Finite Group Databasebeta

← C127×#9474 #44573147

Subgroups — C127×#9474 #44573147

Order 32512.

576 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2973C211yesmaximal, characteristic
2C127×#2486C211yesmaximal, characteristic
3C127×#1823C212yesmaximal, complemented
4C127×#1799C211yesmaximal, characteristic
5C127×#1289C212yesmaximal, complemented
6C2×#123×C127—21no—
7C2×C4×D4×C127C2211yescharacteristic
8C22×C4⋊C4×C127C2211yescharacteristic
9#435×C127—24no—
10#432×C127—21no—
11C2×#99×C127—21no—
12#407×C127—21no—
13C2×C22⋊C8×C127C2212yes—
14#398×C127C412yescomplemented
15#397×C127C412yescomplemented
16#389×C127—21no—
17#381×C127—21no—
18#380×C127—21no—
19#380×C127C2212yes—
20#380×C127C2211yescharacteristic
21#342×C127—21no—
22#340×C127—24no—
23C22×D4×C127D411yescharacteristic
24C23×C4×C127—21no—
25C23×C4×C127D411yescharacteristic
26C23×C4×C127C2311yescharacteristic
27C2×M16×C127—22no—
28C22×C8×C127D414yes—
29#123×C127—44no—
30C4×D4×C127—22no—
31C4×D4×C127—22no—
32C2×C4⋊C4×C127—22no—
33C2×C4⋊C4×C127—22no—
34C2×C4⋊C4×C127—22no—
35C2×C4⋊C4×C127—21no—
36C2×C4⋊C4×C127—21no—
37C2×C4⋊C4×C127—22no—
38C2×C4⋊C4×C127C2×C412yes—
39C2×C4⋊C4×C127C2×C411yescharacteristic
40C2×C22⋊C4×C127—22no—
41C2×C22⋊C4×C127—21no—
42C2×C22⋊C4×C127—22no—
43C2×C22⋊C4×C127C2×C411yescharacteristic
44C2×C22⋊C4×C127D411yescharacteristic
45C2×C42×C127D411yescharacteristic
46C4⋊C8×C127—22no—
47#99×C127—42no—
48C22⋊C8×C127—22no—
49C22⋊C8×C127—22no—
50C22⋊C8×C127—22no—
51#97×C127—22no—
52#95×C127—22no—
53#95×C127—22no—
54#95×C127—22no—
55#95×C127C2×C412yes—
56C24×C127C22⋊C411yescharacteristic
57C24×C127C2×D411yescharacteristic
58C2×D4×C127—22no—
59C2×D4×C127—21no—
60C2×D4×C127—22no—
61C2×D4×C127—21no—
62C22×C4×C127—21no—
63C22×C4×C127—21no—
64C22×C4×C127—22no—
65C22×C4×C127—22no—
66C22×C4×C127—42no—
67C22×C4×C127—42no—
68C22×C4×C127—42no—
69C22×C4×C127—42no—
70C22×C4×C127—41no—
71C22×C4×C127—41no—
72C22×C4×C127—42no—
73C22×C4×C127C22⋊C411yescharacteristic
74C22×C4×C127C22⋊C411yescharacteristic
75C22×C4×C127C22⋊C411yescharacteristic
76C22×C4×C127C22×C411yescharacteristic
77C22×C4×C127C2×D412yes—
78C22×C4×C127C2×D411yescharacteristic
79C22×C4×C127#4112yes—
80M16×C127—82no—
81C2×C8×C127—24no—
82C2×C8×C127—44no—
83C4⋊C4×C127—22no—
84C4⋊C4×C127—24no—
85C4⋊C4×C127—42no—
86C4⋊C4×C127—44no—
87C4⋊C4×C127—44no—
88C4⋊C4×C127—41no—
89C4⋊C4×C127—41no—
90C22⋊C4×C127—22no—
91C22⋊C4×C127—22no—
92C22⋊C4×C127—44no—
93C22⋊C4×C127—42no—
94C22⋊C4×C127—42no—
95C22⋊C4×C127—42no—
96C42×C127—21no—
97C42×C127—21no—
98C23×C127—21no—
99C23×C127—21no—
100C23×C127—21no—
101C23×C127—41no—
102C23×C127—41no—
103C23×C127—41no—
104C23×C127—41no—
105C23×C127C2×C22⋊C411yescharacteristic
106C23×C127#12112yes—
107C23×C127AGL(1,ℤ/8)11yescharacteristic
108C23×C127AGL(1,ℤ/8)12yes—
109C23×C127#13711yescharacteristic
110D4×C127—42no—
111D4×C127—42no—
112C2×C4×C127—24no—
113C2×C4×C127—22no—
114C2×C4×C127—21no—
115C2×C4×C127—21no—
116C2×C4×C127—21no—
117C2×C4×C127—21no—
118C2×C4×C127—21no—
119C2×C4×C127—41no—
120C2×C4×C127—42no—
121C2×C4×C127—42no—
122C2×C4×C127—41no—
123C2×C4×C127—41no—
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—81no—
131C2×C4×C127—82no—
132C2×C4×C127—82no—
133C2×C4×C127—82no—
134C2×C4×C127—82no—
135C2×C4×C127—82no—
136C2×C4×C127C4×D412yes—
137C2×C4×C127#12011yescharacteristic
138C2×C4×C127#12311yescharacteristic
139C8×C127—44no—
140C22×C127—21no—
141C22×C127—22no—
142C22×C127—21no—
143C22×C127—22no—
144C22×C127—42no—
145C22×C127—41no—
146C22×C127—41no—
147C22×C127—42no—
148C22×C127—41no—
149C22×C127—41no—
150C22×C127—41no—
151C22×C127—81no—
152C22×C127#38611yescharacteristic
153C22×C127#41711yescharacteristic
154C22×C127#41811yescharacteristic
155C22×C127#46812yes—
156C22×C127#46912yes—
157C4×C127—21no—
158C4×C127—22no—
159C4×C127—41no—
160C4×C127—41no—
161C4×C127—41no—
162C4×C127—82no—
163C4×C127—82no—
164C4×C127—162no—
