Finite Group Databasebeta

← C127×#10734 #44574407

Subgroups — C127×#10734 #44574407

Order 32512.

1326 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×M16×C127C211yesmaximal, characteristic
2C2×#407×C127C211yesmaximal, characteristic
3C22×C22⋊C8×C127C211yesmaximal, characteristic
4C2×#341×C127C214yesmaximal, complemented
5C24×C4×C127C2211yescharacteristic
6C22×M16×C127—22no—
7C22×M16×C127—21no—
8C22×M16×C127—28no—
9C22×M16×C127C414yes—
10C22×M16×C127C2212yes—
11C22×M16×C127C2212yes—
12C23×C8×C127—21no—
13C23×C8×C127C2212yes—
14#407×C127—22no—
15#407×C127C414yes—
16C2×C22⋊C8×C127—22no—
17C2×C22⋊C8×C127—22no—
18C2×C22⋊C8×C127—21no—
19C2×C22⋊C8×C127—21no—
20C2×C22⋊C8×C127C412yes—
21C2×C22⋊C8×C127C412yes—
22#341×C127—28no—
23C25×C127Q811yescharacteristic
24C23×C4×C127—24no—
25C23×C4×C127—24no—
26C23×C4×C127C2×C412yes—
27C23×C4×C127C2×C411yescharacteristic
28C23×C4×C127C2×C411yescharacteristic
29C23×C4×C127C2×C412yes—
30C23×C4×C127D412yes—
31C23×C4×C127D412yes—
32C23×C4×C127D411yescharacteristic
33C23×C4×C127D411yescharacteristic
34C23×C4×C127Q811yescharacteristic
35C23×C4×C127C2311yescharacteristic
36C2×M16×C127—216no—
37C2×M16×C127—28no—
38C2×M16×C127—24no—
39C2×M16×C127—22no—
40C2×M16×C127—24no—
41C2×M16×C127—216no—
42C2×M16×C127—22no—
43C2×M16×C127—24no—
44C2×M16×C127—24no—
45C2×M16×C127C2×C414yes—
46C2×M16×C127C2×C414yes—
47C2×M16×C127D418yes—
48C22×C8×C127—28no—
49C22×C8×C127—24no—
50C22×C8×C127—22no—
51C22×C8×C127—24no—
52C22×C8×C127—22no—
53C22×C8×C127—22no—
54C22×C8×C127—22no—
55C22×C8×C127—24no—
56C22×C8×C127C2×C414yes—
57C22⋊C8×C127—24no—
58C22⋊C8×C127—24no—
59C22⋊C8×C127—24no—
60C22⋊C8×C127—24no—
61C24×C127—24no—
62C24×C127—24no—
63C24×C127—42no—
64C24×C127C4⋊C411yescharacteristic
65C24×C127C4⋊C412yes—
66C24×C127C4⋊C412yes—
67C24×C127C4⋊C411yescharacteristic
68C24×C127C2×Q811yescharacteristic
69C22×C4×C127—24no—
70C22×C4×C127—24no—
71C22×C4×C127—24no—
72C22×C4×C127—24no—
73C22×C4×C127—24no—
74C22×C4×C127—28no—
75C22×C4×C127—22no—
76C22×C4×C127—24no—
77C22×C4×C127—22no—
78C22×C4×C127—28no—
79C22×C4×C127—24no—
80C22×C4×C127—22no—
81C22×C4×C127—22no—
82C22×C4×C127C4212yes—
83C22×C4×C127C4212yes—
84C22×C4×C127C22⋊C412yes—
85C22×C4×C127C22⋊C412yes—
86C22×C4×C127C22⋊C412yes—
87C22×C4×C127C22⋊C412yes—
88C22×C4×C127C22⋊C412yes—
89C22×C4×C127C22⋊C412yes—
90C22×C4×C127C4⋊C412yes—
91C22×C4×C127C4⋊C412yes—
92C22×C4×C127C4⋊C411yescharacteristic
93C22×C4×C127C4⋊C411yescharacteristic
94C22×C4×C127C22×C411yescharacteristic
95C22×C4×C127C22×C411yescharacteristic
96C22×C4×C127C22×C411yescharacteristic
