Finite Group Databasebeta

← C127×#9471 #44573144

Subgroups — C127×#9471 #44573144

Order 32512.

716 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2973C211yesmaximal, characteristic
2C127×#2409C211yesmaximal, characteristic
3C127×#1799C211yesmaximal, characteristic
4C127×#1787C212yesmaximal, complemented
5C127×#1289C212yesmaximal, complemented
6C23×Q8×C127C2211yescharacteristic
7C2×C22⋊Q8×C127—21no—
8C2×C4×D4×C127C2211yescharacteristic
9#435×C127—24no—
10#432×C127—21no—
11C2×#103×C127—24no—
12C2×#99×C127—21no—
13#407×C127—21no—
14C2×C22⋊C8×C127C2212yes—
15#395×C127C412yescomplemented
16#393×C127C412yescomplemented
17#391×C127—21no—
18#386×C127—21no—
19#385×C127—21no—
20#380×C127C2212yes—
21#380×C127C2211yescharacteristic
22#342×C127—21no—
23C22×Q8×C127—21no—
24C22×Q8×C127—22no—
25C22×Q8×C127—22no—
26C22×Q8×C127—44no—
27C22×Q8×C127C2×C412yes—
28C22×D4×C127D411yescharacteristic
29C23×C4×C127—21no—
30C23×C4×C127D411yescharacteristic
31C23×C4×C127C2311yescharacteristic
32C2×M16×C127—22no—
33C22×C8×C127D414yes—
34C22⋊Q8×C127—44no—
35C4×D4×C127—22no—
36C4×D4×C127—22no—
37C2×C4⋊C4×C127—22no—
38C2×C4⋊C4×C127—21no—
39C2×C4⋊C4×C127—22no—
40C2×C4⋊C4×C127C2×C411yescharacteristic
41C2×C22⋊C4×C127—22no—
42C2×C22⋊C4×C127—21no—
43C2×C22⋊C4×C127—22no—
44C2×C22⋊C4×C127C2×C411yescharacteristic
45C2×C22⋊C4×C127D411yescharacteristic
46C2×C42×C127D411yescharacteristic
47C4⋊C8×C127—22no—
48#103×C127—48no—
49#99×C127—42no—
50C22⋊C8×C127—22no—
51C22⋊C8×C127—22no—
52C22⋊C8×C127—22no—
53#97×C127—22no—
54#95×C127—22no—
55#95×C127—22no—
56#95×C127—22no—
57#95×C127C2×C412yes—
58C24×C127C22⋊C411yescharacteristic
59C24×C127C2×D411yescharacteristic
60C2×Q8×C127—24no—
61C2×Q8×C127—28no—
62C2×Q8×C127—24no—
63C2×Q8×C127—44no—
64C2×Q8×C127—44no—
65C2×Q8×C127—42no—
66C2×Q8×C127—48no—
67C2×Q8×C127—41no—
68C2×Q8×C127—41no—
69C2×D4×C127—22no—
70C2×D4×C127—21no—
71C2×D4×C127—21no—
72C2×D4×C127—22no—
73C22×C4×C127—22no—
74C22×C4×C127—21no—
75C22×C4×C127—21no—
76C22×C4×C127—22no—
77C22×C4×C127—42no—
78C22×C4×C127—44no—
79C22×C4×C127—42no—
80C22×C4×C127—42no—
81C22×C4×C127—42no—
82C22×C4×C127C22⋊C411yescharacteristic
83C22×C4×C127C22⋊C411yescharacteristic
84C22×C4×C127C22⋊C411yescharacteristic
85C22×C4×C127C22×C411yescharacteristic
86C22×C4×C127C2×D412yes—
87C22×C4×C127C2×D411yescharacteristic
88C22×C4×C127#4112yes—
89M16×C127—82no—
90C2×C8×C127—24no—
91C2×C8×C127—44no—
92C4⋊C4×C127—22no—
93C4⋊C4×C127—42no—
94C4⋊C4×C127—44no—
95C4⋊C4×C127—44no—
96C22⋊C4×C127—22no—
97C22⋊C4×C127—22no—
98C22⋊C4×C127—44no—
99C22⋊C4×C127—41no—
100C22⋊C4×C127—41no—
101C22⋊C4×C127—42no—
102C22⋊C4×C127—42no—
103C42×C127—21no—
104C42×C127—21no—
105C23×C127—21no—
106C23×C127—21no—
107C23×C127—21no—
108C23×C127—41no—
109C23×C127—41no—
110C23×C127—41no—
