Finite Group Databasebeta

← C2×#20265782 #27184492

Subgroups — C2×#20265782 #27184492

Order 12928.

1260 conjugacy classes of subgroups; only the 485 normal subgroups are shown.

normal subgroups only

This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 485 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#20265782C2116yesmaximal, direct product factor
2C2×#15692252C211yesmaximal, characteristic, complemented
3C2×#15692247C211yesmaximal, characteristic, complemented
4C2×#15692240C214yesmaximal, complemented
5C2×#15692229C212yesmaximal, complemented
6C2×#15692228C214yesmaximal, complemented
7C2×C4×D404C212yesmaximal, complemented
8C2×#117×C101C211yesmaximal, characteristic, complemented
9C22×D404C2212yes—
10C22×D404C2214yes—
11C22×C22⋊D101C2214yes—
12C22×C4×D101C2214yes—
13#15692252C2218yescomplemented
14#15692247C2218yescomplemented
15#15692240C22132yescomplemented
16#15692229C22116yescomplemented
17#15692228C22132yescomplemented
18C4×D404C22116yescomplemented
19C2×C4⋊Dic101C2212yes—
20C2×#13108053C2214yes—
21C2×#13108051C2214yes—
22C2×#13108051C2214yes—
23C23×C4×C101C2211yescharacteristic
24#117×C101C2218yescomplemented
25C2×C4⋊C4×C101C2212yes—
26C2×C22⋊C4×C101C2212yes—
27C2×C42×C101C2211yescharacteristic
28C2×C42×C101C2211yescharacteristic
29C23×D101C2314yes—
30C2×D404—28no—
31C2×D404—48no—
32C2×D404C2318yes—
33C2×D404C23116yes—
34C2×C22⋊D101—48no—
35C2×C22⋊D101C23116yes—
36C22×Dic101C2314yes—
37C2×C4×D101—48no—
38C2×C4×D101C23116yes—
39C4⋊Dic101C2318yes—
40#13108053C23116yes—
41#13108051C23116yes—
42#13108051C23116yes—
43C24×C101C2311yescharacteristic
44C22×C4×C101—24no—
45C22×C4×C101C2312yes—
46C22×C4×C101C2312yes—
47C22×C4×C101C2311yescharacteristic
48C22×C4×C101C2314yes—
49C22×C4×C101C2311yescharacteristic
50C4⋊C4×C101C2318yes—
51C22⋊C4×C101C2318yes—
52C42×C101C2314yes—
53C42×C101C2314yes—
54C23×C101—22no—
55C23×C101—24no—
56C23×C101C2412yes—
57C23×C101C2411yescharacteristic
58C22×D101—28no—
59C22×D101—28no—
60C22×D101—28no—
61C22×D101C2418yes—
62C2×C4×C101—22no—
63C2×C4×C101—24no—
64C2×C4×C101—24no—
65C2×C4×C101—28no—
66C2×C4×C101#4114yes—
67C2×C4×C101C2414yes—
68C2×C4×C101C2414yes—
69C2×C4×C101C2412yes—
70C2×C4×C101C2412yes—
71C22⋊D101—416no—
72C2×Dic101—28no—
73C2×Dic101C2418yes—
74D404—216no—
75D404—416no—
76C4×D101—416no—
77C22×C101—22no—
78C22×C101—24no—
79C22×C101—44no—
80C22×C101C2×#4112yes—
81C22×C101H(5,𝔽2)14yes—
82C22×C101C2511yescharacteristic
83C2×D101—28no—
84C2×D101—28no—
85C2×D101—28no—
86C2×D101—416no—
87C4×C101—22no—
88C4×C101—24no—
89C4×C101—24no—
90C4×C101C2×#4114yes—
91Dic101—28no—
92C2×C101—42no—
93C2×C101#54014yescomplemented
94C2×C101C22×#4111yescharacteristic
95C2×C101C2×H(5,𝔽2)12yes—
96D101—48no—
97C2×#540—1011nomaximal, Sylow
98C101C2×#54011yescharacteristic, complemented, Sylow
99#540—10116no—
100C2×#127—1011no—
101C2×#125—1011no—
102C2×#123—1014no—
