Finite Group Databasebeta

← C127×#9467 #44573140

Subgroups — C127×#9467 #44573140

Order 32512.

738 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2972C211yesmaximal, 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
9C8×D4×C127—24no—
10#431×C127—21no—
11C2×#103×C127—24no—
12C2×#99×C127—21no—
13C2×C22⋊C8×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
32C22×C8×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—
53C4×C8×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—22no—
71C2×D4×C127SD1612yes—
72C2×D4×C127Q1612yes—
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—
89C2×C8×C127—24no—
90C2×C8×C127—44no—
91C2×C8×C127—82no—
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—42no—
100C22⋊C4×C127—42no—
101C22⋊C4×C127—42no—
102C42×C127—21no—
103C42×C127—21no—
104C23×C127—21no—
105C23×C127—21no—
106C23×C127—41no—
107C23×C127—41no—
108C23×C127—41no—
109C23×C127—41no—
110C23×C127#10312yescomplemented
111C23×C127C2×C22⋊C411yescharacteristic
112C23×C127#12112yes—
113C23×C127C2×SD1611yescharacteristic
114C23×C127C2×Q1611yescharacteristic
115C23×C127#13512yes—
116Q8×C127—28no—
117Q8×C127—44no—
118Q8×C127—44no—
119Q8×C127—44no—
120D4×C127—24no—
121D4×C127—24no—
122C2×C4×C127—21no—
123C2×C4×C127—21no—
124C2×C4×C127—24no—
125C2×C4×C127—22no—
126C2×C4×C127—24no—
127C2×C4×C127—21no—
128C2×C4×C127—21no—
129C2×C4×C127—41no—
130C2×C4×C127—42no—
131C2×C4×C127—42no—
132C2×C4×C127—48no—
133C2×C4×C127—42no—
134C2×C4×C127—42no—
135C2×C4×C127—41no—
136C2×C4×C127—41no—
137C2×C4×C127—42no—
138C2×C4×C127—42no—
139C2×C4×C127—42no—
140C2×C4×C127—81no—
141C2×C4×C127—82no—
142C2×C4×C127—82no—
143C2×C4×C127—82no—
144C2×C4×C127#10312yescomplemented
145C2×C4×C127C4×D412yes—
146C2×C4×C127#12011yescharacteristic
147C2×C4×C127#12311yescharacteristic
148C8×C127—44no—
149C22×C127—21no—
150C22×C127—22no—
151C22×C127—21no—
152C22×C127—22no—
153C22×C127—22no—
154C22×C127—41no—
155C22×C127—41no—
156C22×C127—42no—
157C22×C127—42no—
158C22×C127—41no—
159C22×C127—41no—
160C22×C127—81no—
161C22×C127#38611yescharacteristic
162C22×C127C2×#10311yescharacteristic
163C22×C127#41611yescharacteristic
164C22×C127#46512yes—
165C22×C127#46712yes—
166C4×C127—21no—
167C4×C127—22no—
168C4×C127—22no—
169C4×C127—44no—
170C4×C127—41no—
171C4×C127—41no—
172C4×C127—82no—
173C4×C127—162no—
174C4×C127B(4,𝔽2)12yes—
175#9467C12711yesmaximal, characteristic, direct product factor, Sylow
176C2×C127—21no—
177C2×C127—22no—
178C2×C127—21no—
179C2×C127—22no—
180C2×C127—42no—
181C2×C127#188911yescharacteristic
182C2×C127#189211yescharacteristic
183C2×C127#190911yescharacteristic
184#2972C2×C12711yescharacteristic
185#2409C2×C12711yescharacteristic
186#1799C2×C12711yescharacteristic
187#1787C2×C12712yescomplemented
188#1289C2×C12712yescomplemented
189C127#946711yescharacteristic, direct product factor, Sylow
190C23×Q8C22×C12711yescharacteristic
191C2×C22⋊Q8—21no—
192C2×C4×D4C22×C12711yescharacteristic
193C8×D4—24no—
194#431—21no—
195C2×#103—24no—
196C2×#99—21no—
197C2×C22⋊C8—21no—
198C2×C22⋊C8C22×C12712yes—
199#395C4×C12712yescomplemented
200#393C4×C12712yescomplemented
201#391—21no—
202#386—21no—
203#385—21no—
204#380C22×C12712yes—
205#380C22×C12711yescharacteristic
206#342—21no—
207C22×Q8—21no—
208C22×Q8—22no—
209C22×Q8—22no—
210C22×Q8—44no—
211C22×Q8C2×C4×C12712yes—
