Finite Group Databasebeta

← C127×#7124 #44570797

Subgroups — C127×#7124 #44570797

Order 32512.

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

normal subgroups only

This group has 200 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×#1940C211yesmaximal, characteristic
2C127×#1377C211yesmaximal, characteristic
3C127×#1377C211yesmaximal, characteristic
4C2×M32×C127—21no—
5C2×M32×C127—21no—
6C2×C4⋊C8×C127—21no—
7C2×C4⋊C8×C127C411yescharacteristic
8C2×#97×C127C2211yescharacteristic
9C4×C4⋊C4×C127C411yescharacteristic
10#336×C127—21no—
11C22×C8×C127—21no—
12C22×C8×C127D411yescharacteristic
13C22×C8×C127D411yescharacteristic
14C2×C4⋊C4×C127—21no—
15C2×C42×C127—21no—
16C2×C42×C127C2×C411yescharacteristic
17M32×C127—22no—
18M32×C127—22no—
19M32×C127—41no—
20M32×C127—41no—
21C2×C16×C127—41no—
22C2×C16×C127—41no—
23C4⋊C8×C127—41no—
24C4⋊C8×C127—41no—
25C4⋊C8×C127—41no—
26#97×C127—41no—
27#95×C127C811yescharacteristic
28#95×C127C811yescharacteristic
29C22×C4×C127—21no—
30C22×C4×C127—21no—
31C22×C4×C127C22⋊C411yescharacteristic
32C22×C4×C127C2×C811yescharacteristic
33C22×C4×C127M1611yescharacteristic
34C2×C8×C127—21no—
35C2×C8×C127—21no—
36C2×C8×C127—21no—
37C2×C8×C127—21no—
38C2×C8×C127—41no—
39C2×C8×C127—41no—
40C2×C8×C127—41no—
41C2×C8×C127D811yescharacteristic
42C2×C8×C127SD1611yescharacteristic
43C2×C8×C127SD1611yescharacteristic
44C2×C8×C127Q1611yescharacteristic
45C4⋊C4×C127—42no—
46C42×C127—21no—
47C42×C127—21no—
48C42×C127—41no—
49C42×C127—41no—
50C16×C127—42no—
51C16×C127—42no—
52C23×C127C22⋊C811yescharacteristic
53C2×C4×C127—22no—
54C2×C4×C127—21no—
55C2×C4×C127—21no—
56C2×C4×C127—41no—
57C2×C4×C127—41no—
58C2×C4×C127—41no—
59C2×C4×C127—41no—
60C2×C4×C127—41no—
61C2×C4×C127—41no—
62C2×C4×C127—41no—
63C2×C4×C127#9911yescharacteristic
64C2×C4×C127#10111yescharacteristic
65C2×C4×C127#10211yescharacteristic
66C2×C4×C127#10311yescharacteristic
67C2×C4×C127#10411yescharacteristic
68C2×C4×C127#10411yescharacteristic
69C8×C127—21no—
70C8×C127—21no—
71C8×C127—21no—
72C8×C127—21no—
73C8×C127—81no—
74C22×C127—21no—
75C22×C127—21no—
76C22×C127#32411yescharacteristic
77C22×C127D4⋊C811yescharacteristic
78C22×C127Q8⋊C811yescharacteristic
79C4×C127—42no—
80C4×C127—41no—
81C4×C127—41no—
82C4×C127—81no—
83C4×C127#32711yescharacteristic
84C4×C127#32811yescharacteristic
85C4×C127#33011yescharacteristic
86C4×C127#33211yescharacteristic
87#7124C12711yesmaximal, characteristic, direct product factor, Sylow
88C2×C127—21no—
89C2×C127—21no—
90C2×C127#127111yescharacteristic
91C2×C127#132711yescharacteristic
92C2×C127#132811yescharacteristic
93#1940C2×C12711yescharacteristic
94#1377C2×C12711yescharacteristic
95#1377C2×C12711yescharacteristic
96C127#712411yescharacteristic, direct product factor, Sylow
97C2×M32—21no—
98C2×M32—21no—
99C2×C4⋊C8—21no—
100C2×C4⋊C8C4×C12711yescharacteristic
101C2×#97C22×C12711yescharacteristic
102C4×C4⋊C4C4×C12711yescharacteristic
103#336—21no—
104C22×C8—21no—
105C22×C8D4×C12711yescharacteristic
106C22×C8D4×C12711yescharacteristic
107C2×C4⋊C4—21no—
108C2×C42—21no—
109C2×C42C2×C4×C12711yescharacteristic
110M32—22no—
111M32—22no—
112M32—41no—
113M32—41no—
114C2×C16—41no—
115C2×C16—41no—
116C4⋊C8—41no—
117C4⋊C8—41no—
118C4⋊C8—41no—
119#97—41no—
120#95C8×C12711yescharacteristic
121#95C8×C12711yescharacteristic
122C22×C4—21no—
123C22×C4—21no—
124C22×C4C22⋊C4×C12711yescharacteristic
125C22×C4C2×C8×C12711yescharacteristic
126C22×C4M16×C12711yescharacteristic
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—21no—
131C2×C8—41no—
132C2×C8—41no—
133C2×C8—41no—
134C2×C8D8×C12711yescharacteristic
135C2×C8SD16×C12711yescharacteristic
136C2×C8SD16×C12711yescharacteristic
137C2×C8Q16×C12711yescharacteristic
138C4⋊C4—42no—
139C42—21no—
140C42—21no—
141C42—41no—
142C42—41no—
143C16—42no—
144C16—42no—
145C23C22⋊C8×C12711yescharacteristic
146C2×C4—22no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4#99×C12711yescharacteristic
157C2×C4#101×C12711yescharacteristic
158C2×C4#102×C12711yescharacteristic
159C2×C4#103×C12711yescharacteristic
160C2×C4#104×C12711yescharacteristic
161C2×C4#104×C12711yescharacteristic
162C8—21no—
163C8—21no—
164C8—21no—
165C8—21no—
166C8—81no—
167C22—21no—
168C22—21no—
169C22#324×C12711yescharacteristic
170C22D4⋊C8×C12711yescharacteristic
171C22Q8⋊C8×C12711yescharacteristic
172C4—42no—
173C4—41no—
174C4—41no—
175C4—81no—
176C4#327×C12711yescharacteristic
177C4#328×C12711yescharacteristic
178C4#330×C12711yescharacteristic
179C4#332×C12711yescharacteristic
180C2—21no—
181C2—21no—
182C2C127×#127111yescharacteristic
183C2C127×#132711yescharacteristic
184C2C127×#132811yescharacteristic
subgroupG/H
centerC2×C4×C127#99
commutatorC22×C4C2×C8×C127
Frattini, cosocleC2×#97C22×C127
socleC22×C127#324
prime radicalC23×C127C22⋊C8
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C22×C4×C127 ◁ C2×#97×C127 ◁ G

Complements

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

NH ≅ G/Ntype
87. #7124C127direct (N × H)
96. C127#7124direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#19402
C127×#13772
#7124127