Finite Group Databasebeta

← C127×#19077 #44582750

Subgroups — C127×#19077 #44582750

Order 32512.

996 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 996 conjugacy classes of subgroups — too many to draw. Only its 230 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×#3550C211yesmaximal, characteristic, complemented
2C127×#3151C211yesmaximal, characteristic
3C127×#3138C212yesmaximal, complemented
4C127×#1657C218yesmaximal, complemented
5C127×#1526C212yesmaximal, complemented
6C127×#1525C211yesmaximal, characteristic, complemented
7C2×AGL(1,ℤ/8)×C127—22no—
8#563×C127C2214yescomplemented
9#559×C127—21no—
10Q82×C127—21no—
11#556×C127—22no—
12D4×Q8×C127—22no—
13#542×C127—24no—
14#536×C127—22no—
15#533×C127C2212yes—
16#532×C127C2211yescharacteristic
17C2×#127×C127C2211yescharacteristic
18#496×C127C2214yes—
19#493×C127—21no—
20#492×C127—21no—
21#490×C127C2218yes—
22#486×C127—22no—
23#486×C127—22no—
24#418×C127—24no—
25C4×M16×C127C2212yes—
26C4×M16×C127C2211yescharacteristic
27#330×C127C2218yescomplemented
28#329×C127C2214yescomplemented
29C2×#41×C127D412yes—
30C22×Q8×C127—22no—
31C22×D4×C127—21no—
32C22×D4×C127—22no—
33AGL(1,ℤ/8)×C127—48no—
34C2×SD16×C127—24no—
35C2×D8×C127—24no—
36C2×M16×C127—21no—
37C2×M16×C127—22no—
38C4⋊Q8×C127—24no—
39C4⋊Q8×C127—24no—
40C4⋊Q8×C127D411yescharacteristic
41C4⋊Q8×C127D412yes—
42C4⋊Q8×C127D412yes—
43#127×C127—22no—
44#127×C127—21no—
45#127×C127D411yescharacteristic
46#127×C127C2312yes—
47#126×C127—28no—
48#125×C127C2314yes—
49#124×C127—24no—
50#124×C127—24no—
51#124×C127C2312yes—
52#123×C127—24no—
53#123×C127—24no—
54C22⋊Q8×C127—24no—
55C22⋊Q8×C127—22no—
56C22⋊Q8×C127—22no—
57C22⋊Q8×C127—28no—
58#121×C127—22no—
59C4×Q8×C127—24no—
60C4×Q8×C127—22no—
61C4×Q8×C127—22no—
62C4×D4×C127—24no—
63C4×D4×C127—22no—
64#117×C127—22no—
65#117×C127D414yes—
66C2×C42×C127C2311yescharacteristic
67#102×C127—28no—
68#102×C127—28no—
69#97×C127C2312yes—
70#97×C127C2314yes—
71C4×C8×C127—22no—
72C4×C8×C127—21no—
73C24×C127—41no—
74#41×C127—44no—
75C2×Q8×C127—24no—
76C2×Q8×C127—22no—
77C2×Q8×C127—22no—
78C2×Q8×C127—84no—
79C2×Q8×C127C2×D412yes—
80C2×D4×C127—22no—
81C2×D4×C127—22no—
82C2×D4×C127—24no—
83C2×D4×C127—22no—
84C2×D4×C127—44no—
85C2×D4×C127—48no—
86C2×D4×C127—41no—
87C2×D4×C127—42no—
88C2×D4×C127C2×D412yes—
89C22×C4×C127—24no—
90C22×C4×C127—22no—
91C22×C4×C127C2×D412yes—
92C22×C4×C127C2×D411yescharacteristic
93SD16×C127—48no—
94D8×C127—48no—
95M16×C127—24no—
96M16×C127—44no—
97C2×C8×C127—22no—
98C2×C8×C127—24no—
99C4⋊C4×C127—28no—
100C4⋊C4×C127—22no—
101C4⋊C4×C127—22no—
102C4⋊C4×C127—22no—
103C4⋊C4×C127—24no—
104C4⋊C4×C127—24no—
