Finite Group Databasebeta

← #30638374

Subgroups — #30638374

Order 16256.

164 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 57 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
1#22550279C211yesmaximal, characteristic
2#22550228C211yesmaximal, characteristic
3#22550227C211yesmaximal, characteristic
4#22550226C211yesmaximal, characteristic
5#22550226C211yesmaximal, characteristic
6#22549598C211yesmaximal, characteristic
7#498×C127C211yesmaximal, characteristic
8#16861209C2211yescharacteristic
9#16861209C2211yescharacteristic
10#16861142—22no—
11#16861134—22no—
12#16861133—22no—
13#16861133—22no—
14#16861132—22no—
15C4×C127⋊C8C2211yescharacteristic
16C4×C127⋊C8C2211yescharacteristic
17C4⋊Q8×C127C2211yescharacteristic
18C4⋊Q8×C127C2211yescharacteristic
19#106×C127—22no—
20C4×C8×C127C2211yescharacteristic
21C2×Dic254—21no—
22C2×Dic254—21no—
23C2×C127⋊C8D412yes—
24C2×C127⋊C8D412yes—
25C4⋊Dic127—21no—
26C4⋊Dic127—21no—
27C4⋊Dic127—21no—
28C4⋊Dic127—21no—
29C2×Q8×C127—21no—
30C2×Q8×C127—21no—
31C2×C8×C127D412yes—
32C4⋊C4×C127—21no—
33C4⋊C4×C127—21no—
34C4⋊C4×C127—21no—
35C4⋊C4×C127—21no—
36C42×C127C2311yescharacteristic
37Dic254—42no—
38Dic254—42no—
39C2×Dic127—41no—
40C2×Dic127—41no—
41C127⋊C8—22no—
42C127⋊C8—22no—
43Q8×C127—42no—
44Q8×C127—42no—
45C2×C4×C127—41no—
46C2×C4×C127—41no—
47C2×C4×C127C2×D411yescharacteristic
48C2×C4×C127C2×D411yescharacteristic
49C2×C4×C127C2×D411yescharacteristic
50C8×C127—22no—
51C22×C127#12711yescharacteristic
52C4×C127—81no—
53C4×C127—81no—
54C4×C127#13512yes—
55C4×C127#13712yes—
56C4×C127#13712yes—
57Dic127—81no—
58Dic127—81no—
59C2×C127#49511yescharacteristic
60C2×C127#49711yescharacteristic
61C2×C127#49711yescharacteristic
62#1718—1271nomaximal, Sylow
63C127#171811yescharacteristic, complemented, Sylow
64#500—1271no—
65#498D12711yescharacteristic
66#487—1271no—
67#487—1271no—
68#487—1271no—
69#487—1271no—
70#322—1271no—
71C4⋊Q8—1271no—
72C4⋊Q8—1271no—
73C4⋊Q8C2×D12711yescharacteristic
74C4⋊Q8C2×D12711yescharacteristic
75#107—2542no—
76#106—22no—
77#103—2542no—
78#103—2542no—
79#103—2542no—
80#103—2542no—
81C4×C8—1271no—
82C4×C8—1271no—
83C4×C8C2×D12711yescharacteristic
84C2×Q8—21no—
85C2×Q8—21no—
86C2×Q8—2541no—
87C2×Q8—2541no—
88C2×C8—1272no—
89C2×C8—1272no—
90C2×C8C22⋊D12712yes—
91C4⋊C4—21no—
92C4⋊C4—21no—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—2541no—
96C4⋊C4—2541no—
97C4⋊C4—2541no—
98C4⋊C4—2541no—
99C42C22×D12711yescharacteristic
100Q8—42no—
101Q8—42no—
102Q8—5082no—
103Q8—5082no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—5081no—
107C2×C4—5081no—
108C2×C4D4×D12711yescharacteristic
109C2×C4D4×D12711yescharacteristic
110C2×C4C2×C22⋊D12711yescharacteristic
111C8—22no—
112C8—2542no—
113C8—2542no—
114C22#1686120511yescharacteristic
115C4—81no—
116C4—81no—
117C4—10161no—
118C4—10161no—
119C4#1686123012yes—
120C4#1686123812yes—
121C4#1686124012yes—
122C2#2255025711yescharacteristic
123C2#2255026711yescharacteristic
124C2#2255026811yescharacteristic
subgroupG/H
centerC22#16861205
commutator, cosocleC42×C127C23
FrattiniC42C22×D127
Fitting#498×C127C2
socle, prime radicalC22×C127#127
hypercenter#498D127
hypocenterC127#1718
LCSG ▷ C42×C127 ▷ C22×C127 ▷ C127
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
63. C127#1718semidirect

Maximal subgroups

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

subgroupindex
#225502792
#225502282
#225502272
#225502262
#225495982
#498×C1272
#1718127