Finite Group Databasebeta

← C127×#7111 #44570784

Subgroups — C127×#7111 #44570784

Order 32512.

234 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 74 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×#1971C211yesmaximal, characteristic
2C127×#1377C211yesmaximal, characteristic
3C127×#1275C211yesmaximal, characteristic
4C22×Q16×C127C411yescharacteristic
5C2×M32×C127—21no—
6#431×C127—21no—
7C2×#106×C127C411yescharacteristic
8C2×#103×C127—21no—
9C2×#97×C127C2211yescharacteristic
10#391×C127—21no—
11C22×Q8×C127—21no—
12C2×Q16×C127—21no—
13C2×Q16×C127—41no—
14C2×Q16×C127—41no—
15C2×Q16×C127C812yescomplemented
16C22×C8×C127C2×C411yescharacteristic
17C22×C8×C127D411yescharacteristic
18C2×C4⋊C4×C127—21no—
19C2×C42×C127D411yescharacteristic
20M32×C127—22no—
21M32×C127—41no—
22C2×C16×C127—41no—
23#106×C127—41no—
24C4⋊C8×C127—41no—
25#103×C127—41no—
26#103×C127—41no—
27C22⋊C8×C127—41no—
28#97×C127—41no—
29C4×C8×C127—22no—
30#95×C127—41no—
31#95×C127—41no—
32C2×Q8×C127—22no—
33C2×Q8×C127—41no—
34C2×Q8×C127—41no—
35C2×Q8×C127—41no—
36C2×Q8×C127—41no—
37C2×Q8×C127—41no—
38C22×C4×C127—41no—
39C22×C4×C127—41no—
40C22×C4×C127C22⋊C411yescharacteristic
41C22×C4×C127D811yescharacteristic
42C22×C4×C127SD1611yescharacteristic
43Q16×C127—42no—
44Q16×C127—42no—
45C2×C8×C127—21no—
46C2×C8×C127—21no—
47C2×C8×C127—21no—
48C2×C8×C127—21no—
49C2×C8×C127—42no—
50C2×C8×C127C2×C811yescharacteristic
51C2×C8×C127M1611yescharacteristic
52C2×C8×C127D811yescharacteristic
53C2×C8×C127SD1611yescharacteristic
54C4⋊C4×C127—41no—
55C4⋊C4×C127—41no—
56C42×C127—21no—
57C42×C127—21no—
58C16×C127—42no—
59C23×C127#10211yescharacteristic
60Q8×C127—42no—
61Q8×C127—42no—
62Q8×C127—81no—
63Q8×C127—81no—
64C2×C4×C127—21no—
65C2×C4×C127—21no—
66C2×C4×C127—41no—
67C2×C4×C127—41no—
68C2×C4×C127—42no—
69C2×C4×C127—81no—
70C2×C4×C127—81no—
71C2×C4×C127—81no—
72C2×C4×C127—81no—
73C2×C4×C127—81no—
74C2×C4×C127C22⋊C811yescharacteristic
75C2×C4×C127#9911yescharacteristic
76C2×C4×C127#10011yescharacteristic
77C2×C4×C127#10211yescharacteristic
78C2×C4×C127#10411yescharacteristic
79C2×C4×C127#10411yescharacteristic
80C8×C127—21no—
81C8×C127—21no—
82C8×C127—21no—
83C8×C127—21no—
84C8×C127—82no—
85C22×C127—21no—
86C22×C127—21no—
87C22×C127D4⋊C811yescharacteristic
88C22×C127#32711yescharacteristic
89C22×C127#33111yescharacteristic
90C4×C127—41no—
91C4×C127—41no—
92C4×C127—82no—
93C4×C127—161no—
94C4×C127#32311yescharacteristic
95C4×C127D4⋊C811yescharacteristic
96C4×C127#32711yescharacteristic
97C4×C127#32911yescharacteristic
98#7111C12711yesmaximal, characteristic, direct product factor, Sylow
99C2×C127—21no—
100C2×C127—21no—
101C2×C127#127011yescharacteristic
102C2×C127#134011yescharacteristic
103C2×C127#134211yescharacteristic