97C22×C4×C127C2×D411yescharacteristic
98C22×C4×C127C2×D411yescharacteristic
99C22×C4×C127C2×D414yes—
100C22×C4×C127C2×D411yescharacteristic
101C22×C4×C127#4114yes—
102M16×C127—216no—
103M16×C127—24no—
104M16×C127—28no—
105M16×C127—28no—
106M16×C127—44no—
107M16×C127C22⋊C418yes—
108C2×C8×C127—216no—
109C2×C8×C127—24no—
110C2×C8×C127—28no—
111C2×C8×C127—24no—
112C2×C8×C127—24no—
113C2×C8×C127—28no—
114C2×C8×C127—42no—
115C2×C8×C127—42no—
116C2×C8×C127—44no—
117C2×C8×C127—42no—
118C2×C8×C127—42no—
119C23×C127—22no—
120C23×C127—22no—
121C23×C127—22no—
122C23×C127—22no—
123C23×C127—24no—
124C23×C127—24no—
125C23×C127—24no—
126C23×C127—24no—
127C23×C127—22no—
128C23×C127—22no—
129C23×C127—22no—
130C23×C127—42no—
131C23×C127—42no—
132C23×C127—416no—
133C23×C127#9512yes—
134C23×C127#9512yes—
135C23×C127#10814yes—
136C23×C127C2×C4⋊C411yescharacteristic
137C23×C127C2×C4⋊C411yescharacteristic
138C23×C127C2×C4⋊C411yescharacteristic
139C23×C127C22⋊Q814yes—
140C2×C4×C127—24no—
141C2×C4×C127—24no—
142C2×C4×C127—22no—
143C2×C4×C127—22no—
144C2×C4×C127—24no—
145C2×C4×C127—24no—
146C2×C4×C127—22no—
147C2×C4×C127—22no—
148C2×C4×C127—22no—
149C2×C4×C127—22no—
150C2×C4×C127—24no—
151C2×C4×C127—24no—
152C2×C4×C127—24no—
153C2×C4×C127—24no—
154C2×C4×C127#9512yes—
155C2×C4×C127#9512yes—
156C2×C4×C127C2×C4211yescharacteristic
157C2×C4×C127C2×C22⋊C412yes—
158C2×C4×C127C2×C22⋊C411yescharacteristic
159C2×C4×C127C2×C22⋊C411yescharacteristic
160C2×C4×C127C2×C22⋊C411yescharacteristic
161C2×C4×C127#11712yes—
162C2×C4×C127C4×D414yes—
163C2×C4×C127C4×D414yes—
164C2×C4×C127#12012yes—
165C2×C4×C127#12012yes—
166C2×C4×C127#12114yes—
167C2×C4×C127#12312yes—
168C2×C4×C127#12312yes—
169C8×C127—28no—
170C8×C127—44no—
171C8×C127—44no—
172C22×C127—28no—
173C22×C127—28no—
174C22×C127—22no—
175C22×C127—21no—
176C22×C127—21no—
177C22×C127—22no—
178C22×C127—21no—
179C22×C127—21no—
180C22×C127—22no—
181C22×C127—22no—
182C22×C127—22no—
183C22×C127—48no—
184C22×C127—48no—
185C22×C127—44no—
186C22×C127#34114yescomplemented
187C22×C127C2×#9511yescharacteristic
188C22×C127#38012yes—
189C22×C127#38512yes—
190C22×C127#38512yes—
191C22×C127C2×#10812yes—
192C22×C127#43012yes—
193C4×C127—22no—
194C4×C127—22no—
195C4×C127C4×C22⋊C412yes—
196C4×C127#37911yescharacteristic
197C4×C127#38111yescharacteristic
198C4×C127#38612yes—
199C4×C127#38612yes—
200#10734C12711yesmaximal, characteristic, direct product factor, Sylow
201C2×C127—24no—
202C2×C127—22no—
203C2×C127—22no—
204C2×C127—42no—
205C2×C127C22⋊#9511yescharacteristic
206C2×C127C2×#34111yescharacteristic
