Finite Group Databasebeta

← C11×#13146 #14590339

Subgroups — C11×#13146 #14590339

Order 2816.

312 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2148C211yesmaximal, characteristic
2C2×C11×#359C211yesmaximal, characteristic
3C11×#2108C211yesmaximal, characteristic, complemented
4C11×#1976C211yesmaximal, characteristic
5C11×#1953C211yesmaximal, characteristic, complemented
6C11×#1389C211yesmaximal, characteristic, complemented
7C11×#1382C211yesmaximal, characteristic, complemented
8C2×C11×#135C2211yescharacteristic
9C2×C11×M32C2211yescharacteristic
10C22×C11×C16C2211yescharacteristic
11C11×#430—21no—
12C2×C11×#108C2211yescharacteristic
13C2×C11×#108C2211yescharacteristic
14C11×#427C2211yescharacteristic
15C11×#421—21no—
16C11×#410—21no—
17C11×#405C2211yescharacteristic
18C11×#362C412yescomplemented
19C11×#361C412yescomplemented
20C11×#359—21no—
21C11×#359—21no—
22C11×#346—21no—
23C4×C11×C16—21no—
24C11×#344—21no—
25C2×C11×#41—21no—
26C11×#135—21no—
27C11×#135—21no—
28C11×#135—21no—
29C11×#135—21no—
30C2×C11×Q16C2×C411yescharacteristic
31C2×C11×SD16—21no—
32C2×C11×D8C2×C411yescharacteristic
33C2×C11×M16—21no—
34C2×C11×M16—21no—
35C2×C11×M16D411yescharacteristic
36C22×C8×C11C2311yescharacteristic
37C11×#117—21no—
38C11×#117D411yescharacteristic
39C11×M32—21no—
40C11×M32C2×C412yes—
41C2×C11×C16—21no—
42C2×C11×C16—21no—
43C2×C11×C16—21no—
44C2×C11×C16D411yescharacteristic
45C2×C11×C16D411yescharacteristic
46C11×#108—21no—
47C11×#108—21no—
48C11×#108—21no—
49C11×#108—42no—
50C11×#108C2×C412yes—
51C11×#107—21no—
52C11×#106—21no—
53C11×#104—42no—
54C11×#99—42no—
55C11×#97—21no—
56C4×C8×C11—21no—
57#13146C1111yesmaximal, characteristic, direct product factor, Sylow
58C11×#41—41no—
59C11×#41—41no—
60C11×#41—41no—
61C11×#41—41no—
62C2×Q8×C11—21no—
63C2×D4×C11—21no—
64C2×D4×C11—41no—
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—21no—
75C11×M16—41no—
76C11×M16—41no—
77C11×M16—41no—
78C11×M16D812yes—
79C2×C8×C11—21no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C2×C8×C11C22×C411yescharacteristic
83C2×C8×C11C2×D411yescharacteristic
84C2×C8×C11#4111yescharacteristic
85C2×C8×C11#4111yescharacteristic
86C2×C8×C11#4111yescharacteristic
87C2×C8×C11#4111yescharacteristic
88C11×C4⋊C4—21no—
89C11×C4⋊C4—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4SD1612yes—
92C42×C11—21no—
93C42×C11—41no—
94C11×C16—22no—
95C11×C16—21no—
96C11×C16—21no—
97#2148C2×C1111yescharacteristic
98C2×#359C2×C1111yescharacteristic
99#2108C2×C1111yescharacteristic, complemented
100#1976C2×C1111yescharacteristic
101#1953C2×C1111yescharacteristic, complemented
102#1389C2×C1111yescharacteristic, complemented
103#1382C2×C1111yescharacteristic, complemented
104C23×C11—41no—
105C23×C11C2×SD1611yescharacteristic
106Q8×C11—41no—
107Q8×C11—41no—
108D4×C11—41no—
109D4×C11—41no—
110D4×C11—81no—
111D4×C11—81no—
112C2×C4×C11—22no—
113C2×C4×C11—41no—
114C2×C4×C11—81no—
115C2×C4×C11—81no—
116C2×C4×C11—81no—
117C2×C4×C11C4×D411yescharacteristic
118C2×C4×C11#12111yescharacteristic
119C2×C4×C11#12411yescharacteristic
120C2×C4×C11C2×D811yescharacteristic
121C2×C4×C11#13511yescharacteristic
122C2×C4×C11#13511yescharacteristic
123C8×C11—22no—
124C8×C11—42no—
125C8×C11—81no—
126C8×C11#11711yescharacteristic
127C8×C11C4×D411yescharacteristic
128C8×C11#12311yescharacteristic
129C8×C11#12611yescharacteristic
130C2×#135C22×C1111yescharacteristic
131C2×M32C22×C1111yescharacteristic
132C22×C16C22×C1111yescharacteristic
133#430—21no—
134C2×#108C22×C1111yescharacteristic
135C2×#108C22×C1111yescharacteristic
136#427C22×C1111yescharacteristic
137#421—21no—
138#410—21no—
139#405C22×C1111yescharacteristic
140#362C4×C1112yescomplemented
