Finite Group Databasebeta

← C2×#31827161 #49134780

Subgroups — C2×#31827161 #49134780

Order 36224.

1252 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827161C2116yesmaximal, direct product factor
2C2×#22583605C212yesmaximal, complemented
3C2×#22583602C211yesmaximal, characteristic, complemented
4C2×#22583592C212yesmaximal, complemented
5C2×#22583584C211yesmaximal, characteristic, complemented
6C2×#22583584C211yesmaximal, characteristic, complemented
7C2×#22583582C212yesmaximal, complemented
8C2×C4×D1132C211yesmaximal, characteristic, complemented
9C2×(C22⋊D283)⋊C4C212yesmaximal, complemented
10C2×#22583569C211yesmaximal, characteristic, complemented
11C22×C4⋊Dic283C211yesmaximal, characteristic, complemented
12C2×C4×D4×C283C211yesmaximal, characteristic, complemented
13C22×D1132C2211yescharacteristic
14C22×C22⋊D283C2212yes—
15C22×C22⋊D283C2212yes—
16C23×Dic283C2212yes—
17C22×C4×D283C2212yes—
18#22583605C22116yescomplemented
19#22583602C2218yescomplemented
20#22583592C22116yescomplemented
21#22583584C2218yescomplemented
22#22583584C2218yescomplemented
23#22583582C22116yescomplemented
24C4×D1132C2218yescomplemented
25(C22⋊D283)⋊C4C22116yescomplemented
26#22583569C2218yescomplemented
27C2×C4⋊Dic283C2211yescharacteristic
28C2×C4⋊Dic283C2211yescharacteristic
29C2×C4⋊Dic283C2212yes—
30C2×C4⋊Dic283C2211yescharacteristic
31C2×C4⋊Dic283C2218yescomplemented
32C2×Dic283⋊C4C2212yes—
33C2×Dic283⋊C4C2212yes—
34C2×C22⋊Dic283C2212yes—
35C2×(C2×D283)⋊C4C2212yes—
36C2×(C2×D283)⋊C4C2212yes—
37C2×(C2×D283)⋊C4C2212yes—
38C2×C4×Dic283C2212yes—
39C22×D4×C283C2211yescharacteristic
40C23×C4×C283C2211yescharacteristic
41C23×C4×C283C2211yescharacteristic
42C4×D4×C283C2218yescomplemented
43C2×C4⋊C4×C283C2211yescharacteristic
44C2×C22⋊C4×C283C2211yescharacteristic
45C2×C22⋊C4×C283C2211yescharacteristic
46C2×C42×C283C2211yescharacteristic
47C23×D283C2312yes—
48C2×D1132—24no—
49C2×D1132C2314yes—
50C2×C22⋊D283—28no—
51C2×C22⋊D283—44no—
52C2×C22⋊D283C2318yes—
53C2×C22⋊D283C2318yes—
54C22×Dic283—44no—
55C22×Dic283C2312yes—
56C22×Dic283C2312yes—
57C22×Dic283C2312yes—
58C22×Dic283C2318yes—
59C2×C4×D283—44no—
60C2×C4×D283C2318yes—
61C4⋊Dic283C2314yes—
62C4⋊Dic283C2314yes—
63C4⋊Dic283C2318yes—
64C4⋊Dic283C2314yes—
65Dic283⋊C4C2318yes—
66Dic283⋊C4C2318yes—
67C22⋊Dic283C2318yes—
68(C2×D283)⋊C4C2318yes—
69(C2×D283)⋊C4C2318yes—
70(C2×D283)⋊C4C2318yes—
71C4×Dic283C2318yes—
72C24×C283C2311yescharacteristic
73C24×C283C2311yescharacteristic
74C2×D4×C283—24no—
75C2×D4×C283C2314yes—
76C22×C4×C283—24no—
77C22×C4×C283—24no—
78C22×C4×C283C2311yescharacteristic
79C22×C4×C283C2311yescharacteristic
80C22×C4×C283C2311yescharacteristic
81C22×C4×C283C2311yescharacteristic
82C22×C4×C283C2314yes—
83C22×C4×C283C2314yes—
84C22×C4×C283C2311yescharacteristic
85C4⋊C4×C283C2314yes—
86C22⋊C4×C283C2314yes—
87C22⋊C4×C283C2314yes—
88C42×C283C2314yes—
89C22×D283—24no—
90C22×D283—24no—
91C22×D283—24no—
92C22×D283C2414yes—
