Finite Group Databasebeta

← C127×#9588 #44573261

Subgroups — C127×#9588 #44573261

Order 32512.

304 conjugacy classes of subgroups.

The subgroup lattice has 288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#1574C211yesmaximal, characteristic, complemented
2C127×#1543C211yesmaximal, characteristic
3C127×#1492C211yesmaximal, characteristic
4C127×#1484C211yesmaximal, characteristic
5C127×#1452C211yesmaximal, characteristic, complemented
6C127×#1299C211yesmaximal, characteristic, complemented
7C127×#1278C211yesmaximal, characteristic, complemented
8#532×C127C2211yescharacteristic
9#431×C127C2211yescharacteristic
10#431×C127C2211yescharacteristic
11#431×C127C2211yescharacteristic
12#423×C127C2211yescharacteristic
13C4×M16×C127C2211yescharacteristic
14C2×C4×C8×C127C2211yescharacteristic
15#335×C127—21no—
16#334×C127—21no—
17#333×C127C411yescharacteristic
18#333×C127C411yescharacteristic
19#331×C127C411yescharacteristic
20#331×C127C411yescharacteristic
21D4⋊C8×C127—21no—
22D4⋊C8×C127—21no—
23D4⋊C8×C127—22no—
24#322×C127—22no—
25C2×#41×C127—21no—
26C2×M16×C127—21no—
27C2×M16×C127—21no—
28C22×C8×C127—21no—
29C4⋊Q8×C127C2×C411yescharacteristic
30#127×C127C2×C411yescharacteristic
31#124×C127—21no—
32#121×C127—21no—
33#121×C127—21no—
34C4×D4×C127—21no—
35C4×D4×C127—21no—
36C2×C42×C127C2311yescharacteristic
37C4⋊C8×C127—21no—
38C4⋊C8×C127—21no—
39C4⋊C8×C127C2×C411yescharacteristic
40C4⋊C8×C127C2×C411yescharacteristic
41C4⋊C8×C127C2×C411yescharacteristic
42C4⋊C8×C127C2×C411yescharacteristic
43C4⋊C8×C127D411yescharacteristic
44C4⋊C8×C127D411yescharacteristic
45C22⋊C8×C127—21no—
46C22⋊C8×C127—21no—
47C22⋊C8×C127—21no—
48#97×C127—21no—
49C4×C8×C127—21no—
50C4×C8×C127—21no—
51C4×C8×C127—21no—
52C4×C8×C127—21no—
53C4×C8×C127—21no—
54C4×C8×C127D412yes—
55#41×C127—81no—
56#41×C127—81no—
57C2×Q8×C127—21no—
58C2×D4×C127—21no—
59C2×D4×C127—21no—
60C2×D4×C127—21no—
61C2×D4×C127—41no—
62C22×C4×C127—41no—
63C22×C4×C127#4111yescharacteristic
64C22×C4×C127#4111yescharacteristic
65C22×C4×C127#4111yescharacteristic
66M16×C127—22no—
67M16×C127—41no—
68M16×C127—81no—
69C2×C8×C127—21no—
70C2×C8×C127—21no—
71C2×C8×C127—21no—
72C2×C8×C127—21no—
73C2×C8×C127—21no—
74C2×C8×C127—21no—
75C2×C8×C127—22no—
76C2×C8×C127—41no—
77C2×C8×C127—41no—
78C2×C8×C127—41no—
79C2×C8×C127—41no—
80C4⋊C4×C127—21no—
81C4⋊C4×C127—21no—
82C22⋊C4×C127—41no—
83C22⋊C4×C127—41no—
84C42×C127C22×C411yescharacteristic
85C42×C127C2×D411yescharacteristic
86C42×C127C2×D411yescharacteristic
87C42×C127#4111yescharacteristic
88C23×C127—41no—
89C23×C127#12611yescharacteristic
90Q8×C127—81no—
91D4×C127—41no—
92D4×C127—41no—
93D4×C127—41no—
94D4×C127—41no—
95D4×C127—81no—
96D4×C127—82no—
97C2×C4×C127—21no—
98C2×C4×C127—21no—
99C2×C4×C127—21no—
100C2×C4×C127—21no—
101C2×C4×C127—21no—
102C2×C4×C127—21no—
103C2×C4×C127—41no—
104C2×C4×C127—81no—
105C2×C4×C127—81no—
106C2×C4×C127#11711yescharacteristic
107C2×C4×C127C4×D411yescharacteristic
108C2×C4×C127C4×D411yescharacteristic
109C2×C4×C127#12111yescharacteristic
110C2×C4×C127#12311yescharacteristic
111C2×C4×C127#12411yescharacteristic
112C8×C127—42no—
113C8×C127—42no—
114C8×C127—41no—
115C8×C127—41no—
116C8×C127—41no—
117C8×C127—41no—
118C8×C127—41no—
119C8×C127—41no—
120C8×C127—81no—
121C22×C127—21no—
122C22×C127—21no—
123C22×C127—21no—
124C22×C127—81no—
125C22×C127—81no—
126C22×C127—81no—
127C22×C127#38811yescharacteristic
128C4×C127—21no—
129C4×C127—21no—
130C4×C127—21no—
131C4×C127—81no—
132C4×C127#44311yescharacteristic
133C4×C127#44411yescharacteristic
134C4×C127#44411yescharacteristic
135C4×C127#44411yescharacteristic
136C4×C127#47111yescharacteristic
137C4×C127#47211yescharacteristic
138#9588C12711yesmaximal, characteristic, direct product factor, Sylow
139C2×C127—41no—
140C2×C127—161no—
141C2×C127#192911yescharacteristic
142C2×C127#193111yescharacteristic
