Finite Group Databasebeta

← C11×#13137 #14590330

Subgroups — C11×#13137 #14590330

Order 2816.

316 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2161C211yesmaximal, characteristic, complemented
2C11×#2148C211yesmaximal, characteristic
3C11×#2143C211yesmaximal, characteristic
4C11×#1974C211yesmaximal, characteristic
5C4×C11×#108C211yesmaximal, characteristic, complemented
6C11×#1388C211yesmaximal, characteristic, complemented
7C11×#1376C211yesmaximal, characteristic, complemented
8C2×C11×#135C2211yescharacteristic
9C2×C11×M32C2211yescharacteristic
10C2×C11×M32C2211yescharacteristic
11C2×C11×#108C2211yescharacteristic
12C2×C11×#108C2211yescharacteristic
13C2×C11×#108C2211yescharacteristic
14C2×C11×#104—21no—
15C11×#408—21no—
16C4×C11×M16—21no—
17C2×C4×C8×C11C2211yescharacteristic
18C11×#368—22no—
19C11×#362C412yescomplemented
20C11×#361C412yescomplemented
21C11×#359—22no—
22C11×#341—21no—
23C2×C11×#41—21no—
24C11×#135—21no—
25C11×#135—21no—
26C11×#135—21no—
27C11×#135—21no—
28C2×C11×Q16C2×C411yescharacteristic
29C2×C11×SD16—21no—
30C2×C11×D8C2×C411yescharacteristic
31C2×C11×M16—21no—
32C2×C11×M16—21no—
33C2×C11×M16—21no—
34C22×C8×C11D411yescharacteristic
35C22×C8×C11C2311yescharacteristic
36C2×C42×C11D411yescharacteristic
37C11×M32—21no—
38C11×M32—21no—
39C11×M32—21no—
40C11×M32C2×C412yes—
41C2×C11×C16—21no—
42C2×C11×C16—21no—
43C11×#108—21no—
44C11×#108—21no—
45C11×#108—21no—
46C11×#108—21no—
47C11×#108C2×C412yes—
48C11×#108D412yes—
49C11×#104—41no—
50C11×#104—41no—
51C11×C22⋊C8—42no—
52C11×#97—41no—
53C4×C8×C11—21no—
54C4×C8×C11—21no—
55C4×C8×C11—41no—
56#13137C1111yesmaximal, characteristic, direct product factor, Sylow
57C11×#41—41no—
58C11×#41—41no—
59C11×#41—41no—
60C11×#41—41no—
61C2×Q8×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11—41no—
64C22×C4×C11—21no—
65C22×C4×C11—41no—
66C22×C4×C11C2×D411yescharacteristic
67C11×Q16—21no—
68C11×Q16—21no—
69C11×SD16—41no—
70C11×SD16—41no—
71C11×D8—21no—
72C11×D8—21no—
73C11×M16—22no—
74C11×M16—22no—
75C11×M16—41no—
76C11×M16—41no—
77C11×M16—41no—
78C11×M16—41no—
79C2×C8×C11—21no—
80C2×C8×C11—21no—
81C2×C8×C11—21no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C2×C8×C11C22×C411yescharacteristic
86C2×C8×C11C2×D411yescharacteristic
87C2×C8×C11#4111yescharacteristic
88C2×C8×C11#4111yescharacteristic
89C2×C8×C11#4111yescharacteristic
90C2×C8×C11#4111yescharacteristic
91C42×C11—21no—
92C42×C11D811yescharacteristic
93C42×C11D811yescharacteristic
94C11×C16—22no—
95C11×C16—41no—
96#2161C2×C1111yescharacteristic, complemented
97#2148C2×C1111yescharacteristic
98#2143C2×C1111yescharacteristic
99#1974C2×C1111yescharacteristic
100C4×#108C2×C1111yescharacteristic, complemented
101#1388C2×C1111yescharacteristic, complemented
102#1376C2×C1111yescharacteristic, complemented
103C23×C11—41no—
104C23×C11#13711yescharacteristic
105Q8×C11—41no—
106Q8×C11—41no—
107D4×C11—41no—
108D4×C11—41no—
109D4×C11—81no—
110D4×C11—81no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—42no—
114C2×C4×C11—41no—
115C2×C4×C11—81no—
116C2×C4×C11—81no—
117C2×C4×C11C4×D411yescharacteristic
118C2×C4×C11#12111yescharacteristic
119C2×C4×C11#12311yescharacteristic
120C2×C4×C11C2×D811yescharacteristic
121C2×C4×C11#13511yescharacteristic
122C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
123C8×C11—42no—
124C8×C11—42no—
125C8×C11—41no—
126C8×C11—81no—
127C8×C11#11711yescharacteristic
128C8×C11C4×D411yescharacteristic
129C8×C11#12411yescharacteristic
130C8×C11#12611yescharacteristic
131C2×#135C22×C1111yescharacteristic
132C2×M32C22×C1111yescharacteristic
133C2×M32C22×C1111yescharacteristic
134C2×#108C22×C1111yescharacteristic
135C2×#108C22×C1111yescharacteristic
136C2×#108C22×C1111yescharacteristic
137C2×#104—21no—
