Finite Group Databasebeta

← C127×#14637 #44578310

Subgroups — C127×#14637 #44578310

Order 32512.

1378 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#396×C127C211yesmaximal, characteristic
2C127×#1445C213yesmaximal, complemented
3C127×#1444C211yesmaximal, characteristic, complemented
4C127×#1443C211yesmaximal, characteristic, complemented
5C127×#1441C213yesmaximal, complemented
6C127×#1439C213yesmaximal
7C127×C22⋊#95C213yesmaximal
8C24×C4×C127C2211yescharacteristic
9C22×C4⋊C4×C127C2213yes—
10C22×C4⋊C4×C127C2213yes—
11C22×C22⋊C4×C127C2213yes—
12C22×C22⋊C4×C127C2213yes—
13#396×C127C418yescomplemented
14C2×#95×C127C2213yes—
15C2×#95×C127C2213yes—
16C2×#95×C127C2213yes—
17C2×#95×C127C2213yes—
18C2×#95×C127C2213yes—
19C2×#95×C127C2213yes—
20C2×#95×C127C2213yes—
21C2×#95×C127C2211yescharacteristic
22C25×C127C2311yescharacteristic
23C23×C4×C127—43no—
24C23×C4×C127—43no—
25C23×C4×C127Q814yes—
26C23×C4×C127C2313yes—
27C23×C4×C127C2313yes—
28C23×C4×C127C2313yes—
29C23×C4×C127C2313yes—
30C23×C4×C127C2311yescharacteristic
31C23×C4×C127C2311yescharacteristic
32C2×C4⋊C4×C127—43no—
33C2×C4⋊C4×C127—43no—
34C2×C4⋊C4×C127—43no—
35C2×C4⋊C4×C127—43no—
36C2×C4⋊C4×C127—43no—
37C2×C4⋊C4×C127C2×C4112yescomplemented
38C2×C22⋊C4×C127—26no—
39C2×C22⋊C4×C127—43no—
40C2×C22⋊C4×C127—43no—
41C2×C22⋊C4×C127—43no—
42C2×C22⋊C4×C127—43no—
43C2×C22⋊C4×C127C2×C4112yes—
44#95×C127—43no—
45#95×C127—43no—
46#95×C127—43no—
47#95×C127—43no—
48#95×C127—43no—
49#95×C127—43no—
50#95×C127—43no—
51#95×C127C2×C414yescomplemented
52C24×C127—23no—
53C24×C127—23no—
54C24×C127—23no—
55C24×C127—23no—
56C24×C127C22×C412yes—
57C24×C127C2×Q812yes—
58C24×C127#4112yes—
59C24×C127C2411yescharacteristic
60C22×C4×C127—23no—
61C22×C4×C127—23no—
62C22×C4×C127—23no—
63C22×C4×C127—23no—
64C22×C4×C127—23no—
65C22×C4×C127—23no—
66C22×C4×C127—23no—
67C22×C4×C127—23no—
68C22×C4×C127—23no—
69C22×C4×C127—23no—
70C22×C4×C127—23no—
71C22×C4×C127—23no—
72C22×C4×C127—23no—
73C22×C4×C127—23no—
74C22×C4×C127—23no—
75C22×C4×C127—23no—
76C22×C4×C127—23no—
77C22×C4×C127—23no—
78C22×C4×C127—23no—
79C22×C4×C127—23no—
80C22×C4×C127—23no—
81C22×C4×C127—23no—
82C22×C4×C127—23no—
83C22×C4×C127—23no—
84C22×C4×C127—23no—
85C22×C4×C127—23no—
86C22×C4×C127—23no—
87C22×C4×C127—23no—
88C22×C4×C127—23no—
89C22×C4×C127—23no—
90C22×C4×C127—412no—
91C22×C4×C127—44no—
92C22×C4×C127—412no—
93C22×C4×C127C22×C416yes—
94C22×C4×C127C22×C416yes—
95C22×C4×C127C2×Q812yes—
96C22×C4×C127C2×Q812yes—
97C4⋊C4×C127—412no—
98C4⋊C4×C127—412no—
99C22⋊C4×C127—412no—
100C22⋊C4×C127—412no—
101C23×C127—26no—
102C23×C127—26no—
103C23×C127—26no—
104C23×C127—26no—
105C23×C127—26no—
106C23×C127—26no—
107C23×C127—41no—
108C23×C127—43no—
109C23×C127—43no—
110C23×C127—43no—
111C23×C127—43no—
112C23×C127—43no—
113C23×C127C4×Q814yes—
114C23×C127C23×C411yescharacteristic
115C23×C127C22×Q811yescharacteristic
116C23×C127C2×#4111yescharacteristic
117C23×C127H(5,𝔽2)13yes—
118C23×C127H(5,𝔽2)13yes—
119C23×C127H(5,𝔽2)13yes—
120C23×C1272−1+413yes—
