Finite Group Databasebeta

← C127×#11721 #44575394

Subgroups — C127×#11721 #44575394

Order 32512.

452 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2396C211yesmaximal, characteristic
2C127×#1742C211yesmaximal, characteristic
3C127×#1458C211yesmaximal, characteristic
4C127×#1354C212yesmaximal, complemented
5C127×#1353C212yesmaximal, complemented
6C22×M16×C127—21no—
7C2×C4×Q8×C127C411yescharacteristic
8C2×#117×C127C2211yescharacteristic
9#431×C127—21no—
10#400×C127C2211yescharacteristic
11#399×C127C411yescharacteristic
12#398×C127—21no—
13#396×C127—21no—
14#395×C127C2211yescharacteristic
15#393×C127C411yescharacteristic
16C4×C4⋊C4×C127—21no—
17C4×C4⋊C4×C127C411yescharacteristic
18C4×C22⋊C4×C127—21no—
19#343×C127—21no—
20#343×C127C2212yes—
21#324×C127C2212yes—
22#323×C127—21no—
23C22×Q8×C127C2×C411yescharacteristic
24C23×C4×C127D411yescharacteristic
25C2×M16×C127—24no—
26C2×M16×C127—22no—
27C2×M16×C127—41no—
28C2×M16×C127—42no—
29C22×C8×C127—41no—
30C4×Q8×C127—41no—
31C4×Q8×C127—41no—
32#117×C127—41no—
33#117×C127—41no—
34C2×C4⋊C4×C127—21no—
35C2×C4⋊C4×C127—21no—
36C2×C4⋊C4×C127—21no—
37C2×C4⋊C4×C127—21no—
38C2×C4⋊C4×C127C2×C411yescharacteristic
39C2×C4⋊C4×C127D411yescharacteristic
40C2×C4⋊C4×C127C2311yescharacteristic
41C2×C22⋊C4×C127—21no—
42C2×C22⋊C4×C127—21no—
43C2×C22⋊C4×C127C2×C411yescharacteristic
44C2×C22⋊C4×C127D411yescharacteristic
45C2×C42×C127—21no—
46C2×C42×C127—21no—
47C2×C42×C127C2×C411yescharacteristic
48C2×C42×C127D411yescharacteristic
49C4⋊C8×C127—41no—
50C22⋊C8×C127—22no—
51C4×C8×C127—41no—
52#95×C127—21no—
53#95×C127—21no—
54#95×C127—21no—
55#95×C127—21no—
56#95×C127C2×C411yescharacteristic
57#95×C127C2×C411yescharacteristic
58C24×C127C22⋊C411yescharacteristic
59C2×Q8×C127—42no—
60C2×Q8×C127—41no—
61C22×C4×C127—21no—
62C22×C4×C127—21no—
63C22×C4×C127—22no—
64C22×C4×C127—21no—
65C22×C4×C127—21no—
66C22×C4×C127—21no—
67C22×C4×C127—21no—
68C22×C4×C127C22⋊C411yescharacteristic
69C22×C4×C127C22⋊C411yescharacteristic
70C22×C4×C127C22⋊C411yescharacteristic
71C22×C4×C127SD1612yes—
72C22×C4×C127Q1612yes—
73C22×C4×C127C22×C411yescharacteristic
74C22×C4×C127C2×D411yescharacteristic
75C22×C4×C127C2×D411yescharacteristic
76M16×C127—24no—
77M16×C127—44no—
78M16×C127—42no—
79C2×C8×C127—42no—
80C2×C8×C127—44no—
81C2×C8×C127—42no—
82C4⋊C4×C127—41no—
83C4⋊C4×C127—41no—
84C4⋊C4×C127—41no—
85C4⋊C4×C127—42no—
86C4⋊C4×C127—42no—
87C4⋊C4×C127—42no—
88C4⋊C4×C127—42no—
89C22⋊C4×C127—41no—
90C22⋊C4×C127—41no—
91C22⋊C4×C127—42no—
92C22⋊C4×C127—42no—
93C42×C127—21no—
94C42×C127—21no—
95C42×C127—21no—
96C42×C127—21no—
97C42×C127—41no—
98C42×C127—41no—
99C42×C127—42no—
100C23×C127—21no—
101C23×C127—21no—
102C23×C127—41no—
103C23×C127—41no—
104C23×C127#10312yes—
105C23×C127C2×C22⋊C411yescharacteristic
106Q8×C127—42no—
107Q8×C127—42no—
108C2×C4×C127—21no—
109C2×C4×C127—21no—
110C2×C4×C127—22no—
111C2×C4×C127—22no—
112C2×C4×C127—22no—
113C2×C4×C127—22no—
114C2×C4×C127—22no—
115C2×C4×C127—22no—
116C2×C4×C127—21no—
117C2×C4×C127—21no—
118C2×C4×C127—21no—
119C2×C4×C127—21no—
120C2×C4×C127—41no—
121C2×C4×C127—41no—
122C2×C4×C127—41no—
123C2×C4×C127—41no—
124C2×C4×C127—41no—
125C2×C4×C127—41no—
126C2×C4×C127—41no—
127C2×C4×C127—41no—
128C2×C4×C127—41no—
129C2×C4×C127—41no—
130C2×C4×C127—41no—
131C2×C4×C127—41no—
132C2×C4×C127—41no—
133C2×C4×C127—41no—
134C2×C4×C127#9911yescharacteristic
135C2×C4×C127#9911yescharacteristic
136C2×C4×C127#10312yes—
137C2×C4×C127#10412yes—
138C2×C4×C127C2×SD1611yescharacteristic
139C2×C4×C127C2×Q1611yescharacteristic
140C8×C127—44no—
141C8×C127—82no—
142C22×C127—21no—
143C22×C127—21no—
144C22×C127—22no—
145C22×C127—42no—
146C22×C127—41no—
147C22×C127—41no—
148C22×C127—81no—
149C22×C127C2×#9911yescharacteristic
150C22×C127C2×#10311yescharacteristic
151C22×C127C2×#10411yescharacteristic
152C4×C127—21no—
153C4×C127—21no—
154C4×C127—42no—
155C4×C127—41no—
156C4×C127—42no—
157C4×C127—41no—
158C4×C127—41no—