93D1132—28no—
94C22⋊D283—216no—
95C22⋊D283—48no—
96C2×Dic283—24no—
97C2×Dic283—24no—
98C2×Dic283—24no—
99C2×Dic283—48no—
100C2×Dic283C2414yes—
101C2×Dic283C2414yes—
102C2×Dic283C2414yes—
103C4×D283—48no—
104C23×C283—22no—
105C23×C283—22no—
106C23×C283—22no—
107C23×C283—22no—
108C23×C283—22no—
109C23×C283#4114yes—
110C23×C283C2412yes—
111C23×C283C2412yes—
112C23×C283C2411yescharacteristic
113D4×C283—28no—
114C2×C4×C283—22no—
115C2×C4×C283—22no—
116C2×C4×C283—22no—
117C2×C4×C283—22no—
118C2×C4×C283—28no—
119C2×C4×C283—28no—
120C2×C4×C283#4114yes—
121C2×C4×C283C2412yes—
122C2×C4×C283C2412yes—
123C2×C4×C283C2412yes—
124C2×C4×C283C2412yes—
125C2×C4×C283C2412yes—
126C22×C283—28no—
127C22×C283—22no—
128C22×C283—22no—
129C22×C283—22no—
130C22×C283—22no—
131C22×C283—22no—
132C22×C283—44no—
133C22×C283C2×#4112yes—
134C22×C283C2×#4114yes—
135C22×C283C2×#4112yes—
136C22×C283H(5,𝔽2)12yes—
137C22×C283C2511yescharacteristic
138C2×D283—24no—
139C2×D283—24no—
140C2×D283—24no—
141C2×D283—48no—
142C4×C283—22no—
143C4×C283—22no—
144C4×C283—22no—
145C4×C283—22no—
146C4×C283C2×#4114yes—
147Dic283—24no—
148Dic283—24no—
149Dic283—24no—
150C2×C283—24no—
151C2×C283—42no—
152C2×C283#55314yescomplemented
153C2×C283C22×#4111yescharacteristic
154C2×C283C22×#4111yescharacteristic
155C2×C283C2×H(5,𝔽2)11yescharacteristic
156D283—44no—
157C283C2×#55311yescharacteristic, complemented, Sylow
158C2×#553—2831nomaximal, Sylow
159#553—28316no—
160C2×#126—2832no—
161C2×#125—2831no—
162C2×#123—2832no—
163C2×#121—2832no—
164C2×#121—2831no—
165C2×#121—2831no—
166C2×C4×D4—2832no—
167C2×C4×D4—2831no—
168C2×C4×D4D28311yescharacteristic, complemented
169C2×#117—2831no—
170C22×C4⋊C4—2831no—
171C22×D4—2832no—
172C22×D4—2832no—
173C22×D4—2831no—
174C22×D4C2×D28311yescharacteristic
175C23×C4—2832no—
176C23×C4—2832no—
177C23×C4C2×D28311yescharacteristic
178C23×C4C2×D28311yescharacteristic
179#126—28316no—
180#125—2838no—
181#123—28316no—
182#121—28316no—
183#121—2838no—
184#121—2838no—
185C4×D4—28316no—
186C4×D4—2838no—
187C4×D4C2×D28318yescomplemented
188#117—2838no—
189C2×C4⋊C4—2831no—
190C2×C4⋊C4—2831no—
191C2×C4⋊C4—2832no—
192C2×C4⋊C4—2838no—
193C2×C4⋊C4—2831no—
194C2×C4⋊C4—2832no—
195C2×C4⋊C4—2832no—
196C2×C4⋊C4C2×D28311yescharacteristic
197C2×C22⋊C4—2832no—
198C2×C22⋊C4—2832no—
199C2×C22⋊C4—2832no—
200C2×C22⋊C4—2832no—
201C2×C22⋊C4C2×D28311yescharacteristic
202C2×C22⋊C4C2×D28311yescharacteristic
203C2×C42—2832no—
204C2×C42C2×D28311yescharacteristic
205C24—2832no—
206C24C22×D28311yescharacteristic
207C24C22×D28311yescharacteristic
208C2×D4—24no—
209C2×D4—2838no—
210C2×D4—2838no—
211C2×D4—2834no—
212C2×D4—5668no—
213C2×D4—5664no—
214C2×D4—11324no—
215C2×D4C22×D28314yes—
216C22×C4—24no—
217C22×C4—24no—
218C22×C4—2832no—
219C22×C4—2832no—
220C22×C4—2832no—
221C22×C4—2838no—
222C22×C4—2838no—
223C22×C4—11324no—
224C22×C4—11324no—
225C22×C4C22×D28314yes—
226C22×C4C22×D28314yes—
227C22×C4C22×D28311yescharacteristic
