Finite Group Databasebeta

← C127×#8460 #44572133

Subgroups — C127×#8460 #44572133

Order 32512.

658 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 154 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×#3502C211yesmaximal, characteristic
2C127×#1985C211yesmaximal, characteristic
3C127×#1552C212yesmaximal
4C127×#1531C212yesmaximal
5C127×#1467C211yesmaximal, characteristic
6Q82×C127—22no—
7#557×C127—22no—
8#557×C127—24no—
9#544×C127—22no—
10#544×C127C412yes—
11#533×C127—22no—
12#533×C127C2212yes—
13#519×C127C412yes—
14C2×C4×Q8×C127C2211yescharacteristic
15#432×C127C2212yes—
16C2×C4⋊C8×C127C2211yescharacteristic
17C2×#97×C127C2211yescharacteristic
18#336×C127—22no—
19#332×C127—22no—
20#332×C127—22no—
21#330×C127—24no—
22#324×C127—22no—
23C22×Q8×C127C2×C411yescharacteristic
24C22×C8×C127—21no—
25C22×C8×C127—21no—
26C4⋊Q8×C127—22no—
27C4⋊Q8×C127—22no—
28C4⋊Q8×C127—28no—
29C4⋊Q8×C127—24no—
30C4⋊Q8×C127D412yes—
31C4⋊Q8×C127D412yes—
32#125×C127—24no—
33#125×C127—28no—
34#125×C127—24no—
35#125×C127D414yes—
36C22⋊Q8×C127—24no—
37C22⋊Q8×C127—22no—
38C22⋊Q8×C127—22no—
39C4×Q8×C127—24no—
40C4×Q8×C127—24no—
41C4×Q8×C127—24no—
42C4×Q8×C127—24no—
43C4×Q8×C127—22no—
44C4×Q8×C127—22no—
45C4×Q8×C127—22no—
46C4×Q8×C127—22no—
47#117×C127—24no—
48#117×C127C2×C414yes—
49C2×C4⋊C4×C127C2×C411yescharacteristic
50C2×C4⋊C4×C127D412yes—
51C2×C42×C127D412yes—
52C2×C42×C127C2311yescharacteristic
53C4⋊C8×C127—22no—
54C4⋊C8×C127—22no—
55C22⋊C8×C127—22no—
56#97×C127—22no—
57#97×C127—22no—
58C2×Q8×C127—24no—
59C2×Q8×C127—24no—
60C2×Q8×C127—22no—
61C2×Q8×C127—22no—
62C2×Q8×C127—22no—
63C22×C4×C127C22⋊C412yes—
64C22×C4×C127C22⋊C412yes—
65C22×C4×C127C22×C411yescharacteristic
66C22×C4×C127C2×D411yescharacteristic
67C22×C4×C127C2×D411yescharacteristic
68C2×C8×C127—22no—
69C2×C8×C127—41no—
70C2×C8×C127—41no—
71C2×C8×C127—42no—
72C2×C8×C127—42no—
73C2×C8×C127—41no—
74C4⋊C4×C127—24no—
75C4⋊C4×C127—24no—
76C4⋊C4×C127—24no—
77C4⋊C4×C127—28no—
78C4⋊C4×C127—22no—
79C4⋊C4×C127—24no—
80C4⋊C4×C127—24no—
81C4⋊C4×C127—22no—
82C4⋊C4×C127—22no—
83C4⋊C4×C127—24no—
84C4⋊C4×C127C22⋊C414yes—
85C4⋊C4×C127C22⋊C414yes—
86C22⋊C4×C127—24no—
87C42×C127—28no—
88C42×C127—24no—
89C42×C127—22no—
90C42×C127—22no—
91C42×C127C2×D412yes—
92C42×C127C2×D412yes—
93C23×C127C2×C22⋊C411yescharacteristic
94Q8×C127—28no—
95Q8×C127—42no—
96Q8×C127—42no—
97Q8×C127—82no—
98Q8×C127—84no—
99C2×C4×C127—22no—
100C2×C4×C127—22no—
101C2×C4×C127—22no—
102C2×C4×C127—21no—
103C2×C4×C127—21no—
104C2×C4×C127—24no—
105C2×C4×C127—24no—
106C2×C4×C127—22no—
107C2×C4×C127—41no—
108C2×C4×C127—42no—
109C2×C4×C127#10114yes—
110C2×C4×C127C2×C22⋊C412yes—
111C2×C4×C127#12011yescharacteristic
112C2×C4×C127#12012yes—
113C2×C4×C127#12011yescharacteristic
114C8×C127—42no—
115C8×C127—82no—
116C8×C127—81no—
117C22×C127—21no—
118C22×C127—21no—
119C22×C127#37911yescharacteristic
120C22×C127C2×#10112yes—
121C4×C127—21no—
122C4×C127—22no—
123C4×C127—24no—
124C4×C127—22no—
125C4×C127—44no—
126C4×C127—42no—
127C4×C127—44no—
128C4×C127#45411yescharacteristic
129C4×C127#45611yescharacteristic