207C2×C127#173811yescharacteristic
208C2×C127#185514yes—
209C23×M16C2×C12711yescharacteristic
210C2×#407C2×C12711yescharacteristic
211C22×C22⋊C8C2×C12711yescharacteristic
212C2×#341C2×C12714yescomplemented
213C127#1073411yescharacteristic, direct product factor, Sylow
214C24×C4C22×C12711yescharacteristic
215C22×M16—22no—
216C22×M16—21no—
217C22×M16—28no—
218C22×M16C4×C12714yes—
219C22×M16C22×C12712yes—
220C22×M16C22×C12712yes—
221C23×C8—21no—
222C23×C8C22×C12712yes—
223#407—22no—
224#407C4×C12714yes—
225C2×C22⋊C8—22no—
226C2×C22⋊C8—22no—
227C2×C22⋊C8—21no—
228C2×C22⋊C8—21no—
229C2×C22⋊C8C4×C12712yes—
230C2×C22⋊C8C4×C12712yes—
231#341—28no—
232C25Q8×C12711yescharacteristic
233C23×C4—24no—
234C23×C4—24no—
235C23×C4C2×C4×C12712yes—
236C23×C4C2×C4×C12711yescharacteristic
237C23×C4C2×C4×C12711yescharacteristic
238C23×C4C2×C4×C12712yes—
239C23×C4D4×C12711yescharacteristic
240C23×C4D4×C12712yes—
241C23×C4D4×C12711yescharacteristic
242C23×C4D4×C12712yes—
243C23×C4Q8×C12711yescharacteristic
244C23×C4C23×C12711yescharacteristic
245C2×M16—216no—
246C2×M16—28no—
247C2×M16—24no—
248C2×M16—22no—
249C2×M16—24no—
250C2×M16—216no—
251C2×M16—22no—
252C2×M16—24no—
253C2×M16—24no—
254C2×M16C2×C4×C12714yes—
255C2×M16C2×C4×C12714yes—
256C2×M16D4×C12718yes—
257C22×C8—28no—
258C22×C8—24no—
259C22×C8—22no—
260C22×C8—24no—
261C22×C8—22no—
262C22×C8—22no—
263C22×C8—22no—
264C22×C8—24no—
265C22×C8C2×C4×C12714yes—
266C22⋊C8—24no—
267C22⋊C8—24no—
268C22⋊C8—24no—
269C22⋊C8—24no—
270C24—24no—
271C24—24no—
272C24—42no—
273C24C4⋊C4×C12711yescharacteristic
274C24C4⋊C4×C12712yes—
275C24C4⋊C4×C12712yes—
276C24C4⋊C4×C12711yescharacteristic
277C24C2×Q8×C12711yescharacteristic
278C22×C4—24no—
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—28no—
284C22×C4—22no—
285C22×C4—24no—
286C22×C4—22no—
287C22×C4—28no—
288C22×C4—22no—
289C22×C4—24no—
290C22×C4—22no—
291C22×C4C42×C12712yes—
292C22×C4C42×C12712yes—
293C22×C4C22⋊C4×C12712yes—
294C22×C4C22⋊C4×C12712yes—
295C22×C4C22⋊C4×C12712yes—
296C22×C4C22⋊C4×C12712yes—
297C22×C4C22⋊C4×C12712yes—
298C22×C4C22⋊C4×C12712yes—
299C22×C4C4⋊C4×C12712yes—
300C22×C4C4⋊C4×C12712yes—
301C22×C4C4⋊C4×C12711yescharacteristic
302C22×C4C4⋊C4×C12711yescharacteristic
303C22×C4C22×C4×C12711yescharacteristic
304C22×C4C22×C4×C12711yescharacteristic
305C22×C4C22×C4×C12711yescharacteristic
306C22×C4C2×D4×C12711yescharacteristic
307C22×C4C2×D4×C12711yescharacteristic
308C22×C4C2×D4×C12711yescharacteristic
309C22×C4C2×D4×C12714yes—
310C22×C4#41×C12714yes—
311M16—216no—
312M16—24no—
313M16—28no—
314M16—28no—
