Finite Group Databasebeta

← C2×#22550029 #30647914

Subgroups — C2×#22550029 #30647914

Order 16256.

996 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 996 conjugacy classes of subgroups — too many to draw. Only its 181 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×D508C211yesmaximal, characteristic
2C22×#14523237C212yesmaximal, complemented
3C2×#16861188C211yesmaximal, characteristic, complemented
4#22550029C218yesmaximal, direct product factor
5C2×#16861131C212yesmaximal, complemented
6C2×C22⋊C8×C127C211yesmaximal, characteristic, complemented
7C24×D127—21no—
8C22×Dic254C2211yescharacteristic, complemented
9C22×D508—28no—
10C22×D508—22no—
11C22×D508—21no—
12C22×D508C2214yes—
13C22×D508C2212yes—
14C2×#14523237—28no—
15C2×#14523237C2218yescomplemented
16#16861188—22no—
17#16861188C2214yescomplemented
18C2×C4⋊Dic127C2211yescharacteristic, complemented
19C2×Dic127⋊C4—21no—
20C2×C22⋊Dic127—21no—
21#16861131C2218yescomplemented
22C23×C4×C127C2211yescharacteristic
23C22×C8×C127C2212yescomplemented
24C22⋊C8×C127C2214yescomplemented
25C23×D127—28no—
26C23×D127—24no—
27C23×D127—22no—
28C23×D127—44no—
29C23×D127—44no—
30C2×Dic254—21no—
31C2×Dic254—24no—
32C2×Dic254C2312yescomplemented
33C2×D508—28no—
34C2×D508—216no—
35C2×D508—216no—
36C2×D508—24no—
37C2×D508—24no—
38C2×D508—22no—
39C2×D508D418yes—
40C2×D508C2314yes—
41C22×Dic127—21no—
42C22×Dic127—21no—
43#14523237—216no—
44C4⋊Dic127—21no—
45C4⋊Dic127C2312yescomplemented
46Dic127⋊C4—24no—
47C22⋊Dic127—24no—
48C24×C127D411yescharacteristic
49C22×C4×C127—24no—
50C22×C4×C127D412yes—
51C22×C4×C127D411yescharacteristic
52C22×C4×C127C2312yes—
53C22×C4×C127C2311yescharacteristic
54C2×C8×C127—24no—
55C2×C8×C127C2314yescomplemented
56C22×D127—216no—
57C22×D127—28no—
58C22×D127—24no—
59C22×D127—48no—
60C22×D127—432no—
61C22×D127—44no—
62C22×D127—48no—
63C22×D127—44no—
64Dic254—24no—
65Dic254—42no—
66D508—216no—
67D508—28no—
68D508—24no—
69D508C2×D418yes—
70C2×Dic127—22no—
71C2×Dic127—22no—
72C2×Dic127—42no—
73C2×Dic127—42no—
74C23×C127—22no—
75C23×C127—22no—
76C23×C127SD1614yescomplemented
77C23×C127C2×D412yes—
78C23×C127C2×D411yescharacteristic
79C2×C4×C127—22no—
80C2×C4×C127—24no—
81C2×C4×C127—24no—
82C2×C4×C127C2×D414yes—
83C2×C4×C127C2×D412yes—
84C2×C4×C127C2×D411yescharacteristic
85C2×C4×C127C2411yescharacteristic
86C8×C127—24no—
87C22×C127—22no—
88C22×C127—22no—
89C22×C127—28no—
90C22×C127#12012yes—
91C22×C127C2×SD1612yes—
92C22×C127C2×SD1614yescomplemented
93C22×C127AGL(1,ℤ/8)12yes—
94C22×C127C22×D411yescharacteristic
95C2×D127—28no—
96C2×D127—432no—
97C2×D127—44no—
98C2×D127—44no—
99C2×D127—416no—
100C4×C127—22no—
101C4×C127#12012yes—
102C4×C127C22×D412yes—
103Dic127—42no—
104Dic127—42no—
105C2×C127—24no—
106C2×C127#45014yescomplemented
107C2×C127C2×#12011yescharacteristic
108C2×C127C22×SD1611yescharacteristic
109C2×C127C2×AGL(1,ℤ/8)11yescharacteristic
110D127—48no—
111C2×#450—1271nomaximal, Sylow
112C127C2×#45011yescharacteristic, complemented, Sylow
113C23×D4—1271no—
114C22×SD16—1272no—
115C2×C22⋊Q8—1271no—
116#450—1278no—
117C2×#102—1272no—
118C2×C22⋊C8D12711yescharacteristic, complemented
119C25—2541no—
120C22×Q8—1271no—
