Finite Group Databasebeta

← C127×#7429 #44571102

Subgroups — C127×#7429 #44571102

Order 32512.

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

normal subgroups only

This group has 196 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×#2026C211yesmaximal, characteristic
2C127×#1394C211yesmaximal, characteristic
3C127×#1319C211yesmaximal, characteristic
4C2×#125×C127C411yescharacteristic
5C2×#103×C127—21no—
6C2×#101×C127—21no—
7#391×C127C2211yescharacteristic
8#340×C127—21no—
9#336×C127C411yescharacteristic
10#324×C127—21no—
11C22×Q8×C127D411yescharacteristic
12C2×M16×C127—41no—
13C22×C8×C127—21no—
14#125×C127—42no—
15C2×C4⋊C4×C127—21no—
16C2×C4⋊C4×C127—41no—
17C2×C4⋊C4×C127D411yescharacteristic
18C2×C42×C127C2×C411yescharacteristic
19#103×C127—42no—
20#101×C127—22no—
21#101×C127—41no—
22C22⋊C8×C127—41no—
23#95×C127—41no—
24C2×Q8×C127—21no—
25C2×Q8×C127—41no—
26C2×Q8×C127—41no—
27C2×Q8×C127SD1611yescharacteristic
28C2×Q8×C127Q1611yescharacteristic
29C22×C4×C127—21no—
30C22×C4×C127—21no—
31C22×C4×C127—21no—
32C22×C4×C127—41no—
33C22×C4×C127C22⋊C411yescharacteristic
34M16×C127—42no—
35M16×C127—81no—
36C2×C8×C127—41no—
37C2×C8×C127—41no—
38C2×C8×C127—41no—
39C2×C8×C127—81no—
40C2×C8×C127—81no—
41C4⋊C4×C127—22no—
42C4⋊C4×C127—41no—
43C4⋊C4×C127—41no—
44C4⋊C4×C127—42no—
45C4⋊C4×C127—42no—
46C42×C127—41no—
47C23×C127#9911yescharacteristic
48Q8×C127—41no—
49Q8×C127—41no—
50Q8×C127—81no—
51C2×C4×C127—21no—
52C2×C4×C127—21no—
53C2×C4×C127—21no—
54C2×C4×C127—21no—
55C2×C4×C127—41no—
56C2×C4×C127—41no—
57C2×C4×C127—41no—
58C2×C4×C127—41no—
59C2×C4×C127—41no—
60C2×C4×C127—42no—
61C2×C4×C127—41no—
62C2×C4×C127—81no—
63C2×C4×C127—81no—
64C2×C4×C127—81no—
65C2×C4×C127#10311yescharacteristic
66C2×C4×C127#10411yescharacteristic
67C8×C127—81no—
68C8×C127—82no—
69C8×C127—161no—
70C22×C127—21no—
71C22×C127—21no—
72C22×C127#32811yescharacteristic
73C22×C127AΣL(1,𝔽16)11yescharacteristic
74C22×C127#35411yescharacteristic
75C4×C127—21no—
76C4×C127—21no—
77C4×C127—41no—
78C4×C127—41no—
79C4×C127—81no—
80C4×C127—82no—
81C4×C127—81no—
82#7429C12711yesmaximal, characteristic, direct product factor, Sylow
83C2×C127—21no—
84C2×C127—21no—
85C2×C127#135111yescharacteristic
86C2×C127#141311yescharacteristic
87C2×C127#141411yescharacteristic
88#2026C2×C12711yescharacteristic
89#1394C2×C12711yescharacteristic
90#1319C2×C12711yescharacteristic
91C127#742911yescharacteristic, direct product factor, Sylow
92C2×#125C4×C12711yescharacteristic
93C2×#103—21no—
94C2×#101—21no—
95#391C22×C12711yescharacteristic
96#340—21no—
97#336C4×C12711yescharacteristic
98#324—21no—
99C22×Q8D4×C12711yescharacteristic
100C2×M16—41no—
101C22×C8—21no—
102#125—42no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4D4×C12711yescharacteristic
106C2×C42C2×C4×C12711yescharacteristic
107#103—42no—
108#101—22no—
109#101—41no—
110C22⋊C8—41no—
111#95—41no—
112C2×Q8—21no—
113C2×Q8—41no—
114C2×Q8—41no—
115C2×Q8SD16×C12711yescharacteristic
116C2×Q8Q16×C12711yescharacteristic
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—21no—
120C22×C4—41no—
121C22×C4C22⋊C4×C12711yescharacteristic
122M16—42no—
123M16—81no—
124C2×C8—41no—
125C2×C8—41no—
126C2×C8—41no—
127C2×C8—81no—
128C2×C8—81no—
129C4⋊C4—22no—
130C4⋊C4—41no—
131C4⋊C4—41no—
132C4⋊C4—42no—
133C4⋊C4—42no—
134C42—41no—
135C23#99×C12711yescharacteristic
136Q8—41no—
137Q8—41no—
138Q8—81no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—42no—
149C2×C4—41no—
150C2×C4—81no—
151C2×C4—81no—
152C2×C4—81no—
153C2×C4#103×C12711yescharacteristic
154C2×C4#104×C12711yescharacteristic
155C8—81no—
156C8—82no—
157C8—161no—
158C22—21no—
159C22—21no—
160C22#328×C12711yescharacteristic
161C22AΣL(1,𝔽16)×C12711yescharacteristic
162C22#354×C12711yescharacteristic
163C4—21no—
164C4—21no—
165C4—41no—
166C4—41no—
167C4—81no—
168C4—82no—
169C4—81no—
170C2—21no—
171C2—21no—
172C2C127×#135111yescharacteristic
173C2C127×#141311yescharacteristic
174C2C127×#141411yescharacteristic
subgroupG/H
center, socleC22×C127#354
commutatorC2×C42C2×C4×C127
Frattini, cosocle#391C22×C127
prime radicalC23×C127#99
LCSG ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C127 ◁ C22×C4×C127 ◁ #391×C127 ◁ G

Complements

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

NH ≅ G/Ntype
82. #7429C127direct (N × H)
91. C127#7429direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#20262
C127×#13942
C127×#13192
#7429127