159C4×C127—41no—
160C4×C127—81no—
161C4×C127—81no—
162C4×C127#32812yes—
163C4×C127#32812yes—
164#11721C12711yesmaximal, characteristic, direct product factor, Sylow
165C2×C127—21no—
166C2×C127—21no—
167C2×C127—42no—
168C2×C127C2×#32811yescharacteristic
169C2×C127#212011yescharacteristic
170C2×C127#213211yescharacteristic
171#2396C2×C12711yescharacteristic
172#1742C2×C12711yescharacteristic
173#1458C2×C12711yescharacteristic
174#1354C2×C12712yescomplemented
175#1353C2×C12712yescomplemented
176C127#1172111yescharacteristic, direct product factor, Sylow
177C22×M16—21no—
178C2×C4×Q8C4×C12711yescharacteristic
179C2×#117C22×C12711yescharacteristic
180#431—21no—
181#400C22×C12711yescharacteristic
182#399C4×C12711yescharacteristic
183#398—21no—
184#396—21no—
185#395C22×C12711yescharacteristic
186#393C4×C12711yescharacteristic
187C4×C4⋊C4—21no—
188C4×C4⋊C4C4×C12711yescharacteristic
189C4×C22⋊C4—21no—
190#343—21no—
191#343C22×C12712yes—
192#324C22×C12712yes—
193#323—21no—
194C22×Q8C2×C4×C12711yescharacteristic
195C23×C4D4×C12711yescharacteristic
196C2×M16—24no—
197C2×M16—22no—
198C2×M16—41no—
199C2×M16—42no—
200C22×C8—41no—
201C4×Q8—41no—
202C4×Q8—41no—
203#117—41no—
204#117—41no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4C2×C4×C12711yescharacteristic
210C2×C4⋊C4D4×C12711yescharacteristic
211C2×C4⋊C4C23×C12711yescharacteristic
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4C2×C4×C12711yescharacteristic
215C2×C22⋊C4D4×C12711yescharacteristic
216C2×C42—21no—
217C2×C42—21no—
218C2×C42C2×C4×C12711yescharacteristic
219C2×C42D4×C12711yescharacteristic
220C4⋊C8—41no—
221C22⋊C8—22no—
222C4×C8—41no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95C2×C4×C12711yescharacteristic
228#95C2×C4×C12711yescharacteristic
229C24C22⋊C4×C12711yescharacteristic
230C2×Q8—42no—
231C2×Q8—41no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—22no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4C22⋊C4×C12711yescharacteristic
240C22×C4C22⋊C4×C12711yescharacteristic
241C22×C4C22⋊C4×C12711yescharacteristic
242C22×C4SD16×C12712yes—
243C22×C4Q16×C12712yes—
244C22×C4C22×C4×C12711yescharacteristic
245C22×C4C2×D4×C12711yescharacteristic
246C22×C4C2×D4×C12711yescharacteristic
247M16—24no—
248M16—44no—
249M16—42no—
250C2×C8—42no—
251C2×C8—44no—
252C2×C8—42no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C42—21no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—41no—
269C42—41no—
270C42—42no—
271C23—21no—
272C23—21no—
273C23—41no—
274C23—41no—
275C23#103×C12712yes—
276C23C2×C22⋊C4×C12711yescharacteristic
277Q8—42no—
278Q8—42no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4#99×C12711yescharacteristic
306C2×C4#99×C12711yescharacteristic
307C2×C4#103×C12712yes—
308C2×C4#104×C12712yes—
309C2×C4C2×SD16×C12711yescharacteristic
310C2×C4C2×Q16×C12711yescharacteristic
311C8—44no—
312C8—82no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—42no—
317C22—41no—
318C22—41no—
319C22—81no—
320C22C2×#99×C12711yescharacteristic
321C22C2×#103×C12711yescharacteristic
322C22C2×#104×C12711yescharacteristic
323C4—21no—
324C4—21no—
325C4—42no—
326C4—41no—
327C4—42no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—81no—
332C4—81no—
333C4#328×C12712yes—
334C4#328×C12712yes—
335C2—21no—
336C2—21no—
337C2—42no—
338C2C2×#328×C12711yescharacteristic
339C2C127×#212011yescharacteristic
340C2C127×#213211yescharacteristic
subgroupG/H
centerC2×C4×C127#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
socleC22×C127C2×#99
prime radicalC24×C127C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C22×C4×C127 ◁ C2×#117×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1354C2semidirect
5. C127×#1353C2semidirect
164. #11721C127direct (N × H)
174. #1354C2×C127semidirect
175. #1353C2×C127semidirect
176. C127#11721direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#23962
C127×#17422
C127×#14582
C127×#13542
C127×#13532
#11721127