Finite Group Databasebeta

← C127×#13156 #44576829

Subgroups — C127×#13156 #44576829

Order 32512.

306 conjugacy classes of subgroups.

The subgroup lattice has 280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2148C211yesmaximal, characteristic
2C2×#360×C127C211yesmaximal, characteristic
3C127×#2110C211yesmaximal, characteristic, complemented
4C127×#1976C211yesmaximal, characteristic
5C127×#1951C211yesmaximal, characteristic, complemented
6C127×#1389C211yesmaximal, characteristic, complemented
7C127×#1386C211yesmaximal, characteristic, complemented
8C2×#135×C127C2211yescharacteristic
9C2×M32×C127C2211yescharacteristic
10C2×M32×C127C2211yescharacteristic
11C2×#108×C127C2211yescharacteristic
12#428×C127—21no—
13#427×C127C2211yescharacteristic
14C2×#106×C127C2211yescharacteristic
15#421×C127—21no—
16#410×C127—21no—
17#405×C127C2211yescharacteristic
18#362×C127C412yescomplemented
19#361×C127C412yescomplemented
20#360×C127—22no—
21#347×C127—22no—
22#343×C127—21no—
23C2×#41×C127—21no—
24#135×C127—21no—
25#135×C127—21no—
26#135×C127—21no—
27#135×C127—21no—
28C2×Q16×C127C2×C411yescharacteristic
29C2×SD16×C127—21no—
30C2×D8×C127C2×C411yescharacteristic
31C2×M16×C127—21no—
32C2×M16×C127D411yescharacteristic
33C22×C8×C127C2311yescharacteristic
34#117×C127—21no—
35#117×C127D411yescharacteristic
36C2×C4⋊C4×C127—21no—
37M32×C127—21no—
38M32×C127—21no—
39M32×C127C2×C412yes—
40M32×C127D412yes—
41C2×C16×C127—21no—
42C2×C16×C127—21no—
43#108×C127—21no—
44#108×C127C2×C412yes—
45#107×C127—21no—
46#107×C127—41no—
47#106×C127—21no—
48#106×C127—21no—
49#106×C127—21no—
50#106×C127—41no—
51#104×C127—42no—
52#99×C127—42no—
53#97×C127—21no—
54C4×C8×C127—21no—
55#41×C127—41no—
56#41×C127—41no—
57#41×C127—41no—
58#41×C127—41no—
59C2×Q8×C127—21no—
60C2×D4×C127—21no—
61C2×D4×C127—41no—
62C22×C4×C127—41no—
63C22×C4×C127—41no—
64C22×C4×C127C2×D411yescharacteristic
65Q16×C127—21no—
66Q16×C127—21no—
67SD16×C127—41no—
68SD16×C127—41no—
69D8×C127—21no—
70D8×C127—21no—
71M16×C127—22no—
72M16×C127—21no—
73M16×C127—21no—
74M16×C127—41no—
75C2×C8×C127—21no—
76C2×C8×C127—41no—
77C2×C8×C127C22×C411yescharacteristic
78C2×C8×C127C2×D411yescharacteristic
79C2×C8×C127#4111yescharacteristic
80C2×C8×C127#4111yescharacteristic
81C2×C8×C127#4111yescharacteristic
82C2×C8×C127#4111yescharacteristic
83C4⋊C4×C127—21no—
84C4⋊C4×C127—41no—
85C4⋊C4×C127—41no—
86C4⋊C4×C127—41no—
87C22⋊C4×C127—21no—
88C22⋊C4×C127—41no—
89C42×C127—21no—
90C42×C127—41no—
91C16×C127—22no—
92C16×C127—22no—
93C23×C127—41no—
94C23×C127AGL(1,ℤ/8)11yescharacteristic
95Q8×C127—41no—
96Q8×C127—41no—
97D4×C127—41no—
98D4×C127—41no—
99D4×C127—81no—
100D4×C127—81no—
101C2×C4×C127—41no—
102C2×C4×C127—41no—
103C2×C4×C127—81no—
104C2×C4×C127—81no—
105C2×C4×C127—81no—
106C2×C4×C127—81no—
107C2×C4×C127—161no—
108C2×C4×C127C4×D411yescharacteristic
109C2×C4×C127#12111yescharacteristic
110C2×C4×C127#12411yescharacteristic
111C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
112C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
113C2×C4×C127#13711yescharacteristic
114C8×C127—42no—
115C8×C127—41no—
116C8×C127#11711yescharacteristic
117C8×C127C4×D411yescharacteristic
118C8×C127#12311yescharacteristic
119C8×C127#12611yescharacteristic
120C22×C127—41no—
121C22×C127—81no—
122C22×C127—161no—
123C22×C127#44011yescharacteristic
124C22×C127#46911yescharacteristic
125C22×C127#49011yescharacteristic
126C4×C127—81no—
127C4×C127—81no—
128C4×C127—161no—
129C4×C127—161no—
130C4×C127#38811yescharacteristic
131C4×C127#44211yescharacteristic
132C4×C127#46811yescharacteristic
133C4×C127#48911yescharacteristic
134#13156C12711yesmaximal, characteristic, direct product factor, Sylow
135C2×C127—21no—
136C2×C127—21no—
137C2×C127—21no—
138C2×C127—161no—
139C2×C127#193611yescharacteristic
140#2148C2×C12711yescharacteristic
