Finite Group Databasebeta

← C127×#16993 #44580666

Subgroups — C127×#16993 #44580666

Order 32512.

1294 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#395×C127C212yesmaximal
2C2×#391×C127C211yesmaximal, characteristic
3C2×#389×C127C211yesmaximal, characteristic
4C127×#1444C212yesmaximal
5C127×#1442C212yesmaximal
6C127×#1442C214yesmaximal
7C127×#1441C212yesmaximal
8C127×#1434C211yesmaximal, characteristic
9C23×Q8×C127C2211yescharacteristic
10C22×C4⋊C4×C127C2212yes—
11C22×C4⋊C4×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2214yes—
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C42×C127C2211yescharacteristic
16#395×C127—28no—
17#391×C127—24no—
18#389×C127—24no—
19C2×#95×C127C2212yes—
20C2×#95×C127C2214yes—
21C2×#95×C127C2214yes—
22C2×#95×C127C2212yes—
23C2×#95×C127C2212yes—
24C2×#95×C127C2212yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2214yes—
27C2×#95×C127C2212yes—
28C22×Q8×C127—22no—
29C22×Q8×C127—22no—
30C22×Q8×C127—42no—
31C22×Q8×C127—42no—
32C22×Q8×C127D414yes—
33C23×C4×C127C2312yes—
34C23×C4×C127C2312yes—
35C23×C4×C127C2311yescharacteristic
36C23×C4×C127C2312yes—
37C23×C4×C127C2314yes—
38C23×C4×C127C2312yes—
39C23×C4×C127C2311yescharacteristic
40C23×C4×C127C2311yescharacteristic
41C2×C4⋊C4×C127—22no—
42C2×C4⋊C4×C127—24no—
43C2×C4⋊C4×C127—22no—
44C2×C4⋊C4×C127—24no—
45C2×C4⋊C4×C127—22no—
46C2×C4⋊C4×C127—28no—
47C2×C4⋊C4×C127—24no—
48C2×C4⋊C4×C127—24no—
49C2×C4⋊C4×C127—42no—
50C2×C4⋊C4×C127—42no—
51C2×C4⋊C4×C127—44no—
52C2×C4⋊C4×C127—44no—
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—24no—
60#95×C127—28no—
61#95×C127—42no—
62#95×C127—44no—
63#95×C127Q818yescomplemented
64C24×C127C2411yescharacteristic
65C2×Q8×C127—28no—
66C2×Q8×C127—48no—
67C2×Q8×C127—44no—
68C2×Q8×C127—44no—
69C2×Q8×C127—48no—
70C22×C4×C127—22no—
71C22×C4×C127—22no—
72C22×C4×C127—22no—
73C22×C4×C127—22no—
74C22×C4×C127—22no—
75C22×C4×C127—24no—
76C22×C4×C127—22no—
77C22×C4×C127—22no—
78C22×C4×C127—24no—
79C22×C4×C127—22no—
80C22×C4×C127—22no—
81C22×C4×C127—22no—
82C22×C4×C127—22no—
83C22×C4×C127—24no—
84C22×C4×C127—24no—
85C22×C4×C127—24no—
86C22×C4×C127—24no—
87C22×C4×C127—22no—
88C22×C4×C127—22no—
89C22×C4×C127—24no—
90C22×C4×C127—22no—
91C22×C4×C127—24no—
92C22×C4×C127—22no—
93C22×C4×C127—22no—
94C22×C4×C127—22no—
95C22×C4×C127—22no—
96C22×C4×C127—24no—
97C22×C4×C127—22no—
98C22×C4×C127—24no—
99C22×C4×C127—24no—
100C22×C4×C127—24no—
101C22×C4×C127—24no—
102C22×C4×C127C2×D412yes—
103C22×C4×C127C2×D414yes—
104C22×C4×C127C2×D412yes—
105C22×C4×C127C2×D412yes—
106C22×C4×C127C2×D412yes—
107C22×C4×C127C2×Q818yes—
108C22×C4×C127C2×Q814yes—
109C22×C4×C127#4114yes—
110C22×C4×C127#4112yes—
111C4⋊C4×C127—28no—
112C4⋊C4×C127—44no—
113C4⋊C4×C127—44no—
114C4⋊C4×C127—416no—
115C4⋊C4×C127—48no—
116C42×C127—44no—
117C23×C127C22×D411yescharacteristic
118C23×C127C22×D411yescharacteristic
119C23×C127C22×Q812yes—
120C23×C127C2×#4111yescharacteristic
121C23×C127C2×#4112yes—
122C23×C127H(5,𝔽2)12yes—
123C23×C127H(5,𝔽2)12yes—
124C23×C1272−1+412yes—
125C23×C1272−1+412yes—
126Q8×C127—416no—
127C2×C4×C127—22no—
128C2×C4×C127—22no—
129C2×C4×C127—22no—
130C2×C4×C127—24no—
