Finite Group Databasebeta

← #49131269

Subgroups — #49131269

Order 36224.

448 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 145 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#31827022C211yesmaximal, characteristic, complemented
2#31826795C212yesmaximal, complemented
3#31826755C212yesmaximal, complemented
4#31826670C212yesmaximal, complemented
5#31826616C212yesmaximal
6C4×#17985380C214yesmaximal, complemented
7#31826518C211yesmaximal, characteristic, complemented
8C2×C4×D4×C283C211yesmaximal, characteristic
9C2×#17985380C2214yes—
10#22583610C2211yescharacteristic, complemented
11#22583610C2211yescharacteristic, complemented
12#22583602—21no—
13#22583589—21no—
14#22583589C2212yes—
15C4×Dic566—21no—
16C4×Dic566C2212yescomplemented
17#22583569—21no—
18#22583541C2214yescomplemented
19C4⋊(C283⋊C8)C2212yescomplemented
20#22583533C2214yescomplemented
21#22583531C2214yes—
22C22⋊(C283⋊C8)C2212yes—
23C4×C283⋊C8C2212yescomplemented
24C22×D4×C283C2211yescharacteristic
25C23×C4×C283—21no—
26C4×D4×C283—21no—
27C4×D4×C283—21no—
28C4×D4×C283C2212yes—
29C4×D4×C283C2212yes—
30C2×C4⋊C4×C283C2211yescharacteristic
31C2×C22⋊C4×C283—21no—
32C2×C42×C283C2211yescharacteristic
33C2×Dic566—21no—
34C2×Dic566C2312yes—
35#17985380—28no—
36C2×C283⋊C8C2314yes—
37C4⋊Dic283—21no—
38C4⋊Dic283—21no—
39C4⋊Dic283—21no—
40C4⋊Dic283C2312yes—
41Dic283⋊C4—22no—
42Dic283⋊C4—22no—
43C22⋊Dic283—22no—
44C4×Dic283—22no—
45C24×C283—21no—
46C2×D4×C283—24no—
47C2×D4×C283—21no—
48C2×D4×C283C2312yes—
49C22×C4×C283—21no—
50C22×C4×C283—22no—
51C22×C4×C283—22no—
52C22×C4×C283—44no—
53C22×C4×C283D411yescharacteristic
54C22×C4×C283D411yescharacteristic
55C22×C4×C283C2311yescharacteristic
56C4⋊C4×C283—21no—
57C4⋊C4×C283C2312yes—
58C22⋊C4×C283—22no—
59C22⋊C4×C283—22no—
60C42×C283D411yescharacteristic
61C42×C283D411yescharacteristic
62C42×C283C2311yescharacteristic
63C42×C283C2311yescharacteristic
64Dic566—24no—
65Dic566—42no—
66C2×Dic283—22no—
67C2×Dic283—22no—
68C283⋊C8—24no—
69C23×C283—24no—
70C23×C283—22no—
71C23×C283—42no—
72C23×C283—42no—
73C23×C283C2×D411yescharacteristic
74D4×C283—24no—
75D4×C283—22no—
76D4×C283#4114yes—
77C2×C4×C283—22no—
78C2×C4×C283—22no—
79C2×C4×C283—41no—
80C2×C4×C283—42no—
81C2×C4×C283—44no—
82C2×C4×C283—44no—
83C2×C4×C283SD1614yescomplemented
84C2×C4×C283C2×D411yescharacteristic
85C2×C4×C283C2×D411yescharacteristic
86C2×C4×C283C2×D411yescharacteristic
87C2×C4×C283C2×D411yescharacteristic
88C2×C4×C283C2×D411yescharacteristic
89C2×C4×C283C2411yescharacteristic
90C22×C283—21no—
91C22×C283—21no—
92C22×C283—24no—
93C22×C283—48no—
94C22×C283—42no—
95C22×C283—42no—
96C22×C283C2×SD1612yes—
97C22×C283C22×D411yescharacteristic
98C4×C283—21no—
99C4×C283—21no—
100C4×C283—21no—
101C4×C283—42no—
102C4×C283C2×SD1612yes—
103C4×C283C2×SD1612yes—
104C4×C283C2×#4112yes—
105Dic283—42no—
106Dic283—42no—
107C2×C283—22no—
108C2×C283—44no—
109C2×C283#52511yescharacteristic
110C2×C283C22×SD1611yescharacteristic
111C2×C283#57511yescharacteristic
112C283#310111yescharacteristic, complemented, Sylow
113#3101—2831nomaximal, Sylow
114#533—2831no—
