Finite Group Databasebeta

← C2×#31826611 #49130463

Subgroups — C2×#31826611 #49130463

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×#17985381C211yesmaximal, characteristic, complemented
3C22×#17985377C211yesmaximal, characteristic, complemented
4C2×#22583585C211yesmaximal, characteristic, complemented
5#31826611C218yesmaximal, direct product factor
6C2×#22583533C211yesmaximal, characteristic, complemented
7C2×(C2×D283)⋊C8C211yesmaximal, characteristic, complemented
8C2×#102×C283C211yesmaximal, characteristic, complemented
9C2×#17985391—24no—
10C2×#17985391—22no—
11C2×#17985391—24no—
12C2×#17985391C2214yescomplemented
13C22×Dic566C2211yescharacteristic
14C22×D1132—21no—
15C22×D1132C2211yescharacteristic
16C22×C22⋊D283—21no—
17C23×Dic283—21no—
18C22×C4×D283C2211yescharacteristic
19C2×#17985381—24no—
20C2×#17985381C2214yescomplemented
21C2×#17985377—24no—
22C2×#17985377C2214yescomplemented
23C22×C283⋊C8C2211yescharacteristic
24#22583585—22no—
25#22583585C2214yescomplemented
26C2×(C2×D283)⋊C4—21no—
27#22583533C2214yescomplemented
28(C2×D283)⋊C8C2214yescomplemented
29C22×D4×C283C2211yescharacteristic
30C22×C8×C283C2211yescharacteristic
31C2×C4⋊C4×C283C2211yescharacteristic
32#102×C283C2214yescomplemented
33C23×D283—21no—
34C23×D283D411yescharacteristic
35#17985391—216no—
36#17985391—28no—
37#17985391—28no—
38C2×Dic566—21no—
39C2×Dic566—22no—
40C2×Dic566D414yescomplemented
41C2×Dic566C2312yes—
42C2×D1132—24no—
43C2×D1132—22no—
44C2×D1132—22no—
45C2×D1132—21no—
46C2×D1132—44no—
47C2×D1132C2312yes—
48C2×C22⋊D283—28no—
49C2×C22⋊D283—24no—
50C22×Dic283—28no—
51C22×Dic283—24no—
52C22×Dic283—21no—
53C22×Dic283D411yescharacteristic
54C2×C4×D283—22no—
55C2×C4×D283—22no—
56C2×C4×D283D412yes—
57C2×C4×D283C2312yes—
58#17985381—28no—
59#17985377—28no—
60C2×C283⋊C8—22no—
61C2×C283⋊C8C2312yes—
62(C2×D283)⋊C4—24no—
63C24×C283—21no—
64C2×D4×C283—21no—
65C2×D4×C283—22no—
66C2×D4×C283D414yescomplemented
67C2×D4×C283C2312yes—
68C22×C4×C283—21no—
69C22×C4×C283C2311yescharacteristic
70C2×C8×C283—22no—
71C2×C8×C283C2312yes—
72C4⋊C4×C283—21no—
73C4⋊C4×C283C2312yes—
74C22×D283—22no—
75C22×D283—22no—
76C22×D283—22no—
77C22×D283—22no—
78C22×D283—42no—
79C22×D283—42no—
80C22×D283—42no—
81C22×D283C2×D412yes—
82Dic566—24no—
83Dic566—22no—
84Dic566C2×D414yescomplemented
85D1132—22no—
86D1132—22no—
87D1132—48no—
88D1132—42no—
89C22⋊D283—216no—
90C2×Dic283—216no—
91C2×Dic283—22no—
92C2×Dic283—24no—
93C2×Dic283—22no—
94C2×Dic283C2×D412yes—
95C4×D283—24no—
96C4×D283—22no—
97C4×D283—22no—
98C283⋊C8—22no—
99C23×C283—24no—
100C23×C283—22no—
101C23×C283—42no—
102C23×C283—42no—
103C23×C283C2×D411yescharacteristic
104D4×C283—24no—
105D4×C283—22no—
106D4×C283C2×D414yescomplemented
107C2×C4×C283—22no—
108C2×C4×C283—42no—
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#12012yes—
119C22×C283#13512yes—
120C22×C283AGL(1,ℤ/8)12yes—
121C22×C283C22×D411yescharacteristic
122C2×D283—22no—
123C2×D283—22no—
124C2×D283—22no—
125C2×D283—44no—
126C2×D283—42no—
127C2×D283—42no—
128C2×D283—42no—
129C2×D283—84no—
130C4×C283—42no—
131C4×C283#12012yes—
132C4×C283C22×D411yescharacteristic
133C4×C283C22×D411yescharacteristic
134Dic283—22no—
135Dic283—24no—
136C2×C283—44no—
137C2×C283#44914yescomplemented
138C2×C283C2×#12011yescharacteristic
139C2×C283C2×#13511yescharacteristic
140C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
141D283—42no—
142D283—82no—
143C283C2×#44911yescharacteristic, complemented, Sylow
144C2×#449—2831nomaximal, Sylow
145C22×#41—2831no—
146C22×SD16—2831no—
147C22×D8—2831no—
148C2×#121—2831no—
149#449—2838no—
150C2×#103—2831no—
