Finite Group Databasebeta

← C2×#22549671 #30640391

Subgroups — C2×#22549671 #30640391

Order 16256.

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

normal subgroups only

This group has 284 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
2#22549671C214yesmaximal, direct product factor
3C2×#124×C127C211yesmaximal, characteristic
4C2×C22⋊Dic127—22no—
5#16861124—22no—
6#16861124C2214yes—
7C22×Q8×C127C411yescharacteristic, complemented
8C22×D4×C127C2211yescharacteristic
9#124×C127—22no—
10#124×C127C412yescomplemented
11#124×C127C2212yes—
12C2×C22⋊C4×C127—22no—
13C2×C42×C127C411yescharacteristic, complemented
14C22×Dic127—42no—
15C22⋊Dic127—24no—
16C22⋊Dic127—42no—
17C24×C127D412yes—
18C2×Q8×C127—21no—
19C2×Q8×C127—41no—
20C2×Q8×C127—41no—
21C2×Q8×C127C2×C412yescomplemented
22C2×D4×C127—41no—
23C2×D4×C127—41no—
24C2×D4×C127C2×C411yescharacteristic
25C2×D4×C127D412yes—
26C2×D4×C127C2311yescharacteristic
27C22×C4×C127—21no—
28C22×C4×C127—21no—
29C22×C4×C127C2×C411yescharacteristic
30C22⋊C4×C127—24no—
31C22⋊C4×C127—24no—
32C42×C127—21no—
33C42×C127C2×C412yescomplemented
34C2×Dic127—44no—
35C2×Dic127—84no—
36C23×C127—22no—
37C23×C127—22no—
38C23×C127—44no—
39C23×C127C22⋊C412yes—
40C23×C127C22⋊C411yescharacteristic
41C23×C127C2×D412yes—
42Q8×C127—42no—
43Q8×C127—42no—
44D4×C127—41no—
45D4×C127—42no—
46D4×C127—41no—
47C2×C4×C127—21no—
48C2×C4×C127—21no—
49C2×C4×C127—22no—
50C2×C4×C127—22no—
51C2×C4×C127—42no—
52C2×C4×C127—41no—
53C2×C4×C127—41no—
54C2×C4×C127C22⋊C411yescharacteristic
55C2×C4×C127C22×C411yescharacteristic
56C22×C127—22no—
57C22×C127—22no—
58C22×C127—22no—
59C22×C127—42no—
60C22×C127—42no—
61C22×C127—44no—
62C22×C127—82no—
63C22×C127#9911yescharacteristic
64C22×C127#9911yescharacteristic
65C22×C127C2×C22⋊C411yescharacteristic
66C4×C127—21no—
67C4×C127—21no—
68C4×C127—42no—
69C4×C127—42no—
70Dic127—84no—
71C2×C127—21no—
72C2×C127—21no—
73C2×C127—42no—
74C2×C127—42no—
75C2×C127#35412yescomplemented
76C2×C127C2×#9911yescharacteristic
77C2×#354—1271nomaximal, Sylow
78C127C2×#35411yescharacteristic, complemented, Sylow
79C2×#124D12711yescharacteristic
80C2×#99—1272no—
81#354—1274no—
82C22×Q8Dic12711yescharacteristic, complemented
83C22×D4C2×D12711yescharacteristic
84#124—22no—
85#124Dic12712yescomplemented
86#124C2×D12712yes—
87C2×C22⋊C4—22no—
88C2×C22⋊C4—2542no—
89C2×C42Dic12711yescharacteristic, complemented
90#99—1274no—
91#99—2542no—
92C24C22⋊D12712yes—
93C2×Q8—21no—
94C2×Q8—41no—
95C2×Q8—41no—
96C2×Q8C2×Dic12712yescomplemented
97C2×D4—41no—
98C2×D4—41no—
99C2×D4C2×Dic12711yescharacteristic
100C2×D4C22⋊D12712yes—
101C2×D4C22×D12711yescharacteristic
102C22×C4—21no—
103C22×C4—21no—
104C22×C4—5082no—
105C22×C4C2×Dic12711yescharacteristic
106C22⋊C4—24no—
107C22⋊C4—24no—
108C22⋊C4—5082no—
109C22⋊C4—2544no—
110C42—21no—
111C42C2×Dic12712yescomplemented
112C23—22no—
113C23—22no—
114C23—44no—
115C23C22⋊Dic12712yes—
116C23C22⋊Dic12711yescharacteristic
117C23C2×C22⋊D12712yes—
118Q8—42no—
119Q8—42no—
120D4—41no—
121D4—42no—
122D4—41no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—22no—
126C2×C4—22no—
127C2×C4—42no—
128C2×C4—41no—
129C2×C4—41no—
130C2×C4—10164no—
131C2×C4—5084no—
132C2×C4C22⋊Dic12711yescharacteristic
133C2×C4C22×Dic12711yescharacteristic
134C22—22no—
135C22—22no—
136C22—22no—
137C22—42no—
138C22—42no—
139C22—44no—
140C22—82no—
141C22#1686112411yescharacteristic
142C22#1686112411yescharacteristic
143C22C2×C22⋊Dic12711yescharacteristic
144C4—21no—
145C4—21no—
146C4—42no—
147C4—42no—
148C4—10164no—
149C2—21no—
150C2—21no—
151C2—42no—
152C2—42no—
153C2#2254967112yesdirect product factor
154C2C2×#1686112411yescharacteristic
subgroupG/H
centerC22#16861124
commutatorC2×C4×C127C22×C4
FrattiniC2×D4C22×D127
FittingC2×#124×C127C2
socleC22×C127#99
prime radicalC22×D4×C127C22
cosocleC2×D4×C127C23
hypercenterC2×#124D127
hypocenterC127C2×#354
LCSG ▷ C2×C4×C127 ▷ C22×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. #22549671C2direct (N × H)
7. C22×Q8×C127C4semidirect
10. #124×C127C4semidirect
13. C2×C42×C127C4semidirect
21. C2×Q8×C127C2×C4semidirect
33. C42×C127C2×C4semidirect
75. C2×C127#354semidirect
78. C127C2×#354semidirect
82. C22×Q8Dic127semidirect
85. #124Dic127semidirect
89. C2×C42Dic127semidirect
96. C2×Q8C2×Dic127semidirect
111. C42C2×Dic127semidirect
153. C2#22549671direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168611242
#225496712
C2×#124×C1272
C2×#354127