Finite Group Databasebeta

← C127×#7430 #44571103

Subgroups — C127×#7430 #44571103

Order 32512.

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

normal subgroups only

This group has 236 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×#2027C211yesmaximal, characteristic
2C127×#1393C211yesmaximal, characteristic
3C127×#1270C211yesmaximal, characteristic
4#544×C127C411yescharacteristic, complemented
5#418×C127—21no—
6C2×#99×C127—21no—
7#390×C127C2211yescharacteristic
8#343×C127C411yescharacteristic, complemented
9#339×C127—21no—
10#336×C127—21no—
11C22×D4×C127D411yescharacteristic
12C2×M16×C127—21no—
13C22×C8×C127—41no—
14C4⋊Q8×C127—41no—
15#125×C127—41no—
16C22⋊Q8×C127—41no—
17#117×C127—21no—
18C2×C4⋊C4×C127C2×C411yescharacteristic
19C2×C22⋊C4×C127—41no—
20C2×C22⋊C4×C127—41no—
21C2×C42×C127D411yescharacteristic
22#102×C127—41no—
23#102×C127—41no—
24#99×C127—22no—
25#99×C127—41no—
26C24×C127—21no—
27C2×Q8×C127—41no—
28C2×D4×C127—21no—
29C2×D4×C127—41no—
30C2×D4×C127—41no—
31C2×D4×C127SD1611yescharacteristic
32C2×D4×C127Q1611yescharacteristic
33C22×C4×C127—21no—
34C22×C4×C127—21no—
35C22×C4×C127—81no—
36C22×C4×C127C22⋊C411yescharacteristic
37M16×C127—41no—
38M16×C127—41no—
39C2×C8×C127—41no—
40C2×C8×C127—42no—
41C2×C8×C127—81no—
42C2×C8×C127—81no—
43C4⋊C4×C127—21no—
44C4⋊C4×C127—21no—
45C4⋊C4×C127—41no—
46C4⋊C4×C127—41no—
47C4⋊C4×C127—42no—
48C22⋊C4×C127—41no—
49C22⋊C4×C127—42no—
50C22⋊C4×C127—81no—
51C22⋊C4×C127—81no—
52C22⋊C4×C127—81no—
53C42×C127—41no—
54C42×C127—41no—
55C23×C127—21no—
56C23×C127—21no—
57C23×C127—41no—
58C23×C127—41no—
59C23×C127—81no—
60C23×C127—81no—
61C23×C127#9911yescharacteristic
62Q8×C127—161no—
63D4×C127—41no—
64D4×C127—41no—
65D4×C127—81no—
66C2×C4×C127—21no—
67C2×C4×C127—21no—
68C2×C4×C127—21no—
69C2×C4×C127—21no—
70C2×C4×C127—41no—
71C2×C4×C127—41no—
72C2×C4×C127—41no—
73C2×C4×C127—41no—
74C2×C4×C127—41no—
75C2×C4×C127—81no—
76C2×C4×C127—82no—
77C2×C4×C127—161no—
78C2×C4×C127—161no—
79C2×C4×C127#10311yescharacteristic
80C2×C4×C127#10411yescharacteristic
81C8×C127—81no—
82C8×C127—82no—
83C22×C127—21no—
84C22×C127—21no—
85C22×C127—41no—
86C22×C127—41no—
87C22×C127—81no—
88C22×C127—81no—
89C22×C127—81no—
90C22×C127—81no—
91C22×C127—161no—
92C22×C127#32811yescharacteristic
93C22×C127AΣL(1,𝔽16)11yescharacteristic
94C22×C127#35411yescharacteristic
95C4×C127—21no—
96C4×C127—21no—
97C4×C127—41no—
98C4×C127—41no—
99C4×C127—81no—
100C4×C127—81no—
101C4×C127—81no—
102C4×C127—162no—
103#7430C12711yesmaximal, characteristic, direct product factor, Sylow
104C2×C127—21no—
105C2×C127—21no—
106C2×C127—81no—
107C2×C127—81no—
108C2×C127#135111yescharacteristic
109C2×C127#140211yescharacteristic
110C2×C127#140411yescharacteristic
111#2027C2×C12711yescharacteristic
112#1393C2×C12711yescharacteristic
113#1270C2×C12711yescharacteristic
114C127#743011yescharacteristic, direct product factor, Sylow
115#544C4×C12711yescharacteristic, complemented
116#418—21no—
117C2×#99—21no—
118#390C22×C12711yescharacteristic
119#343C4×C12711yescharacteristic, complemented
120#339—21no—
121#336—21no—
122C22×D4D4×C12711yescharacteristic
123C2×M16—21no—
124C22×C8—41no—
125C4⋊Q8—41no—
126#125—41no—
127C22⋊Q8—41no—
128#117—21no—
129C2×C4⋊C4C2×C4×C12711yescharacteristic
130C2×C22⋊C4—41no—
131C2×C22⋊C4—41no—
132C2×C42D4×C12711yescharacteristic
133#102—41no—
134#102—41no—
135#99—22no—
136#99—41no—
137C24—21no—
138C2×Q8—41no—
139C2×D4—21no—
140C2×D4—41no—
141C2×D4—41no—
142C2×D4SD16×C12711yescharacteristic
143C2×D4Q16×C12711yescharacteristic
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—81no—
147C22×C4C22⋊C4×C12711yescharacteristic
148M16—41no—
149M16—41no—
150C2×C8—41no—
151C2×C8—42no—
152C2×C8—81no—
153C2×C8—81no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—41no—
157C4⋊C4—41no—
158C4⋊C4—42no—
159C22⋊C4—41no—
160C22⋊C4—42no—
161C22⋊C4—81no—
162C22⋊C4—81no—
163C22⋊C4—81no—
164C42—41no—
165C42—41no—
166C23—21no—
167C23—21no—
168C23—41no—
169C23—41no—
170C23—81no—
171C23—81no—
172C23#99×C12711yescharacteristic
173Q8—161no—
174D4—41no—
175D4—41no—
176D4—81no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—81no—
187C2×C4—82no—
188C2×C4—161no—
189C2×C4—161no—
190C2×C4#103×C12711yescharacteristic
191C2×C4#104×C12711yescharacteristic
192C8—81no—
193C8—82no—
194C22—21no—
195C22—21no—
196C22—41no—
197C22—41no—
198C22—81no—
199C22—81no—
200C22—81no—
201C22—81no—
202C22—161no—
203C22#328×C12711yescharacteristic
204C22AΣL(1,𝔽16)×C12711yescharacteristic
205C22#354×C12711yescharacteristic
206C4—21no—
207C4—21no—
208C4—41no—
209C4—41no—
210C4—81no—
211C4—81no—
212C4—81no—
213C4—162no—
214C2—21no—
215C2—21no—
216C2—81no—
217C2—81no—
218C2C127×#135111yescharacteristic
219C2C127×#140211yescharacteristic
220C2C127×#140411yescharacteristic
subgroupG/H
center, socleC22×C127AΣL(1,𝔽16)
commutatorC2×C4⋊C4C2×C4×C127
Frattini, cosocle#390C22×C127
prime radicalC22×D4×C127D4
LCSG ▷ C2×C4⋊C4 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C127 ◁ C22×C4×C127 ◁ #390×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. #544×C127C4semidirect
8. #343×C127C4semidirect
103. #7430C127direct (N × H)
114. C127#7430direct (N × H)
115. #544C4×C127semidirect
119. #343C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#20272
C127×#13932
C127×#12702
#7430127