Finite Group Databasebeta

← C127×#16992 #44580665

Subgroups — C127×#16992 #44580665

Order 32512.

1230 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#398×C127C212yesmaximal
2C2×#389×C127C211yesmaximal, characteristic
3C2×#389×C127C211yesmaximal, characteristic
4C127×#1444C212yesmaximal
5C127×#1442C212yesmaximal
6C127×#1441C212yesmaximal
7C127×#1441C214yesmaximal
8C127×#1434C211yesmaximal, characteristic
9C22×C4⋊C4×C127C2212yes—
10C22×C4⋊C4×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2214yes—
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2212yes—
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C42×C127C2211yescharacteristic
17#398×C127—28no—
18#389×C127—24no—
19#389×C127—24no—
20C2×#95×C127C2212yes—
21C2×#95×C127C2214yes—
22C2×#95×C127C2212yes—
23C2×#95×C127C2212yes—
24C2×#95×C127C2212yes—
25C2×#95×C127C2214yes—
26C2×#95×C127C2214yes—
27C2×#95×C127C2212yes—
28C23×C4×C127C2312yes—
29C23×C4×C127C2312yes—
30C23×C4×C127C2311yescharacteristic
31C23×C4×C127C2312yes—
32C23×C4×C127C2314yes—
33C23×C4×C127C2312yes—
34C23×C4×C127C2311yescharacteristic
35C23×C4×C127C2311yescharacteristic
36C2×C4⋊C4×C127—22no—
37C2×C4⋊C4×C127—22no—
38C2×C4⋊C4×C127—24no—
39C2×C4⋊C4×C127—22no—
40C2×C4⋊C4×C127—24no—
41C2×C4⋊C4×C127—22no—
42C2×C4⋊C4×C127—22no—
43C2×C4⋊C4×C127—24no—
44C2×C4⋊C4×C127—28no—
45C2×C4⋊C4×C127—24no—
46C2×C4⋊C4×C127—28no—
47C2×C4⋊C4×C127—24no—
48C2×C4⋊C4×C127—44no—
49C2×C4⋊C4×C127—42no—
50C2×C4⋊C4×C127—42no—
51C2×C4⋊C4×C127—44no—
52C2×C4⋊C4×C127D414yes—
53C2×C42×C127—42no—
54C2×C42×C127D414yes—
55#95×C127—24no—
56#95×C127—24no—
57#95×C127—24no—
58#95×C127—28no—
59#95×C127—42no—
60#95×C127—44no—
61#95×C127—44no—
62#95×C127Q818yes—
63C24×C127C2411yescharacteristic
64C22×C4×C127—22no—
65C22×C4×C127—22no—
66C22×C4×C127—22no—
67C22×C4×C127—22no—
68C22×C4×C127—24no—
69C22×C4×C127—22no—
70C22×C4×C127—22no—
71C22×C4×C127—22no—
72C22×C4×C127—22no—
73C22×C4×C127—22no—
74C22×C4×C127—24no—
75C22×C4×C127—22no—
76C22×C4×C127—24no—
77C22×C4×C127—22no—
78C22×C4×C127—24no—
79C22×C4×C127—22no—
80C22×C4×C127—24no—
81C22×C4×C127—22no—
82C22×C4×C127—22no—
83C22×C4×C127—24no—
84C22×C4×C127—22no—
85C22×C4×C127—24no—
86C22×C4×C127—24no—
87C22×C4×C127—22no—
88C22×C4×C127—22no—
89C22×C4×C127—22no—
90C22×C4×C127—22no—
91C22×C4×C127—24no—
92C22×C4×C127—24no—
93C22×C4×C127—24no—
94C22×C4×C127—24no—
95C22×C4×C127—24no—
96C22×C4×C127C2×D412yes—
97C22×C4×C127C2×D414yes—
98C22×C4×C127C2×D412yes—
99C22×C4×C127C2×D412yes—
100C22×C4×C127C2×D412yes—
101C22×C4×C127C2×Q818yes—
102C22×C4×C127C2×Q814yes—
103C22×C4×C127#4114yes—
104C22×C4×C127#4112yes—
105C4⋊C4×C127—28no—
106C4⋊C4×C127—28no—
107C4⋊C4×C127—416no—
108C4⋊C4×C127—44no—
109C4⋊C4×C127—44no—
110C4⋊C4×C127—48no—
111C4⋊C4×C127—48no—
112C42×C127—44no—
113C23×C127C22×D411yescharacteristic
114C23×C127C22×D411yescharacteristic
115C23×C127C22×Q812yes—
116C23×C127C2×#4111yescharacteristic
117C23×C127C2×#4112yes—
118C23×C127H(5,𝔽2)12yes—
119C23×C127H(5,𝔽2)12yes—
120C23×C1272−1+412yes—
121C23×C1272−1+412yes—
