Finite Group Databasebeta

← C11×#33382 #14610575

Subgroups — C11×#33382 #14610575

Order 2816.

1124 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#578C211yesmaximal, characteristic
2C2×C11×#504C211yesmaximal, characteristic, complemented
3C11×#2913C211yesmaximal, characteristic, complemented
4C11×#2141C213yesmaximal, complemented
5C11×#2139C213yesmaximal, complemented
6C11×#2138C213yesmaximal, complemented
7C2×C11×#358C213yesmaximal, complemented
8C2×C11×2−1+4—21no—
9C11×#578—24no—
10C11×#578C418yescomplemented
11C2×C11×#137—23no—
12C2×C11×#135C2213yes—
13C22×C11×Q16C2213yes—
14C2×C11×#131C2211yescharacteristic
15C11×#520—21no—
16C11×#504—24no—
17C2×C11×M32C2213yes—
18C22×C11×C16C2213yes—
19C11×#428—23no—
20C11×#427C2213yes—
21C2×C11×#107C2213yes—
22C11×#358C2213yes—
23C11×#358C2216yes—
24C11×#358C2213yes—
25C11×#357C2211yescharacteristic
26C11×#357C2213yes—
27C11×2−1+4—28no—
28C11×2−1+4—44no—
29C2×C11×#41—23no—
30C2×C11×#41—43no—
31C2×C11×#41D411yescharacteristic
32C22×Q8×C11—23no—
33C22×Q8×C11—41no—
34C11×#137—224no—
35C11×#135—26no—
36C11×#135C2×C4112yescomplemented
37C2×C11×Q16—23no—
38C2×C11×Q16—26no—
39C2×C11×Q16C2×C4112yescomplemented
40C2×C11×Q16C2313yes—
41C2×C11×SD16—23no—
42C2×C11×D8C2311yescharacteristic
43C11×#131C2×C414yes—
44C11×#131D414yes—
45C2×C11×M16D413yes—
46C22×C8×C11C2313yes—
47C4×Q8×C11—41no—
48C4×D4×C11—43no—
49C11×#117—23no—
50C2×C11×C4⋊C4—23no—
51C11×M32—26no—
52C2×C11×C16—26no—
53C2×C11×C16C2311yescharacteristic
54C2×C11×C16C2313yes—
55C11×#107—23no—
56C11×#107C2313yes—
57C11×#107C2311yescharacteristic
58C11×#106—23no—
59#33382C1111yesmaximal, characteristic, direct product factor, Sylow
60C11×#41—212no—
61C11×#41—424no—
62C11×#41—46no—
63C11×#41C22⋊C414yes—
64C11×#41SD1614yes—
65C2×Q8×C11—212no—
66C2×Q8×C11—23no—
67C2×Q8×C11—48no—
68C2×Q8×C11—43no—
69C2×Q8×C11—46no—
70C2×Q8×C11D811yescharacteristic
71C2×D4×C11—21no—
72C2×D4×C11—43no—
73C2×D4×C11D813yes—
74C22×C4×C11—43no—
75C22×C4×C11—43no—
76C22×C4×C11—43no—
77C22×C4×C11C2×D413yes—
78C11×Q16—212no—
79C11×Q16—23no—
80C11×Q16C22×C416yes—
81C11×SD16—212no—
82C11×D8—21no—
83C11×D8C22×C412yes—
84C11×M16C22⋊C4112yes—
85C2×C8×C11C22×C416yes—
86C2×C8×C11C2×D416yes—
87C2×C8×C11C2×D413yes—
88C2×C8×C11C2411yescharacteristic
89C11×C4⋊C4—21no—
90C11×C4⋊C4—23no—
91C11×C4⋊C4—43no—
92C11×C22⋊C4—43no—
93C42×C11—43no—
94C11×C16—21no—
95C11×C16—23no—
96C2×#578C2×C1111yescharacteristic
97C2×#504C2×C1111yescharacteristic, complemented
98#2913C2×C1111yescharacteristic, complemented
99#2141C2×C1113yescomplemented
100#2139C2×C1113yescomplemented
101#2138C2×C1113yescomplemented
102C2×#358C2×C1113yescomplemented
103C23×C11—41no—
104C23×C11C2×D813yes—
105Q8×C11—26no—
106Q8×C11—43no—
107Q8×C11—412no—
108Q8×C11#10214yes—
109D4×C11—22no—
110D4×C11—412no—
111D4×C11—41no—
112D4×C11#102112yes—
113C2×C4×C11—43no—
114C2×C4×C11—412no—
115C2×C4×C11—412no—
116C2×C4×C11—41no—
117C2×C4×C11—43no—
118C2×C4×C11—163no—
119C2×C4×C11C2×C22⋊C416yes—
120C2×C4×C11C2×D813yes—
121C2×C4×C11C2×SD1616yes—
122C2×C4×C11C22×D411yescharacteristic
123C8×C11C2×C22⋊C416yes—
124C8×C11C23×C411yescharacteristic
125C8×C11C22×D411yescharacteristic
126C2×2−1+4—21no—
127#578—24no—
128#578C4×C1118yescomplemented
129C2×#137—23no—
130C2×#135C22×C1113yes—
131C22×Q16C22×C1113yes—
132C2×#131C22×C1111yescharacteristic
133#520—21no—
134#504—24no—
135C2×M32C22×C1113yes—
136C22×C16C22×C1113yes—
137#428—23no—
138#427C22×C1113yes—
139C2×#107C22×C1113yes—
140#358C22×C1113yes—
141#358C22×C1116yes—
142#358C22×C1113yes—
143#357C22×C1111yescharacteristic
144#357C22×C1113yes—
