Finite Group Databasebeta

← C127×#12851 #44576524

Subgroups — C127×#12851 #44576524

Order 32512.

416 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 162 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×#2873C211yesmaximal, characteristic
2C2×#349×C127C212yesmaximal
3C127×#1378C214yesmaximal, complemented
4C22×M16×C127C411yescharacteristic
5C22×M16×C127C2211yescharacteristic
6C2×#117×C127C411yescharacteristic
7C2×M32×C127C2214yes—
8#405×C127—22no—
9#405×C127C412yes—
10#405×C127C2212yes—
11C4×M16×C127—22no—
12#349×C127—22no—
13#349×C127—22no—
14C23×C4×C127C2×C411yescharacteristic
15C2×M16×C127—21no—
16C2×M16×C127—24no—
17C2×M16×C127—24no—
18C2×M16×C127C2×C412yes—
19C2×M16×C127D412yes—
20C2×M16×C127D412yes—
21C22×C8×C127—21no—
22C22×C8×C127C2×C411yescharacteristic
23C22×C8×C127C2311yescharacteristic
24#117×C127—21no—
25#117×C127—21no—
26#117×C127C812yes—
27#117×C127C2×C412yes—
28C2×C4⋊C4×C127—21no—
29C2×C22⋊C4×C127C812yes—
30C2×C42×C127—21no—
31M32×C127—24no—
32M32×C127—24no—
33C2×C16×C127—24no—
34#97×C127—22no—
35#97×C127—22no—
36C4×C8×C127—22no—
37C4×C8×C127—22no—
38C24×C127C2×C811yescharacteristic
39C22×C4×C127—22no—
40C22×C4×C127—22no—
41C22×C4×C127—22no—
42C22×C4×C127C22⋊C411yescharacteristic
43C22×C4×C127C22⋊C411yescharacteristic
44C22×C4×C127C2×C811yescharacteristic
45C22×C4×C127M1611yescharacteristic
46C22×C4×C127M1611yescharacteristic
47C22×C4×C127C22×C411yescharacteristic
48M16×C127—24no—
49M16×C127—22no—
50M16×C127—24no—
51M16×C127—24no—
52M16×C127M1614yes—
53C2×C8×C127—24no—
54C2×C8×C127—22no—
55C2×C8×C127—22no—
56C2×C8×C127C22⋊C412yes—
57C2×C8×C127C2×D412yes—
58C2×C8×C127#4114yes—
59C4⋊C4×C127—22no—
60C4⋊C4×C127—22no—
61C22⋊C4×C127—22no—
62C22⋊C4×C127C2×C814yes—
63C42×C127—22no—
64C42×C127—22no—
65C16×C127—44no—
66C23×C127—22no—
67C23×C127—81no—
68C23×C127C22⋊C811yescharacteristic
69C23×C127C22⋊C811yescharacteristic
70C23×C127C22×C811yescharacteristic
71C2×C4×C127—22no—
72C2×C4×C127—21no—
73C2×C4×C127—21no—
74C2×C4×C127—21no—
75C2×C4×C127—21no—
76C2×C4×C127—22no—
77C2×C4×C127—22no—
78C2×C4×C127—24no—
79C2×C4×C127—82no—
80C2×C4×C127C22⋊C811yescharacteristic
81C2×C4×C127C22⋊C811yescharacteristic
82C2×C4×C127C2×C22⋊C411yescharacteristic
83C2×C4×C127#11712yes—
84C2×C4×C127C2×M1612yes—
85C2×C4×C127C2×M1611yescharacteristic
86C8×C127—22no—
87C8×C127—24no—
88C8×C127#12314yes—
89C22×C127—21no—
90C22×C127—21no—
91C22×C127—41no—
92C22×C127—41no—
93C22×C127—41no—
94C22×C127—82no—
95C22×C127C2×C22⋊C811yescharacteristic
96C22×C127#43112yes—
97C4×C127—21no—
98C4×C127—21no—
99C4×C127—44no—
100C4×C127#38111yescharacteristic
101C4×C127#40711yescharacteristic
102C4×C127#43212yes—
103#12851C12711yesmaximal, characteristic, direct product factor, Sylow
104C2×C127—21no—
105C2×C127—22no—
106C2×C127—41no—
107C2×C127—41no—
