Finite Group Databasebeta

← C127×#15467 #44579140

Subgroups — C127×#15467 #44579140

Order 32512.

2882 conjugacy classes of subgroups; only the 374 normal subgroups are shown.

normal subgroups only

This group has 2882 conjugacy classes of subgroups — too many to draw. Only its 374 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#393×C127C213yesmaximal, complemented
2C2×#379×C127C213yesmaximal
3C127×#1440C216yesmaximal, complemented
4C127×#1437C213yesmaximal, complemented
5C26×C127C2211yescharacteristic
6C23×Q8×C127C2211yescharacteristic, complemented
7C22×C22⋊C4×C127C2213yes—
8C22×C22⋊C4×C127C2216yes—
9C22×C22⋊C4×C127C2216yes—
10C22×C22⋊C4×C127C2213yes—
11C22×C42×C127C2211yescharacteristic, complemented
12#393×C127—212no—
13#379×C127—212no—
14C2×#95×C127C2216yescomplemented
15C2×#95×C127C2213yescomplemented
16C2×#95×C127C2213yescomplemented
17C2×#95×C127C2212yescomplemented
18C25×C127—26no—
19C25×C127—212no—
20C25×C127—41no—
21C25×C127—43no—
22C25×C127—42no—
23C25×C127C2313yes—
24C22×Q8×C127—26no—
25C22×Q8×C127—43no—
26C22×Q8×C127—41no—
27C23×C4×C127C2316yes—
28C23×C4×C127C2313yes—
29C23×C4×C127C2313yes—
30C2×C22⋊C4×C127—26no—
31C2×C22⋊C4×C127—212no—
32C2×C22⋊C4×C127—212no—
33C2×C22⋊C4×C127—212no—
34C2×C22⋊C4×C127—212no—
35C2×C22⋊C4×C127—212no—
36C2×C22⋊C4×C127—43no—
37C2×C22⋊C4×C127—43no—
38C2×C22⋊C4×C127—46no—
39C2×C22⋊C4×C127—46no—
40C2×C22⋊C4×C127D4112yes—
41C2×C42×C127—41no—
42C2×C42×C127—42no—
43#95×C127—212no—
44#95×C127—26no—
45#95×C127—43no—
46#95×C127—42no—
47C24×C127—26no—
48C24×C127—26no—
49C24×C127—26no—
50C24×C127—23no—
51C24×C127—23no—
52C24×C127—26no—
53C24×C127—26no—
54C24×C127—224no—
55C24×C127—412no—
56C24×C127—424no—
57C24×C127—412no—
58C24×C127—424no—
59C24×C127—412no—
60C24×C127—424no—
61C24×C127—44no—
62C24×C127—44no—
63C24×C127—412no—
64C24×C127C2×D416yes—
65C24×C127#41112yes—
66C24×C127C2411yescharacteristic
67C2×Q8×C127—412no—
68C2×Q8×C127—412no—
69C2×Q8×C127—44no—
70C22×C4×C127—26no—
71C22×C4×C127—26no—
72C22×C4×C127—23no—
73C22×C4×C127—23no—
74C22×C4×C127—26no—
75C22×C4×C127—23no—
76C22×C4×C127—23no—
77C22×C4×C127—26no—
78C22×C4×C127—26no—
79C22×C4×C127—26no—
80C22×C4×C127—26no—
81C22×C4×C127—26no—
82C22×C4×C127—26no—
83C22×C4×C127—26no—
84C22×C4×C127—26no—
85C22×C4×C127C2×D416yes—
86C22×C4×C127C2×D416yes—
87C22⋊C4×C127—412no—
88C22⋊C4×C127—424no—
89C22⋊C4×C127—424no—
90C22⋊C4×C127—412no—
91C42×C127—44no—
92C23×C127—26no—
93C23×C127—212no—
94C23×C127—26no—
95C23×C127—212no—
96C23×C127—212no—
97C23×C127—212no—
98C23×C127—212no—
99C23×C127—212no—
100C23×C127—212no—
101C23×C127—212no—
102C23×C127—448no—
103C23×C127—496no—
104C23×C127—416no—
105C23×C127—448no—
106C23×C127—432no—
107C23×C127—46no—
