Finite Group Databasebeta

← C2×#31826786 #49131142

Subgroups — C2×#31826786 #49131142

Order 36224.

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

normal subgroups only

This group has 468 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×#22583569C211yesmaximal, characteristic, complemented
2#31826786C218yesmaximal, direct product factor
3C2×#22583543C211yesmaximal, characteristic, complemented
4C2×#22583541C211yesmaximal, characteristic, complemented
5C2×#22583531C211yesmaximal, characteristic, complemented
6C2×#22583531C211yesmaximal, characteristic, complemented
7C2×C22⋊(C283⋊C8)C211yesmaximal, characteristic, complemented
8C2×#121×C283C211yesmaximal, characteristic
9C22×C283⋊C8C2211yescharacteristic
10C22×C283⋊C8C2211yescharacteristic
11#22583569—22no—
12#22583569C2214yescomplemented
13C2×C4⋊Dic283C2211yescharacteristic
14C2×C4⋊Dic283C2211yescharacteristic
15C2×C22⋊Dic283—21no—
16C2×C4×Dic283—21no—
17#22583543C2214yescomplemented
18#22583541C2214yescomplemented
19#22583531C2214yescomplemented
20#22583531C2214yescomplemented
21C22⋊(C283⋊C8)C2214yescomplemented
22C22×D4×C283—21no—
23C22×D4×C283C2211yescharacteristic
24C23×C4×C283C2211yescharacteristic
25#121×C283—22no—
26#121×C283C2214yes—
27C2×C4⋊C4×C283C2211yescharacteristic
28C2×C22⋊C4×C283—21no—
29C22×Dic283—21no—
30C22×Dic283—21no—
31C2×C283⋊C8—22no—
32C2×C283⋊C8—22no—
33C2×C283⋊C8C2312yes—
34C2×C283⋊C8C2312yes—
35C4⋊Dic283—21no—
36C4⋊Dic283—21no—
37C4⋊Dic283C2312yes—
38C4⋊Dic283C2312yes—
39C22⋊Dic283—24no—
40C4×Dic283—24no—
41C24×C283—21no—
42C24×C283D411yescharacteristic
43C2×D4×C283—24no—
44C2×D4×C283—21no—
45C2×D4×C283—22no—
46C2×D4×C283—22no—
47C2×D4×C283—44no—
48C2×D4×C283C2312yes—
49C22×C4×C283—22no—
50C22×C4×C283—22no—
51C22×C4×C283—21no—
52C22×C4×C283D411yescharacteristic
53C22×C4×C283D412yes—
54C22×C4×C283C2312yes—
55C22×C4×C283C2311yescharacteristic
56C4⋊C4×C283—21no—
57C4⋊C4×C283C2312yes—
58C22⋊C4×C283—24no—
59C2×Dic283—22no—
60C2×Dic283—22no—
61C2×Dic283—42no—
62C2×Dic283—42no—
63C283⋊C8—22no—
64C283⋊C8—22no—
65C23×C283—22no—
66C23×C283—22no—
67C23×C283—22no—
68C23×C283—22no—
69C23×C283—42no—
70C23×C283—42no—
71C23×C283—42no—
72C23×C283C2×D412yes—
73C23×C283C2×D411yescharacteristic
74D4×C283—22no—
75D4×C283—22no—
76D4×C283—48no—
77D4×C283—42no—
78C2×C4×C283—22no—
79C2×C4×C283—24no—
80C2×C4×C283—22no—
81C2×C4×C283—22no—
82C2×C4×C283—22no—
83C2×C4×C283—42no—
84C2×C4×C283C2×D412yes—
85C2×C4×C283C2×D411yescharacteristic
86C2×C4×C283#4112yes—
87C2×C4×C283#4112yes—
88C2×C4×C283C2411yescharacteristic
89C22×C283—22no—
90C22×C283—22no—
91C22×C283—22no—
92C22×C283—44no—
93C22×C283—42no—
94C22×C283—42no—
95C22×C283—42no—
96C22×C283—84no—
97C22×C283#12312yes—
98C22×C283#13512yes—
99C22×C283AGL(1,ℤ/8)12yes—
100C22×C283C22×D411yescharacteristic
101C4×C283—22no—
102C4×C283—42no—
103C4×C283#12312yes—
104C4×C283C2×#4111yescharacteristic
105C4×C283C2×#4111yescharacteristic
106Dic283—42no—
107Dic283—42no—
108C2×C283—42no—
109C2×C283—82no—
110C2×C283#48214yescomplemented
111C2×C283C2×#12311yescharacteristic
112C2×C283C2×#13511yescharacteristic
113C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
