Finite Group Databasebeta

← C2×#22550109 #30648295

Subgroups — C2×#22550109 #30648295

Order 16256.

616 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C22×C8×D127C211yesmaximal, characteristic, complemented
2C2×#16861180C212yesmaximal, complemented
3#22550109C218yesmaximal, direct product factor
4C2×#16861143C211yesmaximal, characteristic, complemented
5C2×#16861130C212yesmaximal, complemented
6C22×D8×C127C211yesmaximal, characteristic, complemented
7C22×C22⋊D127—22no—
8C22×C4×D127C2211yescharacteristic
9C22×C127⋊C8C2211yescharacteristic
10C2×C8×D127—24no—
11C2×C8×D127C2214yescomplemented
12#16861180—24no—
13#16861180C2218yescomplemented
14C2×C4⋊Dic127C2212yes—
15C2×C22⋊Dic127—22no—
16#16861143C2214yescomplemented
17#16861130C2218yescomplemented
18C22×D4×C127C2212yes—
19C2×D8×C127—24no—
20C2×D8×C127C2214yescomplemented
21C22×C8×C127C2211yescharacteristic
22C23×D127D411yescharacteristic
23C2×C22⋊D127—28no—
24C2×C22⋊D127—48no—
25C22×Dic127—22no—
26C22×Dic127D411yescharacteristic
27C2×C4×D127—22no—
28C2×C4×D127—22no—
29C2×C4×D127D412yes—
30C2×C4×D127C2312yes—
31C2×C127⋊C8—22no—
32C2×C127⋊C8C2312yes—
33C8×D127—28no—
34C4⋊Dic127—22no—
35C4⋊Dic127C2314yes—
36C22⋊Dic127—28no—
37C24×C127—22no—
38C2×D4×C127—24no—
39C2×D4×C127—22no—
40C2×D4×C127—24no—
41C2×D4×C127C2314yes—
42C22×C4×C127C2311yescharacteristic
43D8×C127—28no—
44C2×C8×C127D414yescomplemented
45C2×C8×C127C2312yes—
46C22×D127—22no—
47C22×D127—22no—
48C22×D127D814yescomplemented
49C22×D127C2×D412yes—
50C22⋊D127—416no—
51C2×Dic127—22no—
52C2×Dic127—24no—
53C2×Dic127—44no—
54C2×Dic127C2×D412yes—
55C4×D127—24no—
56C4×D127—22no—
57C4×D127—22no—
58C127⋊C8—22no—
59C23×C127—24no—
60C23×C127—44no—
61C23×C127—44no—
62C23×C127—44no—
63C23×C127C2×D411yescharacteristic
64D4×C127—24no—
65D4×C127—24no—
66D4×C127—44no—
67C2×C4×C127C2×D411yescharacteristic
68C2×C4×C127C2×D412yes—
69C2×C4×C127#4112yes—
70C2×C4×C127C2411yescharacteristic
71C8×C127C2×D414yescomplemented
72C22×C127—44no—
73C22×C127—44no—
74C22×C127—44no—
75C22×C127—88no—
76C22×C127#12112yes—
77C22×C127C2×D812yes—
78C22×C127#13512yes—
79C22×C127C22×D411yescharacteristic
80C2×D127—22no—
81C2×D127—22no—
82C2×D127—28no—
83C2×D127C2×D814yescomplemented
84C4×C127#12112yes—
85C4×C127C22×D411yescharacteristic
86C4×C127C2×#4111yescharacteristic
87Dic127—22no—
88Dic127—44no—
89C2×C127—84no—
90C2×C127#46614yescomplemented
91C2×C127C2×#12111yescharacteristic
92C2×C127C22×D811yescharacteristic
93C2×C127C2×#13511yescharacteristic
94D127—24no—
95C2×#466—1271nomaximal, Sylow
96C127C2×#46611yescharacteristic, complemented, Sylow
97C22×D8D12711yescharacteristic, complemented
98C23×C8—1271no—
99C2×#121—1272no—
100#466—1278no—
101C2×#107—1271no—
102C2×#102—1272no—