108C23×C127—46no—
109C23×C127—46no—
110C23×C127—46no—
111C23×C127—43no—
112C23×C127—46no—
113C23×C127—43no—
114C23×C127—46no—
115C23×C127—43no—
116C23×C127—43no—
117C23×C127#124112yes—
118C23×C127C22×D413yes—
119C23×C127C2×#4116yes—
120C23×C127H(5,𝔽2)11yescharacteristic
121C23×C127H(5,𝔽2)13yes—
122C23×C127H(5,𝔽2)12yes—
123Q8×C127—416no—
124C2×C4×C127—26no—
125C2×C4×C127—26no—
126C2×C4×C127—212no—
127C2×C4×C127—212no—
128C2×C4×C127—46no—
129C2×C4×C127—46no—
130C2×C4×C127—43no—
131C2×C4×C127—43no—
132C2×C4×C127—43no—
133C2×C4×C127—43no—
134C2×C4×C127—46no—
135C2×C4×C127—46no—
136C2×C4×C127—46no—
137C2×C4×C127—46no—
138C2×C4×C127—46no—
139C2×C4×C127—46no—
140C2×C4×C127—46no—
141C22×C127—212no—
142C22×C127—224no—
143C22×C127—464no—
144C22×C127—412no—
145C22×C127—46no—
146C22×C127—46no—
147C22×C127—412no—
148C22×C127—412no—
149C22×C127—412no—
150C22×C127—412no—
151C22×C127#52513yes—
152C22×C127C2×#12413yes—
153C22×C127#53413yes—
154C22×C127#53816yes—
155C22×C127D4213yes—
156C22×C127#54616yes—
157C22×C127#55113yes—
158C22×C127#55116yes—
159C22×C127H(3,𝔽4)11yescharacteristic
160C22×C127H(3,𝔽4)11yescharacteristic
161C4×C127—46no—
162C4×C127—46no—
163C4×C127—86no—
164#15467C12711yesmaximal, characteristic, direct product factor, Sylow
165C2×C127—412no—
166C2×C127#247216yes—
167C2×C127#256113yes—
168C2×C127#267911yescharacteristic
169C2×C127#268413yes—
170C2×C127#273612yes—
171C2×#393C2×C12713yescomplemented
172C2×#379C2×C12713yes—
173#1440C2×C12716yescomplemented
174#1437C2×C12713yescomplemented
175C127#1546711yescharacteristic, direct product factor, Sylow
176C26C22×C12711yescharacteristic
177C23×Q8C22×C12711yescharacteristic, complemented
178C22×C22⋊C4C22×C12713yes—
179C22×C22⋊C4C22×C12716yes—
180C22×C22⋊C4C22×C12716yes—
181C22×C22⋊C4C22×C12713yes—
182C22×C42C22×C12711yescharacteristic, complemented
183#393—212no—
184#379—212no—
185C2×#95C22×C12716yescomplemented
186C2×#95C22×C12713yescomplemented
187C2×#95C22×C12713yescomplemented
188C2×#95C22×C12712yescomplemented
189C25—26no—
190C25—212no—
191C25—41no—
192C25—43no—
193C25—42no—
194C25C23×C12713yes—
195C22×Q8—26no—
196C22×Q8—43no—
197C22×Q8—41no—
198C23×C4C23×C12716yes—
199C23×C4C23×C12713yes—
200C23×C4C23×C12713yes—
201C2×C22⋊C4—26no—
202C2×C22⋊C4—212no—
203C2×C22⋊C4—212no—
204C2×C22⋊C4—212no—
205C2×C22⋊C4—212no—
206C2×C22⋊C4—212no—
207C2×C22⋊C4—43no—
208C2×C22⋊C4—43no—
209C2×C22⋊C4—46no—
210C2×C22⋊C4—46no—
211C2×C22⋊C4D4×C127112yes—
212C2×C42—41no—
213C2×C42—42no—
214#95—212no—
215#95—26no—
216#95—43no—
217#95—42no—
218C24—26no—
219C24—26no—
220C24—26no—
221C24—23no—
222C24—23no—
223C24—26no—
224C24—26no—
225C24—224no—
226C24—412no—
227C24—424no—
228C24—424no—
229C24—412no—
