Finite Group Databasebeta

← C127×#13489 #44577162

Subgroups — C127×#13489 #44577162

Order 32512.

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

normal subgroups only

This group has 278 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
1C127×#2148C211yesmaximal, characteristic
2C127×#2138C211yesmaximal, characteristic
3C127×#1976C211yesmaximal, characteristic
4C127×#1833C211yesmaximal, characteristic, complemented
5C127×#1384C211yesmaximal, characteristic, complemented
6C127×#1382C211yesmaximal, characteristic, complemented
7C127×#1379C211yesmaximal, characteristic, complemented
8C2×#135×C127C2211yescharacteristic
9C2×M32×C127C2211yescharacteristic
10C22×C16×C127C2211yescharacteristic
11C2×#108×C127C2211yescharacteristic
12#427×C127C2211yescharacteristic
13#427×C127C2211yescharacteristic
14#421×C127—21no—
15#410×C127—21no—
16#405×C127C2211yescharacteristic
17#362×C127—21no—
18#361×C127—21no—
19#358×C127—21no—
20#357×C127—21no—
21#344×C127—21no—
22H(3,ℤ/4)×C127—21no—
23C2×#41×C127—21no—
24#135×C127—21no—
25#135×C127—21no—
26#135×C127—21no—
27#135×C127—21no—
28C2×Q16×C127D411yescharacteristic
29C2×SD16×C127—21no—
30C2×D8×C127D411yescharacteristic
31C2×M16×C127—21no—
32C2×M16×C127D411yescharacteristic
33C22×C8×C127C2311yescharacteristic
34#117×C127—21no—
35#117×C127—21no—
36#117×C127D411yescharacteristic
37M32×C127—21no—
38M32×C127—21no—
39C2×C16×C127—21no—
40C2×C16×C127—21no—
41C2×C16×C127—21no—
42C2×C16×C127—21no—
43#108×C127—21no—
44#108×C127—21no—
45#107×C127—21no—
46#107×C127—21no—
47#106×C127—21no—
48#106×C127—21no—
49#104×C127—42no—
50#99×C127—42no—
51#97×C127—21no—
52C4×C8×C127—21no—
53#41×C127—41no—
54#41×C127—41no—
55#41×C127—41no—
56#41×C127—41no—
57C2×Q8×C127—21no—
58C2×D4×C127—21no—
59C2×D4×C127—41no—
60C22×C4×C127—41no—
61C22×C4×C127C2×D411yescharacteristic
62Q16×C127—21no—
63Q16×C127—21no—
64SD16×C127—41no—
65SD16×C127—41no—
66D8×C127—21no—
67D8×C127—21no—
68M16×C127—21no—
69M16×C127—21no—
70M16×C127—41no—
71M16×C127—41no—
72C2×C8×C127—21no—
73C2×C8×C127—41no—
74C2×C8×C127C2×D411yescharacteristic
75C2×C8×C127#4111yescharacteristic
76C2×C8×C127#4111yescharacteristic
77C2×C8×C127#4111yescharacteristic
78C2×C8×C127#4111yescharacteristic
79C2×C8×C127#4111yescharacteristic
80C4⋊C4×C127—21no—
81C4⋊C4×C127—41no—
82C4⋊C4×C127—41no—
83C22⋊C4×C127—21no—
84C22⋊C4×C127—41no—
85C22⋊C4×C127—41no—
86C42×C127—21no—
87C42×C127—41no—
88C42×C127—41no—
89C16×C127—41no—
90C16×C127—41no—
91C23×C127—41no—
92C23×C127AGL(1,ℤ/8)11yescharacteristic
93Q8×C127—41no—
94Q8×C127—41no—
95D4×C127—41no—
96D4×C127—41no—
97D4×C127—81no—
98D4×C127—81no—
99C2×C4×C127—41no—
100C2×C4×C127—41no—
101C2×C4×C127—81no—
102C2×C4×C127—81no—
103C2×C4×C127—81no—
104C2×C4×C127—81no—
105C2×C4×C127#12111yescharacteristic
106C2×C4×C127#12311yescharacteristic
107C2×C4×C127#12411yescharacteristic
108C2×C4×C127#13511yescharacteristic
109C2×C4×C127#13511yescharacteristic
110C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
111C8×C127—41no—
112C8×C127—81no—
113C8×C127#12311yescharacteristic
114C8×C127#12311yescharacteristic
115C8×C127#12611yescharacteristic
116C8×C127#12611yescharacteristic
117C22×C127—41no—
118C22×C127—81no—
119C22×C127—161no—
120C22×C127#46311yescharacteristic
121C22×C127#48211yescharacteristic
122C22×C127#49011yescharacteristic
123C4×C127—81no—
124C4×C127—81no—
125C4×C127—161no—
126C4×C127—161no—
127C4×C127#39711yescharacteristic
128C4×C127#46311yescharacteristic
129C4×C127#48211yescharacteristic
130C4×C127#48811yescharacteristic
131#13489C12711yesmaximal, characteristic, direct product factor, Sylow
132C2×C127—21no—
133C2×C127—21no—
134C2×C127—21no—
135C2×C127—161no—
