Finite Group Databasebeta

← C127×#9640 #44573313

Subgroups — C127×#9640 #44573313

Order 32512.

582 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#124×C127C211yesmaximal, characteristic
2C127×#1842C211yesmaximal, characteristic, complemented
3C127×#1744C211yesmaximal, characteristic, complemented
4C2×Q8⋊C8×C127C212yesmaximal, complemented
5C2×D4⋊C8×C127C212yesmaximal
6C2×#124×C127C411yescharacteristic
7C2×C4×Q8×C127C2211yescharacteristic
8C2×C4×D4×C127C2211yescharacteristic
9C2×C4⋊C8×C127—22no—
10C2×C4⋊C8×C127C2212yes—
11C2×C4×C8×C127C2212yes—
12#391×C127C411yescharacteristic
13#390×C127C411yescharacteristic
14#388×C127—22no—
15#382×C127C411yescharacteristic
16C4×C22⋊C4×C127—22no—
17C43×C127C2211yescharacteristic
18#336×C127—22no—
19Q8⋊C8×C127—24no—
20D4⋊C8×C127—24no—
21C22×Q8×C127C2×C411yescharacteristic
22C22×D4×C127C2×C411yescharacteristic
23C23×C4×C127—21no—
24C22×C8×C127—22no—
25C22×C8×C127—22no—
26#124×C127—22no—
27#124×C127C814yescomplemented
28C4×Q8×C127—22no—
29C4×Q8×C127—22no—
30C4×D4×C127—22no—
31C4×D4×C127—22no—
32C2×C4⋊C4×C127—21no—
33C2×C4⋊C4×C127C2×C411yescharacteristic
34C2×C4⋊C4×C127C2×C411yescharacteristic
35C2×C22⋊C4×C127—22no—
36C2×C22⋊C4×C127—22no—
37C2×C22⋊C4×C127—21no—
38C2×C42×C127—21no—
39C2×C42×C127C2×C411yescharacteristic
40C2×C42×C127C2×C411yescharacteristic
41C2×C42×C127D412yes—
42C2×C42×C127D412yes—
43C2×C42×C127C2311yescharacteristic
44C4⋊C8×C127—22no—
45C4⋊C8×C127—22no—
46C4⋊C8×C127—44no—
47C4×C8×C127—22no—
48C4×C8×C127D414yes—
49#95×C127—22no—
50#95×C127—22no—
51C24×C127—21no—
52C2×Q8×C127—21no—
53C2×Q8×C127—22no—
54C2×Q8×C127—22no—
55C2×Q8×C127C2×C812yes—
56C2×D4×C127—22no—
57C2×D4×C127—21no—
58C2×D4×C127—22no—
59C2×D4×C127C2×C812yes—
60C22×C4×C127—21no—
61C22×C4×C127—21no—
62C22×C4×C127—21no—
63C22×C4×C127—41no—
64C22×C4×C127—41no—
65C22×C4×C127—42no—
66C22×C4×C127—42no—
67C22×C4×C127C22⋊C412yes—
68C22×C4×C127C22⋊C412yes—
69C22×C4×C127C22×C411yescharacteristic
70C22×C4×C127C2×D411yescharacteristic
71C22×C4×C127C2×D411yescharacteristic
72C2×C8×C127—24no—
73C2×C8×C127—44no—
74C2×C8×C127—42no—
75C2×C8×C127—44no—
76C4⋊C4×C127—22no—
77C4⋊C4×C127—22no—
78C4⋊C4×C127—42no—
79C22⋊C4×C127—28no—
80C22⋊C4×C127—44no—
81C22⋊C4×C127—42no—
82C42×C127—22no—
83C42×C127—22no—
84C42×C127—22no—
85C42×C127—42no—
86C42×C127—41no—
87C42×C127—41no—
88C42×C127C2×C812yes—
89C42×C127M1612yes—
90C42×C127C2×D412yes—
91C42×C127#4112yes—
92C23×C127—22no—
93C23×C127—41no—
94C23×C127—41no—
95C23×C127—42no—
96C23×C127—42no—
97C23×C127C2×C22⋊C411yescharacteristic
98Q8×C127—24no—
99Q8×C127—42no—
100D4×C127—24no—
101D4×C127—42no—
102C2×C4×C127—22no—