103C22×D4—2542no—
104C22×D4C2×D12712yes—
105C23×C4—1271no—
106C2×D8—24no—
107C2×D8C2×D12714yescomplemented
108C22×C8—1271no—
109C22×C8—1274no—
110C22×C8—2544no—
111C22×C8C2×D12711yescharacteristic
112#121—1278no—
113#121—2544no—
114C2×C4⋊C4—1272no—
115C2×C22⋊C4—2542no—
116#107—1274no—
117#102—1278no—
118C24—22no—
119C24—1271no—
120C2×D4—22no—
121C2×D4—24no—
122C2×D4—24no—
123C2×D4—5088no—
124C2×D4—2548no—
125C2×D4C22×D12714yes—
126C22×C4—1271no—
127C22×C4—1272no—
128C22×C4—1272no—
129C22×C4—2542no—
130C22×C4—2542no—
131C22×C4—2542no—
132C22×C4C22×D12711yescharacteristic
133D8—28no—
134C2×C8—1272no—
135C2×C8—2542no—
136C2×C8—2548no—
137C2×C8C22⋊D12714yescomplemented
138C2×C8C22×D12712yes—
139C4⋊C4—1274no—
140C4⋊C4—2542no—
141C22⋊C4—2548no—
142C23—24no—
143C23—44no—
144C23—44no—
145C23—44no—
146C23—1274no—
147C23—1272no—
148C23—2542no—
149C23—2542no—
150C23D4×D12711yescharacteristic
151D4—24no—
152D4—24no—
153D4—44no—
154D4—50816no—
155C2×C4—1272no—
156C2×C4—5084no—
157C2×C4—2544no—
158C2×C4—2542no—
159C2×C4—2542no—
160C2×C4—2542no—
161C2×C4—2544no—
162C2×C4D4×D12711yescharacteristic
163C2×C4C2×C22⋊D12712yes—
164C2×C4#1452324712yes—
165C2×C4C23×D12711yescharacteristic
166C8—2542no—
167C8C2×C22⋊D12714yescomplemented
168C22—44no—
169C22—44no—
170C22—44no—
171C22—88no—
172C22—1274no—
173C22—2548no—
174C22—2542no—
175C22—2542no—
176C22#1686118012yes—
177C22D8×D12712yes—
178C22#1686122812yes—
179C22C2×D4×D12711yescharacteristic
180C4—5084no—
181C4—2542no—
182C4#1686118012yes—
183C4C22×C22⋊D12711yescharacteristic
184C4C2×#1452324711yescharacteristic
185C2—84no—
186C2—2544no—
187C2#2255010914yesdirect product factor
188C2C2×#1686118011yescharacteristic
189C2C2×D8×D12711yescharacteristic
190C2C2×#1686122811yescharacteristic
subgroupG/H
centerC23D4×D127
commutator, cosocleC2×C4×C127C24
FrattiniC2×C4C23×D127
FittingC22×D8×C127C2
socleC23×C127C2×D4
hypercenterC22×D8D127
hypocenterC127C2×#466
LCSG ▷ C2×C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×C8×D127C2semidirect
2. C2×#16861180C2semidirect
3. #22550109C2direct (N × H)
4. C2×#16861143C2semidirect
5. C2×#16861130C2semidirect
6. C22×D8×C127C2semidirect
11. C2×C8×D127C22semidirect
13. #16861180C22semidirect
16. #16861143C22semidirect
17. #16861130C22semidirect
20. C2×D8×C127C22semidirect
44. C2×C8×C127D4semidirect
48. C22×D127D8semidirect
71. C8×C127C2×D4semidirect
83. C2×D127C2×D8semidirect
90. C2×C127#466semidirect
96. C127C2×#466semidirect
97. C22×D8D127semidirect
107. C2×D8C2×D127semidirect
137. C2×C8C22⋊D127semidirect
167. C8C2×C22⋊D127semidirect
187. C2#22550109direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C8×D1272
C2×#168611802
#225501092
C2×#168611432
C2×#168611302
C22×D8×C1272
C2×#466127