Finite Group Databasebeta

← C127×#8530 #44572203

Subgroups — C127×#8530 #44572203

Order 32512.

888 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 888 conjugacy classes of subgroups — too many to draw. Only its 150 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
1C127×#3549C211yesmaximal, characteristic
2C127×#1962C213yesmaximal, complemented
3C127×#1560C213yesmaximal, complemented
4H(3,𝔽4)×C127C414yescomplemented
5#555×C127—23no—
6D42×C127—23no—
7#535×C127—26no—
8#532×C127C2213yes—
9#423×C127C2213yescomplemented
10C2×#104×C127—26no—
11C43×C127C2211yescharacteristic, complemented
12#333×C127—23no—
13#331×C127—23no—
14C2×#41×C127D416yes—
15C22×D4×C127—26no—
16C2×M16×C127—23no—
17C4⋊Q8×C127D413yes—
18#127×C127—24no—
19#127×C127D413yes—
20#124×C127—212no—
21#124×C127C2×C416yes—
22#121×C127—212no—
23#121×C127—26no—
24#120×C127—24no—
25#120×C127—212no—
26C4×D4×C127—26no—
27#117×C127—26no—
28C2×C42×C127—23no—
29C2×C42×C127C2311yescharacteristic
30C4⋊C8×C127—26no—
31#104×C127—412no—
32C24×C127—24no—
33#41×C127—46no—
34#41×C127—46no—
35C2×Q8×C127C22⋊C416yes—
36C2×D4×C127—212no—
37C2×D4×C127—26no—
38C2×D4×C127—26no—
39C2×D4×C127—86no—
40C2×D4×C127—86no—
41C2×D4×C127C22⋊C416yes—
42C22×C4×C127—26no—
43C22×C4×C127—41no—
44C22×C4×C127C2×D413yes—
45M16×C127—46no—
46C2×C8×C127—43no—
47C4⋊C4×C127—26no—
48C22⋊C4×C127—212no—
49C22⋊C4×C127—212no—
50C42×C127—24no—
51C42×C127—26no—
52C42×C127—43no—
53C42×C127C22×C411yescharacteristic
54C42×C127C2×D413yes—
55C23×C127—26no—
56C23×C127—812no—
57C23×C127#12011yescharacteristic
58Q8×C127—46no—
59D4×C127—46no—
60D4×C127—46no—
61D4×C127—46no—
62D4×C127—86no—
63D4×C127—812no—
64C2×C4×C127—23no—
65C2×C4×C127—23no—
66C2×C4×C127—26no—
67C2×C4×C127—46no—
68C2×C4×C127—46no—
69C2×C4×C127—46no—
70C2×C4×C127C2×C22⋊C413yes—
71C2×C4×C127#12013yes—
72C8×C127—83no—
73C22×C127—23no—
74C22×C127—46no—
75C22×C127—412no—
76C22×C127—168no—
77C22×C127#37911yescharacteristic
78C4×C127—23no—
79C4×C127—44no—
80C4×C127—46no—
81C4×C127#45313yes—
82C4×C127#45513yes—
83#8530C12711yesmaximal, characteristic, direct product factor, Sylow
84C2×C127—41no—
85C2×C127—86no—
86C2×C127#179213yes—
87#3549C2×C12711yescharacteristic
88#1962C2×C12713yescomplemented
89#1560C2×C12713yescomplemented
90C127#853011yescharacteristic, direct product factor, Sylow
91H(3,𝔽4)C4×C12714yescomplemented
92#555—23no—
93D42—23no—
94#535—26no—
95#532C22×C12713yes—
96#423C22×C12713yescomplemented
97C2×#104—26no—
98C43C22×C12711yescharacteristic, complemented
99#333—23no—
100#331—23no—
101C2×#41D4×C12716yes—
102C22×D4—26no—
103C2×M16—23no—
104C4⋊Q8D4×C12713yes—
105#127—24no—
106#127D4×C12713yes—
107#124—212no—
108#124C2×C4×C12716yes—
109#121—212no—
110#121—26no—
111#120—24no—
112#120—212no—
113C4×D4—26no—
114#117—26no—
115C2×C42—23no—
116C2×C42C23×C12711yescharacteristic
117C4⋊C8—26no—
118#104—412no—
119C24—24no—
120#41—46no—
121#41—46no—
122C2×Q8C22⋊C4×C12716yes—
123C2×D4—212no—
124C2×D4—26no—
125C2×D4—26no—
126C2×D4—86no—
127C2×D4—86no—
128C2×D4C22⋊C4×C12716yes—
129C22×C4—26no—
130C22×C4—41no—
131C22×C4C2×D4×C12713yes—
132M16—46no—
133C2×C8—43no—
134C4⋊C4—26no—
135C22⋊C4—212no—
136C22⋊C4—212no—
137C42—24no—
138C42—26no—
139C42—43no—
140C42C22×C4×C12711yescharacteristic
141C42C2×D4×C12713yes—
142C23—26no—
143C23—812no—
144C23#120×C12711yescharacteristic
145Q8—46no—
146D4—46no—
147D4—46no—
148D4—46no—
149D4—86no—
150D4—812no—
151C2×C4—23no—
152C2×C4—23no—
153C2×C4—26no—
154C2×C4—46no—
155C2×C4—46no—
156C2×C4—46no—
157C2×C4C2×C22⋊C4×C12713yes—
158C2×C4#120×C12713yes—
159C8—83no—
160C22—23no—
161C22—46no—
162C22—412no—
163C22—168no—
164C22#379×C12711yescharacteristic
165C4—23no—
166C4—44no—
167C4—46no—
168C4#453×C12713yes—
169C4#455×C12713yes—
170C2—41no—
171C2—86no—
172C2C127×#179213yes—
subgroupG/H
center, socleC22×C127#379
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC127×#3549C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1962C2semidirect
3. C127×#1560C2semidirect
4. H(3,𝔽4)×C127C4semidirect
9. #423×C127C22semidirect
11. C43×C127C22semidirect
83. #8530C127direct (N × H)
88. #1962C2×C127semidirect
89. #1560C2×C127semidirect
90. C127#8530direct (N × H)
91. H(3,𝔽4)C4×C127semidirect
96. #423C22×C127semidirect
98. C43C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35492
C127×#19622
C127×#15602
#8530127