115C2×C4×D4D28311yescharacteristic
116#483—2832no—
117#476—2832no—
118#461—2832no—
119#450—2832no—
120C4×SD16—2834no—
121#431—2831no—
122C22×D4C2×D28311yescharacteristic
123C23×C4—21no—
124C2×SD16—2834no—
125C4⋊Q8—2831no—
126C4⋊Q8—2831no—
127#125—5661no—
128C22⋊Q8—2832no—
129C22⋊Q8—5661no—
130C4×Q8—2832no—
131C4×Q8—5661no—
132C4×D4—21no—
133C4×D4—21no—
134C4×D4C2×D28312yes—
135C4×D4C2×D28312yes—
136#117—5661no—
137C2×C4⋊C4C2×D28311yescharacteristic
138C2×C22⋊C4—21no—
139C2×C42C2×D28311yescharacteristic
140#106—2834no—
141C4⋊C8—2832no—
142#103—2834no—
143#102—2834no—
144C22⋊C8—2832no—
145C4×C8—2832no—
146C24—21no—
147C2×Q8—2832no—
148C2×Q8—5661no—
149C2×D4—24no—
150C2×D4—21no—
151C2×D4C22×D28312yes—
152C22×C4—21no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—44no—
156C22×C4C22⋊D28311yescharacteristic
157C22×C4C22⋊D28311yescharacteristic
158C22×C4C22×D28311yescharacteristic
159SD16—5668no—
160C2×C8—2834no—
161C4⋊C4—21no—
162C4⋊C4—2832no—
163C4⋊C4—5662no—
164C4⋊C4—5662no—
165C4⋊C4—5661no—
166C4⋊C4—5661no—
167C4⋊C4—5661no—
168C4⋊C4C22×D28312yes—
169C22⋊C4—22no—
170C22⋊C4—22no—
171C22⋊C4—5662no—
172C42—5662no—
173C42C22⋊D28311yescharacteristic
174C42C22⋊D28311yescharacteristic
175C42C22×D28311yescharacteristic
176C42C22×D28311yescharacteristic
177C23—24no—
178C23—22no—
179C23—42no—
180C23—42no—
181C23C2×C22⋊D28311yescharacteristic
182Q8—5664no—
183Q8—11322no—
184D4—24no—
185D4—22no—
186D4#1798539214yes—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—41no—
190C2×C4—42no—
191C2×C4—44no—
192C2×C4—44no—
193C2×C4—5662no—
194C2×C4—5662no—
195C2×C4#1798538014yescomplemented
196C2×C4C2×C22⋊D28311yescharacteristic
197C2×C4C2×C22⋊D28311yescharacteristic
198C2×C4C2×C22⋊D28311yescharacteristic
199C2×C4C2×C22⋊D28311yescharacteristic
200C2×C4C2×C22⋊D28311yescharacteristic
201C2×C4C23×D28311yescharacteristic
202C8—5664no—
203C22—21no—
204C22—21no—
205C22—24no—
206C22—48no—
207C22—42no—
208C22—42no—
209C22C2×#1798538012yes—
210C22C22×C22⋊D28311yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—11322no—
216C4—11322no—
217C4C2×#1798538012yes—
218C4C2×#1798538012yes—
219C4C2×#1798539212yes—
220C2—22no—
221C2—44no—
222C2#3182697611yescharacteristic
223C2C22×#1798538011yescharacteristic
224C2#3182726311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×C4×D4×C283C2
socleC22×C283C22×D4
prime radicalC22×D4×C283C22
hypercenterC2×C4×D4D283
hypocenterC283#3101
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #31827022C2semidirect
2. #31826795C2semidirect
3. #31826755C2semidirect
4. #31826670C2semidirect
6. C4×#17985380C2semidirect
7. #31826518C2semidirect
10. #22583610C22semidirect
11. #22583610C22semidirect
16. C4×Dic566C22semidirect
18. #22583541C22semidirect
19. C4⋊(C283⋊C8)C22semidirect
20. #22583533C22semidirect
23. C4×C283⋊C8C22semidirect
83. C2×C4×C283SD16semidirect
112. C283#3101semidirect
195. C2×C4#17985380semidirect

Maximal subgroups

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

subgroupindex
#318270222
#318267952
#318267552
#318266702
#318266162
C4×#179853802
#318265182
C2×C4×D4×C2832
#3101283