Finite Group Databasebeta

← C2×#22549673 #30640408

Subgroups — C2×#22549673 #30640408

Order 16256.

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

normal subgroups only

This group has 260 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×#16861128C212yesmaximal, complemented
2#22549673C214yesmaximal, direct product factor
3C2×#124×C127C211yesmaximal, characteristic
4C2×#14523232—22no—
5#16861128—22no—
6#16861128C2214yescomplemented
7C22×Q8×C127C2211yescharacteristic
8C22×D4×C127C411yescharacteristic
9#124×C127—22no—
10#124×C127C412yes—
11#124×C127C2212yes—
12C2×C22⋊C4×C127—22no—
13C2×C42×C127C411yescharacteristic
14#14523232—24no—
15#14523232—42no—
16C2×C127⋊C8—42no—
17C24×C127—21no—
18C2×Q8×C127—41no—
19C2×Q8×C127—41no—
20C2×Q8×C127C2×C411yescharacteristic
21C2×Q8×C127D412yes—
22C2×Q8×C127C2311yescharacteristic
23C2×D4×C127—21no—
24C2×D4×C127—41no—
25C2×D4×C127—41no—
26C2×D4×C127C2×C412yes—
27C22×C4×C127—21no—
28C22×C4×C127C2×C411yescharacteristic
29C22×C4×C127D412yes—
30C22⋊C4×C127—24no—
31C22⋊C4×C127—24no—
32C42×C127—21no—
33C42×C127C2×C412yes—
34C127⋊C8—44no—
35C23×C127—22no—
36C23×C127—44no—
37C23×C127—41no—
38C23×C127—41no—
39C23×C127C22⋊C411yescharacteristic
40Q8×C127—41no—
41Q8×C127—42no—
42Q8×C127—41no—
43D4×C127—42no—
44D4×C127—42no—
45C2×C4×C127—21no—
46C2×C4×C127—21no—
47C2×C4×C127—22no—
48C2×C4×C127—22no—
49C2×C4×C127—22no—
50C2×C4×C127—42no—
51C2×C4×C127C22⋊C411yescharacteristic
52C2×C4×C127C22⋊C412yes—
53C2×C4×C127C22×C411yescharacteristic
54C2×C4×C127C2×D412yes—
55C22×C127—22no—
56C22×C127—44no—
57C22×C127—42no—
58C22×C127—82no—
59C22×C127—82no—
60C22×C127#9911yescharacteristic
61C22×C127#9911yescharacteristic
62C22×C127C2×C22⋊C411yescharacteristic
63C4×C127—21no—
64C4×C127—22no—
65C4×C127—21no—
66C4×C127—22no—
67C4×C127—42no—
68C2×C127—21no—
69C2×C127—21no—
70C2×C127—82no—
71C2×C127#35512yescomplemented
72C2×C127C2×#9911yescharacteristic
73C2×#355—1271nomaximal, Sylow
74C127C2×#35511yescharacteristic, complemented, Sylow
75C2×#124D12711yescharacteristic
76C2×#101—1272no—
77#355—1274no—
78C22×Q8C2×D12711yescharacteristic
79C22×D4Dic12711yescharacteristic
80C2×M16—2542no—
81#124—22no—
82#124Dic12712yes—
83#124C2×D12712yes—
84C2×C22⋊C4—22no—
85C2×C42Dic12711yescharacteristic
86#101—1274no—
87#101—2542no—
88C24—21no—
89C2×Q8—41no—
90C2×Q8—41no—
91C2×Q8C2×Dic12711yescharacteristic
92C2×Q8C22⋊D12712yes—
93C2×Q8C22×D12711yescharacteristic
94C2×D4—21no—
95C2×D4—41no—
96C2×D4—41no—
97C2×D4C2×Dic12712yes—
98C22×C4—21no—
99C22×C4C2×Dic12711yescharacteristic
100C22×C4C22⋊D12712yes—
101M16—5082no—
102M16—2544no—
103C2×C8—5082no—
104C22⋊C4—24no—
105C22⋊C4—24no—
106C42—21no—
107C42C2×Dic12712yes—
108C23—22no—
109C23—44no—
110C23—41no—
111C23—41no—
112C23C22⋊Dic12711yescharacteristic
113Q8—41no—
114Q8—42no—
115Q8—41no—
116D4—42no—
117D4—42no—
118C2×C4—22no—
119C2×C4—21no—
120C2×C4—22no—
121C2×C4—21no—
122C2×C4—22no—
123C2×C4—42no—
124C2×C4C22⋊Dic12711yescharacteristic
125C2×C4C22⋊Dic12712yes—
126C2×C4C22×Dic12711yescharacteristic
127C2×C4C2×C22⋊D12712yes—
128C8—5084no—
129C22—22no—
130C22—44no—
131C22—42no—
132C22—82no—
133C22—82no—
134C22#1686112411yescharacteristic
135C22#1686112411yescharacteristic
136C22C2×C22⋊Dic12711yescharacteristic
137C4—22no—
138C4—21no—
139C4—22no—
140C4—21no—
141C4—42no—
142C2—21no—
143C2—21no—
144C2—82no—
145C2#2254967312yesdirect product factor
146C2C2×#1686112411yescharacteristic
subgroupG/H
centerC22#16861124
commutatorC2×C4×C127C22×C4
FrattiniC2×Q8C22×D127
FittingC2×#124×C127C2
socleC22×C127#99
prime radicalC22×D4×C127C4
cosocleC2×Q8×C127C23
hypercenterC2×#124D127
hypocenterC127C2×#355
LCSG ▷ C2×C4×C127 ▷ C22×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#16861128C2semidirect
2. #22549673C2direct (N × H)
6. #16861128C22semidirect
71. C2×C127#355semidirect
74. C127C2×#355semidirect
145. C2#22549673direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168611282
#225496732
C2×#124×C1272
C2×#355127