136C2×C127#207311yescharacteristic
137#2148C2×C12711yescharacteristic
138#2138C2×C12711yescharacteristic
139#1976C2×C12711yescharacteristic
140#1833C2×C12711yescharacteristic, complemented
141#1384C2×C12711yescharacteristic, complemented
142#1382C2×C12711yescharacteristic, complemented
143#1379C2×C12711yescharacteristic, complemented
144C127#1348911yescharacteristic, direct product factor, Sylow
145C2×#135C22×C12711yescharacteristic
146C2×M32C22×C12711yescharacteristic
147C22×C16C22×C12711yescharacteristic
148C2×#108C22×C12711yescharacteristic
149#427C22×C12711yescharacteristic
150#427C22×C12711yescharacteristic
151#421—21no—
152#410—21no—
153#405C22×C12711yescharacteristic
154#362—21no—
155#361—21no—
156#358—21no—
157#357—21no—
158#344—21no—
159H(3,ℤ/4)—21no—
160C2×#41—21no—
161#135—21no—
162#135—21no—
163#135—21no—
164#135—21no—
165C2×Q16D4×C12711yescharacteristic
166C2×SD16—21no—
167C2×D8D4×C12711yescharacteristic
168C2×M16—21no—
169C2×M16D4×C12711yescharacteristic
170C22×C8C23×C12711yescharacteristic
171#117—21no—
172#117—21no—
173#117D4×C12711yescharacteristic
174M32—21no—
175M32—21no—
176C2×C16—21no—
177C2×C16—21no—
178C2×C16—21no—
179C2×C16—21no—
180#108—21no—
181#108—21no—
182#107—21no—
183#107—21no—
184#106—21no—
185#106—21no—
186#104—42no—
187#99—42no—
188#97—21no—
189C4×C8—21no—
190#41—41no—
191#41—41no—
192#41—41no—
193#41—41no—
194C2×Q8—21no—
195C2×D4—21no—
196C2×D4—41no—
197C22×C4—41no—
198C22×C4C2×D4×C12711yescharacteristic
199Q16—21no—
200Q16—21no—
201SD16—41no—
202SD16—41no—
203D8—21no—
204D8—21no—
205M16—21no—
206M16—21no—
207M16—41no—
208M16—41no—
209C2×C8—21no—
210C2×C8—41no—
211C2×C8C2×D4×C12711yescharacteristic
212C2×C8#41×C12711yescharacteristic
213C2×C8#41×C12711yescharacteristic
214C2×C8#41×C12711yescharacteristic
215C2×C8#41×C12711yescharacteristic
216C2×C8#41×C12711yescharacteristic
217C4⋊C4—21no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C22⋊C4—21no—
221C22⋊C4—41no—
222C22⋊C4—41no—
223C42—21no—
224C42—41no—
225C42—41no—
226C16—41no—
227C16—41no—
228C23—41no—
229C23AGL(1,ℤ/8)×C12711yescharacteristic
230Q8—41no—
231Q8—41no—
232D4—41no—
233D4—41no—
234D4—81no—
235D4—81no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—81no—
239C2×C4—81no—
240C2×C4—81no—
241C2×C4—81no—
242C2×C4#121×C12711yescharacteristic
243C2×C4#123×C12711yescharacteristic
244C2×C4#124×C12711yescharacteristic
245C2×C4#135×C12711yescharacteristic
246C2×C4#135×C12711yescharacteristic
247C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
248C8—41no—
249C8—81no—
250C8#123×C12711yescharacteristic
251C8#123×C12711yescharacteristic
252C8#126×C12711yescharacteristic
253C8#126×C12711yescharacteristic
254C22—41no—
255C22—81no—
256C22—161no—
257C22#463×C12711yescharacteristic
258C22#482×C12711yescharacteristic
259C22#490×C12711yescharacteristic
260C4—81no—
261C4—81no—
262C4—161no—
263C4—161no—
264C4#397×C12711yescharacteristic
265C4#463×C12711yescharacteristic
266C4#482×C12711yescharacteristic
267C4#488×C12711yescharacteristic
268C2—21no—
269C2—21no—
270C2—21no—
271C2—161no—
272C2C127×#207311yescharacteristic
subgroupG/H
centerC4×C127#482
commutator, Frattini, cosocleC22×C8C23×C127
socleC2×C127#2073
prime radicalC2×#135×C127C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×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×#1384C2semidirect
6. C127×#1382C2semidirect
7. C127×#1379C2semidirect
131. #13489C127direct (N × H)
140. #1833C2×C127semidirect
141. #1384C2×C127semidirect
142. #1382C2×C127semidirect
143. #1379C2×C127semidirect
144. C127#13489direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#21482
C127×#21382
C127×#19762
C127×#18332
C127×#13842
C127×#13822
C127×#13792
#13489127