Finite Group Databasebeta

← C127×#19063 #44582736

Subgroups — C127×#19063 #44582736

Order 32512.

806 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3556C211yesmaximal, characteristic, complemented
2C127×#3235C212yesmaximal
3C127×#3135C211yesmaximal, characteristic
4C127×#1663C214yesmaximal, complemented
5C127×#1658C214yesmaximal, complemented
6C127×#1537C211yesmaximal, characteristic, complemented
7C127×#1531C212yesmaximal, complemented
8#564×C127C2214yes—
9#557×C127—22no—
10#557×C127—22no—
11#557×C127—22no—
12#541×C127—22no—
13#541×C127—24no—
14#533×C127C2211yescharacteristic
15#533×C127C2212yes—
16#532×C127C2211yescharacteristic
17#501×C127C2214yes—
18#491×C127C2212yes—
19#490×C127C2212yes—
20#490×C127C2214yes—
21#489×C127—22no—
22#482×C127—24no—
23#476×C127—22no—
24#474×C127—22no—
25#432×C127C2212yes—
26#416×C127—22no—
27C2×#97×C127C2211yescharacteristic
28#330×C127C2218yes—
29#330×C127C2214yes—
30C2×#41×C127—21no—
31C22×C8×C127—21no—
32C4⋊Q8×C127—24no—
33C4⋊Q8×C127—22no—
34C4⋊Q8×C127D412yes—
35C4⋊Q8×C127D412yes—
36C4⋊Q8×C127D412yes—
37C4⋊Q8×C127C2311yescharacteristic
38#127×C127C2311yescharacteristic
39#126×C127—28no—
40#125×C127—24no—
41#125×C127—22no—
42#125×C127—28no—
43#125×C127—28no—
44#125×C127—28no—
45#125×C127C2314yes—
46#125×C127C2312yes—
47#124×C127—21no—
48C22⋊Q8×C127—22no—
49C22⋊Q8×C127—22no—
50C22⋊Q8×C127—22no—
51#121×C127—22no—
52C4×Q8×C127—24no—
53C4×Q8×C127—24no—
54C4×Q8×C127—24no—
55C4×Q8×C127—22no—
56C4×Q8×C127—22no—
57C4×Q8×C127—22no—
58C4×D4×C127—22no—
59#117×C127D412yes—
60#117×C127D414yes—
61C2×C42×C127C2311yescharacteristic
62#107×C127—24no—
63#106×C127—24no—
64C4⋊C8×C127—22no—
65#103×C127—24no—
66#102×C127—24no—
67#102×C127—24no—
68#102×C127—24no—
69C22⋊C8×C127—22no—
70#97×C127—21no—
71#97×C127C2314yes—
72#97×C127C2312yes—
73#41×C127—44no—
74C2×Q8×C127—22no—
75C2×Q8×C127—22no—
76C2×Q8×C127—22no—
77C2×Q8×C127—21no—
78C2×D4×C127—22no—
79C2×D4×C127—21no—
80C2×D4×C127—41no—
81C22×C4×C127—41no—
82C22×C4×C127C2×D411yescharacteristic
83C22×C4×C127C2×D412yes—
84C2×C8×C127—22no—
85C2×C8×C127—24no—
86C2×C8×C127—42no—
87C4⋊C4×C127—28no—
88C4⋊C4×C127—28no—
89C4⋊C4×C127—28no—
90C4⋊C4×C127—22no—
91C4⋊C4×C127—22no—
92C4⋊C4×C127—22no—
93C4⋊C4×C127—24no—
94C4⋊C4×C127—24no—
95C4⋊C4×C127—24no—
96C4⋊C4×C127—22no—
97C4⋊C4×C127C2×D414yes—
98C4⋊C4×C127C2×D414yes—
99C4⋊C4×C127C2×D414yes—
100C22⋊C4×C127—22no—
101C22⋊C4×C127—24no—
102C22⋊C4×C127—42no—
103C42×C127—28no—
104C42×C127—24no—
105C42×C127—22no—
106C42×C127C2×D411yescharacteristic
107C42×C127C2×D412yes—
108C42×C127C2411yescharacteristic
109C23×C127—41no—
110C23×C127#12011yescharacteristic
111Q8×C127—44no—
112Q8×C127—44no—
113Q8×C127—42no—
114Q8×C127—44no—
115D4×C127—44no—
116D4×C127—42no—
117D4×C127—82no—
118C2×C4×C127—22no—
119C2×C4×C127—24no—
120C2×C4×C127—24no—
121C2×C4×C127—24no—
122C2×C4×C127—42no—
123C2×C4×C127—41no—
124C2×C4×C127—82no—
125C2×C4×C127#12012yes—
126C2×C4×C127#12011yescharacteristic
127C2×C4×C127C22×D412yes—
128C2×C4×C127C22×D411yescharacteristic
129C8×C127—44no—
130C8×C127—42no—
131C22×C127—21no—
132C22×C127—22no—
133C22×C127—81no—
134C22×C127—82no—
135C22×C127C2×#12011yescharacteristic
136C4×C127—21no—
137C4×C127—22no—
138C4×C127—22no—
139C4×C127—44no—
140C4×C127—44no—
141C4×C127—44no—
142C4×C127—81no—
143C4×C127#45412yes—
144#19063C12711yesmaximal, characteristic, direct product factor, Sylow
145C2×C127—41no—
146C2×C127—161no—
147C2×C127C2×#45411yescharacteristic
148C2×C127#302012yes—
