Finite Group Databasebeta

← C127×#19083 #44582756

Subgroups — C127×#19083 #44582756

Order 32512.

876 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 876 conjugacy classes of subgroups — too many to draw. Only its 230 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
1C127×#3556C211yesmaximal, characteristic, complemented
2C127×#3138C213yesmaximal
3C127×#1658C218yesmaximal, complemented
4C127×#1526C213yesmaximal, complemented
5#564×C127C2214yescomplemented
6#557×C127—26no—
7#541×C127—26no—
8#533×C127C2213yes—
9C2×#127×C127C2211yescharacteristic
10#490×C127C22112yes—
11#486×C127—26no—
12#418×C127—26no—
13C4×M16×C127C2213yes—
14#330×C127C22112yescomplemented
15C22×D4×C127—23no—
16C2×M16×C127—23no—
17C4⋊Q8×C127—26no—
18C4⋊Q8×C127D416yes—
19#127×C127—23no—
20#127×C127C2312yes—
21#126×C127—28no—
22#125×C127—26no—
23#125×C127—224no—
24#125×C127C2316yes—
25C22⋊Q8×C127—26no—
26C4×Q8×C127—212no—
27C4×Q8×C127—26no—
28#117×C127D416yes—
29C2×C42×C127C2311yescharacteristic
30#102×C127—224no—
31#97×C127C2316yes—
32C4×C8×C127—23no—
33C24×C127—41no—
34C2×Q8×C127—26no—
35C2×D4×C127—26no—
36C2×D4×C127—412no—
37C2×D4×C127—43no—
38C22×C4×C127C2×D413yes—
39M16×C127—46no—
40C2×C8×C127—26no—
41C4⋊C4×C127—224no—
42C4⋊C4×C127—26no—
43C4⋊C4×C127—212no—
44C4⋊C4×C127C2×D4112yes—
45C22⋊C4×C127—26no—
46C42×C127—28no—
47C42×C127—26no—
48C42×C127C2×D413yes—
49C42×C127C2411yescharacteristic
50C23×C127—42no—
51C23×C127—86no—
52C23×C127#12011yescharacteristic
53Q8×C127—412no—
54D4×C127—412no—
55D4×C127—86no—
56C2×C4×C127—26no—
57C2×C4×C127—212no—
58C2×C4×C127#12013yes—
59C2×C4×C127C22×D413yes—
60C8×C127—46no—
61C22×C127—23no—
62C22×C127—86no—
63C22×C127—164no—
64C22×C127C2×#12011yescharacteristic
65C4×C127—23no—
66C4×C127—412no—
67C4×C127#45416yes—
68#19083C12711yesmaximal, characteristic, direct product factor, Sylow
69C2×C127—41no—
70C2×C127—162no—
71C2×C127C2×#45413yes—
72#3556C2×C12711yescharacteristic, complemented
73#3138C2×C12713yes—
74#1658C2×C12718yescomplemented
75#1526C2×C12713yescomplemented
76C127#1908311yescharacteristic, direct product factor, Sylow
77#564C22×C12714yescomplemented
78#557—26no—
79#541—26no—
80#533C22×C12713yes—
81C2×#127C22×C12711yescharacteristic
82#490C22×C127112yes—
83#486—26no—
84#418—26no—
85C4×M16C22×C12713yes—
86#330C22×C127112yescomplemented
87C22×D4—23no—
88C2×M16—23no—
89C4⋊Q8—26no—
90C4⋊Q8D4×C12716yes—
91#127—23no—
92#127C23×C12712yes—
93#126—28no—
94#125—26no—
95#125—224no—
96#125C23×C12716yes—
97C22⋊Q8—26no—
98C4×Q8—212no—
99C4×Q8—26no—
100#117D4×C12716yes—
101C2×C42C23×C12711yescharacteristic
102#102—224no—
103#97C23×C12716yes—
104C4×C8—23no—
105C24—41no—
106C2×Q8—26no—
107C2×D4—26no—
108C2×D4—412no—
109C2×D4—43no—
110C22×C4C2×D4×C12713yes—
111M16—46no—
112C2×C8—26no—
113C4⋊C4—224no—
114C4⋊C4—26no—
115C4⋊C4—212no—
116C4⋊C4C2×D4×C127112yes—
117C22⋊C4—26no—
118C42—28no—
119C42—26no—
120C42C2×D4×C12713yes—
121C42C24×C12711yescharacteristic
122C23—42no—
123C23—86no—
124C23#120×C12711yescharacteristic
125Q8—412no—
126D4—412no—
127D4—86no—
128C2×C4—26no—
129C2×C4—212no—
130C2×C4#120×C12713yes—
131C2×C4C22×D4×C12713yes—
132C8—46no—
133C22—23no—
134C22—86no—
135C22—164no—
136C22C2×#120×C12711yescharacteristic
137C4—23no—
138C4—412no—
139C4#454×C12716yes—
140C2—41no—
141C2—162no—
142C2C2×#454×C12713yes—
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC42C24×C127
prime radicalC2×#127×C127C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3556C2semidirect
3. C127×#1658C2semidirect
4. C127×#1526C2semidirect
5. #564×C127C22semidirect
14. #330×C127C22semidirect
68. #19083C127direct (N × H)
72. #3556C2×C127semidirect
74. #1658C2×C127semidirect
75. #1526C2×C127semidirect
76. C127#19083direct (N × H)
77. #564C22×C127semidirect
86. #330C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35562
C127×#31382
C127×#16582
C127×#15262
#19083127