Finite Group Databasebeta

← C127×#12877 #44576550

Subgroups — C127×#12877 #44576550

Order 32512.

366 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 138 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×#2916C211yesmaximal, characteristic
2C127×#2113C211yesmaximal, characteristic
3C127×#1812C211yesmaximal, characteristic
4C127×#1389C212yesmaximal, complemented
5C127×#1382C212yesmaximal, complemented
6#568×C127—21no—
7C2×#131×C127C2211yescharacteristic
8C2×M32×C127C2211yescharacteristic
9C22×C16×C127C2211yescharacteristic
10#430×C127—21no—
11#430×C127C414yescomplemented
12C2×#108×C127—22no—
13C2×#108×C127C2212yes—
14#427×C127C2212yes—
15#410×C127—21no—
16C22⋊C16×C127—22no—
17H(3,ℤ/4)×C127—21no—
18C2×#41×C127D411yescharacteristic
19#131×C127—22no—
20#131×C127—22no—
21#131×C127—44no—
22C2×M16×C127—24no—
23C2×M16×C127—22no—
24C2×M16×C127C2×C412yes—
25C2×M16×C127D411yescharacteristic
26C22×C8×C127D412yes—
27C22×C8×C127C2311yescharacteristic
28#117×C127—22no—
29M32×C127—22no—
30C2×C16×C127—21no—
31C2×C16×C127—21no—
32C2×C16×C127—22no—
33#108×C127—24no—
34#108×C127—22no—
35#108×C127C2×C414yes—
36#107×C127—22no—
37#106×C127—22no—
38#99×C127—42no—
39#41×C127—22no—
40#41×C127—22no—
41C2×Q8×C127Q1611yescharacteristic
42C2×D4×C127SD1612yes—
43C2×D4×C127Q1611yescharacteristic
44C22×C4×C127C22⋊C412yes—
45C22×C4×C127C2×D411yescharacteristic
46M16×C127—22no—
47M16×C127—24no—
48M16×C127—24no—
49M16×C127—44no—
50M16×C127—42no—
51C2×C8×C127—22no—
52C2×C8×C127—22no—
53C2×C8×C127—44no—
54C2×C8×C127—42no—
55C2×C8×C127C22⋊C412yes—
56C2×C8×C127C22×C411yescharacteristic
57C2×C8×C127C2×D411yescharacteristic
58C2×C8×C127#4112yes—
59C2×C8×C127#4112yes—
60C4⋊C4×C127—42no—
61C22⋊C4×C127—42no—
62C42×C127—42no—
63C16×C127—41no—
64C16×C127—41no—
65C23×C127#10312yes—
66C23×C127C2×SD1611yescharacteristic
67Q8×C127—22no—
68D4×C127—24no—
69D4×C127—22no—
70C2×C4×C127—22no—
71C2×C4×C127—22no—
72C2×C4×C127—82no—
73C2×C4×C127#10312yes—
74C2×C4×C127C2×C22⋊C411yescharacteristic
75C2×C4×C127#12312yes—
76C2×C4×C127C2×Q1611yescharacteristic
77C2×C4×C127AGL(1,ℤ/8)12yes—
78C8×C127—22no—
79C8×C127—44no—
80C8×C127#11712yes—
81C8×C127#12311yescharacteristic
82C8×C127#12311yescharacteristic
83C22×C127—22no—
84C22×C127—41no—
85C22×C127—42no—
86C22×C127C2×#10311yescharacteristic
87C22×C127#48112yes—
88C4×C127—22no—
89C4×C127—162no—
90C4×C127#38111yescharacteristic
91C4×C127#41811yescharacteristic
92C4×C127#48412yes—
93#12877C12711yesmaximal, characteristic, direct product factor, Sylow
94C2×C127—22no—
95C2×C127—21no—
96C2×C127—42no—
97C2×C127#182411yescharacteristic
98#2916C2×C12711yescharacteristic
99#2113C2×C12711yescharacteristic
100#1812C2×C12711yescharacteristic
101#1389C2×C12712yescomplemented
102#1382C2×C12712yescomplemented
103C127#1287711yescharacteristic, direct product factor, Sylow
104#568—21no—
105C2×#131C22×C12711yescharacteristic
106C2×M32C22×C12711yescharacteristic
107C22×C16C22×C12711yescharacteristic
108#430—21no—
109#430C4×C12714yescomplemented
110C2×#108—22no—
111C2×#108C22×C12712yes—
112#427C22×C12712yes—
113#410—21no—
114C22⋊C16—22no—
115H(3,ℤ/4)—21no—
116C2×#41D4×C12711yescharacteristic
117#131—22no—
118#131—22no—
119#131—44no—
120C2×M16—24no—
121C2×M16—22no—
122C2×M16C2×C4×C12712yes—
123C2×M16D4×C12711yescharacteristic
124C22×C8D4×C12712yes—
125C22×C8C23×C12711yescharacteristic
126#117—22no—
127M32—22no—
128C2×C16—21no—
129C2×C16—21no—
130C2×C16—22no—
131#108—24no—
132#108—22no—
133#108C2×C4×C12714yes—
134#107—22no—
135#106—22no—
136#99—42no—
137#41—22no—
138#41—22no—
139C2×Q8Q16×C12711yescharacteristic
140C2×D4SD16×C12712yes—
141C2×D4Q16×C12711yescharacteristic
142C22×C4C22⋊C4×C12712yes—
143C22×C4C2×D4×C12711yescharacteristic
144M16—22no—
145M16—24no—
146M16—24no—
147M16—44no—
148M16—42no—
149C2×C8—22no—
150C2×C8—22no—
151C2×C8—44no—
152C2×C8—42no—
153C2×C8C22⋊C4×C12712yes—
154C2×C8C22×C4×C12711yescharacteristic
155C2×C8C2×D4×C12711yescharacteristic
156C2×C8#41×C12712yes—
157C2×C8#41×C12712yes—
158C4⋊C4—42no—
159C22⋊C4—42no—
160C42—42no—
161C16—41no—
162C16—41no—
163C23#103×C12712yes—
164C23C2×SD16×C12711yescharacteristic
165Q8—22no—
166D4—24no—
167D4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—82no—
171C2×C4#103×C12712yes—
172C2×C4C2×C22⋊C4×C12711yescharacteristic
173C2×C4#123×C12712yes—
174C2×C4C2×Q16×C12711yescharacteristic
175C2×C4AGL(1,ℤ/8)×C12712yes—
176C8—22no—
177C8—44no—
178C8#117×C12712yes—
179C8#123×C12711yescharacteristic
180C8#123×C12711yescharacteristic
181C22—22no—
182C22—41no—
183C22—42no—
184C22C2×#103×C12711yescharacteristic
185C22#481×C12712yes—
186C4—22no—
187C4—162no—
188C4#381×C12711yescharacteristic
189C4#418×C12711yescharacteristic
190C4#484×C12712yes—
191C2—22no—
192C2—21no—
193C2—42no—
194C2C127×#182411yescharacteristic
subgroupG/H
centerC4×C127#418
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
socleC2×C127#1824
prime radicalC2×#41×C127D4
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C22×C4×C127 ◁ C2×#131×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1389C2semidirect
5. C127×#1382C2semidirect
11. #430×C127C4semidirect
93. #12877C127direct (N × H)
101. #1389C2×C127semidirect
102. #1382C2×C127semidirect
103. C127#12877direct (N × H)
109. #430C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#29162
C127×#21132
C127×#18122
C127×#13892
C127×#13822
#12877127