Finite Group Databasebeta

← C127×#8492 #44572165

Subgroups — C127×#8492 #44572165

Order 32512.

692 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 142 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×#3550C211yesmaximal, characteristic
2C127×#1963C211yesmaximal, characteristic
3C127×#1559C212yesmaximal, complemented
4C127×#1536C211yesmaximal, characteristic
5C127×#1506C212yesmaximal, complemented
6#563×C127—22no—
7#559×C127C412yescomplemented
8Q82×C127C412yescomplemented
9#556×C127—22no—
10D4×Q8×C127—22no—
11#542×C127—24no—
12#536×C127—22no—
13#533×C127C2212yes—
14#532×C127C2211yescharacteristic
15#432×C127C2212yes—
16#423×C127C2211yescharacteristic
17C2×#104×C127—22no—
18#376×C127C2211yescharacteristic
19#333×C127—22no—
20#332×C127—22no—
21#329×C127—22no—
22#328×C127—24no—
23C2×#41×C127D412yes—
24C22×Q8×C127—22no—
25C2×M16×C127—21no—
26C4⋊Q8×C127—24no—
27C4⋊Q8×C127—24no—
28C4⋊Q8×C127C2×C411yescharacteristic
29C4⋊Q8×C127D412yes—
30C4⋊Q8×C127D412yes—
31#127×C127C2×C411yescharacteristic
32#126×C127—28no—
33#125×C127—22no—
34#124×C127—24no—
35#124×C127—24no—
36#124×C127D412yes—
37#123×C127—24no—
38#123×C127—24no—
39C22⋊Q8×C127—24no—
40C22⋊Q8×C127—28no—
41C22⋊Q8×C127—22no—
42C22⋊Q8×C127D414yes—
43#121×C127—22no—
44C4×Q8×C127—24no—
45C4×Q8×C127—22no—
46C4×Q8×C127C2×C414yes—
47C4×D4×C127—24no—
48C4×D4×C127—22no—
49#117×C127—22no—
50#117×C127—22no—
51C2×C42×C127—21no—
52C2×C42×C127C2311yescharacteristic
53C4⋊C8×C127—22no—
54C4⋊C8×C127—22no—
55#104×C127—44no—
56C22⋊C8×C127—22no—
57#97×C127—22no—
58#95×C127—22no—
59#41×C127—42no—
60#41×C127—42no—
61C2×Q8×C127—24no—
62C2×Q8×C127—22no—
63C2×Q8×C127—82no—
64C2×Q8×C127—82no—
65C2×Q8×C127C22⋊C414yes—
66C2×Q8×C127C22⋊C412yes—
67C2×D4×C127—22no—
68C2×D4×C127—22no—
69C2×D4×C127C22⋊C412yes—
70C22×C4×C127—24no—
71C22×C4×C127—22no—
72C22×C4×C127—41no—
73C22×C4×C127C2×D411yescharacteristic
74C22×C4×C127C2×D412yes—
75M16×C127—42no—
76C2×C8×C127—42no—
77C2×C8×C127—41no—
78C4⋊C4×C127—28no—
79C4⋊C4×C127—22no—
80C4⋊C4×C127—24no—
81C4⋊C4×C127—22no—
82C4⋊C4×C127—22no—
83C4⋊C4×C127—22no—
84C4⋊C4×C127—24no—
85C4⋊C4×C127C22⋊C414yes—
86C22⋊C4×C127—24no—
87C22⋊C4×C127—28no—
88C22⋊C4×C127—24no—
89C22⋊C4×C127—24no—
90C42×C127—24no—
91C42×C127—24no—
92C42×C127—22no—
93C42×C127—41no—
94C42×C127C22×C411yescharacteristic
95C42×C127C2×D411yescharacteristic
96C42×C127C2×D412yes—
97C23×C127—22no—
98C23×C127#12011yescharacteristic
99Q8×C127—44no—
100Q8×C127—42no—
101Q8×C127—42no—
102Q8×C127—42no—
103Q8×C127—84no—
104D4×C127—42no—
105D4×C127—44no—
106D4×C127—82no—
107C2×C4×C127—21no—
108C2×C4×C127—21no—
109C2×C4×C127—24no—
110C2×C4×C127—22no—
111C2×C4×C127—24no—
112C2×C4×C127—42no—
113C2×C4×C127—42no—
114C2×C4×C127—42no—
115C2×C4×C127—42no—
116C2×C4×C127—84no—
117C2×C4×C127—82no—
118C2×C4×C127C2×C22⋊C412yes—
119C2×C4×C127C2×C22⋊C411yescharacteristic
120C2×C4×C127#12012yes—
121C2×C4×C127#12011yescharacteristic
122C8×C127—82no—
123C8×C127—81no—
124C22×C127—21no—
125C22×C127—22no—
126C22×C127—42no—
127C22×C127—44no—
128C22×C127#37911yescharacteristic
129C4×C127—21no—
130C4×C127—22no—
131C4×C127—22no—
132C4×C127—42no—
133C4×C127—44no—
134C4×C127—44no—
135C4×C127—82no—
136C4×C127#45311yescharacteristic
137C4×C127#45511yescharacteristic
138#8492C12711yesmaximal, characteristic, direct product factor, Sylow
139C2×C127—41no—
