Finite Group Databasebeta

← C127×#7431 #44571104

Subgroups — C127×#7431 #44571104

Order 32512.

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

normal subgroups only

This group has 206 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×#2028C211yesmaximal, characteristic
2C127×#1394C211yesmaximal, characteristic
3C127×#1272C211yesmaximal, characteristic
4#544×C127C411yescharacteristic
5#419×C127—21no—
6C2×#101×C127—21no—
7#391×C127C2211yescharacteristic
8#343×C127C411yescharacteristic
9#339×C127—21no—
10#336×C127—21no—
11C22×Q8×C127D411yescharacteristic
12C2×M16×C127—21no—
13C2×M16×C127—41no—
14C22×C8×C127—41no—
15C4⋊Q8×C127—41no—
16#125×C127—41no—
17C22⋊Q8×C127—41no—
18#117×C127—21no—
19C2×C4⋊C4×C127C2×C411yescharacteristic
20C2×C42×C127D411yescharacteristic
21#103×C127—41no—
22#103×C127—41no—
23#101×C127—22no—
24#101×C127—41no—
25#95×C127—41no—
26C2×Q8×C127—21no—
27C2×Q8×C127—41no—
28C2×Q8×C127—41no—
29C2×Q8×C127—41no—
30C2×Q8×C127SD1611yescharacteristic
31C2×Q8×C127Q1611yescharacteristic
32C22×C4×C127—21no—
33C22×C4×C127—21no—
34C22×C4×C127—21no—
35C22×C4×C127C22⋊C411yescharacteristic
36M16×C127—42no—
37M16×C127—41no—
38M16×C127—41no—
39M16×C127—81no—
40C2×C8×C127—41no—
41C2×C8×C127—42no—
42C2×C8×C127—81no—
43C2×C8×C127—81no—
44C2×C8×C127—81no—
45C4⋊C4×C127—21no—
46C4⋊C4×C127—21no—
47C4⋊C4×C127—41no—
48C4⋊C4×C127—41no—
49C4⋊C4×C127—42no—
50C22⋊C4×C127—41no—
51C42×C127—41no—
52C42×C127—41no—
53C23×C127#9911yescharacteristic
54Q8×C127—41no—
55Q8×C127—41no—
56Q8×C127—81no—
57Q8×C127—161no—
58C2×C4×C127—21no—
59C2×C4×C127—21no—
60C2×C4×C127—21no—
61C2×C4×C127—21no—
62C2×C4×C127—21no—
63C2×C4×C127—21no—
64C2×C4×C127—41no—
65C2×C4×C127—41no—
66C2×C4×C127—41no—
67C2×C4×C127—41no—
68C2×C4×C127—41no—
69C2×C4×C127—41no—
70C2×C4×C127—41no—
71C2×C4×C127—81no—
72C2×C4×C127#10311yescharacteristic
73C2×C4×C127#10411yescharacteristic
74C8×C127—81no—
75C8×C127—82no—
76C8×C127—82no—
77C22×C127—21no—
78C22×C127—21no—
79C22×C127#32811yescharacteristic
80C22×C127AΣL(1,𝔽16)11yescharacteristic
81C22×C127#35411yescharacteristic
82C4×C127—21no—
83C4×C127—21no—
84C4×C127—41no—
85C4×C127—41no—
86C4×C127—41no—
87C4×C127—41no—
88C4×C127—81no—
89C4×C127—81no—
90C4×C127—81no—
91#7431C12711yesmaximal, characteristic, direct product factor, Sylow
92C2×C127—21no—
93C2×C127—21no—
94C2×C127#135111yescharacteristic
95C2×C127#140311yescharacteristic
96C2×C127#140511yescharacteristic
97#2028C2×C12711yescharacteristic
98#1394C2×C12711yescharacteristic
99#1272C2×C12711yescharacteristic
100C127#743111yescharacteristic, direct product factor, Sylow
101#544C4×C12711yescharacteristic
102#419—21no—
103C2×#101—21no—
104#391C22×C12711yescharacteristic
105#343C4×C12711yescharacteristic
106#339—21no—
107#336—21no—
108C22×Q8D4×C12711yescharacteristic
109C2×M16—21no—
110C2×M16—41no—
111C22×C8—41no—
112C4⋊Q8—41no—
113#125—41no—
114C22⋊Q8—41no—
115#117—21no—
116C2×C4⋊C4C2×C4×C12711yescharacteristic
117C2×C42D4×C12711yescharacteristic
118#103—41no—
119#103—41no—
120#101—22no—
121#101—41no—
122#95—41no—
123C2×Q8—21no—
124C2×Q8—41no—
125C2×Q8—41no—
126C2×Q8—41no—
127C2×Q8SD16×C12711yescharacteristic
128C2×Q8Q16×C12711yescharacteristic
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4C22⋊C4×C12711yescharacteristic
133M16—42no—
134M16—41no—
135M16—41no—
136M16—81no—
137C2×C8—41no—
138C2×C8—42no—
139C2×C8—81no—
140C2×C8—81no—
141C2×C8—81no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—41no—
145C4⋊C4—41no—
146C4⋊C4—42no—
147C22⋊C4—41no—
148C42—41no—
149C42—41no—
150C23#99×C12711yescharacteristic
151Q8—41no—
152Q8—41no—
153Q8—81no—
154Q8—161no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—81no—
169C2×C4#103×C12711yescharacteristic
170C2×C4#104×C12711yescharacteristic
171C8—81no—
172C8—82no—
173C8—82no—
174C22—21no—
175C22—21no—
176C22#328×C12711yescharacteristic
177C22AΣL(1,𝔽16)×C12711yescharacteristic
178C22#354×C12711yescharacteristic
179C4—21no—
180C4—21no—
181C4—41no—
182C4—41no—
183C4—41no—
184C4—41no—
185C4—81no—
186C4—81no—
187C4—81no—
188C2—21no—
189C2—21no—
190C2C127×#135111yescharacteristic
191C2C127×#140311yescharacteristic
192C2C127×#140511yescharacteristic
subgroupG/H
center, socleC22×C127AΣL(1,𝔽16)
commutatorC2×C4⋊C4C2×C4×C127
Frattini, cosocle#391C22×C127
prime radicalC23×C127#99
LCSG ▷ C2×C4⋊C4 ▷ 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
91. #7431C127direct (N × H)
100. C127#7431direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#20282
C127×#13942
C127×#12722
#7431127