Finite Group Databasebeta

← C127×#11896 #44575569

Subgroups — C127×#11896 #44575569

Order 32512.

390 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#467×C127C211yesmaximal, characteristic
2C127×#2112C211yesmaximal, characteristic
3C127×#1810C211yesmaximal, characteristic
4C127×#1350C214yesmaximal, complemented
5C22×Q16×C127C411yescharacteristic
6C23×C8×C127C2211yescharacteristic
7C2×C22⋊Q8×C127—21no—
8C2×M32×C127—21no—
9#467×C127—21no—
10#467×C127—21no—
11#467×C127C412yes—
12#467×C127C2212yes—
13C2×#108×C127—21no—
14C2×#107×C127C411yescharacteristic
15C2×#103×C127—21no—
16#407×C127—21no—
17C22⋊C16×C127—21no—
18C22⋊C16×C127C2212yes—
19#341×C127C2212yes—
20C22×Q8×C127—21no—
21C23×C4×C127D411yescharacteristic
22C2×Q16×C127—21no—
23C2×Q16×C127—42no—
24C2×Q16×C127C2×C412yes—
25C2×M16×C127—22no—
26C22×C8×C127—42no—
27C22×C8×C127C2×C411yescharacteristic
28C22×C8×C127C2×C411yescharacteristic
29C22×C8×C127D411yescharacteristic
30C22×C8×C127D411yescharacteristic
31C22×C8×C127D411yescharacteristic
32C22×C8×C127C2311yescharacteristic
33C22⋊Q8×C127—22no—
34C22⋊Q8×C127—22no—
35C22⋊Q8×C127—41no—
36C22⋊Q8×C127—41no—
37C2×C4⋊C4×C127—21no—
38C2×C4⋊C4×C127—41no—
39C2×C22⋊C4×C127—41no—
40M32×C127—42no—
41C2×C16×C127—22no—
42#108×C127—42no—
43#107×C127—21no—
44#107×C127C2×C412yes—
45#103×C127—22no—
46#103×C127—22no—
47C22⋊C8×C127—41no—
48C22⋊C8×C127—41no—
49C24×C127SD1611yescharacteristic
50C2×Q8×C127—22no—
51C2×Q8×C127—42no—
52C2×Q8×C127—42no—
53C2×Q8×C127—41no—
54C22×C4×C127—41no—
55C22×C4×C127—41no—
56C22×C4×C127—41no—
57C22×C4×C127—41no—
58C22×C4×C127C22⋊C411yescharacteristic
59C22×C4×C127C22⋊C411yescharacteristic
60C22×C4×C127D811yescharacteristic
61C22×C4×C127D811yescharacteristic
62C22×C4×C127SD1611yescharacteristic
63C22×C4×C127C2×D411yescharacteristic
64Q16×C127—42no—
65Q16×C127—42no—
66M16×C127—42no—
67M16×C127—42no—
68C2×C8×C127—22no—
69C2×C8×C127—22no—
70C2×C8×C127—22no—
71C2×C8×C127—41no—
72C2×C8×C127—41no—
73C2×C8×C127—41no—
74C2×C8×C127—42no—
75C2×C8×C127C22⋊C411yescharacteristic
76C2×C8×C127C22⋊C411yescharacteristic
77C2×C8×C127C22×C411yescharacteristic
78C2×C8×C127C2×D411yescharacteristic
79C4⋊C4×C127—22no—
80C4⋊C4×C127—41no—
81C4⋊C4×C127—42no—
82C4⋊C4×C127—42no—
83C22⋊C4×C127—42no—
84C22⋊C4×C127—42no—
85C16×C127—42no—
86C23×C127—22no—
87C23×C127—41no—
88C23×C127—41no—
89C23×C127#10211yescharacteristic
90C23×C127#10211yescharacteristic
91C23×C127C2×SD1611yescharacteristic
92Q8×C127—42no—
93Q8×C127—42no—
94Q8×C127—82no—
95C2×C4×C127—21no—
96C2×C4×C127—21no—
97C2×C4×C127—21no—
98C2×C4×C127—21no—
99C2×C4×C127—21no—
100C2×C4×C127—21no—
101C2×C4×C127—41no—
102C2×C4×C127—41no—
103C2×C4×C127—41no—
104C2×C4×C127—42no—
105C2×C4×C127—42no—
106C2×C4×C127—82no—
107C2×C4×C127—82no—
108C2×C4×C127#10211yescharacteristic
109C2×C4×C127#10211yescharacteristic
110C2×C4×C127C2×C22⋊C411yescharacteristic
111C2×C4×C127C2×D811yescharacteristic
112C8×C127—21no—
113C8×C127—21no—
114C8×C127—21no—
115C8×C127—82no—
116C8×C127#9912yes—
117C22×C127—21no—
118C22×C127—21no—
119C22×C127—21no—
120C22×C127—21no—
121C22×C127—21no—
122C22×C127—21no—
123C22×C127—21no—
124C22×C127—21no—
125C22×C127—44no—
126C22×C127#36212yes—
127C22×C127C2×#10211yescharacteristic
128C4×C127—21no—
129C4×C127—21no—
130C4×C127—21no—
131C4×C127—82no—
132C4×C127—82no—
133C4×C127C2×#9911yescharacteristic
134C4×C127#42111yescharacteristic
135#11896C12711yesmaximal, characteristic, direct product factor, Sylow
