Finite Group Databasebeta

← #49131190

Subgroups — #49131190

Order 36224.

414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 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#31826803C214yesmaximal, complemented
3#31826786C214yesmaximal, complemented
4#31826508C212yesmaximal, complemented
5#31826466C212yesmaximal, complemented
6#31826429C211yesmaximal, characteristic, complemented
7#525×C283C211yesmaximal, characteristic
8C2×#17985376C2212yes—
9#22583569—22no—
10#22583569C2214yes—
11C2×C4⋊Dic283C2212yes—
12C2×C22⋊Dic283—21no—
13C2×C4×Dic283—21no—
14#22583543C2214yescomplemented
15#22583541C2214yescomplemented
16#22583534C2214yescomplemented
17#22583531C2214yescomplemented
18C22⋊(C283⋊C8)C2214yes—
19C2×#41×C283C2211yescharacteristic
20C23×C4×C283C2211yescharacteristic
21#123×C283—21no—
22C22⋊Q8×C283C2212yes—
23#121×C283C2212yes—
24#120×C283—21no—
25C4×D4×C283—22no—
26#117×C283C2211yescharacteristic
27C22×Dic283—22no—
28#17985376—24no—
29C2×C283⋊C8C2314yes—
30C4⋊Dic283—22no—
31C4⋊Dic283C2314yes—
32C22⋊Dic283—24no—
33C4×Dic283—24no—
34C24×C283D411yescharacteristic
35#41×C283—24no—
36C2×Q8×C283C2311yescharacteristic
37C2×D4×C283—22no—
38C2×D4×C283—21no—
39C2×D4×C283C2311yescharacteristic
40C22×C4×C283—24no—
41C22×C4×C283—21no—
42C22×C4×C283D411yescharacteristic
43C22×C4×C283D412yes—
44C22×C4×C283C2312yes—
45C22×C4×C283C2311yescharacteristic
46C4⋊C4×C283—22no—
47C4⋊C4×C283C2312yes—
48C22⋊C4×C283—21no—
49C22⋊C4×C283—22no—
50C22⋊C4×C283—22no—
51C42×C283—21no—
52C2×Dic283—24no—
53C2×Dic283—44no—
54C283⋊C8—24no—
55C23×C283—22no—
56C23×C283—21no—
57C23×C283—42no—
58C23×C283C2×D412yes—
59C23×C283C2×D411yescharacteristic
60Q8×C283—22no—
61D4×C283—22no—
62D4×C283—44no—
63D4×C283—42no—
64C2×C4×C283—22no—
65C2×C4×C283—24no—
66C2×C4×C283—24no—
67C2×C4×C283—22no—
68C2×C4×C283—21no—
69C2×C4×C283—42no—
70C2×C4×C283C2×D412yes—
71C2×C4×C283C2×D411yescharacteristic
72C2×C4×C283#4114yes—
73C2×C4×C283C2411yescharacteristic
74C22×C283—22no—
75C22×C283—22no—
76C22×C283—22no—
77C22×C283—22no—
78C22×C283—44no—
79C22×C283—41no—
80C22×C283—42no—
81C22×C283#12312yes—
82C22×C283C22×D411yescharacteristic
83C4×C283—22no—
84C4×C283—41no—
85C4×C283—42no—
86C4×C283#12312yes—
87C4×C283C2×#4112yes—
88Dic283—44no—
89C2×C283—22no—
90C2×C283—42no—
91C2×C283—81no—
92C2×C283C2×#12311yescharacteristic
93C2×C283#57512yes—
94C283#309311yescharacteristic, complemented, Sylow
95#3093—2831nomaximal, Sylow
96#525D28311yescharacteristic
97C2×#117—2831no—
98#485—2834no—
99#482—2834no—
100#428—2832no—
101#417—2832no—
102#407—2831no—
103C2×#41C2×D28311yescharacteristic
104C23×C4C2×D28311yescharacteristic
105C2×M16—2832no—
106#123—21no—
107C22⋊Q8C2×D28312yes—
108#121C2×D28312yes—
109#120—21no—
110C4×D4—22no—
111#117—2834no—
112#117—5662no—
113#117C2×D28311yescharacteristic
114C2×C4⋊C4—2832no—
115C2×C22⋊C4—5661no—
116C2×C42—5661no—
117#107—2834no—
118#106—2834no—
119#103—2834no—
120#102—2834no—
121C22⋊C8—2834no—
122C24C22⋊D28311yescharacteristic
123#41—24no—
124C2×Q8C22×D28311yescharacteristic
125C2×D4—22no—
126C2×D4—21no—
127C2×D4C22×D28311yescharacteristic
128C22×C4—24no—
129C22×C4—21no—
130C22×C4—5662no—
131C22×C4C22⋊D28311yescharacteristic
132C22×C4C22⋊D28312yes—
133C22×C4C22×D28312yes—
134C22×C4C22×D28311yescharacteristic
135M16—5664no—
136C2×C8—2834no—
137C4⋊C4—22no—
138C4⋊C4—2834no—
139C4⋊C4—5662no—
140C4⋊C4C22×D28312yes—
141C22⋊C4—21no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—5664no—
145C42—21no—
146C42—5664no—
147C23—22no—
148C23—21no—
149C23—42no—
150C23C2×C22⋊D28312yes—
151C23C2×C22⋊D28311yescharacteristic
152Q8—22no—
153D4—22no—
154D4—44no—
155D4—42no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—42no—
162C2×C4—5664no—
163C2×C4—11324no—
164C2×C4C2×C22⋊D28312yes—
165C2×C4C2×C22⋊D28311yescharacteristic
166C2×C4#1798539114yes—
167C2×C4C23×D28311yescharacteristic
168C8—5664no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—41no—
175C22—42no—
176C22#2258359112yes—
177C22C22×C22⋊D28311yescharacteristic
178C4—22no—
179C4—41no—
180C4—42no—
181C4—11324no—
182C4#2258359112yes—
183C4C2×#1798539112yes—
184C2—22no—
185C2—42no—
186C2—81no—
187C2C2×#2258359111yescharacteristic
188C2#3182726312yes—
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting, prime radical#525×C283C2
socleC22×C283C22×D4
hypercenter#525D283
hypocenterC283#3093
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#22583569C2semidirect
2. #31826803C2semidirect
3. #31826786C2semidirect
4. #31826508C2semidirect
5. #31826466C2semidirect
6. #31826429C2semidirect
14. #22583543C22semidirect
15. #22583541C22semidirect
16. #22583534C22semidirect
17. #22583531C22semidirect
94. C283#3093semidirect

Maximal subgroups

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

subgroupindex
C2×#225835692
#318268032
#318267862
#318265082
#318264662
#318264292
#525×C2832
#3093283