103C2×C4×C127—22no—
104C2×C4×C127—22no—
105C2×C4×C127—22no—
106C2×C4×C127—22no—
107C2×C4×C127—22no—
108C2×C4×C127—22no—
109C2×C4×C127—41no—
110C2×C4×C127—41no—
111C2×C4×C127—41no—
112C2×C4×C127—41no—
113C2×C4×C127—42no—
114C2×C4×C127—42no—
115C2×C4×C127—82no—
116C2×C4×C127—81no—
117C2×C4×C127—81no—
118C2×C4×C127C22⋊C814yes—
119C2×C4×C127C4×D412yes—
120C2×C4×C127#12112yes—
121C2×C4×C127#12411yescharacteristic
122C2×C4×C127#12711yescharacteristic
123C2×C4×C127C22×C811yescharacteristic
124C2×C4×C127C2×M1611yescharacteristic
125C2×C4×C127#13112yes—
126C2×C4×C127AGL(1,ℤ/8)12yes—
127C2×C4×C127#13712yes—
128C8×C127—44no—
129C8×C127—82no—
130C22×C127—42no—
131C22×C127—44no—
132C22×C127—81no—
133C22×C127—81no—
134C22×C127—82no—
135C22×C127#39011yescharacteristic
136C22×C127C2×C22⋊C811yescharacteristic
137C22×C127#40811yescharacteristic
138C22×C127#41712yes—
139C22×C127#42112yes—
140C4×C127—22no—
141C4×C127—24no—
142C4×C127—42no—
143C4×C127—42no—
144C4×C127—81no—
145C4×C127—81no—
146C4×C127C8×D412yes—
147C4×C127#43612yes—
148C4×C127#48912yes—
149C4×C127#49611yescharacteristic
150C4×C127#49711yescharacteristic
151#9640C12711yesmaximal, characteristic, direct product factor, Sylow
152C2×C127—82no—
153C2×C127#147712yes—
154C2×C127#149512yes—
155C2×C127#195411yescharacteristic
156C2×C127#195911yescharacteristic
157C2×C127#196311yescharacteristic
158C4×#124C2×C12711yescharacteristic
159#1842C2×C12711yescharacteristic, complemented
160#1744C2×C12711yescharacteristic, complemented
161C2×Q8⋊C8C2×C12712yescomplemented
162C2×D4⋊C8C2×C12712yes—
163C127#964011yescharacteristic, direct product factor, Sylow
164C2×#124C4×C12711yescharacteristic
165C2×C4×Q8C22×C12711yescharacteristic
166C2×C4×D4C22×C12711yescharacteristic
167C2×C4⋊C8—22no—
168C2×C4⋊C8C22×C12712yes—
169C2×C4×C8C22×C12712yes—
170#391C4×C12711yescharacteristic
171#390C4×C12711yescharacteristic
172#388—22no—
173#382C4×C12711yescharacteristic
174C4×C22⋊C4—22no—
175C43C22×C12711yescharacteristic
176#336—22no—
177Q8⋊C8—24no—
178D4⋊C8—24no—
179C22×Q8C2×C4×C12711yescharacteristic
180C22×D4C2×C4×C12711yescharacteristic
181C23×C4—21no—
182C22×C8—22no—
183C22×C8—22no—
184#124—22no—
185#124C8×C12714yescomplemented
186C4×Q8—22no—
187C4×Q8—22no—
188C4×D4—22no—
189C4×D4—22no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4C2×C4×C12711yescharacteristic
192C2×C4⋊C4C2×C4×C12711yescharacteristic
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—21no—
196C2×C42—21no—
197C2×C42C2×C4×C12711yescharacteristic
198C2×C42C2×C4×C12711yescharacteristic
199C2×C42D4×C12712yes—
200C2×C42D4×C12712yes—
201C2×C42C23×C12711yescharacteristic
202C4⋊C8—22no—
