Finite Group Databasebeta

← C127×#14301 #44577974

Subgroups — C127×#14301 #44577974

Order 32512.

1830 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C127C211yesmaximal, characteristic, complemented
2C2×#393×C127C211yesmaximal, characteristic
3C2×#388×C127C213yesmaximal
4C127×#1446C211yesmaximal, characteristic, complemented
5C127×#1444C213yesmaximal, complemented
6C127×#1439C213yesmaximal
7C127×#1434C213yesmaximal, complemented
8C23×Q8×C127C2211yescharacteristic
9C2×C4×Q8×C127—212no—
10C22×C4⋊C4×C127C2213yes—
11C22×C4⋊C4×C127C2213yes—
12C22×C22⋊C4×C127C2211yescharacteristic
13C22×C22⋊C4×C127C2213yes—
14C22×C22⋊C4×C127C2213yes—
15C22×C42×C127C2213yes—
16#393×C127C418yescomplemented
17#388×C127—212no—
18C2×#95×C127C2213yes—
19C2×#95×C127C2213yes—
20C2×#95×C127C2213yes—
21C2×#95×C127C2216yes—
22C2×#95×C127C2213yes—
23C25×C127C2311yescharacteristic
24C22×Q8×C127—26no—
25C22×Q8×C127—26no—
26C22×Q8×C127C2×C414yes—
27C23×C4×C127C2311yescharacteristic
28C23×C4×C127C2313yes—
29C23×C4×C127C2313yes—
30C23×C4×C127C2313yes—
31C23×C4×C127C2313yes—
32C23×C4×C127C2311yescharacteristic
33C4×Q8×C127—232no—
34C2×C4⋊C4×C127—212no—
35C2×C4⋊C4×C127—26no—
36C2×C4⋊C4×C127—26no—
37C2×C4⋊C4×C127—46no—
38C2×C22⋊C4×C127—26no—
39C2×C22⋊C4×C127—26no—
40C2×C22⋊C4×C127—26no—
41C2×C22⋊C4×C127—26no—
42C2×C22⋊C4×C127—46no—
43C2×C22⋊C4×C127C2×C4112yes—
44C2×C42×C127—212no—
45C2×C42×C127D4112yes—
46#95×C127—26no—
47#95×C127—26no—
48#95×C127—26no—
49#95×C127—46no—
50#95×C127C2×C4112yes—
51C24×C127—23no—
52C24×C127—23no—
53C24×C127—23no—
54C24×C127—21no—
55C24×C127—21no—
56C24×C127—23no—
57C24×C127C22×C412yes—
58C24×C127C2411yescharacteristic
59C2×Q8×C127—28no—
60C2×Q8×C127—224no—
61C2×Q8×C127—224no—
62C22×C4×C127—26no—
63C22×C4×C127—26no—
64C22×C4×C127—21no—
65C22×C4×C127—23no—
66C22×C4×C127—23no—
67C22×C4×C127—26no—
68C22×C4×C127—23no—
69C22×C4×C127—23no—
70C22×C4×C127—26no—
71C22×C4×C127—26no—
72C22×C4×C127—26no—
73C22×C4×C127—23no—
74C22×C4×C127—23no—
75C22×C4×C127—23no—
76C22×C4×C127—26no—
77C22×C4×C127—26no—
78C22×C4×C127—23no—
79C22×C4×C127—23no—
80C22×C4×C127—23no—
81C22×C4×C127—21no—
82C22×C4×C127C22×C416yes—
83C22×C4×C127C22×C416yes—
84C22×C4×C127C2×D416yes—
85C22×C4×C127C2×D416yes—
86C22×C4×C127C2×D416yes—
87C22×C4×C127#4116yes—
88C4⋊C4×C127—224no—
89C4⋊C4×C127—412no—
90C22⋊C4×C127—224no—
91C22⋊C4×C127—412no—
92C22⋊C4×C127—44no—
93C42×C127—224no—
94C23×C127—26no—
95C23×C127—22no—
96C23×C127—26no—
97C23×C127—41no—
98C23×C127—43no—
99C23×C127—43no—
100C23×C127—43no—
101C23×C127—43no—
102C23×C127—43no—
103C23×C127—43no—
104C23×C127—43no—
105C23×C127—46no—
106C23×C127C23×C411yescharacteristic
107C23×C127C22×D413yes—
108C23×C127C2×#4113yes—
109C23×C127H(5,𝔽2)13yes—
110C23×C1272−1+411yescharacteristic
