Finite Group Databasebeta

← C127×#12633 #44576306

Subgroups — C127×#12633 #44576306

Order 32512.

460 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2931C211yesmaximal, characteristic
2C127×#2132C211yesmaximal, characteristic
3C127×#2126C211yesmaximal, characteristic
4C127×#1757C212yesmaximal, complemented
5C127×#1395C212yesmaximal, complemented
6C2×#131×C127C411yescharacteristic, complemented
7C2×#131×C127C2211yescharacteristic
8#532×C127C2211yescharacteristic
9#436×C127—22no—
10C8×D4×C127—22no—
11#423×C127C411yescharacteristic, complemented
12#413×C127C2212yes—
13#410×C127C2212yes—
14#408×C127C411yescharacteristic, complemented
15#408×C127C2211yescharacteristic
16#405×C127—22no—
17C2×C4×C8×C127C411yescharacteristic, complemented
18#356×C127C412yescomplemented
19#355×C127C412yescomplemented
20#354×C127C412yes—
21#353×C127C412yes—
22#344×C127—22no—
23C2×#41×C127C2×C411yescharacteristic
24C2×#41×C127C2311yescharacteristic
25#131×C127—41no—
26#131×C127—41no—
27#131×C127—41no—
28#131×C127—41no—
29C2×M16×C127—21no—
30C2×M16×C127—22no—
31C2×M16×C127C2×C411yescharacteristic
32C2×M16×C127C2×C411yescharacteristic
33C2×M16×C127D412yes—
34C22×C8×C127—21no—
35C22×C8×C127C2×C411yescharacteristic
36C22×C8×C127C2×C411yescharacteristic
37C22×C8×C127D412yes—
38C4⋊Q8×C127C2×C411yescharacteristic
39#127×C127C2×C411yescharacteristic
40#124×C127C2×C411yescharacteristic
41#124×C127C2×C411yescharacteristic
42#121×C127—22no—
43C4×D4×C127—22no—
44#117×C127—22no—
45C2×C42×C127C2×C411yescharacteristic
46C4⋊C8×C127—22no—
47#101×C127C2×C414yes—
48#100×C127—22no—
49#99×C127—22no—
50#99×C127C2×C414yes—
51C22⋊C8×C127—22no—
52C22⋊C8×C127—22no—
53#97×C127—42no—
54C4×C8×C127—21no—
55C4×C8×C127—21no—
56C4×C8×C127—42no—
57#41×C127—41no—
58#41×C127—41no—
59#41×C127—41no—
60#41×C127—41no—
61C2×Q8×C127C4211yescharacteristic
62C2×Q8×C127C22×C411yescharacteristic
63C2×D4×C127—21no—
64C2×D4×C127—22no—
65C2×D4×C127C4211yescharacteristic
66C2×D4×C127C22×C411yescharacteristic
67C2×D4×C127#4112yes—
68C22×C4×C127—21no—
69C22×C4×C127—21no—
70C22×C4×C127C22×C411yescharacteristic
71C22×C4×C127C2×D412yes—
72M16×C127—24no—
73M16×C127—41no—
74M16×C127—42no—
75M16×C127—42no—
76M16×C127—42no—
77M16×C127—41no—
78C2×C8×C127—22no—
79C2×C8×C127—21no—
80C2×C8×C127—22no—
81C2×C8×C127—21no—
82C2×C8×C127—21no—
83C2×C8×C127—21no—
84C2×C8×C127—42no—
85C2×C8×C127—41no—
86C2×C8×C127—41no—
87C2×C8×C127—41no—
88C2×C8×C127C22⋊C411yescharacteristic
89C2×C8×C127C22⋊C412yes—
90C2×C8×C127C22⋊C411yescharacteristic
91C4⋊C4×C127—22no—
92C4⋊C4×C127—42no—
93C22⋊C4×C127—22no—
94C22⋊C4×C127—22no—
95C22⋊C4×C127—24no—
96C42×C127—21no—
97C42×C127—42no—
98C42×C127C4211yescharacteristic
99C42×C127C4211yescharacteristic
100C23×C127—21no—
101C23×C127#11711yescharacteristic
102C23×C127C4×D412yes—
103Q8×C127—41no—
104Q8×C127—41no—
105D4×C127—41no—
106D4×C127—42no—
107D4×C127—41no—
108D4×C127—44no—
109D4×C127—42no—
110C2×C4×C127—21no—
111C2×C4×C127—22no—
112C2×C4×C127—21no—
113C2×C4×C127—22no—
114C2×C4×C127—21no—
115C2×C4×C127—21no—
116C2×C4×C127—21no—
117C2×C4×C127—42no—
118C2×C4×C127—41no—
119C2×C4×C127—41no—
120C2×C4×C127—44no—
121C2×C4×C127C2×C4211yescharacteristic
122C2×C4×C127C2×C22⋊C411yescharacteristic
123C2×C4×C127C4×D412yes—
124C8×C127—22no—
125C8×C127—21no—
126C8×C127—44no—
127C8×C127—41no—
128C8×C127—41no—
129C8×C127#9911yescharacteristic
130C8×C127#9911yescharacteristic
131C22×C127—22no—
132C22×C127—21no—
133C22×C127—41no—
134C22×C127—42no—
135C22×C127—42no—
136C22×C127—41no—
137C22×C127C4×C22⋊C411yescharacteristic
138C4×C127—22no—
139C4×C127—22no—
140C4×C127—21no—
141C4×C127—41no—
142C4×C127—41no—
143C4×C127—84no—
144C4×C127C2×#9911yescharacteristic
145C4×C127#41011yescharacteristic
146#12633C12711yesmaximal, characteristic, direct product factor, Sylow
147C2×C127—21no—
148C2×C127—42no—
149C2×C127—41no—
150C2×C127—81no—
151C2×C127C4×#9911yescharacteristic
152#2931C2×C12711yescharacteristic
153#2132C2×C12711yescharacteristic
154#2126C2×C12711yescharacteristic
