Finite Group Databasebeta

← C127×#7434 #44571107

Subgroups — C127×#7434 #44571107

Order 32512.

224 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 46 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×#2093C211yesmaximal, characteristic
2C127×#1393C211yesmaximal, characteristic
3C127×#1318C211yesmaximal, characteristic
4C2×#107×C127—21no—
5C2×#102×C127—21no—
6C2×#99×C127—21no—
7#390×C127C2211yescharacteristic
8#384×C127C411yescharacteristic, complemented
9#336×C127C411yescharacteristic, complemented
10#324×C127—21no—
11C22×D4×C127D411yescharacteristic
12C22×C8×C127—21no—
13C2×C4⋊C4×C127—21no—
14C2×C4⋊C4×C127—41no—
15C2×C4⋊C4×C127D411yescharacteristic
16C2×C22⋊C4×C127—41no—
17C2×C22⋊C4×C127—41no—
18C2×C42×C127C2×C411yescharacteristic
19#107×C127—42no—
20#102×C127—42no—
21#99×C127—22no—
22#99×C127—41no—
23C22⋊C8×C127—41no—
24C24×C127—21no—
25C2×D4×C127—21no—
26C2×D4×C127—41no—
27C2×D4×C127—41no—
28C2×D4×C127SD1611yescharacteristic
29C2×D4×C127Q1611yescharacteristic
30C22×C4×C127—21no—
31C22×C4×C127—21no—
32C22×C4×C127—41no—
33C22×C4×C127—81no—
34C22×C4×C127C22⋊C411yescharacteristic
35C2×C8×C127—22no—
36C2×C8×C127—41no—
37C2×C8×C127—41no—
38C2×C8×C127—81no—
39C4⋊C4×C127—41no—
40C4⋊C4×C127—41no—
41C4⋊C4×C127—41no—
42C4⋊C4×C127—82no—
43C22⋊C4×C127—42no—
44C22⋊C4×C127—82no—
45C22⋊C4×C127—81no—
46C42×C127—41no—
47C23×C127—21no—
48C23×C127—21no—
49C23×C127—41no—
50C23×C127—41no—
51C23×C127—81no—
52C23×C127—81no—
53C23×C127#9911yescharacteristic
54D4×C127—41no—
55D4×C127—41no—
56D4×C127—81no—
57C2×C4×C127—21no—
58C2×C4×C127—21no—
59C2×C4×C127—22no—
60C2×C4×C127—41no—
61C2×C4×C127—41no—
62C2×C4×C127—41no—
63C2×C4×C127—81no—
64C2×C4×C127—82no—
65C2×C4×C127—82no—
66C2×C4×C127—81no—
67C2×C4×C127—161no—
68C2×C4×C127—161no—
69C2×C4×C127#10311yescharacteristic
70C2×C4×C127#10411yescharacteristic
71C8×C127—42no—
72C8×C127—161no—
73C22×C127—21no—
74C22×C127—21no—
75C22×C127—41no—
76C22×C127—41no—
77C22×C127—81no—
78C22×C127—81no—
79C22×C127—81no—
80C22×C127—81no—
81C22×C127—161no—
82C22×C127#32811yescharacteristic
83C22×C127#35211yescharacteristic
84C22×C127#35311yescharacteristic
85C4×C127—21no—
86C4×C127—21no—
87C4×C127—42no—
88C4×C127—81no—
89C4×C127—162no—
90C4×C127—161no—
91#7434C12711yesmaximal, characteristic, direct product factor, Sylow
92C2×C127—21no—
93C2×C127—21no—
94C2×C127—81no—
95C2×C127—81no—
96C2×C127#135211yescharacteristic
97C2×C127#140711yescharacteristic
98C2×C127#140811yescharacteristic
99#2093C2×C12711yescharacteristic
100#1393C2×C12711yescharacteristic
101#1318C2×C12711yescharacteristic
102C127#743411yescharacteristic, direct product factor, Sylow
103C2×#107—21no—
104C2×#102—21no—
105C2×#99—21no—
106#390C22×C12711yescharacteristic
107#384C4×C12711yescharacteristic, complemented
108#336C4×C12711yescharacteristic, complemented
109#324—21no—
110C22×D4D4×C12711yescharacteristic
111C22×C8—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4D4×C12711yescharacteristic
115C2×C22⋊C4—41no—
116C2×C22⋊C4—41no—
117C2×C42C2×C4×C12711yescharacteristic
118#107—42no—
119#102—42no—
120#99—22no—
121#99—41no—
122C22⋊C8—41no—
123C24—21no—
124C2×D4—21no—
125C2×D4—41no—
126C2×D4—41no—
127C2×D4SD16×C12711yescharacteristic
128C2×D4Q16×C12711yescharacteristic
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—41no—
132C22×C4—81no—
133C22×C4C22⋊C4×C12711yescharacteristic
134C2×C8—22no—
135C2×C8—41no—
136C2×C8—41no—
137C2×C8—81no—
138C4⋊C4—41no—
139C4⋊C4—41no—
140C4⋊C4—41no—
141C4⋊C4—82no—
142C22⋊C4—42no—
143C22⋊C4—82no—
144C22⋊C4—81no—
145C42—41no—
146C23—21no—
147C23—21no—
148C23—41no—
149C23—41no—
150C23—81no—
151C23—81no—
152C23#99×C12711yescharacteristic
153D4—41no—
154D4—41no—
155D4—81no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—81no—
163C2×C4—82no—
164C2×C4—82no—
165C2×C4—81no—
166C2×C4—161no—
167C2×C4—161no—
168C2×C4#103×C12711yescharacteristic
169C2×C4#104×C12711yescharacteristic
170C8—42no—
171C8—161no—
172C22—21no—
173C22—21no—
174C22—41no—
175C22—41no—
176C22—81no—
177C22—81no—
178C22—81no—
179C22—81no—
180C22—161no—
181C22#328×C12711yescharacteristic
182C22#352×C12711yescharacteristic
183C22#353×C12711yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—81no—
188C4—162no—
189C4—161no—
190C2—21no—
191C2—21no—
192C2—81no—
193C2—81no—
194C2C127×#135211yescharacteristic
195C2C127×#140711yescharacteristic
196C2C127×#140811yescharacteristic
subgroupG/H
center, socleC22×C127#353
commutatorC2×C42C2×C4×C127
Frattini, cosocle#390C22×C127
prime radicalC22×D4×C127D4
LCSG ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C127 ◁ C22×C4×C127 ◁ #390×C127 ◁ G

Complements

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

NH ≅ G/Ntype
8. #384×C127C4semidirect
9. #336×C127C4semidirect
91. #7434C127direct (N × H)
102. C127#7434direct (N × H)
107. #384C4×C127semidirect
108. #336C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#20932
C127×#13932
C127×#13182
#7434127