Finite Group Databasebeta

← C127×#14467 #44578140

Subgroups — C127×#14467 #44578140

Order 32512.

1398 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#391×C127C212yesmaximal
2C2×#391×C127C211yesmaximal, characteristic
3C127×#1444C214yesmaximal
4C127×#1441C212yesmaximal
5C127×#1436C214yesmaximal
6C127×C4⋊#95C212yesmaximal
7C23×Q8×C127C2211yescharacteristic
8C22×C4⋊C4×C127C2212yes—
9C22×C4⋊C4×C127C2212yes—
10C22×C4⋊C4×C127C2212yes—
11C22×C4⋊C4×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2212yes—
13C22×C42×C127C2212yes—
14C22×C42×C127C2211yescharacteristic
15#391×C127—28no—
16#391×C127C418yescomplemented
17C2×#95×C127C2214yes—
18C2×#95×C127C2214yes—
19C2×#95×C127C2214yes—
20C2×#95×C127C2212yes—
21C2×#95×C127C2214yes—
22C2×#95×C127C2214yes—
23C22×Q8×C127—41no—
24C22×Q8×C127—41no—
25C22×Q8×C127—41no—
26C22×Q8×C127—41no—
27C22×Q8×C127C2×C414yes—
28C22×Q8×C127D414yes—
29C22×Q8×C127Q814yes—
30C23×C4×C127C2314yes—
31C23×C4×C127C2312yes—
32C23×C4×C127C2314yes—
33C23×C4×C127C2312yes—
34C23×C4×C127C2311yescharacteristic
35C23×C4×C127C2312yes—
36C2×C4⋊C4×C127—24no—
37C2×C4⋊C4×C127—24no—
38C2×C4⋊C4×C127—41no—
39C2×C4⋊C4×C127—41no—
40C2×C4⋊C4×C127—42no—
41C2×C4⋊C4×C127—42no—
42C2×C4⋊C4×C127—42no—
43C2×C4⋊C4×C127—42no—
44C2×C4⋊C4×C127—42no—
45C2×C4⋊C4×C127—42no—
46C2×C4⋊C4×C127—44no—
47C2×C4⋊C4×C127—42no—
48C2×C4⋊C4×C127C2×C414yes—
49C2×C4⋊C4×C127Q818yescomplemented
50C2×C42×C127—24no—
51C2×C42×C127—41no—
52C2×C42×C127—41no—
53C2×C42×C127—42no—
54C2×C42×C127—42no—
55C2×C42×C127C2×C414yes—
56#95×C127—28no—
57#95×C127—28no—
58#95×C127—28no—
59#95×C127—42no—
60#95×C127—44no—
61#95×C127C2×C4116yes—
62C24×C127C2411yescharacteristic
63C2×Q8×C127—44no—
64C2×Q8×C127—44no—
65C2×Q8×C127—44no—
66C2×Q8×C127—44no—
67C2×Q8×C127—44no—
68C2×Q8×C127—44no—
69C2×Q8×C127C4⋊C4116yescomplemented
70C22×C4×C127—22no—
71C22×C4×C127—22no—
72C22×C4×C127—21no—
73C22×C4×C127—21no—
74C22×C4×C127—22no—
75C22×C4×C127—22no—
76C22×C4×C127—22no—
77C22×C4×C127—21no—
78C22×C4×C127—21no—
79C22×C4×C127—22no—
80C22×C4×C127—22no—
81C22×C4×C127—22no—
82C22×C4×C127—24no—
83C22×C4×C127—24no—
84C22×C4×C127—24no—
85C22×C4×C127—22no—
86C22×C4×C127—24no—
87C22×C4×C127—24no—
88C22×C4×C127—24no—
89C22×C4×C127—22no—
90C22×C4×C127—24no—
91C22×C4×C127—24no—
92C22×C4×C127—24no—
93C22×C4×C127—24no—
94C22×C4×C127—24no—
95C22×C4×C127—24no—
96C22×C4×C127—24no—
97C22×C4×C127—24no—
98C22×C4×C127—24no—
99C22×C4×C127C22×C414yes—
100C22×C4×C127C22×C414yes—
101C22×C4×C127C22×C412yes—
