Finite Group Databasebeta

← C127×#13490 #44577163

Subgroups — C127×#13490 #44577163

Order 32512.

292 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C2×#361×C127C211yesmaximal, characteristic
2C127×#2140C211yesmaximal, characteristic
3C127×#1978C211yesmaximal, characteristic
4C127×#1833C211yesmaximal, characteristic, complemented
5C127×#1389C211yesmaximal, characteristic, complemented
6C127×#1388C211yesmaximal, characteristic, complemented
7C127×#1378C211yesmaximal, characteristic, complemented
8C22×D8×C127C2211yescharacteristic
9C2×M32×C127C2211yescharacteristic
10C2×M32×C127C2211yescharacteristic
11C2×#108×C127C2211yescharacteristic
12C2×#108×C127C2211yescharacteristic
13#427×C127C2211yescharacteristic
14#418×C127—21no—
15C2×#100×C127—21no—
16#405×C127C2211yescharacteristic
17#361×C127—22no—
18#357×C127—22no—
19#344×C127—21no—
20H(3,ℤ/4)×C127—21no—
21C22×D4×C127—21no—
22C2×D8×C127—21no—
23C2×D8×C127—21no—
24C2×D8×C127—21no—
25C2×D8×C127—21no—
26C2×D8×C127—21no—
27C2×D8×C127D412yes—
28C2×M16×C127—21no—
29C2×M16×C127—21no—
30C2×M16×C127D411yescharacteristic
31C22×C8×C127C2311yescharacteristic
32#117×C127—21no—
33#117×C127D411yescharacteristic
34M32×C127—21no—
35M32×C127—21no—
36M32×C127—21no—
37M32×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#107×C127—21no—
45#106×C127—21no—
46#102×C127—42no—
47#100×C127—42no—
48#97×C127—21no—
49C4×C8×C127—21no—
50C24×C127—41no—
51C2×D4×C127—22no—
52C2×D4×C127—41no—
53C2×D4×C127—41no—
54C2×D4×C127—41no—
55C2×D4×C127—41no—
56C2×D4×C127—41no—
57C22×C4×C127C2×D411yescharacteristic
58D8×C127—22no—
59D8×C127—22no—
60D8×C127—41no—
61D8×C127—41no—
62M16×C127—21no—
63M16×C127—21no—
64M16×C127—41no—
65M16×C127—41no—
66M16×C127—41no—
67M16×C127—41no—
68C2×C8×C127—21no—
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—21no—
78C4⋊C4×C127—41no—
79C22⋊C4×C127—21no—
80C22⋊C4×C127—41no—
81C42×C127—21no—
82C42×C127—41no—
83C16×C127—41no—
84C16×C127—41no—
85C23×C127—42no—
86C23×C127—81no—
87C23×C127—81no—
88C23×C127—162no—
89C23×C127#13511yescharacteristic
90D4×C127—42no—
91D4×C127—42no—
92D4×C127—81no—
93D4×C127—81no—
94C2×C4×C127—41no—
95C2×C4×C127—81no—
96C2×C4×C127#12111yescharacteristic
97C2×C4×C127#12311yescharacteristic
98C2×C4×C127#12411yescharacteristic
99C2×C4×C127#13511yescharacteristic
100C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
101C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
102C8×C127—41no—
103C8×C127—81no—
104C8×C127—81no—
105C8×C127#12311yescharacteristic
106C8×C127#12311yescharacteristic
107C8×C127#12611yescharacteristic
108C8×C127#12611yescharacteristic
109C22×C127—41no—
110C22×C127—82no—
111C22×C127—162no—
112C22×C127—162no—
113C22×C127—162no—
114C22×C127#46311yescharacteristic
115C22×C127#48211yescharacteristic
116C22×C127#48811yescharacteristic
117C4×C127—81no—
118C4×C127—161no—
119C4×C127#39711yescharacteristic
120C4×C127#46311yescharacteristic
121C4×C127#48211yescharacteristic
122C4×C127#49011yescharacteristic
123#13490C12711yesmaximal, characteristic, direct product factor, Sylow
124C2×C127—21no—
125C2×C127—21no—
126C2×C127—21no—
127C2×C127—162no—
128C2×C127#207311yescharacteristic
129C2×#361C2×C12711yescharacteristic
130#2140C2×C12711yescharacteristic
131#1978C2×C12711yescharacteristic
132#1833C2×C12711yescharacteristic, complemented
133#1389C2×C12711yescharacteristic, complemented