140C2×C127—82no—
141C2×C127#179211yescharacteristic
142C2×C127#179612yes—
143#3550C2×C12711yescharacteristic
144#1963C2×C12711yescharacteristic
145#1559C2×C12712yescomplemented
146#1536C2×C12711yescharacteristic
147#1506C2×C12712yescomplemented
148C127#849211yescharacteristic, direct product factor, Sylow
149#563—22no—
150#559C4×C12712yescomplemented
151Q82C4×C12712yescomplemented
152#556—22no—
153D4×Q8—22no—
154#542—24no—
155#536—22no—
156#533C22×C12712yes—
157#532C22×C12711yescharacteristic
158#432C22×C12712yes—
159#423C22×C12711yescharacteristic
160C2×#104—22no—
161#376C22×C12711yescharacteristic
162#333—22no—
163#332—22no—
164#329—22no—
165#328—24no—
166C2×#41D4×C12712yes—
167C22×Q8—22no—
168C2×M16—21no—
169C4⋊Q8—24no—
170C4⋊Q8—24no—
171C4⋊Q8C2×C4×C12711yescharacteristic
172C4⋊Q8D4×C12712yes—
173C4⋊Q8D4×C12712yes—
174#127C2×C4×C12711yescharacteristic
175#126—28no—
176#125—22no—
177#124—24no—
178#124—24no—
179#124D4×C12712yes—
180#123—24no—
181#123—24no—
182C22⋊Q8—24no—
183C22⋊Q8—28no—
184C22⋊Q8—22no—
185C22⋊Q8D4×C12714yes—
186#121—22no—
187C4×Q8—24no—
188C4×Q8—22no—
189C4×Q8C2×C4×C12714yes—
190C4×D4—24no—
191C4×D4—22no—
192#117—22no—
193#117—22no—
194C2×C42—21no—
195C2×C42C23×C12711yescharacteristic
196C4⋊C8—22no—
197C4⋊C8—22no—
198#104—44no—
199C22⋊C8—22no—
200#97—22no—
201#95—22no—
202#41—42no—
203#41—42no—
204C2×Q8—24no—
205C2×Q8—22no—
206C2×Q8—82no—
207C2×Q8—82no—
208C2×Q8C22⋊C4×C12714yes—
209C2×Q8C22⋊C4×C12712yes—
210C2×D4—22no—
211C2×D4—22no—
212C2×D4C22⋊C4×C12712yes—
213C22×C4—24no—
214C22×C4—22no—
215C22×C4—41no—
216C22×C4C2×D4×C12711yescharacteristic
217C22×C4C2×D4×C12712yes—
218M16—42no—
219C2×C8—42no—
220C2×C8—41no—
221C4⋊C4—28no—
222C4⋊C4—22no—
223C4⋊C4—24no—
224C4⋊C4—22no—
225C4⋊C4—22no—
226C4⋊C4—22no—
227C4⋊C4—24no—
228C4⋊C4C22⋊C4×C12714yes—
229C22⋊C4—24no—
230C22⋊C4—28no—
231C22⋊C4—24no—
232C22⋊C4—24no—
233C42—24no—
234C42—24no—
235C42—22no—
236C42—41no—
237C42C22×C4×C12711yescharacteristic
238C42C2×D4×C12711yescharacteristic
239C42C2×D4×C12712yes—
240C23—22no—
241C23#120×C12711yescharacteristic
242Q8—42no—
243Q8—44no—
244Q8—42no—
245Q8—42no—
246Q8—84no—
247D4—42no—
248D4—44no—
249D4—82no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—24no—
253C2×C4—22no—
254C2×C4—24no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—84no—
260C2×C4—82no—
261C2×C4C2×C22⋊C4×C12712yes—
262C2×C4C2×C22⋊C4×C12711yescharacteristic
263C2×C4#120×C12712yes—
264C2×C4#120×C12711yescharacteristic
265C8—82no—
266C8—81no—
267C22—21no—
268C22—22no—
269C22—42no—
270C22—44no—
271C22#379×C12711yescharacteristic
272C4—21no—
273C4—22no—
274C4—22no—
275C4—42no—
276C4—44no—
277C4—44no—
278C4—82no—
279C4#453×C12711yescharacteristic
280C4#455×C12711yescharacteristic
281C2—41no—
282C2—82no—
283C2C127×#179211yescharacteristic
284C2C127×#179612yes—
subgroupG/H
center, socleC22×C127#379
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radical#532×C127C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1559C2semidirect
5. C127×#1506C2semidirect
7. #559×C127C4semidirect
8. Q82×C127C4semidirect
138. #8492C127direct (N × H)
145. #1559C2×C127semidirect
147. #1506C2×C127semidirect
148. C127#8492direct (N × H)
150. #559C4×C127semidirect
151. Q82C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35502
C127×#19632
C127×#15592
C127×#15362
C127×#15062
#8492127