Finite Group Databasebeta

← C127×#13821 #44577494

Subgroups — C127×#13821 #44577494

Order 32512.

1778 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C127C212yesmaximal
2C2×C4×C4⋊C4×C127C212yesmaximal
3C2×C4×C4⋊C4×C127C212yesmaximal
4C2×C4×C4⋊C4×C127C211yesmaximal, characteristic
5C127×#1436C214yesmaximal
6C127×C4⋊#95C211yesmaximal, characteristic
7C127×#1434C212yesmaximal
8C4×#95×C127C211yesmaximal, characteristic
9C22×C4⋊C4×C127C2212yes—
10C22×C4⋊C4×C127C2214yes—
11C22×C4⋊C4×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C42×C127C2214yes—
14C22×C42×C127C2211yescharacteristic
15C22×C42×C127C2212yes—
16C22×C42×C127C2212yes—
17#389×C127C4116yescomplemented
18C4×C4⋊C4×C127—28no—
19C4×C4⋊C4×C127—28no—
20C4×C4⋊C4×C127C418yescomplemented
21C2×#95×C127C2211yescharacteristic
22C2×#95×C127C2212yes—
23C2×#95×C127C2212yes—
24C2×#95×C127C2214yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2214yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2211yescharacteristic
29C23×C4×C127C2314yes—
30C23×C4×C127C2312yes—
31C23×C4×C127C2311yescharacteristic
32C23×C4×C127C2312yes—
33C23×C4×C127C2312yes—
34C23×C4×C127C2312yes—
35C23×C4×C127C2311yescharacteristic
36C23×C4×C127C2311yescharacteristic
37C2×C4⋊C4×C127—28no—
38C2×C4⋊C4×C127—24no—
39C2×C4⋊C4×C127—28no—
40C2×C4⋊C4×C127—24no—
41C2×C4⋊C4×C127C2×C418yes—
42C2×C4⋊C4×C127C2×C4116yes—
43C2×C4⋊C4×C127C2×C414yes—
44C2×C4⋊C4×C127C2×C418yes—
45C2×C4⋊C4×C127C2×C414yes—
46C2×C4⋊C4×C127D414yes—
47C2×C4⋊C4×C127Q814yes—
48C2×C42×C127—24no—
49C2×C42×C127—24no—
50C2×C42×C127—24no—
51C2×C42×C127—24no—
52C2×C42×C127—24no—
53C2×C42×C127—28no—
54C2×C42×C127—28no—
55C2×C42×C127—44no—
56C2×C42×C127C2×C414yes—
57C2×C42×C127C2×C418yes—
58C2×C42×C127C2×C418yes—
59#95×C127—28no—
60#95×C127—24no—
61#95×C127—22no—
62#95×C127—24no—
63#95×C127—42no—
64#95×C127C2×C418yes—
65#95×C127C2×C4116yes—
66#95×C127D414yes—
67C24×C127C2411yescharacteristic
68C22×C4×C127—22no—
69C22×C4×C127—22no—
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—22no—
79C22×C4×C127—22no—
80C22×C4×C127—22no—
81C22×C4×C127—22no—
82C22×C4×C127—24no—
83C22×C4×C127—24no—
84C22×C4×C127—22no—
85C22×C4×C127—22no—
86C22×C4×C127—22no—
87C22×C4×C127—22no—
88C22×C4×C127—22no—
89C22×C4×C127—24no—
90C22×C4×C127—24no—
91C22×C4×C127—21no—
92C22×C4×C127—24no—
93C22×C4×C127—22no—
94C22×C4×C127—22no—
95C22×C4×C127—24no—
96C22×C4×C127—21no—
97C22×C4×C127C22×C412yes—
98C22×C4×C127C22×C414yes—
99C22×C4×C127C22×C418yes—
100C22×C4×C127C22×C414yes—
101C22×C4×C127C22×C418yes—
102C22×C4×C127C22×C414yes—
103C22×C4×C127C22×C412yes—
104C22×C4×C127C22×C414yes—
105C22×C4×C127C22×C412yes—
106C22×C4×C127C22×C414yes—
107C22×C4×C127C2×D414yes—
108C22×C4×C127C2×D412yes—
109C22×C4×C127C2×D414yes—
110C22×C4×C127C2×D412yes—
111C22×C4×C127C2×Q814yes—
112C22×C4×C127C2×Q812yes—
113C22×C4×C127#4112yes—
114C22×C4×C127#4114yes—
