Finite Group Databasebeta

← C127×#13503 #44577176

Subgroups — C127×#13503 #44577176

Order 32512.

272 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2155C211yesmaximal, characteristic, complemented
2C2×#350×C127C211yesmaximal, characteristic
3C127×#1814C211yesmaximal, characteristic
4C127×#1813C211yesmaximal, characteristic
5C127×#1388C211yesmaximal, characteristic, complemented
6C127×#1382C211yesmaximal, characteristic, complemented
7C127×#1381C211yesmaximal, characteristic, complemented
8C2×#131×C127C2211yescharacteristic
9C2×M32×C127C2211yescharacteristic
10C22×C16×C127C2211yescharacteristic
11C2×#108×C127C2211yescharacteristic
12C2×#108×C127C2211yescharacteristic
13C2×#108×C127C2211yescharacteristic
14#427×C127C2211yescharacteristic
15#421×C127—21no—
16#413×C127—21no—
17#365×C127—22no—
18#350×C127—22no—
19#344×C127—21no—
20#338×C127—21no—
21C2×#41×C127D411yescharacteristic
22#131×C127—21no—
23#131×C127—21no—
24#131×C127—21no—
25#131×C127—21no—
26C2×M16×C127—21no—
27C2×M16×C127—21no—
28C2×M16×C127—21no—
29C2×M16×C127—21no—
30C2×M16×C127D411yescharacteristic
31C22×C8×C127—21no—
32C22×C8×C127C2311yescharacteristic
33#117×C127—21no—
34M32×C127—21no—
35M32×C127D412yes—
36C2×C16×C127—21no—
37C2×C16×C127—21no—
38C2×C16×C127—21no—
39C2×C16×C127—21no—
40#108×C127—21no—
41#108×C127—21no—
42#108×C127—21no—
43#108×C127—21no—
44#108×C127—21no—
45#108×C127—21no—
46#107×C127—21no—
47#106×C127—21no—
48#104×C127—42no—
49#101×C127—41no—
50#100×C127—41no—
51#41×C127—21no—
52#41×C127—21no—
53#41×C127—21no—
54#41×C127—21no—
55C2×Q8×C127SD1611yescharacteristic
56C2×D4×C127—21no—
57C2×D4×C127SD1611yescharacteristic
58C22×C4×C127—21no—
59C22×C4×C127C2×D411yescharacteristic
60M16×C127—21no—
61M16×C127—21no—
62M16×C127—41no—
63M16×C127—41no—
64M16×C127—41no—
65M16×C127—41no—
66M16×C127—41no—
67M16×C127—41no—
68M16×C127—41no—
69M16×C127—41no—
70C2×C8×C127—21no—
71C2×C8×C127—41no—
72C2×C8×C127—41no—
73C2×C8×C127—41no—
74C2×C8×C127—41no—
75C2×C8×C127—41no—
76C2×C8×C127C2×D411yescharacteristic
77C2×C8×C127#4111yescharacteristic
78C2×C8×C127#4111yescharacteristic
79C2×C8×C127#4111yescharacteristic
80C2×C8×C127#4111yescharacteristic
81C2×C8×C127#4111yescharacteristic
82C4⋊C4×C127—41no—
83C22⋊C4×C127—41no—
84C42×C127—41no—
85C16×C127—22no—
86C16×C127—41no—
87C23×C127—21no—
88C23×C127#13711yescharacteristic
89Q8×C127—21no—
90Q8×C127—21no—
91D4×C127—21no—
92D4×C127—21no—
93D4×C127—41no—
94D4×C127—41no—
95C2×C4×C127—21no—
96C2×C4×C127—41no—
97C2×C4×C127—41no—
98C2×C4×C127—81no—
99C2×C4×C127#12111yescharacteristic
100C2×C4×C127#12311yescharacteristic
101C2×C4×C127#12311yescharacteristic
102C2×C4×C127C2×SD1611yescharacteristic
103C2×C4×C127#13511yescharacteristic
104C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
105C8×C127—41no—
106C8×C127—81no—
107C8×C127—81no—
108C8×C127—81no—
109C8×C127#12311yescharacteristic
110C8×C127#12411yescharacteristic
111C8×C127#12611yescharacteristic
112C8×C127#12611yescharacteristic
113C22×C127—41no—
114C22×C127—41no—
115C22×C127—81no—
116C22×C127#46811yescharacteristic
117C22×C127#48311yescharacteristic
118C22×C127#48511yescharacteristic
119C4×C127—41no—
120C4×C127—161no—
121C4×C127#39711yescharacteristic
122C4×C127#46511yescharacteristic
123C4×C127#48111yescharacteristic
124C4×C127#48211yescharacteristic
125#13503C12711yesmaximal, characteristic, direct product factor, Sylow
126C2×C127—21no—
127C2×C127—21no—
128C2×C127—21no—
129C2×C127—81no—
130C2×C127#207711yescharacteristic
131#2155C2×C12711yescharacteristic, complemented
