Finite Group Databasebeta

← C11×#12158 #14589351

Subgroups — C11×#12158 #14589351

Order 2816.

434 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 82 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×#3245C211yesmaximal, characteristic, complemented
2C11×#2184C212yesmaximal, complemented
3C11×#2054C211yesmaximal, characteristic, complemented
4C11×#1347C212yesmaximal, complemented
5C11×#1322C211yesmaximal, characteristic, complemented
6C22×C11×D8C2211yescharacteristic
7C11×#532—21no—
8C2×C11×D16—22no—
9C11×#474—22no—
10C11×#466—21no—
11C11×#466C2212yes—
12C11×#459—22no—
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×C11×#102—21no—
15C11×#390—21no—
16C11×#357—22no—
17C11×C22⋊C16C2212yes—
18C11×#340C2211yescharacteristic
19C2×C11×#41—41no—
20C22×D4×C11—21no—
21C2×C11×D8—21no—
22C2×C11×D8—22no—
23C2×C11×D8—42no—
24C2×C11×D8D412yes—
25C22×C8×C11D411yescharacteristic
26C22×C8×C11C2311yescharacteristic
27C11×C4⋊Q8—21no—
28C11×#127—21no—
29C11×#124—41no—
30C11×#121—22no—
31C11×#121—41no—
32C4×D4×C11—22no—
33C4×D4×C11—41no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C22⋊C4—41no—
36C2×C11×C22⋊C4—41no—
37C2×C42×C11D411yescharacteristic
38C11×D16—44no—
39C2×C11×C16—22no—
40C11×#107—21no—
41C11×#107D412yes—
42C11×C4⋊C8—22no—
43C11×#102—22no—
44C11×#102—22no—
45C11×#102—42no—
46#12158C1111yesmaximal, characteristic, direct product factor, Sylow
47C24×C11—41no—
48C11×#41—82no—
49C11×#41—82no—
50C2×Q8×C11—41no—
51C2×D4×C11—22no—
52C2×D4×C11—22no—
53C2×D4×C11—41no—
54C2×D4×C11—41no—
55C2×D4×C11—41no—
56C2×D4×C11—41no—
57C2×D4×C11—41no—
58C2×D4×C11—42no—
59C2×D4×C11—41no—
60C2×D4×C11—41no—
61C22×C4×C11—42no—
62C22×C4×C11—41no—
63C22×C4×C11D811yescharacteristic
64C22×C4×C11D811yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C11×D8—24no—
67C11×D8—42no—
68C11×D8—42no—
69C11×D8—81no—
70C2×C8×C11—21no—
71C2×C8×C11—41no—
72C2×C8×C11—41no—
73C2×C8×C11C2×D412yes—
74C11×C4⋊C4—22no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C22⋊C4—42no—
79C11×C22⋊C4—42no—
80C11×C22⋊C4—82no—
81C11×C22⋊C4—82no—
82C42×C11—21no—
83C42×C11—21no—
84C11×C16—42no—
85#3245C2×C1111yescharacteristic, complemented
86#2184C2×C1112yescomplemented
87#2054C2×C1111yescharacteristic, complemented
88#1347C2×C1112yescomplemented
89#1322C2×C1111yescharacteristic, complemented
90C23×C11—42no—
91C23×C11—42no—
92C23×C11—81no—
93C23×C11—81no—
94C23×C11—81no—
95C23×C11—81no—
96C23×C11—81no—
97C23×C11—81no—
98C23×C11C2×D811yescharacteristic
99Q8×C11—82no—
100D4×C11—42no—
101D4×C11—42no—
102D4×C11—42no—
103D4×C11—42no—
104D4×C11—81no—
105D4×C11—82no—
106D4×C11—82no—
107D4×C11—82no—
108D4×C11—82no—
109D4×C11—81no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—41no—
116C2×C4×C11—42no—
117C2×C4×C11—84no—
118C2×C4×C11—81no—
119C2×C4×C11—81no—
120C2×C4×C11—81no—
121C2×C4×C11D1612yescomplemented
122C2×C4×C11#12011yescharacteristic
123C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
124C8×C11—22no—
125C8×C11—41no—
126C22×D8C22×C1111yescharacteristic
127#532—21no—
128C2×D16—22no—
129#474—22no—
130#466—21no—
131#466C22×C1112yes—
132#459—22no—
133C2×C4⋊C8C22×C1111yescharacteristic
134C2×#102—21no—
135#390—21no—
136#357—22no—
137C22⋊C16C22×C1112yes—
138#340C22×C1111yescharacteristic
139C22×C11—21no—
140C22×C11—21no—
141C22×C11—82no—
142C22×C11—82no—
143C22×C11—82no—
144C22×C11—82no—
145C22×C11—82no—
146C22×C11—82no—
147C22×C11—161no—
148C22×C11—161no—
149C22×C11—161no—
