Finite Group Databasebeta

← C127×#7125 #44570798

Subgroups — C127×#7125 #44570798

Order 32512.

182 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 70 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×#1946C211yesmaximal, characteristic
2C127×#1375C211yesmaximal, characteristic
3C127×#1281C211yesmaximal, characteristic
4C2×M32×C127—21no—
5#431×C127—21no—
6C2×#108×C127C411yescharacteristic
7#427×C127C411yescharacteristic
8#424×C127—21no—
9C2×#97×C127C2211yescharacteristic
10#339×C127—21no—
11C2×M16×C127—21no—
12C22×C8×C127C2×C411yescharacteristic
13C22×C8×C127D411yescharacteristic
14#117×C127—21no—
15C2×C42×C127D411yescharacteristic
16M32×C127—41no—
17M32×C127—41no—
18C2×C16×C127—22no—
19#108×C127—41no—
20#107×C127—21no—
21#106×C127C812yescomplemented
22C4⋊C8×C127—41no—
23C4⋊C8×C127—41no—
24C4⋊C8×C127—41no—
25C22⋊C8×C127—22no—
26#97×C127—41no—
27C4×C8×C127—41no—
28C22×C4×C127—21no—
29C22×C4×C127C22⋊C411yescharacteristic
30M16×C127—41no—
31M16×C127—41no—
32C2×C8×C127—21no—
33C2×C8×C127—21no—
34C2×C8×C127—21no—
35C2×C8×C127—21no—
36C2×C8×C127—42no—
37C2×C8×C127—41no—
38C2×C8×C127C2×C811yescharacteristic
39C2×C8×C127M1611yescharacteristic
40C2×C8×C127D811yescharacteristic
41C2×C8×C127SD1611yescharacteristic
42C4⋊C4×C127—22no—
43C22⋊C4×C127—41no—
44C42×C127—21no—
45C42×C127—41no—
46C42×C127SD1611yescharacteristic
47C42×C127Q1611yescharacteristic
48C16×C127—42no—
49C23×C127#10411yescharacteristic
50C2×C4×C127—21no—
51C2×C4×C127—21no—
52C2×C4×C127—42no—
53C2×C4×C127—81no—
54C2×C4×C127C22⋊C811yescharacteristic
55C2×C4×C127#9911yescharacteristic
56C2×C4×C127#10111yescharacteristic
57C2×C4×C127#10211yescharacteristic
58C2×C4×C127#10311yescharacteristic
59C2×C4×C127#10411yescharacteristic
60C8×C127—21no—
61C8×C127—21no—
62C8×C127—21no—
63C8×C127—21no—
64C8×C127—82no—
65C8×C127—81no—
66C22×C127—41no—
67C22×C127D4⋊C811yescharacteristic
68C22×C127#32811yescharacteristic
69C22×C127#33011yescharacteristic
70C4×C127—41no—
71C4×C127—41no—
72C4×C127—82no—
73C4×C127#32411yescharacteristic
74C4×C127Q8⋊C811yescharacteristic
75C4×C127#32711yescharacteristic
76C4×C127#33211yescharacteristic
77#7125C12711yesmaximal, characteristic, direct product factor, Sylow
78C2×C127—21no—
79C2×C127—21no—
80C2×C127—21no—
81C2×C127#127111yescharacteristic
82#1946C2×C12711yescharacteristic
83#1375C2×C12711yescharacteristic
84#1281C2×C12711yescharacteristic
85C127#712511yescharacteristic, direct product factor, Sylow
86C2×M32—21no—
87#431—21no—
88C2×#108C4×C12711yescharacteristic
89#427C4×C12711yescharacteristic
90#424—21no—
91C2×#97C22×C12711yescharacteristic
92#339—21no—
93C2×M16—21no—
94C22×C8C2×C4×C12711yescharacteristic
95C22×C8D4×C12711yescharacteristic
96#117—21no—
97C2×C42D4×C12711yescharacteristic
98M32—41no—
99M32—41no—
100C2×C16—22no—
101#108—41no—
102#107—21no—
103#106C8×C12712yescomplemented
104C4⋊C8—41no—
105C4⋊C8—41no—
106C4⋊C8—41no—
107C22⋊C8—22no—
108#97—41no—
109C4×C8—41no—
110C22×C4—21no—
111C22×C4C22⋊C4×C12711yescharacteristic
112M16—41no—
113M16—41no—
114C2×C8—21no—
115C2×C8—21no—
116C2×C8—21no—
117C2×C8—21no—
118C2×C8—42no—
119C2×C8—41no—
120C2×C8C2×C8×C12711yescharacteristic
121C2×C8M16×C12711yescharacteristic
122C2×C8D8×C12711yescharacteristic
123C2×C8SD16×C12711yescharacteristic
124C4⋊C4—22no—
125C22⋊C4—41no—
126C42—21no—
127C42—41no—
128C42SD16×C12711yescharacteristic
129C42Q16×C12711yescharacteristic
130C16—42no—
131C23#104×C12711yescharacteristic
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—42no—
135C2×C4—81no—
136C2×C4C22⋊C8×C12711yescharacteristic
137C2×C4#99×C12711yescharacteristic
138C2×C4#101×C12711yescharacteristic
139C2×C4#102×C12711yescharacteristic
140C2×C4#103×C12711yescharacteristic
141C2×C4#104×C12711yescharacteristic
142C8—21no—
143C8—21no—
144C8—21no—
145C8—21no—
146C8—82no—
147C8—81no—
148C22—41no—
149C22D4⋊C8×C12711yescharacteristic
150C22#328×C12711yescharacteristic
151C22#330×C12711yescharacteristic
152C4—41no—
153C4—41no—
154C4—82no—
155C4#324×C12711yescharacteristic
156C4Q8⋊C8×C12711yescharacteristic
157C4#327×C12711yescharacteristic
158C4#332×C12711yescharacteristic
159C2—21no—
160C2—21no—
161C2—21no—
162C2C127×#127111yescharacteristic
subgroupG/H
centerC4×C127#327
commutatorC2×C8C2×C8×C127
Frattini, cosocleC2×#97C22×C127
socleC2×C127#1271
prime radicalC23×C127#104
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C22×C4×C127 ◁ C2×#97×C127 ◁ G

Complements

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

NH ≅ G/Ntype
21. #106×C127C8semidirect
77. #7125C127direct (N × H)
85. C127#7125direct (N × H)
103. #106C8×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#19462
C127×#13752
C127×#12812
#7125127