165C4×C127#45812yes—
166#9474C12711yesmaximal, characteristic, direct product factor, Sylow
167C2×C127—21no—
168C2×C127—22no—
169C2×C127—21no—
170C2×C127—22no—
171C2×C127—81no—
172C2×C127#189011yescharacteristic
173C2×C127#189511yescharacteristic
174C2×C127#190911yescharacteristic
175#2973C2×C12711yescharacteristic
176#2486C2×C12711yescharacteristic
177#1823C2×C12712yescomplemented
178#1799C2×C12711yescharacteristic
179#1289C2×C12712yescomplemented
180C127#947411yescharacteristic, direct product factor, Sylow
181C2×#123—21no—
182C2×C4×D4C22×C12711yescharacteristic
183C22×C4⋊C4C22×C12711yescharacteristic
184#435—24no—
185#432—21no—
186C2×#99—21no—
187#407—21no—
188C2×C22⋊C8C22×C12712yes—
189#398C4×C12712yescomplemented
190#397C4×C12712yescomplemented
191#389—21no—
192#381—21no—
193#380—21no—
194#380C22×C12712yes—
195#380C22×C12711yescharacteristic
196#342—21no—
197#340—24no—
198C22×D4D4×C12711yescharacteristic
199C23×C4—21no—
200C23×C4D4×C12711yescharacteristic
201C23×C4C23×C12711yescharacteristic
202C2×M16—22no—
203C22×C8D4×C12714yes—
204#123—44no—
205C4×D4—22no—
206C4×D4—22no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4C2×C4×C12712yes—
214C2×C4⋊C4C2×C4×C12711yescharacteristic
215C2×C22⋊C4—22no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4C2×C4×C12711yescharacteristic
219C2×C22⋊C4D4×C12711yescharacteristic
220C2×C42D4×C12711yescharacteristic
221C4⋊C8—22no—
222#99—42no—
223C22⋊C8—22no—
224C22⋊C8—22no—
225C22⋊C8—22no—
226#97—22no—
227#95—22no—
228#95—22no—
229#95—22no—
230#95C2×C4×C12712yes—
231C24C22⋊C4×C12711yescharacteristic
232C24C2×D4×C12711yescharacteristic
233C2×D4—22no—
234C2×D4—21no—
235C2×D4—22no—
236C2×D4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—42no—
248C22×C4C22⋊C4×C12711yescharacteristic
249C22×C4C22⋊C4×C12711yescharacteristic
250C22×C4C22⋊C4×C12711yescharacteristic
251C22×C4C22×C4×C12711yescharacteristic
252C22×C4C2×D4×C12712yes—
253C22×C4C2×D4×C12711yescharacteristic
254C22×C4#41×C12712yes—
255M16—82no—
256C2×C8—24no—
257C2×C8—44no—
258C4⋊C4—22no—
259C4⋊C4—24no—
260C4⋊C4—42no—
261C4⋊C4—44no—
262C4⋊C4—44no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C22⋊C4—22no—
266C22⋊C4—22no—
267C22⋊C4—44no—
268C22⋊C4—42no—
269C22⋊C4—42no—
270C22⋊C4—42no—
271C42—21no—
272C42—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23C2×C22⋊C4×C12711yescharacteristic
281C23#121×C12712yes—
282C23AGL(1,ℤ/8)×C12711yescharacteristic
283C23AGL(1,ℤ/8)×C12712yes—
284C23#137×C12711yescharacteristic
285D4—42no—
286D4—42no—
287C2×C4—24no—
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—81no—
306C2×C4—82no—
307C2×C4—82no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4—82no—
311C2×C4C4×D4×C12712yes—
312C2×C4#120×C12711yescharacteristic
313C2×C4#123×C12711yescharacteristic
314C8—44no—
315C22—21no—
316C22—22no—
317C22—21no—
318C22—22no—
319C22—42no—
320C22—41no—
321C22—41no—
322C22—42no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—81no—
327C22#386×C12711yescharacteristic
328C22#417×C12711yescharacteristic
329C22#418×C12711yescharacteristic
330C22#468×C12712yes—
331C22#469×C12712yes—
332C4—21no—
333C4—22no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—82no—
338C4—82no—
339C4—162no—
340C4#458×C12712yes—
341C2—21no—
342C2—22no—
343C2—21no—
344C2—22no—
345C2—81no—
346C2C127×#189011yescharacteristic
347C2C127×#189511yescharacteristic
348C2C127×#190911yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC22×D4×C127D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1823C2semidirect
5. C127×#1289C2semidirect
14. #398×C127C4semidirect
15. #397×C127C4semidirect
166. #9474C127direct (N × H)
177. #1823C2×C127semidirect
179. #1289C2×C127semidirect
180. C127#9474direct (N × H)
189. #398C4×C127semidirect
190. #397C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#29732
C127×#24862
C127×#18232
C127×#17992
C127×#12892
#9474127