Finite Group Databasebeta

← C127×#12492 #44576165

Subgroups — C127×#12492 #44576165

Order 32512.

268 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 82 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×#2207C212yesmaximal, complemented
2C127×#1712C211yesmaximal, characteristic
3C127×#1591C211yesmaximal, characteristic, complemented
4C127×#1367C211yesmaximal, characteristic, complemented
5C127×#1361C212yesmaximal, complemented
6C2×SD32×C127—22no—
7#493×C127—21no—
8#493×C127—21no—
9#493×C127C2212yes—
10#446×C127—21no—
11C4×Q16×C127C2211yescharacteristic
12C4⋊C16×C127C2212yes—
13#357×C127—22no—
14#335×C127C2211yescharacteristic
15Q8⋊C8×C127—21no—
16C82×C127C2211yescharacteristic
17C2×Q16×C127D411yescharacteristic
18C2×D8×C127—22no—
19C2×D8×C127—22no—
20C2×D8×C127—42no—
21C2×D8×C127—41no—
22C2×D8×C127—41no—
23#127×C127—22no—
24C4×Q8×C127—21no—
25SD32×C127—44no—
26C2×C16×C127—22no—
27#107×C127D411yescharacteristic
28C4⋊C8×C127—21no—
29C4⋊C8×C127—41no—
30#103×C127—21no—
31#97×C127—41no—
32C4×C8×C127D411yescharacteristic
33C4×C8×C127D411yescharacteristic
34C4×C8×C127C2311yescharacteristic
35C2×Q8×C127—21no—
36C2×D4×C127—42no—
37C2×D4×C127—42no—
38C2×D4×C127—42no—
39Q16×C127—22no—
40D8×C127—42no—
41D8×C127—42no—
42D8×C127—82no—
43D8×C127—84no—
44D8×C127—82no—
45D8×C127—82no—
46C2×C8×C127—21no—
47C2×C8×C127—41no—
48C2×C8×C127D811yescharacteristic
49C2×C8×C127D811yescharacteristic
50C2×C8×C127C2×D411yescharacteristic
51C2×C8×C127#4111yescharacteristic
52C4⋊C4×C127—21no—
53C4⋊C4×C127—41no—
54C42×C127—41no—
55C42×C127C2×D411yescharacteristic
56C16×C127—42no—
57C23×C127—82no—
58Q8×C127—41no—
59Q8×C127—41no—
60D4×C127—84no—
61D4×C127—82no—
62D4×C127—82no—
63D4×C127—82no—
64D4×C127—82no—
65C2×C4×C127—41no—
66C2×C4×C127—41no—
67C2×C4×C127#12111yescharacteristic
68C2×C4×C127C2×D811yescharacteristic
69C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
70C8×C127—22no—
71C8×C127—21no—
72C8×C127—21no—
73C8×C127—81no—
74C8×C127SD3212yescomplemented
75C8×C127AGL(1,ℤ/8)12yes—
76C22×C127—162no—
77C22×C127—162no—
78C22×C127—162no—
79C22×C127#45911yescharacteristic
80C4×C127—21no—
81C4×C127—81no—
82C4×C127—81no—
83C4×C127#46911yescharacteristic
84C4×C127#47211yescharacteristic
85C4×C127C2×SD3211yescharacteristic
86C4×C127#50911yescharacteristic
87#12492C12711yesmaximal, characteristic, direct product factor, Sylow
88C2×C127—322no—
89C2×C127#168711yescharacteristic
90C2×C127#220711yescharacteristic
91C2×C127#221311yescharacteristic
92#2207C2×C12712yescomplemented
93#1712C2×C12711yescharacteristic
94#1591C2×C12711yescharacteristic, complemented
95#1367C2×C12711yescharacteristic, complemented
96#1361C2×C12712yescomplemented
97C127#1249211yescharacteristic, direct product factor, Sylow
98C2×SD32—22no—
99#493—21no—
100#493—21no—
101#493C22×C12712yes—
102#446—21no—
103C4×Q16C22×C12711yescharacteristic
104C4⋊C16C22×C12712yes—
105#357—22no—
106#335C22×C12711yescharacteristic
107Q8⋊C8—21no—
108C82C22×C12711yescharacteristic
109C2×Q16D4×C12711yescharacteristic
110C2×D8—22no—
111C2×D8—22no—
112C2×D8—42no—
113C2×D8—41no—
114C2×D8—41no—
115#127—22no—
116C4×Q8—21no—
117SD32—44no—
118C2×C16—22no—
119#107D4×C12711yescharacteristic
120C4⋊C8—21no—
121C4⋊C8—41no—
122#103—21no—
123#97—41no—
124C4×C8D4×C12711yescharacteristic
125C4×C8D4×C12711yescharacteristic
126C4×C8C23×C12711yescharacteristic
127C2×Q8—21no—
128C2×D4—42no—
129C2×D4—42no—
130C2×D4—42no—
131Q16—22no—
132D8—42no—
133D8—42no—
134D8—82no—
135D8—84no—
136D8—82no—
137D8—82no—
138C2×C8—21no—
139C2×C8—41no—
140C2×C8D8×C12711yescharacteristic
141C2×C8D8×C12711yescharacteristic
142C2×C8C2×D4×C12711yescharacteristic
143C2×C8#41×C12711yescharacteristic
144C4⋊C4—21no—
145C4⋊C4—41no—
146C42—41no—
147C42C2×D4×C12711yescharacteristic
148C16—42no—
149C23—82no—
150Q8—41no—
151Q8—41no—
152D4—84no—
153D4—82no—
154D4—82no—
155D4—82no—
156D4—82no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4#121×C12711yescharacteristic
160C2×C4C2×D8×C12711yescharacteristic
161C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
162C8—22no—
163C8—21no—
164C8—21no—
165C8—81no—
166C8SD32×C12712yescomplemented
167C8AGL(1,ℤ/8)×C12712yes—
168C22—162no—
169C22—162no—
170C22—162no—
171C22#459×C12711yescharacteristic
172C4—21no—
173C4—81no—
174C4—81no—
175C4#469×C12711yescharacteristic
176C4#472×C12711yescharacteristic
177C4C2×SD32×C12711yescharacteristic
178C4#509×C12711yescharacteristic
179C2—322no—
180C2C127×#168711yescharacteristic
181C2C127×#220711yescharacteristic
182C2C127×#221311yescharacteristic
subgroupG/H
center, socleC22×C127#459
commutator, Frattini, cosocleC4×C8C23×C127
prime radicalC127×#1712C2
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ C82×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2207C2semidirect
3. C127×#1591C2semidirect
4. C127×#1367C2semidirect
5. C127×#1361C2semidirect
74. C8×C127SD32semidirect
87. #12492C127direct (N × H)
92. #2207C2×C127semidirect
94. #1591C2×C127semidirect
95. #1367C2×C127semidirect
96. #1361C2×C127semidirect
97. C127#12492direct (N × H)
166. C8SD32×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#22072
C127×#17122
C127×#15912
C127×#13672
C127×#13612
#12492127