Finite Group Databasebeta

← C11×#12121 #14589314

Subgroups — C11×#12121 #14589314

Order 2816.

470 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C11×#2607C211yesmaximal, characteristic, complemented
2C11×#2022C211yesmaximal, characteristic
3C11×#1601C212yesmaximal
4C11×#1351C212yesmaximal, complemented
5C11×#1317C211yesmaximal, characteristic, complemented
6C11×#534C2211yescharacteristic
7C2×C11×#123—21no—
8C11×#448—22no—
9C2×C11×#99—21no—
10C11×#399—21no—
11C11×#393C2212yes—
12C11×#391—22no—
13C11×#387—22no—
14C11×#381C2211yescharacteristic
15C4×C11×C22⋊C4—21no—
16C11×#342C2211yescharacteristic
17C11×#327—22no—
18C11×#323C2212yes—
19C22×Q8×C11D412yes—
20C22×D4×C11—21no—
21C23×C4×C11D411yescharacteristic
22C2×C11×SD16—42no—
23C11×#123—42no—
24C11×#123—41no—
25C11×#123—42no—
26C11×#121—22no—
27C11×#120—41no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—41no—
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4—41no—
34C2×C11×C22⋊C4D411yescharacteristic
35C2×C11×C22⋊C4C2311yescharacteristic
36C2×C42×C11—21no—
37C2×C42×C11—21no—
38C11×#103—42no—
39C11×#99—42no—
40C11×C22⋊C8—22no—
41C11×#95—22no—
42C11×#95—21no—
43C11×#95—22no—
44C11×#95—22no—
45C11×#95D412yes—
46#12121C1111yesmaximal, characteristic, direct product factor, Sylow
47C24×C11—21no—
48C24×C11C2×D411yescharacteristic
49C2×Q8×C11—44no—
50C2×Q8×C11—42no—
51C2×D4×C11—22no—
52C2×D4×C11—41no—
53C2×D4×C11—41no—
54C2×D4×C11—41no—
55C2×D4×C11—41no—
56C2×D4×C11—41no—
57C2×D4×C11—41no—
58C22×C4×C11—21no—
59C22×C4×C11—22no—
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—22no—
64C22×C4×C11—41no—
65C22×C4×C11—41no—
66C22×C4×C11—41no—
67C22×C4×C11SD1612yescomplemented
68C22×C4×C11C2×D412yes—
69C11×SD16—84no—
70C2×C8×C11—42no—
71C11×C4⋊C4—22no—
72C11×C4⋊C4—44no—
73C11×C4⋊C4—44no—
74C11×C4⋊C4—81no—
75C11×C22⋊C4—22no—
76C11×C22⋊C4—41no—
77C11×C22⋊C4—44no—
78C11×C22⋊C4—42no—
79C11×C22⋊C4—44no—
80C11×C22⋊C4—41no—
81C11×C22⋊C4—41no—
82C42×C11—81no—
83C42×C11—81no—
84#2607C2×C1111yescharacteristic, complemented
85#2022C2×C1111yescharacteristic
86#1601C2×C1112yes—
87#1351C2×C1112yescomplemented
88#1317C2×C1111yescharacteristic, complemented
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—42no—
92C23×C11—41no—
93C23×C11—41no—
94C23×C11—41no—
95C23×C11—82no—
96C23×C11#12011yescharacteristic
97C23×C11C2×SD1611yescharacteristic
98C23×C11#13711yescharacteristic
99Q8×C11—44no—
100Q8×C11—82no—
101D4×C11—82no—
102D4×C11—81no—
103D4×C11—81no—
104D4×C11—81no—
105D4×C11—81no—
106C2×C4×C11—24no—
107C2×C4×C11—22no—
108C2×C4×C11—22no—
109C2×C4×C11—42no—
110C2×C4×C11—41no—
111C2×C4×C11—41no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—41no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—41no—
121C2×C4×C11—42no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—81no—
125C2×C4×C11—82no—
126C8×C11—82no—
127#534C22×C1111yescharacteristic
128C2×#123—21no—
129#448—22no—
130C2×#99—21no—
131#399—21no—
132#393C22×C1112yes—
133#391—22no—
134#387—22no—
135#381C22×C1111yescharacteristic
136C4×C22⋊C4—21no—
137#342C22×C1111yescharacteristic
138#327—22no—
139#323C22×C1112yes—
140C22×C11—22no—
141C22×C11—21no—
142C22×C11—21no—
143C22×C11—41no—