141#361C4×C1112yescomplemented
142#359—21no—
143#359—21no—
144#346—21no—
145C4×C16—21no—
146#344—21no—
147C22×C11—41no—
148C22×C11—81no—
149C22×C11—161no—
150C22×C11C4×SD1611yescharacteristic
151C22×C11#46511yescharacteristic
152C22×C11#48611yescharacteristic
153C4×C11—42no—
154C4×C11—81no—
155C4×C11—161no—
156C4×C11#38811yescharacteristic
157C4×C11C4×D811yescharacteristic
158C4×C11#46611yescharacteristic
159C4×C11#48811yescharacteristic
160C2×#41—21no—
161#135—21no—
162#135—21no—
163#135—21no—
164#135—21no—
165C2×Q16C2×C4×C1111yescharacteristic
166C2×SD16—21no—
167C2×D8C2×C4×C1111yescharacteristic
168C2×M16—21no—
169C2×M16—21no—
170C2×M16D4×C1111yescharacteristic
171C22×C8C23×C1111yescharacteristic
172#117—21no—
173#117D4×C1111yescharacteristic
174M32—21no—
175M32C2×C4×C1112yes—
176C2×C16—21no—
177C2×C16—21no—
178C2×C16—21no—
179C2×C16D4×C1111yescharacteristic
180C2×C16D4×C1111yescharacteristic
181#108—21no—
182#108—21no—
183#108—21no—
184#108—42no—
185#108C2×C4×C1112yes—
186#107—21no—
187#106—21no—
188#104—42no—
189#99—42no—
190#97—21no—
191C4×C8—21no—
192C2×C11—21no—
193C2×C11—21no—
194C2×C11—21no—
195C2×C11—161no—
196C2×C11#193411yescharacteristic
197#41—41no—
198#41—41no—
199#41—41no—
200#41—41no—
201C2×Q8—21no—
202C2×D4—21no—
203C2×D4—41no—
204C22×C4—41no—
205C22×C4C2×D4×C1111yescharacteristic
206Q16—21no—
207Q16—21no—
208SD16—41no—
209SD16—41no—
210D8—21no—
211D8—21no—
212M16—21no—
213M16—22no—
214M16—41no—
215M16—41no—
216M16—41no—
217M16C11×D812yes—
218C2×C8—21no—
219C2×C8—41no—
220C2×C8—41no—
221C2×C8C22×C4×C1111yescharacteristic
222C2×C8C2×D4×C1111yescharacteristic
223C2×C8C11×#4111yescharacteristic
224C2×C8C11×#4111yescharacteristic
225C2×C8C11×#4111yescharacteristic
226C2×C8C11×#4111yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—41no—
229C22⋊C4—41no—
230C22⋊C4C11×SD1612yes—
231C42—21no—
232C42—41no—
233C16—22no—
234C16—21no—
235C16—21no—
236C11#1314611yescharacteristic, direct product factor, Sylow
237C23—41no—
238C23C2×C11×SD1611yescharacteristic
239Q8—41no—
240Q8—41no—
241D4—41no—
242D4—41no—
243D4—81no—
244D4—81no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4C4×D4×C1111yescharacteristic
251C2×C4C11×#12111yescharacteristic
252C2×C4C11×#12411yescharacteristic
253C2×C4C2×C11×D811yescharacteristic
254C2×C4C11×#13511yescharacteristic
255C2×C4C11×#13511yescharacteristic
256C8—22no—
257C8—42no—
258C8—81no—
259C8C11×#11711yescharacteristic
260C8C4×D4×C1111yescharacteristic
261C8C11×#12311yescharacteristic
262C8C11×#12611yescharacteristic
263C22—41no—
264C22—81no—
265C22—161no—
266C22C4×C11×SD1611yescharacteristic
267C22C11×#46511yescharacteristic
268C22C11×#48611yescharacteristic
269C4—42no—
270C4—81no—
271C4—161no—
272C4C11×#38811yescharacteristic
273C4C4×C11×D811yescharacteristic
274C4C11×#46611yescharacteristic
275C4C11×#48811yescharacteristic
276C2—21no—
277C2—21no—
278C2—21no—
279C2—161no—
280C2C11×#193411yescharacteristic
subgroupG/H
centerC4×C11#466
commutatorC2×C8C22×C4×C11
Frattini, cosocleC22×C8C23×C11
socleC2×C11#1934
prime radicalC2×C11×#135C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C11 ◁ C22×C4×C11 ◁ C11×#405 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2108C2semidirect
5. C11×#1953C2semidirect
6. C11×#1389C2semidirect
7. C11×#1382C2semidirect
18. C11×#362C4semidirect
19. C11×#361C4semidirect
57. #13146C11direct (N × H)
99. #2108C2×C11semidirect
101. #1953C2×C11semidirect
102. #1389C2×C11semidirect
103. #1382C2×C11semidirect
140. #362C4×C11semidirect
141. #361C4×C11semidirect
236. C11#13146direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#21482
C2×C11×#3592
C11×#21082
C11×#19762
C11×#19532
C11×#13892
C11×#13822
#1314611