Finite Group Databasebeta

← C2×#31826613 #49130465

Subgroups — C2×#31826613 #49130465

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×#17985393C211yesmaximal, characteristic, complemented
2C22×#17985379C211yesmaximal, characteristic, complemented
3C22×D2264C211yesmaximal, characteristic, complemented
4C2×#22583585C211yesmaximal, characteristic, complemented
5#31826613C218yesmaximal, direct product factor
6C2×#22583530C211yesmaximal, characteristic, complemented
7C2×(C2×D283)⋊C8C211yesmaximal, characteristic, complemented
8C2×#103×C283C211yesmaximal, characteristic, complemented
9C2×#17985393—24no—
10C2×#17985393—22no—
11C2×#17985393—24no—
12C2×#17985393C2214yescomplemented
13C22×D1132—21no—
14C22×D1132—21no—
15C22×D1132C2211yescharacteristic
16C22×D1132C2211yescharacteristic
17C22×C4×D283—21no—
18C22×C4×D283C2211yescharacteristic
19C2×#17985379—24no—
20C2×#17985379C2214yescomplemented
21C2×D2264—24no—
22C2×D2264C2214yescomplemented
23C22×C283⋊C8C2211yescharacteristic
24#22583585—22no—
25#22583585C2214yescomplemented
26C2×(C2×D283)⋊C4—21no—
27#22583530C2214yescomplemented
28(C2×D283)⋊C8C2214yescomplemented
29C22×Q8×C283C2211yescharacteristic
30C22×C8×C283C2211yescharacteristic
31C2×C4⋊C4×C283C2211yescharacteristic
32#103×C283C2214yescomplemented
33C23×D283—21no—
34C23×D283—21no—
35C23×D283D411yescharacteristic
36#17985393—216no—
37#17985393—28no—
38#17985393—28no—
39C2×D1132—28no—
40C2×D1132—24no—
41C2×D1132—24no—
42C2×D1132—21no—
43C2×D1132—22no—
44C2×D1132—22no—
45C2×D1132—22no—
46C2×D1132—21no—
47C2×D1132—44no—
48C2×D1132D414yescomplemented
49C2×D1132C2312yes—
50C2×D1132C2312yes—
51C22×Dic283D411yescharacteristic
52C2×C4×D283—28no—
53C2×C4×D283—24no—
54C2×C4×D283—22no—
55C2×C4×D283—22no—
56C2×C4×D283D412yes—
57C2×C4×D283C2312yes—
58#17985379—28no—
59D2264—28no—
60C2×C283⋊C8—22no—
61C2×C283⋊C8C2312yes—
62(C2×D283)⋊C4—24no—
63C2×Q8×C283—22no—
64C2×Q8×C283—21no—
65C2×Q8×C283D414yescomplemented
66C2×Q8×C283C2312yes—
67C22×C4×C283—21no—
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—24no—
76C22×D283—22no—
77C22×D283—22no—
78C22×D283—22no—
79C22×D283—22no—
80C22×D283—42no—
81C22×D283—42no—
82C22×D283—42no—
83C22×D283—42no—
84C22×D283—42no—
85C22×D283C2×D412yes—
86D1132—216no—
87D1132—24no—
88D1132—22no—
89D1132—22no—
90D1132—22no—
91D1132—48no—
92D1132—42no—
93D1132C2×D414yescomplemented
94C2×Dic283—22no—
95C2×Dic283C2×D412yes—
96C4×D283—216no—
97C4×D283—24no—
98C4×D283—22no—
99C4×D283—22no—
100C283⋊C8—22no—
101C23×C283C2×D411yescharacteristic
102Q8×C283—24no—
103Q8×C283—22no—
104Q8×C283C2×D414yescomplemented
105C2×C4×C283—24no—
106C2×C4×C283—22no—
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#12012yes—
115C22×C283#13512yes—
116C22×C283AGL(1,ℤ/8)12yes—
117C22×C283C22×D411yescharacteristic
118C2×D283—22no—
119C2×D283—24no—
120C2×D283—22no—
121C2×D283—22no—
122C2×D283—42no—
123C2×D283—42no—
124C2×D283—44no—
125C2×D283—48no—
126C2×D283—42no—
127C2×D283—42no—
128C2×D283—42no—
129C2×D283—84no—
130C4×C283—24no—
131C4×C283—42no—
132C4×C283#12012yes—
133C4×C283C22×D411yescharacteristic
134C4×C283C22×D411yescharacteristic
135Dic283—22no—
136C2×C283#44914yescomplemented
137C2×C283C2×#12011yescharacteristic
138C2×C283C2×#13511yescharacteristic
139C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
