Finite Group Databasebeta

← C127×#10568 #44574241

Subgroups — C127×#10568 #44574241

Order 32512.

560 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2659C211yesmaximal, characteristic
2C127×#1853C212yesmaximal
3C127×#1442C211yesmaximal, characteristic
4C127×#1294C212yesmaximal
5C127×#1280C211yesmaximal, characteristic
6C2×C22⋊Q8×C127—21no—
7C22×C4⋊C4×C127C2211yescharacteristic
8C2×#106×C127—22no—
9C2×C22⋊C8×C127C2212yes—
10#398×C127—22no—
11#395×C127—22no—
12#380×C127—21no—
13#380×C127C2212yes—
14C2×#95×C127—21no—
15C2×#95×C127—21no—
16C2×#95×C127C2211yescharacteristic
17C2×#95×C127C2211yescharacteristic
18#340×C127—22no—
19C22×Q8×C127—21no—
20C23×C4×C127—21no—
21C23×C4×C127—21no—
22C23×C4×C127D411yescharacteristic
23C23×C4×C127D411yescharacteristic
24C23×C4×C127C2311yescharacteristic
25C22×C8×C127—22no—
26C22⋊Q8×C127—42no—
27C22⋊Q8×C127—42no—
28C2×C4⋊C4×C127—22no—
29C2×C4⋊C4×C127—22no—
30C2×C4⋊C4×C127—21no—
31C2×C4⋊C4×C127—21no—
32C2×C4⋊C4×C127—21no—
33C2×C4⋊C4×C127—42no—
34C2×C4⋊C4×C127D412yes—
35C2×C4⋊C4×C127D412yes—
36C2×C22⋊C4×C127—22no—
37#106×C127—44no—
38C22⋊C8×C127—22no—
39C22⋊C8×C127Q814yescomplemented
40#95×C127—22no—
41#95×C127—22no—
42#95×C127—22no—
43#95×C127—21no—
44#95×C127—42no—
45#95×C127—42no—
46#95×C127Q812yescomplemented
47C24×C127C2×D411yescharacteristic
48C2×Q8×C127—42no—
49C2×Q8×C127—81no—
50C2×Q8×C127—81no—
51C22×C4×C127—21no—
52C22×C4×C127—21no—
53C22×C4×C127—21no—
54C22×C4×C127—21no—
55C22×C4×C127—22no—
56C22×C4×C127—22no—
57C22×C4×C127—22no—
58C22×C4×C127—22no—
59C22×C4×C127—41no—
60C22×C4×C127—41no—
61C22×C4×C127—41no—
62C22×C4×C127—41no—
63C22×C4×C127—41no—
64C22×C4×C127—41no—
65C22×C4×C127—41no—
66C22×C4×C127—41no—
67C22×C4×C127—41no—
68C22×C4×C127—41no—
69C22×C4×C127—41no—
70C22×C4×C127—41no—
71C22×C4×C127—41no—
72C22×C4×C127—41no—
73C22×C4×C127—41no—
74C22×C4×C127—41no—
75C22×C4×C127—41no—
76C22×C4×C127—41no—
77C22×C4×C127SD1612yes—
78C22×C4×C127SD1612yes—
79C22×C4×C127C2×D412yes—
80C22×C4×C127C2×Q812yes—
81C22×C4×C127C2×Q811yescharacteristic
82C22×C4×C127#4111yescharacteristic
83C2×C8×C127—24no—
84C2×C8×C127—42no—
85C2×C8×C127—42no—
86C4⋊C4×C127—24no—
87C4⋊C4×C127—42no—
88C4⋊C4×C127—42no—
89C4⋊C4×C127—42no—
90C4⋊C4×C127—42no—
91C4⋊C4×C127—44no—
92C4⋊C4×C127—81no—
93C4⋊C4×C127—81no—
94C22⋊C4×C127—42no—
95C22⋊C4×C127—42no—
96C23×C127—21no—
97C23×C127—21no—
98C23×C127—21no—
99C23×C127—21no—
100C23×C127#12011yescharacteristic
101C23×C127C22⋊Q811yescharacteristic
102C23×C127C4⋊Q811yescharacteristic
103C23×C127C2×SD1611yescharacteristic
104C23×C127C2×SD1611yescharacteristic
105C23×C127AGL(1,ℤ/8)11yescharacteristic
106C23×C127#13711yescharacteristic
107Q8×C127—84no—
108C2×C4×C127—22no—
109C2×C4×C127—22no—
110C2×C4×C127—22no—
111C2×C4×C127—22no—
112C2×C4×C127—42no—
113C2×C4×C127—41no—
114C2×C4×C127—41no—
115C2×C4×C127—41no—
116C2×C4×C127—41no—
117C2×C4×C127—41no—
118C2×C4×C127—41no—
119C2×C4×C127—42no—
120C2×C4×C127—42no—
121C2×C4×C127—42no—
122C2×C4×C127—42no—
123C2×C4×C127—42no—
124C2×C4×C127—42no—
125C2×C4×C127—42no—
126C2×C4×C127—42no—
127C2×C4×C127—42no—
128C2×C4×C127—42no—
129C2×C4×C127—42no—
130C2×C4×C127—42no—
131C2×C4×C127—42no—
132C2×C4×C127—42no—
133C2×C4×C127—81no—
134C2×C4×C127—81no—
135C2×C4×C127—81no—
136C2×C4×C127—81no—
137C2×C4×C127—81no—
138C2×C4×C127—81no—
139C2×C4×C127—81no—
140C2×C4×C127—81no—
141C2×C4×C127—81no—
142C2×C4×C127—81no—
143C2×C4×C127C22⋊Q812yes—
144C2×C4×C127C4⋊Q812yes—
145C8×C127—44no—
146C22×C127—21no—
147C22×C127—21no—
148C22×C127—21no—
149C22×C127—21no—
150C22×C127—21no—
151C22×C127—21no—
152C22×C127—21no—
153C22×C127—21no—
154C22×C127—21no—
155C22×C127—21no—
156C22×C127—21no—
157C22×C127—21no—
158C22×C127#39511yescharacteristic
159C22×C127#44811yescharacteristic
160C22×C127#45011yescharacteristic
161C22×C127#45411yescharacteristic
162C22×C127#45511yescharacteristic
163C22×C127B(4,𝔽2)11yescharacteristic
