Finite Group Databasebeta

← C11×#13466 #14590659

Subgroups — C11×#13466 #14590659

Order 2816.

314 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×#2155C211yesmaximal, characteristic, complemented
2C11×#2150C211yesmaximal, characteristic, complemented
3C11×#2145C211yesmaximal, characteristic
4C11×#2143C211yesmaximal, characteristic
5C11×#1974C211yesmaximal, characteristic
6C11×#1945C211yesmaximal, characteristic, complemented
7C11×#1388C211yesmaximal, characteristic, complemented
8C2×C11×#135C2211yescharacteristic
9C2×C11×M32C2211yescharacteristic
10C2×C11×M32C2211yescharacteristic
11C2×C11×#108C2211yescharacteristic
12C2×C11×#108C2211yescharacteristic
13C11×#427C2211yescharacteristic
14C11×#424—21no—
15C2×C11×#104—21no—
16C11×#408—21no—
17C2×C4×C8×C11C2211yescharacteristic
18C11×#365—22no—
19C11×C4⋊C16—22no—
20C11×#360—22no—
21C11×#359—22no—
22C11×#339—21no—
23C2×C11×#41—21no—
24C11×#135—21no—
25C11×#135—21no—
26C11×#135—21no—
27C11×#135—21no—
28C2×C11×Q16Q811yescharacteristic
29C2×C11×SD16—21no—
30C2×C11×D8Q811yescharacteristic
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×M32—21no—
41C2×C11×C16—21no—
42C2×C11×C16D412yes—
43C11×#108—21no—
44C11×#108—21no—
45C11×#108—21no—
46C11×#108—21no—
47C11×#107—21no—
48C11×#106D412yes—
49C11×C4⋊C8—42no—
50C11×#104—41no—
51C11×#104—41no—
52C11×C22⋊C8—42no—
53C4×C8×C11—21no—
54C4×C8×C11—21no—
55#13466C1111yesmaximal, 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—41no—
73C11×M16—41no—
74C11×M16—41no—
75C11×M16—41no—
76C2×C8×C11—21no—
77C2×C8×C11—21no—
78C2×C8×C11—21no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C2×C8×C11C2×D411yescharacteristic
82C2×C8×C11C2×D411yescharacteristic
83C2×C8×C11C2×Q811yescharacteristic
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—41no—
91C42×C11SD1611yescharacteristic
92C42×C11SD1611yescharacteristic
93C11×C16—22no—
94C11×C16—41no—
95#2155C2×C1111yescharacteristic, complemented
96#2150C2×C1111yescharacteristic, complemented
97#2145C2×C1111yescharacteristic
98#2143C2×C1111yescharacteristic
99#1974C2×C1111yescharacteristic
100#1945C2×C1111yescharacteristic, complemented
101#1388C2×C1111yescharacteristic, complemented
102C23×C11—41no—
103C23×C11#13511yescharacteristic
104Q8×C11—41no—
105Q8×C11—41no—
106D4×C11—41no—
107D4×C11—41no—
108D4×C11—81no—
109D4×C11—81no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11—41no—
115C2×C4×C11—81no—
116C2×C4×C11—81no—
117C2×C4×C11#12111yescharacteristic
118C2×C4×C11#12111yescharacteristic
119C2×C4×C11C22⋊Q811yescharacteristic
120C2×C4×C11C2×SD1611yescharacteristic
121C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
123C8×C11—41no—
124C8×C11—81no—
125C8×C11—81no—
126C8×C11#12111yescharacteristic
127C8×C11C22⋊Q811yescharacteristic
128C8×C11C22⋊Q811yescharacteristic
129C8×C11#12611yescharacteristic
130C2×#135C22×C1111yescharacteristic
131C2×M32C22×C1111yescharacteristic
132C2×M32C22×C1111yescharacteristic
133C2×#108C22×C1111yescharacteristic
134C2×#108C22×C1111yescharacteristic
135#427C22×C1111yescharacteristic
136#424—21no—
137C2×#104—21no—
138#408—21no—
139C2×C4×C8C22×C1111yescharacteristic
140#365—22no—
141C4⋊C16—22no—
142#360—22no—
143#359—22no—
144#339—21no—
145C22×C11—41no—
146C22×C11—82no—
147C22×C11—81no—
148C22×C11#46311yescharacteristic
149C22×C11#46511yescharacteristic
