Finite Group Databasebeta

← C127×#1677 #30634629

Subgroups — C127×#1677 #30634629

Order 16256.

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

normal subgroups only

This group has 176 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#486×C127C211yesmaximal, characteristic, complemented
2#476×C127C211yesmaximal, characteristic, complemented
3#459×C127C211yesmaximal, characteristic
4C8×D4×C127C211yesmaximal, characteristic, complemented
5#334×C127C211yesmaximal, characteristic, complemented
6#333×C127C211yesmaximal, characteristic, complemented
7#331×C127C211yesmaximal, characteristic, complemented
8C2×D8×C127—21no—
9C22×C8×C127—21no—
10C4⋊Q8×C127C2211yescharacteristic
11#127×C127C2211yescharacteristic
12C4×D4×C127C2211yescharacteristic
13#106×C127—21no—
14C4⋊C8×C127C2211yescharacteristic
15C4⋊C8×C127C2211yescharacteristic
16C4⋊C8×C127C2211yescharacteristic
17#102×C127—21no—
18#102×C127—21no—
19#102×C127—21no—
20#102×C127—21no—
21C22⋊C8×C127—21no—
22C4×C8×C127C2211yescharacteristic
23C2×Q8×C127—21no—
24C2×D4×C127—21no—
25C2×D4×C127—21no—
26C2×D4×C127—21no—
27C2×D4×C127D411yescharacteristic
28C22×C4×C127—21no—
29D8×C127—42no—
30C2×C8×C127—21no—
31C2×C8×C127—21no—
32C2×C8×C127—21no—
33C2×C8×C127—42no—
34C2×C8×C127D411yescharacteristic
35C2×C8×C127D411yescharacteristic
36C4⋊C4×C127—21no—
37C4⋊C4×C127—21no—
38C4⋊C4×C127D411yescharacteristic
39C22⋊C4×C127—21no—
40C42×C127C2311yescharacteristic
41C23×C127—21no—
42C23×C127—41no—
43Q8×C127—81no—
44D4×C127—21no—
45D4×C127—41no—
46D4×C127—41no—
47D4×C127—41no—
48D4×C127—41no—
49D4×C127—81no—
50D4×C127SD1612yes—
51C2×C4×C127—21no—
52C2×C4×C127—41no—
53C2×C4×C127—41no—
54C2×C4×C127—41no—
55C2×C4×C127C2×D411yescharacteristic
56C2×C4×C127C2×D411yescharacteristic
57C2×C4×C127#4111yescharacteristic
58C8×C127—21no—
59C8×C127—21no—
60C8×C127—41no—
61C8×C127—41no—
62C8×C127—41no—
63C22×C127—22no—
64C22×C127—41no—
65C22×C127—41no—
66C22×C127—81no—
67C22×C127—81no—
68C22×C127—81no—
69C22×C127#12111yescharacteristic
70C4×C127—21no—
71C4×C127—41no—
72C4×C127—81no—
73C4×C127C2×SD1611yescharacteristic
74C4×C127#13511yescharacteristic
75C4×C127#13511yescharacteristic
76C4×C127AGL(1,ℤ/8)11yescharacteristic
77C2×C127—42no—
78C2×C127—161no—
79C2×C127#46311yescharacteristic
80C2×C127#46511yescharacteristic
81C2×C127#47211yescharacteristic
82#1677C12711yesmaximal, characteristic, direct product factor, Sylow
83C127#167711yescharacteristic, direct product factor, Sylow
84#486C2×C12711yescharacteristic, complemented
85#476C2×C12711yescharacteristic, complemented
86#459C2×C12711yescharacteristic
87C8×D4C2×C12711yescharacteristic, complemented
88#334C2×C12711yescharacteristic, complemented
89#333C2×C12711yescharacteristic, complemented
90#331C2×C12711yescharacteristic, complemented
91C2×D8—21no—
92C22×C8—21no—
93C4⋊Q8C22×C12711yescharacteristic
94#127C22×C12711yescharacteristic
95C4×D4C22×C12711yescharacteristic
96#106—21no—
97C4⋊C8C22×C12711yescharacteristic
98C4⋊C8C22×C12711yescharacteristic
99C4⋊C8C22×C12711yescharacteristic
100#102—21no—
101#102—21no—
102#102—21no—
103#102—21no—
104C22⋊C8—21no—
105C4×C8C22×C12711yescharacteristic
106C2×Q8—21no—
107C2×D4—21no—
108C2×D4—21no—
109C2×D4—21no—
110C2×D4D4×C12711yescharacteristic
111C22×C4—21no—
112D8—42no—
113C2×C8—21no—
114C2×C8—21no—
115C2×C8—21no—
116C2×C8—42no—
117C2×C8D4×C12711yescharacteristic
118C2×C8D4×C12711yescharacteristic
119C4⋊C4—21no—
120C4⋊C4—21no—
121C4⋊C4D4×C12711yescharacteristic
122C22⋊C4—21no—
123C42C23×C12711yescharacteristic
124C23—21no—
125C23—41no—
126Q8—81no—
127D4—21no—
128D4—41no—
129D4—41no—
130D4—41no—
131D4—41no—
132D4—81no—
133D4SD16×C12712yes—
134C2×C4—21no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4C2×D4×C12711yescharacteristic
139C2×C4C2×D4×C12711yescharacteristic
140C2×C4#41×C12711yescharacteristic
141C8—21no—
142C8—21no—
143C8—41no—
144C8—41no—
145C8—41no—
146C22—22no—
147C22—41no—
148C22—41no—
149C22—81no—
150C22—81no—
151C22—81no—
152C22#121×C12711yescharacteristic
153C4—21no—
154C4—41no—
155C4—81no—
156C4C2×SD16×C12711yescharacteristic
157C4#135×C12711yescharacteristic
158C4#135×C12711yescharacteristic
159C4AGL(1,ℤ/8)×C12711yescharacteristic
160C2—42no—
161C2—161no—
162C2#463×C12711yescharacteristic
163C2#465×C12711yescharacteristic
164C2#472×C12711yescharacteristic
subgroupG/H
center, socleC22×C127#121
commutator, Frattini, cosocleC42C23×C127
prime radical#459×C127C2
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. #486×C127C2semidirect
2. #476×C127C2semidirect
4. C8×D4×C127C2semidirect
5. #334×C127C2semidirect
6. #333×C127C2semidirect
7. #331×C127C2semidirect
82. #1677C127direct (N × H)
83. C127#1677direct (N × H)
84. #486C2×C127semidirect
85. #476C2×C127semidirect
87. C8×D4C2×C127semidirect
88. #334C2×C127semidirect
89. #333C2×C127semidirect
90. #331C2×C127semidirect

Maximal subgroups

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

subgroupindex
#486×C1272
#476×C1272
#459×C1272
C8×D4×C1272
#334×C1272
#333×C1272
#331×C1272
#1677127