111C23×C1272−1+411yescharacteristic
112C23×C1272−1+413yes—
113Q8×C127—232no—
114C2×C4×C127—212no—
115C2×C4×C127—26no—
116C2×C4×C127—26no—
117C2×C4×C127—212no—
118C2×C4×C127—26no—
119C2×C4×C127—26no—
120C2×C4×C127—26no—
121C2×C4×C127—212no—
122C2×C4×C127—26no—
123C2×C4×C127—26no—
124C2×C4×C127—26no—
125C2×C4×C127—43no—
126C2×C4×C127—46no—
127C2×C4×C127—43no—
128C2×C4×C127—46no—
129C2×C4×C127—46no—
130C2×C4×C127—41no—
131C2×C4×C127—43no—
132C2×C4×C127—43no—
133C2×C4×C127—43no—
134C2×C4×C127—43no—
135C2×C4×C127—43no—
136C2×C4×C127—46no—
137C2×C4×C127—46no—
138C2×C4×C127C4×D4112yes—
139C2×C4×C127#12014yes—
140C22×C127—46no—
141C22×C127—46no—
142C22×C127—42no—
143C22×C127—81no—
144C22×C127—81no—
145C22×C127—83no—
146C22×C127—83no—
147C22×C127C2×C4×D413yes—
148C22×C127#51911yescharacteristic
149C22×C127#52013yes—
150C22×C127C2×#12011yescharacteristic
151C22×C127#52513yes—
152C22×C127#53513yes—
153C22×C127#53613yes—
154C22×C127#53613yes—
155C22×C127#53713yes—
156C22×C127#54113yes—
157C22×C127#54213yes—
158C22×C127#54216yes—
159C4×C127—24no—
160C4×C127—212no—
161C4×C127—46no—
162C4×C127—46no—
163C4×C127—81no—
164C4×C127—83no—
165#14301C12711yesmaximal, characteristic, direct product factor, Sylow
166C2×C127—82no—
167C2×C127C4×#12011yescharacteristic
168C2×C127#232313yes—
169C2×C127#232613yes—
170C2×C127#261411yescharacteristic
171C2×C127#261511yescharacteristic
172C2×C127#263213yes—
173C2×C127#263713yes—
174C22×C4×Q8C2×C12711yescharacteristic, complemented
175C2×#393C2×C12711yescharacteristic
176C2×#388C2×C12713yes—
177#1446C2×C12711yescharacteristic, complemented
178#1444C2×C12713yescomplemented
179#1439C2×C12713yes—
180#1434C2×C12713yescomplemented
181C127#1430111yescharacteristic, direct product factor, Sylow
182C23×Q8C22×C12711yescharacteristic
183C2×C4×Q8—212no—
184C22×C4⋊C4C22×C12713yes—
185C22×C4⋊C4C22×C12713yes—
186C22×C22⋊C4C22×C12711yescharacteristic
187C22×C22⋊C4C22×C12713yes—
188C22×C22⋊C4C22×C12713yes—
189C22×C42C22×C12713yes—
190#393C4×C12718yescomplemented
191#388—212no—
192C2×#95C22×C12713yes—
193C2×#95C22×C12713yes—
194C2×#95C22×C12713yes—
195C2×#95C22×C12716yes—
196C2×#95C22×C12713yes—
197C25C23×C12711yescharacteristic
198C22×Q8—26no—
199C22×Q8—26no—
200C22×Q8C2×C4×C12714yes—
201C23×C4C23×C12711yescharacteristic
202C23×C4C23×C12713yes—
203C23×C4C23×C12713yes—
204C23×C4C23×C12713yes—
205C23×C4C23×C12713yes—
206C23×C4C23×C12711yescharacteristic
207C4×Q8—232no—
208C2×C4⋊C4—212no—
209C2×C4⋊C4—26no—
210C2×C4⋊C4—26no—
211C2×C4⋊C4—46no—
212C2×C22⋊C4—26no—
213C2×C22⋊C4—26no—
214C2×C22⋊C4—26no—
215C2×C22⋊C4—26no—
216C2×C22⋊C4—46no—
217C2×C22⋊C4C2×C4×C127112yes—
218C2×C42—212no—
219C2×C42D4×C127112yes—
220#95—26no—
221#95—26no—
222#95—26no—
223#95—46no—
224#95C2×C4×C127112yes—
