Finite Group Databasebeta

← C2×#31826712 #49130850

Subgroups — C2×#31826712 #49130850

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×#17985381C211yesmaximal, characteristic, complemented
2C22×#17985375C211yesmaximal, characteristic, complemented
3C2×#22583590C211yesmaximal, characteristic, complemented
4C2×#22583585C211yesmaximal, characteristic
5#31826712C218yesmaximal, direct product factor
6C2×#22583533C211yesmaximal, characteristic, complemented
7C2×#22583530C211yesmaximal, characteristic, complemented
8C2×#107×C283C211yesmaximal, characteristic, complemented
9C22×Dic566C2211yescharacteristic
10C22×D1132—21no—
11C22×D1132C2211yescharacteristic
12C22×C4×D283C2211yescharacteristic
13C2×#17985381—24no—
14C2×#17985381C2214yescomplemented
15C2×#17985375—24no—
16C2×#17985375C2214yescomplemented
17C22×C283⋊C8C2211yescharacteristic
18#22583590—22no—
19#22583590C2214yescomplemented
20#22583585—22no—
21#22583585C2214yes—
22C2×C4⋊Dic283—21no—
23C2×(C2×D283)⋊C4—21no—
24C2×(C2×D283)⋊C4—21no—
25#22583533C2214yescomplemented
26#22583530C2214yescomplemented
27C22×C8×C283C2211yescharacteristic
28C2×C4⋊C4×C283C2211yescharacteristic
29C2×C4⋊C4×C283C2211yescharacteristic
30#107×C283C2214yescomplemented
31C23×D283—21no—
32C23×D283D411yescharacteristic
33C2×Dic566—21no—
34C2×Dic566—22no—
35C2×Dic566—22no—
36C2×Dic566C2312yes—
37C2×D1132—24no—
38C2×D1132—22no—
39C2×D1132—21no—
40C2×D1132—22no—
41C2×D1132—44no—
42C2×D1132C2312yes—
43C22×Dic283—21no—
44C22×Dic283D411yescharacteristic
45C2×C4×D283—22no—
46C2×C4×D283—22no—
47C2×C4×D283D412yes—
48C2×C4×D283C2312yes—
49#17985381—28no—
50#17985375—28no—
51C2×C283⋊C8—22no—
52C2×C283⋊C8C2312yes—
53C4⋊Dic283—24no—
54(C2×D283)⋊C4—24no—
55(C2×D283)⋊C4—24no—
56C22×C4×C283—21no—
57C22×C4×C283—21no—
58C22×C4×C283C2311yescharacteristic
59C2×C8×C283D414yescomplemented
60C2×C8×C283C2312yes—
61C4⋊C4×C283—21no—
62C4⋊C4×C283—21no—
63C4⋊C4×C283C2312yes—
64C4⋊C4×C283C2312yes—
65C22×D283—22no—
66C22×D283—22no—
67C22×D283—22no—
68C22×D283—22no—
69C22×D283—42no—
70C22×D283—42no—
71C22×D283—42no—
72C22×D283C2×D412yes—
73Dic566—22no—
74Dic566—22no—
75Dic566—42no—
76D1132—22no—
77D1132—22no—
78D1132—48no—
79D1132—42no—
80C2×Dic283—22no—
81C2×Dic283—22no—
82C2×Dic283—42no—
83C2×Dic283C2×D412yes—
84C4×D283—24no—
85C4×D283—22no—
86C4×D283—22no—
87C283⋊C8—22no—
88C23×C283C2×D411yescharacteristic
89C2×C4×C283—22no—
90C2×C4×C283—22no—
91C2×C4×C283—42no—
92C2×C4×C283—42no—
93C2×C4×C283C2×D411yescharacteristic
94C2×C4×C283C2×D412yes—
95C2×C4×C283#4112yes—
96C2×C4×C283C2411yescharacteristic
97C8×C283C2×D414yescomplemented
98C22×C283#12112yes—
99C22×C283AGL(1,ℤ/8)12yes—
100C22×C283#13712yes—
101C22×C283C22×D411yescharacteristic
102C2×D283—22no—
103C2×D283—22no—
104C2×D283—22no—
105C2×D283—44no—
106C2×D283—42no—
107C2×D283—42no—
108C2×D283—42no—
109C2×D283—84no—
110C4×C283—42no—
111C4×C283—42no—
112C4×C283#12112yes—
113C4×C283C22×D411yescharacteristic
114C4×C283C2×#4111yescharacteristic
115Dic283—22no—
116Dic283—42no—
117C2×C283#46814yescomplemented
118C2×C283C2×#12111yescharacteristic
119C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
120C2×C283C2×#13711yescharacteristic
121D283—42no—
122D283—82no—
123C283C2×#46811yescharacteristic, complemented, Sylow
124C2×#468—2831nomaximal, Sylow
125C22×SD16—2831no—
126C22×M16—2831no—
