Finite Group Databasebeta

← C127×#11467 #44575140

Subgroups — C127×#11467 #44575140

Order 32512.

418 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#435×C127C211yesmaximal, characteristic
2C127×#2112C211yesmaximal, characteristic, complemented
3C2×C22⋊C16×C127C211yesmaximal, characteristic, complemented
4C127×#1322C212yesmaximal, complemented
5C127×#1314C212yesmaximal, complemented
6C22×M16×C127C411yescharacteristic
7C23×C8×C127C2211yescharacteristic
8C2×C4×D4×C127C411yescharacteristic
9C2×M32×C127—21no—
10C22×C16×C127—21no—
11#435×C127—21no—
12#435×C127—21no—
13#435×C127—21no—
14#435×C127—21no—
15C2×C4⋊C8×C127C2211yescharacteristic
16C2×C22⋊C8×C127C411yescharacteristic
17C2×C22⋊C8×C127C2211yescharacteristic
18C2×#97×C127C411yescharacteristic
19C22⋊C16×C127—21no—
20C22⋊C16×C127—21no—
21C22⋊C16×C127C2212yes—
22C22⋊C16×C127C2212yes—
23C22×D4×C127C811yescharacteristic
24C23×C4×C127C2×C411yescharacteristic
25C23×C4×C127C2×C411yescharacteristic
26C2×M16×C127—21no—
27C2×M16×C127—21no—
28C2×M16×C127—42no—
29C22×C8×C127—42no—
30C22×C8×C127C2×C411yescharacteristic
31C22×C8×C127C2×C411yescharacteristic
32C22×C8×C127C2×C411yescharacteristic
33C22×C8×C127D411yescharacteristic
34C22×C8×C127D411yescharacteristic
35C22×C8×C127D411yescharacteristic
36C22×C8×C127D411yescharacteristic
37C22×C8×C127C2311yescharacteristic
38C4×D4×C127—21no—
39C4×D4×C127—21no—
40C4×D4×C127—21no—
41C4×D4×C127—21no—
42C2×C4⋊C4×C127C811yescharacteristic
43C2×C22⋊C4×C127C811yescharacteristic
44C2×C22⋊C4×C127C811yescharacteristic
45C2×C42×C127C2×C411yescharacteristic
46M32×C127—42no—
47C2×C16×C127—22no—
48C2×C16×C127—22no—
49C2×C16×C127—42no—
50C4⋊C8×C127—21no—
51C4⋊C8×C127—21no—
52C22⋊C8×C127—21no—
53C22⋊C8×C127—21no—
54C22⋊C8×C127—21no—
55C22⋊C8×C127—21no—
56#97×C127—21no—
57#97×C127—21no—
58C24×C127C2×C811yescharacteristic
59C24×C127C2×C811yescharacteristic
60C2×D4×C127—21no—
61C2×D4×C127—21no—
62C2×D4×C127—42no—
63C22×C4×C127—21no—
64C22×C4×C127—21no—
65C22×C4×C127—41no—
66C22×C4×C127—41no—
67C22×C4×C127—41no—
68C22×C4×C127—41no—
69C22×C4×C127C22⋊C411yescharacteristic
70C22×C4×C127C22⋊C411yescharacteristic
71C22×C4×C127C2×C811yescharacteristic
72C22×C4×C127C2×C811yescharacteristic
73C22×C4×C127C2×C811yescharacteristic
74C22×C4×C127C2×C811yescharacteristic
75C22×C4×C127M1611yescharacteristic
76C22×C4×C127M1611yescharacteristic
77C22×C4×C127C22×C411yescharacteristic
78M16×C127—42no—
79M16×C127—42no—
80C2×C8×C127—22no—
81C2×C8×C127—22no—
82C2×C8×C127—22no—
83C2×C8×C127—21no—
84C2×C8×C127—21no—
85C2×C8×C127—41no—
86C2×C8×C127—41no—
87C2×C8×C127—41no—
88C2×C8×C127—41no—
89C2×C8×C127—41no—
90C2×C8×C127C22⋊C411yescharacteristic
91C2×C8×C127C22⋊C411yescharacteristic
92C2×C8×C127C2×D411yescharacteristic
93C2×C8×C127C2×D411yescharacteristic
94C4⋊C4×C127—21no—
95C4⋊C4×C127—21no—
96C22⋊C4×C127—21no—
97C22⋊C4×C127—21no—
98C22⋊C4×C127—21no—
99C22⋊C4×C127—21no—
100C42×C127—21no—
101C42×C127—21no—
