Finite Group Databasebeta

← C127×#12934 #44576607

Subgroups — C127×#12934 #44576607

Order 32512.

394 conjugacy classes of subgroups.

The subgroup lattice has 306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2912C211yesmaximal, characteristic
2C127×#2155C211yesmaximal, characteristic, complemented
3C2×#365×C127C211yesmaximal, characteristic, complemented
4C127×#2117C211yesmaximal, characteristic
5C127×#1814C211yesmaximal, characteristic
6C127×#1386C211yesmaximal, characteristic, complemented
7C127×#1384C211yesmaximal, characteristic, complemented
8C2×#131×C127C2211yescharacteristic
9#520×C127—21no—
10C2×M32×C127C2211yescharacteristic
11C2×M32×C127C2211yescharacteristic
12C2×#108×C127C2211yescharacteristic
13#428×C127—21no—
14#428×C127—22no—
15#427×C127—21no—
16#427×C127C2211yescharacteristic
17#427×C127C2211yescharacteristic
18C2×#106×C127—21no—
19C2×#106×C127C2211yescharacteristic
20#421×C127—21no—
21#365×C127—22no—
22#365×C127—21no—
23#365×C127—21no—
24#350×C127C414yescomplemented
25#344×C127—21no—
26C2×#41×C127D411yescharacteristic
27#131×C127—21no—
28#131×C127—21no—
29#131×C127C2×C412yes—
30#131×C127Q812yes—
31C2×M16×C127—21no—
32C2×M16×C127—21no—
33C2×M16×C127D411yescharacteristic
34C22×C8×C127—21no—
35C22×C8×C127C2311yescharacteristic
36C4×Q8×C127—41no—
37C4×D4×C127—42no—
38C4×D4×C127—41no—
39#117×C127—22no—
40#117×C127—21no—
41#117×C127—21no—
42C2×C4⋊C4×C127—22no—
43C2×C4⋊C4×C127—21no—
44M32×C127—21no—
45M32×C127—21no—
46M32×C127—21no—
47M32×C127C2×C412yescomplemented
48C2×C16×C127—21no—
49C2×C16×C127C2×C412yescomplemented
50#108×C127—21no—
51#108×C127—21no—
52#107×C127—22no—
53#107×C127—21no—
54#107×C127—21no—
55#106×C127—22no—
56#106×C127—21no—
57#106×C127—21no—
58#106×C127D411yescharacteristic
59#106×C127D412yes—
60#106×C127D411yescharacteristic
61#104×C127—42no—
62#41×C127—21no—
63#41×C127—21no—
64#41×C127C4⋊C412yes—
65#41×C127SD1612yes—
66C2×Q8×C127SD1611yescharacteristic
67C2×D4×C127—21no—
68C2×D4×C127SD1611yescharacteristic
69C22×C4×C127—21no—
70C22×C4×C127—42no—
71C22×C4×C127—41no—
72C22×C4×C127C2×D411yescharacteristic
73M16×C127—21no—
74M16×C127—22no—
75M16×C127—22no—
76M16×C127—41no—
77M16×C127—41no—
78M16×C127C4⋊C412yes—
79C2×C8×C127—21no—
80C2×C8×C127—22no—
81C2×C8×C127—22no—
82C2×C8×C127—41no—
83C2×C8×C127C22×C411yescharacteristic
84C2×C8×C127C2×D411yescharacteristic
85C2×C8×C127C2×D411yescharacteristic
86C2×C8×C127C2×Q811yescharacteristic
87C2×C8×C127#4111yescharacteristic
88C2×C8×C127#4111yescharacteristic
89C4⋊C4×C127—21no—
90C4⋊C4×C127—22no—
91C4⋊C4×C127—21no—
92C4⋊C4×C127—42no—
93C4⋊C4×C127—41no—
94C4⋊C4×C127—41no—
95C22⋊C4×C127—42no—
96C22⋊C4×C127—41no—
97C22⋊C4×C127—41no—
98C42×C127—42no—
99C42×C127—41no—
100C42×C127—41no—
101C16×C127—22no—
102C16×C127—22no—
