Finite Group Databasebeta

← C127×#7035 #44570708

Subgroups — C127×#7035 #44570708

Order 32512.

844 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 844 conjugacy classes of subgroups — too many to draw. Only its 138 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×#1779C211yesmaximal, characteristic
2C127×C22⋊#95C212yesmaximal
3C24×C4×C127C2211yescharacteristic
4C22×C22⋊C4×C127—22no—
5C2×C22⋊C8×C127—22no—
6C2×C22⋊C8×C127C412yescomplemented
7C2×#95×C127—22no—
8C2×#95×C127C414yescomplemented
9C25×C127D411yescharacteristic
10C23×C4×C127—24no—
11C23×C4×C127—42no—
12C23×C4×C127—44no—
13C23×C4×C127C2×C411yescharacteristic
14C23×C4×C127C2×C412yes—
15C23×C4×C127D412yes—
16C23×C4×C127Q811yescharacteristic
17C22×C8×C127—22no—
18C2×C22⋊C4×C127—28no—
19C2×C22⋊C4×C127—44no—
20C2×C22⋊C4×C127—42no—
21C2×C22⋊C4×C127—42no—
22C22⋊C8×C127—44no—
23C22⋊C8×C127—42no—
24#95×C127—44no—
25#95×C127—44no—
26C24×C127—24no—
27C24×C127—24no—
28C24×C127—41no—
29C24×C127—41no—
30C24×C127C22⋊C412yes—
31C24×C127C4⋊C411yescharacteristic
32C24×C127D811yescharacteristic
33C24×C127SD1612yes—
34C24×C127Q1611yescharacteristic
35C22×C4×C127—24no—
36C22×C4×C127—24no—
37C22×C4×C127—24no—
38C22×C4×C127—22no—
39C22×C4×C127—28no—
40C22×C4×C127—42no—
41C22×C4×C127—42no—
42C22×C4×C127—42no—
43C22×C4×C127—42no—
44C22×C4×C127—41no—
45C22×C4×C127—42no—
46C22×C4×C127—416no—
47C22×C4×C127—44no—
48C22×C4×C127—44no—
49C22×C4×C127—44no—
50C22×C4×C127—44no—
51C22×C4×C127—44no—
52C22×C4×C127—44no—
53C22×C4×C127C4211yescharacteristic
54C22×C4×C127C22⋊C411yescharacteristic
55C22×C4×C127C4⋊C412yes—
56C2×C8×C127—44no—
57C2×C8×C127—42no—
58C22⋊C4×C127—48no—
59C22⋊C4×C127—48no—
60C23×C127—22no—
61C23×C127—22no—
62C23×C127—22no—
63C23×C127—22no—
64C23×C127—24no—
65C23×C127—24no—
66C23×C127—24no—
67C23×C127—24no—
68C23×C127—21no—
69C23×C127—22no—
70C23×C127—21no—
71C23×C127—22no—
72C23×C127—41no—
73C23×C127—42no—
74C23×C127—41no—
75C23×C127—44no—
76C23×C127—48no—
77C23×C127—44no—
78C23×C127#9511yescharacteristic
79C23×C127#9914yes—
80C23×C127#10212yes—
81C23×C127#10312yes—
82C23×C127#10414yes—
83C23×C127#10611yescharacteristic
84C23×C127#10711yescharacteristic
85C2×C4×C127—22no—
86C2×C4×C127—22no—
87C2×C4×C127—21no—
88C2×C4×C127—22no—
89C2×C4×C127—22no—
90C2×C4×C127—22no—
91C2×C4×C127—48no—
92C2×C4×C127—44no—
93C2×C4×C127—48no—
94C2×C4×C127—44no—
95C2×C4×C127—48no—
96C2×C4×C127—48no—
97C2×C4×C127—48no—
98C2×C4×C127—84no—
99C2×C4×C127—84no—
100C2×C4×C127—84no—
101C2×C4×C127—84no—
102C2×C4×C127#9912yes—
103C8×C127—82no—
104C22×C127—24no—
105C22×C127—24no—
106C22×C127—22no—
107C22×C127—22no—
108C22×C127—22no—
109C22×C127—22no—
110C22×C127—24no—
111C22×C127—24no—
112C22×C127—21no—
113C22×C127—21no—
114C22×C127—22no—
115C22×C127—22no—
116C22×C127—44no—
117C22×C127—48no—
118C22×C127—44no—
119C22×C127—42no—
120C22×C127—41no—
121C22×C127—41no—
122C22×C127#32714yes—
123C22×C127#32814yes—
124C22×C127H(3,ℤ/4)11yescharacteristic
125C22×C127#33912yes—
126C22×C127#34011yescharacteristic
127C22×C127#34212yes—
128C22×C127#34211yescharacteristic
129C4×C127—22no—
130C4×C127—41no—
131C4×C127—42no—
132C4×C127—88no—
133#7035C12711yesmaximal, characteristic, direct product factor, Sylow
134C2×C127—24no—
135C2×C127—24no—
136C2×C127—41no—
137C2×C127—41no—
138C2×C127#128412yes—