104#1971C2×C12711yescharacteristic
105#1377C2×C12711yescharacteristic
106#1275C2×C12711yescharacteristic
107C127#711111yescharacteristic, direct product factor, Sylow
108C22×Q16C4×C12711yescharacteristic
109C2×M32—21no—
110#431—21no—
111C2×#106C4×C12711yescharacteristic
112C2×#103—21no—
113C2×#97C22×C12711yescharacteristic
114#391—21no—
115C22×Q8—21no—
116C2×Q16—21no—
117C2×Q16—41no—
118C2×Q16—41no—
119C2×Q16C8×C12712yescomplemented
120C22×C8C2×C4×C12711yescharacteristic
121C22×C8D4×C12711yescharacteristic
122C2×C4⋊C4—21no—
123C2×C42D4×C12711yescharacteristic
124M32—22no—
125M32—41no—
126C2×C16—41no—
127#106—41no—
128C4⋊C8—41no—
129#103—41no—
130#103—41no—
131C22⋊C8—41no—
132#97—41no—
133C4×C8—22no—
134#95—41no—
135#95—41no—
136C2×Q8—22no—
137C2×Q8—41no—
138C2×Q8—41no—
139C2×Q8—41no—
140C2×Q8—41no—
141C2×Q8—41no—
142C22×C4—41no—
143C22×C4—41no—
144C22×C4C22⋊C4×C12711yescharacteristic
145C22×C4D8×C12711yescharacteristic
146C22×C4SD16×C12711yescharacteristic
147Q16—42no—
148Q16—42no—
149C2×C8—21no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—42no—
154C2×C8C2×C8×C12711yescharacteristic
155C2×C8M16×C12711yescharacteristic
156C2×C8D8×C12711yescharacteristic
157C2×C8SD16×C12711yescharacteristic
158C4⋊C4—41no—
159C4⋊C4—41no—
160C42—21no—
161C42—21no—
162C16—42no—
163C23#102×C12711yescharacteristic
164Q8—42no—
165Q8—42no—
166Q8—81no—
167Q8—81no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—42no—
173C2×C4—81no—
174C2×C4—81no—
175C2×C4—81no—
176C2×C4—81no—
177C2×C4—81no—
178C2×C4C22⋊C8×C12711yescharacteristic
179C2×C4#99×C12711yescharacteristic
180C2×C4#100×C12711yescharacteristic
181C2×C4#102×C12711yescharacteristic
182C2×C4#104×C12711yescharacteristic
183C2×C4#104×C12711yescharacteristic
184C8—21no—
185C8—21no—
186C8—21no—
187C8—21no—
188C8—82no—
189C22—21no—
190C22—21no—
191C22D4⋊C8×C12711yescharacteristic
192C22#327×C12711yescharacteristic
193C22#331×C12711yescharacteristic
194C4—41no—
195C4—41no—
196C4—82no—
197C4—161no—
198C4#323×C12711yescharacteristic
199C4D4⋊C8×C12711yescharacteristic
200C4#327×C12711yescharacteristic
201C4#329×C12711yescharacteristic
202C2—21no—
203C2—21no—
204C2C127×#127011yescharacteristic
205C2C127×#134011yescharacteristic
206C2C127×#134211yescharacteristic
subgroupG/H
center, socleC22×C127#327
commutatorC2×C8C2×C8×C127
Frattini, cosocleC2×#97C22×C127
prime radicalC23×C127#102
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×#97×C127 ◁ G

Complements

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

NH ≅ G/Ntype
15. C2×Q16×C127C8semidirect
98. #7111C127direct (N × H)
107. C127#7111direct (N × H)
119. C2×Q16C8×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#19712
C127×#13772
C127×#12752
#7111127