Finite Group Databasebeta

← C127×#13077 #44576750

Subgroups — C127×#13077 #44576750

Order 32512.

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

normal subgroups only

This group has 470 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
1C127×#3407C211yesmaximal, characteristic, complemented
2C127×#3060C211yesmaximal, characteristic
3C127×#2145C212yesmaximal, complemented
4C127×#1812C211yesmaximal, characteristic, complemented
5C127×#1386C212yesmaximal, complemented
6C2×#135×C127C2211yescharacteristic
7C2×#131×C127C2211yescharacteristic
8#537×C127—21no—
9#504×C127—24no—
10C2×M32×C127—22no—
11C2×M32×C127C2212yes—
12#470×C127C412yescomplemented
13#469×C127C412yescomplemented
14#465×C127—22no—
15#427×C127C2212yes—
16C2×#106×C127C2211yescharacteristic
17#417×C127—21no—
18#410×C127—21no—
19#360×C127—24no—
20H(3,ℤ/4)×C127—21no—
21C2×#41×C127—21no—
22C2×#41×C127D411yescharacteristic
23#135×C127—22no—
24#135×C127—22no—
25C2×Q16×C127C2×C411yescharacteristic
26C2×SD16×C127—21no—
27C2×D8×C127C2×C411yescharacteristic
28#131×C127—22no—
29#131×C127—22no—
30C2×M16×C127C2×C412yes—
31C2×M16×C127D411yescharacteristic
32C22×C8×C127D412yes—
33C22×C8×C127C2311yescharacteristic
34C22⋊Q8×C127—22no—
35C22⋊Q8×C127—41no—
36#121×C127—22no—
37#121×C127—42no—
38#121×C127—41no—
39#117×C127—22no—
40C2×C4⋊C4×C127—21no—
41M32×C127—24no—
42M32×C127—22no—
43M32×C127D414yescomplemented
44C2×C16×C127—24no—
45C2×C16×C127—22no—
46#107×C127—22no—
47#106×C127—21no—
48#106×C127—22no—
49#106×C127C2×C412yes—
50#103×C127—22no—
51#102×C127—22no—
52#99×C127—42no—
53#41×C127—22no—
54#41×C127—22no—
55#41×C127—42no—
56#41×C127—42no—
57C2×Q8×C127—21no—
58C2×Q8×C127SD1611yescharacteristic
59C2×D4×C127—21no—
60C2×D4×C127—41no—
61C2×D4×C127—42no—
62C2×D4×C127D812yes—
63C2×D4×C127SD1611yescharacteristic
64C22×C4×C127—41no—
65C22×C4×C127—41no—
66C22×C4×C127C22⋊C412yes—
67C22×C4×C127C2×D411yescharacteristic
68Q16×C127—22no—
69SD16×C127—41no—
70SD16×C127—41no—
71D8×C127—22no—
72M16×C127—22no—
73M16×C127—24no—
74C2×C8×C127—22no—
75C2×C8×C127—22no—
76C2×C8×C127C22⋊C412yes—
77C2×C8×C127C22×C411yescharacteristic
78C2×C8×C127C2×D412yes—
79C2×C8×C127C2×D411yescharacteristic
80C2×C8×C127#4112yes—
81C4⋊C4×C127—22no—
82C4⋊C4×C127—42no—
83C4⋊C4×C127—41no—
84C4⋊C4×C127—42no—
85C22⋊C4×C127—42no—
86C22⋊C4×C127—42no—
87C22⋊C4×C127—42no—
88C42×C127—42no—
89C16×C127—24no—
90C23×C127—41no—
91C23×C127#10212yes—
92C23×C127C2×D811yescharacteristic
93Q8×C127—22no—
94Q8×C127—41no—
95Q8×C127—41no—
96D4×C127—24no—
97D4×C127—22no—
98D4×C127—41no—
99D4×C127—41no—
100D4×C127—82no—
101D4×C127—162no—
102C2×C4×C127—22no—
103C2×C4×C127—22no—
104C2×C4×C127—42no—
105C2×C4×C127—41no—
106C2×C4×C127—82no—
107C2×C4×C127—82no—
108C2×C4×C127—161no—
109C2×C4×C127#10212yes—
110C2×C4×C127C2×C22⋊C411yescharacteristic
111C2×C4×C127#12112yes—
112C2×C4×C127C2×SD1611yescharacteristic
113C2×C4×C127#13512yes—
114C8×C127—22no—
115C8×C127C4×D412yes—
116C8×C127#12011yescharacteristic
117C8×C127#12311yescharacteristic
118C22×C127—22no—
119C22×C127—41no—
120C22×C127—42no—
121C22×C127—81no—
122C22×C127—81no—
123C22×C127—81no—
124C22×C127C2×#10211yescharacteristic
125C22×C127#46612yes—
126C4×C127—22no—
127C4×C127—82no—
128C4×C127—81no—
129C4×C127—162no—
130C4×C127#38611yescharacteristic
131C4×C127#41611yescharacteristic
132C4×C127#46512yes—
133#13077C12711yesmaximal, characteristic, direct product factor, Sylow
134C2×C127—21no—
135C2×C127—22no—
136C2×C127—42no—
137C2×C127—161no—
138C2×C127#189311yescharacteristic
