Finite Group Databasebeta

← C127×#11814 #44575487

Subgroups — C127×#11814 #44575487

Order 32512.

434 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 106 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×#400×C127C211yesmaximal, characteristic
2C127×#1821C211yesmaximal, characteristic
3C127×#1463C211yesmaximal, characteristic
4C127×#1353C214yesmaximal, complemented
5C22×C4⋊C4×C127C411yescharacteristic
6C22×C4⋊C4×C127C2211yescharacteristic
7#407×C127—21no—
8#407×C127—21no—
9#400×C127—21no—
10#400×C127—21no—
11#400×C127C412yes—
12#400×C127C2212yes—
13C2×#95×C127—21no—
14C2×#95×C127—21no—
15C2×#95×C127C411yescharacteristic
16#343×C127—21no—
17#343×C127C2212yes—
18#324×C127—21no—
19#324×C127C2212yes—
20C23×C4×C127—21no—
21C23×C4×C127—21no—
22C23×C4×C127C2×C411yescharacteristic
23C23×C4×C127D411yescharacteristic
24C23×C4×C127D411yescharacteristic
25C2×M16×C127—22no—
26C2×M16×C127—41no—
27C2×C4⋊C4×C127—21no—
28C2×C4⋊C4×C127—41no—
29C2×C4⋊C4×C127—41no—
30C2×C4⋊C4×C127—41no—
31C2×C4⋊C4×C127—41no—
32C2×C4⋊C4×C127C2×C412yes—
33C2×C4⋊C4×C127C2×C411yescharacteristic
34C2×C4⋊C4×C127D411yescharacteristic
35C2×C4⋊C4×C127D411yescharacteristic
36C2×C4⋊C4×C127C2311yescharacteristic
37C22⋊C8×C127—22no—
38C22⋊C8×C127—41no—
39C22⋊C8×C127—41no—
40C22⋊C8×C127—41no—
41#95×C127—22no—
42#95×C127—22no—
43#95×C127—21no—
44#95×C127—22no—
45#95×C127—22no—
46#95×C127C2×C412yes—
47C24×C127C22⋊C411yescharacteristic
48C22×C4×C127—21no—
49C22×C4×C127—21no—
50C22×C4×C127—21no—
51C22×C4×C127—21no—
52C22×C4×C127—21no—
53C22×C4×C127—21no—
54C22×C4×C127—22no—
55C22×C4×C127—22no—
56C22×C4×C127—22no—
57C22×C4×C127—41no—
58C22×C4×C127—42no—
59C22×C4×C127—42no—
60C22×C4×C127—42no—
61C22×C4×C127—42no—
62C22×C4×C127—44no—
63C22×C4×C127—42no—
64C22×C4×C127—41no—
65C22×C4×C127—41no—
66C22×C4×C127C22⋊C411yescharacteristic
67C22×C4×C127C22⋊C411yescharacteristic
68C22×C4×C127C22⋊C411yescharacteristic
69C22×C4×C127C22×C411yescharacteristic
70C22×C4×C127C2×D411yescharacteristic
71C22×C4×C127C2×D411yescharacteristic
72M16×C127—42no—
73M16×C127—42no—
74M16×C127—82no—
75C2×C8×C127—42no—
76C2×C8×C127—42no—
77C4⋊C4×C127—41no—
78C4⋊C4×C127—41no—
79C4⋊C4×C127—41no—
80C4⋊C4×C127—41no—
81C4⋊C4×C127—42no—
82C4⋊C4×C127—42no—
83C23×C127—22no—
84C23×C127—22no—
85C23×C127—21no—
86C23×C127—21no—
87C23×C127#9911yescharacteristic
88C23×C127#9911yescharacteristic
89C23×C127C2×C22⋊C411yescharacteristic
90C2×C4×C127—21no—
91C2×C4×C127—21no—
92C2×C4×C127—21no—
93C2×C4×C127—21no—
94C2×C4×C127—21no—
95C2×C4×C127—21no—
96C2×C4×C127—21no—
97C2×C4×C127—21no—
98C2×C4×C127—21no—
99C2×C4×C127—42no—
100C2×C4×C127—42no—
101C2×C4×C127—42no—
102C2×C4×C127—42no—
103C2×C4×C127—42no—
104C2×C4×C127—41no—
105C2×C4×C127—41no—
106C2×C4×C127—41no—
107C2×C4×C127—41no—
108C2×C4×C127—42no—
109C2×C4×C127—42no—
110C2×C4×C127—44no—
111C2×C4×C127—42no—
112C2×C4×C127—42no—
113C2×C4×C127—81no—
114C2×C4×C127—84no—
115C2×C4×C127—82no—
116C2×C4×C127—82no—
117C2×C4×C127#13712yes—
118C8×C127—82no—
119C8×C127—82no—
120C22×C127—24no—
121C22×C127—24no—
122C22×C127—21no—
123C22×C127—21no—
124C22×C127—21no—
125C22×C127—21no—
126C22×C127—21no—
127C22×C127—21no—
128C22×C127#35212yes—
129C22×C127#35512yes—
130C22×C127C2×#9911yescharacteristic
131C22×C127#41911yescharacteristic
132C22×C127#42111yescharacteristic