212C22×D4D4×C12711yescharacteristic
213C23×C4—21no—
214C23×C4D4×C12711yescharacteristic
215C23×C4C23×C12711yescharacteristic
216C22×C8—22no—
217C22×C8D4×C12714yes—
218C22⋊Q8—44no—
219C4×D4—22no—
220C4×D4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4C2×C4×C12711yescharacteristic
225C2×C22⋊C4—22no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—22no—
228C2×C22⋊C4C2×C4×C12711yescharacteristic
229C2×C22⋊C4D4×C12711yescharacteristic
230C2×C42D4×C12711yescharacteristic
231C4⋊C8—22no—
232#103—48no—
233#99—42no—
234C22⋊C8—22no—
235C22⋊C8—22no—
236C22⋊C8—22no—
237C4×C8—22no—
238#95—22no—
239#95—22no—
240#95—22no—
241#95C2×C4×C12712yes—
242C24C22⋊C4×C12711yescharacteristic
243C24C2×D4×C12711yescharacteristic
244C2×Q8—24no—
245C2×Q8—28no—
246C2×Q8—24no—
247C2×Q8—44no—
248C2×Q8—44no—
249C2×Q8—42no—
250C2×Q8—48no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×D4—22no—
254C2×D4—22no—
255C2×D4SD16×C12712yes—
256C2×D4Q16×C12712yes—
257C22×C4—22no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—42no—
262C22×C4—44no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4C22⋊C4×C12711yescharacteristic
267C22×C4C22⋊C4×C12711yescharacteristic
268C22×C4C22⋊C4×C12711yescharacteristic
269C22×C4C22×C4×C12711yescharacteristic
270C22×C4C2×D4×C12712yes—
271C22×C4C2×D4×C12711yescharacteristic
272C22×C4#41×C12712yes—
273C2×C8—24no—
274C2×C8—44no—
275C2×C8—82no—
276C4⋊C4—22no—
277C4⋊C4—42no—
278C4⋊C4—44no—
279C4⋊C4—44no—
280C22⋊C4—22no—
281C22⋊C4—22no—
282C22⋊C4—44no—
283C22⋊C4—42no—
284C22⋊C4—42no—
285C22⋊C4—42no—
286C42—21no—
287C42—21no—
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23#103×C12712yescomplemented
295C23C2×C22⋊C4×C12711yescharacteristic
296C23#121×C12712yes—
297C23C2×SD16×C12711yescharacteristic
298C23C2×Q16×C12711yescharacteristic
299C23#135×C12712yes—
300Q8—28no—
301Q8—44no—
302Q8—44no—
303Q8—44no—
304D4—24no—
305D4—24no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—24no—
309C2×C4—22no—
310C2×C4—24no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—48no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—81no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4#103×C12712yescomplemented
329C2×C4C4×D4×C12712yes—
330C2×C4#120×C12711yescharacteristic
331C2×C4#123×C12711yescharacteristic
332C8—44no—
333C22—21no—
334C22—22no—
335C22—21no—
336C22—22no—
337C22—22no—
338C22—41no—
339C22—41no—
340C22—42no—
341C22—42no—
342C22—41no—
343C22—41no—
344C22—81no—
345C22#386×C12711yescharacteristic
346C22C2×#103×C12711yescharacteristic
347C22#416×C12711yescharacteristic
348C22#465×C12712yes—
349C22#467×C12712yes—
350C4—21no—
351C4—22no—
352C4—22no—
353C4—44no—
354C4—41no—
355C4—41no—
356C4—82no—
357C4—162no—
358C4B(4,𝔽2)×C12712yes—
359C2—21no—
360C2—22no—
361C2—21no—
362C2—22no—
363C2—42no—
364C2C127×#188911yescharacteristic
365C2C127×#189211yescharacteristic
366C2C127×#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
110. C23×C127#103semidirect
144. C2×C4×C127#103semidirect
175. #9467C127direct (N × H)
187. #1787C2×C127semidirect
188. #1289C2×C127semidirect
189. C127#9467direct (N × H)
199. #395C4×C127semidirect
200. #393C4×C127semidirect
294. C23#103×C127semidirect
328. C2×C4#103×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#29722
C127×#24092
C127×#17992
C127×#17872
C127×#12892
#9467127