Finite Group Databasebeta

← #49131633

Subgroups — #49131633

Order 36224.

484 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 129 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
1#31827018C211yesmaximal, characteristic, complemented
2C2×#22583606C211yesmaximal, characteristic
3#31826828C214yesmaximal, complemented
4#31826810C214yesmaximal, complemented
5#31826471C211yesmaximal, characteristic, complemented
6#31826470C211yesmaximal, characteristic, complemented
7#31826469C211yesmaximal, characteristic, complemented
8M16×Dic283C211yesmaximal, characteristic, complemented
9#418×C283C211yesmaximal, characteristic, complemented
10C22×D1132C2211yescharacteristic
11C22×C22⋊D283—22no—
12C2×#17985376C2211yescharacteristic
13#22583609C2212yescomplemented
14#22583606—22no—
15#22583606C2212yes—
16#22583606C2212yes—
17#22583601C2212yescomplemented
18#22583587—22no—
19C4×Dic566—22no—
20#22583569C2211yescharacteristic
21C2×C4×Dic283C2211yescharacteristic
22#22583532C2214yescomplemented
23#22583531C2214yescomplemented
24#22583530C2214yescomplemented
25#22583520C2212yescomplemented
26C8×Dic283C2212yescomplemented
27C22×D4×C283C2211yescharacteristic
28C2×M16×C283C2211yescharacteristic
29#117×C283C2211yescharacteristic
30#102×C283C2214yescomplemented
31C23×D283—21no—
32C2×Dic566—22no—
33C2×D1132—21no—
34C2×D1132—22no—
35C2×D1132—22no—
36C2×D1132C2312yes—
37C2×C22⋊D283—24no—
38C2×C22⋊D283—24no—
39C2×C22⋊D283—48no—
40C22×Dic283D412yes—
41#17985376—22no—
42C2×C283⋊C8C2312yes—
43C4⋊Dic283—22no—
44C4⋊Dic283C2312yes—
45Dic283⋊C4—22no—
46Dic283⋊C4—22no—
47C22⋊Dic283—21no—
48C4×Dic283—21no—
49C4×Dic283D412yes—
50C4×Dic283C2311yescharacteristic
51C4×Dic283C2311yescharacteristic
52C24×C283—21no—
53C2×D4×C283—21no—
54C2×D4×C283—22no—
55C2×D4×C283—22no—
56C2×D4×C283C2312yes—
57C22×C4×C283C2311yescharacteristic
58M16×C283—22no—
59C2×C8×C283C2312yes—
60C4⋊C4×C283C2312yes—
61C22⋊C4×C283—21no—
62C42×C283—21no—
63C22×D283—22no—
64C22×D283—44no—
65C22×D283—42no—
66Dic566—44no—
67D1132—22no—
68D1132—22no—
69D1132—42no—
70C22⋊D283—48no—
71C22⋊D283—48no—
72C2×Dic283—24no—
73C2×Dic283—22no—
74C2×Dic283C2×D412yes—
75C2×Dic283C2×D412yes—
76C283⋊C8—22no—
77C23×C283—22no—
78C23×C283—44no—
79C23×C283—42no—
80C23×C283C2×D411yescharacteristic
81D4×C283—22no—
82D4×C283—22no—
83D4×C283—42no—
84C2×C4×C283—22no—
85C2×C4×C283C2×D411yescharacteristic
86C2×C4×C283#4112yes—
87C2×C4×C283#4112yes—
88C2×C4×C283C2411yescharacteristic
89C8×C283—22no—
90C22×C283—22no—
91C22×C283—42no—
92C22×C283—44no—
93C22×C283—84no—
94C22×C283#12412yes—
95C22×C283C22×D411yescharacteristic
96C2×D283—42no—
97C2×D283—44no—
98C2×D283—84no—
99C4×C283—42no—
100C4×C283#12412yes—
101C4×C283C2×#4111yescharacteristic
102C4×C283C2×#4111yescharacteristic
103Dic283—22no—
104Dic283—42no—
105Dic283AGL(1,ℤ/8)14yes—
106C2×C283—22no—
107C2×C283—82no—
108C2×C283C2×#12411yescharacteristic
109C2×C283C2×AGL(1,ℤ/8)12yes—
110D283—82no—