150C22×C11#47811yescharacteristic
151C4×C11—22no—
152C4×C11—41no—
153C4×C11—82no—
154C4×C11—81no—
155C4×C11#39611yescharacteristic
156C4×C11#46011yescharacteristic
157C4×C11#46911yescharacteristic
158C4×C11#47611yescharacteristic
159C2×#41—21no—
160#135—21no—
161#135—21no—
162#135—21no—
163#135—21no—
164C2×Q16Q8×C1111yescharacteristic
165C2×SD16—21no—
166C2×D8Q8×C1111yescharacteristic
167C2×M16—21no—
168C2×M16—21no—
169C22×C8D4×C1111yescharacteristic
170C22×C8C23×C1111yescharacteristic
171#117—21no—
172C2×C42D4×C1111yescharacteristic
173M32—21no—
174M32—21no—
175M32—21no—
176M32—21no—
177C2×C16—21no—
178C2×C16D4×C1112yes—
179#108—21no—
180#108—21no—
181#108—21no—
182#108—21no—
183#107—21no—
184#106D4×C1112yes—
185C4⋊C8—42no—
186#104—41no—
187#104—41no—
188C22⋊C8—42no—
189C4×C8—21no—
190C4×C8—21no—
191C2×C11—21no—
192C2×C11—21no—
193C2×C11—21no—
194C2×C11—161no—
195C2×C11#206511yescharacteristic
196#41—41no—
197#41—41no—
198#41—41no—
199#41—41no—
200C2×Q8—21no—
201C2×D4—21no—
202C2×D4—41no—
203C22×C4—21no—
204C22×C4—41no—
205C22×C4C2×D4×C1111yescharacteristic
206Q16—21no—
207Q16—21no—
208SD16—41no—
209SD16—41no—
210D8—21no—
211D8—21no—
212M16—41no—
213M16—41no—
214M16—41no—
215M16—41no—
216C2×C8—21no—
217C2×C8—21no—
218C2×C8—21no—
219C2×C8—41no—
220C2×C8—41no—
221C2×C8C2×D4×C1111yescharacteristic
222C2×C8C2×D4×C1111yescharacteristic
223C2×C8C2×Q8×C1111yescharacteristic
224C2×C8C11×#4111yescharacteristic
225C2×C8C11×#4111yescharacteristic
226C2×C8C11×#4111yescharacteristic
227C4⋊C4—22no—
228C22⋊C4—41no—
229C42—21no—
230C42—41no—
231C42C11×SD1611yescharacteristic
232C42C11×SD1611yescharacteristic
233C16—22no—
234C16—41no—
235C11#1346611yescharacteristic, direct product factor, Sylow
236C23—41no—
237C23C11×#13511yescharacteristic
238Q8—41no—
239Q8—41no—
240D4—41no—
241D4—41no—
242D4—81no—
243D4—81no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4C11×#12111yescharacteristic
252C2×C4C11×#12111yescharacteristic
253C2×C4C11×C22⋊Q811yescharacteristic
254C2×C4C2×C11×SD1611yescharacteristic
255C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
256C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
257C8—41no—
258C8—81no—
259C8—81no—
260C8C11×#12111yescharacteristic
261C8C11×C22⋊Q811yescharacteristic
262C8C11×C22⋊Q811yescharacteristic
263C8C11×#12611yescharacteristic
264C22—41no—
265C22—82no—
266C22—81no—
267C22C11×#46311yescharacteristic
268C22C11×#46511yescharacteristic
269C22C11×#47811yescharacteristic
270C4—22no—
271C4—41no—
272C4—82no—
273C4—81no—
274C4C11×#39611yescharacteristic
275C4C11×#46011yescharacteristic
276C4C11×#46911yescharacteristic
277C4C11×#47611yescharacteristic
278C2—21no—
279C2—21no—
280C2—21no—
281C2—161no—
282C2C11×#206511yescharacteristic
subgroupG/H
centerC4×C11#469
commutator, Frattini, cosocleC22×C8C23×C11
socleC2×C11#2065
prime radicalC2×C11×#135C22
LCSG ▷ C22×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×#2155C2semidirect
2. C11×#2150C2semidirect
6. C11×#1945C2semidirect
7. C11×#1388C2semidirect
55. #13466C11direct (N × H)
95. #2155C2×C11semidirect
96. #2150C2×C11semidirect
100. #1945C2×C11semidirect
101. #1388C2×C11semidirect
235. C11#13466direct (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×#21502
C11×#21452
C11×#21432
C11×#19742
C11×#19452
C11×#13882
#1346611