225C24—23no—
226C24—23no—
227C24—23no—
228C24—21no—
229C24—21no—
230C24—23no—
231C24C22×C4×C12712yes—
232C24C24×C12711yescharacteristic
233C2×Q8—28no—
234C2×Q8—224no—
235C2×Q8—224no—
236C22×C4—26no—
237C22×C4—26no—
238C22×C4—21no—
239C22×C4—23no—
240C22×C4—23no—
241C22×C4—26no—
242C22×C4—23no—
243C22×C4—23no—
244C22×C4—26no—
245C22×C4—26no—
246C22×C4—26no—
247C22×C4—23no—
248C22×C4—23no—
249C22×C4—23no—
250C22×C4—26no—
251C22×C4—26no—
252C22×C4—23no—
253C22×C4—23no—
254C22×C4—23no—
255C22×C4—21no—
256C22×C4C22×C4×C12716yes—
257C22×C4C22×C4×C12716yes—
258C22×C4C2×D4×C12716yes—
259C22×C4C2×D4×C12716yes—
260C22×C4C2×D4×C12716yes—
261C22×C4#41×C12716yes—
262C4⋊C4—224no—
263C4⋊C4—412no—
264C22⋊C4—224no—
265C22⋊C4—412no—
266C22⋊C4—44no—
267C42—224no—
268C23—26no—
269C23—22no—
270C23—26no—
271C23—41no—
272C23—43no—
273C23—43no—
274C23—43no—
275C23—43no—
276C23—43no—
277C23—43no—
278C23—43no—
279C23—46no—
280C23C23×C4×C12711yescharacteristic
281C23C22×D4×C12713yes—
282C23C2×#41×C12713yes—
283C23H(5,𝔽2)×C12713yes—
284C232−1+4×C12711yescharacteristic
285C232−1+4×C12711yescharacteristic
286C232−1+4×C12713yes—
287Q8—232no—
288C2×C4—212no—
289C2×C4—26no—
290C2×C4—26no—
291C2×C4—212no—
292C2×C4—26no—
293C2×C4—26no—
294C2×C4—26no—
295C2×C4—212no—
296C2×C4—26no—
297C2×C4—26no—
298C2×C4—26no—
299C2×C4—43no—
300C2×C4—46no—
301C2×C4—43no—
302C2×C4—46no—
303C2×C4—46no—
304C2×C4—41no—
305C2×C4—43no—
306C2×C4—43no—
307C2×C4—43no—
308C2×C4—43no—
309C2×C4—43no—
310C2×C4—46no—
311C2×C4—46no—
312C2×C4C4×D4×C127112yes—
313C2×C4#120×C12714yes—
314C22—46no—
315C22—46no—
316C22—42no—
317C22—81no—
318C22—81no—
319C22—83no—
320C22—83no—
321C22C2×C4×D4×C12713yes—
322C22#519×C12711yescharacteristic
323C22#520×C12713yes—
324C22C2×#120×C12711yescharacteristic
325C22#525×C12713yes—
326C22#535×C12713yes—
327C22#536×C12713yes—
328C22#536×C12713yes—
329C22#537×C12713yes—
330C22#541×C12713yes—
331C22#542×C12713yes—
332C22#542×C12716yes—
333C4—24no—
334C4—212no—
335C4—46no—
336C4—46no—
337C4—81no—
338C4—83no—
339C2—82no—
340C2C4×#120×C12711yescharacteristic
341C2C127×#232313yes—
342C2C127×#232613yes—
343C2C127×#261411yescharacteristic
344C2C127×#261511yescharacteristic
345C2C127×#263213yes—
346C2C127×#263713yes—
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C4×Q8×C127C2semidirect
4. C127×#1446C2semidirect
5. C127×#1444C2semidirect
7. C127×#1434C2semidirect
16. #393×C127C4semidirect
165. #14301C127direct (N × H)
174. C22×C4×Q8C2×C127semidirect
177. #1446C2×C127semidirect
178. #1444C2×C127semidirect
180. #1434C2×C127semidirect
181. C127#14301direct (N × H)
190. #393C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C1272
C2×#393×C1272
C2×#388×C1272
C127×#14462
C127×#14442
C127×#14392
C127×#14342
#14301127