151C2×#102D28311yescharacteristic, complemented
152C2×C22⋊C8—2831no—
153C2×#41—2834no—
154C2×#41—5662no—
155C2×#41—5664no—
156C2×#41—5664no—
157C22×Q8—2831no—
158C22×D4—2831no—
159C22×D4—5661no—
160C22×D4—5661no—
161C22×D4C2×D28311yescharacteristic
162C23×C4—2831no—
163C23×C4—5661no—
164C2×SD16—2834no—
165C2×SD16—5664no—
166C2×D8—2834no—
167C2×D8—5664no—
168C22×C8—2831no—
169C22×C8C2×D28311yescharacteristic
170#121—2834no—
171#121—5662no—
172C2×C4⋊C4C2×D28311yescharacteristic
173C2×C22⋊C4—5661no—
174#103—2834no—
175#102C2×D28314yescomplemented
176C22⋊C8—2834no—
177C24—21no—
178C24—2831no—
179C24—5661no—
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—2832no—
190C2×D4—5664no—
191C2×D4—5664no—
192C2×D4—5668no—
193C2×D4—5662no—
194C2×D4—5661no—
195C2×D4—5662no—
196C2×D4—11324no—
197C2×D4D113214yescomplemented
198C2×D4C22×D28312yes—
199C22×C4—21no—
200C22×C4—2831no—
201C22×C4—2832no—
202C22×C4—2832no—
203C22×C4—5664no—
204C22×C4—5668no—
205C22×C4—5661no—
206C22×C4—5662no—
207C22×C4—5662no—
208C22×C4C22×D28311yescharacteristic
209SD16—5668no—
210D8—5668no—
211C2×C8—22no—
212C2×C8—2832no—
213C2×C8—5662no—
214C2×C8C22×D28312yes—
215C4⋊C4—21no—
216C4⋊C4C22×D28312yes—
217C22⋊C4—5664no—
218C23—24no—
219C23—22no—
220C23—42no—
221C23—42no—
222C23—2832no—
223C23—5662no—
224C23—5662no—
225C23—5662no—
226C23—5662no—
227C23—11322no—
228C23—11322no—
229C23—11322no—
230C23D4×D28311yescharacteristic
231Q8—2834no—
232Q8—5664no—
233Q8—5662no—
234D4—24no—
235D4—22no—
236D4—56616no—
237D4—5662no—
238D4—5662no—
239D4—11328no—
240D4—11322no—
241D4C2×D113214yescomplemented
242C2×C4—22no—
243C2×C4—42no—
244C2×C4—2832no—
245C2×C4—56616no—
246C2×C4—5662no—
247C2×C4—5664no—
248C2×C4—5662no—
249C2×C4—5664no—
250C2×C4—5662no—
251C2×C4—5662no—
252C2×C4D4×D28311yescharacteristic
253C2×C4D4×D28312yes—
254C2×C4C2×D113212yes—
255C2×C4C23×D28311yescharacteristic
256C8—22no—
257C8—5662no—
258C22—24no—
259C22—42no—
260C22—42no—
261C22—48no—
262C22—5662no—
263C22—5662no—
264C22—5662no—
265C22—11324no—
266C22—11322no—
267C22—11322no—
268C22—11322no—
269C22—22644no—
270C22#2258358012yes—
271C22#2258363112yes—
272C22#2258363412yes—
273C22C2×D4×D28311yescharacteristic
274C4—42no—
275C4—5662no—
276C4—5664no—
277C4#2258358012yes—
278C4C2×D4×D28311yescharacteristic
279C4C22×D113211yescharacteristic
280C2—44no—
281C2—11322no—
282C2—22642no—
283C2#3182661114yesdirect product factor
284C2C2×#2258358011yescharacteristic
285C2C2×#2258363111yescharacteristic
286C2C2×#2258363411yescharacteristic
subgroupG/H
centerC23D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#102×C283C2
socleC23×C283C2×D4
hypercenterC2×#102D283
hypocenterC283C2×#449
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×#17985391C2semidirect
2. C22×#17985381C2semidirect
3. C22×#17985377C2semidirect
4. C2×#22583585C2semidirect
5. #31826611C2direct (N × H)
6. C2×#22583533C2semidirect
7. C2×(C2×D283)⋊C8C2semidirect
8. C2×#102×C283C2semidirect
12. C2×#17985391C22semidirect
20. C2×#17985381C22semidirect
22. C2×#17985377C22semidirect
25. #22583585C22semidirect
27. #22583533C22semidirect
28. (C2×D283)⋊C8C22semidirect
32. #102×C283C22semidirect
40. C2×Dic566D4semidirect
66. C2×D4×C283D4semidirect
84. Dic566C2×D4semidirect
106. D4×C283C2×D4semidirect
137. C2×C283#449semidirect
143. C283C2×#449semidirect
151. C2×#102D283semidirect
175. #102C2×D283semidirect
197. C2×D4D1132semidirect
241. D4C2×D1132semidirect
283. C2#31826611direct (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×#179853812
C22×#179853772
C2×#225835852
#318266112
C2×#225835332
C2×(C2×D283)⋊C82
C2×#102×C2832
C2×#449283