121C22×D4—1272no—
122C22×D4—1274no—
123C22×D4—2548no—
124C22×D4—2542no—
125C22×D4—2541no—
126C23×C4C2×D12711yescharacteristic
127C2×SD16—1278no—
128C2×SD16—2548no—
129C22×C8C2×D12712yescomplemented
130C22⋊Q8—1274no—
131C22⋊Q8—2542no—
132C2×C4⋊C4—1271no—
133C2×C4⋊C4—2541no—
134C2×C22⋊C4—2541no—
135#102—1278no—
136C22⋊C8C2×D12714yescomplemented
137C24—5084no—
138C24—5084no—
139C24—2548no—
140C24—2544no—
141C24—2542no—
142C24D50811yescharacteristic
143C2×Q8—1272no—
144C2×Q8—2544no—
145C2×Q8—2541no—
146C2×D4—1278no—
147C2×D4—1274no—
148C2×D4—25416no—
149C2×D4—2548no—
150C2×D4—25416no—
151C2×D4—2544no—
152C2×D4—2544no—
153C2×D4—2542no—
154C22×C4—24no—
155C22×C4—2541no—
156C22×C4—2541no—
157C22×C4D50812yes—
158C22×C4D50811yescharacteristic
159C22×C4C22×D12712yes—
160C22×C4C22×D12711yescharacteristic
161SD16—25416no—
162C2×C8—24no—
163C2×C8C22×D12714yescomplemented
164C4⋊C4—1272no—
165C4⋊C4—2544no—
166C4⋊C4—2541no—
167C22⋊C4—2544no—
168C23—22no—
169C23—22no—
170C23—50832no—
171C23—5088no—
172C23—5084no—
173C23—5088no—
174C23—5084no—
175C23—25416no—
176C23—2544no—
177C23—2548no—
178C23#1452323714yescomplemented
179C23C2×D50812yes—
180C23C2×D50811yescharacteristic
181Q8—5082no—
182Q8—2544no—
183D4—1278no—
184D4—25416no—
185D4—2544no—
186D4—2548no—
187C2×C4—22no—
188C2×C4—24no—
189C2×C4—24no—
190C2×C4—5082no—
191C2×C4—5082no—
192C2×C4—2542no—
193C2×C4—2542no—
194C2×C4D4×D12714yes—
195C2×C4C2×D50812yes—
196C2×C4C2×D50811yescharacteristic
197C2×C4C23×D12711yescharacteristic
198C8—24no—
199C22—28no—
200C22—22no—
201C22—22no—
202C22—50832no—
203C22—50816no—
204C22—5084no—
205C22—5084no—
206C22—2548no—
207C22#1686117912yes—
208C22C2×#1452323712yes—
209C22C2×#1452323714yescomplemented
210C22#1686123712yes—
211C22C22×D50811yescharacteristic
212C4—22no—
213C4—5082no—
214C4—5082no—
215C4#1686117912yes—
216C4C2×D4×D12712yes—
217C2—24no—
218C2—5088no—
219C2#2255002914yesdirect product factor
220C2C2×#1686117911yescharacteristic
221C2C22×#1452323711yescharacteristic
222C2C2×#1686123711yescharacteristic
subgroupG/H
centerC23C2×D508
commutator, cosocleC2×C4×C127C24
FrattiniC2×C4C23×D127
FittingC2×C22⋊C8×C127C2
socleC23×C127C2×D4
prime radicalC23×D508C2
hypercenterC2×C22⋊C8D127
hypocenterC127C2×#450
LCSG ▷ C2×C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C22×#14523237C2semidirect
3. C2×#16861188C2semidirect
4. #22550029C2direct (N × H)
5. C2×#16861131C2semidirect
6. C2×C22⋊C8×C127C2semidirect
8. C22×Dic254C22semidirect
15. C2×#14523237C22semidirect
17. #16861188C22semidirect
18. C2×C4⋊Dic127C22semidirect
21. #16861131C22semidirect
23. C22×C8×C127C22semidirect
24. C22⋊C8×C127C22semidirect
32. C2×Dic254C23semidirect
45. C4⋊Dic127C23semidirect
55. C2×C8×C127C23semidirect
76. C23×C127SD16semidirect
92. C22×C127C2×SD16semidirect
106. C2×C127#450semidirect
112. C127C2×#450semidirect
118. C2×C22⋊C8D127semidirect
129. C22×C8C2×D127semidirect
136. C22⋊C8C2×D127semidirect
163. C2×C8C22×D127semidirect
178. C23#14523237semidirect
209. C22C2×#14523237semidirect
219. C2#22550029direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D5082
C22×#145232372
C2×#168611882
#225500292
C2×#168611312
C2×C22⋊C8×C1272
C2×#450127