102C16×C127—42no—
103C16×C127—42no—
104C23×C127—22no—
105C23×C127—22no—
106C23×C127—21no—
107C23×C127—22no—
108C23×C127—41no—
109C23×C127—41no—
110C23×C127—41no—
111C23×C127C22⋊C811yescharacteristic
112C23×C127C22⋊C811yescharacteristic
113C23×C127C22×C811yescharacteristic
114D4×C127—42no—
115D4×C127—42no—
116C2×C4×C127—21no—
117C2×C4×C127—21no—
118C2×C4×C127—21no—
119C2×C4×C127—21no—
120C2×C4×C127—21no—
121C2×C4×C127—21no—
122C2×C4×C127—21no—
123C2×C4×C127—21no—
124C2×C4×C127—21no—
125C2×C4×C127—22no—
126C2×C4×C127—41no—
127C2×C4×C127—41no—
128C2×C4×C127—41no—
129C2×C4×C127—42no—
130C2×C4×C127—41no—
131C2×C4×C127—41no—
132C2×C4×C127—41no—
133C2×C4×C127—41no—
134C2×C4×C127C22⋊C811yescharacteristic
135C2×C4×C127C22⋊C811yescharacteristic
136C2×C4×C127C2×C22⋊C411yescharacteristic
137C2×C4×C127C2×M1611yescharacteristic
138C8×C127—21no—
139C8×C127—21no—
140C8×C127—21no—
141C8×C127—41no—
142C8×C127—41no—
143C8×C127#9912yes—
144C22×C127—21no—
145C22×C127—21no—
146C22×C127—21no—
147C22×C127—21no—
148C22×C127—21no—
149C22×C127—21no—
150C22×C127—21no—
151C22×C127—44no—
152C22×C127—41no—
153C22×C127—41no—
154C22×C127—41no—
155C22×C127—82no—
156C22×C127#34912yes—
157C22×C127C2×C22⋊C811yescharacteristic
158C22×C127#50412yes—
159C4×C127—21no—
160C4×C127—21no—
161C4×C127—21no—
162C4×C127—41no—
163C4×C127—41no—
164C4×C127—41no—
165C4×C127C2×#9911yescharacteristic
166C4×C127#41311yescharacteristic
167#11467C12711yesmaximal, characteristic, direct product factor, Sylow
168C2×C127—22no—
169C2×C127—22no—
170C2×C127—41no—
171C2×C127—81no—
172C2×C127#145911yescharacteristic
173C2×C127#211311yescharacteristic
174C2×C127C2×#34911yescharacteristic
175C2×#435C2×C12711yescharacteristic
176#2112C2×C12711yescharacteristic, complemented
177C2×C22⋊C16C2×C12711yescharacteristic, complemented
178#1322C2×C12712yescomplemented
179#1314C2×C12712yescomplemented
180C127#1146711yescharacteristic, direct product factor, Sylow
181C22×M16C4×C12711yescharacteristic
182C23×C8C22×C12711yescharacteristic
183C2×C4×D4C4×C12711yescharacteristic
184C2×M32—21no—
185C22×C16—21no—
186#435—21no—
187#435—21no—
188#435—21no—
189#435—21no—
190C2×C4⋊C8C22×C12711yescharacteristic
191C2×C22⋊C8C4×C12711yescharacteristic
192C2×C22⋊C8C22×C12711yescharacteristic
193C2×#97C4×C12711yescharacteristic
194C22⋊C16—21no—
195C22⋊C16—21no—
196C22⋊C16C22×C12712yes—
197C22⋊C16C22×C12712yes—
198C22×D4C8×C12711yescharacteristic
199C23×C4C2×C4×C12711yescharacteristic
200C23×C4C2×C4×C12711yescharacteristic
201C2×M16—21no—
202C2×M16—21no—
203C2×M16—42no—
204C22×C8—42no—
205C22×C8C2×C4×C12711yescharacteristic
206C22×C8C2×C4×C12711yescharacteristic
207C22×C8C2×C4×C12711yescharacteristic
208C22×C8D4×C12711yescharacteristic
209C22×C8D4×C12711yescharacteristic
210C22×C8D4×C12711yescharacteristic
211C22×C8D4×C12711yescharacteristic
212C22×C8C23×C12711yescharacteristic
213C4×D4—21no—
214C4×D4—21no—
215C4×D4—21no—
216C4×D4—21no—