115C22×C4×C127#4114yes—
116C4⋊C4×C127—232no—
117C4⋊C4×C127—216no—
118C4⋊C4×C127C42116yescomplemented
119C4⋊C4×C127C4⋊C4116yescomplemented
120C42×C127—28no—
121C42×C127—216no—
122C42×C127—216no—
123C42×C127—416no—
124C23×C127C23×C411yescharacteristic
125C23×C127C23×C412yes—
126C23×C127C22×D411yescharacteristic
127C23×C127C22×D411yescharacteristic
128C23×C127C22×Q811yescharacteristic
129C23×C127C2×#4112yes—
130C23×C127C2×#4111yescharacteristic
131C23×C127C2×#4112yes—
132C23×C127H(5,𝔽2)11yescharacteristic
133C23×C1272−1+412yes—
134C23×C1272−1+411yescharacteristic
135C2×C4×C127—22no—
136C2×C4×C127—24no—
137C2×C4×C127—24no—
138C2×C4×C127—24no—
139C2×C4×C127—28no—
140C2×C4×C127—24no—
141C2×C4×C127—28no—
142C2×C4×C127—22no—
143C2×C4×C127—24no—
144C2×C4×C127—24no—
145C2×C4×C127—24no—
146C2×C4×C127—24no—
147C2×C4×C127—24no—
148C2×C4×C127—24no—
149C2×C4×C127—24no—
150C2×C4×C127—24no—
151C2×C4×C127—24no—
152C2×C4×C127—24no—
153C2×C4×C127—24no—
154C2×C4×C127—24no—
155C2×C4×C127—22no—
156C2×C4×C127—24no—
157C2×C4×C127—28no—
158C2×C4×C127—28no—
159C2×C4×C127—22no—
160C2×C4×C127—24no—
161C2×C4×C127—24no—
162C2×C4×C127—22no—
163C2×C4×C127—28no—
164C2×C4×C127—44no—
165C2×C4×C127—44no—
166C2×C4×C127—42no—
167C2×C4×C127—44no—
168C2×C4×C127—42no—
169C2×C4×C127—42no—
170C2×C4×C127—42no—
171C2×C4×C127—44no—
172C2×C4×C127—42no—
173C2×C4×C127—42no—
174C2×C4×C127C2×C4218yes—
175C2×C4×C127C2×C4214yes—
176C2×C4×C127C2×C4⋊C418yes—
177C2×C4×C127C2×C4⋊C414yes—
178C2×C4×C127#11714yes—
179C2×C4×C127C4×D414yes—
180C2×C4×C127C4×D418yes—
181C2×C4×C127C4×D418yes—
182C2×C4×C127C4×Q818yes—
183C22×C127C22×C4211yescharacteristic
184C22×C127C22×C4⋊C411yescharacteristic
185C22×C127C2×#11711yescharacteristic
186C22×C127C2×C4×D411yescharacteristic
187C22×C127C2×C4×D412yes—
188C22×C127C2×C4×D412yes—
189C22×C127C2×C4×Q812yes—
190C22×C127C4×#4111yescharacteristic
191C22×C127C4×#4112yes—
192C22×C127#51911yescharacteristic
193C22×C127#51912yes—
194C22×C127#52011yescharacteristic
195C22×C127#52012yes—
196C22×C127D4211yescharacteristic
197C22×C127#54712yes—
198C22×C127#54711yescharacteristic
199C22×C127#54812yes—
200C22×C127D4×Q811yescharacteristic
201C22×C127#55212yes—
202C22×C127#55312yes—
203C22×C127#55411yescharacteristic
204C22×C127#55612yes—
205C22×C127#55712yes—
206C4×C127—24no—
207C4×C127—28no—
208C4×C127—28no—
209C4×C127—28no—
210C4×C127—42no—
211C4×C127—48no—
212C4×C127—44no—
213C4×C127C4×C4⋊C418yescomplemented
214#13821C12711yesmaximal, characteristic, direct product factor, Sylow
215C2×C127C2×C4×C4⋊C411yescharacteristic
216C2×C127C42×D411yescharacteristic
217C2×C127#227611yescharacteristic
218C2×C127#234411yescharacteristic
219C2×C127#234711yescharacteristic
220C2×C127D4×C4⋊C411yescharacteristic
221C2×C127#235111yescharacteristic
222C2×C127#236112yes—
223C2×C127#236212yes—
224C2×C127#236512yes—
225C2×C127#237012yes—
226C2×#389C2×C12712yes—