102C22×C4×C127C22×C414yes—
103C22×C4×C127C2×D412yes—
104C22×C4×C127C2×D414yes—
105C22×C4×C127C2×Q818yes—
106C22×C4×C127C2×Q814yes—
107C22×C4×C127C2×Q812yes—
108C22×C4×C127C2×Q814yes—
109C22×C4×C127#4114yes—
110C4⋊C4×C127—44no—
111C4⋊C4×C127—48no—
112C4⋊C4×C127—48no—
113C4⋊C4×C127—48no—
114C4⋊C4×C127—48no—
115C42×C127—44no—
116C42×C127—48no—
117C23×C127C23×C411yescharacteristic
118C23×C127C22×D411yescharacteristic
119C23×C127C22×Q811yescharacteristic
120C23×C127C22×Q812yes—
121C23×C127C2×#4112yes—
122C23×C127H(5,𝔽2)11yescharacteristic
123C23×C127H(5,𝔽2)11yescharacteristic
124C23×C127H(5,𝔽2)11yescharacteristic
125C23×C127H(5,𝔽2)11yescharacteristic
126C23×C127H(5,𝔽2)12yes—
127C23×C1272−1+412yes—
128Q8×C127—416no—
129C2×C4×C127—24no—
130C2×C4×C127—22no—
131C2×C4×C127—22no—
132C2×C4×C127—24no—
133C2×C4×C127—24no—
134C2×C4×C127—24no—
135C2×C4×C127—24no—
136C2×C4×C127—24no—
137C2×C4×C127—22no—
138C2×C4×C127—22no—
139C2×C4×C127—24no—
140C2×C4×C127—24no—
141C2×C4×C127—24no—
142C2×C4×C127—22no—
143C2×C4×C127—24no—
144C2×C4×C127—22no—
145C2×C4×C127—24no—
146C2×C4×C127—24no—
147C2×C4×C127—24no—
148C2×C4×C127—28no—
149C2×C4×C127—28no—
150C2×C4×C127—28no—
151C2×C4×C127—28no—
152C2×C4×C127—44no—
153C2×C4×C127—44no—
154C2×C4×C127—44no—
155C2×C4×C127—42no—
156C2×C4×C127—44no—
157C2×C4×C127—44no—
158C2×C4×C127—42no—
159C2×C4×C127—44no—
160C2×C4×C127—44no—
161C2×C4×C127—44no—
162C2×C4×C127—44no—
163C2×C4×C127—44no—
164C2×C4×C127—44no—
165C2×C4×C127—44no—
166C2×C4×C127C2×C4⋊C418yes—
167C2×C4×C127C2×C4⋊C414yes—
168C2×C4×C127C4×Q818yes—
169C22×C127C22×C4⋊C411yescharacteristic
170C22×C127C2×C4×Q812yes—
171C22×C127#51811yescharacteristic
172C22×C127#51811yescharacteristic
173C22×C127#52012yes—
174C22×C127#53411yescharacteristic
175C22×C127#53411yescharacteristic
176C22×C127#53812yes—
177C22×C127#53912yes—
178C22×C127#54311yescharacteristic
179C22×C127#54311yescharacteristic
180C22×C127#54312yes—
181C22×C127#54412yes—
182C22×C127D4×Q812yes—
183C22×C127#55012yes—
184C22×C127#55412yes—
185C22×C127#55511yescharacteristic
186C22×C127#55712yes—
187C22×C127Q8212yes—
188C22×C127Q8211yescharacteristic
189C22×C127H(3,𝔽4)11yescharacteristic
190C22×C127#56212yes—
191C22×C127#56311yescharacteristic
192C4×C127—24no—
193C4×C127—28no—
194C4×C127—28no—
195C4×C127—44no—
196C4×C127—48no—
197C4×C127—84no—
198#14467C12711yesmaximal, characteristic, direct product factor, Sylow
199C2×C127#231511yescharacteristic
200C2×C127#232912yes—
201C2×C127Q8×C4⋊C412yes—
202C2×C127#236911yescharacteristic
