Finite Group Databasebeta

← C127×#11470 #44575143

Subgroups — C127×#11470 #44575143

Order 32512.

392 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2929C211yesmaximal, characteristic
2C127×#2112C211yesmaximal, characteristic, complemented
3C2×C22⋊C16×C127C211yesmaximal, characteristic, complemented
4C127×#1323C212yesmaximal, complemented
5C127×#1315C212yesmaximal, complemented
6C2×#131×C127C411yescharacteristic
7C23×C8×C127C2211yescharacteristic
8#525×C127C411yescharacteristic
9C2×M32×C127—21no—
10C22×C16×C127—21no—
11#435×C127—21no—
12#435×C127—21no—
13C8×D4×C127—21no—
14C8×D4×C127—21no—
15#424×C127C2211yescharacteristic
16#408×C127C2211yescharacteristic
17#407×C127C411yescharacteristic
18#405×C127C411yescharacteristic
19C22⋊C16×C127—21no—
20C22⋊C16×C127—21no—
21C22⋊C16×C127C2212yes—
22C22⋊C16×C127C2212yes—
23C2×#41×C127C2×C411yescharacteristic
24C23×C4×C127C2×C411yescharacteristic
25#131×C127—42no—
26C2×M16×C127—21no—
27C2×M16×C127C2×C411yescharacteristic
28C2×M16×C127C2×C411yescharacteristic
29C22×C8×C127—21no—
30C22×C8×C127—42no—
31C22×C8×C127C2×C411yescharacteristic
32C22×C8×C127D411yescharacteristic
33C22×C8×C127D411yescharacteristic
34C22×C8×C127D411yescharacteristic
35C22×C8×C127D411yescharacteristic
36C22×C8×C127C2311yescharacteristic
37#123×C127—21no—
38C22⋊Q8×C127C811yescharacteristic
39C22⋊Q8×C127C811yescharacteristic
40#121×C127C811yescharacteristic
41#121×C127C811yescharacteristic
42#120×C127—21no—
43C4×D4×C127—21no—
44C4×D4×C127—21no—
45#117×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—
57C4×C8×C127—21no—
58C24×C127M1611yescharacteristic
59#41×C127—41no—
60#41×C127—41no—
61C2×Q8×C127C2×C811yescharacteristic
62C2×D4×C127—21no—
63C2×D4×C127—21no—
64C2×D4×C127—21no—
65C2×D4×C127C2×C811yescharacteristic
66C22×C4×C127—21no—
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×C127M1611yescharacteristic
74C22×C4×C127C22×C411yescharacteristic
75M16×C127—42no—
76M16×C127—41no—
77M16×C127—41no—
78C2×C8×C127—22no—
79C2×C8×C127—22no—
80C2×C8×C127—22no—
81C2×C8×C127—21no—
82C2×C8×C127—21no—
83C2×C8×C127—41no—
84C2×C8×C127—41no—
85C2×C8×C127—41no—
86C2×C8×C127—42no—
87C2×C8×C127C22⋊C411yescharacteristic
88C2×C8×C127C22⋊C411yescharacteristic
89C2×C8×C127C2×D411yescharacteristic
90C2×C8×C127C2×D411yescharacteristic
91C4⋊C4×C127—21no—
92C4⋊C4×C127—21no—
93C4⋊C4×C127C2×C811yescharacteristic
94C4⋊C4×C127C2×C811yescharacteristic
95C22⋊C4×C127—21no—
96C22⋊C4×C127—21no—
97C22⋊C4×C127—21no—
98C22⋊C4×C127—21no—
99C22⋊C4×C127—21no—
100C42×C127—21no—
101C16×C127—42no—
102C16×C127—42no—
103C23×C127—22no—
104C23×C127—21no—
105C23×C127—41no—
106C23×C127—41no—
107C23×C127C22⋊C811yescharacteristic
108C23×C127C22⋊C811yescharacteristic
109C23×C127C2×M1611yescharacteristic
110Q8×C127—41no—
111D4×C127—41no—
112D4×C127—42no—
113D4×C127—42no—
114D4×C127—42no—
115C2×C4×C127—21no—
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—41no—
125C2×C4×C127—41no—
126C2×C4×C127—41no—
127C2×C4×C127—41no—
128C2×C4×C127—41no—
129C2×C4×C127C22⋊C811yescharacteristic
130C2×C4×C127C22⋊C811yescharacteristic
131C2×C4×C127C2×C22⋊C411yescharacteristic
132C2×C4×C127C22×C811yescharacteristic
133C8×C127—21no—
134C8×C127—21no—
135C8×C127—21no—
136C8×C127—41no—
137C8×C127—41no—
138C8×C127#9912yes—
139C22×C127—21no—
140C22×C127—21no—
141C22×C127—21no—
142C22×C127—21no—
143C22×C127—21no—
144C22×C127—21no—
145C22×C127—21no—
146C22×C127—21no—
147C22×C127—44no—
148C22×C127—41no—
149C22×C127—41no—
150C22×C127—41no—
151C22×C127#35012yes—
152C22×C127C2×C22⋊C811yescharacteristic
153C4×C127—21no—
154C4×C127—21no—
155C4×C127—21no—
156C4×C127—41no—
157C4×C127—41no—
158C4×C127—41no—
159C4×C127C2×#9911yescharacteristic
160C4×C127#41311yescharacteristic
161#11470C12711yesmaximal, characteristic, direct product factor, Sylow
162C2×C127—22no—
163C2×C127—41no—
164C2×C127—41no—
165C2×C127—81no—
166C2×C127#145911yescharacteristic
167C2×C127C2×#35011yescharacteristic
168C2×C127#211711yescharacteristic
169#2929C2×C12711yescharacteristic
