Finite Group Databasebeta

← C127×#9470 #44573143

Subgroups — C127×#9470 #44573143

Order 32512.

598 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2972C211yesmaximal, 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
9C8×D4×C127—24no—
10#431×C127—21no—
11C2×#99×C127—21no—
12C2×C22⋊C8×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
27C22×C8×C127—22no—
28C22×C8×C127D414yes—
29#123×C127—42no—
30#123×C127—42no—
31C4×D4×C127—22no—
32C4×D4×C127—22no—
33C2×C4⋊C4×C127—22no—
34C2×C4⋊C4×C127—22no—
35C2×C4⋊C4×C127—22no—
36C2×C4⋊C4×C127—21no—
37C2×C4⋊C4×C127—21no—
38C2×C4⋊C4×C127—22no—
39C2×C4⋊C4×C127C2×C412yes—
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#99×C127—42no—
49C22⋊C8×C127—22no—
50C22⋊C8×C127—22no—
51C22⋊C8×C127—22no—
52C4×C8×C127—22no—
53#95×C127—22no—
54#95×C127—22no—
55#95×C127—22no—
56#95×C127C2×C412yes—
57C24×C127C22⋊C411yescharacteristic
58C24×C127C2×D411yescharacteristic
59C2×D4×C127—22no—
60C2×D4×C127—22no—
61C2×D4×C127D812yes—
62C2×D4×C127SD1612yes—
63C22×C4×C127—21no—
64C22×C4×C127—21no—
65C22×C4×C127—22no—
66C22×C4×C127—22no—
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×C127—42no—
74C22×C4×C127C22⋊C411yescharacteristic
75C22×C4×C127C22⋊C411yescharacteristic
76C22×C4×C127C22⋊C411yescharacteristic
77C22×C4×C127C22×C411yescharacteristic
78C22×C4×C127C2×D412yes—
79C22×C4×C127C2×D411yescharacteristic
80C22×C4×C127#4112yes—
81C2×C8×C127—24no—
82C2×C8×C127—44no—
83C2×C8×C127—82no—
84C4⋊C4×C127—22no—
85C4⋊C4×C127—24no—
86C4⋊C4×C127—42no—
87C4⋊C4×C127—44no—
88C4⋊C4×C127—44no—
89C4⋊C4×C127—41no—
90C4⋊C4×C127—41no—
91C22⋊C4×C127—22no—
92C22⋊C4×C127—22no—
93C22⋊C4×C127—44no—
94C22⋊C4×C127—41no—
95C22⋊C4×C127—41no—
96C22⋊C4×C127—42no—
97C22⋊C4×C127—42no—
98C42×C127—21no—
99C42×C127—21no—
100C23×C127—21no—
101C23×C127—21no—
102C23×C127—41no—
103C23×C127—41no—
104C23×C127—41no—
105C23×C127—41no—
106C23×C127#10212yes—
107C23×C127C2×C22⋊C411yescharacteristic
108C23×C127#12112yes—
109C23×C127C2×D811yescharacteristic
110C23×C127C2×SD1611yescharacteristic
111C23×C127#13512yes—
112D4×C127—24no—
113D4×C127—24no—
114C2×C4×C127—21no—
115C2×C4×C127—21no—
116C2×C4×C127—24no—
117C2×C4×C127—22no—
118C2×C4×C127—21no—
119C2×C4×C127—21no—
120C2×C4×C127—41no—
121C2×C4×C127—42no—
122C2×C4×C127—42no—
123C2×C4×C127—41no—
124C2×C4×C127—41no—
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—81no—
132C2×C4×C127—82no—
133C2×C4×C127—82no—
134C2×C4×C127—82no—
135C2×C4×C127—82no—
136C2×C4×C127—82no—
137C2×C4×C127#10212yes—
138C2×C4×C127C4×D412yes—
139C2×C4×C127#12011yescharacteristic
140C2×C4×C127#12311yescharacteristic
141C8×C127—44no—
142C22×C127—21no—
143C22×C127—22no—
144C22×C127—21no—
145C22×C127—22no—
146C22×C127—22no—
147C22×C127—41no—
148C22×C127—41no—
149C22×C127—42no—
150C22×C127—42no—
151C22×C127—41no—
152C22×C127—41no—
153C22×C127—81no—
154C22×C127#38611yescharacteristic
155C22×C127C2×#10211yescharacteristic
156C22×C127#41611yescharacteristic
157C22×C127#46512yes—
158C22×C127#46612yes—
159C4×C127—21no—
160C4×C127—22no—
161C4×C127—22no—
162C4×C127—41no—
163C4×C127—41no—
164C4×C127—82no—
165C4×C127—82no—
166C4×C127—162no—
167C4×C127#45812yes—
168#9470C12711yesmaximal, characteristic, direct product factor, Sylow
169C2×C127—21no—
170C2×C127—22no—
171C2×C127—21no—
172C2×C127—22no—
173C2×C127—42no—
174C2×C127#189011yescharacteristic
175C2×C127#189311yescharacteristic
176C2×C127#190911yescharacteristic
177#2972C2×C12711yescharacteristic
178#2486C2×C12711yescharacteristic
