Finite Group Databasebeta

← C2×#31826787 #49131143

Subgroups — C2×#31826787 #49131143

Order 36224.

468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22583581C211yesmaximal, characteristic
2C2×#22583568C211yesmaximal, characteristic, complemented
3#31826787C218yesmaximal, direct product factor
4C2×#22583544C211yesmaximal, characteristic, complemented
5C2×#22583541C211yesmaximal, characteristic, complemented
6C2×#22583531C211yesmaximal, characteristic, complemented
7C2×(C2×D283)⋊C8C211yesmaximal, characteristic, complemented
8C2×#102×C283C211yesmaximal, characteristic, complemented
9C22×C22⋊D283—21no—
10C22×C4×D283C2211yescharacteristic
11C22×C283⋊C8C2211yescharacteristic
12#22583581—22no—
13#22583581C2214yes—
14#22583568—22no—
15#22583568C2214yescomplemented
16C2×C4⋊Dic283C2211yescharacteristic
17C2×C4⋊Dic283C2211yescharacteristic
18C2×C22⋊Dic283—21no—
19C2×(C2×D283)⋊C4—21no—
20C2×C4×Dic283—21no—
21#22583544C2214yescomplemented
22#22583541C2214yescomplemented
23#22583531C2214yescomplemented
24(C2×D283)⋊C8C2214yescomplemented
25C22×D4×C283C2211yescharacteristic
26C22×C8×C283C2211yescharacteristic
27C2×C4⋊C4×C283C2211yescharacteristic
28#102×C283C2214yescomplemented
29C23×D283D411yescharacteristic
30C2×C22⋊D283—24no—
31C2×C22⋊D283—44no—
32C22×Dic283—21no—
33C22×Dic283—21no—
34C22×Dic283D411yescharacteristic
35C2×C4×D283—22no—
36C2×C4×D283—22no—
37C2×C4×D283D412yes—
38C2×C4×D283C2312yes—
39C2×C283⋊C8—22no—
40C2×C283⋊C8C2312yes—
41C4⋊Dic283—21no—
42C4⋊Dic283—21no—
43C4⋊Dic283C2312yes—
44C4⋊Dic283C2312yes—
45C22⋊Dic283—24no—
46(C2×D283)⋊C4—24no—
47C4×Dic283—24no—
48C24×C283—21no—
49C2×D4×C283—21no—
50C2×D4×C283—22no—
51C2×D4×C283—22no—
52C2×D4×C283C2312yes—
53C22×C4×C283—21no—
54C22×C4×C283C2311yescharacteristic
55C2×C8×C283—22no—
56C2×C8×C283C2312yes—
57C4⋊C4×C283—21no—
58C4⋊C4×C283C2312yes—
59C22×D283—22no—
60C22×D283—22no—
61C22×D283—22no—
62C22×D283C2×D412yes—
63C22⋊D283—48no—
64C2×Dic283—22no—
65C2×Dic283—22no—
66C2×Dic283—22no—
67C2×Dic283—42no—
68C2×Dic283—42no—
69C2×Dic283C2×D412yes—
70C4×D283—24no—
71C4×D283—22no—
72C4×D283—22no—
73C283⋊C8—22no—
74C23×C283—22no—
75C23×C283—42no—
76C23×C283—42no—
77C23×C283—42no—
78C23×C283C2×D411yescharacteristic
79D4×C283—22no—
80D4×C283—22no—
81D4×C283—42no—
82C2×C4×C283—22no—
83C2×C4×C283—42no—
84C2×C4×C283C2×D411yescharacteristic
85C2×C4×C283#4112yes—
86C2×C4×C283#4112yes—
87C2×C4×C283C2411yescharacteristic
88C8×C283—22no—
89C22×C283—42no—
90C22×C283—42no—
91C22×C283—42no—
92C22×C283—84no—
93C22×C283#12312yes—
94C22×C283#13512yes—
95C22×C283AGL(1,ℤ/8)12yes—
96C22×C283C22×D411yescharacteristic
97C2×D283—22no—
98C2×D283—22no—
99C2×D283—22no—
100C2×D283—44no—
101C4×C283—42no—
102C4×C283#12312yes—
103C4×C283C2×#4111yescharacteristic
104C4×C283C2×#4111yescharacteristic
105Dic283—22no—
106Dic283—42no—
107Dic283—42no—
108C2×C283—82no—
109C2×C283#48214yescomplemented
110C2×C283C2×#12311yescharacteristic
111C2×C283C2×#13511yescharacteristic
112C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
113D283—42no—
114C283C2×#48211yescharacteristic, complemented, Sylow
115C2×#482—2831nomaximal, Sylow