105C4⋊C4×C127C2×D414yes—
106C4⋊C4×C127C2×D414yes—
107C22⋊C4×C127—24no—
108C22⋊C4×C127—28no—
109C22⋊C4×C127—24no—
110C22⋊C4×C127—24no—
111C42×C127—24no—
112C42×C127—24no—
113C42×C127C2×D412yes—
114C42×C127C2×D411yescharacteristic
115C42×C127C2411yescharacteristic
116C23×C127—22no—
117C23×C127—42no—
118C23×C127—82no—
119C23×C127—84no—
120C23×C127#12011yescharacteristic
121Q8×C127—42no—
122Q8×C127—44no—
123Q8×C127—44no—
124Q8×C127—84no—
125D4×C127—42no—
126D4×C127—44no—
127D4×C127—48no—
128D4×C127—44no—
129D4×C127—82no—
130D4×C127—82no—
131D4×C127—84no—
132C2×C4×C127—22no—
133C2×C4×C127—24no—
134C2×C4×C127—24no—
135C2×C4×C127—22no—
136C2×C4×C127—24no—
137C2×C4×C127—44no—
138C2×C4×C127—84no—
139C2×C4×C127#12011yescharacteristic
140C2×C4×C127#12012yes—
141C2×C4×C127C22×D412yes—
142C2×C4×C127C22×D411yescharacteristic
143C8×C127—24no—
144C8×C127—44no—
145C22×C127—21no—
146C22×C127—22no—
147C22×C127—42no—
148C22×C127—44no—
149C22×C127—82no—
150C22×C127—84no—
151C22×C127—164no—
152C22×C127C2×#12011yescharacteristic
153C4×C127—21no—
154C4×C127—22no—
155C4×C127—42no—
156C4×C127—44no—
157C4×C127—44no—
158C4×C127#45312yes—
159C4×C127#45414yes—
160#19077C12711yesmaximal, characteristic, direct product factor, Sylow
161C2×C127—41no—
162C2×C127—82no—
163C2×C127—162no—
164C2×C127C2×#45311yescharacteristic
165C2×C127C2×#45412yes—
166#3550C2×C12711yescharacteristic, complemented
167#3151C2×C12711yescharacteristic
168#3138C2×C12712yescomplemented
169#1657C2×C12718yescomplemented
170#1526C2×C12712yescomplemented
171#1525C2×C12711yescharacteristic, complemented
172C127#1907711yescharacteristic, direct product factor, Sylow
173C2×AGL(1,ℤ/8)—22no—
174#563C22×C12714yescomplemented
175#559—21no—
176Q82—21no—
177#556—22no—
178D4×Q8—22no—
179#542—24no—
180#536—22no—
181#533C22×C12712yes—
182#532C22×C12711yescharacteristic
183C2×#127C22×C12711yescharacteristic
184#496C22×C12714yes—
185#493—21no—
186#492—21no—
187#490C22×C12718yes—
188#486—22no—
189#486—22no—
190#418—24no—
191C4×M16C22×C12712yes—
192C4×M16C22×C12711yescharacteristic
193#330C22×C12718yescomplemented
194#329C22×C12714yescomplemented
195C2×#41D4×C12712yes—
196C22×Q8—22no—
197C22×D4—21no—
198C22×D4—22no—
199AGL(1,ℤ/8)—48no—
200C2×SD16—24no—
201C2×D8—24no—
202C2×M16—21no—
203C2×M16—22no—
204C4⋊Q8—24no—
205C4⋊Q8—24no—
206C4⋊Q8D4×C12711yescharacteristic
207C4⋊Q8D4×C12712yes—
208C4⋊Q8D4×C12712yes—
209#127—22no—
210#127—21no—
211#127D4×C12711yescharacteristic
212#127C23×C12712yes—
213#126—28no—
214#125C23×C12714yes—
215#124—24no—
216#124—24no—
217#124C23×C12712yes—
218#123—24no—
219#123—24no—
220C22⋊Q8—24no—
221C22⋊Q8—22no—
222C22⋊Q8—22no—