203C2×C127#237911yescharacteristic
204C2×C127#273212yes—
205C2×C127#273311yescharacteristic
206C2×C127#273411yescharacteristic
207C2×C127#280612yes—
208C2×C127#280911yescharacteristic
209C2×C127#281111yescharacteristic
210C2×#391C2×C12712yes—
211C2×#391C2×C12711yescharacteristic
212#1444C2×C12714yes—
213#1441C2×C12712yes—
214#1436C2×C12714yes—
215C4⋊#95C2×C12712yes—
216C127#1446711yescharacteristic, direct product factor, Sylow
217C23×Q8C22×C12711yescharacteristic
218C22×C4⋊C4C22×C12712yes—
219C22×C4⋊C4C22×C12712yes—
220C22×C4⋊C4C22×C12712yes—
221C22×C4⋊C4C22×C12711yescharacteristic
222C22×C4⋊C4C22×C12712yes—
223C22×C42C22×C12712yes—
224C22×C42C22×C12711yescharacteristic
225#391—28no—
226#391C4×C12718yescomplemented
227C2×#95C22×C12714yes—
228C2×#95C22×C12714yes—
229C2×#95C22×C12714yes—
230C2×#95C22×C12712yes—
231C2×#95C22×C12714yes—
232C2×#95C22×C12714yes—
233C22×Q8—41no—
234C22×Q8—41no—
235C22×Q8—41no—
236C22×Q8—41no—
237C22×Q8C2×C4×C12714yes—
238C22×Q8D4×C12714yes—
239C22×Q8Q8×C12714yes—
240C23×C4C23×C12714yes—
241C23×C4C23×C12712yes—
242C23×C4C23×C12714yes—
243C23×C4C23×C12712yes—
244C23×C4C23×C12711yescharacteristic
245C23×C4C23×C12712yes—
246C2×C4⋊C4—24no—
247C2×C4⋊C4—24no—
248C2×C4⋊C4—41no—
249C2×C4⋊C4—41no—
250C2×C4⋊C4—42no—
251C2×C4⋊C4—42no—
252C2×C4⋊C4—42no—
253C2×C4⋊C4—42no—
254C2×C4⋊C4—42no—
255C2×C4⋊C4—42no—
256C2×C4⋊C4—44no—
257C2×C4⋊C4—42no—
258C2×C4⋊C4C2×C4×C12714yes—
259C2×C4⋊C4Q8×C12718yescomplemented
260C2×C42—24no—
261C2×C42—41no—
262C2×C42—41no—
263C2×C42—42no—
264C2×C42—42no—
265C2×C42C2×C4×C12714yes—
266#95—28no—
267#95—28no—
268#95—28no—
269#95—42no—
270#95—44no—
271#95C2×C4×C127116yes—
272C24C24×C12711yescharacteristic
273C2×Q8—44no—
274C2×Q8—44no—
275C2×Q8—44no—
276C2×Q8—44no—
277C2×Q8—44no—
278C2×Q8—44no—
279C2×Q8C4⋊C4×C127116yescomplemented
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—24no—
293C22×C4—24no—
294C22×C4—24no—
295C22×C4—22no—
296C22×C4—24no—
297C22×C4—24no—
298C22×C4—24no—
299C22×C4—22no—
300C22×C4—24no—
301C22×C4—24no—
302C22×C4—24no—
303C22×C4—24no—
304C22×C4—24no—
305C22×C4—24no—
306C22×C4—24no—
307C22×C4—24no—
308C22×C4—24no—
309C22×C4C22×C4×C12714yes—
310C22×C4C22×C4×C12714yes—
311C22×C4C22×C4×C12712yes—
312C22×C4C22×C4×C12714yes—
313C22×C4C2×D4×C12712yes—
314C22×C4C2×D4×C12714yes—
315C22×C4C2×Q8×C12718yes—
316C22×C4C2×Q8×C12714yes—
317C22×C4C2×Q8×C12712yes—
318C22×C4C2×Q8×C12714yes—
319C22×C4#41×C12714yes—
320C4⋊C4—44no—
321C4⋊C4—48no—
322C4⋊C4—48no—
323C4⋊C4—48no—
