Finite Group Databasebeta

← C11×#13140 #14590333

Subgroups — C11×#13140 #14590333

Order 2816.

314 conjugacy classes of subgroups.

The subgroup lattice has 278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2155C211yesmaximal, characteristic, complemented
2C11×#2148C211yesmaximal, characteristic
3C11×#2145C211yesmaximal, characteristic
4C11×#1975C211yesmaximal, characteristic
5C11×#1773C211yesmaximal, characteristic, complemented
6C11×#1385C211yesmaximal, characteristic, complemented
7C11×#1377C211yesmaximal, characteristic, complemented
8C2×C11×#135C2211yescharacteristic
9C2×C11×M32C2211yescharacteristic
10C2×C11×M32C2211yescharacteristic
11C2×C11×#108C2211yescharacteristic
12C2×C11×#108C2211yescharacteristic
13C11×#427C2211yescharacteristic
14C2×C11×#104—21no—
15C11×#408—21no—
16C11×#405—21no—
17C2×C11×#97C2211yescharacteristic
18C11×#365—22no—
19C11×#362C412yescomplemented
20C11×#361C412yescomplemented
21C11×#360—22no—
22C11×#339—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—
33C22×C8×C11D411yescharacteristic
34C22×C8×C11C2311yescharacteristic
35C11×#117—21no—
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×#108C2×C412yes—
47C11×#107—21no—
48C11×#106D412yes—
49C11×#104—42no—
50C11×C22⋊C8—42no—
51C11×#97—21no—
52C11×#97—21no—
53C11×#97—41no—
54C4×C8×C11—41no—
55#13140C1111yesmaximal, characteristic, direct product factor, Sylow
56C11×#41—41no—
57C11×#41—41no—
58C11×#41—41no—
59C11×#41—41no—
60C2×Q8×C11—21no—
61C2×D4×C11—21no—
62C2×D4×C11—41no—
63C22×C4×C11—21no—
64C22×C4×C11—41no—
65C22×C4×C11C2×D411yescharacteristic
66C11×Q16—21no—
67C11×Q16—21no—
68C11×SD16—41no—
69C11×SD16—41no—
70C11×D8—21no—
71C11×D8—21no—
72C11×M16—22no—
73C11×M16—41no—
74C11×M16—41no—
75C11×M16—41no—
76C2×C8×C11—21no—
77C2×C8×C11—21no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C2×C8×C11SD1612yes—
81C2×C8×C11C22×C411yescharacteristic
82C2×C8×C11C2×D411yescharacteristic
83C2×C8×C11#4111yescharacteristic
84C2×C8×C11#4111yescharacteristic
85C2×C8×C11#4111yescharacteristic
86C2×C8×C11#4111yescharacteristic
87C11×C4⋊C4—22no—
88C11×C22⋊C4—41no—
89C42×C11—21no—
90C42×C11—21no—
91C42×C11—41no—
92C11×C16—22no—
93C11×C16—41no—
94#2155C2×C1111yescharacteristic, complemented
95#2148C2×C1111yescharacteristic
96#2145C2×C1111yescharacteristic
97#1975C2×C1111yescharacteristic
98#1773C2×C1111yescharacteristic, complemented
99#1385C2×C1111yescharacteristic, complemented
100#1377C2×C1111yescharacteristic, complemented
101C23×C11—41no—
102C23×C11#13511yescharacteristic
103Q8×C11—41no—
104Q8×C11—41no—
105D4×C11—41no—
106D4×C11—41no—
107D4×C11—81no—
108D4×C11—81no—
109C2×C4×C11—41no—
110C2×C4×C11—42no—
111C2×C4×C11—41no—
112C2×C4×C11—81no—
113C2×C4×C11—81no—
114C2×C4×C11—81no—
115C2×C4×C11C4×D411yescharacteristic
116C2×C4×C11#12111yescharacteristic
117C2×C4×C11#12311yescharacteristic
118C2×C4×C11C2×SD1611yescharacteristic
119C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
121C8×C11—22no—
122C8×C11—42no—
123C8×C11—81no—
124C8×C11#11711yescharacteristic
125C8×C11C4×D411yescharacteristic
126C8×C11#12411yescharacteristic
127C8×C11#12611yescharacteristic
128C2×#135C22×C1111yescharacteristic
129C2×M32C22×C1111yescharacteristic
130C2×M32C22×C1111yescharacteristic
131C2×#108C22×C1111yescharacteristic
132C2×#108C22×C1111yescharacteristic
133#427C22×C1111yescharacteristic
134C2×#104—21no—
135#408—21no—
136#405—21no—
137C2×#97C22×C1111yescharacteristic
138#365—22no—
139#362C4×C1112yescomplemented
140#361C4×C1112yescomplemented
141#360—22no—
142#339—21no—
143C22×C11—41no—
144C22×C11—82no—
145C22×C11—81no—
