Finite Group Databasebeta

← C127×#1704 #30634656

Subgroups — C127×#1704 #30634656

Order 16256.

140 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 64 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#487×C127C211yesmaximal, characteristic
2#477×C127C211yesmaximal, characteristic
3#475×C127C211yesmaximal, characteristic
4#446×C127C211yesmaximal, characteristic
5#334×C127C211yesmaximal, characteristic
6#333×C127C211yesmaximal, characteristic
7#332×C127C211yesmaximal, characteristic
8C4⋊Q8×C127C2211yescharacteristic
9C4⋊Q8×C127C2211yescharacteristic
10C4×Q8×C127C2211yescharacteristic
11#107×C127—21no—
12#106×C127—21no—
13C4⋊C8×C127—21no—
14C4⋊C8×C127C2211yescharacteristic
15C4⋊C8×C127C2211yescharacteristic
16C4⋊C8×C127C2211yescharacteristic
17#103×C127—21no—
18#103×C127—21no—
19#103×C127—21no—
20#103×C127—21no—
21#97×C127—21no—
22C4×C8×C127C2211yescharacteristic
23C2×Q8×C127—21no—
24C2×Q8×C127—21no—
25C2×Q8×C127D411yescharacteristic
26C2×C8×C127—21no—
27C2×C8×C127—21no—
28C2×C8×C127—21no—
29C2×C8×C127D411yescharacteristic
30C2×C8×C127D411yescharacteristic
31C4⋊C4×C127—21no—
32C4⋊C4×C127—21no—
33C4⋊C4×C127—21no—
34C4⋊C4×C127—21no—
35C4⋊C4×C127—21no—
36C4⋊C4×C127D411yescharacteristic
37C42×C127—21no—
38C42×C127C2311yescharacteristic
39Q8×C127—21no—
40Q8×C127—21no—
41Q8×C127—41no—
42Q8×C127—41no—
43Q8×C127—81no—
44C2×C4×C127—21no—
45C2×C4×C127—21no—
46C2×C4×C127—41no—
47C2×C4×C127—41no—
48C2×C4×C127C2×D411yescharacteristic
49C2×C4×C127C2×D411yescharacteristic
50C2×C4×C127#4111yescharacteristic
51C8×C127—21no—
52C8×C127—21no—
53C8×C127—41no—
54C8×C127—41no—
55C8×C127—41no—
56C22×C127#12111yescharacteristic
57C4×C127—21no—
58C4×C127—41no—
59C4×C127—41no—
60C4×C127—81no—
61C4×C127—81no—
62C4×C127#13511yescharacteristic
63C4×C127#13711yescharacteristic
64C4×C127#13711yescharacteristic
65C4×C127#13711yescharacteristic
66C2×C127#46411yescharacteristic
67C2×C127#47011yescharacteristic
68C2×C127#47111yescharacteristic
69#1704C12711yesmaximal, characteristic, direct product factor, Sylow
70C127#170411yescharacteristic, direct product factor, Sylow
71#487C2×C12711yescharacteristic
72#477C2×C12711yescharacteristic
73#475C2×C12711yescharacteristic
74#446C2×C12711yescharacteristic
75#334C2×C12711yescharacteristic
76#333C2×C12711yescharacteristic
77#332C2×C12711yescharacteristic
78C4⋊Q8C22×C12711yescharacteristic
79C4⋊Q8C22×C12711yescharacteristic
80C4×Q8C22×C12711yescharacteristic
81#107—21no—
82#106—21no—
83C4⋊C8—21no—
84C4⋊C8C22×C12711yescharacteristic
85C4⋊C8C22×C12711yescharacteristic
86C4⋊C8C22×C12711yescharacteristic
87#103—21no—
88#103—21no—
89#103—21no—
90#103—21no—
91#97—21no—
92C4×C8C22×C12711yescharacteristic
93C2×Q8—21no—
94C2×Q8—21no—
95C2×Q8D4×C12711yescharacteristic
96C2×C8—21no—
97C2×C8—21no—
98C2×C8—21no—
99C2×C8D4×C12711yescharacteristic
100C2×C8D4×C12711yescharacteristic
101C4⋊C4—21no—
102C4⋊C4—21no—
103C4⋊C4—21no—
104C4⋊C4—21no—
105C4⋊C4—21no—
106C4⋊C4D4×C12711yescharacteristic
107C42—21no—
108C42C23×C12711yescharacteristic
109Q8—21no—
110Q8—21no—
111Q8—41no—
112Q8—41no—
113Q8—81no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4C2×D4×C12711yescharacteristic
119C2×C4C2×D4×C12711yescharacteristic
120C2×C4#41×C12711yescharacteristic
121C8—21no—
122C8—21no—
123C8—41no—
124C8—41no—
125C8—41no—
126C22#121×C12711yescharacteristic
127C4—21no—
128C4—41no—
129C4—41no—
130C4—81no—
131C4—81no—
132C4#135×C12711yescharacteristic
133C4#137×C12711yescharacteristic
134C4#137×C12711yescharacteristic
135C4#137×C12711yescharacteristic
136C2#464×C12711yescharacteristic
137C2#470×C12711yescharacteristic
138C2#471×C12711yescharacteristic
subgroupG/H
center, socle, prime radicalC22×C127#121
commutator, Frattini, cosocleC42C23×C127
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
69. #1704C127direct (N × H)
70. C127#1704direct (N × H)

Maximal subgroups

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

subgroupindex
#487×C1272
#477×C1272
#475×C1272
#446×C1272
#334×C1272
#333×C1272
#332×C1272
#1704127