Finite Group Databasebeta

← C2×#31826789 #49131145

Subgroups — C2×#31826789 #49131145

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×#22583584C211yesmaximal, characteristic
2#31826789C218yesmaximal, direct product factor
3C2×#22583543C211yesmaximal, characteristic, complemented
4C2×#22583541C211yesmaximal, characteristic, complemented
5C2×#22583530C211yesmaximal, characteristic, complemented
6C2×#22583530C211yesmaximal, characteristic, complemented
7C2×C22⋊(C283⋊C8)C211yesmaximal, characteristic, complemented
8C2×#117×C283C211yesmaximal, characteristic, complemented
9C22×D1132C2211yescharacteristic
10C22×C22⋊D283—21no—
11C22×C283⋊C8C2211yescharacteristic
12C22×C283⋊C8C2211yescharacteristic
13#22583584—22no—
14#22583584C2214yes—
15C2×C4⋊Dic283C2211yescharacteristic
16C2×(C2×D283)⋊C4—21no—
17#22583543C2214yescomplemented
18#22583541C2214yescomplemented
19#22583530C2214yescomplemented
20#22583530C2214yescomplemented
21C22⋊(C283⋊C8)C2214yescomplemented
22C23×C4×C283C2211yescharacteristic
23#117×C283—22no—
24#117×C283C2214yescomplemented
25C2×C4⋊C4×C283C2211yescharacteristic
26C2×C4⋊C4×C283C2211yescharacteristic
27C2×C22⋊C4×C283—21no—
28C2×C42×C283—21no—
29C23×D283—21no—
30C2×D1132—21no—
31C2×D1132—22no—
32C2×D1132—22no—
33C2×D1132C2312yes—
34C2×C22⋊D283—24no—
35C2×C22⋊D283—44no—
36C22×Dic283—21no—
37C2×C283⋊C8—22no—
38C2×C283⋊C8—22no—
39C2×C283⋊C8C2312yes—
40C2×C283⋊C8C2312yes—
41C4⋊Dic283—21no—
42C4⋊Dic283C2312yes—
43(C2×D283)⋊C4—24no—
44C24×C283D411yescharacteristic
45C22×C4×C283—22no—
46C22×C4×C283—22no—
47C22×C4×C283—21no—
48C22×C4×C283—21no—
49C22×C4×C283D411yescharacteristic
50C22×C4×C283D412yes—
51C22×C4×C283C2312yes—
52C22×C4×C283C2311yescharacteristic
53C4⋊C4×C283—21no—
54C4⋊C4×C283—21no—
55C4⋊C4×C283C2312yes—
56C4⋊C4×C283C2312yes—
57C22⋊C4×C283—24no—
58C42×C283—24no—
59C22×D283—22no—
60C22×D283—42no—
61C22×D283—42no—
62C22×D283—42no—
63D1132—22no—
64D1132—22no—
65D1132—42no—
66C22⋊D283—48no—
67C2×Dic283—22no—
68C2×Dic283—42no—
69C283⋊C8—22no—
70C283⋊C8—22no—
71C23×C283—22no—
72C23×C283—22no—
73C23×C283—22no—
74C23×C283C2×D412yes—
75C23×C283C2×D411yescharacteristic
76C2×C4×C283—22no—
77C2×C4×C283—24no—
78C2×C4×C283—22no—
79C2×C4×C283—22no—
80C2×C4×C283—22no—
81C2×C4×C283—22no—
82C2×C4×C283—42no—
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#12312yes—
94C22×C283#13512yes—
95C22×C283AGL(1,ℤ/8)12yes—
96C22×C283C22×D411yescharacteristic
97C2×D283—42no—
98C2×D283—42no—
99C2×D283—42no—
100C2×D283—84no—
101C4×C283—22no—
102C4×C283—42no—
103C4×C283—42no—
104C4×C283#12312yes—
105C4×C283C2×#4111yescharacteristic
106C4×C283C2×#4111yescharacteristic
107Dic283—42no—
108C2×C283—42no—
109C2×C283#48214yescomplemented
110C2×C283C2×#12311yescharacteristic
111C2×C283C2×#13511yescharacteristic
112C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
113D283—82no—
114C283C2×#48211yescharacteristic, complemented, Sylow
115C2×#482—2831nomaximal, Sylow
116C2×#121—2831no—
