Finite Group Databasebeta

← #27173708

Subgroups — #27173708

Order 12928.

1160 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 229 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
1C23×C22⋊D101C211yesmaximal, characteristic
2C2×C22⋊C4×D101C212yesmaximal, complemented
3#20265053C218yesmaximal, complemented
4#20265038C212yesmaximal, complemented
5#20265033C211yesmaximal, characteristic, complemented
6#379×C101C211yesmaximal, characteristic, complemented
7C24×D101C2211yescharacteristic
8C22×C22⋊D101—28no—
9C22×C22⋊D101C418yescomplemented
10C22×C22⋊D101C2214yes—
11C23×Dic101C2211yescharacteristic
12C22×C4×D101C2214yescomplemented
13C2×C22⋊Dic101C2212yes—
14C2×C22⋊Dic101C2214yescomplemented
15C2×#13108051C2214yescomplemented
16C22⋊C4×D101—28no—
17#15692162C2218yescomplemented
18C25×C101C2211yescharacteristic
19C2×C22⋊C4×C101C2212yes—
20C2×C22⋊C4×C101C2214yescomplemented
21C23×D101—44no—
22C23×D101C2×C414yes—
23C23×D101D418yes—
24C23×D101C2312yes—
25C2×C22⋊D101—232no—
26C2×C22⋊D101—28no—
27C2×C22⋊D101—28no—
28C2×C22⋊D101C2×C4116yescomplemented
29C22×Dic101—24no—
30C22×Dic101C2×C414yescomplemented
31C22×Dic101C2314yes—
32C22×Dic101C2312yes—
33C2×C4×D101—28no—
34C2×C4×D101—48no—
35C22⋊Dic101—24no—
36C22⋊Dic101—44no—
37#13108051—28no—
38C24×C101—24no—
39C24×C101—44no—
40C24×C101C2×C414yescomplemented
41C24×C101C2312yes—
42C24×C101C2311yescharacteristic
43C22×C4×C101C2314yes—
44C22⋊C4×C101—24no—
45C22⋊C4×C101—44no—
46C23×C101—24no—
47C23×C101—28no—
48C23×C101—24no—
49C23×C101—24no—
50C23×C101—24no—
51C23×C101—48no—
52C23×C101—416no—
53C23×C101C22×C414yes—
54C23×C101C22×C412yes—
55C23×C101C2×D414yes—
56C23×C101C2411yescharacteristic
57C22×D101—28no—
58C22×D101—48no—
59C22×D101—416no—
60C22×D101C22⋊C4116yescomplemented
61C22×D101C22×C414yes—
62C22×D101C2×D414yes—
63C22×D101C2×D414yes—
64C2×C4×C101—24no—
65C2×C4×C101—28no—
66C22⋊D101—232no—
67C2×Dic101—28no—
68C2×Dic101—24no—
69C2×Dic101—24no—
70C2×Dic101—28no—
71C2×Dic101C22×C414yes—
72C4×D101—416no—
73C22×C101—24no—
74C22×C101—28no—
75C22×C101—24no—
76C22×C101—24no—
77C22×C101—24no—
78C22×C101—416no—
79C22×C101—48no—
80C22×C101C2×C22⋊C414yes—
81C22×C101C23×C411yescharacteristic
82C22×C101C22×D412yes—
83C22×C101H(5,𝔽2)14yes—
84C2×D101—28no—
85C2×D101—28no—
86C2×D101—28no—
87C2×D101—416no—
88C2×D101C2×C22⋊C418yes—
89C4×C101—44no—
90Dic101—24no—
91Dic101—44no—
92C2×C101—24no—
93C2×C101—44no—
94C2×C101C22×C22⋊C411yescharacteristic
95C2×C101#51812yes—
96C2×C101#53414yes—
97D101—28no—
98#2308—1011nomaximal, Sylow
99C101#230811yescharacteristic, complemented, Sylow
100C23×D4—1011no—
101C22×C22⋊C4—1012no—
