Finite Group Databasebeta

← C127×#10570 #44574243

Subgroups — C127×#10570 #44574243

Order 32512.

604 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2659C211yesmaximal, characteristic
2C127×#1853C212yesmaximal
3C127×#1444C211yesmaximal, characteristic
4C127×#1294C212yesmaximal
5C127×#1280C211yesmaximal, characteristic
6C2×C22⋊Q8×C127—21no—
7C22×C4⋊C4×C127—21no—
8C22×C4⋊C4×C127C2211yescharacteristic
9C2×#106×C127—22no—
10C2×C22⋊C8×C127C2212yes—
11#398×C127—22no—
12#395×C127—22no—
13#380×C127—21no—
14#380×C127C2212yes—
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×C127—42no—
35C2×C4⋊C4×C127—42no—
36C2×C4⋊C4×C127—42no—
37C2×C4⋊C4×C127D412yes—
38C2×C4⋊C4×C127D412yes—
39C2×C22⋊C4×C127—22no—
40#106×C127—44no—
41C22⋊C8×C127—22no—
42C22⋊C8×C127Q814yescomplemented
43#95×C127—22no—
44#95×C127—22no—
45#95×C127—22no—
46#95×C127—21no—
47#95×C127—42no—
48#95×C127Q812yescomplemented
49C24×C127C2×D411yescharacteristic
50C2×Q8×C127—42no—
51C2×Q8×C127—81no—
52C2×Q8×C127—81no—
53C22×C4×C127—22no—
54C22×C4×C127—22no—
55C22×C4×C127—21no—
56C22×C4×C127—21no—
57C22×C4×C127—22no—
58C22×C4×C127—21no—
59C22×C4×C127—21no—
60C22×C4×C127—22no—
61C22×C4×C127—22no—
62C22×C4×C127—22no—
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×C127—41no—
78C22×C4×C127—41no—
79C22×C4×C127SD1612yes—
80C22×C4×C127SD1612yes—
81C22×C4×C127C2×D412yes—
82C22×C4×C127C2×Q812yes—
83C22×C4×C127C2×Q811yescharacteristic
84C22×C4×C127#4111yescharacteristic
85C2×C8×C127—24no—
86C2×C8×C127—42no—
87C2×C8×C127—42no—
88C4⋊C4×C127—24no—
89C4⋊C4×C127—42no—
90C4⋊C4×C127—42no—
91C4⋊C4×C127—42no—
92C4⋊C4×C127—42no—
93C4⋊C4×C127—44no—
94C4⋊C4×C127—48no—
95C4⋊C4×C127—81no—
96C4⋊C4×C127—81no—
97C22⋊C4×C127—42no—
98C22⋊C4×C127—42no—
99C23×C127—21no—
100C23×C127—21no—
101C23×C127—21no—
102C23×C127—21no—
103C23×C127#12011yescharacteristic
104C23×C127C22⋊Q811yescharacteristic
105C23×C127C4⋊Q811yescharacteristic
106C23×C127C2×SD1611yescharacteristic
107C23×C127C2×SD1611yescharacteristic
108C23×C127AGL(1,ℤ/8)11yescharacteristic
109C23×C127#13711yescharacteristic
110Q8×C127—84no—
111C2×C4×C127—22no—
112C2×C4×C127—22no—
113C2×C4×C127—24no—
114C2×C4×C127—22no—
115C2×C4×C127—22no—
116C2×C4×C127—42no—
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—41no—
125C2×C4×C127—41no—
126C2×C4×C127—41no—
127C2×C4×C127—41no—
128C2×C4×C127—42no—
129C2×C4×C127—42no—
130C2×C4×C127—42no—
131C2×C4×C127—42no—
132C2×C4×C127—42no—
133C2×C4×C127—42no—
134C2×C4×C127—42no—
135C2×C4×C127—42no—
136C2×C4×C127—42no—
137C2×C4×C127—42no—
138C2×C4×C127—42no—
139C2×C4×C127—42no—
140C2×C4×C127—81no—
141C2×C4×C127—81no—
142C2×C4×C127—81no—
143C2×C4×C127—81no—
144C2×C4×C127—81no—
145C2×C4×C127—81no—
146C2×C4×C127C22⋊Q812yes—
147C2×C4×C127C4⋊Q812yes—
148C8×C127—44no—
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—21no—
159C22×C127—21no—
160C22×C127—21no—
161C22×C127#39511yescharacteristic
162C22×C127#44811yescharacteristic
163C22×C127#45011yescharacteristic
164C22×C127#45311yescharacteristic
165C22×C127#45611yescharacteristic
166C22×C127B(4,𝔽2)11yescharacteristic
167C22×C127#45811yescharacteristic
168C22×C127#47511yescharacteristic
169C22×C127#47611yescharacteristic
170C22×C127#49811yescharacteristic
171C22×C127#50111yescharacteristic
172C4×C127—22no—
173C4×C127—22no—
174C4×C127—44no—
175C4×C127—42no—
176C4×C127—42no—
177C4×C127—82no—
178C4×C127—82no—
179C4×C127—82no—
180#10570C12711yesmaximal, characteristic, direct product factor, Sylow
181C2×C127—21no—
182C2×C127—21no—
183C2×C127—21no—
184C2×C127—21no—
185C2×C127#159611yescharacteristic