127C2×C22⋊Q8—2831no—
128C2×#121—2831no—
129#468—2838no—
130C2×#107D28311yescharacteristic, complemented
131C2×#103—2831no—
132C2×#102—2831no—
133C22×Q8—2831no—
134C22×D4—2831no—
135C22×D4—5661no—
136C23×C4—2831no—
137C2×SD16—2834no—
138C2×SD16—5664no—
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—5661no—
148C2×C4⋊C4C2×D28311yescharacteristic
149C2×C4⋊C4C2×D28311yescharacteristic
150C2×C22⋊C4—5661no—
151C2×C22⋊C4—5661no—
152#107C2×D28314yescomplemented
153#103—2834no—
154#102—2834no—
155C24—2831no—
156C24—5661no—
157C2×Q8—2832no—
158C2×Q8—5661no—
159C2×Q8—5662no—
160C2×Q8—5662no—
161C2×D4—2832no—
162C2×D4—5664no—
163C2×D4—5661no—
164C2×D4—5662no—
165C2×D4—5662no—
166C2×D4—11324no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—2831no—
170C22×C4—2832no—
171C22×C4—2832no—
172C22×C4—5662no—
173C22×C4—5662no—
174C22×C4—5661no—
175C22×C4C22×D28311yescharacteristic
176SD16—5668no—
177M16—5668no—
178C2×C8—2832no—
179C2×C8—5662no—
180C2×C8D113214yescomplemented
181C2×C8C22×D28312yes—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—5664no—
185C4⋊C4C22×D28312yes—
186C4⋊C4C22×D28312yes—
187C22⋊C4—5664no—
188C22⋊C4—5664no—
189C23—2832no—
190C23—5662no—
191C23—5662no—
192C23—5662no—
193C23—5662no—
194C23—11322no—
195C23—11322no—
196C23—11322no—
197C23D4×D28311yescharacteristic
198Q8—5662no—
199Q8—5662no—
200Q8—11322no—
201D4—5662no—
202D4—5662no—
203D4—11328no—
204D4—11322no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—2832no—
210C2×C4—5662no—
211C2×C4—5664no—
212C2×C4—5662no—
213C2×C4—5662no—
214C2×C4—5662no—
215C2×C4—11322no—
216C2×C4D4×D28311yescharacteristic
217C2×C4C2×D113212yes—
218C2×C4#1798539312yes—
219C2×C4C23×D28311yescharacteristic
220C8—5662no—
221C8C2×D113214yescomplemented
222C22—5662no—
223C22—5662no—
224C22—5662no—
225C22—11324no—
226C22—11322no—
227C22—11322no—
228C22—11322no—
229C22—22644no—
230C22#2258358512yes—
231C22#2258363412yes—
232C22#2258364212yes—
233C22C2×D4×D28311yescharacteristic
234C4—42no—
235C4—42no—
236C4—5662no—
237C4—11322no—
238C4#2258358512yes—
239C4C22×D113211yescharacteristic
240C4C2×#1798539311yescharacteristic
241C2—11322no—
242C2—22642no—
243C2#3182671214yesdirect product factor
244C2C2×#2258358511yescharacteristic
245C2C2×#2258363411yescharacteristic
246C2C2×#2258364211yescharacteristic
subgroupG/H
centerC23D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#107×C283C2
socleC23×C283C2×D4
prime radicalC2×#22583585C2
hypercenterC2×#107D283
hypocenterC283C2×#468
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C22×#17985381C2semidirect
2. C22×#17985375C2semidirect
3. C2×#22583590C2semidirect
5. #31826712C2direct (N × H)
6. C2×#22583533C2semidirect
7. C2×#22583530C2semidirect
8. C2×#107×C283C2semidirect
14. C2×#17985381C22semidirect
16. C2×#17985375C22semidirect
19. #22583590C22semidirect
25. #22583533C22semidirect
26. #22583530C22semidirect
30. #107×C283C22semidirect
59. C2×C8×C283D4semidirect
97. C8×C283C2×D4semidirect
117. C2×C283#468semidirect
123. C283C2×#468semidirect
130. C2×#107D283semidirect
152. #107C2×D283semidirect
180. C2×C8D1132semidirect
221. C8C2×D1132semidirect
243. C2#31826712direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#179853812
C22×#179853752
C2×#225835902
C2×#225835852
#318267122
C2×#225835332
C2×#225835302
C2×#107×C2832
C2×#468283