Finite Group Databasebeta

← C127×#1691 #30634643

Subgroups — C127×#1691 #30634643

Order 16256.

160 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 68 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#498×C127C211yesmaximal, characteristic, complemented
2#476×C127C211yesmaximal, characteristic
3#461×C127C211yesmaximal, characteristic
4#436×C127C211yesmaximal, characteristic
5#335×C127C211yesmaximal, characteristic, complemented
6#333×C127C211yesmaximal, characteristic, complemented
7#332×C127C211yesmaximal, characteristic, complemented
8C2×SD16×C127—21no—
9C2×M16×C127—21no—
10C4⋊Q8×C127C2211yescharacteristic
11C4⋊Q8×C127C2211yescharacteristic
12C4×D4×C127C2211yescharacteristic
13#106×C127—21no—
14#106×C127—21no—
15#106×C127—21no—
16C4⋊C8×C127C2211yescharacteristic
17C4⋊C8×C127C2211yescharacteristic
18C4⋊C8×C127C2211yescharacteristic
19#103×C127—21no—
20#102×C127—21no—
21C22⋊C8×C127—21no—
22C4×C8×C127C2211yescharacteristic
23C2×Q8×C127—21no—
24C2×Q8×C127—21no—
25C2×D4×C127D411yescharacteristic
26C22×C4×C127—21no—
27SD16×C127—42no—
28M16×C127—42no—
29C2×C8×C127—21no—
30C2×C8×C127—21no—
31C2×C8×C127—21no—
32C2×C8×C127D411yescharacteristic
33C2×C8×C127D411yescharacteristic
34C4⋊C4×C127—21no—
35C4⋊C4×C127—21no—
36C4⋊C4×C127—21no—
37C4⋊C4×C127—21no—
38C4⋊C4×C127D411yescharacteristic
39C22⋊C4×C127—21no—
40C42×C127C2311yescharacteristic
41C23×C127—21no—
42Q8×C127—41no—
43Q8×C127—41no—
44Q8×C127—81no—
45D4×C127—21no—
46D4×C127—21no—
47C2×C4×C127—21no—
48C2×C4×C127—41no—
49C2×C4×C127—41no—
50C2×C4×C127—41no—
51C2×C4×C127—41no—
52C2×C4×C127C2×D411yescharacteristic
53C2×C4×C127C2×D411yescharacteristic
54C2×C4×C127#4111yescharacteristic
55C8×C127—21no—
56C8×C127—41no—
57C8×C127—41no—
58C8×C127—41no—
59C8×C127SD1612yescomplemented
60C22×C127—41no—
61C22×C127—41no—
62C22×C127—41no—
63C22×C127#12111yescharacteristic
64C4×C127—21no—
65C4×C127—41no—
66C4×C127—81no—
67C4×C127—81no—
68C4×C127C2×SD1611yescharacteristic
69C4×C127AGL(1,ℤ/8)11yescharacteristic
70C4×C127#13711yescharacteristic
71C4×C127#13711yescharacteristic
72C2×C127—81no—
73C2×C127#46111yescharacteristic
74C2×C127#46811yescharacteristic
75C2×C127#47111yescharacteristic
76#1691C12711yesmaximal, characteristic, direct product factor, Sylow
77C127#169111yescharacteristic, direct product factor, Sylow
78#498C2×C12711yescharacteristic, complemented
79#476C2×C12711yescharacteristic
80#461C2×C12711yescharacteristic
81#436C2×C12711yescharacteristic
82#335C2×C12711yescharacteristic, complemented
83#333C2×C12711yescharacteristic, complemented
84#332C2×C12711yescharacteristic, complemented
85C2×SD16—21no—
86C2×M16—21no—
87C4⋊Q8C22×C12711yescharacteristic
88C4⋊Q8C22×C12711yescharacteristic
89C4×D4C22×C12711yescharacteristic
90#106—21no—
91#106—21no—
92#106—21no—
93C4⋊C8C22×C12711yescharacteristic
94C4⋊C8C22×C12711yescharacteristic
95C4⋊C8C22×C12711yescharacteristic
96#103—21no—
97#102—21no—
98C22⋊C8—21no—
99C4×C8C22×C12711yescharacteristic
100C2×Q8—21no—
101C2×Q8—21no—
102C2×D4D4×C12711yescharacteristic
103C22×C4—21no—
104SD16—42no—
105M16—42no—
106C2×C8—21no—
107C2×C8—21no—
108C2×C8—21no—
109C2×C8D4×C12711yescharacteristic
110C2×C8D4×C12711yescharacteristic
111C4⋊C4—21no—
112C4⋊C4—21no—
113C4⋊C4—21no—
114C4⋊C4—21no—
115C4⋊C4D4×C12711yescharacteristic
116C22⋊C4—21no—
117C42C23×C12711yescharacteristic
118C23—21no—
119Q8—41no—
120Q8—41no—
121Q8—81no—
122D4—21no—
123D4—21no—
124C2×C4—21no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4C2×D4×C12711yescharacteristic
130C2×C4C2×D4×C12711yescharacteristic
131C2×C4#41×C12711yescharacteristic
132C8—21no—
133C8—41no—
134C8—41no—
135C8—41no—
136C8SD16×C12712yescomplemented
137C22—41no—
138C22—41no—
139C22—41no—
140C22#121×C12711yescharacteristic
141C4—21no—
142C4—41no—
143C4—81no—
144C4—81no—
145C4C2×SD16×C12711yescharacteristic
146C4AGL(1,ℤ/8)×C12711yescharacteristic
147C4#137×C12711yescharacteristic
148C4#137×C12711yescharacteristic
149C2—81no—
150C2#461×C12711yescharacteristic
151C2#468×C12711yescharacteristic
152C2#471×C12711yescharacteristic
subgroupG/H
center, socleC22×C127#121
commutator, Frattini, cosocleC42C23×C127
prime radicalC2×D4×C127D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. #498×C127C2semidirect
5. #335×C127C2semidirect
6. #333×C127C2semidirect
7. #332×C127C2semidirect
59. C8×C127SD16semidirect
76. #1691C127direct (N × H)
77. C127#1691direct (N × H)
78. #498C2×C127semidirect
82. #335C2×C127semidirect
83. #333C2×C127semidirect
84. #332C2×C127semidirect
136. C8SD16×C127semidirect

Maximal subgroups

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

subgroupindex
#498×C1272
#476×C1272
#461×C1272
#436×C1272
#335×C1272
#333×C1272
#332×C1272
#1691127