146C22×C11C4×SD1611yescharacteristic
147C22×C11#46311yescharacteristic
148C22×C11#48211yescharacteristic
149C4×C11—82no—
150C4×C11—81no—
151C4×C11—81no—
152C4×C11#38811yescharacteristic
153C4×C11#44211yescharacteristic
154C4×C11#46011yescharacteristic
155C4×C11#48111yescharacteristic
156C2×#41—21no—
157#135—21no—
158#135—21no—
159#135—21no—
160#135—21no—
161C2×Q16C2×C4×C1111yescharacteristic
162C2×SD16—21no—
163C2×D8C2×C4×C1111yescharacteristic
164C2×M16—21no—
165C2×M16—21no—
166C22×C8D4×C1111yescharacteristic
167C22×C8C23×C1111yescharacteristic
168#117—21no—
169C2×C42D4×C1111yescharacteristic
170M32—21no—
171M32—21no—
172M32—21no—
173M32C2×C4×C1112yes—
174C2×C16—21no—
175C2×C16—21no—
176#108—21no—
177#108—21no—
178#108—21no—
179#108C2×C4×C1112yes—
180#107—21no—
181#106D4×C1112yes—
182#104—42no—
183C22⋊C8—42no—
184#97—21no—
185#97—21no—
186#97—41no—
187C4×C8—41no—
188C2×C11—21no—
189C2×C11—21no—
190C2×C11—21no—
191C2×C11—161no—
192C2×C11#192611yescharacteristic
193#41—41no—
194#41—41no—
195#41—41no—
196#41—41no—
197C2×Q8—21no—
198C2×D4—21no—
199C2×D4—41no—
200C22×C4—21no—
201C22×C4—41no—
202C22×C4C2×D4×C1111yescharacteristic
203Q16—21no—
204Q16—21no—
205SD16—41no—
206SD16—41no—
207D8—21no—
208D8—21no—
209M16—22no—
210M16—41no—
211M16—41no—
212M16—41no—
213C2×C8—21no—
214C2×C8—21no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8C11×SD1612yes—
218C2×C8C22×C4×C1111yescharacteristic
219C2×C8C2×D4×C1111yescharacteristic
220C2×C8C11×#4111yescharacteristic
221C2×C8C11×#4111yescharacteristic
222C2×C8C11×#4111yescharacteristic
223C2×C8C11×#4111yescharacteristic
224C4⋊C4—22no—
225C22⋊C4—41no—
226C42—21no—
227C42—21no—
228C42—41no—
229C16—22no—
230C16—41no—
231C11#1314011yescharacteristic, direct product factor, Sylow
232C23—41no—
233C23C11×#13511yescharacteristic
234Q8—41no—
235Q8—41no—
236D4—41no—
237D4—41no—
238D4—81no—
239D4—81no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—41no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4C4×D4×C1111yescharacteristic
247C2×C4C11×#12111yescharacteristic
248C2×C4C11×#12311yescharacteristic
249C2×C4C2×C11×SD1611yescharacteristic
250C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
251C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
252C8—22no—
253C8—42no—
254C8—81no—
255C8C11×#11711yescharacteristic
256C8C4×D4×C1111yescharacteristic
257C8C11×#12411yescharacteristic
258C8C11×#12611yescharacteristic
259C22—41no—
260C22—82no—
261C22—81no—
262C22C4×C11×SD1611yescharacteristic
263C22C11×#46311yescharacteristic
264C22C11×#48211yescharacteristic
265C4—81no—
266C4—82no—
267C4—81no—
268C4C11×#38811yescharacteristic
269C4C11×#44211yescharacteristic
270C4C11×#46011yescharacteristic
271C4C11×#48111yescharacteristic
272C2—21no—
273C2—21no—
274C2—21no—
275C2—161no—
276C2C11×#192611yescharacteristic
subgroupG/H
centerC4×C11#481
commutatorC2×C8C22×C4×C11
Frattini, cosocleC22×C8C23×C11
socleC2×C11#1926
prime radicalC2×C11×#135C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C11 ◁ C22×C4×C11 ◁ C2×C11×#97 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2155C2semidirect
5. C11×#1773C2semidirect
6. C11×#1385C2semidirect
7. C11×#1377C2semidirect
19. C11×#362C4semidirect
20. C11×#361C4semidirect
55. #13140C11direct (N × H)
94. #2155C2×C11semidirect
98. #1773C2×C11semidirect
99. #1385C2×C11semidirect
100. #1377C2×C11semidirect
139. #362C4×C11semidirect
140. #361C4×C11semidirect
231. C11#13140direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#21552
C11×#21482
C11×#21452
C11×#19752
C11×#17732
C11×#13852
C11×#13772
#1314011