164C22×C127#45811yescharacteristic
165C22×C127#47511yescharacteristic
166C22×C127#47611yescharacteristic
167C22×C127#49811yescharacteristic
168C22×C127#50111yescharacteristic
169C4×C127—22no—
170C4×C127—22no—
171C4×C127—42no—
172C4×C127—42no—
173C4×C127—82no—
174C4×C127—82no—
175C4×C127—82no—
176C4×C127—82no—
177#10568C12711yesmaximal, characteristic, direct product factor, Sylow
178C2×C127—21no—
179C2×C127—21no—
180C2×C127—21no—
181C2×C127—21no—
182C2×C127#159911yescharacteristic
183C2×C127#160111yescharacteristic
184C2×C127#160811yescharacteristic
185C2×C127#161611yescharacteristic
186C2×C127#205811yescharacteristic
187C2×C127#206111yescharacteristic
188C2×C127#206211yescharacteristic
189#2659C2×C12711yescharacteristic
190#1853C2×C12712yes—
191#1442C2×C12711yescharacteristic
192#1294C2×C12712yes—
193#1280C2×C12711yescharacteristic
194C127#1056811yescharacteristic, direct product factor, Sylow
195C2×C22⋊Q8—21no—
196C22×C4⋊C4C22×C12711yescharacteristic
197C2×#106—22no—
198C2×C22⋊C8C22×C12712yes—
199#398—22no—
200#395—22no—
201#380—21no—
202#380C22×C12712yes—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95C22×C12711yescharacteristic
206C2×#95C22×C12711yescharacteristic
207#340—22no—
208C22×Q8—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4D4×C12711yescharacteristic
212C23×C4D4×C12711yescharacteristic
213C23×C4C23×C12711yescharacteristic
214C22×C8—22no—
215C22⋊Q8—42no—
216C22⋊Q8—42no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—42no—
223C2×C4⋊C4D4×C12712yes—
224C2×C4⋊C4D4×C12712yes—
225C2×C22⋊C4—22no—
226#106—44no—
227C22⋊C8—22no—
228C22⋊C8Q8×C12714yescomplemented
229#95—22no—
230#95—22no—
231#95—22no—
232#95—21no—
233#95—42no—
234#95—42no—
235#95Q8×C12712yescomplemented
236C24C2×D4×C12711yescharacteristic
237C2×Q8—42no—
238C2×Q8—81no—
239C2×Q8—81no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4SD16×C12712yes—
267C22×C4SD16×C12712yes—
268C22×C4C2×D4×C12712yes—
269C22×C4C2×Q8×C12712yes—
270C22×C4C2×Q8×C12711yescharacteristic
271C22×C4#41×C12711yescharacteristic
272C2×C8—24no—
273C2×C8—42no—
274C2×C8—42no—
275C4⋊C4—24no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4—44no—
281C4⋊C4—81no—
282C4⋊C4—81no—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23#120×C12711yescharacteristic
290C23C22⋊Q8×C12711yescharacteristic
291C23C4⋊Q8×C12711yescharacteristic
292C23C2×SD16×C12711yescharacteristic
293C23C2×SD16×C12711yescharacteristic
294C23AGL(1,ℤ/8)×C12711yescharacteristic
295C23#137×C12711yescharacteristic
296Q8—84no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4C22⋊Q8×C12712yes—
333C2×C4C4⋊Q8×C12712yes—
334C8—44no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22#395×C12711yescharacteristic
348C22#448×C12711yescharacteristic
349C22#450×C12711yescharacteristic
350C22#454×C12711yescharacteristic
351C22#455×C12711yescharacteristic
352C22B(4,𝔽2)×C12711yescharacteristic
353C22#458×C12711yescharacteristic
354C22#475×C12711yescharacteristic
355C22#476×C12711yescharacteristic
356C22#498×C12711yescharacteristic
357C22#501×C12711yescharacteristic
358C4—22no—
359C4—22no—
360C4—42no—
361C4—42no—
362C4—82no—
363C4—82no—
364C4—82no—
365C4—82no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—21no—
370C2C127×#159911yescharacteristic
371C2C127×#160111yescharacteristic
372C2C127×#160811yescharacteristic
373C2C127×#161611yescharacteristic
374C2C127×#205811yescharacteristic
375C2C127×#206111yescharacteristic
376C2C127×#206211yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutator, Frattini, cosocleC23×C4C23×C127
prime radicalC24×C127C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
39. C22⋊C8×C127Q8semidirect
46. #95×C127Q8semidirect
177. #10568C127direct (N × H)
194. C127#10568direct (N × H)
228. C22⋊C8Q8×C127semidirect
235. #95Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#26592
C127×#18532
C127×#14422
C127×#12942
C127×#12802
#10568127