Finite Group Databasebeta

← C11×#19008 #14596201

Subgroups — C11×#19008 #14596201

Order 2816.

786 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 786 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#564C211yesmaximal, characteristic
2C11×#3236C212yesmaximal
3C11×#3166C211yesmaximal, characteristic
4C11×#1663C218yesmaximal, complemented
5C11×#1534C211yesmaximal, characteristic
6C11×#1528C212yesmaximal
7C11×#564—22no—
8C11×#564—24no—
9C11×#564C2214yes—
10C11×#533C2211yescharacteristic
11C2×C11×#125—22no—
12C2×C11×#125—22no—
13C2×C11×#125—22no—
14C2×C11×#125C2211yescharacteristic
15C2×C11×#125C2212yes—
16C11×#501C2214yes—
17C11×#501C2214yes—
18C11×#499—22no—
19C11×#491C2214yes—
20C11×#484—22no—
21C11×#483—22no—
22C11×#479—24no—
23C11×#432C2212yes—
24C11×#428—22no—
25C4×C11×M16C2211yescharacteristic
26C11×#330C2218yes—
27C11×#330C2214yes—
28C2×C11×M16—21no—
29C11×C4⋊Q8C2312yes—
30C11×#125—28no—
31C11×#125—28no—
32C11×#125—28no—
33C11×#125—28no—
34C11×#125—28no—
35C11×#125—28no—
36C11×#125—22no—
37C11×#125—22no—
38C11×#125—22no—
39C11×#125—21no—
40C11×#125D412yes—
41C11×#125D414yes—
42C11×#125C2314yes—
43C11×#125C2312yes—
44C11×C22⋊Q8—22no—
45C4×Q8×C11—22no—
46C11×#117—21no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4D412yes—
54C2×C11×C4⋊C4D412yes—
55C2×C11×C4⋊C4D412yes—
56C2×C42×C11—22no—
57C2×C42×C11C2311yescharacteristic
58C11×#107—24no—
59C11×#107—24no—
60C11×#106—24no—
61C11×#106—24no—
62C11×C4⋊C8—22no—
63C11×#103—24no—
64C11×#103—24no—
65C11×C22⋊C8—22no—
66C11×#97C2314yes—
67C11×#97C2312yes—
68C4×C8×C11—21no—
69#19008C1111yesmaximal, characteristic, direct product factor, Sylow
70C2×Q8×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D412yes—
76C11×M16—24no—
77C2×C8×C11—22no—
78C2×C8×C11—24no—
79C11×C4⋊C4—28no—
80C11×C4⋊C4—28no—
81C11×C4⋊C4—28no—
82C11×C4⋊C4—24no—
83C11×C4⋊C4—24no—
84C11×C4⋊C4—24no—
85C11×C4⋊C4—22no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—24no—
89C11×C4⋊C4—24no—
90C11×C4⋊C4—24no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—42no—
94C11×C4⋊C4C2×D414yes—
95C11×C4⋊C4C2×D414yes—
96C11×C4⋊C4C2×D414yes—
97C11×C22⋊C4—41no—
98C42×C11—28no—
99C42×C11—41no—
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D412yes—
102C42×C11C2411yescharacteristic
103C2×#564C2×C1111yescharacteristic
104#3236C2×C1112yes—
105#3166C2×C1111yescharacteristic
106#1663C2×C1118yescomplemented
107#1534C2×C1111yescharacteristic
108#1528C2×C1112yes—
109C23×C11#12011yescharacteristic
110Q8×C11—44no—
111C2×C4×C11—22no—
112C2×C4×C11—24no—
113C2×C4×C11—24no—
114C2×C4×C11—24no—
115C2×C4×C11—42no—
116C2×C4×C11—44no—
117C2×C4×C11—44no—
118C2×C4×C11—44no—
119C2×C4×C11—42no—
120C2×C4×C11#12011yescharacteristic
121C2×C4×C11#12012yes—
122C2×C4×C11C22×D411yescharacteristic
123C2×C4×C11C22×D412yes—
124C8×C11—24no—
125C8×C11—44no—
126#564—24no—
127#564—22no—
128#564C22×C1114yes—