131C2×C4×C127—22no—
132C2×C4×C127—24no—
133C2×C4×C127—28no—
134C2×C4×C127—24no—
135C2×C4×C127—24no—
136C2×C4×C127—22no—
137C2×C4×C127—28no—
138C2×C4×C127—22no—
139C2×C4×C127—22no—
140C2×C4×C127—28no—
141C2×C4×C127—24no—
142C2×C4×C127—28no—
143C2×C4×C127—24no—
144C2×C4×C127—28no—
145C2×C4×C127—42no—
146C2×C4×C127—44no—
147C2×C4×C127—42no—
148C2×C4×C127—42no—
149C2×C4×C127—42no—
150C2×C4×C127—44no—
151C2×C4×C127—44no—
152C2×C4×C127—44no—
153C2×C4×C127—42no—
154C2×C4×C127—42no—
155C2×C4×C127—44no—
156C2×C4×C127—44no—
157C2×C4×C127—42no—
158C2×C4×C127—42no—
159C2×C4×C127—42no—
160C2×C4×C127—44no—
161C2×C4×C127—42no—
162C2×C4×C127—42no—
163C2×C4×C127—42no—
164C2×C4×C127—44no—
165C2×C4×C127—48no—
166C2×C4×C127#12114yes—
167C2×C4×C127C4⋊Q814yes—
168C22×C127C2×#12111yescharacteristic
169C22×C127#52511yescharacteristic
170C22×C127C2×C4⋊Q811yescharacteristic
171C22×C127#53411yescharacteristic
172C22×C127#53412yes—
173C22×C127#53511yescharacteristic
174C22×C127#53611yescharacteristic
175C22×C127#53611yescharacteristic
176C22×C127#53812yes—
177C22×C127#54214yes—
178C22×C127#54414yes—
179C22×C127#54812yes—
180C22×C127D4×Q812yes—
181C22×C127#55212yes—
182C22×C127#55414yes—
183C22×C127#55712yes—
184C22×C127#56314yes—
185C4×C127—24no—
186C4×C127—24no—
187C4×C127—42no—
188C4×C127—44no—
189C4×C127—48no—
190C4×C127—44no—
191C4×C127—82no—
192C4×C127—82no—
193#16993C12711yesmaximal, characteristic, direct product factor, Sylow
194C2×C127#253611yescharacteristic
195C2×C127#254611yescharacteristic
196C2×C127#258311yescharacteristic
197C2×C127#261711yescharacteristic
198C2×C127#263211yescharacteristic
199C2×C127#266011yescharacteristic
200C2×C127#272914yes—
201C2×C127#277414yes—
202C2×C127#281711yescharacteristic
203C2×#395C2×C12712yes—
204C2×#391C2×C12711yescharacteristic
205C2×#389C2×C12711yescharacteristic
206#1444C2×C12712yes—
207#1442C2×C12712yes—
208#1442C2×C12714yes—
209#1441C2×C12712yes—
210#1434C2×C12711yescharacteristic
211C127#1699311yescharacteristic, direct product factor, Sylow
212C23×Q8C22×C12711yescharacteristic
213C22×C4⋊C4C22×C12712yes—
214C22×C4⋊C4C22×C12711yescharacteristic
215C22×C4⋊C4C22×C12714yes—
216C22×C4⋊C4C22×C12711yescharacteristic
217C22×C4⋊C4C22×C12711yescharacteristic
218C22×C42C22×C12711yescharacteristic
219#395—28no—
220#391—24no—
221#389—24no—
222C2×#95C22×C12712yes—
223C2×#95C22×C12714yes—
224C2×#95C22×C12714yes—
225C2×#95C22×C12712yes—
226C2×#95C22×C12712yes—
227C2×#95C22×C12712yes—
228C2×#95C22×C12712yes—
229C2×#95C22×C12714yes—
230C2×#95C22×C12712yes—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—42no—
234C22×Q8—42no—
235C22×Q8D4×C12714yes—
236C23×C4C23×C12712yes—
237C23×C4C23×C12712yes—
238C23×C4C23×C12712yes—
239C23×C4C23×C12711yescharacteristic
240C23×C4C23×C12714yes—
241C23×C4C23×C12712yes—
242C23×C4C23×C12711yescharacteristic
243C23×C4C23×C12711yescharacteristic
244C2×C4⋊C4—22no—
245C2×C4⋊C4—24no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—24no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—28no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—42no—
253C2×C4⋊C4—42no—
254C2×C4⋊C4—44no—
255C2×C4⋊C4—44no—
256C2×C42—42no—
