Finite Group Databasebeta

← C127×#11461 #44575134

Subgroups — C127×#11461 #44575134

Order 32512.

320 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#433×C127C211yesmaximal, characteristic
2C127×#2163C211yesmaximal, characteristic, complemented
3C127×#2162C211yesmaximal, characteristic, complemented
4C127×#1322C212yesmaximal, complemented
5C127×#1314C212yesmaximal
6C2×#117×C127C411yescharacteristic
7#433×C127—21no—
8#433×C127—21no—
9#433×C127—21no—
10#433×C127—21no—
11C2×C4⋊C8×C127C411yescharacteristic
12C2×C4⋊C8×C127C2211yescharacteristic
13C2×C22⋊C8×C127C411yescharacteristic
14C2×C22⋊C8×C127C2211yescharacteristic
15C2×#97×C127C411yescharacteristic
16C2×C4×C8×C127C2211yescharacteristic
17C4⋊C16×C127—21no—
18C4⋊C16×C127—21no—
19C22⋊C16×C127C2212yes—
20C22⋊C16×C127C2212yes—
21#346×C127—21no—
22C4×C16×C127—21no—
23C23×C4×C127C2×C411yescharacteristic
24C22×C8×C127C2×C411yescharacteristic
25C22×C8×C127C2×C411yescharacteristic
26C22×C8×C127C2×C411yescharacteristic
27C22×C8×C127C2311yescharacteristic
28#117×C127—21no—
29#117×C127—21no—
30#117×C127—21no—
31#117×C127—21no—
32C2×C4⋊C4×C127C811yescharacteristic
33C2×C4⋊C4×C127C811yescharacteristic
34C2×C22⋊C4×C127C811yescharacteristic
35C2×C22⋊C4×C127C811yescharacteristic
36C2×C42×C127C2×C411yescharacteristic
37C2×C42×C127C2×C411yescharacteristic
38C2×C16×C127—22no—
39C2×C16×C127—22no—
40C4⋊C8×C127—21no—
41C4⋊C8×C127—21no—
42C4⋊C8×C127—21no—
43C4⋊C8×C127—21no—
44C22⋊C8×C127—21no—
45C22⋊C8×C127—21no—
46C22⋊C8×C127—21no—
47C22⋊C8×C127—21no—
48#97×C127—21no—
49#97×C127—21no—
50C4×C8×C127D411yescharacteristic
51C4×C8×C127D411yescharacteristic
52C4×C8×C127D411yescharacteristic
53C4×C8×C127D411yescharacteristic
54C24×C127C2×C811yescharacteristic
55C22×C4×C127—21no—
56C22×C4×C127—21no—
57C22×C4×C127—41no—
58C22×C4×C127—41no—
59C22×C4×C127C2×C811yescharacteristic
60C22×C4×C127C2×C811yescharacteristic
61C22×C4×C127C2×C811yescharacteristic
62C22×C4×C127C2×C811yescharacteristic
63C22×C4×C127C2×C811yescharacteristic
64C22×C4×C127C22×C411yescharacteristic
65C2×C8×C127—21no—
66C2×C8×C127—21no—
67C2×C8×C127—41no—
68C2×C8×C127—41no—
69C2×C8×C127—41no—
70C2×C8×C127—41no—
71C2×C8×C127C22⋊C411yescharacteristic
72C2×C8×C127C22⋊C411yescharacteristic
73C2×C8×C127C2×D411yescharacteristic
74C2×C8×C127C2×D411yescharacteristic
75C4⋊C4×C127—21no—
76C4⋊C4×C127—21no—
77C4⋊C4×C127—21no—
78C4⋊C4×C127—21no—
79C22⋊C4×C127—21no—
80C22⋊C4×C127—21no—
81C22⋊C4×C127—21no—
82C22⋊C4×C127—21no—
83C42×C127—21no—
84C42×C127—21no—
85C42×C127C22⋊C411yescharacteristic
86C42×C127C22⋊C411yescharacteristic
87C42×C127M1611yescharacteristic
88C42×C127M1611yescharacteristic
89C16×C127—42no—
90C16×C127—42no—
91C23×C127—21no—
92C23×C127—22no—
93C23×C127—41no—
94C23×C127—41no—
95C23×C127C22×C811yescharacteristic
96C2×C4×C127—22no—
97C2×C4×C127—21no—
98C2×C4×C127—21no—
99C2×C4×C127—21no—
100C2×C4×C127—21no—
101C2×C4×C127—21no—
102C2×C4×C127—22no—
103C2×C4×C127—41no—
104C2×C4×C127—42no—
105C2×C4×C127—41no—
106C2×C4×C127—41no—
107C2×C4×C127—41no—
108C2×C4×C127—41no—
109C2×C4×C127C22⋊C811yescharacteristic
110C2×C4×C127C22⋊C811yescharacteristic
111C2×C4×C127C22⋊C811yescharacteristic
112C2×C4×C127C22⋊C811yescharacteristic
113C2×C4×C127C2×C22⋊C411yescharacteristic
114C2×C4×C127C2×M1611yescharacteristic
115C8×C127—21no—
116C8×C127—21no—
117C8×C127—21no—
118C8×C127—21no—
119C8×C127—41no—
120C8×C127—41no—
121C22×C127—21no—
122C22×C127—21no—
123C22×C127—41no—
124C22×C127—41no—
125C22×C127—41no—
126C22×C127—82no—
127C22×C127C2×C22⋊C811yescharacteristic
128C22×C127#50412yes—
129C4×C127—21no—
130C4×C127—21no—
131C4×C127—21no—
132C4×C127—21no—
133C4×C127—21no—
134C4×C127—41no—
135C4×C127—41no—
136C4×C127—41no—
137C4×C127#41011yescharacteristic
138C4×C127#41311yescharacteristic
139#11461C12711yesmaximal, characteristic, direct product factor, Sylow
140C2×C127—22no—
141C2×C127—81no—
142C2×C127#145811yescharacteristic
