Finite Group Databasebeta

← C2×#31826607 #49130459

Subgroups — C2×#31826607 #49130459

Order 36224.

812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 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×#17985391C211yesmaximal, characteristic, complemented
2C22×#17985380C211yesmaximal, characteristic, complemented
3C2×#22583581C211yesmaximal, characteristic, complemented
4#31826607C218yesmaximal, direct product factor
5C2×#22583535C211yesmaximal, characteristic, complemented
6C2×#22583531C211yesmaximal, characteristic, complemented
7C2×(C2×D283)⋊C8C211yesmaximal, characteristic, complemented
8C22×D8×C283C211yesmaximal, characteristic, complemented
9C2×#17985391—24no—
10C2×#17985391—22no—
11C2×#17985391—24no—
12C2×#17985391C2214yescomplemented
13C22×Dic566C2211yescharacteristic
14C22×C22⋊D283—21no—
15C22×C22⋊D283—21no—
16C23×Dic283—21no—
17C22×C4×D283C2211yescharacteristic
18C2×#17985380—24no—
19C2×#17985380C2214yescomplemented
20C22×C283⋊C8C2211yescharacteristic
21#22583581—22no—
22#22583581C2214yescomplemented
23C2×C4⋊Dic283C2211yescharacteristic
24C2×C22⋊Dic283—21no—
25#22583535C2214yescomplemented
26#22583531C2214yescomplemented
27(C2×D283)⋊C8C2214yescomplemented
28C22×D4×C283C2211yescharacteristic
29C22×D4×C283C2211yescharacteristic
30C2×D8×C283—24no—
31C2×D8×C283C2214yescomplemented
32C22×C8×C283C2211yescharacteristic
33C23×D283D411yescharacteristic
34#17985391—216no—
35#17985391—28no—
36#17985391—28no—
37C2×Dic566—21no—
38C2×Dic566—22no—
39C2×Dic566D414yescomplemented
40C2×Dic566C2312yes—
41C2×C22⋊D283—28no—
42C2×C22⋊D283—24no—
43C2×C22⋊D283—24no—
44C2×C22⋊D283—44no—
45C22×Dic283—28no—
46C22×Dic283—24no—
47C22×Dic283—21no—
48C22×Dic283—21no—
49C22×Dic283D411yescharacteristic
50C2×C4×D283—22no—
51C2×C4×D283—22no—
52C2×C4×D283D412yes—
53C2×C4×D283C2312yes—
54#17985380—28no—
55C2×C283⋊C8—22no—
56C2×C283⋊C8C2312yes—
57C4⋊Dic283—21no—
58C4⋊Dic283C2312yes—
59C22⋊Dic283—24no—
60C24×C283—21no—
61C24×C283—21no—
62C2×D4×C283—21no—
63C2×D4×C283—22no—
64C2×D4×C283—22no—
65C2×D4×C283—22no—
66C2×D4×C283—21no—
67C2×D4×C283D414yescomplemented
68C2×D4×C283C2312yes—
69C2×D4×C283C2312yes—
70C22×C4×C283C2311yescharacteristic
71D8×C283—28no—
72C2×C8×C283—22no—
73C2×C8×C283C2312yes—
74C22×D283—22no—
75C22×D283—22no—
76C22×D283—22no—
77C22×D283C2×D412yes—
78Dic566—24no—
79Dic566—22no—
80Dic566C2×D414yescomplemented
81C22⋊D283—216no—
82C22⋊D283—48no—
83C2×Dic283—216no—
84C2×Dic283—22no—
85C2×Dic283—24no—
86C2×Dic283—22no—
87C2×Dic283—22no—
88C2×Dic283—42no—
89C2×Dic283C2×D412yes—
90C4×D283—24no—
91C4×D283—22no—
92C4×D283—22no—
93C283⋊C8—22no—
94C23×C283—24no—
95C23×C283—22no—
96C23×C283—22no—
97C23×C283—42no—
98C23×C283—42no—
99C23×C283—42no—
100C23×C283—42no—
101C23×C283—42no—
102C23×C283C2×D411yescharacteristic
103D4×C283—24no—
104D4×C283—22no—
105D4×C283—22no—
106D4×C283—22no—
107D4×C283—42no—
108D4×C283C2×D414yescomplemented
109C2×C4×C283C2×D411yescharacteristic
110C2×C4×C283C2×D412yes—
111C2×C4×C283C2×D412yes—
112C2×C4×C283C2411yescharacteristic
113C8×C283—22no—
114C22×C283—24no—
115C22×C283—42no—
116C22×C283—42no—
117C22×C283—48no—
118C22×C283—42no—
119C22×C283—42no—
120C22×C283—42no—
121C22×C283—84no—
122C22×C283#12012yes—
123C22×C283#13512yes—
124C22×C283AGL(1,ℤ/8)12yes—
125C22×C283C22×D411yescharacteristic
126C2×D283—22no—
127C2×D283—22no—
128C2×D283—22no—
129C2×D283—44no—
130C4×C283#12012yes—
131C4×C283C22×D411yescharacteristic
132C4×C283C22×D411yescharacteristic
133Dic283—22no—
134Dic283—24no—
135Dic283—42no—
136C2×C283—44no—
137C2×C283—82no—
138C2×C283#44914yescomplemented
139C2×C283C2×#12011yescharacteristic
140C2×C283C2×#13511yescharacteristic
141C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
142D283—42no—
143C283C2×#44911yescharacteristic, complemented, Sylow
144C2×#449—2831nomaximal, Sylow