143C2×C127#193811yescharacteristic
144#1574C2×C12711yescharacteristic, complemented
145#1543C2×C12711yescharacteristic
146#1492C2×C12711yescharacteristic
147#1484C2×C12711yescharacteristic
148#1452C2×C12711yescharacteristic, complemented
149#1299C2×C12711yescharacteristic, complemented
150#1278C2×C12711yescharacteristic, complemented
151C127#958811yescharacteristic, direct product factor, Sylow
152#532C22×C12711yescharacteristic
153#431C22×C12711yescharacteristic
154#431C22×C12711yescharacteristic
155#431C22×C12711yescharacteristic
156#423C22×C12711yescharacteristic
157C4×M16C22×C12711yescharacteristic
158C2×C4×C8C22×C12711yescharacteristic
159#335—21no—
160#334—21no—
161#333C4×C12711yescharacteristic
162#333C4×C12711yescharacteristic
163#331C4×C12711yescharacteristic
164#331C4×C12711yescharacteristic
165D4⋊C8—21no—
166D4⋊C8—21no—
167D4⋊C8—22no—
168#322—22no—
169C2×#41—21no—
170C2×M16—21no—
171C2×M16—21no—
172C22×C8—21no—
173C4⋊Q8C2×C4×C12711yescharacteristic
174#127C2×C4×C12711yescharacteristic
175#124—21no—
176#121—21no—
177#121—21no—
178C4×D4—21no—
179C4×D4—21no—
180C2×C42C23×C12711yescharacteristic
181C4⋊C8—21no—
182C4⋊C8—21no—
183C4⋊C8C2×C4×C12711yescharacteristic
184C4⋊C8C2×C4×C12711yescharacteristic
185C4⋊C8C2×C4×C12711yescharacteristic
186C4⋊C8C2×C4×C12711yescharacteristic
187C4⋊C8D4×C12711yescharacteristic
188C4⋊C8D4×C12711yescharacteristic
189C22⋊C8—21no—
190C22⋊C8—21no—
191C22⋊C8—21no—
192#97—21no—
193C4×C8—21no—
194C4×C8—21no—
195C4×C8—21no—
196C4×C8—21no—
197C4×C8—21no—
198C4×C8D4×C12712yes—
199#41—81no—
200#41—81no—
201C2×Q8—21no—
202C2×D4—21no—
203C2×D4—21no—
204C2×D4—21no—
205C2×D4—41no—
206C22×C4—41no—
207C22×C4#41×C12711yescharacteristic
208C22×C4#41×C12711yescharacteristic
209C22×C4#41×C12711yescharacteristic
210M16—22no—
211M16—41no—
212M16—81no—
213C2×C8—21no—
214C2×C8—21no—
215C2×C8—21no—
216C2×C8—21no—
217C2×C8—21no—
218C2×C8—21no—
219C2×C8—22no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8—41no—
223C2×C8—41no—
224C4⋊C4—21no—
225C4⋊C4—21no—
226C22⋊C4—41no—
227C22⋊C4—41no—
228C42C22×C4×C12711yescharacteristic
229C42C2×D4×C12711yescharacteristic
230C42C2×D4×C12711yescharacteristic
231C42#41×C12711yescharacteristic
232C23—41no—
233C23#126×C12711yescharacteristic
234Q8—81no—
235D4—41no—
236D4—41no—
237D4—41no—
238D4—41no—
239D4—81no—
240D4—82no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—41no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4#117×C12711yescharacteristic
251C2×C4C4×D4×C12711yescharacteristic
252C2×C4C4×D4×C12711yescharacteristic
253C2×C4#121×C12711yescharacteristic
254C2×C4#123×C12711yescharacteristic
255C2×C4#124×C12711yescharacteristic
256C8—42no—
257C8—42no—
258C8—41no—
259C8—41no—
260C8—41no—
261C8—41no—
262C8—41no—
263C8—41no—
264C8—81no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—81no—
269C22—81no—
270C22—81no—
271C22#388×C12711yescharacteristic
272C4—21no—
273C4—21no—
274C4—21no—
275C4—81no—
276C4#443×C12711yescharacteristic
277C4#444×C12711yescharacteristic
278C4#444×C12711yescharacteristic
279C4#444×C12711yescharacteristic
280C4#471×C12711yescharacteristic
281C4#472×C12711yescharacteristic
282C2—41no—
283C2—161no—
284C2C127×#192911yescharacteristic
285C2C127×#193111yescharacteristic
286C2C127×#193811yescharacteristic
subgroupG/H
centerC2×C4×C127#121
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
socleC22×C127#388
prime radical#532×C127C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#1574C2semidirect
5. C127×#1452C2semidirect
6. C127×#1299C2semidirect
7. C127×#1278C2semidirect
138. #9588C127direct (N × H)
144. #1574C2×C127semidirect
148. #1452C2×C127semidirect
149. #1299C2×C127semidirect
150. #1278C2×C127semidirect
151. C127#9588direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#15742
C127×#15432
C127×#14922
C127×#14842
C127×#14522
C127×#12992
C127×#12782
#9588127