Finite Group Databasebeta

← C127×#16964 #44580637

Subgroups — C127×#16964 #44580637

Order 32512.

1226 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#400×C127C212yesmaximal
2C2×#398×C127C212yesmaximal
3C2×#389×C127C211yesmaximal, characteristic
4C2×#382×C127C211yesmaximal, characteristic
5C127×#1445C212yesmaximal
6C127×#1445C214yesmaximal
7C127×#1444C212yesmaximal
8C127×#1434C211yesmaximal, characteristic
9C22×C4⋊C4×C127C2211yescharacteristic
10C22×C4⋊C4×C127C2212yes—
11C22×C4⋊C4×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2214yes—
15C22×C42×C127C2211yescharacteristic
16#400×C127—28no—
17#398×C127—28no—
18#389×C127—24no—
19#382×C127—24no—
20C2×#95×C127C2214yes—
21C2×#95×C127C2214yes—
22C2×#95×C127C2214yes—
23C2×#95×C127C2212yes—
24C2×#95×C127C2212yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C23×C4×C127C2312yes—
30C23×C4×C127C2312yes—
31C23×C4×C127C2312yes—
32C23×C4×C127C2311yescharacteristic
33C23×C4×C127C2314yes—
34C23×C4×C127C2312yes—
35C23×C4×C127C2311yescharacteristic
36C23×C4×C127C2311yescharacteristic
37C2×C4⋊C4×C127—22no—
38C2×C4⋊C4×C127—24no—
39C2×C4⋊C4×C127—22no—
40C2×C4⋊C4×C127—22no—
41C2×C4⋊C4×C127—22no—
42C2×C4⋊C4×C127—24no—
43C2×C4⋊C4×C127—28no—
44C2×C4⋊C4×C127—24no—
45C2×C4⋊C4×C127—24no—
46C2×C4⋊C4×C127—24no—
47C2×C4⋊C4×C127—24no—
48C2×C4⋊C4×C127—28no—
49C2×C4⋊C4×C127—24no—
50C2×C4⋊C4×C127—44no—
51C2×C42×C127—24no—
52C2×C42×C127D414yes—
53#95×C127—24no—
54#95×C127—24no—
55#95×C127—24no—
56#95×C127—28no—
57#95×C127—28no—
58#95×C127—28no—
59#95×C127—24no—
60#95×C127—42no—
61#95×C127D418yes—
62C24×C127C2411yescharacteristic
63C22×C4×C127—22no—
64C22×C4×C127—22no—
65C22×C4×C127—22no—
66C22×C4×C127—22no—
67C22×C4×C127—22no—
68C22×C4×C127—22no—
69C22×C4×C127—22no—
70C22×C4×C127—24no—
71C22×C4×C127—22no—
72C22×C4×C127—22no—
73C22×C4×C127—24no—
74C22×C4×C127—21no—
75C22×C4×C127—24no—
76C22×C4×C127—22no—
77C22×C4×C127—22no—
78C22×C4×C127—24no—
79C22×C4×C127—24no—
80C22×C4×C127—21no—
81C22×C4×C127—24no—
82C22×C4×C127—22no—
83C22×C4×C127—22no—
84C22×C4×C127—22no—
85C22×C4×C127—24no—
86C22×C4×C127—22no—
87C22×C4×C127—22no—
88C22×C4×C127—22no—
89C22×C4×C127—24no—
90C22×C4×C127—24no—
91C22×C4×C127—24no—
92C22×C4×C127—22no—
93C22×C4×C127—24no—
94C22×C4×C127—24no—
95C22×C4×C127—24no—
96C22×C4×C127—22no—
97C22×C4×C127C2×D412yes—
98C22×C4×C127C2×D418yes—
99C22×C4×C127C2×D412yes—
100C22×C4×C127C2×D414yes—
101C22×C4×C127C2×D412yes—
102C22×C4×C127#4114yes—
103C22×C4×C127#4114yes—
104C4⋊C4×C127—28no—
105C4⋊C4×C127—416no—
106C4⋊C4×C127—44no—
107C4⋊C4×C127—48no—
108C4⋊C4×C127—44no—
109C4⋊C4×C127—44no—
110C42×C127—28no—
111C23×C127C22×D411yescharacteristic
112C23×C127C22×D412yes—
113C23×C127C2×#4112yes—
114C23×C127C2×#4112yes—
115C23×C127H(5,𝔽2)11yescharacteristic
116C23×C1272−1+412yes—
117C23×C1272−1+412yes—
118C23×C1272−1+412yes—
119C23×C1272−1+411yescharacteristic
120C2×C4×C127—22no—
121C2×C4×C127—22no—
122C2×C4×C127—22no—
123C2×C4×C127—22no—
124C2×C4×C127—28no—
125C2×C4×C127—28no—