111C23×C127—41no—
112C23×C127C2×C22⋊C411yescharacteristic
113C23×C127#12112yes—
114C23×C127AGL(1,ℤ/8)11yescharacteristic
115C23×C127#13711yescharacteristic
116C23×C127#13712yes—
117Q8×C127—28no—
118Q8×C127—44no—
119Q8×C127—44no—
120Q8×C127—44no—
121D4×C127—42no—
122D4×C127—42no—
123C2×C4×C127—24no—
124C2×C4×C127—22no—
125C2×C4×C127—24no—
126C2×C4×C127—21no—
127C2×C4×C127—21no—
128C2×C4×C127—21no—
129C2×C4×C127—21no—
130C2×C4×C127—21no—
131C2×C4×C127—41no—
132C2×C4×C127—42no—
133C2×C4×C127—42no—
134C2×C4×C127—48no—
135C2×C4×C127—42no—
136C2×C4×C127—42no—
137C2×C4×C127—41no—
138C2×C4×C127—41no—
139C2×C4×C127—42no—
140C2×C4×C127—42no—
141C2×C4×C127—42no—
142C2×C4×C127—81no—
143C2×C4×C127—82no—
144C2×C4×C127—82no—
145C2×C4×C127—82no—
146C2×C4×C127C4×D412yes—
147C2×C4×C127#12011yescharacteristic
148C2×C4×C127#12311yescharacteristic
149C8×C127—44no—
150C22×C127—21no—
151C22×C127—22no—
152C22×C127—21no—
153C22×C127—22no—
154C22×C127—41no—
155C22×C127—41no—
156C22×C127—42no—
157C22×C127—42no—
158C22×C127—41no—
159C22×C127—41no—
160C22×C127—41no—
161C22×C127—81no—
162C22×C127#38611yescharacteristic
163C22×C127#41711yescharacteristic
164C22×C127#41911yescharacteristic
165C22×C127#46812yes—
166C22×C127#47012yes—
167C4×C127—21no—
168C4×C127—22no—
169C4×C127—44no—
170C4×C127—41no—
171C4×C127—41no—
172C4×C127—41no—
173C4×C127—82no—
174C4×C127—162no—
175C4×C127B(4,𝔽2)12yes—
176#9471C12711yesmaximal, characteristic, direct product factor, Sylow
177C2×C127—21no—
178C2×C127—22no—
179C2×C127—21no—
180C2×C127—22no—
181C2×C127—81no—
182C2×C127#188911yescharacteristic
183C2×C127#189411yescharacteristic
184C2×C127#190911yescharacteristic
185#2973C2×C12711yescharacteristic
186#2409C2×C12711yescharacteristic
187#1799C2×C12711yescharacteristic
188#1787C2×C12712yescomplemented
189#1289C2×C12712yescomplemented
190C127#947111yescharacteristic, direct product factor, Sylow
191C23×Q8C22×C12711yescharacteristic
192C2×C22⋊Q8—21no—
193C2×C4×D4C22×C12711yescharacteristic
194#435—24no—
195#432—21no—
196C2×#103—24no—
197C2×#99—21no—
198#407—21no—
199C2×C22⋊C8C22×C12712yes—
200#395C4×C12712yescomplemented
201#393C4×C12712yescomplemented
202#391—21no—
203#386—21no—
204#385—21no—
205#380C22×C12712yes—
206#380C22×C12711yescharacteristic
207#342—21no—
208C22×Q8—21no—
209C22×Q8—22no—
210C22×Q8—22no—
211C22×Q8—44no—
212C22×Q8C2×C4×C12712yes—
213C22×D4D4×C12711yescharacteristic
214C23×C4—21no—
215C23×C4D4×C12711yescharacteristic
216C23×C4C23×C12711yescharacteristic
217C2×M16—22no—
218C22×C8D4×C12714yes—
219C22⋊Q8—44no—
220C4×D4—22no—
221C4×D4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4C2×C4×C12711yescharacteristic
226C2×C22⋊C4—22no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4C2×C4×C12711yescharacteristic
230C2×C22⋊C4D4×C12711yescharacteristic