116C2×#121—2831no—
117C2×#117—2831no—
118#482—2838no—
119C2×#107—2831no—
120C2×#106—2831no—
121C2×#102—2831no—
122C2×#102D28311yescharacteristic, complemented
123C2×C22⋊C8—2831no—
124C22×D4—5661no—
125C22×D4C2×D28311yescharacteristic
126C23×C4—2831no—
127C22×C8—2831no—
128C22×C8C2×D28311yescharacteristic
129#121—2834no—
130#121—5662no—
131#117—2834no—
132#117—5662no—
133C2×C4⋊C4—2831no—
134C2×C4⋊C4—2831no—
135C2×C4⋊C4C2×D28311yescharacteristic
136C2×C22⋊C4—5661no—
137C2×C22⋊C4—5661no—
138C2×C42—5661no—
139#107—2834no—
140#106—2834no—
141#102—2834no—
142#102C2×D28314yescomplemented
143C22⋊C8—2834no—
144C24—21no—
145C24—2831no—
146C2×D4—21no—
147C2×D4—22no—
148C2×D4—22no—
149C2×D4—5664no—
150C2×D4—11324no—
151C2×D4C22×D28312yes—
152C22×C4—21no—
153C22×C4—2831no—
154C22×C4—2832no—
155C22×C4—2832no—
156C22×C4—5662no—
157C22×C4—5662no—
158C22×C4—5661no—
159C22×C4—5661no—
160C22×C4C22×D28311yescharacteristic
161C2×C8—22no—
162C2×C8—2832no—
163C2×C8—5662no—
164C2×C8C22×D28312yes—
165C4⋊C4—21no—
166C4⋊C4—2832no—
167C4⋊C4—2832no—
168C4⋊C4—5661no—
169C4⋊C4—5661no—
170C4⋊C4C22×D28312yes—
171C22⋊C4—5664no—
172C22⋊C4—5664no—
173C42—5664no—
174C23—22no—
175C23—42no—
176C23—42no—
177C23—42no—
178C23—2832no—
179C23—5662no—
180C23—5662no—
181C23—5662no—
182C23D4×D28311yescharacteristic
183D4—22no—
184D4—22no—
185D4—42no—
186D4—11328no—
187C2×C4—22no—
188C2×C4—42no—
189C2×C4—2832no—
190C2×C4—5662no—
191C2×C4—5664no—
192C2×C4—5662no—
193C2×C4—5662no—
194C2×C4—5662no—
195C2×C4—5662no—
196C2×C4—11322no—
197C2×C4—11322no—
198C2×C4D4×D28311yescharacteristic
199C2×C4#1798539112yes—
200C2×C4#1798539212yes—
201C2×C4C23×D28311yescharacteristic
202C8—22no—
203C8—5662no—
204C22—42no—
205C22—42no—
206C22—42no—
207C22—84no—
208C22—5662no—
209C22—5662no—
210C22—5662no—
211C22—11324no—
212C22#2258359212yes—
213C22#2258362912yes—
214C22#2258363712yes—
215C22C2×D4×D28311yescharacteristic
216C4—42no—
217C4—5662no—
218C4—11322no—
219C4—11322no—
220C4#2258359212yes—
221C4C2×#1798539111yescharacteristic
222C4C2×#1798539211yescharacteristic
223C2—82no—
224C2—11322no—
225C2#3182678714yesdirect product factor
226C2C2×#2258359211yescharacteristic
227C2C2×#2258362911yescharacteristic
228C2C2×#2258363711yescharacteristic
subgroupG/H
centerC23D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#102×C283C2
socleC23×C283C2×D4
prime radicalC2×#22583581C2
hypercenterC2×#102D283
hypocenterC283C2×#482
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#22583568C2semidirect
3. #31826787C2direct (N × H)
4. C2×#22583544C2semidirect
5. C2×#22583541C2semidirect
6. C2×#22583531C2semidirect
7. C2×(C2×D283)⋊C8C2semidirect
8. C2×#102×C283C2semidirect
15. #22583568C22semidirect
21. #22583544C22semidirect
22. #22583541C22semidirect
23. #22583531C22semidirect
24. (C2×D283)⋊C8C22semidirect
28. #102×C283C22semidirect
109. C2×C283#482semidirect
114. C283C2×#482semidirect
122. C2×#102D283semidirect
142. #102C2×D283semidirect
225. C2#31826787direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#225835812
C2×#225835682
#318267872
C2×#225835442
C2×#225835412
C2×#225835312
C2×(C2×D283)⋊C82
C2×#102×C2832
C2×#482283