145C22×C11—23no—
146C22×C11—23no—
147C22×C11—42no—
148C22×C11—81no—
149C22×C11—81no—
150C22×C11C2×#10216yes—
151C22×C11C22×D811yescharacteristic
152C4×C11—46no—
153C4×C11—83no—
154C4×C11—81no—
155C4×C11C2×#10216yes—
156C4×C11C22×C22⋊C411yescharacteristic
157C4×C11C22×SD1611yescharacteristic
1582−1+4—28no—
1592−1+4—44no—
160C2×#41—23no—
161C2×#41—43no—
162C2×#41D4×C1111yescharacteristic
163C22×Q8—23no—
164C22×Q8—41no—
165#137—224no—
166#135—26no—
167#135C2×C4×C11112yescomplemented
168C2×Q16—23no—
169C2×Q16—26no—
170C2×Q16C2×C4×C11112yescomplemented
171C2×Q16C23×C1113yes—
172C2×SD16—23no—
173C2×D8C23×C1111yescharacteristic
174#131C2×C4×C1114yes—
175#131D4×C1114yes—
176C2×M16D4×C1113yes—
177C22×C8C23×C1113yes—
178C4×Q8—41no—
179C4×D4—43no—
180#117—23no—
181C2×C4⋊C4—23no—
182M32—26no—
183C2×C16—26no—
184C2×C16C23×C1111yescharacteristic
185C2×C16C23×C1113yes—
186#107—23no—
187#107C23×C1113yes—
188#107C23×C1111yescharacteristic
189#106—23no—
190C2×C11—26no—
191C2×C11—82no—
192C2×C11C22×#10211yescharacteristic
193C2×C11#341611yescharacteristic
194C2×C11#341711yescharacteristic
195#41—212no—
196#41—424no—
197#41—46no—
198#41C11×C22⋊C414yes—
199#41C11×SD1614yes—
200C2×Q8—212no—
201C2×Q8—23no—
202C2×Q8—48no—
203C2×Q8—43no—
204C2×Q8—46no—
205C2×Q8C11×D811yescharacteristic
206C2×D4—21no—
207C2×D4—43no—
208C2×D4C11×D813yes—
209C22×C4—43no—
210C22×C4—43no—
211C22×C4—43no—
212C22×C4C2×D4×C1113yes—
213Q16—212no—
214Q16—23no—
215Q16C22×C4×C1116yes—
216SD16—212no—
217D8—21no—
218D8C22×C4×C1112yes—
219M16C11×C22⋊C4112yes—
220C2×C8C22×C4×C1116yes—
221C2×C8C2×D4×C1113yes—
222C2×C8C2×D4×C1116yes—
223C2×C8C24×C1111yescharacteristic
224C4⋊C4—21no—
225C4⋊C4—23no—
226C4⋊C4—43no—
227C22⋊C4—43no—
228C42—43no—
229C16—21no—
230C16—23no—
231C11#3338211yescharacteristic, direct product factor, Sylow
232C23—41no—
233C23C2×C11×D813yes—
234Q8—26no—
235Q8—412no—
236Q8—43no—
237Q8C11×#10214yes—
238D4—22no—
239D4—412no—
240D4—41no—
241D4C11×#102112yes—
242C2×C4—412no—
243C2×C4—43no—
244C2×C4—412no—
245C2×C4—41no—
246C2×C4—43no—
247C2×C4—163no—
248C2×C4C2×C11×C22⋊C416yes—
249C2×C4C2×C11×D813yes—
250C2×C4C2×C11×SD1616yes—
251C2×C4C22×D4×C1111yescharacteristic
252C8C2×C11×C22⋊C416yes—
253C8C23×C4×C1111yescharacteristic
254C8C22×D4×C1111yescharacteristic
255C22—23no—
256C22—23no—
257C22—42no—
258C22—81no—
259C22—81no—
260C22C2×C11×#10216yes—
261C22C22×C11×D811yescharacteristic
262C4—46no—
263C4—83no—
264C4—81no—
265C4C2×C11×#10216yes—
266C4C22×C11×C22⋊C411yescharacteristic
267C4C22×C11×SD1611yescharacteristic
268C2—26no—
269C2—82no—
270C2C22×C11×#10211yescharacteristic
271C2C11×#341611yescharacteristic
272C2C11×#341711yescharacteristic
subgroupG/H
center, socleC22×C11C22×D8
commutatorC8C23×C4×C11
Frattini, cosocleC2×C8C24×C11
prime radicalC2×C11×#578C2
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C11×#41 ◁ C2×C11×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#504C2semidirect
3. C11×#2913C2semidirect
4. C11×#2141C2semidirect
5. C11×#2139C2semidirect
6. C11×#2138C2semidirect
7. C2×C11×#358C2semidirect
10. C11×#578C4semidirect
36. C11×#135C2×C4semidirect
39. C2×C11×Q16C2×C4semidirect
59. #33382C11direct (N × H)
97. C2×#504C2×C11semidirect
98. #2913C2×C11semidirect
99. #2141C2×C11semidirect
100. #2139C2×C11semidirect
101. #2138C2×C11semidirect
102. C2×#358C2×C11semidirect
128. #578C4×C11semidirect
167. #135C2×C4×C11semidirect
170. C2×Q16C2×C4×C11semidirect
231. C11#33382direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5782
C2×C11×#5042
C11×#29132
C11×#21412
C11×#21392
C11×#21382
C2×C11×#3582
#3338211