139#3407C2×C12711yescharacteristic, complemented
140#3060C2×C12711yescharacteristic
141#2145C2×C12712yescomplemented
142#1812C2×C12711yescharacteristic, complemented
143#1386C2×C12712yescomplemented
144C127#1307711yescharacteristic, direct product factor, Sylow
145C2×#135C22×C12711yescharacteristic
146C2×#131C22×C12711yescharacteristic
147#537—21no—
148#504—24no—
149C2×M32—22no—
150C2×M32C22×C12712yes—
151#470C4×C12712yescomplemented
152#469C4×C12712yescomplemented
153#465—22no—
154#427C22×C12712yes—
155C2×#106C22×C12711yescharacteristic
156#417—21no—
157#410—21no—
158#360—24no—
159H(3,ℤ/4)—21no—
160C2×#41—21no—
161C2×#41D4×C12711yescharacteristic
162#135—22no—
163#135—22no—
164C2×Q16C2×C4×C12711yescharacteristic
165C2×SD16—21no—
166C2×D8C2×C4×C12711yescharacteristic
167#131—22no—
168#131—22no—
169C2×M16C2×C4×C12712yes—
170C2×M16D4×C12711yescharacteristic
171C22×C8D4×C12712yes—
172C22×C8C23×C12711yescharacteristic
173C22⋊Q8—22no—
174C22⋊Q8—41no—
175#121—22no—
176#121—42no—
177#121—41no—
178#117—22no—
179C2×C4⋊C4—21no—
180M32—24no—
181M32—22no—
182M32D4×C12714yescomplemented
183C2×C16—24no—
184C2×C16—22no—
185#107—22no—
186#106—21no—
187#106—22no—
188#106C2×C4×C12712yes—
189#103—22no—
190#102—22no—
191#99—42no—
192#41—22no—
193#41—22no—
194#41—42no—
195#41—42no—
196C2×Q8—21no—
197C2×Q8SD16×C12711yescharacteristic
198C2×D4—21no—
199C2×D4—41no—
200C2×D4—42no—
201C2×D4D8×C12712yes—
202C2×D4SD16×C12711yescharacteristic
203C22×C4—41no—
204C22×C4—41no—
205C22×C4C22⋊C4×C12712yes—
206C22×C4C2×D4×C12711yescharacteristic
207Q16—22no—
208SD16—41no—
209SD16—41no—
210D8—22no—
211M16—22no—
212M16—24no—
213C2×C8—22no—
214C2×C8—22no—
215C2×C8C22⋊C4×C12712yes—
216C2×C8C22×C4×C12711yescharacteristic
217C2×C8C2×D4×C12712yes—
218C2×C8C2×D4×C12711yescharacteristic
219C2×C8#41×C12712yes—
220C4⋊C4—22no—
221C4⋊C4—42no—
222C4⋊C4—41no—
223C4⋊C4—42no—
224C22⋊C4—42no—
225C22⋊C4—42no—
226C22⋊C4—42no—
227C42—42no—
228C16—24no—
229C23—41no—
230C23#102×C12712yes—
231C23C2×D8×C12711yescharacteristic
232Q8—22no—
233Q8—41no—
234Q8—41no—
235D4—24no—
236D4—22no—
237D4—41no—
238D4—41no—
239D4—82no—
240D4—162no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—82no—
246C2×C4—82no—
247C2×C4—161no—
248C2×C4#102×C12712yes—
249C2×C4C2×C22⋊C4×C12711yescharacteristic
250C2×C4#121×C12712yes—
251C2×C4C2×SD16×C12711yescharacteristic
252C2×C4#135×C12712yes—
253C8—22no—
254C8C4×D4×C12712yes—
255C8#120×C12711yescharacteristic
256C8#123×C12711yescharacteristic
257C22—22no—
258C22—41no—
259C22—42no—
260C22—81no—
261C22—81no—
262C22—81no—
263C22C2×#102×C12711yescharacteristic
264C22#466×C12712yes—
265C4—22no—
266C4—82no—
267C4—81no—
268C4—162no—
269C4#386×C12711yescharacteristic
270C4#416×C12711yescharacteristic
271C4#465×C12712yes—
272C2—21no—
273C2—22no—
274C2—42no—
275C2—161no—
276C2C127×#189311yescharacteristic
subgroupG/H
center, socleC2×C127#1893
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC127×#3060C2
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
1. C127×#3407C2semidirect
3. C127×#2145C2semidirect
4. C127×#1812C2semidirect
5. C127×#1386C2semidirect
12. #470×C127C4semidirect
13. #469×C127C4semidirect
43. M32×C127D4semidirect
133. #13077C127direct (N × H)
139. #3407C2×C127semidirect
141. #2145C2×C127semidirect
142. #1812C2×C127semidirect
143. #1386C2×C127semidirect
144. C127#13077direct (N × H)
151. #470C4×C127semidirect
152. #469C4×C127semidirect
182. M32D4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#34072
C127×#30602
C127×#21452
C127×#18122
C127×#13862
#13077127