Finite Group Databasebeta

← C2×#31826708 #49130846

Subgroups — C2×#31826708 #49130846

Order 36224.

544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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×#17985375C211yesmaximal, characteristic, complemented
2C2×#22583586C211yesmaximal, characteristic, complemented
3C2×#22583581C211yesmaximal, characteristic
4#31826708C218yesmaximal, direct product factor
5C2×#22583544C211yesmaximal, characteristic, complemented
6C2×#22583534C211yesmaximal, characteristic, complemented
7C2×#22583531C211yesmaximal, characteristic, complemented
8C22×SD16×C283C211yesmaximal, characteristic, complemented
9C22×C22⋊D283—21no—
10C22×C4×D283C2211yescharacteristic
11C2×#17985375—24no—
12C2×#17985375C2214yescomplemented
13C22×C283⋊C8C2211yescharacteristic
14#22583586—22no—
15#22583586C2214yescomplemented
16#22583581—22no—
17#22583581C2214yes—
18C2×C4⋊Dic283C2211yescharacteristic
19C2×C4⋊Dic283C2211yescharacteristic
20C2×Dic283⋊C4—21no—
21C2×C22⋊Dic283—21no—
22C2×(C2×D283)⋊C4—21no—
23#22583544C2214yescomplemented
24#22583534C2214yescomplemented
25#22583531C2214yescomplemented
26C22×Q8×C283C2211yescharacteristic
27C22×D4×C283C2211yescharacteristic
28C2×SD16×C283—24no—
29C2×SD16×C283C2214yescomplemented
30C22×C8×C283C2211yescharacteristic
31C23×D283D411yescharacteristic
32C2×C22⋊D283—24no—
33C2×C22⋊D283—44no—
34C22×Dic283—21no—
35C22×Dic283—21no—
36C22×Dic283D411yescharacteristic
37C2×C4×D283—22no—
38C2×C4×D283—22no—
39C2×C4×D283D412yes—
40C2×C4×D283C2312yes—
41#17985375—28no—
42C2×C283⋊C8—22no—
43C2×C283⋊C8C2312yes—
44C4⋊Dic283—21no—
45C4⋊Dic283—21no—
46C4⋊Dic283C2312yes—
47C4⋊Dic283C2312yes—
48Dic283⋊C4—24no—
49C22⋊Dic283—24no—
50(C2×D283)⋊C4—24no—
51C24×C283—21no—
52C2×Q8×C283—21no—
53C2×Q8×C283—22no—
54C2×Q8×C283—22no—
55C2×Q8×C283C2312yes—
56C2×D4×C283—22no—
57C2×D4×C283—21no—
58C2×D4×C283—22no—
59C2×D4×C283C2312yes—
60C22×C4×C283—21no—
61C22×C4×C283C2311yescharacteristic
62SD16×C283—28no—
63C2×C8×C283D414yescomplemented
64C2×C8×C283C2312yes—
65C22×D283—22no—
66C22×D283—22no—
67C22×D283—22no—
68C22×D283C2×D412yes—
69C22⋊D283—48no—
70C2×Dic283—22no—
71C2×Dic283—22no—
72C2×Dic283—22no—
73C2×Dic283—42no—
74C2×Dic283—42no—
75C2×Dic283C2×D412yes—
76C4×D283—24no—
77C4×D283—22no—
78C4×D283—22no—
79C283⋊C8—22no—
80C23×C283—22no—
81C23×C283—42no—
82C23×C283—42no—
83C23×C283—42no—
84C23×C283C2×D411yescharacteristic
85Q8×C283—22no—
86Q8×C283—22no—
87Q8×C283—42no—
88D4×C283—22no—
89D4×C283—22no—
90D4×C283—42no—
91C2×C4×C283—22no—
92C2×C4×C283—42no—
93C2×C4×C283C2×D411yescharacteristic
94C2×C4×C283C2×D412yes—
95C2×C4×C283#4112yes—
96C2×C4×C283C2411yescharacteristic
97C8×C283C2×D414yescomplemented
98C22×C283—42no—
99C22×C283—42no—
100C22×C283—42no—
101C22×C283—84no—
102C22×C283#12112yes—
103C22×C283AGL(1,ℤ/8)12yes—
104C22×C283#13712yes—
105C22×C283C22×D411yescharacteristic
106C2×D283—22no—
107C2×D283—22no—
108C2×D283—22no—
109C2×D283—44no—
110C4×C283—42no—
111C4×C283#12112yes—
112C4×C283C22×D411yescharacteristic
113C4×C283C2×#4111yescharacteristic
114Dic283—22no—
115Dic283—42no—
116Dic283—42no—
117C2×C283—82no—
118C2×C283#46814yescomplemented
119C2×C283C2×#12111yescharacteristic
120C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
121C2×C283C2×#13711yescharacteristic
122D283—42no—
123C283C2×#46811yescharacteristic, complemented, Sylow
124C2×#468—2831nomaximal, Sylow
125C22×SD16D28311yescharacteristic, complemented