186C2×C127#160411yescharacteristic
187C2×C127#161111yescharacteristic
188C2×C127#161311yescharacteristic
189C2×C127#205811yescharacteristic
190C2×C127#206011yescharacteristic
191C2×C127#206211yescharacteristic
192#2659C2×C12711yescharacteristic
193#1853C2×C12712yes—
194#1444C2×C12711yescharacteristic
195#1294C2×C12712yes—
196#1280C2×C12711yescharacteristic
197C127#1057011yescharacteristic, direct product factor, Sylow
198C2×C22⋊Q8—21no—
199C22×C4⋊C4—21no—
200C22×C4⋊C4C22×C12711yescharacteristic
201C2×#106—22no—
202C2×C22⋊C8C22×C12712yes—
203#398—22no—
204#395—22no—
205#380—21no—
206#380C22×C12712yes—
207C2×#95—21no—
208C2×#95C22×C12711yescharacteristic
209C2×#95C22×C12711yescharacteristic
210#340—22no—
211C22×Q8—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4D4×C12711yescharacteristic
215C23×C4D4×C12711yescharacteristic
216C23×C4C23×C12711yescharacteristic
217C22×C8—22no—
218C22⋊Q8—42no—
219C22⋊Q8—42no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—42no—
226C2×C4⋊C4—42no—
227C2×C4⋊C4—42no—
228C2×C4⋊C4—42no—
229C2×C4⋊C4D4×C12712yes—
230C2×C4⋊C4D4×C12712yes—
231C2×C22⋊C4—22no—
232#106—44no—
233C22⋊C8—22no—
234C22⋊C8Q8×C12714yescomplemented
235#95—22no—
236#95—22no—
237#95—22no—
238#95—21no—
239#95—42no—
240#95Q8×C12712yescomplemented
241C24C2×D4×C12711yescharacteristic
242C2×Q8—42no—
243C2×Q8—81no—
244C2×Q8—81no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—22no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
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×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4SD16×C12712yes—
272C22×C4SD16×C12712yes—
273C22×C4C2×D4×C12712yes—
274C22×C4C2×Q8×C12712yes—
275C22×C4C2×Q8×C12711yescharacteristic
276C22×C4#41×C12711yescharacteristic
277C2×C8—24no—
278C2×C8—42no—
279C2×C8—42no—
280C4⋊C4—24no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—42no—
284C4⋊C4—42no—
285C4⋊C4—44no—
286C4⋊C4—48no—
287C4⋊C4—81no—
288C4⋊C4—81no—
289C22⋊C4—42no—
290C22⋊C4—42no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23#120×C12711yescharacteristic
296C23C22⋊Q8×C12711yescharacteristic
297C23C4⋊Q8×C12711yescharacteristic
298C23C2×SD16×C12711yescharacteristic
299C23C2×SD16×C12711yescharacteristic
300C23AGL(1,ℤ/8)×C12711yescharacteristic
301C23#137×C12711yescharacteristic
302Q8—84no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—24no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4C22⋊Q8×C12712yes—
339C2×C4C4⋊Q8×C12712yes—
340C8—44no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22#395×C12711yescharacteristic
354C22#448×C12711yescharacteristic
355C22#450×C12711yescharacteristic
356C22#453×C12711yescharacteristic
357C22#456×C12711yescharacteristic
358C22B(4,𝔽2)×C12711yescharacteristic
359C22#458×C12711yescharacteristic
360C22#475×C12711yescharacteristic
361C22#476×C12711yescharacteristic
362C22#498×C12711yescharacteristic
363C22#501×C12711yescharacteristic
364C4—22no—
365C4—22no—
366C4—44no—
367C4—42no—
368C4—42no—
369C4—82no—
370C4—82no—
371C4—82no—
372C2—21no—
373C2—21no—
374C2—21no—
375C2—21no—
376C2C127×#159611yescharacteristic
377C2C127×#160411yescharacteristic
378C2C127×#161111yescharacteristic
379C2C127×#161311yescharacteristic
380C2C127×#205811yescharacteristic
381C2C127×#206011yescharacteristic
382C2C127×#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
42. C22⋊C8×C127Q8semidirect
48. #95×C127Q8semidirect
180. #10570C127direct (N × H)
197. C127#10570direct (N × H)
234. C22⋊C8Q8×C127semidirect
240. #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×#14442
C127×#12942
C127×#12802
#10570127