121C2×C4×C127—26no—
122C2×C4×C127—26no—
123C2×C4×C127—26no—
124C2×C4×C127—26no—
125C2×C4×C127—26no—
126C2×C4×C127—26no—
127C2×C4×C127—26no—
128C2×C4×C127—26no—
129C2×C4×C127—416no—
130C2×C4×C127—43no—
131C2×C4×C127—43no—
132C2×C4×C127—43no—
133C2×C4×C127—43no—
134C2×C4×C127—41no—
135C2×C4×C127—41no—
136C2×C4×C127—43no—
137C2×C4×C127—43no—
138C2×C4×C127—43no—
139C2×C4×C127—43no—
140C2×C4×C127—43no—
141C2×C4×C127—43no—
142C2×C4×C127—43no—
143C2×C4×C127—43no—
144C2×C4×C127—43no—
145C2×C4×C127—43no—
146C2×C4×C127—43no—
147C2×C4×C127—43no—
148C2×C4×C127—43no—
149C2×C4×C127—43no—
150C2×C4×C127—43no—
151C2×C4×C127—43no—
152C2×C4×C127—43no—
153C2×C4×C127—43no—
154C2×C4×C127—43no—
155C2×C4×C127—43no—
156C22×C127—212no—
157C22×C127—42no—
158C22×C127—46no—
159C22×C127—46no—
160C22×C127—42no—
161C22×C127—46no—
162C22×C127—42no—
163C22×C127C2×C4×Q811yescharacteristic
164C22×C127#51813yes—
165C22×C127#52013yes—
166C22×C127#53813yes—
167C22×C127#53913yes—
168C22×C127#54313yes—
169C22×C127#54413yes—
170C22×C127#56013yes—
171C22×C127#56011yescharacteristic
172C22×C127#56013yes—
173C22×C127#56213yes—
174C22×C127#56213yes—
175C22×C127#56313yes—
176C4×C127—42no—
177C4×C127—42no—
178C4×C127—46no—
179C4×C127—46no—
180C4×C127—83no—
181C4×C127—83no—
182#14637C12711yesmaximal, characteristic, direct product factor, Sylow
183C2×C127—44no—
184C2×C127#232913yes—
185C2×C127#237713yes—
186C2×C127#238311yescharacteristic
187C2×C127#282511yescharacteristic
188C2×C127#282713yes—
189C2×C127#284113yes—
190C2×C127#284211yescharacteristic
191C2×#396C2×C12711yescharacteristic
192#1445C2×C12713yescomplemented
193#1444C2×C12711yescharacteristic, complemented
194#1443C2×C12711yescharacteristic, complemented
195#1441C2×C12713yescomplemented
196#1439C2×C12713yes—
197C22⋊#95C2×C12713yes—
198C127#1463711yescharacteristic, direct product factor, Sylow
199C24×C4C22×C12711yescharacteristic
200C22×C4⋊C4C22×C12713yes—
201C22×C4⋊C4C22×C12713yes—
202C22×C22⋊C4C22×C12713yes—
203C22×C22⋊C4C22×C12713yes—
204#396C4×C12718yescomplemented
205C2×#95C22×C12713yes—
206C2×#95C22×C12713yes—
207C2×#95C22×C12713yes—
208C2×#95C22×C12713yes—
209C2×#95C22×C12713yes—
210C2×#95C22×C12713yes—
211C2×#95C22×C12713yes—
212C2×#95C22×C12711yescharacteristic
213C25C23×C12711yescharacteristic
214C23×C4—43no—
215C23×C4—43no—
216C23×C4Q8×C12714yes—
217C23×C4C23×C12713yes—
218C23×C4C23×C12713yes—
219C23×C4C23×C12713yes—
220C23×C4C23×C12713yes—
221C23×C4C23×C12711yescharacteristic
222C23×C4C23×C12711yescharacteristic
223C2×C4⋊C4—43no—
224C2×C4⋊C4—43no—
225C2×C4⋊C4—43no—
226C2×C4⋊C4—43no—
227C2×C4⋊C4—43no—
228C2×C4⋊C4C2×C4×C127112yescomplemented
229C2×C22⋊C4—26no—
230C2×C22⋊C4—43no—
231C2×C22⋊C4—43no—
232C2×C22⋊C4—43no—
233C2×C22⋊C4—43no—
234C2×C22⋊C4C2×C4×C127112yes—
235#95—43no—
236#95—43no—
237#95—43no—
238#95—43no—
239#95—43no—
240#95—43no—
241#95—43no—
242#95C2×C4×C12714yescomplemented
243C24—23no—
244C24—23no—
245C24—23no—
246C24—23no—
247C24C22×C4×C12712yes—
248C24C2×Q8×C12712yes—
249C24#41×C12712yes—