126C22×M16—2831no—
127C2×C22⋊Q8—2831no—
128C2×#121—2831no—
129#468—2838no—
130C2×#107—2831no—
131C2×#103—2831no—
132C2×#102—2831no—
133C22×Q8C2×D28311yescharacteristic
134C22×D4—5661no—
135C22×D4C2×D28311yescharacteristic
136C23×C4—2831no—
137C2×SD16—24no—
138C2×SD16C2×D28314yescomplemented
139C2×M16—2834no—
140C2×M16—5664no—
141C22×C8—2831no—
142C22×C8C2×D28311yescharacteristic
143C22⋊Q8—2834no—
144C22⋊Q8—5662no—
145#121—2834no—
146#121—5662no—
147C2×C4⋊C4—2831no—
148C2×C4⋊C4—2831no—
149C2×C4⋊C4—5661no—
150C2×C22⋊C4—5661no—
151C2×C22⋊C4—5661no—
152#107—2834no—
153#103—2834no—
154#102—2834no—
155C24—21no—
156C24—2831no—
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8C22×D28312yes—
161C2×D4—21no—
162C2×D4—22no—
163C2×D4—22no—
164C2×D4—5664no—
165C2×D4—11324no—
166C2×D4C22×D28312yes—
167C22×C4—21no—
168C22×C4—2831no—
169C22×C4—2832no—
170C22×C4—2832no—
171C22×C4—5662no—
172C22×C4—5662no—
173C22×C4—5661no—
174C22×C4—5661no—
175C22×C4C22×D28311yescharacteristic
176SD16—28no—
177M16—5668no—
178C2×C8—2832no—
179C2×C8—5662no—
180C2×C8C22⋊D28314yescomplemented
181C2×C8C22×D28312yes—
182C4⋊C4—2832no—
183C4⋊C4—2832no—
184C4⋊C4—5664no—
185C4⋊C4—5661no—
186C4⋊C4—5661no—
187C22⋊C4—5664no—
188C22⋊C4—5664no—
189C23—22no—
190C23—42no—
191C23—42no—
192C23—42no—
193C23—2832no—
194C23—5662no—
195C23—5662no—
196C23—5662no—
197C23D4×D28311yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—42no—
201D4—22no—
202D4—22no—
203D4—42no—
204D4—11328no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—2832no—
208C2×C4—5662no—
209C2×C4—5664no—
210C2×C4—5662no—
211C2×C4—5662no—
212C2×C4—5662no—
213C2×C4—5662no—
214C2×C4—11322no—
215C2×C4—11322no—
216C2×C4D4×D28311yescharacteristic
217C2×C4C2×C22⋊D28312yes—
218C2×C4#1798539112yes—
219C2×C4C23×D28311yescharacteristic
220C8—5662no—
221C8C2×C22⋊D28314yescomplemented
222C22—42no—
223C22—42no—
224C22—42no—
225C22—84no—
226C22—5662no—
227C22—5662no—
228C22—5662no—
229C22—11324no—
230C22#2258358112yes—
231C22#2258363712yes—
232C22#2258363912yes—
233C22C2×D4×D28311yescharacteristic
234C4—42no—
235C4—5662no—
236C4—11322no—
237C4—11322no—
238C4#2258358112yes—
239C4C22×C22⋊D28311yescharacteristic
240C4C2×#1798539111yescharacteristic
241C2—82no—
242C2—11322no—
243C2#3182670814yesdirect product factor
244C2C2×#2258358111yescharacteristic
245C2C2×#2258363711yescharacteristic
246C2C2×#2258363911yescharacteristic
subgroupG/H
centerC23D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC22×SD16×C283C2
socleC23×C283C2×D4
prime radicalC2×#22583581C2
hypercenterC22×SD16D283
hypocenterC283C2×#468
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×#17985375C2semidirect
2. C2×#22583586C2semidirect
4. #31826708C2direct (N × H)
5. C2×#22583544C2semidirect
6. C2×#22583534C2semidirect
7. C2×#22583531C2semidirect
8. C22×SD16×C283C2semidirect
12. C2×#17985375C22semidirect
15. #22583586C22semidirect
23. #22583544C22semidirect
24. #22583534C22semidirect
25. #22583531C22semidirect
29. C2×SD16×C283C22semidirect
63. C2×C8×C283D4semidirect
97. C8×C283C2×D4semidirect
118. C2×C283#468semidirect
123. C283C2×#468semidirect
125. C22×SD16D283semidirect
138. C2×SD16C2×D283semidirect
180. C2×C8C22⋊D283semidirect
221. C8C2×C22⋊D283semidirect
243. C2#31826708direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#179853752
C2×#225835862
C2×#225835812
#318267082
C2×#225835442
C2×#225835342
C2×#225835312
C22×SD16×C2832
C2×#468283