150C22×C11—161no—
151C22×C11#44711yescharacteristic
152C22×C11C2×D1611yescharacteristic
153C22×C11#50911yescharacteristic
154C4×C11—21no—
155C4×C11—22no—
156C4×C11—41no—
157C4×C11—82no—
158C4×C11—161no—
159C4×C11#45411yescharacteristic
160C4×C11B(4,𝔽2)11yescharacteristic
161C2×#41—41no—
162C22×D4—21no—
163C2×D8—21no—
164C2×D8—22no—
165C2×D8—42no—
166C2×D8D4×C1112yes—
167C22×C8D4×C1111yescharacteristic
168C22×C8C23×C1111yescharacteristic
169C4⋊Q8—21no—
170#127—21no—
171#124—41no—
172#121—22no—
173#121—41no—
174C4×D4—22no—
175C4×D4—41no—
176C2×C4⋊C4—21no—
177C2×C22⋊C4—41no—
178C2×C22⋊C4—41no—
179C2×C42D4×C1111yescharacteristic
180D16—44no—
181C2×C16—22no—
182#107—21no—
183#107D4×C1112yes—
184C4⋊C8—22no—
185#102—22no—
186#102—22no—
187#102—42no—
188C2×C11—21no—
189C2×C11—21no—
190C2×C11—162no—
191C2×C11—162no—
192C2×C11#159811yescharacteristic
193C2×C11#218411yescharacteristic
194C2×C11#219011yescharacteristic
195C24—41no—
196#41—82no—
197#41—82no—
198C2×Q8—41no—
199C2×D4—22no—
200C2×D4—22no—
201C2×D4—41no—
202C2×D4—41no—
203C2×D4—41no—
204C2×D4—41no—
205C2×D4—41no—
206C2×D4—42no—
207C2×D4—41no—
208C2×D4—41no—
209C22×C4—42no—
210C22×C4—41no—
211C22×C4C11×D811yescharacteristic
212C22×C4C11×D811yescharacteristic
213C22×C4C2×D4×C1111yescharacteristic
214D8—24no—
215D8—42no—
216D8—42no—
217D8—81no—
218C2×C8—21no—
219C2×C8—41no—
220C2×C8—41no—
221C2×C8C2×D4×C1112yes—
222C4⋊C4—22no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C22⋊C4—42no—
227C22⋊C4—42no—
228C22⋊C4—82no—
229C22⋊C4—82no—
230C42—21no—
231C42—21no—
232C16—42no—
233C11#1215811yescharacteristic, direct product factor, Sylow
234C23—42no—
235C23—42no—
236C23—81no—
237C23—81no—
238C23—81no—
239C23—81no—
240C23—81no—
241C23—81no—
242C23C2×C11×D811yescharacteristic
243Q8—82no—
244D4—42no—
245D4—42no—
246D4—42no—
247D4—42no—
248D4—81no—
249D4—82no—
250D4—82no—
251D4—82no—
252D4—82no—
253D4—81no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—84no—
262C2×C4—81no—
263C2×C4—81no—
264C2×C4—81no—
265C2×C4C11×D1612yescomplemented
266C2×C4C11×#12011yescharacteristic
267C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
268C8—22no—
269C8—41no—
270C22—21no—
271C22—21no—
272C22—82no—
273C22—82no—
274C22—82no—
275C22—82no—
276C22—82no—
277C22—82no—
278C22—161no—
279C22—161no—
280C22—161no—
281C22—161no—
282C22C11×#44711yescharacteristic
283C22C2×C11×D1611yescharacteristic
284C22C11×#50911yescharacteristic
285C4—22no—
286C4—21no—
287C4—41no—
288C4—82no—
289C4—161no—
290C4C11×#45411yescharacteristic
291C4C11×B(4,𝔽2)11yescharacteristic
292C2—21no—
293C2—21no—
294C2—162no—
295C2—162no—
296C2C11×#159811yescharacteristic
297C2C11×#218411yescharacteristic
298C2C11×#219011yescharacteristic
subgroupG/H
center, socleC22×C11#447
commutator, Frattini, cosocleC22×C8C23×C11
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C11×C4⋊C8 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3245C2semidirect
2. C11×#2184C2semidirect
3. C11×#2054C2semidirect
4. C11×#1347C2semidirect
5. C11×#1322C2semidirect
46. #12158C11direct (N × H)
85. #3245C2×C11semidirect
86. #2184C2×C11semidirect
87. #2054C2×C11semidirect
88. #1347C2×C11semidirect
89. #1322C2×C11semidirect
121. C2×C4×C11D16semidirect
233. C11#12158direct (N × H)
265. C2×C4C11×D16semidirect

Maximal subgroups

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

subgroupindex
C11×#32452
C11×#21842
C11×#20542
C11×#13472
C11×#13222
#1215811