Finite Group Databasebeta

← C127×#13504 #44577177

Subgroups — C127×#13504 #44577177

Order 32512.

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

normal subgroups only

This group has 278 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
2C127×#2117C211yesmaximal, characteristic
3C127×#1815C211yesmaximal, characteristic
4C127×#1812C211yesmaximal, characteristic
5C127×#1389C211yesmaximal, characteristic, complemented
6C127×#1386C211yesmaximal, characteristic, complemented
7C127×#1386C211yesmaximal, characteristic, complemented
8C2×#131×C127C2211yescharacteristic
9C2×M32×C127C2211yescharacteristic
10C2×M32×C127C2211yescharacteristic
11C2×#108×C127C2211yescharacteristic
12#427×C127C2211yescharacteristic
13#427×C127C2211yescharacteristic
14C2×#106×C127C2211yescharacteristic
15#417×C127—21no—
16#410×C127—21no—
17#365×C127—22no—
18#350×C127—22no—
19#343×C127—21no—
20H(3,ℤ/4)×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×C127D411yescharacteristic
29C22×C8×C127—21no—
30C22×C8×C127C2311yescharacteristic
31#117×C127—21no—
32#117×C127—21no—
33C2×C4⋊C4×C127—21no—
34M32×C127—21no—
35M32×C127—21no—
36M32×C127—21no—
37M32×C127D412yes—
38C2×C16×C127—21no—
39C2×C16×C127—21no—
40#108×C127—21no—
41#108×C127—21no—
42#107×C127—21no—
43#107×C127—21no—
44#106×C127—21no—
45#106×C127—21no—
46#106×C127—21no—
47#106×C127—21no—
48#103×C127—41no—
49#102×C127—41no—
50#99×C127—42no—
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×C127—41no—
60C22×C4×C127C2×D411yescharacteristic
61M16×C127—21no—
62M16×C127—21no—
63M16×C127—41no—
64M16×C127—41no—
65M16×C127—41no—
66M16×C127—41no—
67C2×C8×C127—21no—
68C2×C8×C127—41no—
69C2×C8×C127—41no—
70C2×C8×C127—41no—
71C2×C8×C127C2×D411yescharacteristic
72C2×C8×C127#4111yescharacteristic
73C2×C8×C127#4111yescharacteristic
74C2×C8×C127#4111yescharacteristic
75C2×C8×C127#4111yescharacteristic
76C2×C8×C127#4111yescharacteristic
77C4⋊C4×C127—41no—
78C4⋊C4×C127—41no—
79C4⋊C4×C127—41no—
80C4⋊C4×C127—41no—
81C22⋊C4×C127—41no—
82C22⋊C4×C127—41no—
83C42×C127—41no—
84C42×C127—41no—
85C16×C127—22no—
86C16×C127—41no—
87C23×C127—21no—
88C23×C127AGL(1,ℤ/8)11yescharacteristic
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—81no—
100C2×C4×C127—81no—
101C2×C4×C127—161no—
102C2×C4×C127#12111yescharacteristic
103C2×C4×C127#12311yescharacteristic
104C2×C4×C127#12311yescharacteristic
105C2×C4×C127C2×SD1611yescharacteristic
106C2×C4×C127#13511yescharacteristic
107C2×C4×C127#13711yescharacteristic
108C8×C127—41no—
109C8×C127—81no—
110C8×C127#12311yescharacteristic
111C8×C127#12411yescharacteristic
112C8×C127#12611yescharacteristic
113C8×C127#12611yescharacteristic
114C22×C127—41no—
115C22×C127—41no—
116C22×C127—81no—
117C22×C127#46811yescharacteristic
118C22×C127#48111yescharacteristic
119C22×C127#48211yescharacteristic
120C4×C127—41no—
121C4×C127—161no—
122C4×C127—161no—
123C4×C127—161no—
124C4×C127#39711yescharacteristic
125C4×C127#46511yescharacteristic
126C4×C127#48311yescharacteristic
127C4×C127#48511yescharacteristic
128#13504C12711yesmaximal, characteristic, direct product factor, Sylow
129C2×C127—21no—
130C2×C127—21no—
131C2×C127—21no—
132C2×C127—81no—
133C2×C127#207711yescharacteristic
134#2155C2×C12711yescharacteristic, complemented
135#2117C2×C12711yescharacteristic
136#1815C2×C12711yescharacteristic
137#1812C2×C12711yescharacteristic
138#1389C2×C12711yescharacteristic, complemented