126C2×C4×C127—22no—
127C2×C4×C127—24no—
128C2×C4×C127—22no—
129C2×C4×C127—28no—
130C2×C4×C127—22no—
131C2×C4×C127—24no—
132C2×C4×C127—28no—
133C2×C4×C127—28no—
134C2×C4×C127—24no—
135C2×C4×C127—42no—
136C2×C4×C127—42no—
137C2×C4×C127—42no—
138C2×C4×C127—44no—
139C2×C4×C127—42no—
140C2×C4×C127—44no—
141C2×C4×C127—42no—
142C2×C4×C127—42no—
143C2×C4×C127—44no—
144C2×C4×C127—44no—
145C2×C4×C127—42no—
146C2×C4×C127—42no—
147C2×C4×C127—42no—
148C2×C4×C127—42no—
149C2×C4×C127—42no—
150C2×C4×C127—42no—
151C2×C4×C127—42no—
152C2×C4×C127—48no—
153C2×C4×C127—42no—
154C2×C4×C127—42no—
155C2×C4×C127—44no—
156C2×C4×C127—44no—
157C2×C4×C127—44no—
158C2×C4×C127—44no—
159C2×C4×C127#12314yes—
160C2×C4×C127#12714yes—
161C22×C127C2×#12311yescharacteristic
162C22×C127#52511yescharacteristic
163C22×C127C2×#12711yescharacteristic
164C22×C127#53611yescharacteristic
165C22×C127#53611yescharacteristic
166C22×C127#53611yescharacteristic
167C22×C127#53614yes—
168C22×C127#53711yescharacteristic
169C22×C127#54112yes—
170C22×C127#54114yes—
171C22×C127#54212yes—
172C22×C127#54612yes—
173C22×C127#54714yes—
174C22×C127#54812yes—
175C22×C127#55214yes—
176C22×C127#56312yes—
177C22×C127#56412yes—
178C4×C127—24no—
179C4×C127—24no—
180C4×C127—42no—
181C4×C127—48no—
182C4×C127—44no—
183C4×C127—82no—
184C4×C127—82no—
185C4×C127—82no—
186#16964C12711yesmaximal, characteristic, direct product factor, Sylow
187C2×C127#248411yescharacteristic
188C2×C127#250111yescharacteristic
189C2×C127#254011yescharacteristic
190C2×C127#262511yescharacteristic
191C2×C127#263411yescharacteristic
192C2×C127#265811yescharacteristic
193C2×C127#269814yes—
194C2×C127#271914yes—
195C2×C127#282211yescharacteristic
196C2×#400C2×C12712yes—
197C2×#398C2×C12712yes—
198C2×#389C2×C12711yescharacteristic
199C2×#382C2×C12711yescharacteristic
200#1445C2×C12712yes—
201#1445C2×C12714yes—
202#1444C2×C12712yes—
203#1434C2×C12711yescharacteristic
204C127#1696411yescharacteristic, direct product factor, Sylow
205C22×C4⋊C4C22×C12711yescharacteristic
206C22×C4⋊C4C22×C12712yes—
207C22×C4⋊C4C22×C12711yescharacteristic
208C22×C4⋊C4C22×C12711yescharacteristic
209C22×C4⋊C4C22×C12711yescharacteristic
210C22×C4⋊C4C22×C12714yes—
211C22×C42C22×C12711yescharacteristic
212#400—28no—
213#398—28no—
214#389—24no—
215#382—24no—
216C2×#95C22×C12714yes—
217C2×#95C22×C12714yes—
218C2×#95C22×C12714yes—
219C2×#95C22×C12712yes—
220C2×#95C22×C12712yes—
221C2×#95C22×C12712yes—
222C2×#95C22×C12712yes—
223C2×#95C22×C12712yes—
224C2×#95C22×C12712yes—
225C23×C4C23×C12712yes—
226C23×C4C23×C12712yes—
227C23×C4C23×C12712yes—
228C23×C4C23×C12714yes—
229C23×C4C23×C12711yescharacteristic
230C23×C4C23×C12712yes—
231C23×C4C23×C12711yescharacteristic
232C23×C4C23×C12711yescharacteristic
233C2×C4⋊C4—22no—
234C2×C4⋊C4—24no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—24no—
239C2×C4⋊C4—28no—
240C2×C4⋊C4—24no—
241C2×C4⋊C4—24no—
242C2×C4⋊C4—24no—
243C2×C4⋊C4—24no—
244C2×C4⋊C4—28no—
245C2×C4⋊C4—24no—