111C283#313811yescharacteristic, complemented, Sylow
112#3138—2831nomaximal, Sylow
113#533—2831no—
114C2×#127—2831no—
115#490—2834no—
116#486—2834no—
117#418—2831no—
118#418—2831no—
119#418—2831no—
120#418D28311yescharacteristic, complemented
121C4×M16—2831no—
122C22×D4—2831no—
123C22×D4—5662no—
124C22×D4C2×D28311yescharacteristic
125C2×M16—2831no—
126C2×M16C2×D28311yescharacteristic
127C4⋊Q8—2832no—
128#127—2832no—
129#127—2832no—
130#127—5662no—
131#125—2832no—
132C22⋊Q8—5662no—
133C4×Q8—5662no—
134#117—2831no—
135#117C2×D28311yescharacteristic
136C2×C42—2831no—
137#102—2834no—
138#102—2834no—
139#102—2834no—
140#102C2×D28314yescomplemented
141#97—2832no—
142C4×C8—2832no—
143C24—21no—
144C24—5661no—
145C2×Q8—5662no—
146C2×D4—21no—
147C2×D4—22no—
148C2×D4—22no—
149C2×D4—2832no—
150C2×D4—5664no—
151C2×D4—5664no—
152C2×D4—5661no—
153C2×D4—5662no—
154C2×D4—5662no—
155C2×D4—11328no—
156C2×D4C22×D28312yes—
157C22×C4—2832no—
158C22×C4C22×D28311yescharacteristic
159M16—22no—
160M16—5662no—
161C2×C8—2832no—
162C2×C8C22×D28312yes—
163C4⋊C4—2832no—
164C4⋊C4—5662no—
165C4⋊C4—5662no—
166C4⋊C4—5662no—
167C4⋊C4C22×D28312yes—
168C22⋊C4—21no—
169C22⋊C4—5661no—
170C42—21no—
171C42—2832no—
172C42—2831no—
173C42—2831no—
174C42—5661no—
175C23—22no—
176C23—44no—
177C23—42no—
178C23—5662no—
179C23—11324no—
180C23—11322no—
181C23D4×D28311yescharacteristic
182Q8—11324no—
183D4—22no—
184D4—22no—
185D4—42no—
186D4—5662no—
187D4—5662no—
188D4—11328no—
189D4—11328no—
190D4—11322no—
191C2×C4—22no—
192C2×C4—2832no—
193C2×C4—2832no—
194C2×C4—5664no—
195C2×C4—5662no—
196C2×C4D4×D28311yescharacteristic
197C2×C4#1798539112yes—
198C2×C4#1798539212yes—
199C2×C4C23×D28311yescharacteristic
200C8—22no—
201C8—5662no—
202C22—22no—
203C22—42no—
204C22—44no—
205C22—84no—
206C22—11322no—
207C22—11324no—
208C22—22644no—
209C22#2258359612yes—
210C22C2×D4×D28311yescharacteristic
211C4—42no—
212C4—2834no—
213C4—5662no—
214C4—11322no—
215C4#2258359612yes—
216C4C2×#1798539111yescharacteristic
217C4C2×#1798539211yescharacteristic
218C2—22no—
219C2—82no—
220C2—22642no—
221C2C2×#2258359611yescharacteristic
222C2AGL(1,ℤ/8)×D28312yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#418×C283C2
socleC22×C283C22×D4
prime radicalC2×#22583606C2
hypercenter#418D283
hypocenterC283#3138
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #31827018C2semidirect
3. #31826828C2semidirect
4. #31826810C2semidirect
5. #31826471C2semidirect
6. #31826470C2semidirect
7. #31826469C2semidirect
8. M16×Dic283C2semidirect
9. #418×C283C2semidirect
13. #22583609C22semidirect
17. #22583601C22semidirect
22. #22583532C22semidirect
23. #22583531C22semidirect
24. #22583530C22semidirect
25. #22583520C22semidirect
26. C8×Dic283C22semidirect
30. #102×C283C22semidirect
111. C283#3138semidirect
120. #418D283semidirect
140. #102C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318270182
C2×#225836062
#318268282
#318268102
#318264712
#318264702
#318264692
M16×Dic2832
#418×C2832
#3138283