Finite Group Databasebeta

← C127×#2210 #30635162

Subgroups — C127×#2210 #30635162

Order 16256.

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

normal subgroups only

This group has 170 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
1C2×SD32×C127C211yesmaximal, characteristic, complemented
2C2×D16×C127C211yesmaximal, characteristic
3#495×C127C211yesmaximal, characteristic, complemented
4C4×D8×C127C211yesmaximal, characteristic, complemented
5C4⋊C16×C127C211yesmaximal, characteristic, complemented
6#358×C127C211yesmaximal, characteristic, complemented
7#357×C127C211yesmaximal, characteristic, complemented
8C2×Q16×C127C2211yescharacteristic
9C2×SD16×C127—21no—
10C2×D8×C127C2211yescharacteristic
11C2×D8×C127C2211yescharacteristic
12#124×C127—21no—
13C4×D4×C127—21no—
14SD32×C127—22no—
15D16×C127—22no—
16C2×C16×C127C2211yescharacteristic
17C2×C16×C127C2211yescharacteristic
18#107×C127C2211yescharacteristic
19#102×C127—21no—
20C4×C8×C127C2211yescharacteristic
21C2×Q8×C127—21no—
22C2×D4×C127—21no—
23C2×D4×C127—21no—
24C22×C4×C127—41no—
25Q16×C127—21no—
26Q16×C127—21no—
27SD16×C127—42no—
28D8×C127—21no—
29D8×C127—21no—
30D8×C127—21no—
31D8×C127D412yes—
32C2×C8×C127D411yescharacteristic
33C2×C8×C127C2311yescharacteristic
34C4⋊C4×C127—21no—
35C22⋊C4×C127—41no—
36C22⋊C4×C127—41no—
37C22⋊C4×C127—41no—
38C42×C127D411yescharacteristic
39C16×C127—21no—
40C16×C127—21no—
41C23×C127—41no—
42C23×C127—41no—
43Q8×C127—41no—
44Q8×C127—41no—
45D4×C127—22no—
46D4×C127—41no—
47D4×C127—41no—
48D4×C127—41no—
49C2×C4×C127—41no—
50C2×C4×C127—41no—
51C2×C4×C127—82no—
52C2×C4×C127D811yescharacteristic
53C2×C4×C127D811yescharacteristic
54C2×C4×C127C2×D411yescharacteristic
55C8×C127—21no—
56C8×C127C2×D411yescharacteristic
57C8×C127#4111yescharacteristic
58C22×C127—42no—
59C22×C127—81no—
60C22×C127—81no—
61C22×C127—81no—
62C22×C127—81no—
63C22×C127—81no—
64C22×C127C2×D811yescharacteristic
65C4×C127—21no—
66C4×C127—21no—
67C4×C127—81no—
68C4×C127—81no—
69C4×C127#12111yescharacteristic
70C4×C127AGL(1,ℤ/8)11yescharacteristic
71C2×C127—82no—
72C2×C127—161no—
73C2×C127#45911yescharacteristic
74C2×C127#50811yescharacteristic
75C2×C127#50911yescharacteristic
76#2210C12711yesmaximal, characteristic, direct product factor, Sylow
77C127#221011yescharacteristic, direct product factor, Sylow
78C2×SD32C2×C12711yescharacteristic, complemented
79C2×D16C2×C12711yescharacteristic
80#495C2×C12711yescharacteristic, complemented
81C4×D8C2×C12711yescharacteristic, complemented
82C4⋊C16C2×C12711yescharacteristic, complemented
83#358C2×C12711yescharacteristic, complemented
84#357C2×C12711yescharacteristic, complemented
85C2×Q16C22×C12711yescharacteristic
86C2×SD16—21no—
87C2×D8C22×C12711yescharacteristic
88C2×D8C22×C12711yescharacteristic
89#124—21no—
90C4×D4—21no—
91SD32—22no—
92D16—22no—
93C2×C16C22×C12711yescharacteristic
94C2×C16C22×C12711yescharacteristic
95#107C22×C12711yescharacteristic
96#102—21no—
97C4×C8C22×C12711yescharacteristic
98C2×Q8—21no—
99C2×D4—21no—
100C2×D4—21no—
101C22×C4—41no—
102Q16—21no—
103Q16—21no—
104SD16—42no—
105D8—21no—
106D8—21no—
107D8—21no—
108D8D4×C12712yes—
109C2×C8D4×C12711yescharacteristic
110C2×C8C23×C12711yescharacteristic
111C4⋊C4—21no—
112C22⋊C4—41no—
113C22⋊C4—41no—
114C22⋊C4—41no—
115C42D4×C12711yescharacteristic
116C16—21no—
117C16—21no—
118C23—41no—
119C23—41no—
120Q8—41no—
121Q8—41no—
122D4—22no—
123D4—41no—
124D4—41no—
125D4—41no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—82no—
129C2×C4D8×C12711yescharacteristic
130C2×C4D8×C12711yescharacteristic
131C2×C4C2×D4×C12711yescharacteristic
132C8—21no—
133C8C2×D4×C12711yescharacteristic
134C8#41×C12711yescharacteristic
135C22—42no—
136C22—81no—
137C22—81no—
138C22—81no—
139C22—81no—
140C22—81no—
141C22C2×D8×C12711yescharacteristic
142C4—21no—
143C4—21no—
144C4—81no—
145C4—81no—
146C4#121×C12711yescharacteristic
147C4AGL(1,ℤ/8)×C12711yescharacteristic
148C2—82no—
149C2—161no—
150C2#459×C12711yescharacteristic
151C2#508×C12711yescharacteristic
152C2#509×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×D8
commutator, Frattini, cosocleC2×C8C23×C127
prime radicalC2×D16×C127C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×SD32×C127C2semidirect
3. #495×C127C2semidirect
4. C4×D8×C127C2semidirect
5. C4⋊C16×C127C2semidirect
6. #358×C127C2semidirect
7. #357×C127C2semidirect
76. #2210C127direct (N × H)
77. C127#2210direct (N × H)
78. C2×SD32C2×C127semidirect
80. #495C2×C127semidirect
81. C4×D8C2×C127semidirect
82. C4⋊C16C2×C127semidirect
83. #358C2×C127semidirect
84. #357C2×C127semidirect

Maximal subgroups

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

subgroupindex
C2×SD32×C1272
C2×D16×C1272
#495×C1272
C4×D8×C1272
C4⋊C16×C1272
#358×C1272
#357×C1272
#2210127