Finite Group Databasebeta

← C2×#31826635 #49130587

Subgroups — C2×#31826635 #49130587

Order 36224.

844 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 844 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#22583655C211yesmaximal, characteristic, complemented
2C2×#22583638C212yesmaximal, complemented
3C2×#22583606C211yesmaximal, characteristic, complemented
4#31826635C218yesmaximal, direct product factor
5C2×#22583536C212yesmaximal, complemented
6C2×#100×C283C211yesmaximal, characteristic, complemented
7#22583655—24no—
8#22583655—22no—
9#22583655C2214yescomplemented
10C2×#17985392C2212yes—
11C2×#17985391—22no—
12C22×D1132C2211yescharacteristic, complemented
13C22×C22⋊D283—22no—
14C22×C22⋊D283—22no—
15C2×D4×D283—22no—
16#22583638—24no—
17#22583638C2218yescomplemented
18C2×#17985381—22no—
19C2×D2264—22no—
20#22583606—22no—
21#22583606C2214yescomplemented
22C2×C4×Dic283C2211yescharacteristic, complemented
23#22583536C2218yescomplemented
24C22×D4×C283C2211yescharacteristic
25C2×M16×C283C2212yescomplemented
26#100×C283C2214yescomplemented
27C23×D283—22no—
28C23×D283—21no—
29#17985392—22no—
30#17985392—22no—
31#17985392D414yescomplemented
32#17985392C2314yes—
33#17985391—28no—
34#17985391—28no—
35C2×Dic566D412yescomplemented
36C2×D1132—22no—
37C2×D1132—22no—
38C2×D1132—21no—
39C2×D1132D412yescomplemented
40C2×D1132C2312yescomplemented
41C2×C22⋊D283—24no—
42C2×C22⋊D283—28no—
43C2×C22⋊D283—22no—
44C2×C22⋊D283—28no—
45C2×C22⋊D283—28no—
46C2×C22⋊D283—48no—
47D4×D283—28no—
48D4×D283—28no—
49C22×Dic283—22no—
50C22×Dic283—21no—
51C2×C4×D283—22no—
52#17985381—28no—
53D2264—28no—
54C4×Dic283—21no—
55C4×Dic283C2312yescomplemented
56C24×C283D412yes—
57C2×D4×C283—22no—
58C2×D4×C283—22no—
59C2×D4×C283D412yes—
60C2×D4×C283C2312yes—
61C22×C4×C283C2311yescharacteristic
62M16×C283—22no—
63M16×C283C2314yescomplemented
64C2×C8×C283—22no—
65C22×D283—22no—
66C22×D283—28no—
67C22×D283—22no—
68C22×D283—44no—
69C22×D283—41no—
70C22×D283—41no—
71C22×D283—84no—
72Dic566—22no—
73Dic566C2×D414yescomplemented
74D1132—22no—
75D1132—24no—
76D1132—42no—
77D1132C2×D414yescomplemented
78C22⋊D283—216no—
79C22⋊D283—24no—
80C22⋊D283—24no—
81C22⋊D283—416no—
82C2×Dic283—28no—
83C2×Dic283—24no—
84C2×Dic283—22no—
85C2×Dic283—22no—
86C4×D283—24no—
87C4×D283—24no—
88C23×C283—22no—
89C23×C283—22no—
90C23×C283—44no—
91C23×C283C2×D411yescharacteristic
92C23×C283C2×D414yes—
93D4×C283—24no—
94D4×C283—24no—
95C2×C4×C283C2×D412yes—
96C2×C4×C283C2×D412yes—
97C2×C4×C283C2×D411yescharacteristic
98C2×C4×C283C2411yescharacteristic
99C8×C283—24no—
100C22×C283—22no—
101C22×C283—24no—
102C22×C283—44no—
103C22×C283—44no—
104C22×C283—82no—
105C22×C283#12011yescharacteristic
106C22×C283#12011yescharacteristic
107C22×C283C22×D411yescharacteristic
108C2×D283—24no—
109C2×D283—44no—
110C2×D283—44no—
111C2×D283—42no—
112C2×D283—88no—
113C2×D283—82no—
114C2×D283—82no—
115C4×C283#12012yes—
116C4×C283C22×D412yes—
117Dic283—24no—
118Dic283—24no—
119C2×C283—21no—
120C2×C283—21no—
121C2×C283—44no—
122C2×C283#45312yescomplemented
123C2×C283C2×#12011yescharacteristic
124D283—44no—
125D283—82no—
126C283C2×#45311yescharacteristic, complemented, Sylow
127C2×#453—2831nomaximal, Sylow
128C2×H(5,𝔽2)—2831no—
129C2×AGL(1,ℤ/8)—2832no—
130C2×#127—2831no—
131#453—2838no—
132C2×#104—2832no—
