Finite Group Databasebeta

← #44560294

Subgroups — #44560294

Order 32128.

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×#22548674C211yesmaximal, characteristic, complemented
2#30632025C214yesmaximal, complemented
3#30632008C214yesmaximal, complemented
4#30631730C212yesmaximal, complemented
5#30631688C212yesmaximal, complemented
6#30631651C211yesmaximal, characteristic, complemented
7#525×C251C211yesmaximal, characteristic
8C2×#16860794C2212yes—
9#22548674—22no—
10#22548674C2214yes—
11C2×C4⋊Dic251C2212yes—
12C2×C22⋊Dic251—21no—
13C2×C4×Dic251—21no—
14#22548648C2214yescomplemented
15#22548646C2214yescomplemented
16#22548639C2214yescomplemented
17#22548636C2214yescomplemented
18C22⋊(C251⋊C8)C2214yes—
19C2×#41×C251C2211yescharacteristic
20C23×C4×C251C2211yescharacteristic
21#123×C251—21no—
22C22⋊Q8×C251C2212yes—
23#121×C251C2212yes—
24#120×C251—21no—
25C4×D4×C251—22no—
26#117×C251C2211yescharacteristic
27C22×Dic251—22no—
28#16860794—24no—
29C2×C251⋊C8C2314yes—
30C4⋊Dic251—22no—
31C4⋊Dic251C2314yes—
32C22⋊Dic251—24no—
33C4×Dic251—24no—
34C24×C251D411yescharacteristic
35#41×C251—24no—
36C2×Q8×C251C2311yescharacteristic
37C2×D4×C251—22no—
38C2×D4×C251—21no—
39C2×D4×C251C2311yescharacteristic
40C22×C4×C251—24no—
41C22×C4×C251—21no—
42C22×C4×C251D412yes—
43C22×C4×C251D411yescharacteristic
44C22×C4×C251C2312yes—
45C22×C4×C251C2311yescharacteristic
46C4⋊C4×C251—22no—
47C4⋊C4×C251C2312yes—
48C22⋊C4×C251—21no—
49C22⋊C4×C251—22no—
50C22⋊C4×C251—22no—
51C42×C251—21no—
52C2×Dic251—24no—
53C2×Dic251—44no—
54C251⋊C8—24no—
55C23×C251—22no—
56C23×C251—21no—
57C23×C251—42no—
58C23×C251C2×D412yes—
59C23×C251C2×D411yescharacteristic
60Q8×C251—22no—
61D4×C251—22no—
62D4×C251—44no—
63D4×C251—42no—
64C2×C4×C251—22no—
65C2×C4×C251—24no—
66C2×C4×C251—24no—
67C2×C4×C251—22no—
68C2×C4×C251—21no—
69C2×C4×C251—42no—
70C2×C4×C251C2×D412yes—
71C2×C4×C251C2×D411yescharacteristic
72C2×C4×C251#4114yes—
73C2×C4×C251C2411yescharacteristic
74C22×C251—22no—
75C22×C251—22no—
76C22×C251—22no—
77C22×C251—22no—
78C22×C251—44no—
79C22×C251—41no—
80C22×C251—42no—
81C22×C251#12312yes—
82C22×C251C22×D411yescharacteristic
83C4×C251—22no—
84C4×C251—41no—
85C4×C251—42no—
86C4×C251#12312yes—
87C4×C251C2×#4112yes—
88Dic251—44no—
89C2×C251—22no—
90C2×C251—42no—
91C2×C251—81no—
92C2×C251C2×#12311yescharacteristic
93C2×C251#57512yes—
94C251#309311yescharacteristic, complemented, Sylow
95#3093—2511nomaximal, Sylow
96#525D25111yescharacteristic
97C2×#117—2511no—
98#485—2514no—
99#482—2514no—
100#428—2512no—
101#417—2512no—
102#407—2511no—
103C2×#41C2×D25111yescharacteristic
104C23×C4C2×D25111yescharacteristic
105C2×M16—2512no—
106#123—21no—
107C22⋊Q8C2×D25112yes—
108#121C2×D25112yes—
109#120—21no—
110C4×D4—22no—
111#117—5022no—
112#117—2514no—
113#117C2×D25111yescharacteristic
114C2×C4⋊C4—2512no—
115C2×C22⋊C4—5021no—
116C2×C42—5021no—
117#107—2514no—
118#106—2514no—
119#103—2514no—
120#102—2514no—
121C22⋊C8—2514no—
122C24C22⋊D25111yescharacteristic
123#41—24no—
124C2×Q8C22×D25111yescharacteristic
125C2×D4—22no—
126C2×D4—21no—
127C2×D4C22×D25111yescharacteristic
128C22×C4—24no—
129C22×C4—21no—
130C22×C4—5022no—
131C22×C4C22⋊D25111yescharacteristic
132C22×C4C22⋊D25112yes—
133C22×C4C22×D25112yes—
134C22×C4C22×D25111yescharacteristic
135M16—5024no—
136C2×C8—2514no—
137C4⋊C4—22no—
138C4⋊C4—5022no—
139C4⋊C4—2514no—
140C4⋊C4C22×D25112yes—
141C22⋊C4—21no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—5024no—
145C42—21no—
146C42—5024no—
147C23—22no—
148C23—21no—
149C23—42no—
150C23C2×C22⋊D25112yes—
151C23C2×C22⋊D25111yescharacteristic
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—10044no—
163C2×C4—5024no—
164C2×C4C2×C22⋊D25112yes—
165C2×C4C2×C22⋊D25111yescharacteristic
166C2×C4#1686080914yes—
167C2×C4C23×D25111yescharacteristic
168C8—5024no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—42no—
175C22—41no—
176C22#2254869612yes—
177C22C22×C22⋊D25111yescharacteristic
178C4—22no—
179C4—42no—
180C4—41no—
181C4—10044no—
182C4#2254869612yes—
183C4C2×#1686080912yes—
184C2—22no—
185C2—42no—
186C2—81no—
187C2C2×#2254869611yescharacteristic
188C2#3063248512yes—
subgroupG/H
centerC22C22×C22⋊D251
commutator, cosocleC2×C4×C251C24
FrattiniC2×C4C23×D251
Fitting, prime radical#525×C251C2
socleC22×C251C22×D4
hypercenter#525D251
hypocenterC251#3093
LCSG ▷ C2×C4×C251 ▷ C2×C251 ▷ C251
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#22548674C2semidirect
2. #30632025C2semidirect
3. #30632008C2semidirect
4. #30631730C2semidirect
5. #30631688C2semidirect
6. #30631651C2semidirect
14. #22548648C22semidirect
15. #22548646C22semidirect
16. #22548639C22semidirect
17. #22548636C22semidirect
94. C251#3093semidirect

Maximal subgroups

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

subgroupindex
C2×#225486742
#306320252
#306320082
#306317302
#306316882
#306316512
#525×C2512
#3093251