122C2×C4×C127—22no—
123C2×C4×C127—22no—
124C2×C4×C127—22no—
125C2×C4×C127—22no—
126C2×C4×C127—24no—
127C2×C4×C127—24no—
128C2×C4×C127—28no—
129C2×C4×C127—24no—
130C2×C4×C127—24no—
131C2×C4×C127—22no—
132C2×C4×C127—22no—
133C2×C4×C127—22no—
134C2×C4×C127—28no—
135C2×C4×C127—24no—
136C2×C4×C127—28no—
137C2×C4×C127—28no—
138C2×C4×C127—24no—
139C2×C4×C127—28no—
140C2×C4×C127—42no—
141C2×C4×C127—42no—
142C2×C4×C127—42no—
143C2×C4×C127—42no—
144C2×C4×C127—44no—
145C2×C4×C127—44no—
146C2×C4×C127—44no—
147C2×C4×C127—42no—
148C2×C4×C127—44no—
149C2×C4×C127—42no—
150C2×C4×C127—44no—
151C2×C4×C127—44no—
152C2×C4×C127—42no—
153C2×C4×C127—42no—
154C2×C4×C127—42no—
155C2×C4×C127—42no—
156C2×C4×C127—42no—
157C2×C4×C127—42no—
158C2×C4×C127—44no—
159C2×C4×C127—44no—
160C2×C4×C127—48no—
161C2×C4×C127#12114yes—
162C2×C4×C127C4⋊Q814yes—
163C22×C127C2×#12111yescharacteristic
164C22×C127#52511yescharacteristic
165C22×C127C2×C4⋊Q811yescharacteristic
166C22×C127#53411yescharacteristic
167C22×C127#53511yescharacteristic
168C22×C127#53611yescharacteristic
169C22×C127#53611yescharacteristic
170C22×C127#53712yes—
171C22×C127#53912yes—
172C22×C127#54114yes—
173C22×C127#54414yes—
174C22×C127#54612yes—
175C22×C127D4×Q812yes—
176C22×C127#55312yes—
177C22×C127#55414yes—
178C22×C127#55712yes—
179C22×C127#56214yes—
180C4×C127—24no—
181C4×C127—24no—
182C4×C127—42no—
183C4×C127—48no—
184C4×C127—44no—
185C4×C127—44no—
186C4×C127—82no—
187C4×C127—82no—
188#16992C12711yesmaximal, characteristic, direct product factor, Sylow
189C2×C127#253511yescharacteristic
190C2×C127#254611yescharacteristic
191C2×C127#258311yescharacteristic
192C2×C127#261811yescharacteristic
193C2×C127#263411yescharacteristic
194C2×C127#266011yescharacteristic
195C2×C127#270414yes—
196C2×C127#280214yes—
197C2×C127#281611yescharacteristic
198C2×#398C2×C12712yes—
199C2×#389C2×C12711yescharacteristic
200C2×#389C2×C12711yescharacteristic
201#1444C2×C12712yes—
202#1442C2×C12712yes—
203#1441C2×C12712yes—
204#1441C2×C12714yes—
205#1434C2×C12711yescharacteristic
206C127#1699211yescharacteristic, direct product factor, Sylow
207C22×C4⋊C4C22×C12712yes—
208C22×C4⋊C4C22×C12711yescharacteristic
209C22×C4⋊C4C22×C12714yes—
210C22×C4⋊C4C22×C12711yescharacteristic
211C22×C4⋊C4C22×C12711yescharacteristic
212C22×C4⋊C4C22×C12712yes—
213C22×C4⋊C4C22×C12711yescharacteristic
214C22×C42C22×C12711yescharacteristic
215#398—28no—
216#389—24no—
217#389—24no—
218C2×#95C22×C12712yes—
219C2×#95C22×C12714yes—
220C2×#95C22×C12712yes—
221C2×#95C22×C12712yes—
222C2×#95C22×C12712yes—
223C2×#95C22×C12714yes—
224C2×#95C22×C12714yes—
225C2×#95C22×C12712yes—
226C23×C4C23×C12712yes—
227C23×C4C23×C12712yes—
228C23×C4C23×C12712yes—
229C23×C4C23×C12711yescharacteristic
230C23×C4C23×C12714yes—
231C23×C4C23×C12712yes—
232C23×C4C23×C12711yescharacteristic
233C23×C4C23×C12711yescharacteristic
234C2×C4⋊C4—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—24no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—24no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—24no—