130#8460C12711yesmaximal, characteristic, direct product factor, Sylow
131C2×C127—22no—
132C2×C127#178411yescharacteristic
133C2×C127#179311yescharacteristic
134C2×C127#179411yescharacteristic
135#3502C2×C12711yescharacteristic
136#1985C2×C12711yescharacteristic
137#1552C2×C12712yes—
138#1531C2×C12712yes—
139#1467C2×C12711yescharacteristic
140C127#846011yescharacteristic, direct product factor, Sylow
141Q82—22no—
142#557—22no—
143#557—24no—
144#544—22no—
145#544C4×C12712yes—
146#533—22no—
147#533C22×C12712yes—
148#519C4×C12712yes—
149C2×C4×Q8C22×C12711yescharacteristic
150#432C22×C12712yes—
151C2×C4⋊C8C22×C12711yescharacteristic
152C2×#97C22×C12711yescharacteristic
153#336—22no—
154#332—22no—
155#332—22no—
156#330—24no—
157#324—22no—
158C22×Q8C2×C4×C12711yescharacteristic
159C22×C8—21no—
160C22×C8—21no—
161C4⋊Q8—22no—
162C4⋊Q8—22no—
163C4⋊Q8—28no—
164C4⋊Q8—24no—
165C4⋊Q8D4×C12712yes—
166C4⋊Q8D4×C12712yes—
167#125—24no—
168#125—28no—
169#125—24no—
170#125D4×C12714yes—
171C22⋊Q8—24no—
172C22⋊Q8—22no—
173C22⋊Q8—22no—
174C4×Q8—24no—
175C4×Q8—24no—
176C4×Q8—24no—
177C4×Q8—24no—
178C4×Q8—22no—
179C4×Q8—22no—
180C4×Q8—22no—
181C4×Q8—22no—
182#117—24no—
183#117C2×C4×C12714yes—
184C2×C4⋊C4C2×C4×C12711yescharacteristic
185C2×C4⋊C4D4×C12712yes—
186C2×C42D4×C12712yes—
187C2×C42C23×C12711yescharacteristic
188C4⋊C8—22no—
189C4⋊C8—22no—
190C22⋊C8—22no—
191#97—22no—
192#97—22no—
193C2×Q8—24no—
194C2×Q8—24no—
195C2×Q8—22no—
196C2×Q8—22no—
197C2×Q8—22no—
198C22×C4C22⋊C4×C12712yes—
199C22×C4C22⋊C4×C12712yes—
200C22×C4C22×C4×C12711yescharacteristic
201C22×C4C2×D4×C12711yescharacteristic
202C22×C4C2×D4×C12711yescharacteristic
203C2×C8—22no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8—42no—
207C2×C8—42no—
208C2×C8—41no—
209C4⋊C4—24no—
210C4⋊C4—24no—
211C4⋊C4—24no—
212C4⋊C4—28no—
213C4⋊C4—22no—
214C4⋊C4—24no—
215C4⋊C4—24no—
216C4⋊C4—22no—
217C4⋊C4—22no—
218C4⋊C4—24no—
219C4⋊C4C22⋊C4×C12714yes—
220C4⋊C4C22⋊C4×C12714yes—
221C22⋊C4—24no—
222C42—28no—
223C42—24no—
224C42—22no—
225C42—22no—
226C42C2×D4×C12712yes—
227C42C2×D4×C12712yes—
228C23C2×C22⋊C4×C12711yescharacteristic
229Q8—28no—
230Q8—42no—
231Q8—42no—
232Q8—82no—
233Q8—84no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—24no—
240C2×C4—24no—
241C2×C4—22no—
242C2×C4—41no—
243C2×C4—42no—
244C2×C4#101×C12714yes—
245C2×C4C2×C22⋊C4×C12712yes—
246C2×C4#120×C12711yescharacteristic
247C2×C4#120×C12712yes—
248C2×C4#120×C12711yescharacteristic
249C8—42no—
250C8—82no—
251C8—81no—
252C22—21no—
253C22—21no—
254C22#379×C12711yescharacteristic
255C22C2×#101×C12712yes—
256C4—24no—
257C4—22no—
258C4—21no—
259C4—22no—
260C4—44no—
261C4—42no—
262C4—44no—
263C4#454×C12711yescharacteristic
264C4#456×C12711yescharacteristic
265C2—22no—
266C2C127×#178411yescharacteristic
267C2C127×#179311yescharacteristic
268C2C127×#179411yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC23×C127C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
130. #8460C127direct (N × H)
140. C127#8460direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#35022
C127×#19852
C127×#15522
C127×#15312
C127×#14672
#8460127