315M16—44no—
316M16C22⋊C4×C12718yes—
317C2×C8—216no—
318C2×C8—24no—
319C2×C8—28no—
320C2×C8—24no—
321C2×C8—24no—
322C2×C8—28no—
323C2×C8—42no—
324C2×C8—42no—
325C2×C8—44no—
326C2×C8—42no—
327C2×C8—42no—
328C23—22no—
329C23—22no—
330C23—22no—
331C23—22no—
332C23—24no—
333C23—24no—
334C23—24no—
335C23—24no—
336C23—22no—
337C23—22no—
338C23—22no—
339C23—42no—
340C23—42no—
341C23—416no—
342C23#95×C12712yes—
343C23#95×C12712yes—
344C23#108×C12714yes—
345C23C2×C4⋊C4×C12711yescharacteristic
346C23C2×C4⋊C4×C12711yescharacteristic
347C23C2×C4⋊C4×C12711yescharacteristic
348C23C22⋊Q8×C12714yes—
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—24no—
354C2×C4—24no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—24no—
360C2×C4—24no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4#95×C12712yes—
364C2×C4#95×C12712yes—
365C2×C4C2×C42×C12711yescharacteristic
366C2×C4C2×C22⋊C4×C12712yes—
367C2×C4C2×C22⋊C4×C12711yescharacteristic
368C2×C4C2×C22⋊C4×C12711yescharacteristic
369C2×C4C2×C22⋊C4×C12711yescharacteristic
370C2×C4#117×C12712yes—
371C2×C4C4×D4×C12714yes—
372C2×C4C4×D4×C12714yes—
373C2×C4#120×C12712yes—
374C2×C4#120×C12712yes—
375C2×C4#121×C12714yes—
376C2×C4#123×C12712yes—
377C2×C4#123×C12712yes—
378C8—28no—
379C8—44no—
380C8—44no—
381C22—28no—
382C22—28no—
383C22—22no—
384C22—21no—
385C22—21no—
386C22—22no—
387C22—21no—
388C22—21no—
389C22—22no—
390C22—22no—
391C22—22no—
392C22—48no—
393C22—48no—
394C22—44no—
395C22#341×C12714yescomplemented
396C22C2×#95×C12711yescharacteristic
397C22#380×C12712yes—
398C22#385×C12712yes—
399C22#385×C12712yes—
400C22C2×#108×C12712yes—
401C22#430×C12712yes—
402C4—22no—
403C4—22no—
404C4C4×C22⋊C4×C12712yes—
405C4#379×C12711yescharacteristic
406C4#381×C12711yescharacteristic
407C4#386×C12712yes—
408C4#386×C12712yes—
409C2—24no—
410C2—22no—
411C2—22no—
412C2—42no—
413C2C127×C22⋊#9511yescharacteristic
414C2C2×#341×C12711yescharacteristic
415C2C127×#173811yescharacteristic
416C2C127×#185514yes—
subgroupG/H
centerC22×C4×C127C2×D4
commutatorC2×C4C2×C42×C127
Frattini, cosocleC23×C4C23×C127
socleC23×C127C2×C4⋊C4
prime radicalC25×C127Q8
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ C24×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#341×C127C2semidirect
186. C22×C127#341semidirect
200. #10734C127direct (N × H)
212. C2×#341C2×C127semidirect
213. C127#10734direct (N × H)
395. C22#341×C127semidirect

Maximal subgroups

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

subgroupindex
C23×M16×C1272
C2×#407×C1272
C22×C22⋊C8×C1272
C2×#341×C1272
#10734127