250C24C24×C12711yescharacteristic
251C22×C4—23no—
252C22×C4—23no—
253C22×C4—23no—
254C22×C4—23no—
255C22×C4—23no—
256C22×C4—23no—
257C22×C4—23no—
258C22×C4—23no—
259C22×C4—23no—
260C22×C4—23no—
261C22×C4—23no—
262C22×C4—23no—
263C22×C4—23no—
264C22×C4—23no—
265C22×C4—23no—
266C22×C4—23no—
267C22×C4—23no—
268C22×C4—23no—
269C22×C4—23no—
270C22×C4—23no—
271C22×C4—23no—
272C22×C4—23no—
273C22×C4—23no—
274C22×C4—23no—
275C22×C4—23no—
276C22×C4—23no—
277C22×C4—23no—
278C22×C4—23no—
279C22×C4—23no—
280C22×C4—23no—
281C22×C4—412no—
282C22×C4—44no—
283C22×C4—412no—
284C22×C4C22×C4×C12716yes—
285C22×C4C22×C4×C12716yes—
286C22×C4C2×Q8×C12712yes—
287C22×C4C2×Q8×C12712yes—
288C4⋊C4—412no—
289C4⋊C4—412no—
290C22⋊C4—412no—
291C22⋊C4—412no—
292C23—26no—
293C23—26no—
294C23—26no—
295C23—26no—
296C23—26no—
297C23—26no—
298C23—41no—
299C23—43no—
300C23—43no—
301C23—43no—
302C23—43no—
303C23—43no—
304C23C4×Q8×C12714yes—
305C23C23×C4×C12711yescharacteristic
306C23C22×Q8×C12711yescharacteristic
307C23C2×#41×C12711yescharacteristic
308C23H(5,𝔽2)×C12713yes—
309C23H(5,𝔽2)×C12713yes—
310C23H(5,𝔽2)×C12713yes—
311C232−1+4×C12713yes—
312C2×C4—26no—
313C2×C4—26no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—26no—
317C2×C4—26no—
318C2×C4—26no—
319C2×C4—26no—
320C2×C4—416no—
321C2×C4—43no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—43no—
325C2×C4—43no—
326C2×C4—43no—
327C2×C4—43no—
328C2×C4—43no—
329C2×C4—43no—
330C2×C4—43no—
331C2×C4—43no—
332C2×C4—43no—
333C2×C4—43no—
334C2×C4—43no—
335C2×C4—43no—
336C2×C4—43no—
337C2×C4—43no—
338C2×C4—43no—
339C2×C4—43no—
340C2×C4—43no—
341C2×C4—43no—
342C2×C4—43no—
343C2×C4—43no—
344C2×C4—43no—
345C2×C4—43no—
346C2×C4—43no—
347C22—212no—
348C22—42no—
349C22—46no—
350C22—46no—
351C22—42no—
352C22—46no—
353C22—42no—
354C22C2×C4×Q8×C12711yescharacteristic
355C22#518×C12713yes—
356C22#520×C12713yes—
357C22#538×C12713yes—
358C22#539×C12713yes—
359C22#543×C12713yes—
360C22#544×C12713yes—
361C22#560×C12713yes—
362C22#560×C12711yescharacteristic
363C22#560×C12713yes—
364C22#562×C12713yes—
365C22#562×C12713yes—
366C22#563×C12713yes—
367C4—42no—
368C4—42no—
369C4—46no—
370C4—46no—
371C4—83no—
372C4—83no—
373C2—44no—
374C2C127×#232913yes—
375C2C127×#237713yes—
376C2C127×#238311yescharacteristic
377C2C127×#282511yescharacteristic
378C2C127×#282713yes—
379C2C127×#284113yes—
380C2C127×#284211yescharacteristic
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
2. C127×#1445C2semidirect
3. C127×#1444C2semidirect
4. C127×#1443C2semidirect
5. C127×#1441C2semidirect
13. #396×C127C4semidirect
37. C2×C4⋊C4×C127C2×C4semidirect
51. #95×C127C2×C4semidirect
182. #14637C127direct (N × H)
192. #1445C2×C127semidirect
193. #1444C2×C127semidirect
194. #1443C2×C127semidirect
195. #1441C2×C127semidirect
198. C127#14637direct (N × H)
204. #396C4×C127semidirect
228. C2×C4⋊C4C2×C4×C127semidirect
242. #95C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#396×C1272
C127×#14452
C127×#14442
C127×#14432
C127×#14412
C127×#14392
C127×C22⋊#952
#14637127