141C2×#360C2×C12711yescharacteristic
142#2110C2×C12711yescharacteristic, complemented
143#1976C2×C12711yescharacteristic
144#1951C2×C12711yescharacteristic, complemented
145#1389C2×C12711yescharacteristic, complemented
146#1386C2×C12711yescharacteristic, complemented
147C127#1315611yescharacteristic, direct product factor, Sylow
148C2×#135C22×C12711yescharacteristic
149C2×M32C22×C12711yescharacteristic
150C2×M32C22×C12711yescharacteristic
151C2×#108C22×C12711yescharacteristic
152#428—21no—
153#427C22×C12711yescharacteristic
154C2×#106C22×C12711yescharacteristic
155#421—21no—
156#410—21no—
157#405C22×C12711yescharacteristic
158#362C4×C12712yescomplemented
159#361C4×C12712yescomplemented
160#360—22no—
161#347—22no—
162#343—21no—
163C2×#41—21no—
164#135—21no—
165#135—21no—
166#135—21no—
167#135—21no—
168C2×Q16C2×C4×C12711yescharacteristic
169C2×SD16—21no—
170C2×D8C2×C4×C12711yescharacteristic
171C2×M16—21no—
172C2×M16D4×C12711yescharacteristic
173C22×C8C23×C12711yescharacteristic
174#117—21no—
175#117D4×C12711yescharacteristic
176C2×C4⋊C4—21no—
177M32—21no—
178M32—21no—
179M32C2×C4×C12712yes—
180M32D4×C12712yes—
181C2×C16—21no—
182C2×C16—21no—
183#108—21no—
184#108C2×C4×C12712yes—
185#107—21no—
186#107—41no—
187#106—21no—
188#106—21no—
189#106—21no—
190#106—41no—
191#104—42no—
192#99—42no—
193#97—21no—
194C4×C8—21no—
195#41—41no—
196#41—41no—
197#41—41no—
198#41—41no—
199C2×Q8—21no—
200C2×D4—21no—
201C2×D4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4C2×D4×C12711yescharacteristic
205Q16—21no—
206Q16—21no—
207SD16—41no—
208SD16—41no—
209D8—21no—
210D8—21no—
211M16—22no—
212M16—21no—
213M16—21no—
214M16—41no—
215C2×C8—21no—
216C2×C8—41no—
217C2×C8C22×C4×C12711yescharacteristic
218C2×C8C2×D4×C12711yescharacteristic
219C2×C8#41×C12711yescharacteristic
220C2×C8#41×C12711yescharacteristic
221C2×C8#41×C12711yescharacteristic
222C2×C8#41×C12711yescharacteristic
223C4⋊C4—21no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C22⋊C4—21no—
228C22⋊C4—41no—
229C42—21no—
230C42—41no—
231C16—22no—
232C16—22no—
233C23—41no—
234C23AGL(1,ℤ/8)×C12711yescharacteristic
235Q8—41no—
236Q8—41no—
237D4—41no—
238D4—41no—
239D4—81no—
240D4—81no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4—81no—
247C2×C4—161no—
248C2×C4C4×D4×C12711yescharacteristic
249C2×C4#121×C12711yescharacteristic
250C2×C4#124×C12711yescharacteristic
251C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
252C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
253C2×C4#137×C12711yescharacteristic
254C8—42no—
255C8—41no—
256C8#117×C12711yescharacteristic
257C8C4×D4×C12711yescharacteristic
258C8#123×C12711yescharacteristic
259C8#126×C12711yescharacteristic
260C22—41no—
261C22—81no—
262C22—161no—
263C22#440×C12711yescharacteristic
264C22#469×C12711yescharacteristic
265C22#490×C12711yescharacteristic
266C4—81no—
267C4—81no—
268C4—161no—
269C4—161no—
270C4#388×C12711yescharacteristic
271C4#442×C12711yescharacteristic
272C4#468×C12711yescharacteristic
273C4#489×C12711yescharacteristic
274C2—21no—
275C2—21no—
276C2—21no—
277C2—161no—
278C2C127×#193611yescharacteristic
subgroupG/H
center, socleC2×C127#1936
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC2×#135×C127C22
LCSG ▷ C2×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
3. C127×#2110C2semidirect
5. C127×#1951C2semidirect
6. C127×#1389C2semidirect
7. C127×#1386C2semidirect
18. #362×C127C4semidirect
19. #361×C127C4semidirect
134. #13156C127direct (N × H)
142. #2110C2×C127semidirect
144. #1951C2×C127semidirect
145. #1389C2×C127semidirect
146. #1386C2×C127semidirect
147. C127#13156direct (N × H)
158. #362C4×C127semidirect
159. #361C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#21482
C2×#360×C1272
C127×#21102
C127×#19762
C127×#19512
C127×#13892
C127×#13862
#13156127