Finite Group Databasebeta

← C2×#31826645 #49130593

Subgroups — C2×#31826645 #49130593

Order 36224.

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

normal subgroups only

This group has 760 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
2C2×#22583643C212yesmaximal, complemented
3C2×#22583597C211yesmaximal, characteristic, complemented
4#31826645C218yesmaximal, direct product factor
5C2×#22583536C212yesmaximal, complemented
6C2×#100×C283C211yesmaximal, characteristic, complemented
7#22583655—24no—
8#22583655—22no—
9#22583655C2214yes—
10C2×#17985392C2212yes—
11C2×#17985391—22no—
12C22×Dic566C2211yescharacteristic, complemented
13C22×C22⋊D283—22no—
14C2×D4×D283—22no—
15#22583643—24no—
16#22583643C2218yescomplemented
17C2×Dic1132—22no—
18C2×#17985381—22no—
19#22583597—22no—
20#22583597C2214yescomplemented
21C2×C22⋊Dic283—22no—
22C2×C4×Dic283C2211yescharacteristic, complemented
23#22583536C2218yescomplemented
24C22×D4×C283C2211yescharacteristic
25C2×M16×C283C2212yescomplemented
26#100×C283C2214yescomplemented
27C23×D283—22no—
28#17985392—22no—
29#17985392—22no—
30#17985392D414yes—
31#17985392C2314yes—
32#17985391—28no—
33#17985391—28no—
34C2×Dic566—21no—
35C2×Dic566—22no—
36C2×Dic566—22no—
37C2×Dic566D412yes—
38C2×Dic566C2312yescomplemented
39C2×D1132D412yes—
40C2×C22⋊D283—24no—
41C2×C22⋊D283—28no—
42C2×C22⋊D283—22no—
43C2×C22⋊D283—28no—
44D4×D283—28no—
45D4×D283—28no—
46C22×Dic283—22no—
47C22×Dic283—21no—
48C22×Dic283—21no—
49C2×C4×D283—22no—
50Dic1132—28no—
51#17985381—28no—
52C22⋊Dic283—28no—
53C4×Dic283—21no—
54C4×Dic283C2312yescomplemented
55C24×C283D412yes—
56C2×D4×C283—22no—
57C2×D4×C283—22no—
58C2×D4×C283D412yes—
59C2×D4×C283C2312yes—
60C22×C4×C283C2311yescharacteristic
61M16×C283—22no—
62M16×C283C2314yescomplemented
63C2×C8×C283—22no—
64C22×D283—22no—
65C22×D283—28no—
66C22×D283—84no—
67Dic566—22no—
68Dic566—24no—
69Dic566—42no—
70Dic566C2×D414yes—
71D1132—22no—
72D1132C2×D414yes—
73C22⋊D283—216no—
74C22⋊D283—24no—
75C22⋊D283—24no—
76C2×Dic283—28no—
77C2×Dic283—22no—
78C2×Dic283—22no—
79C2×Dic283—22no—
80C2×Dic283—42no—
81C2×Dic283—41no—
82C2×Dic283—41no—
83C4×D283—24no—
84C4×D283—24no—
85C23×C283—22no—
86C23×C283—22no—
87C23×C283—44no—
88C23×C283C2×D411yescharacteristic
89C23×C283C2×D414yes—
90D4×C283—24no—
91D4×C283—24no—
92C2×C4×C283C2×D412yes—
93C2×C4×C283C2×D412yes—
94C2×C4×C283C2×D411yescharacteristic
95C2×C4×C283C2411yescharacteristic
96C8×C283—24no—
97C22×C283—22no—
98C22×C283—24no—
99C22×C283—44no—
100C22×C283—44no—
101C22×C283—82no—
102C22×C283#12011yescharacteristic
103C22×C283#12011yescharacteristic
104C22×C283C22×D411yescharacteristic
105C2×D283—24no—
106C2×D283—44no—
107C2×D283—88no—
108C4×C283#12012yes—
109C4×C283C22×D412yes—
110Dic283—24no—
111Dic283—42no—
112Dic283—42no—
113C2×C283—21no—
114C2×C283—21no—
115C2×C283—44no—
116C2×C283#45512yescomplemented
117C2×C283C2×#12011yescharacteristic
118D283—44no—
119C283C2×#45511yescharacteristic, complemented, Sylow
120C2×#455—2831nomaximal, Sylow
121C2×H(5,𝔽2)—2831no—
122C2×#137—2832no—
123C2×#124—2831no—
124#455—2838no—