257C2×C42D4×C12714yes—
258#95—24no—
259#95—24no—
260#95—24no—
261#95—28no—
262#95—24no—
263#95—28no—
264#95—42no—
265#95—44no—
266#95Q8×C12718yescomplemented
267C24C24×C12711yescharacteristic
268C2×Q8—28no—
269C2×Q8—48no—
270C2×Q8—44no—
271C2×Q8—44no—
272C2×Q8—48no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—24no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—24no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—24no—
287C22×C4—24no—
288C22×C4—24no—
289C22×C4—24no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—24no—
293C22×C4—22no—
294C22×C4—24no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—24no—
300C22×C4—22no—
301C22×C4—24no—
302C22×C4—24no—
303C22×C4—24no—
304C22×C4—24no—
305C22×C4C2×D4×C12712yes—
306C22×C4C2×D4×C12714yes—
307C22×C4C2×D4×C12712yes—
308C22×C4C2×D4×C12712yes—
309C22×C4C2×D4×C12712yes—
310C22×C4C2×Q8×C12718yes—
311C22×C4C2×Q8×C12714yes—
312C22×C4#41×C12714yes—
313C22×C4#41×C12712yes—
314C4⋊C4—28no—
315C4⋊C4—44no—
316C4⋊C4—44no—
317C4⋊C4—416no—
318C4⋊C4—48no—
319C42—44no—
320C23C22×D4×C12711yescharacteristic
321C23C22×D4×C12711yescharacteristic
322C23C22×Q8×C12712yes—
323C23C2×#41×C12711yescharacteristic
324C23C2×#41×C12712yes—
325C23H(5,𝔽2)×C12712yes—
326C23H(5,𝔽2)×C12712yes—
327C232−1+4×C12712yes—
328C232−1+4×C12712yes—
329Q8—416no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—24no—
334C2×C4—22no—
335C2×C4—24no—
336C2×C4—28no—
337C2×C4—24no—
338C2×C4—24no—
339C2×C4—22no—
340C2×C4—28no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—28no—
344C2×C4—24no—
345C2×C4—28no—
346C2×C4—24no—
347C2×C4—28no—
348C2×C4—42no—
349C2×C4—44no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—44no—
354C2×C4—44no—
355C2×C4—44no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—44no—
359C2×C4—44no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—44no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—44no—
368C2×C4—48no—
369C2×C4#121×C12714yes—
370C2×C4C4⋊Q8×C12714yes—
371C22C2×#121×C12711yescharacteristic
372C22#525×C12711yescharacteristic
373C22C2×C4⋊Q8×C12711yescharacteristic
374C22#534×C12711yescharacteristic
375C22#534×C12712yes—
376C22#535×C12711yescharacteristic
377C22#536×C12711yescharacteristic
378C22#536×C12711yescharacteristic
379C22#538×C12712yes—
380C22#542×C12714yes—
381C22#544×C12714yes—
382C22#548×C12712yes—
383C22D4×Q8×C12712yes—
384C22#552×C12712yes—
385C22#554×C12714yes—
386C22#557×C12712yes—
387C22#563×C12714yes—
388C4—24no—
389C4—24no—
390C4—44no—
391C4—48no—
392C4—44no—
393C4—42no—
394C4—82no—
395C4—82no—
396C2C127×#253611yescharacteristic
397C2C127×#254611yescharacteristic
398C2C127×#258311yescharacteristic
399C2C127×#261711yescharacteristic
400C2C127×#263211yescharacteristic
401C2C127×#266011yescharacteristic
402C2C127×#272914yes—
403C2C127×#277414yes—
404C2C127×#281711yescharacteristic
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
63. #95×C127Q8semidirect
193. #16993C127direct (N × H)
211. C127#16993direct (N × H)
266. #95Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#395×C1272
C2×#391×C1272
C2×#389×C1272
C127×#14442
C127×#14422
C127×#14412
C127×#14342
#16993127