242C2×C4⋊C4—28no—
243C2×C4⋊C4—24no—
244C2×C4⋊C4—28no—
245C2×C4⋊C4—24no—
246C2×C4⋊C4—44no—
247C2×C4⋊C4—42no—
248C2×C4⋊C4—42no—
249C2×C4⋊C4—44no—
250C2×C4⋊C4D4×C12714yes—
251C2×C42—42no—
252C2×C42D4×C12714yes—
253#95—24no—
254#95—24no—
255#95—24no—
256#95—28no—
257#95—42no—
258#95—44no—
259#95—44no—
260#95Q8×C12718yes—
261C24C24×C12711yescharacteristic
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—24no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—24no—
273C22×C4—22no—
274C22×C4—24no—
275C22×C4—22no—
276C22×C4—24no—
277C22×C4—22no—
278C22×C4—24no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—24no—
282C22×C4—22no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—24no—
290C22×C4—24no—
291C22×C4—24no—
292C22×C4—24no—
293C22×C4—24no—
294C22×C4C2×D4×C12712yes—
295C22×C4C2×D4×C12714yes—
296C22×C4C2×D4×C12712yes—
297C22×C4C2×D4×C12712yes—
298C22×C4C2×D4×C12712yes—
299C22×C4C2×Q8×C12718yes—
300C22×C4C2×Q8×C12714yes—
301C22×C4#41×C12714yes—
302C22×C4#41×C12712yes—
303C4⋊C4—28no—
304C4⋊C4—28no—
305C4⋊C4—416no—
306C4⋊C4—44no—
307C4⋊C4—44no—
308C4⋊C4—48no—
309C4⋊C4—48no—
310C42—44no—
311C23C22×D4×C12711yescharacteristic
312C23C22×D4×C12711yescharacteristic
313C23C22×Q8×C12712yes—
314C23C2×#41×C12711yescharacteristic
315C23C2×#41×C12712yes—
316C23H(5,𝔽2)×C12712yes—
317C23H(5,𝔽2)×C12712yes—
318C232−1+4×C12712yes—
319C232−1+4×C12712yes—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—24no—
325C2×C4—24no—
326C2×C4—28no—
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—28no—
333C2×C4—24no—
334C2×C4—28no—
335C2×C4—28no—
336C2×C4—24no—
337C2×C4—28no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—42no—
346C2×C4—44no—
347C2×C4—42no—
348C2×C4—44no—
349C2×C4—44no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—44no—
357C2×C4—44no—
358C2×C4—48no—
359C2×C4#121×C12714yes—
360C2×C4C4⋊Q8×C12714yes—
361C22C2×#121×C12711yescharacteristic
362C22#525×C12711yescharacteristic
363C22C2×C4⋊Q8×C12711yescharacteristic
364C22#534×C12711yescharacteristic
365C22#535×C12711yescharacteristic
366C22#536×C12711yescharacteristic
367C22#536×C12711yescharacteristic
368C22#537×C12712yes—
369C22#539×C12712yes—
370C22#541×C12714yes—
371C22#544×C12714yes—
372C22#546×C12712yes—
373C22D4×Q8×C12712yes—
374C22#553×C12712yes—
375C22#554×C12714yes—
376C22#557×C12712yes—
377C22#562×C12714yes—
378C4—24no—
379C4—24no—
380C4—48no—
381C4—44no—
382C4—44no—
383C4—42no—
384C4—82no—
385C4—82no—
386C2C127×#253511yescharacteristic
387C2C127×#254611yescharacteristic
388C2C127×#258311yescharacteristic
389C2C127×#261811yescharacteristic
390C2C127×#263411yescharacteristic
391C2C127×#266011yescharacteristic
392C2C127×#270414yes—
393C2C127×#280214yes—
394C2C127×#281611yescharacteristic
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
188. #16992C127direct (N × H)
206. C127#16992direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#398×C1272
C2×#389×C1272
C127×#14442
C127×#14422
C127×#14412
C127×#14342
#16992127