143C2×C127#211311yescharacteristic
144C2×C127#211511yescharacteristic
145C2×#433C2×C12711yescharacteristic
146#2163C2×C12711yescharacteristic, complemented
147#2162C2×C12711yescharacteristic, complemented
148#1322C2×C12712yescomplemented
149#1314C2×C12712yes—
150C127#1146111yescharacteristic, direct product factor, Sylow
151C2×#117C4×C12711yescharacteristic
152#433—21no—
153#433—21no—
154#433—21no—
155#433—21no—
156C2×C4⋊C8C4×C12711yescharacteristic
157C2×C4⋊C8C22×C12711yescharacteristic
158C2×C22⋊C8C4×C12711yescharacteristic
159C2×C22⋊C8C22×C12711yescharacteristic
160C2×#97C4×C12711yescharacteristic
161C2×C4×C8C22×C12711yescharacteristic
162C4⋊C16—21no—
163C4⋊C16—21no—
164C22⋊C16C22×C12712yes—
165C22⋊C16C22×C12712yes—
166#346—21no—
167C4×C16—21no—
168C23×C4C2×C4×C12711yescharacteristic
169C22×C8C2×C4×C12711yescharacteristic
170C22×C8C2×C4×C12711yescharacteristic
171C22×C8C2×C4×C12711yescharacteristic
172C22×C8C23×C12711yescharacteristic
173#117—21no—
174#117—21no—
175#117—21no—
176#117—21no—
177C2×C4⋊C4C8×C12711yescharacteristic
178C2×C4⋊C4C8×C12711yescharacteristic
179C2×C22⋊C4C8×C12711yescharacteristic
180C2×C22⋊C4C8×C12711yescharacteristic
181C2×C42C2×C4×C12711yescharacteristic
182C2×C42C2×C4×C12711yescharacteristic
183C2×C16—22no—
184C2×C16—22no—
185C4⋊C8—21no—
186C4⋊C8—21no—
187C4⋊C8—21no—
188C4⋊C8—21no—
189C22⋊C8—21no—
190C22⋊C8—21no—
191C22⋊C8—21no—
192C22⋊C8—21no—
193#97—21no—
194#97—21no—
195C4×C8D4×C12711yescharacteristic
196C4×C8D4×C12711yescharacteristic
197C4×C8D4×C12711yescharacteristic
198C4×C8D4×C12711yescharacteristic
199C24C2×C8×C12711yescharacteristic
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4C2×C8×C12711yescharacteristic
205C22×C4C2×C8×C12711yescharacteristic
206C22×C4C2×C8×C12711yescharacteristic
207C22×C4C2×C8×C12711yescharacteristic
208C22×C4C2×C8×C12711yescharacteristic
209C22×C4C22×C4×C12711yescharacteristic
210C2×C8—21no—
211C2×C8—21no—
212C2×C8—41no—
213C2×C8—41no—
214C2×C8—41no—
215C2×C8—41no—
216C2×C8C22⋊C4×C12711yescharacteristic
217C2×C8C22⋊C4×C12711yescharacteristic
218C2×C8C2×D4×C12711yescharacteristic
219C2×C8C2×D4×C12711yescharacteristic
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4—21no—
224C22⋊C4—21no—
225C22⋊C4—21no—
226C22⋊C4—21no—
227C22⋊C4—21no—
228C42—21no—
229C42—21no—
230C42C22⋊C4×C12711yescharacteristic
231C42C22⋊C4×C12711yescharacteristic
232C42M16×C12711yescharacteristic
233C42M16×C12711yescharacteristic
234C16—42no—
235C16—42no—
236C23—21no—
237C23—22no—
238C23—41no—
239C23—41no—
240C23C22×C8×C12711yescharacteristic
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4C22⋊C8×C12711yescharacteristic
255C2×C4C22⋊C8×C12711yescharacteristic
256C2×C4C22⋊C8×C12711yescharacteristic
257C2×C4C22⋊C8×C12711yescharacteristic
258C2×C4C2×C22⋊C4×C12711yescharacteristic
259C2×C4C2×M16×C12711yescharacteristic
260C8—21no—
261C8—21no—
262C8—21no—
263C8—21no—
264C8—41no—
265C8—41no—
266C22—21no—
267C22—21no—
268C22—41no—
269C22—41no—
270C22—41no—
271C22—82no—
272C22C2×C22⋊C8×C12711yescharacteristic
273C22#504×C12712yes—
274C4—21no—
275C4—21no—
276C4—21no—
277C4—21no—
278C4—21no—
279C4—41no—
280C4—41no—
281C4—41no—
282C4#410×C12711yescharacteristic
283C4#413×C12711yescharacteristic
284C2—22no—
285C2—81no—
286C2C127×#145811yescharacteristic
287C2C127×#211311yescharacteristic
288C2C127×#211511yescharacteristic
subgroupG/H
centerC2×C4×C127C2×C22⋊C4
commutatorC23C22×C8×C127
Frattini, cosocleC22×C8C23×C127
socleC22×C127C2×C22⋊C8
prime radicalC24×C127C2×C8
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2163C2semidirect
3. C127×#2162C2semidirect
4. C127×#1322C2semidirect
139. #11461C127direct (N × H)
146. #2163C2×C127semidirect
147. #2162C2×C127semidirect
148. #1322C2×C127semidirect
150. C127#11461direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#433×C1272
C127×#21632
C127×#21622
C127×#13222
C127×#13142
#11461127