117C2×#117D28311yescharacteristic, complemented
118#482—2838no—
119C2×#107—2831no—
120C2×#106—2831no—
121C2×#102—2831no—
122C2×#102—2831no—
123C2×C22⋊C8—2831no—
124C22×D4—2831no—
125C22×D4—5661no—
126C23×C4C2×D28311yescharacteristic
127C22×C8—2831no—
128C22×C8—2831no—
129#121—2834no—
130#121—5662no—
131#117—22no—
132#117C2×D28314yescomplemented
133C2×C4⋊C4—2831no—
134C2×C4⋊C4C2×D28311yescharacteristic
135C2×C4⋊C4C2×D28311yescharacteristic
136C2×C22⋊C4—21no—
137C2×C22⋊C4—5661no—
138C2×C42—21no—
139#107—2834no—
140#106—2834no—
141#102—2834no—
142#102—2834no—
143C22⋊C8—2834no—
144C24—5661no—
145C24C22⋊D28311yescharacteristic
146C2×D4—2832no—
147C2×D4—5664no—
148C2×D4—5661no—
149C2×D4—5662no—
150C2×D4—5662no—
151C2×D4—11324no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—21no—
155C22×C4—21no—
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—21no—
167C4⋊C4—2832no—
168C4⋊C4—5661no—
169C4⋊C4C22×D28312yes—
170C4⋊C4C22×D28312yes—
171C22⋊C4—24no—
172C22⋊C4—5664no—
173C42—24no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23—5662no—
178C23—11322no—
179C23—11322no—
180C23—11322no—
181C23C2×C22⋊D28312yes—
182C23C2×C22⋊D28311yescharacteristic
183D4—5662no—
184D4—5662no—
185D4—11328no—
186D4—11322no—
187C2×C4—22no—
188C2×C4—24no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—5662no—
196C2×C4—11322no—
197C2×C4C2×C22⋊D28312yes—
198C2×C4C2×C22⋊D28311yescharacteristic
199C2×C4#1798539212yes—
200C2×C4#1798539212yes—
201C2×C4C23×D28311yescharacteristic
202C8—5662no—
203C8—5662no—
204C22—22no—
205C22—22no—
206C22—22no—
207C22—44no—
208C22—11322no—
209C22—11322no—
210C22—11322no—
211C22—22644no—
212C22#2258359312yes—
213C22#2258363012yes—
214C22#2258363512yes—
215C22C22×C22⋊D28311yescharacteristic
216C4—22no—
217C4—42no—
218C4—42no—
219C4—11322no—
220C4#2258359312yes—
221C4C2×#1798539211yescharacteristic
222C4C2×#1798539211yescharacteristic
223C2—42no—
224C2—22642no—
225C2#3182678914yesdirect product factor
226C2C2×#2258359311yescharacteristic
227C2C2×#2258363011yescharacteristic
228C2C2×#2258363511yescharacteristic
subgroupG/H
centerC23C2×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#117×C283C2
socleC23×C283C2×D4
prime radicalC2×#22583584C2
hypercenterC2×#117D283
hypocenterC283C2×#482
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #31826789C2direct (N × H)
3. C2×#22583543C2semidirect
4. C2×#22583541C2semidirect
5. C2×#22583530C2semidirect
6. C2×#22583530C2semidirect
7. C2×C22⋊(C283⋊C8)C2semidirect
8. C2×#117×C283C2semidirect
17. #22583543C22semidirect
18. #22583541C22semidirect
19. #22583530C22semidirect
20. #22583530C22semidirect
21. C22⋊(C283⋊C8)C22semidirect
24. #117×C283C22semidirect
109. C2×C283#482semidirect
114. C283C2×#482semidirect
117. C2×#117D283semidirect
132. #117C2×D283semidirect
225. C2#31826789direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#225835842
#318267892
C2×#225835432
C2×#225835412
C2×#225835302
C2×C22⋊(C283⋊C8)2
C2×#117×C2832
C2×#482283