Finite Group Databasebeta

← C127×#10666 #44574339

Subgroups — C127×#10666 #44574339

Order 32512.

354 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 114 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×#1963C211yesmaximal, characteristic
2C127×#1843C211yesmaximal, characteristic, complemented
3C127×#1570C212yesmaximal, complemented
4C127×#1480C212yesmaximal
5C127×#1274C211yesmaximal, characteristic, complemented
6#532×C127C2211yescharacteristic
7#431×C127C2212yes—
8#423×C127C2211yescharacteristic
9C2×C4⋊C8×C127—22no—
10C2×C4⋊C8×C127C2212yes—
11C2×#104×C127—22no—
12#376×C127C2211yescharacteristic
13#334×C127—24no—
14D4⋊C8×C127—24no—
15C2×#41×C127—21no—
16C2×M16×C127—21no—
17C22×C8×C127—22no—
18C4⋊Q8×C127Q811yescharacteristic
19#127×C127Q811yescharacteristic
20#124×C127—21no—
21#121×C127—22no—
22C4×D4×C127—22no—
23C2×C42×C127D412yes—
24C2×C42×C127C2311yescharacteristic
25C4⋊C8×C127—22no—
26C4⋊C8×C127—22no—
27C4⋊C8×C127—22no—
28C4⋊C8×C127—22no—
29C4⋊C8×C127—44no—
30#104×C127—44no—
31C22⋊C8×C127—22no—
32C4×C8×C127D414yes—
33#95×C127—22no—
34#41×C127—42no—
35#41×C127—42no—
36C2×Q8×C127—21no—
37C2×D4×C127—22no—
38C2×D4×C127—21no—
39C2×D4×C127—41no—
40C22×C4×C127—22no—
41C22×C4×C127—41no—
42C22×C4×C127C2×D411yescharacteristic
43C22×C4×C127#4112yes—
44M16×C127—42no—
45C2×C8×C127—24no—
46C2×C8×C127—42no—
47C2×C8×C127—41no—
48C2×C8×C127—44no—
49C4⋊C4×C127—22no—
50C22⋊C4×C127—42no—
51C42×C127—22no—
52C42×C127SD1614yes—
53C42×C127C2×D412yes—
54C42×C127C2×Q811yescharacteristic
55C42×C127#4111yescharacteristic
56C23×C127—41no—
57C23×C127#12311yescharacteristic
58Q8×C127—42no—
59D4×C127—44no—
60D4×C127—42no—
61D4×C127—82no—
62C2×C4×C127—24no—
63C2×C4×C127—42no—
64C2×C4×C127—44no—
65C2×C4×C127—41no—
66C2×C4×C127—81no—
67C2×C4×C127—81no—
68C2×C4×C127C22⋊Q812yes—
69C2×C4×C127C22⋊Q811yescharacteristic
70C2×C4×C127#12312yes—
71C2×C4×C127#12711yescharacteristic
72C2×C4×C127C2×SD1612yes—
73C2×C4×C127AGL(1,ℤ/8)12yes—
74C8×C127—44no—
75C8×C127—81no—
76C8×C127—82no—
77C22×C127—22no—
78C22×C127—81no—
79C22×C127—82no—
80C22×C127#39911yescharacteristic
81C22×C127#48112yes—
82C4×C127—22no—
83C4×C127—22no—
84C4×C127—44no—
85C4×C127—81no—
86C4×C127#47612yes—
87C4×C127#49211yescharacteristic
88C4×C127#49611yescharacteristic
89#10666C12711yesmaximal, characteristic, direct product factor, Sylow
90C2×C127—22no—
91C2×C127—161no—
92C2×C127#209411yescharacteristic
93C2×C127#209812yes—
94#1963C2×C12711yescharacteristic
95#1843C2×C12711yescharacteristic, complemented
96#1570C2×C12712yescomplemented
97#1480C2×C12712yes—
98#1274C2×C12711yescharacteristic, complemented
99C127#1066611yescharacteristic, direct product factor, Sylow
100#532C22×C12711yescharacteristic
101#431C22×C12712yes—
102#423C22×C12711yescharacteristic
103C2×C4⋊C8—22no—
104C2×C4⋊C8C22×C12712yes—
105C2×#104—22no—
106#376C22×C12711yescharacteristic
107#334—24no—
108D4⋊C8—24no—
109C2×#41—21no—
110C2×M16—21no—
111C22×C8—22no—
112C4⋊Q8Q8×C12711yescharacteristic
113#127Q8×C12711yescharacteristic
114#124—21no—
115#121—22no—
116C4×D4—22no—
117C2×C42D4×C12712yes—
118C2×C42C23×C12711yescharacteristic
119C4⋊C8—22no—
120C4⋊C8—22no—
121C4⋊C8—22no—
122C4⋊C8—22no—
123C4⋊C8—44no—
124#104—44no—
125C22⋊C8—22no—
126C4×C8D4×C12714yes—
127#95—22no—
128#41—42no—
129#41—42no—
130C2×Q8—21no—
131C2×D4—22no—
132C2×D4—21no—
133C2×D4—41no—
134C22×C4—22no—
135C22×C4—41no—
136C22×C4C2×D4×C12711yescharacteristic
137C22×C4#41×C12712yes—
138M16—42no—
139C2×C8—24no—
140C2×C8—42no—
141C2×C8—41no—
142C2×C8—44no—
143C4⋊C4—22no—
144C22⋊C4—42no—
145C42—22no—
146C42SD16×C12714yes—
147C42C2×D4×C12712yes—
148C42C2×Q8×C12711yescharacteristic
149C42#41×C12711yescharacteristic
150C23—41no—
151C23#123×C12711yescharacteristic
152Q8—42no—
153D4—44no—
154D4—42no—
155D4—82no—
156C2×C4—24no—
157C2×C4—42no—
158C2×C4—44no—
159C2×C4—41no—
160C2×C4—81no—
161C2×C4—81no—
162C2×C4C22⋊Q8×C12712yes—
163C2×C4C22⋊Q8×C12711yescharacteristic
164C2×C4#123×C12712yes—
165C2×C4#127×C12711yescharacteristic
166C2×C4C2×SD16×C12712yes—
167C2×C4AGL(1,ℤ/8)×C12712yes—
168C8—44no—
169C8—82no—
170C8—81no—
171C22—22no—
172C22—81no—
173C22—82no—
174C22#399×C12711yescharacteristic
175C22#481×C12712yes—
176C4—22no—
177C4—22no—
178C4—44no—
179C4—81no—
180C4#476×C12712yes—
181C4#492×C12711yescharacteristic
182C4#496×C12711yescharacteristic
183C2—22no—
184C2—161no—
185C2C127×#209411yescharacteristic
186C2C127×#209812yes—
subgroupG/H
centerC2×C4×C127#127
commutator, Frattini, cosocleC2×C42C23×C127
socleC22×C127#399
prime radical#532×C127C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1843C2semidirect
3. C127×#1570C2semidirect
5. C127×#1274C2semidirect
89. #10666C127direct (N × H)
95. #1843C2×C127semidirect
96. #1570C2×C127semidirect
98. #1274C2×C127semidirect
99. C127#10666direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#19632
C127×#18432
C127×#15702
C127×#14802
C127×#12742
#10666127