133C4×C127—22no—
134C4×C127—41no—
135C4×C127—41no—
136C4×C127—41no—
137C4×C127—41no—
138C4×C127—41no—
139C4×C127—82no—
140C4×C127—82no—
141#11814C12711yesmaximal, characteristic, direct product factor, Sylow
142C2×C127—21no—
143C2×C127—22no—
144C2×C127—22no—
145C2×C127—21no—
146C2×C127#151111yescharacteristic
147C2×C127C2×#35211yescharacteristic
148C2×C127C2×#35511yescharacteristic
149C2×#400C2×C12711yescharacteristic
150#1821C2×C12711yescharacteristic
151#1463C2×C12711yescharacteristic
152#1353C2×C12714yescomplemented
153C127#1181411yescharacteristic, direct product factor, Sylow
154C22×C4⋊C4C4×C12711yescharacteristic
155C22×C4⋊C4C22×C12711yescharacteristic
156#407—21no—
157#407—21no—
158#400—21no—
159#400—21no—
160#400C4×C12712yes—
161#400C22×C12712yes—
162C2×#95—21no—
163C2×#95—21no—
164C2×#95C4×C12711yescharacteristic
165#343—21no—
166#343C22×C12712yes—
167#324—21no—
168#324C22×C12712yes—
169C23×C4—21no—
170C23×C4—21no—
171C23×C4C2×C4×C12711yescharacteristic
172C23×C4D4×C12711yescharacteristic
173C23×C4D4×C12711yescharacteristic
174C2×M16—22no—
175C2×M16—41no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4C2×C4×C12712yes—
182C2×C4⋊C4C2×C4×C12711yescharacteristic
183C2×C4⋊C4D4×C12711yescharacteristic
184C2×C4⋊C4D4×C12711yescharacteristic
185C2×C4⋊C4C23×C12711yescharacteristic
186C22⋊C8—22no—
187C22⋊C8—41no—
188C22⋊C8—41no—
189C22⋊C8—41no—
190#95—22no—
191#95—22no—
192#95—21no—
193#95—22no—
194#95—22no—
195#95C2×C4×C12712yes—
196C24C22⋊C4×C12711yescharacteristic
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—41no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—44no—
212C22×C4—42no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4C22⋊C4×C12711yescharacteristic
216C22×C4C22⋊C4×C12711yescharacteristic
217C22×C4C22⋊C4×C12711yescharacteristic
218C22×C4C22×C4×C12711yescharacteristic
219C22×C4C2×D4×C12711yescharacteristic
220C22×C4C2×D4×C12711yescharacteristic
221M16—42no—
222M16—42no—
223M16—82no—
224C2×C8—42no—
225C2×C8—42no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C23—22no—
233C23—22no—
234C23—21no—
235C23—21no—
236C23#99×C12711yescharacteristic
237C23#99×C12711yescharacteristic
238C23C2×C22⋊C4×C12711yescharacteristic
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—44no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—81no—
263C2×C4—84no—
264C2×C4—82no—
265C2×C4—82no—
266C2×C4#137×C12712yes—
267C8—82no—
268C8—82no—
269C22—24no—
270C22—24no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22#352×C12712yes—
278C22#355×C12712yes—
279C22C2×#99×C12711yescharacteristic
280C22#419×C12711yescharacteristic
281C22#421×C12711yescharacteristic
282C4—22no—
283C4—41no—
284C4—41no—
285C4—41no—
286C4—41no—
287C4—41no—
288C4—82no—
289C4—82no—
290C2—21no—
291C2—22no—
292C2—22no—
293C2—21no—
294C2C127×#151111yescharacteristic
295C2C2×#352×C12711yescharacteristic
296C2C2×#355×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC24×C127C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C24×C127 ◁ C22×C4⋊C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1353C2semidirect
141. #11814C127direct (N × H)
152. #1353C2×C127semidirect
153. C127#11814direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#400×C1272
C127×#18212
C127×#14632
C127×#13532
#11814127