Finite Group Databasebeta

← C2×#22549669 #30640388

Subgroups — C2×#22549669 #30640388

Order 16256.

368 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 77 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×#16861124C212yesmaximal, complemented
2#22549669C214yesmaximal, direct product factor
3C2×#127×C127C211yesmaximal, characteristic
4C2×C22⋊Dic127—22no—
5#16861124—22no—
6#16861124C2214yescomplemented
7C22×D4×C127—22no—
8C22×D4×C127C411yescharacteristic, complemented
9C22×D4×C127C2211yescharacteristic
10#127×C127—22no—
11#127×C127C412yescomplemented
12#127×C127C2212yes—
13C2×C42×C127C411yescharacteristic, complemented
14C22×Dic127—42no—
15C22⋊Dic127—24no—
16C22⋊Dic127—42no—
17C24×C127—21no—
18C24×C127D412yes—
19C2×D4×C127—24no—
20C2×D4×C127—24no—
21C2×D4×C127—21no—
22C2×D4×C127—41no—
23C2×D4×C127—41no—
24C2×D4×C127—41no—
25C2×D4×C127—41no—
26C2×D4×C127—48no—
27C2×D4×C127C2×C411yescharacteristic
28C2×D4×C127C2×C412yescomplemented
29C2×D4×C127D412yes—
30C2×D4×C127C2311yescharacteristic
31C22×C4×C127—21no—
32C22×C4×C127C2×C411yescharacteristic
33C42×C127—21no—
34C42×C127C2×C412yescomplemented
35C2×Dic127—44no—
36C2×Dic127—84no—
37C23×C127—22no—
38C23×C127—22no—
39C23×C127—22no—
40C23×C127—44no—
41C23×C127—44no—
42C23×C127—41no—
43C23×C127—41no—
44C23×C127C22⋊C412yes—
45C23×C127C22⋊C411yescharacteristic
46C23×C127C2×D412yes—
47D4×C127—41no—
48D4×C127—42no—
49D4×C127—41no—
50D4×C127—42no—
51D4×C127—48no—
52D4×C127—48no—
53D4×C127—42no—
54C2×C4×C127—24no—
55C2×C4×C127—21no—
56C2×C4×C127—21no—
57C2×C4×C127—22no—
58C2×C4×C127C22⋊C411yescharacteristic
59C2×C4×C127C22×C411yescharacteristic
60C22×C127—22no—
61C22×C127—22no—
62C22×C127—22no—
63C22×C127—42no—
64C22×C127—42no—
65C22×C127—44no—
66C22×C127—44no—
67C22×C127—42no—
68C22×C127—82no—
69C22×C127—82no—
70C22×C127—82no—
71C22×C127#9911yescharacteristic
72C22×C127#9911yescharacteristic
73C22×C127C2×C22⋊C411yescharacteristic
74C4×C127—24no—
75C4×C127—21no—
76C4×C127—21no—
77Dic127—84no—
78C2×C127—21no—
79C2×C127—21no—
80C2×C127—42no—
81C2×C127—42no—
82C2×C127—82no—
83C2×C127#35312yescomplemented
84C2×C127C2×#9911yescharacteristic
85C2×#353—1271nomaximal, Sylow
86C127C2×#35311yescharacteristic, complemented, Sylow
87C2×#127D12711yescharacteristic
88C2×#99—1272no—
89#353—1274no—
90C22×D4—22no—
91C22×D4Dic12711yescharacteristic, complemented
92C22×D4C2×D12711yescharacteristic
93#127—22no—
94#127Dic12712yescomplemented
95#127C2×D12712yes—
96C2×C22⋊C4—2542no—
97C2×C42Dic12711yescharacteristic, complemented
98#99—1274no—
99#99—2542no—
100C24—21no—
101C24C22⋊D12712yes—
102C2×D4—24no—
103C2×D4—24no—
104C2×D4—21no—
105C2×D4—41no—
106C2×D4—41no—
107C2×D4—41no—
108C2×D4—41no—
109C2×D4—48no—
110C2×D4C2×Dic12711yescharacteristic
111C2×D4C2×Dic12712yescomplemented
112C2×D4C22⋊D12712yes—
113C2×D4C22×D12711yescharacteristic
114C22×C4—21no—
115C22×C4—5082no—
116C22×C4C2×Dic12711yescharacteristic
117C22⋊C4—5082no—
118C22⋊C4—2544no—
119C42—21no—
120C42C2×Dic12712yescomplemented
121C23—22no—
122C23—22no—
123C23—22no—
124C23—44no—
125C23—44no—
126C23—41no—
127C23—41no—
128C23C22⋊Dic12712yes—
129C23C22⋊Dic12711yescharacteristic
130C23C2×C22⋊D12712yes—
131D4—41no—
132D4—42no—
133D4—41no—
134D4—42no—
135D4—48no—
136D4—48no—
137D4—42no—
138C2×C4—24no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—22no—
142C2×C4—10164no—
143C2×C4—5084no—
144C2×C4C22⋊Dic12711yescharacteristic
145C2×C4C22×Dic12711yescharacteristic
146C22—22no—
147C22—22no—
148C22—22no—
149C22—42no—
150C22—42no—
151C22—44no—
152C22—44no—
153C22—42no—
154C22—82no—
155C22—82no—
156C22—82no—
157C22#1686112411yescharacteristic
158C22#1686112411yescharacteristic
159C22C2×C22⋊Dic12711yescharacteristic
160C4—24no—
161C4—21no—
162C4—21no—
163C4—10164no—
164C2—21no—
165C2—21no—
166C2—42no—
167C2—42no—
168C2—82no—
169C2#2254966912yesdirect product factor
170C2C2×#1686112411yescharacteristic
subgroupG/H
centerC22#16861124
commutatorC2×C4×C127C22×C4
FrattiniC2×D4C22×D127
Fitting, prime radicalC2×#127×C127C2
socleC22×C127#99
cosocleC2×D4×C127C23
hypercenterC2×#127D127
hypocenterC127C2×#353
LCSG ▷ C2×C4×C127 ▷ C22×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#16861124C2semidirect
2. #22549669C2direct (N × H)
6. #16861124C22semidirect
8. C22×D4×C127C4semidirect
11. #127×C127C4semidirect
13. C2×C42×C127C4semidirect
28. C2×D4×C127C2×C4semidirect
34. C42×C127C2×C4semidirect
83. C2×C127#353semidirect
86. C127C2×#353semidirect
91. C22×D4Dic127semidirect
94. #127Dic127semidirect
97. C2×C42Dic127semidirect
111. C2×D4C2×Dic127semidirect
120. C42C2×Dic127semidirect
169. C2#22549669direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168611242
#225496692
C2×#127×C1272
C2×#353127