144C22×C11—41no—
145C22×C11—42no—
146C22×C11—81no—
147C22×C11—82no—
148C22×C11—81no—
149C22×C11—82no—
150C22×C11—161no—
151C22×C11#44811yescharacteristic
152C22×C11#45311yescharacteristic
153C22×C11B(4,𝔽2)11yescharacteristic
154C4×C11—42no—
155C4×C11—44no—
156C4×C11—42no—
157C4×C11—82no—
158C4×C11—81no—
159C4×C11—82no—
160C4×C11—81no—
161C22×Q8D4×C1112yes—
162C22×D4—21no—
163C23×C4D4×C1111yescharacteristic
164C2×SD16—42no—
165#123—42no—
166#123—41no—
167#123—42no—
168#121—22no—
169#120—41no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—41no—
173C2×C22⋊C4—21no—
174C2×C22⋊C4—22no—
175C2×C22⋊C4—41no—
176C2×C22⋊C4D4×C1111yescharacteristic
177C2×C22⋊C4C23×C1111yescharacteristic
178C2×C42—21no—
179C2×C42—21no—
180#103—42no—
181#99—42no—
182C22⋊C8—22no—
183#95—22no—
184#95—21no—
185#95—22no—
186#95—22no—
187#95D4×C1112yes—
188C2×C11—21no—
189C2×C11—21no—
190C2×C11—41no—
191C2×C11—41no—
192C2×C11—161no—
193C2×C11#159611yescharacteristic
194C2×C11#219712yes—
195C24—21no—
196C24C2×D4×C1111yescharacteristic
197C2×Q8—44no—
198C2×Q8—42no—
199C2×D4—22no—
200C2×D4—41no—
201C2×D4—41no—
202C2×D4—41no—
203C2×D4—41no—
204C2×D4—41no—
205C2×D4—41no—
206C22×C4—21no—
207C22×C4—22no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—22no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4C11×SD1612yescomplemented
216C22×C4C2×D4×C1112yes—
217SD16—84no—
218C2×C8—42no—
219C4⋊C4—22no—
220C4⋊C4—44no—
221C4⋊C4—44no—
222C4⋊C4—81no—
223C22⋊C4—22no—
224C22⋊C4—41no—
225C22⋊C4—44no—
226C22⋊C4—42no—
227C22⋊C4—44no—
228C22⋊C4—41no—
229C22⋊C4—41no—
230C42—81no—
231C42—81no—
232C11#1212111yescharacteristic, direct product factor, Sylow
233C23—21no—
234C23—21no—
235C23—42no—
236C23—41no—
237C23—41no—
238C23—41no—
239C23—82no—
240C23C11×#12011yescharacteristic
241C23C2×C11×SD1611yescharacteristic
242C23C11×#13711yescharacteristic
243Q8—44no—
244Q8—82no—
245D4—82no—
246D4—81no—
247D4—81no—
248D4—81no—
249D4—81no—
250C2×C4—24no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—41no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—41no—
265C2×C4—42no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—81no—
269C2×C4—82no—
270C8—82no—
271C22—22no—
272C22—21no—
273C22—21no—
274C22—41no—
275C22—41no—
276C22—42no—
277C22—81no—
278C22—82no—
279C22—82no—
280C22—81no—
281C22—161no—
282C22C11×#44811yescharacteristic
283C22C11×#45311yescharacteristic
284C22C11×B(4,𝔽2)11yescharacteristic
285C4—42no—
286C4—44no—
287C4—42no—
288C4—82no—
289C4—81no—
290C4—82no—
291C4—81no—
292C2—21no—
293C2—21no—
294C2—41no—
295C2—41no—
296C2—161no—
297C2C11×#159611yescharacteristic
298C2C11×#219712yes—
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C11
prime radicalC11×#534C22
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C11 ◁ C2×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2607C2semidirect
4. C11×#1351C2semidirect
5. C11×#1317C2semidirect
46. #12121C11direct (N × H)
67. C22×C4×C11SD16semidirect
84. #2607C2×C11semidirect
87. #1351C2×C11semidirect
88. #1317C2×C11semidirect
215. C22×C4C11×SD16semidirect
232. C11#12121direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#26072
C11×#20222
C11×#16012
C11×#13512
C11×#13172
#1212111