136C2×C127—22no—
137C2×C127—41no—
138C2×C127—41no—
139C2×C127#151911yescharacteristic
140C2×C127#214311yescharacteristic
141C2×C127C2×#36211yescharacteristic
142C2×#467C2×C12711yescharacteristic
143#2112C2×C12711yescharacteristic
144#1810C2×C12711yescharacteristic
145#1350C2×C12714yescomplemented
146C127#1189611yescharacteristic, direct product factor, Sylow
147C22×Q16C4×C12711yescharacteristic
148C23×C8C22×C12711yescharacteristic
149C2×C22⋊Q8—21no—
150C2×M32—21no—
151#467—21no—
152#467—21no—
153#467C4×C12712yes—
154#467C22×C12712yes—
155C2×#108—21no—
156C2×#107C4×C12711yescharacteristic
157C2×#103—21no—
158#407—21no—
159C22⋊C16—21no—
160C22⋊C16C22×C12712yes—
161#341C22×C12712yes—
162C22×Q8—21no—
163C23×C4D4×C12711yescharacteristic
164C2×Q16—21no—
165C2×Q16—42no—
166C2×Q16C2×C4×C12712yes—
167C2×M16—22no—
168C22×C8—42no—
169C22×C8C2×C4×C12711yescharacteristic
170C22×C8C2×C4×C12711yescharacteristic
171C22×C8D4×C12711yescharacteristic
172C22×C8D4×C12711yescharacteristic
173C22×C8D4×C12711yescharacteristic
174C22×C8C23×C12711yescharacteristic
175C22⋊Q8—22no—
176C22⋊Q8—22no—
177C22⋊Q8—41no—
178C22⋊Q8—41no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—41no—
181C2×C22⋊C4—41no—
182M32—42no—
183C2×C16—22no—
184#108—42no—
185#107—21no—
186#107C2×C4×C12712yes—
187#103—22no—
188#103—22no—
189C22⋊C8—41no—
190C22⋊C8—41no—
191C24SD16×C12711yescharacteristic
192C2×Q8—22no—
193C2×Q8—42no—
194C2×Q8—42no—
195C2×Q8—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4C22⋊C4×C12711yescharacteristic
201C22×C4C22⋊C4×C12711yescharacteristic
202C22×C4D8×C12711yescharacteristic
203C22×C4D8×C12711yescharacteristic
204C22×C4SD16×C12711yescharacteristic
205C22×C4C2×D4×C12711yescharacteristic
206Q16—42no—
207Q16—42no—
208M16—42no—
209M16—42no—
210C2×C8—22no—
211C2×C8—22no—
212C2×C8—22no—
213C2×C8—41no—
214C2×C8—41no—
215C2×C8—41no—
216C2×C8—42no—
217C2×C8C22⋊C4×C12711yescharacteristic
218C2×C8C22⋊C4×C12711yescharacteristic
219C2×C8C22×C4×C12711yescharacteristic
220C2×C8C2×D4×C12711yescharacteristic
221C4⋊C4—22no—
222C4⋊C4—41no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C22⋊C4—42no—
226C22⋊C4—42no—
227C16—42no—
228C23—22no—
229C23—41no—
230C23—41no—
231C23#102×C12711yescharacteristic
232C23#102×C12711yescharacteristic
233C23C2×SD16×C12711yescharacteristic
234Q8—42no—
235Q8—42no—
236Q8—82no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—82no—
249C2×C4—82no—
250C2×C4#102×C12711yescharacteristic
251C2×C4#102×C12711yescharacteristic
252C2×C4C2×C22⋊C4×C12711yescharacteristic
253C2×C4C2×D8×C12711yescharacteristic
254C8—21no—
255C8—21no—
256C8—21no—
257C8—82no—
258C8#99×C12712yes—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—44no—
268C22#362×C12712yes—
269C22C2×#102×C12711yescharacteristic
270C4—21no—
271C4—21no—
272C4—21no—
273C4—82no—
274C4—82no—
275C4C2×#99×C12711yescharacteristic
276C4#421×C12711yescharacteristic
277C2—22no—
278C2—41no—
279C2—41no—
280C2C127×#151911yescharacteristic
281C2C127×#214311yescharacteristic
282C2C2×#362×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC24×C127SD16
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ C23×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1350C2semidirect
135. #11896C127direct (N × H)
145. #1350C2×C127semidirect
146. C127#11896direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#467×C1272
C127×#21122
C127×#18102
C127×#13502
#11896127