324C4⋊C4—48no—
325C42—44no—
326C42—48no—
327C23C23×C4×C12711yescharacteristic
328C23C22×D4×C12711yescharacteristic
329C23C22×Q8×C12711yescharacteristic
330C23C22×Q8×C12712yes—
331C23C2×#41×C12712yes—
332C23H(5,𝔽2)×C12711yescharacteristic
333C23H(5,𝔽2)×C12711yescharacteristic
334C23H(5,𝔽2)×C12711yescharacteristic
335C23H(5,𝔽2)×C12711yescharacteristic
336C23H(5,𝔽2)×C12712yes—
337C232−1+4×C12712yes—
338Q8—416no—
339C2×C4—22no—
340C2×C4—24no—
341C2×C4—22no—
342C2×C4—24no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—24no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—24no—
352C2×C4—22no—
353C2×C4—24no—
354C2×C4—22no—
355C2×C4—24no—
356C2×C4—24no—
357C2×C4—24no—
358C2×C4—28no—
359C2×C4—28no—
360C2×C4—28no—
361C2×C4—28no—
362C2×C4—44no—
363C2×C4—44no—
364C2×C4—44no—
365C2×C4—42no—
366C2×C4—44no—
367C2×C4—44no—
368C2×C4—42no—
369C2×C4—44no—
370C2×C4—44no—
371C2×C4—44no—
372C2×C4—44no—
373C2×C4—44no—
374C2×C4—44no—
375C2×C4—44no—
376C2×C4C2×C4⋊C4×C12718yes—
377C2×C4C2×C4⋊C4×C12714yes—
378C2×C4C4×Q8×C12718yes—
379C22C22×C4⋊C4×C12711yescharacteristic
380C22C2×C4×Q8×C12712yes—
381C22#518×C12711yescharacteristic
382C22#518×C12711yescharacteristic
383C22#520×C12712yes—
384C22#534×C12711yescharacteristic
385C22#534×C12711yescharacteristic
386C22#538×C12712yes—
387C22#539×C12712yes—
388C22#543×C12711yescharacteristic
389C22#543×C12711yescharacteristic
390C22#543×C12712yes—
391C22#544×C12712yes—
392C22D4×Q8×C12712yes—
393C22#550×C12712yes—
394C22#554×C12712yes—
395C22#555×C12711yescharacteristic
396C22#557×C12712yes—
397C22Q82×C12712yes—
398C22Q82×C12711yescharacteristic
399C22H(3,𝔽4)×C12711yescharacteristic
400C22#562×C12712yes—
401C22#563×C12711yescharacteristic
402C4—24no—
403C4—28no—
404C4—28no—
405C4—44no—
406C4—48no—
407C4—84no—
408C2C127×#231511yescharacteristic
409C2C127×#232912yes—
410C2Q8×C4⋊C4×C12712yes—
411C2C127×#236911yescharacteristic
412C2C127×#237911yescharacteristic
413C2C127×#273212yes—
414C2C127×#273311yescharacteristic
415C2C127×#273411yescharacteristic
416C2C127×#280612yes—
417C2C127×#280911yescharacteristic
418C2C127×#281111yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
16. #391×C127C4semidirect
49. C2×C4⋊C4×C127Q8semidirect
69. C2×Q8×C127C4⋊C4semidirect
198. #14467C127direct (N × H)
216. C127#14467direct (N × H)
226. #391C4×C127semidirect
259. C2×C4⋊C4Q8×C127semidirect
279. C2×Q8C4⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#391×C1272
C127×#14442
C127×#14412
C127×#14362
C127×C4⋊#952
#14467127