138#408—21no—
139C4×M16—21no—
140C2×C4×C8C22×C1111yescharacteristic
141#368—22no—
142#362C4×C1112yescomplemented
143#361C4×C1112yescomplemented
144#359—22no—
145#341—21no—
146C22×C11—41no—
147C22×C11—82no—
148C22×C11—81no—
149C22×C11#44011yescharacteristic
150C22×C11#46411yescharacteristic
151C22×C11#48011yescharacteristic
152C4×C11—22no—
153C4×C11—41no—
154C4×C11—81no—
155C4×C11#38811yescharacteristic
156C4×C11C4×D811yescharacteristic
157C4×C11#45911yescharacteristic
158C4×C11#48211yescharacteristic
159C2×#41—21no—
160#135—21no—
161#135—21no—
162#135—21no—
163#135—21no—
164C2×Q16C2×C4×C1111yescharacteristic
165C2×SD16—21no—
166C2×D8C2×C4×C1111yescharacteristic
167C2×M16—21no—
168C2×M16—21no—
169C2×M16—21no—
170C22×C8D4×C1111yescharacteristic
171C22×C8C23×C1111yescharacteristic
172C2×C42D4×C1111yescharacteristic
173M32—21no—
174M32—21no—
175M32—21no—
176M32C2×C4×C1112yes—
177C2×C16—21no—
178C2×C16—21no—
179#108—21no—
180#108—21no—
181#108—21no—
182#108—21no—
183#108C2×C4×C1112yes—
184#108D4×C1112yes—
185#104—41no—
186#104—41no—
187C22⋊C8—42no—
188#97—41no—
189C4×C8—21no—
190C4×C8—21no—
191C4×C8—41no—
192C2×C11—21no—
193C2×C11—21no—
194C2×C11—21no—
195C2×C11—161no—
196C2×C11#192511yescharacteristic
197#41—41no—
198#41—41no—
199#41—41no—
200#41—41no—
201C2×Q8—21no—
202C2×D4—21no—
203C2×D4—41no—
204C22×C4—21no—
205C22×C4—41no—
206C22×C4C2×D4×C1111yescharacteristic
207Q16—21no—
208Q16—21no—
209SD16—41no—
210SD16—41no—
211D8—21no—
212D8—21no—
213M16—22no—
214M16—22no—
215M16—41no—
216M16—41no—
217M16—41no—
218M16—41no—
219C2×C8—21no—
220C2×C8—21no—
221C2×C8—21no—
222C2×C8—41no—
223C2×C8—41no—
224C2×C8—41no—
225C2×C8C22×C4×C1111yescharacteristic
226C2×C8C2×D4×C1111yescharacteristic
227C2×C8C11×#4111yescharacteristic
228C2×C8C11×#4111yescharacteristic
229C2×C8C11×#4111yescharacteristic
230C2×C8C11×#4111yescharacteristic
231C42—21no—
232C42C11×D811yescharacteristic
233C42C11×D811yescharacteristic
234C16—22no—
235C16—41no—
236C11#1313711yescharacteristic, direct product factor, Sylow
237C23—41no—
238C23C11×#13711yescharacteristic
239Q8—41no—
240Q8—41no—
241D4—41no—
242D4—41no—
243D4—81no—
244D4—81no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4C4×D4×C1111yescharacteristic
252C2×C4C11×#12111yescharacteristic
253C2×C4C11×#12311yescharacteristic
254C2×C4C2×C11×D811yescharacteristic
255C2×C4C11×#13511yescharacteristic
256C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
257C8—42no—
258C8—42no—
259C8—41no—
260C8—81no—
261C8C11×#11711yescharacteristic
262C8C4×D4×C1111yescharacteristic
263C8C11×#12411yescharacteristic
264C8C11×#12611yescharacteristic
265C22—41no—
266C22—82no—
267C22—81no—
268C22C11×#44011yescharacteristic
269C22C11×#46411yescharacteristic
270C22C11×#48011yescharacteristic
271C4—22no—
272C4—41no—
273C4—81no—
274C4C11×#38811yescharacteristic
275C4C4×C11×D811yescharacteristic
276C4C11×#45911yescharacteristic
277C4C11×#48211yescharacteristic
278C2—21no—
279C2—21no—
280C2—21no—
281C2—161no—
282C2C11×#192511yescharacteristic
subgroupG/H
centerC4×C11#459
commutatorC2×C8C22×C4×C11
Frattini, cosocleC22×C8C23×C11
socleC2×C11#1925
prime radicalC2×C11×#135C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×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×#2161C2semidirect
5. C4×C11×#108C2semidirect
6. C11×#1388C2semidirect
7. C11×#1376C2semidirect
19. C11×#362C4semidirect
20. C11×#361C4semidirect
56. #13137C11direct (N × H)
96. #2161C2×C11semidirect
100. C4×#108C2×C11semidirect
101. #1388C2×C11semidirect
102. #1376C2×C11semidirect
142. #362C4×C11semidirect
143. #361C4×C11semidirect
236. C11#13137direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#21612
C11×#21482
C11×#21432
C11×#19742
C4×C11×#1082
C11×#13882
C11×#13762
#1313711