Finite Group Databasebeta

← C127×#13325 #44576998

Subgroups — C127×#13325 #44576998

Order 32512.

698 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 146 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
1C22×D16×C127C212yesmaximal, complemented
2C2×#493×C127C211yesmaximal, characteristic, complemented
3C2×#357×C127C212yesmaximal, complemented
4C127×#1970C211yesmaximal, characteristic, complemented
5C127×#1374C211yesmaximal, characteristic, complemented
6C22×D8×C127—21no—
7C22×D8×C127C2212yes—
8C22×D8×C127C2211yescharacteristic
9C2×#127×C127—21no—
10C2×D16×C127—24no—
11C2×D16×C127—24no—
12C2×D16×C127—24no—
13C22×C16×C127C2212yes—
14#493×C127—24no—
15C2×#107×C127C2211yescharacteristic
16C2×#102×C127—21no—
17C2×C4×C8×C127C2211yescharacteristic
18#390×C127—21no—
19#357×C127—24no—
20C22×D4×C127—22no—
21C22×D4×C127—21no—
22C22×D4×C127—42no—
23C2×D8×C127—24no—
24C2×D8×C127—22no—
25C2×D8×C127—22no—
26C2×D8×C127—22no—
27C2×D8×C127—22no—
28C2×D8×C127—22no—
29C2×D8×C127—22no—
30C2×D8×C127—22no—
31C2×D8×C127—21no—
32C2×D8×C127—42no—
33C2×D8×C127—42no—
34C2×D8×C127D414yes—
35C2×D8×C127D412yescomplemented
36C22×C8×C127D411yescharacteristic
37C22×C8×C127C2311yescharacteristic
38#127×C127—24no—
39#127×C127—42no—
40C2×C4⋊C4×C127—21no—
41C2×C22⋊C4×C127—42no—
42C2×C42×C127D411yescharacteristic
43D16×C127—216no—
44C2×C16×C127—22no—
45C2×C16×C127—22no—
46C2×C16×C127D414yescomplemented
47#107×C127—22no—
48#102×C127—42no—
49C4×C8×C127—22no—
50C24×C127—41no—
51C24×C127—42no—
52C2×D4×C127—24no—
53C2×D4×C127—22no—
54C2×D4×C127—48no—
55C2×D4×C127—41no—
56C2×D4×C127—42no—
57C2×D4×C127—41no—
58C2×D4×C127—42no—
59C2×D4×C127—41no—
60C2×D4×C127—42no—
61C2×D4×C127—42no—
62C2×D4×C127—41no—
63C2×D4×C127—42no—
64C2×D4×C127—41no—
65C2×D4×C127—84no—
66C2×D4×C127—84no—
67C22×C4×C127—41no—
68C22×C4×C127D812yes—
69C22×C4×C127C2×D411yescharacteristic
70D8×C127—24no—
71D8×C127—24no—
72D8×C127—24no—
73D8×C127—48no—
74D8×C127—42no—
75D8×C127—42no—
76D8×C127—42no—
77C2×C8×C127—21no—
78C2×C8×C127—21no—
79C2×C8×C127D812yes—
80C2×C8×C127C2×D411yescharacteristic
81C2×C8×C127C2×D412yes—
82C2×C8×C127C2×D412yes—
83C2×C8×C127#4111yescharacteristic
84C4⋊C4×C127—41no—
85C4⋊C4×C127—41no—
86C22⋊C4×C127—84no—
87C42×C127—21no—
88C42×C127—21no—
89C16×C127—24no—
90C23×C127—44no—
91C23×C127—42no—
92C23×C127—81no—
93C23×C127—82no—
94C23×C127—81no—
95C23×C127—82no—
96C23×C127—82no—
97C23×C127—84no—
98C23×C127—84no—
99C23×C127—82no—
100C23×C127C2×D811yescharacteristic
101D4×C127—44no—
102D4×C127—42no—
103D4×C127—44no—
104D4×C127—42no—
105D4×C127—816no—
106D4×C127—81no—
107D4×C127—82no—
108D4×C127—82no—
109D4×C127—81no—
110C2×C4×C127—22no—
111C2×C4×C127—22no—
112C2×C4×C127—81no—
113C2×C4×C127—82no—
114C2×C4×C127D1614yescomplemented
115C2×C4×C127#12011yescharacteristic
116C2×C4×C127#12111yescharacteristic
117C2×C4×C127#12711yescharacteristic
118C2×C4×C127C2×D811yescharacteristic
119C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
121C8×C127—22no—
122C8×C127#12012yes—
123C8×C127#12112yes—
124C22×C127—88no—
125C22×C127—84no—
126C22×C127—84no—
127C22×C127—82no—
128C22×C127—162no—
129C22×C127—164no—
130C22×C127—161no—
131C22×C127—162no—
132C22×C127—162no—
133C22×C127—161no—
134C22×C127#44711yescharacteristic
135C22×C127#45911yescharacteristic
136C22×C127#49311yescharacteristic
137C22×C127C2×D1612yes—
138C22×C127#50912yes—
139C4×C127—24no—
140C4×C127—161no—
141C4×C127#39211yescharacteristic
142C4×C127#44711yescharacteristic
143C4×C127#45911yescharacteristic
144C4×C127#49611yescharacteristic
145#13325C12711yesmaximal, characteristic, direct product factor, Sylow
146C2×C127—164no—
147C2×C127—162no—
148C2×C127#201111yescharacteristic
149C2×C127#218412yes—
150C2×C127#220612yes—
151C2×C127#224611yescharacteristic
152C2×C127#225011yescharacteristic
153C22×D16C2×C12712yescomplemented
154C2×#493C2×C12711yescharacteristic, complemented
155C2×#357C2×C12712yescomplemented