230C24—412no—
231C24—424no—
232C24—44no—
233C24—44no—
234C24—412no—
235C24C2×D4×C12716yes—
236C24#41×C127112yes—
237C24C24×C12711yescharacteristic
238C2×Q8—412no—
239C2×Q8—412no—
240C2×Q8—44no—
241C22×C4—26no—
242C22×C4—26no—
243C22×C4—23no—
244C22×C4—23no—
245C22×C4—26no—
246C22×C4—23no—
247C22×C4—23no—
248C22×C4—26no—
249C22×C4—26no—
250C22×C4—26no—
251C22×C4—26no—
252C22×C4—26no—
253C22×C4—26no—
254C22×C4—26no—
255C22×C4—26no—
256C22×C4C2×D4×C12716yes—
257C22×C4C2×D4×C12716yes—
258C22⋊C4—412no—
259C22⋊C4—424no—
260C22⋊C4—424no—
261C22⋊C4—412no—
262C42—44no—
263C23—26no—
264C23—212no—
265C23—26no—
266C23—212no—
267C23—212no—
268C23—212no—
269C23—212no—
270C23—212no—
271C23—212no—
272C23—212no—
273C23—496no—
274C23—448no—
275C23—416no—
276C23—448no—
277C23—432no—
278C23—46no—
279C23—46no—
280C23—46no—
281C23—46no—
282C23—43no—
283C23—46no—
284C23—43no—
285C23—46no—
286C23—43no—
287C23—43no—
288C23#124×C127112yes—
289C23C22×D4×C12713yes—
290C23C2×#41×C12716yes—
291C23H(5,𝔽2)×C12711yescharacteristic
292C23H(5,𝔽2)×C12713yes—
293C23H(5,𝔽2)×C12712yes—
294Q8—416no—
295C2×C4—26no—
296C2×C4—26no—
297C2×C4—212no—
298C2×C4—212no—
299C2×C4—46no—
300C2×C4—46no—
301C2×C4—43no—
302C2×C4—43no—
303C2×C4—43no—
304C2×C4—43no—
305C2×C4—46no—
306C2×C4—46no—
307C2×C4—46no—
308C2×C4—46no—
309C2×C4—46no—
310C2×C4—46no—
311C2×C4—46no—
312C22—224no—
313C22—212no—
314C22—464no—
315C22—46no—
316C22—46no—
317C22—412no—
318C22—412no—
319C22—412no—
320C22—412no—
321C22—412no—
322C22#525×C12713yes—
323C22C2×#124×C12713yes—
324C22#534×C12713yes—
325C22#538×C12716yes—
326C22D42×C12713yes—
327C22#546×C12716yes—
328C22#551×C12713yes—
329C22#551×C12716yes—
330C22H(3,𝔽4)×C12711yescharacteristic
331C22H(3,𝔽4)×C12711yescharacteristic
332C4—46no—
333C4—46no—
334C4—86no—
335C2—412no—
336C2C127×#247216yes—
337C2C127×#256113yes—
338C2C127×#267911yescharacteristic
339C2C127×#268413yes—
340C2C127×#273612yes—
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC26×C127C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#393×C127C2semidirect
3. C127×#1440C2semidirect
4. C127×#1437C2semidirect
6. C23×Q8×C127C22semidirect
11. C22×C42×C127C22semidirect
14. C2×#95×C127C22semidirect
15. C2×#95×C127C22semidirect
16. C2×#95×C127C22semidirect
17. C2×#95×C127C22semidirect
164. #15467C127direct (N × H)
171. C2×#393C2×C127semidirect
173. #1440C2×C127semidirect
174. #1437C2×C127semidirect
175. C127#15467direct (N × H)
177. C23×Q8C22×C127semidirect
182. C22×C42C22×C127semidirect
185. C2×#95C22×C127semidirect
186. C2×#95C22×C127semidirect
187. C2×#95C22×C127semidirect
188. C2×#95C22×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#393×C1272
C2×#379×C1272
C127×#14402
C127×#14372
#15467127