179#1823C2×C12712yescomplemented
180#1799C2×C12711yescharacteristic
181#1289C2×C12712yescomplemented
182C127#947011yescharacteristic, direct product factor, Sylow
183C2×#123—21no—
184C2×C4×D4C22×C12711yescharacteristic
185C22×C4⋊C4C22×C12711yescharacteristic
186C8×D4—24no—
187#431—21no—
188C2×#99—21no—
189C2×C22⋊C8—21no—
190C2×C22⋊C8C22×C12712yes—
191#398C4×C12712yescomplemented
192#397C4×C12712yescomplemented
193#389—21no—
194#381—21no—
195#380—21no—
196#380C22×C12712yes—
197#380C22×C12711yescharacteristic
198#342—21no—
199#340—24no—
200C22×D4D4×C12711yescharacteristic
201C23×C4—21no—
202C23×C4D4×C12711yescharacteristic
203C23×C4C23×C12711yescharacteristic
204C22×C8—22no—
205C22×C8D4×C12714yes—
206#123—42no—
207#123—42no—
208C4×D4—22no—
209C4×D4—22no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4C2×C4×C12712yes—
217C2×C4⋊C4C2×C4×C12711yescharacteristic
218C2×C22⋊C4—22no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—22no—
221C2×C22⋊C4C2×C4×C12711yescharacteristic
222C2×C22⋊C4D4×C12711yescharacteristic
223C2×C42D4×C12711yescharacteristic
224C4⋊C8—22no—
225#99—42no—
226C22⋊C8—22no—
227C22⋊C8—22no—
228C22⋊C8—22no—
229C4×C8—22no—
230#95—22no—
231#95—22no—
232#95—22no—
233#95C2×C4×C12712yes—
234C24C22⋊C4×C12711yescharacteristic
235C24C2×D4×C12711yescharacteristic
236C2×D4—22no—
237C2×D4—22no—
238C2×D4D8×C12712yes—
239C2×D4SD16×C12712yes—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4C22⋊C4×C12711yescharacteristic
252C22×C4C22⋊C4×C12711yescharacteristic
253C22×C4C22⋊C4×C12711yescharacteristic
254C22×C4C22×C4×C12711yescharacteristic
255C22×C4C2×D4×C12712yes—
256C22×C4C2×D4×C12711yescharacteristic
257C22×C4#41×C12712yes—
258C2×C8—24no—
259C2×C8—44no—
260C2×C8—82no—
261C4⋊C4—22no—
262C4⋊C4—24no—
263C4⋊C4—42no—
264C4⋊C4—44no—
265C4⋊C4—44no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C22⋊C4—22no—
269C22⋊C4—22no—
270C22⋊C4—44no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—42no—
274C22⋊C4—42no—
275C42—21no—
276C42—21no—
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23#102×C12712yes—
284C23C2×C22⋊C4×C12711yescharacteristic
285C23#121×C12712yes—
286C23C2×D8×C12711yescharacteristic
287C23C2×SD16×C12711yescharacteristic
288C23#135×C12712yes—
289D4—24no—
290D4—24no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—24no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—81no—
309C2×C4—82no—
310C2×C4—82no—
311C2×C4—82no—
312C2×C4—82no—
313C2×C4—82no—
314C2×C4#102×C12712yes—
315C2×C4C4×D4×C12712yes—
316C2×C4#120×C12711yescharacteristic
317C2×C4#123×C12711yescharacteristic
318C8—44no—
319C22—21no—
320C22—22no—
321C22—21no—
322C22—22no—
323C22—22no—
324C22—41no—
325C22—41no—
326C22—42no—
327C22—42no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22#386×C12711yescharacteristic
332C22C2×#102×C12711yescharacteristic
333C22#416×C12711yescharacteristic
334C22#465×C12712yes—
335C22#466×C12712yes—
336C4—21no—
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—82no—
342C4—82no—
343C4—162no—
344C4#458×C12712yes—
345C2—21no—
346C2—22no—
347C2—21no—
348C2—22no—
349C2—42no—
350C2C127×#189011yescharacteristic
351C2C127×#189311yescharacteristic
352C2C127×#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
168. #9470C127direct (N × H)
179. #1823C2×C127semidirect
181. #1289C2×C127semidirect
182. C127#9470direct (N × H)
191. #398C4×C127semidirect
192. #397C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#29722
C127×#24862
C127×#18232
C127×#17992
C127×#12892
#9470127