125C2×#104—2832no—
126C2×#100D28311yescharacteristic, complemented
127H(5,𝔽2)—2834no—
128H(5,𝔽2)—5664no—
129H(5,𝔽2)—5662no—
130C2×#41—2832no—
131C2×#41—5662no—
132C22×Q8—2831no—
133C22×D4—5662no—
134C22×D4—5662no—
135C22×D4C2×D28311yescharacteristic
136#137—2838no—
137#137—5664no—
138C2×Q16—5662no—
139C2×SD16—5662no—
140C2×M16C2×D28312yescomplemented
141#124—2834no—
142#124—5662no—
143C2×C22⋊C4—5662no—
144C2×C42—2831no—
145#104—2838no—
146#100C2×D28314yescomplemented
147C24—5662no—
148C24D113212yes—
149#41—2834no—
150#41—2834no—
151#41—5668no—
152#41—5668no—
153#41—5662no—
154#41—5662no—
155C2×Q8—2832no—
156C2×Q8—2832no—
157C2×Q8—5661no—
158C2×Q8—5662no—
159C2×Q8—5662no—
160C2×D4—22no—
161C2×D4—22no—
162C2×D4—2832no—
163C2×D4—5668no—
164C2×D4—5668no—
165C2×D4—5664no—
166C2×D4—5668no—
167C2×D4—5662no—
168C2×D4—5668no—
169C2×D4D113212yes—
170C2×D4C22×D28312yes—
171C22×C4—5662no—
172C22×C4—5662no—
173C22×C4—5661no—
174C22×C4—5661no—
175C22×C4C22×D28311yescharacteristic
176Q16—5668no—
177SD16—5668no—
178M16—22no—
179M16C22×D28314yescomplemented
180C2×C8—22no—
181C22⋊C4—5668no—
182C42—2832no—
183C42—5661no—
184C23—22no—
185C23—22no—
186C23—44no—
187C23—5668no—
188C23—5662no—
189C23—22644no—
190C23C2×D113211yescharacteristic
191C23C2×D113214yes—
192Q8—2834no—
193Q8—5662no—
194Q8—5664no—
195Q8—11322no—
196D4—24no—
197D4—24no—
198D4—2834no—
199D4—56616no—
200D4—5664no—
201D4—5664no—
202D4—5662no—
203C2×C4—5668no—
204C2×C4—5662no—
205C2×C4—5664no—
206C2×C4—5664no—
207C2×C4—5662no—
208C2×C4—5662no—
209C2×C4—11322no—
210C2×C4—11321no—
211C2×C4—11321no—
212C2×C4D4×D28312yes—
213C2×C4D4×D28312yes—
214C2×C4C2×D113211yescharacteristic
215C2×C4C23×D28311yescharacteristic
216C8—24no—
217C22—22no—
218C22—24no—
219C22—44no—
220C22—44no—
221C22—82no—
222C22—5664no—
223C22—11324no—
224C22—22648no—
225C22#2258358011yescharacteristic
226C22#2258358011yescharacteristic
227C22C22×D113211yescharacteristic
228C4—5664no—
229C4—11322no—
230C4—11322no—
231C4#2258358012yes—
232C4C2×D4×D28312yes—
233C2—21no—
234C2—21no—
235C2—44no—
236C2—11324no—
237C2#3182664512yesdirect product factor
238C2C2×#2258358011yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#100×C283C2
socleC22×C283#120
prime radicalC2×#22583655C2
hypercenterC2×#100D283
hypocenterC283C2×#455
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
2. C2×#22583643C2semidirect
3. C2×#22583597C2semidirect
4. #31826645C2direct (N × H)
5. C2×#22583536C2semidirect
6. C2×#100×C283C2semidirect
12. C22×Dic566C22semidirect
16. #22583643C22semidirect
20. #22583597C22semidirect
22. C2×C4×Dic283C22semidirect
23. #22583536C22semidirect
25. C2×M16×C283C22semidirect
26. #100×C283C22semidirect
38. C2×Dic566C23semidirect
54. C4×Dic283C23semidirect
62. M16×C283C23semidirect
116. C2×C283#455semidirect
119. C283C2×#455semidirect
126. C2×#100D283semidirect
140. C2×M16C2×D283semidirect
146. #100C2×D283semidirect
179. M16C22×D283semidirect
237. C2#31826645direct (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×#225836432
C2×#225835972
#318266452
C2×#225835362
C2×#100×C2832
C2×#455283