Finite Group Databasebeta

← C127×#13496 #44577169

Subgroups — C127×#13496 #44577169

Order 32512.

284 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 102 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×#367×C127C211yesmaximal, characteristic, complemented
2C127×#2113C211yesmaximal, characteristic
3C127×#1816C212yesmaximal
4C127×#1387C212yesmaximal, complemented
5C127×#1381C211yesmaximal, characteristic, complemented
6C2×#131×C127C2211yescharacteristic
7C2×M32×C127C2211yescharacteristic
8C22×C16×C127C2211yescharacteristic
9C2×#108×C127C2212yes—
10C2×#107×C127C2212yes—
11#417×C127—22no—
12#367×C127—22no—
13C22⋊C16×C127—22no—
14#343×C127—22no—
15C2×#41×C127D411yescharacteristic
16#131×C127—22no—
17#131×C127—22no—
18C2×M16×C127—21no—
19C2×M16×C127—22no—
20C2×M16×C127D411yescharacteristic
21C22×C8×C127—21no—
22C22×C8×C127C2311yescharacteristic
23C2×C4⋊C4×C127—22no—
24M32×C127—22no—
25C2×C16×C127—22no—
26C2×C16×C127—21no—
27C2×C16×C127D412yes—
28#108×C127—22no—
29#108×C127—22no—
30#107×C127—22no—
31#107×C127—22no—
32#103×C127—42no—
33#102×C127—42no—
34#41×C127—22no—
35#41×C127—22no—
36C2×Q8×C127D811yescharacteristic
37C2×D4×C127—21no—
38C2×D4×C127D811yescharacteristic
39C22×C4×C127—21no—
40C22×C4×C127—42no—
41C22×C4×C127C2×D411yescharacteristic
42M16×C127—22no—
43M16×C127—42no—
44M16×C127—42no—
45M16×C127—42no—
46C2×C8×C127—21no—
47C2×C8×C127—41no—
48C2×C8×C127—41no—
49C2×C8×C127—42no—
50C2×C8×C127C2×D411yescharacteristic
51C2×C8×C127#4112yes—
52C2×C8×C127#4112yes—
53C2×C8×C127#4111yescharacteristic
54C4⋊C4×C127—42no—
55C4⋊C4×C127—42no—
56C16×C127—22no—
57C16×C127—41no—
58C23×C127—21no—
59C23×C127#13511yescharacteristic
60Q8×C127—22no—
61D4×C127—22no—
62D4×C127—42no—
63C2×C4×C127—21no—
64C2×C4×C127—41no—
65C2×C4×C127—41no—
66C2×C4×C127—82no—
67C2×C4×C127—162no—
68C2×C4×C127#12111yescharacteristic
69C2×C4×C127#12312yes—
70C2×C4×C127C2×D811yescharacteristic
71C2×C4×C127#13712yes—
72C8×C127—41no—
73C8×C127—82no—
74C8×C127#12311yescharacteristic
75C8×C127#12411yescharacteristic
76C8×C127#12612yes—
77C22×C127—22no—
78C22×C127—41no—
79C22×C127—42no—
80C22×C127#46611yescharacteristic
81C22×C127#48512yes—
82C4×C127—41no—
83C4×C127—162no—
84C4×C127#39711yescharacteristic
85C4×C127#47011yescharacteristic
86C4×C127#48012yes—
87#13496C12711yesmaximal, characteristic, direct product factor, Sylow
88C2×C127—22no—
89C2×C127—81no—
90C2×C127#207511yescharacteristic
91C2×C127#222312yes—
92C2×#367C2×C12711yescharacteristic, complemented
93#2113C2×C12711yescharacteristic
94#1816C2×C12712yes—
95#1387C2×C12712yescomplemented
96#1381C2×C12711yescharacteristic, complemented
97C127#1349611yescharacteristic, direct product factor, Sylow
98C2×#131C22×C12711yescharacteristic
99C2×M32C22×C12711yescharacteristic
100C22×C16C22×C12711yescharacteristic
101C2×#108C22×C12712yes—
102C2×#107C22×C12712yes—
103#417—22no—
104#367—22no—
105C22⋊C16—22no—
106#343—22no—
107C2×#41D4×C12711yescharacteristic
108#131—22no—
109#131—22no—
110C2×M16—21no—
111C2×M16—22no—
112C2×M16D4×C12711yescharacteristic
113C22×C8—21no—
114C22×C8C23×C12711yescharacteristic
115C2×C4⋊C4—22no—
116M32—22no—
117C2×C16—22no—
118C2×C16—21no—
119C2×C16D4×C12712yes—
120#108—22no—
121#108—22no—
122#107—22no—
123#107—22no—
124#103—42no—
125#102—42no—
126#41—22no—
127#41—22no—
128C2×Q8D8×C12711yescharacteristic
129C2×D4—21no—
130C2×D4D8×C12711yescharacteristic
131C22×C4—21no—
132C22×C4—42no—
133C22×C4C2×D4×C12711yescharacteristic
134M16—22no—
135M16—42no—
136M16—42no—
137M16—42no—
138C2×C8—21no—
139C2×C8—41no—
140C2×C8—41no—
141C2×C8—42no—
142C2×C8C2×D4×C12711yescharacteristic
143C2×C8#41×C12712yes—
144C2×C8#41×C12712yes—
145C2×C8#41×C12711yescharacteristic
146C4⋊C4—42no—
147C4⋊C4—42no—
148C16—22no—
149C16—41no—
150C23—21no—
151C23#135×C12711yescharacteristic
152Q8—22no—
153D4—22no—
154D4—42no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—82no—
159C2×C4—162no—
160C2×C4#121×C12711yescharacteristic
161C2×C4#123×C12712yes—
162C2×C4C2×D8×C12711yescharacteristic
163C2×C4#137×C12712yes—
164C8—41no—
165C8—82no—
166C8#123×C12711yescharacteristic
167C8#124×C12711yescharacteristic
168C8#126×C12712yes—
169C22—22no—
170C22—41no—
171C22—42no—
172C22#466×C12711yescharacteristic
173C22#485×C12712yes—
174C4—41no—
175C4—162no—
176C4#397×C12711yescharacteristic
177C4#470×C12711yescharacteristic
178C4#480×C12712yes—
179C2—22no—
180C2—81no—
181C2C127×#207511yescharacteristic
182C2C127×#222312yes—
subgroupG/H
center, socleC22×C127#466
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC2×#41×C127D4
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×#131×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#367×C127C2semidirect
4. C127×#1387C2semidirect
5. C127×#1381C2semidirect
87. #13496C127direct (N × H)
92. C2×#367C2×C127semidirect
95. #1387C2×C127semidirect
96. #1381C2×C127semidirect
97. C127#13496direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#367×C1272
C127×#21132
C127×#18162
C127×#13872
C127×#13812
#13496127