203C4⋊C8—22no—
204C4⋊C8—44no—
205C4×C8—22no—
206C4×C8D4×C12714yes—
207#95—22no—
208#95—22no—
209C24—21no—
210C2×Q8—21no—
211C2×Q8—22no—
212C2×Q8—22no—
213C2×Q8C2×C8×C12712yes—
214C2×D4—22no—
215C2×D4—21no—
216C2×D4—22no—
217C2×D4C2×C8×C12712yes—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4C22⋊C4×C12712yes—
226C22×C4C22⋊C4×C12712yes—
227C22×C4C22×C4×C12711yescharacteristic
228C22×C4C2×D4×C12711yescharacteristic
229C22×C4C2×D4×C12711yescharacteristic
230C2×C8—24no—
231C2×C8—44no—
232C2×C8—42no—
233C2×C8—44no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—42no—
237C22⋊C4—28no—
238C22⋊C4—44no—
239C22⋊C4—42no—
240C42—22no—
241C42—22no—
242C42—22no—
243C42—42no—
244C42—41no—
245C42—41no—
246C42C2×C8×C12712yes—
247C42M16×C12712yes—
248C42C2×D4×C12712yes—
249C42#41×C12712yes—
250C23—22no—
251C23—41no—
252C23—41no—
253C23—42no—
254C23—42no—
255C23C2×C22⋊C4×C12711yescharacteristic
256Q8—24no—
257Q8—42no—
258D4—24no—
259D4—42no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—82no—
276C2×C4C22⋊C8×C12714yes—
277C2×C4C4×D4×C12712yes—
278C2×C4#121×C12712yes—
279C2×C4#124×C12711yescharacteristic
280C2×C4#127×C12711yescharacteristic
281C2×C4C22×C8×C12711yescharacteristic
282C2×C4C2×M16×C12711yescharacteristic
283C2×C4#131×C12712yes—
284C2×C4AGL(1,ℤ/8)×C12712yes—
285C2×C4#137×C12712yes—
286C8—44no—
287C8—82no—
288C22—42no—
289C22—44no—
290C22—81no—
291C22—81no—
292C22—82no—
293C22#390×C12711yescharacteristic
294C22C2×C22⋊C8×C12711yescharacteristic
295C22#408×C12711yescharacteristic
296C22#417×C12712yes—
297C22#421×C12712yes—
298C4—22no—
299C4—24no—
300C4—42no—
301C4—42no—
302C4—81no—
303C4—81no—
304C4C8×D4×C12712yes—
305C4#436×C12712yes—
306C4#489×C12712yes—
307C4#496×C12711yescharacteristic
308C4#497×C12711yescharacteristic
309C2—82no—
310C2C127×#147712yes—
311C2C127×#149512yes—
312C2C127×#195411yescharacteristic
313C2C127×#195911yescharacteristic
314C2C127×#196311yescharacteristic
subgroupG/H
centerC22×C4×C127C2×D4
commutatorC2×C4C22×C8×C127
Frattini, cosocleC2×C42C23×C127
socleC23×C127C2×C22⋊C4
prime radicalC22×D4×C127C2×C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ C43×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1842C2semidirect
3. C127×#1744C2semidirect
4. C2×Q8⋊C8×C127C2semidirect
27. #124×C127C8semidirect
151. #9640C127direct (N × H)
159. #1842C2×C127semidirect
160. #1744C2×C127semidirect
161. C2×Q8⋊C8C2×C127semidirect
163. C127#9640direct (N × H)
185. #124C8×C127semidirect

Maximal subgroups

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

subgroupindex
C4×#124×C1272
C127×#18422
C127×#17442
C2×Q8⋊C8×C1272
C2×D4⋊C8×C1272
#9640127