103C23×C127—21no—
104C23×C127AGL(1,ℤ/8)11yescharacteristic
105Q8×C127—21no—
106Q8×C127#10612yes—
107D4×C127—22no—
108D4×C127—22no—
109D4×C127—21no—
110D4×C127#10612yes—
111C2×C4×C127—21no—
112C2×C4×C127—22no—
113C2×C4×C127—22no—
114C2×C4×C127—41no—
115C2×C4×C127—42no—
116C2×C4×C127—41no—
117C2×C4×C127—81no—
118C2×C4×C127—161no—
119C2×C4×C127—162no—
120C2×C4×C127C2×C4⋊C411yescharacteristic
121C2×C4×C127#12011yescharacteristic
122C2×C4×C127#12311yescharacteristic
123C2×C4×C127C2×SD1611yescharacteristic
124C2×C4×C127C2×SD1611yescharacteristic
125C2×C4×C127#13711yescharacteristic
126C8×C127—22no—
127C8×C127—81no—
128C8×C127C4×D411yescharacteristic
129C8×C127C4×D411yescharacteristic
130C8×C127C22⋊Q811yescharacteristic
131C8×C127C22⋊Q811yescharacteristic
132C22×C127—22no—
133C22×C127—41no—
134C22×C127—42no—
135C22×C127#42811yescharacteristic
136C22×C127#45011yescharacteristic
137C22×C127#48111yescharacteristic
138C4×C127—22no—
139C4×C127—81no—
140C4×C127—82no—
141C4×C127—81no—
142C4×C127—161no—
143C4×C127#38511yescharacteristic
144C4×C127C2×#10611yescharacteristic
145C4×C127#44811yescharacteristic
146C4×C127#48311yescharacteristic
147#12934C12711yesmaximal, characteristic, direct product factor, Sylow
148C2×C127—21no—
149C2×C127—21no—
150C2×C127—21no—
151C2×C127—42no—
152C2×C127#185311yescharacteristic
153#2912C2×C12711yescharacteristic
154#2155C2×C12711yescharacteristic, complemented
155C2×#365C2×C12711yescharacteristic, complemented
156#2117C2×C12711yescharacteristic
157#1814C2×C12711yescharacteristic
158#1386C2×C12711yescharacteristic, complemented
159#1384C2×C12711yescharacteristic, complemented
160C127#1293411yescharacteristic, direct product factor, Sylow
161C2×#131C22×C12711yescharacteristic
162#520—21no—
163C2×M32C22×C12711yescharacteristic
164C2×M32C22×C12711yescharacteristic
165C2×#108C22×C12711yescharacteristic
166#428—21no—
167#428—22no—
168#427—21no—
169#427C22×C12711yescharacteristic
170#427C22×C12711yescharacteristic
171C2×#106—21no—
172C2×#106C22×C12711yescharacteristic
173#421—21no—
174#365—22no—
175#365—21no—
176#365—21no—
177#350C4×C12714yescomplemented
178#344—21no—
179C2×#41D4×C12711yescharacteristic
180#131—21no—
181#131—21no—
182#131C2×C4×C12712yes—
183#131Q8×C12712yes—
184C2×M16—21no—
185C2×M16—21no—
186C2×M16D4×C12711yescharacteristic
187C22×C8—21no—
188C22×C8C23×C12711yescharacteristic
189C4×Q8—41no—
190C4×D4—42no—
191C4×D4—41no—
192#117—22no—
193#117—21no—
194#117—21no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—21no—
197M32—21no—
198M32—21no—
199M32—21no—
200M32C2×C4×C12712yescomplemented
201C2×C16—21no—
202C2×C16C2×C4×C12712yescomplemented
203#108—21no—
204#108—21no—
205#107—22no—
206#107—21no—
207#107—21no—
208#106—22no—
209#106—21no—
210#106—21no—
