235C2semidirect
3. #5832C2direct (N × H)
4. C2×#947C2semidirect
5. C2×#944C2semidirect
6. C2×#940C2semidirect
7. C2×#939C2semidirect
8. C2×#936C2semidirect
9. C2×C4×#67C2semidirect
10. C22×C4×Dic3C2semidirect
13. C2×C3×#41C22semidirect
23. C2×#235C22semidirect
28. #947C22semidirect
29. #944C22semidirect
30. #940C22semidirect
31. #939C22semidirect
32. #936C22semidirect
33. C4×#67C22semidirect
39. C2×C4×Dic3C22semidirect
41. C22×#41D3semidirect
61. C22×C3×C4D4semidirect
92. C2×#41C2×D3semidirect
134. C2×C3×C4C2×D4semidirect
143. C2×Dic3#41semidirect
177. C22×C4#67semidirect
206. Dic3C2×#41semidirect
236. C2×C4C2×#67semidirect
242. C2×C3#532semidirect
264. C3C2×#532semidirect
268. C2#5832direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#412
C22×#2352
#58322
C2×#9472
C2×#9442
C2×#9402
C2×#9392
C2×#9362
C2×C4×#672
C22×C4×Dic32
C2×#5323