Finite Group Databasebeta

← C11×#13463 #14590656

Subgroups — C11×#13463 #14590656

Order 2816.

484 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2804C211yesmaximal, characteristic
2C11×#1867C212yesmaximal
3C11×#1856C211yesmaximal, characteristic
4C11×#1393C211yesmaximal, characteristic
5C11×#1390C212yesmaximal
6C11×#518C2211yescharacteristic
7C11×#428—21no—
8C2×C11×#100C2211yescharacteristic
9C2×C11×#99C2212yes—
10C11×#400—21no—
11C11×#393—22no—
12C11×#391—21no—
13C11×#390C2211yescharacteristic
14C11×#386C2212yes—
15C11×#385—22no—
16C11×#385—22no—
17C11×#342—22no—
18C11×#339—21no—
19C22×Q8×C11—21no—
20C22×D4×C11C2311yescharacteristic
21C23×C4×C11D412yes—
22C2×C11×M16—21no—
23C4×D4×C11—41no—
24C4×D4×C11—41no—
25C11×#117—21no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—42no—
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C22⋊C4—22no—
31C2×C11×C22⋊C4—22no—
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4—22no—
34C2×C11×C22⋊C4D412yes—
35C2×C42×C11D411yescharacteristic
36C11×#107—41no—
37C11×#106—41no—
38C11×#100—21no—
39C11×#100Q812yescomplemented
40C11×#99—22no—
41C11×#99Q814yescomplemented
42C11×#95—22no—
43C11×#95—22no—
44C11×#95—21no—
45C11×#95—22no—
46C11×#95—42no—
47#13463C1111yesmaximal, characteristic, direct product factor, Sylow
48C24×C11C2×D412yes—
49C2×Q8×C11—42no—
50C2×Q8×C11—81no—
51C2×Q8×C11—81no—
52C2×D4×C11—41no—
53C2×D4×C11—41no—
54C2×D4×C11C2×Q811yescharacteristic
55C2×D4×C11C2×Q812yes—
56C2×D4×C11#4111yescharacteristic
57C22×C4×C11—21no—
58C22×C4×C11—22no—
59C22×C4×C11—21no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11—42no—
64C22×C4×C11—42no—
65C22×C4×C11—82no—
66C22×C4×C11C2×D411yescharacteristic
67C11×M16—22no—
68C11×M16—41no—
69C2×C8×C11—41no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—81no—
74C11×C4⋊C4—81no—
75C11×C4⋊C4—84no—
76C11×C22⋊C4—24no—
77C11×C22⋊C4—44no—
78C11×C22⋊C4—42no—
79C11×C22⋊C4—42no—
80C11×C22⋊C4—41no—
81C11×C22⋊C4—42no—
82C11×C22⋊C4—82no—
83C42×C11—41no—
84C42×C11—41no—
85#2804C2×C1111yescharacteristic
86#1867C2×C1112yes—
87#1856C2×C1111yescharacteristic
88#1393C2×C1111yescharacteristic
89#1390C2×C1112yes—
90C23×C11—22no—
91C23×C11—22no—
92C23×C11—42no—
93C23×C11—42no—
94C23×C11#12011yescharacteristic
95C23×C11C22⋊Q812yes—
96C23×C11C4⋊Q812yes—
97Q8×C11—84no—
98D4×C11—41no—
99D4×C11—42no—
100D4×C11—41no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—22no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—44no—
107C2×C4×C11—42no—
108C2×C4×C11—42no—
109C2×C4×C11—42no—
110C2×C4×C11—42no—
111C2×C4×C11—42no—
112C2×C4×C11—44no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—82no—
119C2×C4×C11—82no—
120C2×C4×C11—82no—
121C2×C4×C11—82no—
122C2×C4×C11—82no—
123C2×C4×C11C22⋊Q811yescharacteristic
124C2×C4×C11C4⋊Q811yescharacteristic
125C8×C11—42no—
126#518C22×C1111yescharacteristic
127#428—21no—
128C2×#100C22×C1111yescharacteristic
129C2×#99C22×C1112yes—
130#400—21no—
131#393—22no—
132#391—21no—
133#390C22×C1111yescharacteristic
134#386C22×C1112yes—
135#385—22no—
136#385—22no—
137#342—22no—
138#339—21no—
139C22×C11—21no—
140C22×C11—21no—
141C22×C11—22no—
142C22×C11—22no—
143C22×C11—42no—
144C22×C11—42no—