140D283—42no—
141D283—44no—
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×#103D28311yescharacteristic, complemented
151C2×#102—2831no—
152C2×C22⋊C8—2831no—
153C2×#41—2834no—
154C2×#41—5662no—
155C2×#41—5664no—
156C2×#41—5664no—
157C22×Q8C2×D28311yescharacteristic
158C22×D4—2831no—
159C22×D4—2831no—
160C22×D4—5661no—
161C22×D4—5661no—
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#103C2×D28314yescomplemented
175#102—2834no—
176C22⋊C8—2834no—
177C24—2831no—
178C24—5661no—
179C24—5661no—
180#41—5668no—
181#41—56616no—
182#41—5668no—
183C2×Q8—22no—
184C2×Q8—21no—
185C2×Q8D113214yescomplemented
186C2×Q8C22×D28312yes—
187C2×D4—2834no—
188C2×D4—2832no—
189C2×D4—2832no—
190C2×D4—5664no—
191C2×D4—5668no—
192C2×D4—5664no—
193C2×D4—5661no—
194C2×D4—5662no—
195C2×D4—5661no—
196C2×D4—5662no—
197C2×D4—5662no—
198C2×D4—11324no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—2831no—
202C22×C4—2832no—
203C22×C4—2832no—
204C22×C4—5664no—
205C22×C4—5668no—
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—2832no—
219C23—5664no—
220C23—5662no—
221C23—5662no—
222C23—5662no—
223C23—5662no—
224C23—5662no—
225C23—11322no—
226C23—11322no—
227C23—11322no—
228C23—11322no—
229C23—11322no—
230C23D4×D28311yescharacteristic
231Q8—24no—
232Q8—22no—
233Q8C2×D113214yescomplemented
234D4—2834no—
235D4—56616no—
236D4—5664no—
237D4—5662no—
238D4—5662no—
239D4—5662no—
240D4—11328no—
241D4—11322no—
242C2×C4—24no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—42no—
246C2×C4—2832no—
247C2×C4—56616no—
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—5664no—
259C22—5662no—
260C22—5662no—
261C22—5662no—
262C22—11322no—
263C22—11322no—
264C22—11324no—
265C22—11328no—
266C22—11322no—
267C22—11322no—
268C22—11322no—
269C22—22644no—
270C22#2258358012yes—
271C22#2258363312yes—
272C22#2258363712yes—
273C22C2×D4×D28311yescharacteristic
274C4—24no—
275C4—42no—
276C4—5662no—
277C4#2258358012yes—
278C4C2×D4×D28311yescharacteristic
279C4C22×D113211yescharacteristic
280C2—11322no—
281C2—11324no—
282C2—22642no—
283C2#3182661314yesdirect product factor
284C2C2×#2258358011yescharacteristic
285C2C2×#2258363311yescharacteristic
286C2C2×#2258363711yescharacteristic
subgroupG/H
centerC23D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#103×C283C2
socleC23×C283C2×D4
hypercenterC2×#103D283
hypocenterC283C2×#449
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C22×#17985393C2semidirect
2. C22×#17985379C2semidirect
3. C22×D2264C2semidirect
4. C2×#22583585C2semidirect
5. #31826613C2direct (N × H)
6. C2×#22583530C2semidirect
7. C2×(C2×D283)⋊C8C2semidirect
8. C2×#103×C283C2semidirect
12. C2×#17985393C22semidirect
20. C2×#17985379C22semidirect
22. C2×D2264C22semidirect
25. #22583585C22semidirect
27. #22583530C22semidirect
28. (C2×D283)⋊C8C22semidirect
32. #103×C283C22semidirect
48. C2×D1132D4semidirect
65. C2×Q8×C283D4semidirect
93. D1132C2×D4semidirect
104. Q8×C283C2×D4semidirect
136. C2×C283#449semidirect
143. C283C2×#449semidirect
150. C2×#103D283semidirect
174. #103C2×D283semidirect
185. C2×Q8D1132semidirect
233. Q8C2×D1132semidirect
283. C2#31826613direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#179853932
C22×#179853792
C22×D22642
C2×#225835852
#318266132
C2×#225835302
C2×(C2×D283)⋊C82
C2×#103×C2832
C2×#449283