170#2112C2×C12711yescharacteristic, complemented
171C2×C22⋊C16C2×C12711yescharacteristic, complemented
172#1323C2×C12712yescomplemented
173#1315C2×C12712yescomplemented
174C127#1147011yescharacteristic, direct product factor, Sylow
175C2×#131C4×C12711yescharacteristic
176C23×C8C22×C12711yescharacteristic
177#525C4×C12711yescharacteristic
178C2×M32—21no—
179C22×C16—21no—
180#435—21no—
181#435—21no—
182C8×D4—21no—
183C8×D4—21no—
184#424C22×C12711yescharacteristic
185#408C22×C12711yescharacteristic
186#407C4×C12711yescharacteristic
187#405C4×C12711yescharacteristic
188C22⋊C16—21no—
189C22⋊C16—21no—
190C22⋊C16C22×C12712yes—
191C22⋊C16C22×C12712yes—
192C2×#41C2×C4×C12711yescharacteristic
193C23×C4C2×C4×C12711yescharacteristic
194#131—42no—
195C2×M16—21no—
196C2×M16C2×C4×C12711yescharacteristic
197C2×M16C2×C4×C12711yescharacteristic
198C22×C8—21no—
199C22×C8—42no—
200C22×C8C2×C4×C12711yescharacteristic
201C22×C8D4×C12711yescharacteristic
202C22×C8D4×C12711yescharacteristic
203C22×C8D4×C12711yescharacteristic
204C22×C8D4×C12711yescharacteristic
205C22×C8C23×C12711yescharacteristic
206#123—21no—
207C22⋊Q8C8×C12711yescharacteristic
208C22⋊Q8C8×C12711yescharacteristic
209#121C8×C12711yescharacteristic
210#121C8×C12711yescharacteristic
211#120—21no—
212C4×D4—21no—
213C4×D4—21no—
214#117C2×C4×C12711yescharacteristic
215M32—42no—
216C2×C16—22no—
217C2×C16—22no—
218C2×C16—42no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C22⋊C8—21no—
222C22⋊C8—21no—
223C22⋊C8—21no—
224C22⋊C8—21no—
225#97—21no—
226C4×C8—21no—
227C24M16×C12711yescharacteristic
228#41—41no—
229#41—41no—
230C2×Q8C2×C8×C12711yescharacteristic
231C2×D4—21no—
232C2×D4—21no—
233C2×D4—21no—
234C2×D4C2×C8×C12711yescharacteristic
235C22×C4—21no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4C22⋊C4×C12711yescharacteristic
239C22×C4C22⋊C4×C12711yescharacteristic
240C22×C4C2×C8×C12711yescharacteristic
241C22×C4C2×C8×C12711yescharacteristic
242C22×C4M16×C12711yescharacteristic
243C22×C4C22×C4×C12711yescharacteristic
244M16—42no—
245M16—41no—
246M16—41no—
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—22no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—42no—
256C2×C8C22⋊C4×C12711yescharacteristic
257C2×C8C22⋊C4×C12711yescharacteristic
258C2×C8C2×D4×C12711yescharacteristic
259C2×C8C2×D4×C12711yescharacteristic
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4C2×C8×C12711yescharacteristic
263C4⋊C4C2×C8×C12711yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C42—21no—
270C16—42no—
271C16—42no—
272C23—22no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23C22⋊C8×C12711yescharacteristic
277C23C22⋊C8×C12711yescharacteristic
278C23C2×M16×C12711yescharacteristic
279Q8—41no—
280D4—41no—
281D4—42no—
282D4—42no—
283D4—42no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4C22⋊C8×C12711yescharacteristic
299C2×C4C22⋊C8×C12711yescharacteristic
300C2×C4C2×C22⋊C4×C12711yescharacteristic
301C2×C4C22×C8×C12711yescharacteristic
302C8—21no—
303C8—21no—
304C8—21no—
305C8—41no—
306C8—41no—
307C8#99×C12712yes—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—44no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22#350×C12712yes—
321C22C2×C22⋊C8×C12711yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4C2×#99×C12711yescharacteristic
329C4#413×C12711yescharacteristic
330C2—22no—
331C2—41no—
332C2—41no—
333C2—81no—
334C2C127×#145911yescharacteristic
335C2C2×#350×C12711yescharacteristic
336C2C127×#211711yescharacteristic
subgroupG/H
centerC2×C4×C127C2×C22⋊C4
commutatorC2×C4C22×C8×C127
Frattini, cosocleC22×C8C23×C127
socleC22×C127C2×C22⋊C8
prime radical#525×C127C4
LCSG ▷ C2×C4 ▷ C22 ▷ 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×#1323C2semidirect
5. C127×#1315C2semidirect
161. #11470C127direct (N × H)
170. #2112C2×C127semidirect
171. C2×C22⋊C16C2×C127semidirect
172. #1323C2×C127semidirect
173. #1315C2×C127semidirect
174. C127#11470direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#29292
C127×#21122
C2×C22⋊C16×C1272
C127×#13232
C127×#13152
#11470127