103C2×#121—1012no—
104C2×#121—1014no—
105C2×C4×D4—1012no—
106C2×#117D10111yescharacteristic, complemented
107C22×D4—1014no—
108C22×D4—1014no—
109C22×D4—1012no—
110C23×C4—1014no—
111C23×C4C2×D10111yescharacteristic
112#127—1018no—
113#125—1018no—
114#123—10132no—
115#121—10116no—
116#121—10132no—
117C4×D4—10116no—
118#117C2×D10118yescomplemented
119C2×C4⋊C4—1012no—
120C2×C4⋊C4—1014no—
121C2×C4⋊C4C2×D10112yes—
122C2×C22⋊C4—1014no—
123C2×C22⋊C4—1014no—
124C2×C22⋊C4C2×D10112yes—
125C2×C42C2×D10111yescharacteristic
126C2×C42C2×D10111yescharacteristic
127C24—1014no—
128C24C22×D10111yescharacteristic
129C2×D4—10116no—
130C2×D4—10116no—
131C2×D4—1018no—
132C2×D4—4048no—
133C2×D4—4048no—
134C2×D4—2028no—
135C22×C4—24no—
136C22×C4—1014no—
137C22×C4—10116no—
138C22×C4—4048no—
139C22×C4C22×D10114yes—
140C22×C4C22×D10112yes—
141C22×C4C22×D10112yes—
142C22×C4C22×D10111yescharacteristic
143C22×C4C22×D10111yescharacteristic
144C4⋊C4—10116no—
145C4⋊C4—1018no—
146C4⋊C4C22×D10118yes—
147C22⋊C4—10116no—
148C22⋊C4—10116no—
149C22⋊C4C22×D10118yes—
150C42C22×D10114yes—
151C42C22×D10114yes—
152C23—22no—
153C23—24no—
154C23—1018no—
155C23—2028no—
156C23—2028no—
157C23—2028no—
158C23C23×D10112yes—
159C23C23×D10111yescharacteristic
160D4—40416no—
161D4—40416no—
162D4—20216no—
163C2×C4—22no—
164C2×C4—24no—
165C2×C4—24no—
166C2×C4—28no—
167C2×C4—1018no—
168C2×C4—40416no—
169C2×C4—2028no—
170C2×C4#1310807414yes—
171C2×C4C23×D10114yes—
172C2×C4C23×D10114yes—
173C2×C4C23×D10112yes—
174C2×C4C23×D10112yes—
175C22—22no—
176C22—24no—
177C22—44no—
178C22—40416no—
179C22—2028no—
180C22—2028no—
181C22—2028no—
182C22C2×#1310807412yes—
183C22#1569230114yes—
184C22C24×D10111yescharacteristic
185C4—22no—
186C4—24no—
187C4—24no—
188C4—2028no—
189C4C2×#1310807414yes—
190C2—42no—
191C2—4048no—
192C2#2026578214yesdirect product factor
193C2C22×#1310807411yescharacteristic
194C2C2×#1569230112yes—
subgroupG/H
centerC23C23×D101
commutator, cosocleC22×C101C25
FrattiniC22C24×D101
FittingC2×#117×C101C2
socleC23×C101C24
hypercenterC2×#117D101
hypocenterC101C2×#540
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #20265782C2direct (N × H)
2. C2×#15692252C2semidirect
3. C2×#15692247C2semidirect
4. C2×#15692240C2semidirect
5. C2×#15692229C2semidirect
6. C2×#15692228C2semidirect
7. C2×C4×D404C2semidirect
8. C2×#117×C101C2semidirect
13. #15692252C22semidirect
14. #15692247C22semidirect
15. #15692240C22semidirect
16. #15692229C22semidirect
17. #15692228C22semidirect
18. C4×D404C22semidirect
24. #117×C101C22semidirect
93. C2×C101#540semidirect
98. C101C2×#540semidirect
106. C2×#117D101semidirect
118. #117C2×D101semidirect
192. C2#20265782direct (N × H)

Maximal subgroups

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

subgroupindex
#202657822
C2×#156922522
C2×#156922472
C2×#156922402
C2×#156922292
C2×#156922282
C2×C4×D4042
C2×#117×C1012
C2×#540101