Finite Group Databasebeta

← C11×#13136 #14590329

Subgroups — C11×#13136 #14590329

Order 2816.

360 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2159C211yesmaximal, characteristic, complemented
2C2×C11×#361C211yesmaximal, characteristic
3C11×#2140C211yesmaximal, characteristic
4C11×#1970C211yesmaximal, characteristic
5C11×#1772C211yesmaximal, characteristic, complemented
6C11×#1387C211yesmaximal, characteristic, complemented
7C11×#1376C211yesmaximal, characteristic, complemented
8C22×C11×D8C2211yescharacteristic
9C2×C11×M32C2211yescharacteristic
10C2×C11×M32C2211yescharacteristic
11C2×C11×#108C2211yescharacteristic
12C11×#427C2211yescharacteristic
13C2×C11×#107C2211yescharacteristic
14C2×C11×#102—21no—
15C11×#405—21no—
16C2×C4×C8×C11C2211yescharacteristic
17C11×#390—21no—
18C11×#367—21no—
19C11×#366—21no—
20C11×#361C414yescomplemented
21C11×#357—21no—
22C11×#357—21no—
23C11×#339—21no—
24C22×D4×C11—21no—
25C2×C11×D8—21no—
26C2×C11×D8—21no—
27C2×C11×D8—21no—
28C2×C11×D8—21no—
29C2×C11×D8—21no—
30C2×C11×D8C2×C412yes—
31C2×C11×M16—21no—
32C22×C8×C11D411yescharacteristic
33C22×C8×C11C2311yescharacteristic
34C11×#117—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C22⋊C4—42no—
37C2×C42×C11D411yescharacteristic
38C11×M32—21no—
39C11×M32—21no—
40C11×M32—21no—
41C11×M32C2×C412yes—
42C2×C11×C16—21no—
43C2×C11×C16—21no—
44C11×#108—21no—
45C11×#108C2×C412yes—
46C11×#107—21no—
47C11×#107—21no—
48C11×#107D411yescharacteristic
49C11×#107D411yescharacteristic
50C11×#106—21no—
51C11×#102—41no—
52C11×#102—41no—
53C11×#97—41no—
54C4×C8×C11—21no—
55C4×C8×C11—21no—
56C4×C8×C11—41no—
57#13136C1111yesmaximal, characteristic, direct product factor, Sylow
58C24×C11—41no—
59C2×D4×C11—22no—
60C2×D4×C11—41no—
61C2×D4×C11—41no—
62C2×D4×C11—41no—
63C2×D4×C11—41no—
64C2×D4×C11—41no—
65C22×C4×C11—21no—
66C22×C4×C11—41no—
67C22×C4×C11C2×D411yescharacteristic
68C11×D8—22no—
69C11×D8—22no—
70C11×D8—41no—
71C11×D8—41no—
72C11×M16—22no—
73C11×M16—41no—
74C2×C8×C11—21no—
75C2×C8×C11—21no—
76C2×C8×C11—41no—
77C2×C8×C11D811yescharacteristic
78C2×C8×C11D811yescharacteristic
79C2×C8×C11C22×C411yescharacteristic
80C2×C8×C11C2×D411yescharacteristic
81C2×C8×C11#4111yescharacteristic
82C2×C8×C11#4111yescharacteristic
83C2×C8×C11#4111yescharacteristic
84C2×C8×C11#4111yescharacteristic
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—84no—
91C42×C11—21no—
92C42×C11—21no—
93C42×C11—41no—
94C11×C16—22no—
95C11×C16—41no—
96#2159C2×C1111yescharacteristic, complemented
97C2×#361C2×C1111yescharacteristic
98#2140C2×C1111yescharacteristic
99#1970C2×C1111yescharacteristic
100#1772C2×C1111yescharacteristic, complemented
101#1387C2×C1111yescharacteristic, complemented
102#1376C2×C1111yescharacteristic, complemented
103C23×C11—42no—
104C23×C11—82no—
105C23×C11—82no—
106C23×C11—81no—
107C23×C11—81no—
108C23×C11AGL(1,ℤ/8)11yescharacteristic
109D4×C11—42no—
110D4×C11—42no—
111D4×C11—81no—
112D4×C11—81no—
113C2×C4×C11—22no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—82no—
119C2×C4×C11—81no—
120C2×C4×C11C4×D411yescharacteristic
121C2×C4×C11#12111yescharacteristic
122C2×C4×C11#12311yescharacteristic
123C2×C4×C11C2×D811yescharacteristic
124C2×C4×C11#13511yescharacteristic
125C2×C4×C11#13711yescharacteristic
126C8×C11—21no—
127C8×C11—21no—
128C8×C11—42no—
129C8×C11#11711yescharacteristic
130C8×C11C4×D411yescharacteristic
131C8×C11#12411yescharacteristic
132C8×C11#12611yescharacteristic
133C22×D8C22×C1111yescharacteristic
134C2×M32C22×C1111yescharacteristic
135C2×M32C22×C1111yescharacteristic
136C2×#108C22×C1111yescharacteristic
137#427C22×C1111yescharacteristic
138C2×#107C22×C1111yescharacteristic
139C2×#102—21no—
140#405—21no—
141C2×C4×C8C22×C1111yescharacteristic
142#390—21no—
143#367—21no—
144#366—21no—
145#361C4×C1114yescomplemented
146#357—21no—
