Finite Group Databasebeta

← C127×#7127 #44570800

Subgroups — C127×#7127 #44570800

Order 32512.

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

normal subgroups only

This group has 202 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×#1944C211yesmaximal, characteristic
2C127×#1377C211yesmaximal, characteristic
3C127×#1275C211yesmaximal, characteristic
4C2×M32×C127—21no—
5#431×C127—21no—
6C2×#107×C127C411yescharacteristic
7C2×#106×C127C411yescharacteristic
8C2×#97×C127C2211yescharacteristic
9#389×C127—21no—
10#340×C127—21no—
11C22×C8×C127C2×C411yescharacteristic
12C22×C8×C127D411yescharacteristic
13C2×C4⋊C4×C127—21no—
14C2×C4⋊C4×C127—21no—
15C2×C4⋊C4×C127—41no—
16C2×C42×C127D411yescharacteristic
17M32×C127—22no—
18M32×C127—41no—
19C2×C16×C127—41no—
20#107×C127—41no—
21#106×C127—21no—
22#106×C127C812yescomplemented
23C4⋊C8×C127—41no—
24C22⋊C8×C127—41no—
25#97×C127—41no—
26C4×C8×C127—22no—
27#95×C127—41no—
28C22×C4×C127—41no—
29C22×C4×C127—41no—
30C22×C4×C127C22⋊C411yescharacteristic
31C22×C4×C127D811yescharacteristic
32C22×C4×C127SD1611yescharacteristic
33C2×C8×C127—21no—
34C2×C8×C127—21no—
35C2×C8×C127—21no—
36C2×C8×C127—21no—
37C2×C8×C127—42no—
38C2×C8×C127C2×C811yescharacteristic
39C2×C8×C127M1611yescharacteristic
40C2×C8×C127SD1611yescharacteristic
41C2×C8×C127Q1611yescharacteristic
42C4⋊C4×C127—22no—
43C4⋊C4×C127—41no—
44C4⋊C4×C127—41no—
45C4⋊C4×C127—41no—
46C4⋊C4×C127—82no—
47C42×C127—21no—
48C42×C127—21no—
49C16×C127—42no—
50C23×C127#10211yescharacteristic
51C2×C4×C127—21no—
52C2×C4×C127—21no—
53C2×C4×C127—41no—
54C2×C4×C127—41no—
55C2×C4×C127—42no—
56C2×C4×C127—81no—
57C2×C4×C127—81no—
58C2×C4×C127—81no—
59C2×C4×C127—81no—
60C2×C4×C127—81no—
61C2×C4×C127C22⋊C811yescharacteristic
62C2×C4×C127#9911yescharacteristic
63C2×C4×C127#10111yescharacteristic
64C2×C4×C127#10311yescharacteristic
65C2×C4×C127#10411yescharacteristic
66C2×C4×C127#10411yescharacteristic
67C8×C127—21no—
68C8×C127—21no—
69C8×C127—21no—
70C8×C127—21no—
71C8×C127—82no—
72C22×C127—21no—
73C22×C127—21no—
74C22×C127D4⋊C811yescharacteristic
75C22×C127#32711yescharacteristic
76C22×C127#33211yescharacteristic
77C4×C127—41no—
78C4×C127—41no—
79C4×C127—82no—
80C4×C127—161no—
81C4×C127#32411yescharacteristic
82C4×C127Q8⋊C811yescharacteristic
83C4×C127#32811yescharacteristic
84C4×C127#33011yescharacteristic
85#7127C12711yesmaximal, characteristic, direct product factor, Sylow
86C2×C127—21no—
87C2×C127—21no—
88C2×C127#127111yescharacteristic
89C2×C127#133911yescharacteristic
90C2×C127#134211yescharacteristic
91#1944C2×C12711yescharacteristic
92#1377C2×C12711yescharacteristic
93#1275C2×C12711yescharacteristic
94C127#712711yescharacteristic, direct product factor, Sylow
95C2×M32—21no—
96#431—21no—
97C2×#107C4×C12711yescharacteristic
98C2×#106C4×C12711yescharacteristic
99C2×#97C22×C12711yescharacteristic
100#389—21no—
101#340—21no—
102C22×C8C2×C4×C12711yescharacteristic
103C22×C8D4×C12711yescharacteristic
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—41no—
107C2×C42D4×C12711yescharacteristic
108M32—22no—
109M32—41no—
110C2×C16—41no—
111#107—41no—
112#106—21no—
113#106C8×C12712yescomplemented
114C4⋊C8—41no—
115C22⋊C8—41no—
116#97—41no—
117C4×C8—22no—
118#95—41no—
119C22×C4—41no—
120C22×C4—41no—
121C22×C4C22⋊C4×C12711yescharacteristic
122C22×C4D8×C12711yescharacteristic
123C22×C4SD16×C12711yescharacteristic
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—42no—
129C2×C8C2×C8×C12711yescharacteristic
130C2×C8M16×C12711yescharacteristic
131C2×C8SD16×C12711yescharacteristic
132C2×C8Q16×C12711yescharacteristic
133C4⋊C4—22no—
134C4⋊C4—41no—
135C4⋊C4—41no—
136C4⋊C4—41no—
137C4⋊C4—82no—
138C42—21no—
139C42—21no—
140C16—42no—
141C23#102×C12711yescharacteristic
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—42no—
147C2×C4—81no—
148C2×C4—81no—
149C2×C4—81no—
150C2×C4—81no—
151C2×C4—81no—
152C2×C4C22⋊C8×C12711yescharacteristic
153C2×C4#99×C12711yescharacteristic
154C2×C4#101×C12711yescharacteristic
155C2×C4#103×C12711yescharacteristic
156C2×C4#104×C12711yescharacteristic
157C2×C4#104×C12711yescharacteristic
158C8—21no—
159C8—21no—
160C8—21no—
161C8—21no—
162C8—82no—
163C22—21no—
164C22—21no—
165C22D4⋊C8×C12711yescharacteristic
166C22#327×C12711yescharacteristic
167C22#332×C12711yescharacteristic
168C4—41no—
169C4—41no—
170C4—82no—
171C4—161no—
172C4#324×C12711yescharacteristic
173C4Q8⋊C8×C12711yescharacteristic
174C4#328×C12711yescharacteristic
175C4#330×C12711yescharacteristic
176C2—21no—
177C2—21no—
178C2C127×#127111yescharacteristic
179C2C127×#133911yescharacteristic
180C2C127×#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
22. #106×C127C8semidirect
85. #7127C127direct (N × H)
94. C127#7127direct (N × H)
113. #106C8×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#19442
C127×#13772
C127×#12752
#7127127