217C2×C4⋊C4C8×C12711yescharacteristic
218C2×C22⋊C4C8×C12711yescharacteristic
219C2×C22⋊C4C8×C12711yescharacteristic
220C2×C42C2×C4×C12711yescharacteristic
221M32—42no—
222C2×C16—22no—
223C2×C16—22no—
224C2×C16—42no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C22⋊C8—21no—
228C22⋊C8—21no—
229C22⋊C8—21no—
230C22⋊C8—21no—
231#97—21no—
232#97—21no—
233C24C2×C8×C12711yescharacteristic
234C24C2×C8×C12711yescharacteristic
235C2×D4—21no—
236C2×D4—21no—
237C2×D4—42no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4C22⋊C4×C12711yescharacteristic
245C22×C4C22⋊C4×C12711yescharacteristic
246C22×C4C2×C8×C12711yescharacteristic
247C22×C4C2×C8×C12711yescharacteristic
248C22×C4C2×C8×C12711yescharacteristic
249C22×C4C2×C8×C12711yescharacteristic
250C22×C4M16×C12711yescharacteristic
251C22×C4M16×C12711yescharacteristic
252C22×C4C22×C4×C12711yescharacteristic
253M16—42no—
254M16—42no—
255C2×C8—22no—
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—21no—
259C2×C8—21no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8C22⋊C4×C12711yescharacteristic
266C2×C8C22⋊C4×C12711yescharacteristic
267C2×C8C2×D4×C12711yescharacteristic
268C2×C8C2×D4×C12711yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C42—21no—
276C42—21no—
277C16—42no—
278C16—42no—
279C23—22no—
280C23—22no—
281C23—21no—
282C23—22no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23C22⋊C8×C12711yescharacteristic
287C23C22⋊C8×C12711yescharacteristic
288C23C22×C8×C12711yescharacteristic
289D4—42no—
290D4—42no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4C22⋊C8×C12711yescharacteristic
310C2×C4C22⋊C8×C12711yescharacteristic
311C2×C4C2×C22⋊C4×C12711yescharacteristic
312C2×C4C2×M16×C12711yescharacteristic
313C8—21no—
314C8—21no—
315C8—21no—
316C8—41no—
317C8—41no—
318C8#99×C12712yes—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—44no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—82no—
331C22#349×C12712yes—
332C22C2×C22⋊C8×C12711yescharacteristic
333C22#504×C12712yes—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4C2×#99×C12711yescharacteristic
341C4#413×C12711yescharacteristic
342C2—22no—
343C2—22no—
344C2—41no—
345C2—81no—
346C2C127×#145911yescharacteristic
347C2C127×#211311yescharacteristic
348C2C2×#349×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127C2×C22⋊C4
commutatorC23C22×C8×C127
Frattini, cosocleC22×C8C23×C127
socleC22×C127C2×C22⋊C8
prime radicalC22×D4×C127C8
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C23×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2112C2semidirect
3. C2×C22⋊C16×C127C2semidirect
4. C127×#1322C2semidirect
5. C127×#1314C2semidirect
167. #11467C127direct (N × H)
176. #2112C2×C127semidirect
177. C2×C22⋊C16C2×C127semidirect
178. #1322C2×C127semidirect
179. #1314C2×C127semidirect
180. C127#11467direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#435×C1272
C127×#21122
C2×C22⋊C16×C1272
C127×#13222
C127×#13142
#11467127