108C2×C127#181711yescharacteristic
109#2873C2×C12711yescharacteristic
110C2×#349C2×C12712yes—
111#1378C2×C12714yescomplemented
112C127#1285111yescharacteristic, direct product factor, Sylow
113C22×M16C4×C12711yescharacteristic
114C22×M16C22×C12711yescharacteristic
115C2×#117C4×C12711yescharacteristic
116C2×M32C22×C12714yes—
117#405—22no—
118#405C4×C12712yes—
119#405C22×C12712yes—
120C4×M16—22no—
121#349—22no—
122#349—22no—
123C23×C4C2×C4×C12711yescharacteristic
124C2×M16—21no—
125C2×M16—24no—
126C2×M16—24no—
127C2×M16C2×C4×C12712yes—
128C2×M16D4×C12712yes—
129C2×M16D4×C12712yes—
130C22×C8—21no—
131C22×C8C2×C4×C12711yescharacteristic
132C22×C8C23×C12711yescharacteristic
133#117—21no—
134#117—21no—
135#117C8×C12712yes—
136#117C2×C4×C12712yes—
137C2×C4⋊C4—21no—
138C2×C22⋊C4C8×C12712yes—
139C2×C42—21no—
140M32—24no—
141M32—24no—
142C2×C16—24no—
143#97—22no—
144#97—22no—
145C4×C8—22no—
146C4×C8—22no—
147C24C2×C8×C12711yescharacteristic
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4C22⋊C4×C12711yescharacteristic
152C22×C4C22⋊C4×C12711yescharacteristic
153C22×C4C2×C8×C12711yescharacteristic
154C22×C4M16×C12711yescharacteristic
155C22×C4M16×C12711yescharacteristic
156C22×C4C22×C4×C12711yescharacteristic
157M16—24no—
158M16—22no—
159M16—24no—
160M16—24no—
161M16M16×C12714yes—
162C2×C8—24no—
163C2×C8—22no—
164C2×C8—22no—
165C2×C8C22⋊C4×C12712yes—
166C2×C8C2×D4×C12712yes—
167C2×C8#41×C12714yes—
168C4⋊C4—22no—
169C4⋊C4—22no—
170C22⋊C4—22no—
171C22⋊C4C2×C8×C12714yes—
172C42—22no—
173C42—22no—
174C16—44no—
175C23—22no—
176C23—81no—
177C23C22⋊C8×C12711yescharacteristic
178C23C22⋊C8×C12711yescharacteristic
179C23C22×C8×C12711yescharacteristic
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—24no—
188C2×C4—82no—
189C2×C4C22⋊C8×C12711yescharacteristic
190C2×C4C22⋊C8×C12711yescharacteristic
191C2×C4C2×C22⋊C4×C12711yescharacteristic
192C2×C4#117×C12712yes—
193C2×C4C2×M16×C12712yes—
194C2×C4C2×M16×C12711yescharacteristic
195C8—22no—
196C8—24no—
197C8#123×C12714yes—
198C22—21no—
199C22—21no—
200C22—41no—
201C22—41no—
202C22—41no—
203C22—82no—
204C22C2×C22⋊C8×C12711yescharacteristic
205C22#431×C12712yes—
206C4—21no—
207C4—21no—
208C4—44no—
209C4#381×C12711yescharacteristic
210C4#407×C12711yescharacteristic
211C4#432×C12712yes—
212C2—21no—
213C2—22no—
214C2—41no—
215C2—41no—
216C2C127×#181711yescharacteristic
subgroupG/H
centerC4×C127#381
commutatorC23C22×C8×C127
Frattini, cosocleC22×C8C23×C127
socleC2×C127#1817
prime radicalC24×C127C2×C8
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C22×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1378C2semidirect
103. #12851C127direct (N × H)
111. #1378C2×C127semidirect
112. C127#12851direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#28732
C2×#349×C1272
C127×#13782
#12851127