223C22⋊Q8—28no—
224#121—22no—
225C4×Q8—24no—
226C4×Q8—22no—
227C4×Q8—22no—
228C4×D4—24no—
229C4×D4—22no—
230#117—22no—
231#117D4×C12714yes—
232C2×C42C23×C12711yescharacteristic
233#102—28no—
234#102—28no—
235#97C23×C12714yes—
236#97C23×C12712yes—
237C4×C8—22no—
238C4×C8—21no—
239C24—41no—
240#41—44no—
241C2×Q8—24no—
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—84no—
245C2×Q8C2×D4×C12712yes—
246C2×D4—22no—
247C2×D4—22no—
248C2×D4—24no—
249C2×D4—22no—
250C2×D4—44no—
251C2×D4—48no—
252C2×D4—41no—
253C2×D4—42no—
254C2×D4C2×D4×C12712yes—
255C22×C4—24no—
256C22×C4—22no—
257C22×C4C2×D4×C12712yes—
258C22×C4C2×D4×C12711yescharacteristic
259SD16—48no—
260D8—48no—
261M16—24no—
262M16—44no—
263C2×C8—22no—
264C2×C8—24no—
265C4⋊C4—28no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—24no—
270C4⋊C4—24no—
271C4⋊C4C2×D4×C12714yes—
272C4⋊C4C2×D4×C12714yes—
273C22⋊C4—24no—
274C22⋊C4—28no—
275C22⋊C4—24no—
276C22⋊C4—24no—
277C42—24no—
278C42—24no—
279C42C2×D4×C12712yes—
280C42C2×D4×C12711yescharacteristic
281C42C24×C12711yescharacteristic
282C23—22no—
283C23—42no—
284C23—82no—
285C23—84no—
286C23#120×C12711yescharacteristic
287Q8—42no—
288Q8—44no—
289Q8—44no—
290Q8—84no—
291D4—42no—
292D4—44no—
293D4—48no—
294D4—44no—
295D4—82no—
296D4—82no—
297D4—84no—
298C2×C4—22no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—22no—
302C2×C4—24no—
303C2×C4—44no—
304C2×C4—84no—
305C2×C4#120×C12711yescharacteristic
306C2×C4#120×C12712yes—
307C2×C4C22×D4×C12712yes—
308C2×C4C22×D4×C12711yescharacteristic
309C8—24no—
310C8—44no—
311C22—21no—
312C22—22no—
313C22—42no—
314C22—44no—
315C22—82no—
316C22—84no—
317C22—164no—
318C22C2×#120×C12711yescharacteristic
319C4—21no—
320C4—22no—
321C4—42no—
322C4—44no—
323C4—44no—
324C4#453×C12712yes—
325C4#454×C12714yes—
326C2—41no—
327C2—82no—
328C2—162no—
329C2C2×#453×C12711yescharacteristic
330C2C2×#454×C12712yes—
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC42C24×C127
prime radicalC127×#3151C2
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×#3550C2semidirect
3. C127×#3138C2semidirect
4. C127×#1657C2semidirect
5. C127×#1526C2semidirect
6. C127×#1525C2semidirect
8. #563×C127C22semidirect
27. #330×C127C22semidirect
28. #329×C127C22semidirect
160. #19077C127direct (N × H)
166. #3550C2×C127semidirect
168. #3138C2×C127semidirect
169. #1657C2×C127semidirect
170. #1526C2×C127semidirect
171. #1525C2×C127semidirect
172. C127#19077direct (N × H)
174. #563C22×C127semidirect
193. #330C22×C127semidirect
194. #329C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35502
C127×#31512
C127×#31382
C127×#16572
C127×#15262
C127×#15252
#19077127