102#386—1018no—
103#381—1012no—
104#379—1011no—
105#379D10111yescharacteristic, complemented
106C25—1011no—
107C25C2×D10111yescharacteristic
108C22×D4—1018no—
109C22×D4—1014no—
110C22×D4—2028no—
111C23×C4—1011no—
112C23×C4—1014no—
113C2×C22⋊C4—1014no—
114C2×C22⋊C4—1012no—
115C2×C22⋊C4—1014no—
116C2×C22⋊C4—2028no—
117C2×C22⋊C4C2×D10112yes—
118C2×C22⋊C4C2×D10114yescomplemented
119#95—1018no—
120C24—24no—
121C24—44no—
122C24—1014no—
123C24—1018no—
124C24—1012no—
125C24—4044no—
126C24C4×D10114yescomplemented
127C24C22×D10112yes—
128C24C22×D10111yescharacteristic
129C2×D4—10116no—
130C2×D4—2028no—
131C2×D4—2028no—
132C2×D4—20232no—
133C22×C4—1014no—
134C22×C4—1012no—
135C22×C4—1014no—
136C22×C4—4048no—
137C22×C4—2028no—
138C22×C4—2024no—
139C22×C4C22×D10114yes—
140C22⋊C4—24no—
141C22⋊C4—44no—
142C22⋊C4—4044no—
143C22⋊C4—2028no—
144C22⋊C4—2024no—
145C23—24no—
146C23—24no—
147C23—24no—
148C23—24no—
149C23—28no—
150C23—48no—
151C23—416no—
152C23—10116no—
153C23—1014no—
154C23—1014no—
155C23—1014no—
156C23—40416no—
157C23—4048no—
158C23—2028no—
159C23C2×C4×D10114yes—
160C23C2×C4×D10112yes—
161C23D4×D10114yes—
162C23C23×D10111yescharacteristic
163D4—20232no—
164C2×C4—24no—
165C2×C4—28no—
166C2×C4—1014no—
167C2×C4—40416no—
168C2×C4—2024no—
169C2×C4—2028no—
170C2×C4—2024no—
171C2×C4—2028no—
172C22—28no—
173C22—24no—
174C22—24no—
175C22—24no—
176C22—24no—
177C22—416no—
178C22—48no—
179C22—1018no—
180C22—40416no—
181C22—2028no—
182C22—2028no—
183C22—2028no—
184C22C22⋊C4×D10114yes—
185C22C22×C4×D10111yescharacteristic
186C22C2×D4×D10112yes—
187C22#1569230014yes—
188C4—44no—
189C4—4044no—
190C4—2024no—
191C2—24no—
192C2—44no—
193C2—2028no—
194C2C2×C22⋊C4×D10111yescharacteristic
195C2#2026565012yes—
196C2#2026573714yes—
subgroupG/H
center, FrattiniC23C23×D101
commutatorC22×C101C23×C4
Fitting#379×C101C2
socle, cosocleC23×C101C24
prime radicalC23×C22⋊D101C2
hypercenter#379D101
hypocenterC101#2308
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C4×D101C2semidirect
3. #20265053C2semidirect
4. #20265038C2semidirect
5. #20265033C2semidirect
6. #379×C101C2semidirect
9. C22×C22⋊D101C4semidirect
12. C22×C4×D101C22semidirect
14. C2×C22⋊Dic101C22semidirect
15. C2×#13108051C22semidirect
17. #15692162C22semidirect
20. C2×C22⋊C4×C101C22semidirect
28. C2×C22⋊D101C2×C4semidirect
30. C22×Dic101C2×C4semidirect
40. C24×C101C2×C4semidirect
60. C22×D101C22⋊C4semidirect
99. C101#2308semidirect
105. #379D101semidirect
118. C2×C22⋊C4C2×D101semidirect
126. C24C4×D101semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊D1012
C2×C22⋊C4×D1012
#202650532
#202650382
#202650332
#379×C1012
#2308101