Finite Group Databasebeta

← C127×#13076 #44576749

Subgroups — C127×#13076 #44576749

Order 32512.

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

normal subgroups only

This group has 466 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×#2143C212yesmaximal, complemented
4C127×#1813C211yesmaximal, characteristic, complemented
5C127×#1383C212yesmaximal, complemented
6C2×#135×C127C2211yescharacteristic
7C2×#131×C127C2211yescharacteristic
8#537×C127—21no—
9#504×C127—24no—
10C2×M32×C127—22no—
11C2×M32×C127C2212yes—
12#470×C127C412yes—
13#469×C127C412yes—
14#465×C127—22no—
15C2×#108×C127C2212yes—
16C2×#106×C127C2211yescharacteristic
17#417×C127—21no—
18#413×C127—21no—
19#359×C127—24no—
20#338×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×C127—22no—
31C2×M16×C127C2×C412yes—
32C2×M16×C127D411yescharacteristic
33C22×C8×C127D412yes—
34C22×C8×C127C2311yescharacteristic
35C22⋊Q8×C127—22no—
36C22⋊Q8×C127—41no—
37#121×C127—22no—
38#121×C127—41no—
39#121×C127—42no—
40C2×C4⋊C4×C127—21no—
41M32×C127—24no—
42M32×C127—22no—
43M32×C127—22no—
44C2×C16×C127—24no—
45C2×C16×C127D414yescomplemented
46#108×C127—22no—
47#108×C127—22no—
48#106×C127—21no—
49#106×C127C2×C412yes—
50#103×C127—22no—
51#102×C127—22no—
52#101×C127—41no—
53#100×C127—41no—
54#41×C127—22no—
55#41×C127—22no—
56#41×C127—42no—
57#41×C127—42no—
58C2×Q8×C127—21no—
59C2×Q8×C127D811yescharacteristic
60C2×D4×C127—21no—
61C2×D4×C127—41no—
62C2×D4×C127—42no—
63C2×D4×C127D811yescharacteristic
64C2×D4×C127SD1612yes—
65C22×C4×C127—41no—
66C22×C4×C127—41no—
67C22×C4×C127C22⋊C412yes—
68C22×C4×C127C2×D411yescharacteristic
69Q16×C127—22no—
70SD16×C127—41no—
71SD16×C127—41no—
72D8×C127—22no—
73M16×C127—22no—
74M16×C127—24no—
75M16×C127—42no—
76M16×C127—42no—
77C2×C8×C127—22no—
78C2×C8×C127—22no—
79C2×C8×C127—42no—
80C2×C8×C127C22⋊C412yes—
81C2×C8×C127C22×C411yescharacteristic
82C2×C8×C127C2×D412yes—
83C2×C8×C127C2×D411yescharacteristic
84C2×C8×C127#4112yes—
85C4⋊C4×C127—22no—
86C4⋊C4×C127—42no—
87C4⋊C4×C127—41no—
88C22⋊C4×C127—42no—
89C22⋊C4×C127—42no—
90C16×C127—24no—
91C23×C127—41no—
92C23×C127#10212yes—
93C23×C127C2×SD1611yescharacteristic
94Q8×C127—22no—
95Q8×C127—41no—
96Q8×C127—41no—
97D4×C127—24no—
98D4×C127—22no—
99D4×C127—41no—
100D4×C127—41no—
101D4×C127—82no—
102D4×C127—162no—
103C2×C4×C127—22no—
104C2×C4×C127—22no—
105C2×C4×C127—42no—
106C2×C4×C127—41no—
107C2×C4×C127—82no—
108C2×C4×C127—161no—
109C2×C4×C127#10212yes—
110C2×C4×C127C2×C22⋊C411yescharacteristic
111C2×C4×C127#12112yes—
112C2×C4×C127C2×D811yescharacteristic
113C2×C4×C127#13512yes—
114C8×C127—22no—
115C8×C127—82no—
116C8×C127C4×D412yes—
117C8×C127#12011yescharacteristic
118C8×C127#12311yescharacteristic
119C22×C127—22no—
120C22×C127—41no—
121C22×C127—42no—
122C22×C127—81no—
123C22×C127—81no—
124C22×C127—81no—
125C22×C127C2×#10211yescharacteristic
126C22×C127#46512yes—
127C4×C127—22no—
128C4×C127—82no—
129C4×C127—81no—
130C4×C127#38611yescharacteristic
131C4×C127#41611yescharacteristic
132C4×C127#46612yes—
