Finite Group Databasebeta

← C2×#22549616 #30637311

Subgroups — C2×#22549616 #30637311

Order 16256.

284 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 93 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×#16861120C212yesmaximal, complemented
2#22549616C214yesmaximal, direct product factor
3C2×#124×C127C211yesmaximal, characteristic
4C22×C127⋊C8—22no—
5#16861120—22no—
6#16861120C2214yescomplemented
7C22×Q8×C127C411yescharacteristic
8C22×D4×C127C411yescharacteristic
9#124×C127—22no—
10#124×C127C412yes—
11#124×C127C2212yes—
12C2×C22⋊C4×C127—22no—
13C2×C42×C127C2211yescharacteristic
14C2×C127⋊C8—28no—
15C2×C127⋊C8—24no—
16C24×C127—21no—
17C2×Q8×C127—21no—
18C2×Q8×C127—42no—
19C2×Q8×C127C2×C412yes—
20C2×D4×C127—21no—
21C2×D4×C127—42no—
22C2×D4×C127C2×C412yes—
23C22×C4×C127—21no—
24C22×C4×C127C2×C411yescharacteristic
25C22×C4×C127D412yes—
26C22⋊C4×C127—24no—
27C22⋊C4×C127—24no—
28C42×C127C2×C411yescharacteristic
29C42×C127D412yes—
30C42×C127C2311yescharacteristic
31C127⋊C8—28no—
32C23×C127—22no—
33C23×C127—42no—
34C23×C127—44no—
35C23×C127C22⋊C411yescharacteristic
36Q8×C127—42no—
37Q8×C127—42no—
38D4×C127—42no—
39D4×C127—42no—
40C2×C4×C127—22no—
41C2×C4×C127—24no—
42C2×C4×C127—22no—
43C2×C4×C127—42no—
44C2×C4×C127C22⋊C412yes—
45C2×C4×C127C22⋊C411yescharacteristic
46C2×C4×C127C22×C411yescharacteristic
47C2×C4×C127C2×D412yes—
48C22×C127—42no—
49C22×C127—44no—
50C22×C127—84no—
51C22×C127#10012yes—
52C22×C127#10414yes—
53C22×C127C2×C22⋊C411yescharacteristic
54C4×C127—21no—
55C4×C127—21no—
56C4×C127—22no—
57C4×C127—22no—
58C4×C127—42no—
59C2×C127—82no—
60C2×C127#32914yescomplemented
61C2×C127C2×#10011yescharacteristic
62C2×C127C2×#10412yes—
63C2×#329—1271nomaximal, Sylow
64C127C2×#32911yescharacteristic, complemented, Sylow
65C2×#124D12711yescharacteristic
66C2×#97—1272no—
67#329—1274no—
68C22×Q8Dic12711yescharacteristic
69C22×D4Dic12711yescharacteristic
70C22×C8—2542no—
71#124—22no—
72#124Dic12712yes—
73#124C2×D12712yes—
74C2×C22⋊C4—22no—
75C2×C42C2×D12711yescharacteristic
76#97—1274no—
77#97—2542no—
78C24—21no—
79C2×Q8—21no—
80C2×Q8—42no—
81C2×Q8C2×Dic12712yes—
82C2×D4—21no—
83C2×D4—42no—
84C2×D4C2×Dic12712yes—
85C22×C4—21no—
86C22×C4C2×Dic12711yescharacteristic
87C22×C4C22⋊D12712yes—
88C2×C8—2548no—
89C2×C8—2544no—
90C22⋊C4—24no—
91C22⋊C4—24no—
92C42C2×Dic12711yescharacteristic
93C42C22⋊D12712yes—
94C42C22×D12711yescharacteristic
95C23—22no—
96C23—42no—
97C23—44no—
98C23C22⋊Dic12711yescharacteristic
99Q8—42no—
100Q8—42no—
101D4—42no—
102D4—42no—
103C2×C4—22no—
104C2×C4—24no—
105C2×C4—22no—
106C2×C4—42no—
107C2×C4C22⋊Dic12712yes—
108C2×C4C22⋊Dic12711yescharacteristic
109C2×C4C22×Dic12711yescharacteristic
110C2×C4C2×C22⋊D12712yes—
111C8—2548no—
112C22—42no—
113C22—44no—
114C22—84no—
115C22#1686112612yes—
116C22#1686113614yes—
117C22C2×C22⋊Dic12711yescharacteristic
118C4—21no—
119C4—21no—
120C4—22no—
121C4—22no—
122C4—42no—
123C2—82no—
124C2#2254961614yesdirect product factor
125C2C2×#1686112611yescharacteristic
126C2C2×#1686113612yes—
subgroupG/H
centerC23C22⋊Dic127
commutatorC2×C4×C127C22×C4
FrattiniC42C22×D127
FittingC2×#124×C127C2
socleC23×C127C22⋊C4
prime radicalC22×D4×C127C4
cosocleC42×C127C23
hypercenterC2×#124D127
hypocenterC127C2×#329
LCSG ▷ C2×C4×C127 ▷ C22×C127 ▷ C127
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#16861120C2semidirect
2. #22549616C2direct (N × H)
6. #16861120C22semidirect
60. C2×C127#329semidirect
64. C127C2×#329semidirect
124. C2#22549616direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168611202
#225496162
C2×#124×C1272
C2×#329127