156#1970C2×C12711yescharacteristic, complemented
157#1374C2×C12711yescharacteristic, complemented
158C127#1332511yescharacteristic, direct product factor, Sylow
159C22×D8—21no—
160C22×D8C22×C12712yes—
161C22×D8C22×C12711yescharacteristic
162C2×#127—21no—
163C2×D16—24no—
164C2×D16—24no—
165C2×D16—24no—
166C22×C16C22×C12712yes—
167#493—24no—
168C2×#107C22×C12711yescharacteristic
169C2×#102—21no—
170C2×C4×C8C22×C12711yescharacteristic
171#390—21no—
172#357—24no—
173C22×D4—22no—
174C22×D4—21no—
175C22×D4—42no—
176C2×D8—24no—
177C2×D8—22no—
178C2×D8—22no—
179C2×D8—22no—
180C2×D8—22no—
181C2×D8—22no—
182C2×D8—22no—
183C2×D8—22no—
184C2×D8—21no—
185C2×D8—42no—
186C2×D8—42no—
187C2×D8D4×C12714yes—
188C2×D8D4×C12712yescomplemented
189C22×C8D4×C12711yescharacteristic
190C22×C8C23×C12711yescharacteristic
191#127—24no—
192#127—42no—
193C2×C4⋊C4—21no—
194C2×C22⋊C4—42no—
195C2×C42D4×C12711yescharacteristic
196D16—216no—
197C2×C16—22no—
198C2×C16—22no—
199C2×C16D4×C12714yescomplemented
200#107—22no—
201#102—42no—
202C4×C8—22no—
203C24—41no—
204C24—42no—
205C2×D4—24no—
206C2×D4—22no—
207C2×D4—48no—
208C2×D4—41no—
209C2×D4—42no—
210C2×D4—42no—
211C2×D4—41no—
212C2×D4—41no—
213C2×D4—42no—
214C2×D4—42no—
215C2×D4—41no—
216C2×D4—42no—
217C2×D4—41no—
218C2×D4—84no—
219C2×D4—84no—
220C22×C4—41no—
221C22×C4D8×C12712yes—
222C22×C4C2×D4×C12711yescharacteristic
223D8—24no—
224D8—24no—
225D8—24no—
226D8—48no—
227D8—42no—
228D8—42no—
229D8—42no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8D8×C12712yes—
233C2×C8C2×D4×C12711yescharacteristic
234C2×C8C2×D4×C12712yes—
235C2×C8C2×D4×C12712yes—
236C2×C8#41×C12711yescharacteristic
237C4⋊C4—41no—
238C4⋊C4—41no—
239C22⋊C4—84no—
240C42—21no—
241C42—21no—
242C16—24no—
243C23—44no—
244C23—42no—
245C23—82no—
246C23—84no—
247C23—84no—
248C23—82no—
249C23—81no—
250C23—82no—
251C23—81no—
252C23—82no—
253C23C2×D8×C12711yescharacteristic
254D4—44no—
255D4—42no—
256D4—44no—
257D4—42no—
258D4—816no—
259D4—82no—
260D4—81no—
261D4—81no—
262D4—82no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—82no—
266C2×C4—81no—
267C2×C4D16×C12714yescomplemented
268C2×C4#120×C12711yescharacteristic
269C2×C4#121×C12711yescharacteristic
270C2×C4#127×C12711yescharacteristic
271C2×C4C2×D8×C12711yescharacteristic
272C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
273C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
274C8—22no—
275C8#120×C12712yes—
276C8#121×C12712yes—
277C22—88no—
278C22—84no—
279C22—84no—
280C22—82no—
281C22—162no—
282C22—164no—
283C22—161no—
284C22—162no—
285C22—162no—
286C22—161no—
287C22#447×C12711yescharacteristic
288C22#459×C12711yescharacteristic
289C22#493×C12711yescharacteristic
290C22C2×D16×C12712yes—
291C22#509×C12712yes—
292C4—24no—
293C4—161no—
294C4#392×C12711yescharacteristic
295C4#447×C12711yescharacteristic
296C4#459×C12711yescharacteristic
297C4#496×C12711yescharacteristic
298C2—164no—
299C2—162no—
300C2C127×#201111yescharacteristic
301C2C127×#218412yes—
302C2C127×#220612yes—
303C2C127×#224611yescharacteristic
304C2C127×#225011yescharacteristic
subgroupG/H
center, socleC23×C127C2×D8
commutator, Frattini, cosocleC22×C8C23×C127
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×D16×C127C2semidirect
2. C2×#493×C127C2semidirect
3. C2×#357×C127C2semidirect
4. C127×#1970C2semidirect
5. C127×#1374C2semidirect
35. C2×D8×C127D4semidirect
46. C2×C16×C127D4semidirect
114. C2×C4×C127D16semidirect
145. #13325C127direct (N × H)
153. C22×D16C2×C127semidirect
154. C2×#493C2×C127semidirect
155. C2×#357C2×C127semidirect
156. #1970C2×C127semidirect
157. #1374C2×C127semidirect
158. C127#13325direct (N × H)
188. C2×D8D4×C127semidirect
199. C2×C16D4×C127semidirect
267. C2×C4D16×C127semidirect

Maximal subgroups

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

subgroupindex
C22×D16×C1272
C2×#493×C1272
C2×#357×C1272
C127×#19702
C127×#13742
#13325127