129#533C22×C1111yescharacteristic
130C2×#125—22no—
131C2×#125—22no—
132C2×#125—22no—
133C2×#125C22×C1111yescharacteristic
134C2×#125C22×C1112yes—
135#501C22×C1114yes—
136#501C22×C1114yes—
137#499—22no—
138#491C22×C1114yes—
139#484—22no—
140#483—22no—
141#479—24no—
142#432C22×C1112yes—
143#428—22no—
144C4×M16C22×C1111yescharacteristic
145#330C22×C1118yes—
146#330C22×C1114yes—
147C22×C11—22no—
148C22×C11#45612yes—
149C22×C11C2×#12011yescharacteristic
150C4×C11—21no—
151C4×C11—21no—
152C4×C11—22no—
153C4×C11—22no—
154C4×C11—44no—
155C4×C11—44no—
156C4×C11—44no—
157C4×C11—82no—
158C2×M16—21no—
159C4⋊Q8C23×C1112yes—
160#125—28no—
161#125—28no—
162#125—28no—
163#125—28no—
164#125—28no—
165#125—28no—
166#125—22no—
167#125—22no—
168#125—22no—
169#125—21no—
170#125D4×C1114yes—
171#125D4×C1112yes—
172#125C23×C1114yes—
173#125C23×C1112yes—
174C22⋊Q8—22no—
175C4×Q8—22no—
176#117—21no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4D4×C1112yes—
184C2×C4⋊C4D4×C1112yes—
185C2×C4⋊C4D4×C1112yes—
186C2×C42—22no—
187C2×C42C23×C1111yescharacteristic
188#107—24no—
189#107—24no—
190#106—24no—
191#106—24no—
192C4⋊C8—22no—
193#103—24no—
194#103—24no—
195C22⋊C8—22no—
196#97C23×C1112yes—
197#97C23×C1114yes—
198C4×C8—21no—
199C2×C11—22no—
200C2×C11C2×#45611yescharacteristic
201C2×C11#302012yes—
202C2×Q8—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4C2×D4×C1111yescharacteristic
207C22×C4C2×D4×C1112yes—
208M16—24no—
209C2×C8—22no—
210C2×C8—24no—
211C4⋊C4—28no—
212C4⋊C4—28no—
213C4⋊C4—28no—
214C4⋊C4—24no—
215C4⋊C4—24no—
216C4⋊C4—24no—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—24no—
221C4⋊C4—24no—
222C4⋊C4—24no—
223C4⋊C4—22no—
224C4⋊C4—22no—
225C4⋊C4—42no—
226C4⋊C4C2×D4×C1114yes—
227C4⋊C4C2×D4×C1114yes—
228C4⋊C4C2×D4×C1114yes—
229C22⋊C4—41no—
230C42—28no—
231C42—41no—
232C42C2×D4×C1111yescharacteristic
233C42C2×D4×C1112yes—
234C42C24×C1111yescharacteristic
235C11#1900811yescharacteristic, direct product factor, Sylow
236C23C11×#12011yescharacteristic
237Q8—44no—
238C2×C4—22no—
239C2×C4—24no—
240C2×C4—24no—
241C2×C4—24no—
242C2×C4—42no—
243C2×C4—44no—
244C2×C4—44no—
245C2×C4—44no—
246C2×C4—42no—
247C2×C4C11×#12011yescharacteristic
248C2×C4C11×#12012yes—
249C2×C4C22×D4×C1111yescharacteristic
250C2×C4C22×D4×C1112yes—
251C8—24no—
252C8—44no—
253C22—22no—
254C22C11×#45612yes—
255C22C2×C11×#12011yescharacteristic
256C4—21no—
257C4—21no—
258C4—22no—
259C4—22no—
260C4—44no—
261C4—44no—
262C4—44no—
263C4—82no—
264C2—22no—
265C2C2×C11×#45611yescharacteristic
266C2C11×#302012yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC23×C11#120
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1663C2semidirect
69. #19008C11direct (N × H)
106. #1663C2×C11semidirect
235. C11#19008direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5642
C11×#32362
C11×#31662
C11×#16632
C11×#15342
C11×#15282
#1900811