145C22×#41—2831no—
146C22×SD16—2831no—
147C22×D8D28311yescharacteristic, complemented
148C2×#121—2831no—
149#449—2838no—
150C2×#103—2831no—
151C2×#102—2831no—
152C2×C22⋊C8—2831no—
153C2×#41—2834no—
154C2×#41—5662no—
155C2×#41—5664no—
156C2×#41—5664no—
157C22×Q8—2831no—
158C22×D4—5661no—
159C22×D4—5661no—
160C22×D4C2×D28311yescharacteristic
161C22×D4C2×D28311yescharacteristic
162C23×C4—2831no—
163C23×C4—5661no—
164C2×SD16—2834no—
165C2×SD16—5664no—
166C2×D8—24no—
167C2×D8C2×D28314yescomplemented
168C22×C8—2831no—
169C22×C8C2×D28311yescharacteristic
170#121—2834no—
171#121—5662no—
172C2×C4⋊C4—2831no—
173C2×C22⋊C4—5661no—
174#103—2834no—
175#102—2834no—
176C22⋊C8—2834no—
177C24—21no—
178C24—21no—
179C24—2831no—
180#41—5668no—
181#41—56616no—
182#41—5668no—
183C2×Q8—2834no—
184C2×Q8—2832no—
185C2×Q8—5661no—
186C2×Q8—5662no—
187C2×D4—21no—
188C2×D4—22no—
189C2×D4—22no—
190C2×D4—21no—
191C2×D4—22no—
192C2×D4—5664no—
193C2×D4—5668no—
194C2×D4—5664no—
195C2×D4—11324no—
196C2×D4C22⋊D28314yescomplemented
197C2×D4C22×D28312yes—
198C2×D4C22×D28312yes—
199C22×C4—2831no—
200C22×C4—2832no—
201C22×C4—2832no—
202C22×C4—5664no—
203C22×C4—5668no—
204C22×C4—5661no—
205C22×C4—5662no—
206C22×C4—5662no—
207C22×C4—5661no—
208C22×C4C22×D28311yescharacteristic
209SD16—5668no—
210D8—28no—
211C2×C8—22no—
212C2×C8—2832no—
213C2×C8—5662no—
214C2×C8C22×D28312yes—
215C4⋊C4—2832no—
216C4⋊C4—5661no—
217C22⋊C4—5664no—
218C23—24no—
219C23—22no—
220C23—22no—
221C23—42no—
222C23—42no—
223C23—42no—
224C23—42no—
225C23—42no—
226C23—2832no—
227C23—5662no—
228C23—5662no—
229C23—5662no—
230C23D4×D28311yescharacteristic
231Q8—2834no—
232Q8—5664no—
233Q8—5662no—
234D4—24no—
235D4—22no—
236D4—22no—
237D4—22no—
238D4—42no—
239D4—56616no—
240D4—11328no—
241D4C2×C22⋊D28314yescomplemented
242C2×C4—2832no—
243C2×C4—56616no—
244C2×C4—5662no—
245C2×C4—5664no—
246C2×C4—5662no—
247C2×C4—5664no—
248C2×C4—5662no—
249C2×C4—5662no—
250C2×C4—5662no—
251C2×C4—11322no—
252C2×C4D4×D28311yescharacteristic
253C2×C4D4×D28312yes—
254C2×C4C2×C22⋊D28312yes—
255C2×C4C23×D28311yescharacteristic
256C8—22no—
257C8—5662no—
258C22—24no—
259C22—42no—
260C22—42no—
261C22—48no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—84no—
266C22—5662no—
267C22—5662no—
268C22—5662no—
269C22—11324no—
270C22#2258357812yes—
271C22#2258362912yes—
272C22#2258363412yes—
273C22C2×D4×D28311yescharacteristic
274C4—5662no—
275C4—5664no—
276C4—11322no—
277C4#2258357812yes—
278C4C2×D4×D28311yescharacteristic
279C4C22×C22⋊D28311yescharacteristic
280C2—44no—
281C2—82no—
282C2—11322no—
283C2#3182660714yesdirect product factor
284C2C2×#2258357811yescharacteristic
285C2C2×#2258362911yescharacteristic
286C2C2×#2258363411yescharacteristic
subgroupG/H
centerC23D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC22×D8×C283C2
socleC23×C283C2×D4
hypercenterC22×D8D283
hypocenterC283C2×#449
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×#17985391C2semidirect
2. C22×#17985380C2semidirect
3. C2×#22583581C2semidirect
4. #31826607C2direct (N × H)
5. C2×#22583535C2semidirect
6. C2×#22583531C2semidirect
7. C2×(C2×D283)⋊C8C2semidirect
8. C22×D8×C283C2semidirect
12. C2×#17985391C22semidirect
19. C2×#17985380C22semidirect
22. #22583581C22semidirect
25. #22583535C22semidirect
26. #22583531C22semidirect
27. (C2×D283)⋊C8C22semidirect
31. C2×D8×C283C22semidirect
39. C2×Dic566D4semidirect
67. C2×D4×C283D4semidirect
80. Dic566C2×D4semidirect
108. D4×C283C2×D4semidirect
138. C2×C283#449semidirect
143. C283C2×#449semidirect
147. C22×D8D283semidirect
167. C2×D8C2×D283semidirect
196. C2×D4C22⋊D283semidirect
241. D4C2×C22⋊D283semidirect
283. C2#31826607direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#179853912
C22×#179853802
C2×#225835812
#318266072
C2×#225835352
C2×#225835312
C2×(C2×D283)⋊C82
C22×D8×C2832
C2×#449283