147#357—21no—
148#339—21no—
149C22×C11—21no—
150C22×C11—21no—
151C22×C11—84no—
152C22×C11—82no—
153C22×C11—162no—
154C22×C11—161no—
155C22×C11—161no—
156C22×C11#44011yescharacteristic
157C22×C11#45911yescharacteristic
158C22×C11#48211yescharacteristic
159C4×C11—42no—
160C4×C11—81no—
161C4×C11—81no—
162C4×C11—161no—
163C4×C11#38811yescharacteristic
164C4×C11C4×D811yescharacteristic
165C4×C11#46411yescharacteristic
166C4×C11#48011yescharacteristic
167C22×D4—21no—
168C2×D8—21no—
169C2×D8—21no—
170C2×D8—21no—
171C2×D8—21no—
172C2×D8—21no—
173C2×D8C2×C4×C1112yes—
174C2×M16—21no—
175C22×C8D4×C1111yescharacteristic
176C22×C8C23×C1111yescharacteristic
177#117—21no—
178C2×C4⋊C4—21no—
179C2×C22⋊C4—42no—
180C2×C42D4×C1111yescharacteristic
181M32—21no—
182M32—21no—
183M32—21no—
184M32C2×C4×C1112yes—
185C2×C16—21no—
186C2×C16—21no—
187#108—21no—
188#108C2×C4×C1112yes—
189#107—21no—
190#107—21no—
191#107D4×C1111yescharacteristic
192#107D4×C1111yescharacteristic
193#106—21no—
194#102—41no—
195#102—41no—
196#97—41no—
197C4×C8—21no—
198C4×C8—21no—
199C4×C8—41no—
200C2×C11—21no—
201C2×C11—21no—
202C2×C11—162no—
203C2×C11#192511yescharacteristic
204C2×C11#221211yescharacteristic
205C2×C11#221311yescharacteristic
206C24—41no—
207C2×D4—22no—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4—41no—
211C2×D4—41no—
212C2×D4—41no—
213C22×C4—21no—
214C22×C4—41no—
215C22×C4C2×D4×C1111yescharacteristic
216D8—22no—
217D8—22no—
218D8—41no—
219D8—41no—
220M16—22no—
221M16—41no—
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—41no—
225C2×C8C11×D811yescharacteristic
226C2×C8C11×D811yescharacteristic
227C2×C8C22×C4×C1111yescharacteristic
228C2×C8C2×D4×C1111yescharacteristic
229C2×C8C11×#4111yescharacteristic
230C2×C8C11×#4111yescharacteristic
231C2×C8C11×#4111yescharacteristic
232C2×C8C11×#4111yescharacteristic
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C22⋊C4—41no—
238C22⋊C4—84no—
239C42—21no—
240C42—21no—
241C42—41no—
242C16—22no—
243C16—41no—
244C11#1313611yescharacteristic, direct product factor, Sylow
245C23—42no—
246C23—82no—
247C23—82no—
248C23—81no—
249C23—81no—
250C23C11×AGL(1,ℤ/8)11yescharacteristic
251D4—42no—
252D4—42no—
253D4—81no—
254D4—81no—
255C2×C4—22no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—82no—
261C2×C4—81no—
262C2×C4C4×D4×C1111yescharacteristic
263C2×C4C11×#12111yescharacteristic
264C2×C4C11×#12311yescharacteristic
265C2×C4C2×C11×D811yescharacteristic
266C2×C4C11×#13511yescharacteristic
267C2×C4C11×#13711yescharacteristic
268C8—21no—
269C8—21no—
270C8—42no—
271C8C11×#11711yescharacteristic
272C8C4×D4×C1111yescharacteristic
273C8C11×#12411yescharacteristic
274C8C11×#12611yescharacteristic
275C22—21no—
276C22—21no—
277C22—84no—
278C22—82no—
279C22—162no—
280C22—161no—
281C22—161no—
282C22C11×#44011yescharacteristic
283C22C11×#45911yescharacteristic
284C22C11×#48211yescharacteristic
285C4—42no—
286C4—81no—
287C4—81no—
288C4—161no—
289C4C11×#38811yescharacteristic
290C4C4×C11×D811yescharacteristic
291C4C11×#46411yescharacteristic
292C4C11×#48011yescharacteristic
293C2—21no—
294C2—21no—
295C2—162no—
296C2C11×#192511yescharacteristic
297C2C11×#221211yescharacteristic
298C2C11×#221311yescharacteristic
subgroupG/H
center, socleC22×C11#459
commutatorC2×C8C22×C4×C11
Frattini, cosocleC22×C8C23×C11
prime radicalC22×C11×D8C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2159C2semidirect
5. C11×#1772C2semidirect
6. C11×#1387C2semidirect
7. C11×#1376C2semidirect
20. C11×#361C4semidirect
57. #13136C11direct (N × H)
96. #2159C2×C11semidirect
100. #1772C2×C11semidirect
101. #1387C2×C11semidirect
102. #1376C2×C11semidirect
145. #361C4×C11semidirect
244. C11#13136direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#21592
C2×C11×#3612
C11×#21402
C11×#19702
C11×#17722
C11×#13872
C11×#13762
#1313611