Finite Group Databasebeta

← C127×#12431 #44576104

Subgroups — C127×#12431 #44576104

Order 32512.

236 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 86 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×#2247C211yesmaximal, characteristic, complemented
2D4×C16×C127C211yesmaximal, characteristic
3C127×#1669C212yesmaximal
4C127×#1371C211yesmaximal, characteristic, complemented
5C127×#1362C212yesmaximal, complemented
6C2×Q32×C127—21no—
7C2×Q32×C127—21no—
8C22×C16×C127—21no—
9#494×C127C2212yes—
10#474×C127—22no—
11C8×D4×C127C2211yescharacteristic
12C4⋊C16×C127C2211yescharacteristic
13C22⋊C16×C127—21no—
14C4×C16×C127C2211yescharacteristic
15#335×C127C2212yes—
16#332×C127—22no—
17C2×Q16×C127—22no—
18C2×Q16×C127—22no—
19C22×C8×C127—21no—
20C4⋊Q8×C127—22no—
21C4×D4×C127D411yescharacteristic
22Q32×C127—42no—
23Q32×C127—42no—
24C2×C16×C127—21no—
25C2×C16×C127—42no—
26C2×C16×C127D411yescharacteristic
27C2×C16×C127D411yescharacteristic
28#107×C127—42no—
29C4⋊C8×C127—22no—
30C4⋊C8×C127D411yescharacteristic
31#102×C127—42no—
32C22⋊C8×C127—21no—
33C4×C8×C127C2311yescharacteristic
34C2×Q8×C127—42no—
35C2×D4×C127D811yescharacteristic
36C22×C4×C127—21no—
37Q16×C127—42no—
38Q16×C127—42no—
39Q16×C127—82no—
40C2×C8×C127—21no—
41C2×C8×C127—41no—
42C2×C8×C127—41no—
43C2×C8×C127—42no—
44C2×C8×C127C2×D411yescharacteristic
45C2×C8×C127#4111yescharacteristic
46C4⋊C4×C127—42no—
47C4⋊C4×C127—42no—
48C4⋊C4×C127D811yescharacteristic
49C22⋊C4×C127—21no—
50C42×C127C2×D411yescharacteristic
51C16×C127—21no—
52C16×C127—41no—
53C16×C127D812yes—
54C23×C127—21no—
55Q8×C127—82no—
56Q8×C127—82no—
57D4×C127—21no—
58D4×C127Q3212yescomplemented
59C2×C4×C127—21no—
60C2×C4×C127—41no—
61C2×C4×C127—41no—
62C2×C4×C127—82no—
63C2×C4×C127#12111yescharacteristic
64C2×C4×C127C2×D811yescharacteristic
65C2×C4×C127#13511yescharacteristic
66C8×C127—21no—
67C8×C127—41no—
68C8×C127—82no—
69C8×C127C2×D811yescharacteristic
70C8×C127AGL(1,ℤ/8)11yescharacteristic
71C22×C127—22no—
72C22×C127—41no—
73C22×C127—41no—
74C22×C127#46611yescharacteristic
75C4×C127—21no—
76C4×C127—41no—
77C4×C127—162no—
78C4×C127#45911yescharacteristic
79C4×C127#47211yescharacteristic
80C4×C127C2×Q3211yescharacteristic
81C4×C127#50811yescharacteristic
82#12431C12711yesmaximal, characteristic, direct product factor, Sylow
83C2×C127—42no—
84C2×C127#166711yescharacteristic
85C2×C127#221611yescharacteristic
86C2×C127#222211yescharacteristic
87#2247C2×C12711yescharacteristic, complemented
88D4×C16C2×C12711yescharacteristic
89#1669C2×C12712yes—
90#1371C2×C12711yescharacteristic, complemented
91#1362C2×C12712yescomplemented
92C127#1243111yescharacteristic, direct product factor, Sylow
93C2×Q32—21no—
94C2×Q32—21no—
95C22×C16—21no—
96#494C22×C12712yes—
97#474—22no—
98C8×D4C22×C12711yescharacteristic
99C4⋊C16C22×C12711yescharacteristic
100C22⋊C16—21no—
101C4×C16C22×C12711yescharacteristic
102#335C22×C12712yes—
103#332—22no—
104C2×Q16—22no—
105C2×Q16—22no—
106C22×C8—21no—
107C4⋊Q8—22no—
108C4×D4D4×C12711yescharacteristic
109Q32—42no—
110Q32—42no—
111C2×C16—21no—
112C2×C16—42no—
113C2×C16D4×C12711yescharacteristic
114C2×C16D4×C12711yescharacteristic
115#107—42no—
116C4⋊C8—22no—
117C4⋊C8D4×C12711yescharacteristic
118#102—42no—
119C22⋊C8—21no—
120C4×C8C23×C12711yescharacteristic
121C2×Q8—42no—
122C2×D4D8×C12711yescharacteristic
123C22×C4—21no—
124Q16—42no—
125Q16—42no—
126Q16—82no—
127C2×C8—21no—
128C2×C8—41no—
129C2×C8—41no—
130C2×C8—42no—
131C2×C8C2×D4×C12711yescharacteristic
132C2×C8#41×C12711yescharacteristic
133C4⋊C4—42no—
134C4⋊C4—42no—
135C4⋊C4D8×C12711yescharacteristic
136C22⋊C4—21no—
137C42C2×D4×C12711yescharacteristic
138C16—21no—
139C16—41no—
140C16D8×C12712yes—
141C23—21no—
142Q8—82no—
143Q8—82no—
144D4—21no—
145D4Q32×C12712yescomplemented
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—82no—
150C2×C4#121×C12711yescharacteristic
151C2×C4C2×D8×C12711yescharacteristic
152C2×C4#135×C12711yescharacteristic
153C8—21no—
154C8—41no—
155C8—82no—
156C8C2×D8×C12711yescharacteristic
157C8AGL(1,ℤ/8)×C12711yescharacteristic
158C22—22no—
159C22—41no—
160C22—41no—
161C22#466×C12711yescharacteristic
162C4—21no—
163C4—41no—
164C4—162no—
165C4#459×C12711yescharacteristic
166C4#472×C12711yescharacteristic
167C4C2×Q32×C12711yescharacteristic
168C4#508×C12711yescharacteristic
169C2—42no—
170C2C127×#166711yescharacteristic
171C2C127×#221611yescharacteristic
172C2C127×#222211yescharacteristic
subgroupG/H
center, socleC22×C127#466
commutator, Frattini, cosocleC4×C8C23×C127
prime radicalC2×D4×C127D8
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ C8×D4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2247C2semidirect
4. C127×#1371C2semidirect
5. C127×#1362C2semidirect
58. D4×C127Q32semidirect
82. #12431C127direct (N × H)
87. #2247C2×C127semidirect
90. #1371C2×C127semidirect
91. #1362C2×C127semidirect
92. C127#12431direct (N × H)
145. D4Q32×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#22472
D4×C16×C1272
C127×#16692
C127×#13712
C127×#13622
#12431127