155#1757C2×C12712yescomplemented
156#1395C2×C12712yescomplemented
157C127#1263311yescharacteristic, direct product factor, Sylow
158C2×#131C4×C12711yescharacteristic, complemented
159C2×#131C22×C12711yescharacteristic
160#532C22×C12711yescharacteristic
161#436—22no—
162C8×D4—22no—
163#423C4×C12711yescharacteristic, complemented
164#413C22×C12712yes—
165#410C22×C12712yes—
166#408C4×C12711yescharacteristic, complemented
167#408C22×C12711yescharacteristic
168#405—22no—
169C2×C4×C8C4×C12711yescharacteristic, complemented
170#356C4×C12712yescomplemented
171#355C4×C12712yescomplemented
172#354C4×C12712yes—
173#353C4×C12712yes—
174#344—22no—
175C2×#41C2×C4×C12711yescharacteristic
176C2×#41C23×C12711yescharacteristic
177#131—41no—
178#131—41no—
179#131—41no—
180#131—41no—
181C2×M16—21no—
182C2×M16—22no—
183C2×M16C2×C4×C12711yescharacteristic
184C2×M16C2×C4×C12711yescharacteristic
185C2×M16D4×C12712yes—
186C22×C8—21no—
187C22×C8C2×C4×C12711yescharacteristic
188C22×C8C2×C4×C12711yescharacteristic
189C22×C8D4×C12712yes—
190C4⋊Q8C2×C4×C12711yescharacteristic
191#127C2×C4×C12711yescharacteristic
192#124C2×C4×C12711yescharacteristic
193#124C2×C4×C12711yescharacteristic
194#121—22no—
195C4×D4—22no—
196#117—22no—
197C2×C42C2×C4×C12711yescharacteristic
198C4⋊C8—22no—
199#101C2×C4×C12714yes—
200#100—22no—
201#99—22no—
202#99C2×C4×C12714yes—
203C22⋊C8—22no—
204C22⋊C8—22no—
205#97—42no—
206C4×C8—21no—
207C4×C8—21no—
208C4×C8—42no—
209#41—41no—
210#41—41no—
211#41—41no—
212#41—41no—
213C2×Q8C42×C12711yescharacteristic
214C2×Q8C22×C4×C12711yescharacteristic
215C2×D4—21no—
216C2×D4—22no—
217C2×D4C42×C12711yescharacteristic
218C2×D4C22×C4×C12711yescharacteristic
219C2×D4#41×C12712yes—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4C22×C4×C12711yescharacteristic
223C22×C4C2×D4×C12712yes—
224M16—24no—
225M16—41no—
226M16—42no—
227M16—42no—
228M16—42no—
229M16—41no—
230C2×C8—22no—
231C2×C8—22no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—42no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8C22⋊C4×C12711yescharacteristic
241C2×C8C22⋊C4×C12712yes—
242C2×C8C22⋊C4×C12711yescharacteristic
243C4⋊C4—22no—
244C4⋊C4—42no—
245C22⋊C4—22no—
246C22⋊C4—22no—
247C22⋊C4—24no—
248C42—21no—
249C42—42no—
250C42C42×C12711yescharacteristic
251C42C42×C12711yescharacteristic
252C23—21no—
253C23#117×C12711yescharacteristic
254C23C4×D4×C12712yes—
255Q8—41no—
256Q8—41no—
257D4—41no—
258D4—42no—
259D4—41no—
260D4—44no—
261D4—42no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—44no—
273C2×C4C2×C42×C12711yescharacteristic
274C2×C4C2×C22⋊C4×C12711yescharacteristic
275C2×C4C4×D4×C12712yes—
276C8—21no—
277C8—22no—
278C8—44no—
279C8—41no—
280C8—41no—
281C8#99×C12711yescharacteristic
282C8#99×C12711yescharacteristic
283C22—22no—
284C22—21no—
285C22—41no—
286C22—42no—
287C22—42no—
288C22—41no—
289C22C4×C22⋊C4×C12711yescharacteristic
290C4—22no—
291C4—22no—
292C4—21no—
293C4—41no—
294C4—41no—
295C4—84no—
296C4C2×#99×C12711yescharacteristic
297C4#410×C12711yescharacteristic
298C2—21no—
299C2—42no—
300C2—41no—
301C2—81no—
302C2C4×#99×C12711yescharacteristic
subgroupG/H
centerC8×C127#99
commutatorC2×C4C2×C42×C127
Frattini, cosocleC2×#41C23×C127
socleC2×C127C4×#99
prime radical#532×C127C22
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C8×C127 ◁ C2×C8×C127 ◁ C2×#131×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1757C2semidirect
5. C127×#1395C2semidirect
6. C2×#131×C127C4semidirect
11. #423×C127C4semidirect
14. #408×C127C4semidirect
17. C2×C4×C8×C127C4semidirect
18. #356×C127C4semidirect
19. #355×C127C4semidirect
146. #12633C127direct (N × H)
155. #1757C2×C127semidirect
156. #1395C2×C127semidirect
157. C127#12633direct (N × H)
158. C2×#131C4×C127semidirect
163. #423C4×C127semidirect
166. #408C4×C127semidirect
169. C2×C4×C8C4×C127semidirect
170. #356C4×C127semidirect
171. #355C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#29312
C127×#21322
C127×#21262
C127×#17572
C127×#13952
#12633127