211#106D4×C12711yescharacteristic
212#106D4×C12712yes—
213#106D4×C12711yescharacteristic
214#104—42no—
215#41—21no—
216#41—21no—
217#41C4⋊C4×C12712yes—
218#41SD16×C12712yes—
219C2×Q8SD16×C12711yescharacteristic
220C2×D4—21no—
221C2×D4SD16×C12711yescharacteristic
222C22×C4—21no—
223C22×C4—42no—
224C22×C4—41no—
225C22×C4C2×D4×C12711yescharacteristic
226M16—21no—
227M16—22no—
228M16—22no—
229M16—41no—
230M16—41no—
231M16C4⋊C4×C12712yes—
232C2×C8—21no—
233C2×C8—22no—
234C2×C8—22no—
235C2×C8—41no—
236C2×C8C22×C4×C12711yescharacteristic
237C2×C8C2×D4×C12711yescharacteristic
238C2×C8C2×D4×C12711yescharacteristic
239C2×C8C2×Q8×C12711yescharacteristic
240C2×C8#41×C12711yescharacteristic
241C2×C8#41×C12711yescharacteristic
242C4⋊C4—21no—
243C4⋊C4—22no—
244C4⋊C4—21no—
245C4⋊C4—42no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C22⋊C4—42no—
249C22⋊C4—41no—
250C22⋊C4—41no—
251C42—42no—
252C42—41no—
253C42—41no—
254C16—22no—
255C16—22no—
256C23—21no—
257C23AGL(1,ℤ/8)×C12711yescharacteristic
258Q8—21no—
259Q8#106×C12712yes—
260D4—22no—
261D4—22no—
262D4—21no—
263D4#106×C12712yes—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—81no—
271C2×C4—161no—
272C2×C4—162no—
273C2×C4C2×C4⋊C4×C12711yescharacteristic
274C2×C4#120×C12711yescharacteristic
275C2×C4#123×C12711yescharacteristic
276C2×C4C2×SD16×C12711yescharacteristic
277C2×C4C2×SD16×C12711yescharacteristic
278C2×C4#137×C12711yescharacteristic
279C8—22no—
280C8—81no—
281C8C4×D4×C12711yescharacteristic
282C8C4×D4×C12711yescharacteristic
283C8C22⋊Q8×C12711yescharacteristic
284C8C22⋊Q8×C12711yescharacteristic
285C22—22no—
286C22—41no—
287C22—42no—
288C22#428×C12711yescharacteristic
289C22#450×C12711yescharacteristic
290C22#481×C12711yescharacteristic
291C4—22no—
292C4—82no—
293C4—81no—
294C4—81no—
295C4—161no—
296C4#385×C12711yescharacteristic
297C4C2×#106×C12711yescharacteristic
298C4#448×C12711yescharacteristic
299C4#483×C12711yescharacteristic
300C2—21no—
301C2—21no—
302C2—21no—
303C2—42no—
304C2C127×#185311yescharacteristic
subgroupG/H
center, socleC2×C127#1853
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC2×#41×C127D4
LCSG ▷ C2×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
2. C127×#2155C2semidirect
3. C2×#365×C127C2semidirect
6. C127×#1386C2semidirect
7. C127×#1384C2semidirect
24. #350×C127C4semidirect
47. M32×C127C2×C4semidirect
49. C2×C16×C127C2×C4semidirect
147. #12934C127direct (N × H)
154. #2155C2×C127semidirect
155. C2×#365C2×C127semidirect
158. #1386C2×C127semidirect
159. #1384C2×C127semidirect
160. C127#12934direct (N × H)
177. #350C4×C127semidirect
200. M32C2×C4×C127semidirect
202. C2×C16C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#29122
C127×#21552
C2×#365×C1272
C127×#21172
C127×#18142
C127×#13862
C127×#13842
#12934127