246C2×C4⋊C4—44no—
247C2×C42—24no—
248C2×C42D4×C12714yes—
249#95—24no—
250#95—24no—
251#95—24no—
252#95—28no—
253#95—28no—
254#95—28no—
255#95—24no—
256#95—42no—
257#95D4×C12718yes—
258C24C24×C12711yescharacteristic
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—24no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—24no—
270C22×C4—21no—
271C22×C4—24no—
272C22×C4—22no—
273C22×C4—24no—
274C22×C4—22no—
275C22×C4—24no—
276C22×C4—21no—
277C22×C4—24no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—24no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—24no—
286C22×C4—24no—
287C22×C4—24no—
288C22×C4—22no—
289C22×C4—24no—
290C22×C4—24no—
291C22×C4—24no—
292C22×C4—22no—
293C22×C4C2×D4×C12712yes—
294C22×C4C2×D4×C12718yes—
295C22×C4C2×D4×C12712yes—
296C22×C4C2×D4×C12714yes—
297C22×C4C2×D4×C12712yes—
298C22×C4#41×C12714yes—
299C22×C4#41×C12714yes—
300C4⋊C4—28no—
301C4⋊C4—416no—
302C4⋊C4—44no—
303C4⋊C4—48no—
304C4⋊C4—44no—
305C4⋊C4—44no—
306C42—28no—
307C23C22×D4×C12711yescharacteristic
308C23C22×D4×C12712yes—
309C23C2×#41×C12712yes—
310C23C2×#41×C12712yes—
311C23H(5,𝔽2)×C12711yescharacteristic
312C232−1+4×C12712yes—
313C232−1+4×C12712yes—
314C232−1+4×C12712yes—
315C232−1+4×C12711yescharacteristic
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—28no—
321C2×C4—28no—
322C2×C4—22no—
323C2×C4—24no—
324C2×C4—22no—
325C2×C4—28no—
326C2×C4—22no—
327C2×C4—24no—
328C2×C4—28no—
329C2×C4—28no—
330C2×C4—24no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—44no—
335C2×C4—42no—
336C2×C4—44no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—44no—
340C2×C4—44no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—48no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4—44no—
355C2×C4#123×C12714yes—
356C2×C4#127×C12714yes—
357C22C2×#123×C12711yescharacteristic
358C22#525×C12711yescharacteristic
359C22C2×#127×C12711yescharacteristic
360C22#536×C12711yescharacteristic
361C22#536×C12711yescharacteristic
362C22#536×C12714yes—
363C22#536×C12711yescharacteristic
364C22#537×C12711yescharacteristic
365C22#541×C12712yes—
366C22#541×C12714yes—
367C22#542×C12712yes—
368C22#546×C12712yes—
369C22#547×C12714yes—
370C22#548×C12712yes—
371C22#552×C12714yes—
372C22#563×C12712yes—
373C22#564×C12712yes—
374C4—24no—
375C4—24no—
376C4—42no—
377C4—48no—
378C4—44no—
379C4—82no—
380C4—82no—
381C4—82no—
382C2C127×#248411yescharacteristic
383C2C127×#250111yescharacteristic
384C2C127×#254011yescharacteristic
385C2C127×#262511yescharacteristic
386C2C127×#263411yescharacteristic
387C2C127×#265811yescharacteristic
388C2C127×#269814yes—
389C2C127×#271914yes—
390C2C127×#282211yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C24
commutator, Frattini, cosocleC24C24×C127
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
186. #16964C127direct (N × H)
204. C127#16964direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#400×C1272
C2×#398×C1272
C2×#389×C1272
C2×#382×C1272
C127×#14452
C127×#14442
C127×#14342
#16964127