Finite Group Databasebeta

← C127×#10634 #44574307

Subgroups — C127×#10634 #44574307

Order 32512.

346 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 98 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×#1961C211yesmaximal, characteristic
2C127×#1838C211yesmaximal, characteristic, complemented
3C127×#1545C212yesmaximal
4C127×#1286C212yesmaximal, complemented
5C127×#1281C211yesmaximal, characteristic, complemented
6C2×#127×C127C2211yescharacteristic
7#431×C127C2212yes—
8#423×C127C2212yes—
9C2×#102×C127—22no—
10C2×#97×C127C2211yescharacteristic
11#382×C127C2211yescharacteristic
12#341×C127—22no—
13#331×C127—24no—
14C22×D4×C127—21no—
15C22×D4×C127—22no—
16C2×M16×C127—22no—
17C22×C8×C127D412yes—
18#127×C127—21no—
19#127×C127—22no—
20#127×C127D412yes—
21C2×C4⋊C4×C127—21no—
22C2×C42×C127C2311yescharacteristic
23C4⋊C8×C127—22no—
24C4⋊C8×C127—22no—
25C4⋊C8×C127—22no—
26#102×C127—44no—
27C22⋊C8×C127—22no—
28#97×C127—22no—
29C4×C8×C127—22no—
30#95×C127—22no—
31C24×C127—41no—
32C2×D4×C127—22no—
33C2×D4×C127—24no—
34C2×D4×C127—41no—
35C2×D4×C127—42no—
36C2×D4×C127—42no—
37C2×D4×C127—42no—
38C2×D4×C127—84no—
39C22×C4×C127—41no—
40C22×C4×C127C2×D411yescharacteristic
41C22×C4×C127#4112yes—
42M16×C127—42no—
43M16×C127—42no—
44C2×C8×C127—22no—
45C2×C8×C127—22no—
46C2×C8×C127—22no—
47C2×C8×C127—42no—
48C2×C8×C127—42no—
49C4⋊C4×C127—42no—
50C42×C127C2×D411yescharacteristic
51C42×C127#4111yescharacteristic
52C42×C127#4112yes—
53C23×C127—42no—
54C23×C127—84no—
55C23×C127—81no—
56C23×C127—81no—
57C23×C127#12411yescharacteristic
58D4×C127—44no—
59D4×C127—84no—
60D4×C127—84no—
61D4×C127—82no—
62C2×C4×C127—42no—
63C2×C4×C127—82no—
64C2×C4×C127—81no—
65C2×C4×C127#12111yescharacteristic
66C2×C4×C127#12312yes—
67C2×C4×C127#12311yescharacteristic
68C2×C4×C127#12612yes—
69C2×C4×C127#13512yes—
70C2×C4×C127AGL(1,ℤ/8)12yes—
71C8×C127—42no—
72C8×C127—82no—
73C8×C127—82no—
74C22×C127—22no—
75C22×C127—82no—
76C22×C127—84no—
77C22×C127—162no—
78C22×C127—162no—
79C22×C127#39711yescharacteristic
80C22×C127#48811yescharacteristic
81C22×C127#49011yescharacteristic
82C4×C127—22no—
83C4×C127—22no—
84C4×C127—161no—
85C4×C127#46312yes—
86C4×C127#48212yes—
87#10634C12711yesmaximal, characteristic, direct product factor, Sylow
88C2×C127—21no—
89C2×C127—21no—
90C2×C127—162no—
91C2×C127#207311yescharacteristic
92C2×C127#208112yes—
93#1961C2×C12711yescharacteristic
94#1838C2×C12711yescharacteristic, complemented
95#1545C2×C12712yes—
96#1286C2×C12712yescomplemented
97#1281C2×C12711yescharacteristic, complemented
98C127#1063411yescharacteristic, direct product factor, Sylow
99C2×#127C22×C12711yescharacteristic
100#431C22×C12712yes—
101#423C22×C12712yes—
102C2×#102—22no—
103C2×#97C22×C12711yescharacteristic
104#382C22×C12711yescharacteristic
105#341—22no—
106#331—24no—
107C22×D4—21no—
108C22×D4—22no—
109C2×M16—22no—
110C22×C8D4×C12712yes—
111#127—21no—
112#127—22no—
113#127D4×C12712yes—
114C2×C4⋊C4—21no—
115C2×C42C23×C12711yescharacteristic
116C4⋊C8—22no—
117C4⋊C8—22no—
118C4⋊C8—22no—
119#102—44no—
120C22⋊C8—22no—
121#97—22no—
122C4×C8—22no—
123#95—22no—
124C24—41no—
125C2×D4—22no—
126C2×D4—24no—
127C2×D4—41no—
128C2×D4—42no—
129C2×D4—42no—
130C2×D4—42no—
131C2×D4—84no—
132C22×C4—41no—
133C22×C4C2×D4×C12711yescharacteristic
134C22×C4#41×C12712yes—
135M16—42no—
136M16—42no—
137C2×C8—22no—
138C2×C8—22no—
139C2×C8—22no—
140C2×C8—42no—
141C2×C8—42no—
142C4⋊C4—42no—
143C42C2×D4×C12711yescharacteristic
144C42#41×C12711yescharacteristic
145C42#41×C12712yes—
146C23—42no—
147C23—84no—
148C23—81no—
149C23—81no—
150C23#124×C12711yescharacteristic
151D4—44no—
152D4—84no—
153D4—84no—
154D4—82no—
155C2×C4—42no—
156C2×C4—82no—
157C2×C4—81no—
158C2×C4#121×C12711yescharacteristic
159C2×C4#123×C12712yes—
160C2×C4#123×C12711yescharacteristic
161C2×C4#126×C12712yes—
162C2×C4#135×C12712yes—
163C2×C4AGL(1,ℤ/8)×C12712yes—
164C8—42no—
165C8—82no—
166C8—82no—
167C22—22no—
168C22—82no—
169C22—84no—
170C22—162no—
171C22—162no—
172C22#397×C12711yescharacteristic
173C22#488×C12711yescharacteristic
174C22#490×C12711yescharacteristic
175C4—22no—
176C4—22no—
177C4—161no—
178C4#463×C12712yes—
179C4#482×C12712yes—
180C2—21no—
181C2—21no—
182C2—162no—
183C2C127×#207311yescharacteristic
184C2C127×#208112yes—
subgroupG/H
center, socleC22×C127#397
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC2×#127×C127C22
LCSG ▷ C2×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×#1838C2semidirect
4. C127×#1286C2semidirect
5. C127×#1281C2semidirect
87. #10634C127direct (N × H)
94. #1838C2×C127semidirect
96. #1286C2×C127semidirect
97. #1281C2×C127semidirect
98. C127#10634direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#19612
C127×#18382
C127×#15452
C127×#12862
C127×#12812
#10634127