227C2×C4×C4⋊C4C2×C12712yes—
228C2×C4×C4⋊C4C2×C12712yes—
229C2×C4×C4⋊C4C2×C12711yescharacteristic
230#1436C2×C12714yes—
231C4⋊#95C2×C12711yescharacteristic
232#1434C2×C12712yes—
233C4×#95C2×C12711yescharacteristic
234C127#1382111yescharacteristic, direct product factor, Sylow
235C22×C4⋊C4C22×C12712yes—
236C22×C4⋊C4C22×C12714yes—
237C22×C4⋊C4C22×C12711yescharacteristic
238C22×C4⋊C4C22×C12711yescharacteristic
239C22×C42C22×C12714yes—
240C22×C42C22×C12711yescharacteristic
241C22×C42C22×C12712yes—
242C22×C42C22×C12712yes—
243#389C4×C127116yescomplemented
244C4×C4⋊C4—28no—
245C4×C4⋊C4—28no—
246C4×C4⋊C4C4×C12718yescomplemented
247C2×#95C22×C12711yescharacteristic
248C2×#95C22×C12712yes—
249C2×#95C22×C12712yes—
250C2×#95C22×C12714yes—
251C2×#95C22×C12712yes—
252C2×#95C22×C12714yes—
253C2×#95C22×C12712yes—
254C2×#95C22×C12711yescharacteristic
255C23×C4C23×C12714yes—
256C23×C4C23×C12712yes—
257C23×C4C23×C12711yescharacteristic
258C23×C4C23×C12712yes—
259C23×C4C23×C12712yes—
260C23×C4C23×C12712yes—
261C23×C4C23×C12711yescharacteristic
262C23×C4C23×C12711yescharacteristic
263C2×C4⋊C4—28no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—28no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4C2×C4×C12718yes—
268C2×C4⋊C4C2×C4×C127116yes—
269C2×C4⋊C4C2×C4×C12714yes—
270C2×C4⋊C4C2×C4×C12718yes—
271C2×C4⋊C4C2×C4×C12714yes—
272C2×C4⋊C4D4×C12714yes—
273C2×C4⋊C4Q8×C12714yes—
274C2×C42—24no—
275C2×C42—24no—
276C2×C42—24no—
277C2×C42—24no—
278C2×C42—24no—
279C2×C42—28no—
280C2×C42—28no—
281C2×C42—44no—
282C2×C42C2×C4×C12714yes—
283C2×C42C2×C4×C12718yes—
284C2×C42C2×C4×C12718yes—
285#95—28no—
286#95—24no—
287#95—22no—
288#95—24no—
289#95—42no—
290#95C2×C4×C12718yes—
291#95C2×C4×C127116yes—
292#95D4×C12714yes—
293C24C24×C12711yescharacteristic
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—24no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—24no—
309C22×C4—24no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—24no—
316C22×C4—24no—
317C22×C4—21no—
318C22×C4—24no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—24no—
322C22×C4—21no—
323C22×C4C22×C4×C12712yes—
324C22×C4C22×C4×C12714yes—
325C22×C4C22×C4×C12718yes—
326C22×C4C22×C4×C12714yes—
327C22×C4C22×C4×C12718yes—
328C22×C4C22×C4×C12714yes—
329C22×C4C22×C4×C12712yes—
330C22×C4C22×C4×C12714yes—
331C22×C4C22×C4×C12712yes—
332C22×C4C22×C4×C12714yes—
333C22×C4C2×D4×C12714yes—
334C22×C4C2×D4×C12712yes—
335C22×C4C2×D4×C12714yes—
336C22×C4C2×D4×C12712yes—
337C22×C4C2×Q8×C12714yes—
338C22×C4C2×Q8×C12712yes—
339C22×C4#41×C12712yes—
340C22×C4#41×C12714yes—
341C22×C4#41×C12714yes—
342C4⋊C4—232no—
343C4⋊C4—216no—
344C4⋊C4C42×C127116yescomplemented
345C4⋊C4C4⋊C4×C127116yescomplemented
346C42—28no—
347C42—216no—
348C42—216no—
349C42—416no—
350C23C23×C4×C12711yescharacteristic
351C23C23×C4×C12712yes—
352C23C22×D4×C12711yescharacteristic