149#3556C2×C12711yescharacteristic, complemented
150#3235C2×C12712yes—
151#3135C2×C12711yescharacteristic
152#1663C2×C12714yescomplemented
153#1658C2×C12714yescomplemented
154#1537C2×C12711yescharacteristic, complemented
155#1531C2×C12712yescomplemented
156C127#1906311yescharacteristic, direct product factor, Sylow
157#564C22×C12714yes—
158#557—22no—
159#557—22no—
160#557—22no—
161#541—22no—
162#541—24no—
163#533C22×C12711yescharacteristic
164#533C22×C12712yes—
165#532C22×C12711yescharacteristic
166#501C22×C12714yes—
167#491C22×C12712yes—
168#490C22×C12712yes—
169#490C22×C12714yes—
170#489—22no—
171#482—24no—
172#476—22no—
173#474—22no—
174#432C22×C12712yes—
175#416—22no—
176C2×#97C22×C12711yescharacteristic
177#330C22×C12714yes—
178#330C22×C12718yes—
179C2×#41—21no—
180C22×C8—21no—
181C4⋊Q8—24no—
182C4⋊Q8—22no—
183C4⋊Q8D4×C12712yes—
184C4⋊Q8D4×C12712yes—
185C4⋊Q8D4×C12712yes—
186C4⋊Q8C23×C12711yescharacteristic
187#127C23×C12711yescharacteristic
188#126—28no—
189#125—24no—
190#125—22no—
191#125—28no—
192#125—28no—
193#125—28no—
194#125C23×C12712yes—
195#125C23×C12714yes—
196#124—21no—
197C22⋊Q8—22no—
198C22⋊Q8—22no—
199C22⋊Q8—22no—
200#121—22no—
201C4×Q8—24no—
202C4×Q8—24no—
203C4×Q8—24no—
204C4×Q8—22no—
205C4×Q8—22no—
206C4×Q8—22no—
207C4×D4—22no—
208#117D4×C12712yes—
209#117D4×C12714yes—
210C2×C42C23×C12711yescharacteristic
211#107—24no—
212#106—24no—
213C4⋊C8—22no—
214#103—24no—
215#102—24no—
216#102—24no—
217#102—24no—
218C22⋊C8—22no—
219#97—21no—
220#97C23×C12712yes—
221#97C23×C12714yes—
222#41—44no—
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—22no—
226C2×Q8—21no—
227C2×D4—22no—
228C2×D4—21no—
229C2×D4—41no—
230C22×C4—41no—
231C22×C4C2×D4×C12711yescharacteristic
232C22×C4C2×D4×C12712yes—
233C2×C8—22no—
234C2×C8—24no—
235C2×C8—42no—
236C4⋊C4—28no—
237C4⋊C4—28no—
238C4⋊C4—28no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—24no—
243C4⋊C4—24no—
244C4⋊C4—24no—
245C4⋊C4—22no—
246C4⋊C4C2×D4×C12714yes—
247C4⋊C4C2×D4×C12714yes—
248C4⋊C4C2×D4×C12714yes—
249C22⋊C4—22no—
250C22⋊C4—24no—
251C22⋊C4—42no—
252C42—28no—
253C42—24no—
254C42—22no—
255C42C2×D4×C12711yescharacteristic
256C42C2×D4×C12712yes—
257C42C24×C12711yescharacteristic
258C23—41no—
259C23#120×C12711yescharacteristic
260Q8—44no—
261Q8—44no—
262Q8—42no—
263Q8—44no—
264D4—42no—
265D4—44no—
266D4—82no—
267C2×C4—22no—
268C2×C4—24no—
269C2×C4—24no—
270C2×C4—24no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—82no—
274C2×C4#120×C12712yes—
275C2×C4#120×C12711yescharacteristic
276C2×C4C22×D4×C12712yes—
277C2×C4C22×D4×C12711yescharacteristic
278C8—42no—
279C8—44no—
280C22—21no—
281C22—22no—
282C22—81no—
283C22—82no—
284C22C2×#120×C12711yescharacteristic
285C4—21no—
286C4—22no—
287C4—22no—
288C4—44no—
289C4—44no—
290C4—44no—
291C4—81no—
292C4#454×C12712yes—
293C2—41no—
294C2—161no—
295C2C2×#454×C12711yescharacteristic
296C2C127×#302012yes—
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC42C24×C127
prime radical#532×C127C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3556C2semidirect
4. C127×#1663C2semidirect
5. C127×#1658C2semidirect
6. C127×#1537C2semidirect
7. C127×#1531C2semidirect
144. #19063C127direct (N × H)
149. #3556C2×C127semidirect
152. #1663C2×C127semidirect
153. #1658C2×C127semidirect
154. #1537C2×C127semidirect
155. #1531C2×C127semidirect
156. C127#19063direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#35562
C127×#32352
C127×#31352
C127×#16632
C127×#16582
C127×#15372
C127×#15312
#19063127