134#1388C2×C12711yescharacteristic, complemented
135#1378C2×C12711yescharacteristic, complemented
136C127#1349011yescharacteristic, direct product factor, Sylow
137C22×D8C22×C12711yescharacteristic
138C2×M32C22×C12711yescharacteristic
139C2×M32C22×C12711yescharacteristic
140C2×#108C22×C12711yescharacteristic
141C2×#108C22×C12711yescharacteristic
142#427C22×C12711yescharacteristic
143#418—21no—
144C2×#100—21no—
145#405C22×C12711yescharacteristic
146#361—22no—
147#357—22no—
148#344—21no—
149H(3,ℤ/4)—21no—
150C22×D4—21no—
151C2×D8—21no—
152C2×D8—21no—
153C2×D8—21no—
154C2×D8—21no—
155C2×D8—21no—
156C2×D8D4×C12712yes—
157C2×M16—21no—
158C2×M16—21no—
159C2×M16D4×C12711yescharacteristic
160C22×C8C23×C12711yescharacteristic
161#117—21no—
162#117D4×C12711yescharacteristic
163M32—21no—
164M32—21no—
165M32—21no—
166M32—21no—
167C2×C16—21no—
168C2×C16—21no—
169#108—21no—
170#108—21no—
171#108—21no—
172#108—21no—
173#107—21no—
174#106—21no—
175#102—42no—
176#100—42no—
177#97—21no—
178C4×C8—21no—
179C24—41no—
180C2×D4—22no—
181C2×D4—41no—
182C2×D4—41no—
183C2×D4—41no—
184C2×D4—41no—
185C2×D4—41no—
186C22×C4C2×D4×C12711yescharacteristic
187D8—22no—
188D8—22no—
189D8—41no—
190D8—41no—
191M16—21no—
192M16—21no—
193M16—41no—
194M16—41no—
195M16—41no—
196M16—41no—
197C2×C8—21no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8C2×D4×C12711yescharacteristic
201C2×C8#41×C12711yescharacteristic
202C2×C8#41×C12711yescharacteristic
203C2×C8#41×C12711yescharacteristic
204C2×C8#41×C12711yescharacteristic
205C2×C8#41×C12711yescharacteristic
206C4⋊C4—21no—
207C4⋊C4—41no—
208C22⋊C4—21no—
209C22⋊C4—41no—
210C42—21no—
211C42—41no—
212C16—41no—
213C16—41no—
214C23—42no—
215C23—81no—
216C23—81no—
217C23—162no—
218C23#135×C12711yescharacteristic
219D4—42no—
220D4—42no—
221D4—81no—
222D4—81no—
223C2×C4—41no—
224C2×C4—81no—
225C2×C4#121×C12711yescharacteristic
226C2×C4#123×C12711yescharacteristic
227C2×C4#124×C12711yescharacteristic
228C2×C4#135×C12711yescharacteristic
229C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
230C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
231C8—41no—
232C8—81no—
233C8—81no—
234C8#123×C12711yescharacteristic
235C8#123×C12711yescharacteristic
236C8#126×C12711yescharacteristic
237C8#126×C12711yescharacteristic
238C22—41no—
239C22—82no—
240C22—162no—
241C22—162no—
242C22—162no—
243C22#463×C12711yescharacteristic
244C22#482×C12711yescharacteristic
245C22#488×C12711yescharacteristic
246C4—81no—
247C4—161no—
248C4#397×C12711yescharacteristic
249C4#463×C12711yescharacteristic
250C4#482×C12711yescharacteristic
251C4#490×C12711yescharacteristic
252C2—21no—
253C2—21no—
254C2—21no—
255C2—162no—
256C2C127×#207311yescharacteristic
subgroupG/H
center, socleC2×C127#2073
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC22×D8×C127C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C22×C4×C127 ◁ #405×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1833C2semidirect
5. C127×#1389C2semidirect
6. C127×#1388C2semidirect
7. C127×#1378C2semidirect
123. #13490C127direct (N × H)
132. #1833C2×C127semidirect
133. #1389C2×C127semidirect
134. #1388C2×C127semidirect
135. #1378C2×C127semidirect
136. C127#13490direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#361×C1272
C127×#21402
C127×#19782
C127×#18332
C127×#13892
C127×#13882
C127×#13782
#13490127