114C283C2×#48211yescharacteristic, complemented, Sylow
115C2×#482—2831nomaximal, Sylow
116C2×#121D28311yescharacteristic
117C2×#117—2831no—
118#482—2838no—
119C2×#107—2831no—
120C2×#106—2831no—
121C2×#102—2831no—
122C2×#102—2831no—
123C2×C22⋊C8—2831no—
124C22×D4—21no—
125C22×D4C2×D28311yescharacteristic
126C23×C4C2×D28311yescharacteristic
127C22×C8—2831no—
128C22×C8—2831no—
129#121—22no—
130#121C2×D28314yes—
131#117—2834no—
132#117—5662no—
133C2×C4⋊C4—2831no—
134C2×C4⋊C4—2831no—
135C2×C4⋊C4C2×D28311yescharacteristic
136C2×C22⋊C4—21no—
137C2×C22⋊C4—5661no—
138C2×C42—5661no—
139#107—2834no—
140#106—2834no—
141#102—2834no—
142#102—2834no—
143C22⋊C8—2834no—
144C24—21no—
145C24C22⋊D28311yescharacteristic
146C2×D4—24no—
147C2×D4—21no—
148C2×D4—22no—
149C2×D4—22no—
150C2×D4—44no—
151C2×D4C22×D28312yes—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—21no—
155C22×C4—5661no—
156C22×C4—5661no—
157C22×C4C22⋊D28312yes—
158C22×C4C22⋊D28311yescharacteristic
159C22×C4C22×D28312yes—
160C22×C4C22×D28311yescharacteristic
161C2×C8—2832no—
162C2×C8—2832no—
163C2×C8—5662no—
164C2×C8—5662no—
165C4⋊C4—21no—
166C4⋊C4—2832no—
167C4⋊C4—2832no—
168C4⋊C4—5661no—
169C4⋊C4—5661no—
170C4⋊C4C22×D28312yes—
171C22⋊C4—24no—
172C22⋊C4—5664no—
173C42—5664no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23—22no—
178C23—42no—
179C23—42no—
180C23—42no—
181C23C2×C22⋊D28312yes—
182C23C2×C22⋊D28311yescharacteristic
183D4—22no—
184D4—22no—
185D4—48no—
186D4—42no—
187C2×C4—22no—
188C2×C4—24no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—42no—
193C2×C4—5662no—
194C2×C4—5662no—
195C2×C4—11322no—
196C2×C4—11322no—
197C2×C4C2×C22⋊D28312yes—
198C2×C4C2×C22⋊D28311yescharacteristic
199C2×C4#1798539112yes—
200C2×C4#1798539112yes—
201C2×C4C23×D28311yescharacteristic
202C8—5662no—
203C8—5662no—
204C22—22no—
205C22—22no—
206C22—22no—
207C22—44no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—84no—
212C22#2258359112yes—
213C22#2258363012yes—
214C22#2258363612yes—
215C22C22×C22⋊D28311yescharacteristic
216C4—22no—
217C4—42no—
218C4—11322no—
219C4—11322no—
220C4#2258359112yes—
221C4C2×#1798539111yescharacteristic
222C4C2×#1798539111yescharacteristic
223C2—42no—
224C2—82no—
225C2#3182678614yesdirect product factor
226C2C2×#2258359111yescharacteristic
227C2C2×#2258363011yescharacteristic
228C2C2×#2258363611yescharacteristic
subgroupG/H
centerC23C2×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting, prime radicalC2×#121×C283C2
socleC23×C283C2×D4
hypercenterC2×#121D283
hypocenterC283C2×#482
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#22583569C2semidirect
2. #31826786C2direct (N × H)
3. C2×#22583543C2semidirect
4. C2×#22583541C2semidirect
5. C2×#22583531C2semidirect
6. C2×#22583531C2semidirect
7. C2×C22⋊(C283⋊C8)C2semidirect
12. #22583569C22semidirect
17. #22583543C22semidirect
18. #22583541C22semidirect
19. #22583531C22semidirect
20. #22583531C22semidirect
21. C22⋊(C283⋊C8)C22semidirect
110. C2×C283#482semidirect
114. C283C2×#482semidirect
225. C2#31826786direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#225835692
#318267862
C2×#225835432
C2×#225835412
C2×#225835312
C2×C22⋊(C283⋊C8)2
C2×#121×C2832
C2×#482283