133#13076C12711yesmaximal, 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#2143C2×C12712yescomplemented
142#1813C2×C12711yescharacteristic, complemented
143#1383C2×C12712yescomplemented
144C127#1307611yescharacteristic, direct product factor, Sylow
145C2×#135C22×C12711yescharacteristic
146C2×#131C22×C12711yescharacteristic
147#537—21no—
148#504—24no—
149C2×M32—22no—
150C2×M32C22×C12712yes—
151#470C4×C12712yes—
152#469C4×C12712yes—
153#465—22no—
154C2×#108C22×C12712yes—
155C2×#106C22×C12711yescharacteristic
156#417—21no—
157#413—21no—
158#359—24no—
159#338—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×M16—22no—
170C2×M16C2×C4×C12712yes—
171C2×M16D4×C12711yescharacteristic
172C22×C8D4×C12712yes—
173C22×C8C23×C12711yescharacteristic
174C22⋊Q8—22no—
175C22⋊Q8—41no—
176#121—22no—
177#121—41no—
178#121—42no—
179C2×C4⋊C4—21no—
180M32—24no—
181M32—22no—
182M32—22no—
183C2×C16—24no—
184C2×C16D4×C12714yescomplemented
185#108—22no—
186#108—22no—
187#106—21no—
188#106C2×C4×C12712yes—
189#103—22no—
190#102—22no—
191#101—41no—
192#100—41no—
193#41—22no—
194#41—22no—
195#41—42no—
196#41—42no—
197C2×Q8—21no—
198C2×Q8D8×C12711yescharacteristic
199C2×D4—21no—
200C2×D4—41no—
201C2×D4—42no—
202C2×D4D8×C12711yescharacteristic
203C2×D4SD16×C12712yes—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4C22⋊C4×C12712yes—
207C22×C4C2×D4×C12711yescharacteristic
208Q16—22no—
209SD16—41no—
210SD16—41no—
211D8—22no—
212M16—22no—
213M16—24no—
214M16—42no—
215M16—42no—
216C2×C8—22no—
217C2×C8—22no—
218C2×C8—42no—
219C2×C8C22⋊C4×C12712yes—
220C2×C8C22×C4×C12711yescharacteristic
221C2×C8C2×D4×C12712yes—
222C2×C8C2×D4×C12711yescharacteristic
223C2×C8#41×C12712yes—
224C4⋊C4—22no—
225C4⋊C4—42no—
226C4⋊C4—41no—
227C22⋊C4—42no—
228C22⋊C4—42no—
229C16—24no—
230C23—41no—
231C23#102×C12712yes—
232C23C2×SD16×C12711yescharacteristic
233Q8—22no—
234Q8—41no—
235Q8—41no—
236D4—24no—
237D4—22no—
238D4—41no—
239D4—41no—
240D4—82no—
241D4—162no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—42no—
245C2×C4—41no—
246C2×C4—82no—
247C2×C4—161no—
248C2×C4#102×C12712yes—
249C2×C4C2×C22⋊C4×C12711yescharacteristic
250C2×C4#121×C12712yes—
251C2×C4C2×D8×C12711yescharacteristic
252C2×C4#135×C12712yes—
253C8—22no—
254C8—82no—
255C8C4×D4×C12712yes—
256C8#120×C12711yescharacteristic
257C8#123×C12711yescharacteristic
258C22—22no—
259C22—41no—
260C22—42no—
261C22—81no—
262C22—81no—
263C22—81no—
264C22C2×#102×C12711yescharacteristic
265C22#465×C12712yes—
266C4—22no—
267C4—82no—
268C4—81no—
269C4#386×C12711yescharacteristic
270C4#416×C12711yescharacteristic
271C4#466×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×#2143C2semidirect
4. C127×#1813C2semidirect
5. C127×#1383C2semidirect
45. C2×C16×C127D4semidirect
133. #13076C127direct (N × H)
139. #3407C2×C127semidirect
141. #2143C2×C127semidirect
142. #1813C2×C127semidirect
143. #1383C2×C127semidirect
144. C127#13076direct (N × H)
184. C2×C16D4×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×#21432
C127×#18132
C127×#13832
#13076127