139C2×C127#128911yescharacteristic
140C2×C127#129412yes—
141C2×C127#129711yescharacteristic
142C2×C127#130411yescharacteristic
143#1779C2×C12711yescharacteristic
144C22⋊#95C2×C12712yes—
145C127#703511yescharacteristic, direct product factor, Sylow
146C24×C4C22×C12711yescharacteristic
147C22×C22⋊C4—22no—
148C2×C22⋊C8—22no—
149C2×C22⋊C8C4×C12712yescomplemented
150C2×#95—22no—
151C2×#95C4×C12714yescomplemented
152C25D4×C12711yescharacteristic
153C23×C4—24no—
154C23×C4—42no—
155C23×C4—44no—
156C23×C4C2×C4×C12711yescharacteristic
157C23×C4C2×C4×C12712yes—
158C23×C4D4×C12712yes—
159C23×C4Q8×C12711yescharacteristic
160C22×C8—22no—
161C2×C22⋊C4—28no—
162C2×C22⋊C4—44no—
163C2×C22⋊C4—42no—
164C2×C22⋊C4—42no—
165C22⋊C8—44no—
166C22⋊C8—42no—
167#95—44no—
168#95—44no—
169C24—24no—
170C24—24no—
171C24—41no—
172C24—41no—
173C24C22⋊C4×C12712yes—
174C24C4⋊C4×C12711yescharacteristic
175C24D8×C12711yescharacteristic
176C24SD16×C12712yes—
177C24Q16×C12711yescharacteristic
178C22×C4—24no—
179C22×C4—24no—
180C22×C4—24no—
181C22×C4—22no—
182C22×C4—28no—
183C22×C4—42no—
184C22×C4—42no—
185C22×C4—42no—
186C22×C4—42no—
187C22×C4—41no—
188C22×C4—42no—
189C22×C4—416no—
190C22×C4—44no—
191C22×C4—44no—
192C22×C4—44no—
193C22×C4—44no—
194C22×C4—44no—
195C22×C4—44no—
196C22×C4C42×C12711yescharacteristic
197C22×C4C22⋊C4×C12711yescharacteristic
198C22×C4C4⋊C4×C12712yes—
199C2×C8—44no—
200C2×C8—42no—
201C22⋊C4—48no—
202C22⋊C4—48no—
203C23—22no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23—24no—
208C23—24no—
209C23—24no—
210C23—24no—
211C23—21no—
212C23—22no—
213C23—21no—
214C23—22no—
215C23—41no—
216C23—42no—
217C23—41no—
218C23—44no—
219C23—44no—
220C23—48no—
221C23#95×C12711yescharacteristic
222C23#99×C12714yes—
223C23#102×C12712yes—
224C23#103×C12712yes—
225C23#104×C12714yes—
226C23#106×C12711yescharacteristic
227C23#107×C12711yescharacteristic
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—48no—
235C2×C4—44no—
236C2×C4—48no—
237C2×C4—44no—
238C2×C4—48no—
239C2×C4—48no—
240C2×C4—48no—
241C2×C4—84no—
242C2×C4—84no—
243C2×C4—84no—
244C2×C4—84no—
245C2×C4#99×C12712yes—
246C8—82no—
247C22—22no—
248C22—22no—
249C22—22no—
250C22—22no—
251C22—24no—
252C22—24no—
253C22—24no—
254C22—24no—
255C22—21no—
256C22—21no—
257C22—22no—
258C22—22no—
259C22—44no—
260C22—48no—
261C22—44no—
262C22—41no—
263C22—41no—
264C22—42no—
265C22#327×C12714yes—
266C22#328×C12714yes—
267C22H(3,ℤ/4)×C12711yescharacteristic
268C22#339×C12712yes—
269C22#340×C12711yescharacteristic
270C22#342×C12711yescharacteristic
271C22#342×C12712yes—
272C4—22no—
273C4—41no—
274C4—42no—
275C4—88no—
276C2—24no—
277C2—24no—
278C2—41no—
279C2—41no—
280C2C127×#128412yes—
281C2C127×#128911yescharacteristic
282C2C127×#129412yes—
283C2C127×#129711yescharacteristic
284C2C127×#130411yescharacteristic
subgroupG/H
center, socleC23×C127#95
commutatorC22×C4C42×C127
Frattini, cosocleC24×C4C22×C127
prime radicalC25×C127D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C24×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
6. C2×C22⋊C8×C127C4semidirect
8. C2×#95×C127C4semidirect
133. #7035C127direct (N × H)
145. C127#7035direct (N × H)
149. C2×C22⋊C8C4×C127semidirect
151. C2×#95C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#17792
C127×C22⋊#952
#7035127