353C23C22×D4×C12711yescharacteristic
354C23C22×Q8×C12711yescharacteristic
355C23C2×#41×C12712yes—
356C23C2×#41×C12711yescharacteristic
357C23C2×#41×C12712yes—
358C23H(5,𝔽2)×C12711yescharacteristic
359C232−1+4×C12712yes—
360C232−1+4×C12711yescharacteristic
361C2×C4—22no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—28no—
366C2×C4—24no—
367C2×C4—28no—
368C2×C4—22no—
369C2×C4—24no—
370C2×C4—24no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—24no—
376C2×C4—24no—
377C2×C4—24no—
378C2×C4—24no—
379C2×C4—24no—
380C2×C4—24no—
381C2×C4—22no—
382C2×C4—24no—
383C2×C4—28no—
384C2×C4—28no—
385C2×C4—22no—
386C2×C4—24no—
387C2×C4—24no—
388C2×C4—22no—
389C2×C4—28no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—42no—
393C2×C4—44no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—44no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4C2×C42×C12718yes—
401C2×C4C2×C42×C12714yes—
402C2×C4C2×C4⋊C4×C12718yes—
403C2×C4C2×C4⋊C4×C12714yes—
404C2×C4#117×C12714yes—
405C2×C4C4×D4×C12714yes—
406C2×C4C4×D4×C12718yes—
407C2×C4C4×D4×C12718yes—
408C2×C4C4×Q8×C12718yes—
409C22C22×C42×C12711yescharacteristic
410C22C22×C4⋊C4×C12711yescharacteristic
411C22C2×#117×C12711yescharacteristic
412C22C2×C4×D4×C12711yescharacteristic
413C22C2×C4×D4×C12712yes—
414C22C2×C4×D4×C12712yes—
415C22C2×C4×Q8×C12712yes—
416C22C4×#41×C12711yescharacteristic
417C22C4×#41×C12712yes—
418C22#519×C12711yescharacteristic
419C22#519×C12712yes—
420C22#520×C12711yescharacteristic
421C22#520×C12712yes—
422C22D42×C12711yescharacteristic
423C22#547×C12712yes—
424C22#547×C12711yescharacteristic
425C22#548×C12712yes—
426C22D4×Q8×C12711yescharacteristic
427C22#552×C12712yes—
428C22#553×C12712yes—
429C22#554×C12711yescharacteristic
430C22#556×C12712yes—
431C22#557×C12712yes—
432C4—24no—
433C4—28no—
434C4—28no—
435C4—28no—
436C4—42no—
437C4—48no—
438C4—44no—
439C4C4×C4⋊C4×C12718yescomplemented
440C2C2×C4×C4⋊C4×C12711yescharacteristic
441C2C42×D4×C12711yescharacteristic
442C2C127×#227611yescharacteristic
443C2C127×#234411yescharacteristic
444C2C127×#234711yescharacteristic
445C2D4×C4⋊C4×C12711yescharacteristic
446C2C127×#235111yescharacteristic
447C2C127×#236112yes—
448C2C127×#236212yes—
449C2C127×#236512yes—
450C2C127×#237012yes—
subgroupG/H
center, socle, prime radicalC24×C127C24
commutatorC22C22×C42×C127
Frattini, cosocleC24C24×C127
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
17. #389×C127C4semidirect
20. C4×C4⋊C4×C127C4semidirect
118. C4⋊C4×C127C42semidirect
119. C4⋊C4×C127C4⋊C4semidirect
213. C4×C127C4×C4⋊C4semidirect
214. #13821C127direct (N × H)
234. C127#13821direct (N × H)
243. #389C4×C127semidirect
246. C4×C4⋊C4C4×C127semidirect
344. C4⋊C4C42×C127semidirect
345. C4⋊C4C4⋊C4×C127semidirect
439. C4C4×C4⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C1272
C2×C4×C4⋊C4×C1272
C127×#14362
C127×C4⋊#952
C127×#14342
C4×#95×C1272
#13821127