228C22×C4C22×D28311yescharacteristic
229C22×C4C22×D28311yescharacteristic
230C22×C4C22×D28311yescharacteristic
231C22×C4C22×D28311yescharacteristic
232C4⋊C4—2838no—
233C4⋊C4—2838no—
234C4⋊C4—2834no—
235C4⋊C4—2834no—
236C4⋊C4—2838no—
237C4⋊C4—2834no—
238C4⋊C4C22×D28314yes—
239C22⋊C4—2838no—
240C22⋊C4—2838no—
241C22⋊C4—2838no—
242C22⋊C4—2838no—
243C22⋊C4C22×D28314yes—
244C22⋊C4C22×D28314yes—
245C42—2838no—
246C42C22×D28314yes—
247C23—22no—
248C23—22no—
249C23—22no—
250C23—22no—
251C23—22no—
252C23—2834no—
253C23—5664no—
254C23—5664no—
255C23—5664no—
256C23#1798539214yes—
257C23C23×D28312yes—
258C23C23×D28312yes—
259C23C23×D28311yescharacteristic
260D4—28no—
261D4—56616no—
262D4—5668no—
263D4—11328no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—28no—
269C2×C4—28no—
270C2×C4—2834no—
271C2×C4—2834no—
272C2×C4—2834no—
273C2×C4—5664no—
274C2×C4—5664no—
275C2×C4—5664no—
276C2×C4—11328no—
277C2×C4—11328no—
278C2×C4#1798539114yes—
279C2×C4C23×D28312yes—
280C2×C4C23×D28312yes—
281C2×C4C23×D28312yes—
282C2×C4C23×D28312yes—
283C2×C4C23×D28312yes—
284C22—22no—
285C22—22no—
286C22—28no—
287C22—22no—
288C22—22no—
289C22—22no—
290C22—44no—
291C22—5664no—
292C22—5664no—
293C22—5664no—
294C22—11328no—
295C22C2×#1798539112yes—
296C22C2×#1798539214yes—
297C22C2×#1798539212yes—
298C22#2258365612yes—
299C22C24×D28311yescharacteristic
300C4—22no—
301C4—22no—
302C4—22no—
303C4—22no—
304C4—5664no—
305C4—5664no—
306C4—5664no—
307C4C2×#1798539114yes—
308C2—24no—
309C2—42no—
310C2—11324no—
311C2#3182716114yesdirect product factor
312C2C22×#1798539111yescharacteristic
313C2C22×#1798539211yescharacteristic
314C2C2×#2258365611yescharacteristic
subgroupG/H
centerC23C23×D283
commutator, cosocleC22×C283C25
FrattiniC22C24×D283
FittingC2×C4×D4×C283C2
socleC23×C283C24
hypercenterC2×C4×D4D283
hypocenterC283C2×#553
LCSG ▷ C22×C283 ▷ C283
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #31827161C2direct (N × H)
2. C2×#22583605C2semidirect
3. C2×#22583602C2semidirect
4. C2×#22583592C2semidirect
5. C2×#22583584C2semidirect
6. C2×#22583584C2semidirect
7. C2×#22583582C2semidirect
8. C2×C4×D1132C2semidirect
9. C2×(C22⋊D283)⋊C4C2semidirect
10. C2×#22583569C2semidirect
11. C22×C4⋊Dic283C2semidirect
12. C2×C4×D4×C283C2semidirect
18. #22583605C22semidirect
19. #22583602C22semidirect
20. #22583592C22semidirect
21. #22583584C22semidirect
22. #22583584C22semidirect
23. #22583582C22semidirect
24. C4×D1132C22semidirect
25. (C22⋊D283)⋊C4C22semidirect
26. #22583569C22semidirect
31. C2×C4⋊Dic283C22semidirect
42. C4×D4×C283C22semidirect
152. C2×C283#553semidirect
157. C283C2×#553semidirect
168. C2×C4×D4D283semidirect
187. C4×D4C2×D283semidirect
311. C2#31827161direct (N × H)

Maximal subgroups

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

subgroupindex
#318271612
C2×#225836052
C2×#225836022
C2×#225835922
C2×#225835842
C2×#225835822
C2×C4×D11322
C2×(C22⋊D283)⋊C42
C2×#225835692
C22×C4⋊Dic2832
C2×C4×D4×C2832
C2×#553283