145C22×C11—42no—
146C22×C11—42no—
147C22×C11—82no—
148C22×C11#39511yescharacteristic
149C22×C11B(4,𝔽2)11yescharacteristic
150C22×C11#45811yescharacteristic
151C4×C11—21no—
152C4×C11—21no—
153C4×C11—42no—
154C4×C11—82no—
155C4×C11—84no—
156C4×C11—81no—
157C4×C11—81no—
158C4×C11—82no—
159C4×C11—81no—
160C22×Q8—21no—
161C22×D4C23×C1111yescharacteristic
162C23×C4D4×C1112yes—
163C2×M16—21no—
164C4×D4—41no—
165C4×D4—41no—
166#117—21no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—42no—
170C2×C4⋊C4D4×C1111yescharacteristic
171C2×C22⋊C4—22no—
172C2×C22⋊C4—22no—
173C2×C22⋊C4—22no—
174C2×C22⋊C4—22no—
175C2×C22⋊C4D4×C1112yes—
176C2×C42D4×C1111yescharacteristic
177#107—41no—
178#106—41no—
179#100—21no—
180#100Q8×C1112yescomplemented
181#99—22no—
182#99Q8×C1114yescomplemented
183#95—22no—
184#95—22no—
185#95—21no—
186#95—22no—
187#95—42no—
188C2×C11—21no—
189C2×C11—21no—
190C2×C11—42no—
191C2×C11—42no—
192C2×C11#206211yescharacteristic
193C2×C11#219811yescharacteristic
194C2×C11#219911yescharacteristic
195C24C2×D4×C1112yes—
196C2×Q8—42no—
197C2×Q8—81no—
198C2×Q8—81no—
199C2×D4—41no—
200C2×D4—41no—
201C2×D4C2×Q8×C1111yescharacteristic
202C2×D4C2×Q8×C1112yes—
203C2×D4C11×#4111yescharacteristic
204C22×C4—21no—
205C22×C4—22no—
206C22×C4—21no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—82no—
213C22×C4C2×D4×C1111yescharacteristic
214M16—22no—
215M16—41no—
216C2×C8—41no—
217C4⋊C4—21no—
218C4⋊C4—21no—
219C4⋊C4—41no—
220C4⋊C4—81no—
221C4⋊C4—81no—
222C4⋊C4—84no—
223C22⋊C4—24no—
224C22⋊C4—44no—
225C22⋊C4—42no—
226C22⋊C4—42no—
227C22⋊C4—41no—
228C22⋊C4—42no—
229C22⋊C4—82no—
230C42—41no—
231C42—41no—
232C11#1346311yescharacteristic, direct product factor, Sylow
233C23—22no—
234C23—22no—
235C23—42no—
236C23—42no—
237C23C11×#12011yescharacteristic
238C23C11×C22⋊Q812yes—
239C23C11×C4⋊Q812yes—
240Q8—84no—
241D4—41no—
242D4—42no—
243D4—41no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—44no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—44no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—82no—
262C2×C4—82no—
263C2×C4—82no—
264C2×C4—82no—
265C2×C4—82no—
266C2×C4C11×C22⋊Q811yescharacteristic
267C2×C4C11×C4⋊Q811yescharacteristic
268C8—42no—
269C22—21no—
270C22—21no—
271C22—22no—
272C22—22no—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—82no—
278C22C11×#39511yescharacteristic
279C22C11×B(4,𝔽2)11yescharacteristic
280C22C11×#45811yescharacteristic
281C4—21no—
282C4—21no—
283C4—42no—
284C4—82no—
285C4—84no—
286C4—81no—
287C4—81no—
288C4—82no—
289C4—81no—
290C2—21no—
291C2—21no—
292C2—42no—
293C2—42no—
294C2C11×#206211yescharacteristic
295C2C11×#219811yescharacteristic
296C2C11×#219911yescharacteristic
subgroupG/H
center, socleC22×C11B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C11
prime radicalC22×D4×C11C23
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C11 ◁ C22×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
39. C11×#100Q8semidirect
41. C11×#99Q8semidirect
47. #13463C11direct (N × H)
180. #100Q8×C11semidirect
182. #99Q8×C11semidirect
232. C11#13463direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28042
C11×#18672
C11×#18562
C11×#13932
C11×#13902
#1346311