231C2×C42D4×C12711yescharacteristic
232C4⋊C8—22no—
233#103—48no—
234#99—42no—
235C22⋊C8—22no—
236C22⋊C8—22no—
237C22⋊C8—22no—
238#97—22no—
239#95—22no—
240#95—22no—
241#95—22no—
242#95C2×C4×C12712yes—
243C24C22⋊C4×C12711yescharacteristic
244C24C2×D4×C12711yescharacteristic
245C2×Q8—24no—
246C2×Q8—28no—
247C2×Q8—24no—
248C2×Q8—44no—
249C2×Q8—44no—
250C2×Q8—42no—
251C2×Q8—48no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×D4—22no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—22no—
258C22×C4—22no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—22no—
262C22×C4—42no—
263C22×C4—44no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4C22⋊C4×C12711yescharacteristic
268C22×C4C22⋊C4×C12711yescharacteristic
269C22×C4C22⋊C4×C12711yescharacteristic
270C22×C4C22×C4×C12711yescharacteristic
271C22×C4C2×D4×C12712yes—
272C22×C4C2×D4×C12711yescharacteristic
273C22×C4#41×C12712yes—
274M16—82no—
275C2×C8—24no—
276C2×C8—44no—
277C4⋊C4—22no—
278C4⋊C4—42no—
279C4⋊C4—44no—
280C4⋊C4—44no—
281C22⋊C4—22no—
282C22⋊C4—22no—
283C22⋊C4—44no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C42—21no—
289C42—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23C2×C22⋊C4×C12711yescharacteristic
298C23#121×C12712yes—
299C23AGL(1,ℤ/8)×C12711yescharacteristic
300C23#137×C12711yescharacteristic
301C23#137×C12712yes—
302Q8—28no—
303Q8—44no—
304Q8—44no—
305Q8—44no—
306D4—42no—
307D4—42no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—24no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—48no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—81no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4C4×D4×C12712yes—
332C2×C4#120×C12711yescharacteristic
333C2×C4#123×C12711yescharacteristic
334C8—44no—
335C22—21no—
336C22—22no—
337C22—21no—
338C22—22no—
339C22—41no—
340C22—41no—
341C22—42no—
342C22—42no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—81no—
347C22#386×C12711yescharacteristic
348C22#417×C12711yescharacteristic
349C22#419×C12711yescharacteristic
350C22#468×C12712yes—
351C22#470×C12712yes—
352C4—21no—
353C4—22no—
354C4—44no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—82no—
359C4—162no—
360C4B(4,𝔽2)×C12712yes—
361C2—21no—
362C2—22no—
363C2—21no—
364C2—22no—
365C2—81no—
366C2C127×#188911yescharacteristic
367C2C127×#189411yescharacteristic
368C2C127×#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
4. C127×#1787C2semidirect
5. C127×#1289C2semidirect
15. #395×C127C4semidirect
16. #393×C127C4semidirect
176. #9471C127direct (N × H)
188. #1787C2×C127semidirect
189. #1289C2×C127semidirect
190. C127#9471direct (N × H)
200. #395C4×C127semidirect
201. #393C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#29732
C127×#24092
C127×#17992
C127×#17872
C127×#12892
#9471127