133C2×#100D28311yescharacteristic, complemented
134H(5,𝔽2)—2834no—
135H(5,𝔽2)—5664no—
136H(5,𝔽2)—5662no—
137C2×#41—2832no—
138C2×#41—5662no—
139C22×D4—2831no—
140C22×D4—5662no—
141C22×D4—5662no—
142C22×D4—5662no—
143C22×D4C2×D28311yescharacteristic
144AGL(1,ℤ/8)—2838no—
145AGL(1,ℤ/8)—5664no—
146C2×SD16—5662no—
147C2×D8—5662no—
148C2×M16C2×D28312yescomplemented
149#127—2834no—
150#127—5662no—
151C2×C42—2831no—
152#104—2838no—
153#100C2×D28314yescomplemented
154C24—5662no—
155C24—5661no—
156C24D113212yes—
157#41—2834no—
158#41—2834no—
159#41—5668no—
160#41—5668no—
161#41—5662no—
162#41—5662no—
163C2×Q8—2832no—
164C2×D4—22no—
165C2×D4—22no—
166C2×D4—2832no—
167C2×D4—2832no—
168C2×D4—5668no—
169C2×D4—5668no—
170C2×D4—5664no—
171C2×D4—5668no—
172C2×D4—5662no—
173C2×D4—5668no—
174C2×D4—5668no—
175C2×D4—5662no—
176C2×D4—5662no—
177C2×D4—5661no—
178C2×D4—11328no—
179C2×D4D113212yes—
180C2×D4C22×D28312yes—
181C22×C4—5662no—
182C22×C4—5661no—
183C22×C4—5662no—
184C22×C4C22×D28311yescharacteristic
185SD16—5668no—
186D8—5668no—
187M16—22no—
188M16C22×D28314yescomplemented
189C2×C8—22no—
190C42—2832no—
191C42—5661no—
192C23—22no—
193C23—22no—
194C23—44no—
195C23—5668no—
196C23—5662no—
197C23—5662no—
198C23—11324no—
199C23—11321no—
200C23—11321no—
201C23—22644no—
202C23C2×D113211yescharacteristic
203C23C2×D113214yes—
204Q8—2834no—
205Q8—5662no—
206D4—24no—
207D4—24no—
208D4—2834no—
209D4—56616no—
210D4—5664no—
211D4—5664no—
212D4—5662no—
213D4—5664no—
214D4—113216no—
215D4—11322no—
216C2×C4—5668no—
217C2×C4—5664no—
218C2×C4—5662no—
219C2×C4—5662no—
220C2×C4—5664no—
221C2×C4—5664no—
222C2×C4D4×D28312yes—
223C2×C4D4×D28312yes—
224C2×C4C2×D113211yescharacteristic
225C2×C4C23×D28311yescharacteristic
226C8—24no—
227C22—22no—
228C22—24no—
229C22—44no—
230C22—44no—
231C22—82no—
232C22—5664no—
233C22—11324no—
234C22—11324no—
235C22—11322no—
236C22—22642no—
237C22—22648no—
238C22—22642no—
239C22#2258358011yescharacteristic
240C22#2258358011yescharacteristic
241C22C22×D113211yescharacteristic
242C4—5664no—
243C4—5664no—
244C4#2258358012yes—
245C4C2×D4×D28312yes—
246C2—21no—
247C2—21no—
248C2—44no—
249C2—11324no—
250C2—22642no—
251C2#3182663512yesdirect product factor
252C2C2×#2258358011yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#100×C283C2
socleC22×C283#120
hypercenterC2×#100D283
hypocenterC283C2×#453
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#22583655C2semidirect
2. C2×#22583638C2semidirect
3. C2×#22583606C2semidirect
4. #31826635C2direct (N × H)
5. C2×#22583536C2semidirect
6. C2×#100×C283C2semidirect
9. #22583655C22semidirect
12. C22×D1132C22semidirect
17. #22583638C22semidirect
21. #22583606C22semidirect
22. C2×C4×Dic283C22semidirect
23. #22583536C22semidirect
25. C2×M16×C283C22semidirect
26. #100×C283C22semidirect
31. #17985392D4semidirect
35. C2×Dic566D4semidirect
39. C2×D1132D4semidirect
40. C2×D1132C23semidirect
55. C4×Dic283C23semidirect
63. M16×C283C23semidirect
73. Dic566C2×D4semidirect
77. D1132C2×D4semidirect
122. C2×C283#453semidirect
126. C283C2×#453semidirect
133. C2×#100D283semidirect
148. C2×M16C2×D283semidirect
153. #100C2×D283semidirect
188. M16C22×D283semidirect
251. C2#31826635direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#225836552
C2×#225836382
C2×#225836062
#318266352
C2×#225835362
C2×#100×C2832
C2×#453283