132C2×#350C2×C12711yescharacteristic
133#1814C2×C12711yescharacteristic
134#1813C2×C12711yescharacteristic
135#1388C2×C12711yescharacteristic, complemented
136#1382C2×C12711yescharacteristic, complemented
137#1381C2×C12711yescharacteristic, complemented
138C127#1350311yescharacteristic, direct product factor, Sylow
139C2×#131C22×C12711yescharacteristic
140C2×M32C22×C12711yescharacteristic
141C22×C16C22×C12711yescharacteristic
142C2×#108C22×C12711yescharacteristic
143C2×#108C22×C12711yescharacteristic
144C2×#108C22×C12711yescharacteristic
145#427C22×C12711yescharacteristic
146#421—21no—
147#413—21no—
148#365—22no—
149#350—22no—
150#344—21no—
151#338—21no—
152C2×#41D4×C12711yescharacteristic
153#131—21no—
154#131—21no—
155#131—21no—
156#131—21no—
157C2×M16—21no—
158C2×M16—21no—
159C2×M16—21no—
160C2×M16—21no—
161C2×M16D4×C12711yescharacteristic
162C22×C8—21no—
163C22×C8C23×C12711yescharacteristic
164#117—21no—
165M32—21no—
166M32D4×C12712yes—
167C2×C16—21no—
168C2×C16—21no—
169C2×C16—21no—
170C2×C16—21no—
171#108—21no—
172#108—21no—
173#108—21no—
174#108—21no—
175#108—21no—
176#108—21no—
177#107—21no—
178#106—21no—
179#104—42no—
180#101—41no—
181#100—41no—
182#41—21no—
183#41—21no—
184#41—21no—
185#41—21no—
186C2×Q8SD16×C12711yescharacteristic
187C2×D4—21no—
188C2×D4SD16×C12711yescharacteristic
189C22×C4—21no—
190C22×C4C2×D4×C12711yescharacteristic
191M16—21no—
192M16—21no—
193M16—41no—
194M16—41no—
195M16—41no—
196M16—41no—
197M16—41no—
198M16—41no—
199M16—41no—
200M16—41no—
201C2×C8—21no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8C2×D4×C12711yescharacteristic
208C2×C8#41×C12711yescharacteristic
209C2×C8#41×C12711yescharacteristic
210C2×C8#41×C12711yescharacteristic
211C2×C8#41×C12711yescharacteristic
212C2×C8#41×C12711yescharacteristic
213C4⋊C4—41no—
214C22⋊C4—41no—
215C42—41no—
216C16—22no—
217C16—41no—
218C23—21no—
219C23#137×C12711yescharacteristic
220Q8—21no—
221Q8—21no—
222D4—21no—
223D4—21no—
224D4—41no—
225D4—41no—
226C2×C4—21no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—81no—
230C2×C4#121×C12711yescharacteristic
231C2×C4#123×C12711yescharacteristic
232C2×C4#123×C12711yescharacteristic
233C2×C4C2×SD16×C12711yescharacteristic
234C2×C4#135×C12711yescharacteristic
235C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
236C8—41no—
237C8—81no—
238C8—81no—
239C8—81no—
240C8#123×C12711yescharacteristic
241C8#124×C12711yescharacteristic
242C8#126×C12711yescharacteristic
243C8#126×C12711yescharacteristic
244C22—41no—
245C22—41no—
246C22—81no—
247C22#468×C12711yescharacteristic
248C22#483×C12711yescharacteristic
249C22#485×C12711yescharacteristic
250C4—41no—
251C4—161no—
252C4#397×C12711yescharacteristic
253C4#465×C12711yescharacteristic
254C4#481×C12711yescharacteristic
255C4#482×C12711yescharacteristic
256C2—21no—
257C2—21no—
258C2—21no—
259C2—81no—
260C2C127×#207711yescharacteristic
subgroupG/H
centerC4×C127#482
commutator, Frattini, cosocleC22×C8C23×C127
socleC2×C127#2077
prime radicalC2×#41×C127D4
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C22×C4×C127 ◁ C2×#131×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2155C2semidirect
5. C127×#1388C2semidirect
6. C127×#1382C2semidirect
7. C127×#1381C2semidirect
125. #13503C127direct (N × H)
131. #2155C2×C127semidirect
135. #1388C2×C127semidirect
136. #1382C2×C127semidirect
137. #1381C2×C127semidirect
138. C127#13503direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#21552
C2×#350×C1272
C127×#18142
C127×#18132
C127×#13882
C127×#13822
C127×#13812
#13503127