Finite Group Databasebeta

← C127×#1683 #30634635

Subgroups — C127×#1683 #30634635

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#487×C127C211yesmaximal, characteristic, complemented
2#476×C127C211yesmaximal, characteristic
3#474×C127C211yesmaximal, characteristic
4C8×D4×C127C211yesmaximal, characteristic
5#335×C127C211yesmaximal, characteristic, complemented
6#333×C127C211yesmaximal, characteristic, complemented
7#332×C127C211yesmaximal, characteristic, complemented
8C22×C8×C127—21no—
9C4⋊Q8×C127C2211yescharacteristic
10C4⋊Q8×C127C2211yescharacteristic
11C4×D4×C127C2211yescharacteristic
12#107×C127—21no—
13#106×C127—21no—
14C4⋊C8×C127C2211yescharacteristic
15C4⋊C8×C127C2211yescharacteristic
16C4⋊C8×C127C2211yescharacteristic
17#103×C127—21no—
18#103×C127—21no—
19#102×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—
27C2×C8×C127—21no—
28C2×C8×C127—21no—
29C2×C8×C127—21no—
30C2×C8×C127—42no—
31C2×C8×C127D411yescharacteristic
32C2×C8×C127D411yescharacteristic
33C4⋊C4×C127—21no—
34C4⋊C4×C127—21no—
35C4⋊C4×C127—21no—
36C4⋊C4×C127—21no—
37C4⋊C4×C127D411yescharacteristic
38C22⋊C4×C127—21no—
39C42×C127C2311yescharacteristic
40C23×C127—21no—
41Q8×C127—41no—
42Q8×C127—41no—
43Q8×C127—81no—
44D4×C127—21no—
45D4×C127Q1612yes—
46C2×C4×C127—21no—
47C2×C4×C127—41no—
48C2×C4×C127—41no—
49C2×C4×C127—41no—
50C2×C4×C127—41no—
51C2×C4×C127C2×D411yescharacteristic
52C2×C4×C127C2×D411yescharacteristic
53C2×C4×C127#4111yescharacteristic
54C8×C127—21no—
55C8×C127—21no—
56C8×C127—41no—
57C8×C127—41no—
58C8×C127—41no—
59C22×C127—22no—
60C22×C127—41no—
61C22×C127—41no—
62C22×C127#12111yescharacteristic
63C4×C127—21no—
64C4×C127—41no—
65C4×C127—81no—
66C4×C127—81no—
67C4×C127C2×Q1611yescharacteristic
68C4×C127#13511yescharacteristic
69C4×C127#13511yescharacteristic
70C4×C127AGL(1,ℤ/8)11yescharacteristic
71C2×C127—42no—
72C2×C127#46311yescharacteristic
73C2×C127#46711yescharacteristic
74C2×C127#47111yescharacteristic
75#1683C12711yesmaximal, characteristic, direct product factor, Sylow
76C127#168311yescharacteristic, direct product factor, Sylow
77#487C2×C12711yescharacteristic, complemented
78#476C2×C12711yescharacteristic
79#474C2×C12711yescharacteristic
80C8×D4C2×C12711yescharacteristic
81#335C2×C12711yescharacteristic, complemented
82#333C2×C12711yescharacteristic, complemented
83#332C2×C12711yescharacteristic, complemented
84C22×C8—21no—
85C4⋊Q8C22×C12711yescharacteristic
86C4⋊Q8C22×C12711yescharacteristic
87C4×D4C22×C12711yescharacteristic
88#107—21no—
89#106—21no—
90C4⋊C8C22×C12711yescharacteristic
91C4⋊C8C22×C12711yescharacteristic
92C4⋊C8C22×C12711yescharacteristic
93#103—21no—
94#103—21no—
95#102—21no—
96#102—21no—
97C22⋊C8—21no—
98C4×C8C22×C12711yescharacteristic
99C2×Q8—21no—
100C2×Q8—21no—
101C2×D4D4×C12711yescharacteristic
102C22×C4—21no—
103C2×C8—21no—
104C2×C8—21no—
105C2×C8—21no—
106C2×C8—42no—
107C2×C8D4×C12711yescharacteristic
108C2×C8D4×C12711yescharacteristic
109C4⋊C4—21no—
110C4⋊C4—21no—
111C4⋊C4—21no—
112C4⋊C4—21no—
113C4⋊C4D4×C12711yescharacteristic
114C22⋊C4—21no—
115C42C23×C12711yescharacteristic
116C23—21no—
117Q8—41no—
118Q8—41no—
119Q8—81no—
120D4—21no—
121D4Q16×C12712yes—
122C2×C4—21no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4C2×D4×C12711yescharacteristic
128C2×C4C2×D4×C12711yescharacteristic
129C2×C4#41×C12711yescharacteristic
130C8—21no—
131C8—21no—
132C8—41no—
133C8—41no—
134C8—41no—
135C22—22no—
136C22—41no—
137C22—41no—
138C22#121×C12711yescharacteristic
139C4—21no—
140C4—41no—
141C4—81no—
142C4—81no—
143C4C2×Q16×C12711yescharacteristic
144C4#135×C12711yescharacteristic
145C4#135×C12711yescharacteristic
146C4AGL(1,ℤ/8)×C12711yescharacteristic
147C2—42no—
148C2#463×C12711yescharacteristic
149C2#467×C12711yescharacteristic
150C2#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. #487×C127C2semidirect
5. #335×C127C2semidirect
6. #333×C127C2semidirect
7. #332×C127C2semidirect
75. #1683C127direct (N × H)
76. C127#1683direct (N × H)
77. #487C2×C127semidirect
81. #335C2×C127semidirect
82. #333C2×C127semidirect
83. #332C2×C127semidirect

Maximal subgroups

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

subgroupindex
#487×C1272
#476×C1272
#474×C1272
C8×D4×C1272
#335×C1272
#333×C1272
#332×C1272
#1683127