139#1386C2×C12711yescharacteristic, complemented
140#1386C2×C12711yescharacteristic, complemented
141C127#1350411yescharacteristic, direct product factor, Sylow
142C2×#131C22×C12711yescharacteristic
143C2×M32C22×C12711yescharacteristic
144C2×M32C22×C12711yescharacteristic
145C2×#108C22×C12711yescharacteristic
146#427C22×C12711yescharacteristic
147#427C22×C12711yescharacteristic
148C2×#106C22×C12711yescharacteristic
149#417—21no—
150#410—21no—
151#365—22no—
152#350—22no—
153#343—21no—
154H(3,ℤ/4)—21no—
155C2×#41D4×C12711yescharacteristic
156#131—21no—
157#131—21no—
158#131—21no—
159#131—21no—
160C2×M16—21no—
161C2×M16—21no—
162C2×M16D4×C12711yescharacteristic
163C22×C8—21no—
164C22×C8C23×C12711yescharacteristic
165#117—21no—
166#117—21no—
167C2×C4⋊C4—21no—
168M32—21no—
169M32—21no—
170M32—21no—
171M32D4×C12712yes—
172C2×C16—21no—
173C2×C16—21no—
174#108—21no—
175#108—21no—
176#107—21no—
177#107—21no—
178#106—21no—
179#106—21no—
180#106—21no—
181#106—21no—
182#103—41no—
183#102—41no—
184#99—42no—
185#41—21no—
186#41—21no—
187#41—21no—
188#41—21no—
189C2×Q8SD16×C12711yescharacteristic
190C2×D4—21no—
191C2×D4SD16×C12711yescharacteristic
192C22×C4—21no—
193C22×C4—41no—
194C22×C4C2×D4×C12711yescharacteristic
195M16—21no—
196M16—21no—
197M16—41no—
198M16—41no—
199M16—41no—
200M16—41no—
201C2×C8—21no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8C2×D4×C12711yescharacteristic
206C2×C8#41×C12711yescharacteristic
207C2×C8#41×C12711yescharacteristic
208C2×C8#41×C12711yescharacteristic
209C2×C8#41×C12711yescharacteristic
210C2×C8#41×C12711yescharacteristic
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C22⋊C4—41no—
216C22⋊C4—41no—
217C42—41no—
218C42—41no—
219C16—22no—
220C16—41no—
221C23—21no—
222C23AGL(1,ℤ/8)×C12711yescharacteristic
223Q8—21no—
224Q8—21no—
225D4—21no—
226D4—21no—
227D4—41no—
228D4—41no—
229C2×C4—21no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—81no—
233C2×C4—81no—
234C2×C4—81no—
235C2×C4—161no—
236C2×C4#121×C12711yescharacteristic
237C2×C4#123×C12711yescharacteristic
238C2×C4#123×C12711yescharacteristic
239C2×C4C2×SD16×C12711yescharacteristic
240C2×C4#135×C12711yescharacteristic
241C2×C4#137×C12711yescharacteristic
242C8—41no—
243C8—81no—
244C8#123×C12711yescharacteristic
245C8#124×C12711yescharacteristic
246C8#126×C12711yescharacteristic
247C8#126×C12711yescharacteristic
248C22—41no—
249C22—41no—
250C22—81no—
251C22#468×C12711yescharacteristic
252C22#481×C12711yescharacteristic
253C22#482×C12711yescharacteristic
254C4—41no—
255C4—161no—
256C4—161no—
257C4—161no—
258C4#397×C12711yescharacteristic
259C4#465×C12711yescharacteristic
260C4#483×C12711yescharacteristic
261C4#485×C12711yescharacteristic
262C2—21no—
263C2—21no—
264C2—21no—
265C2—81no—
266C2C127×#207711yescharacteristic
subgroupG/H
center, socleC2×C127#2077
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC2×#41×C127D4
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×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×#1389C2semidirect
6. C127×#1386C2semidirect
7. C127×#1386C2semidirect
128. #13504C127direct (N × H)
134. #2155C2×C127semidirect
138. #1389C2×C127semidirect
139. #1386C2×C127semidirect
140. #1386C2×C127semidirect
141. C127#13504direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#21552
C127×#21172
C127×#18152
C127×#18122
C127×#13892
C127×#13862
#13504127