Finite Group Databasebeta

← C11×#13414 #14590607

Subgroups — C11×#13414 #14590607

Order 2816.

456 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#495C211yesmaximal, characteristic
2C2×C11×#362C211yesmaximal, characteristic, complemented
3C2×C11×#361C211yesmaximal, characteristic
4C11×#2141C211yesmaximal, characteristic, complemented
5C11×#2140C211yesmaximal, characteristic
6C11×#1945C211yesmaximal, characteristic, complemented
7C11×#1376C211yesmaximal, characteristic, complemented
8C22×C11×Q16C2211yescharacteristic
9C22×C11×SD16—21no—
10C22×C11×D8C2211yescharacteristic
11C2×C11×#124—21no—
12C2×C11×M32C2211yescharacteristic
13C2×C11×M32C2211yescharacteristic
14C11×#495—22no—
15C11×#495—22no—
16C2×C11×#108C2211yescharacteristic
17C11×#427C2211yescharacteristic
18C11×#424—21no—
19C2×C4×C8×C11C2211yescharacteristic
20C11×#362—22no—
21C11×#361—22no—
22C11×#358—22no—
23C11×#357—22no—
24C11×#339—21no—
25C22×Q8×C11—21no—
26C22×D4×C11—21no—
27C2×C11×Q16—21no—
28C2×C11×Q16—21no—
29C2×C11×Q16—21no—
30C2×C11×Q16—21no—
31C2×C11×Q16—21no—
32C2×C11×Q16D412yes—
33C2×C11×SD16—24no—
34C2×C11×SD16—42no—
35C2×C11×SD16—42no—
36C2×C11×D8—21no—
37C2×C11×D8—21no—
38C2×C11×D8—21no—
39C2×C11×D8—21no—
40C2×C11×D8—21no—
41C2×C11×D8D412yes—
42C2×C11×M16—21no—
43C22×C8×C11D411yescharacteristic
44C22×C8×C11C2311yescharacteristic
45C11×#124—24no—
46C11×#124—42no—
47C11×#117—21no—
48C2×C11×C22⋊C4—42no—
49C2×C42×C11D411yescharacteristic
50C11×M32—21no—
51C11×M32—21no—
52C11×M32—21no—
53C11×M32—21no—
54C2×C11×C16—21no—
55C2×C11×C16—21no—
56C11×#108—21no—
57C11×#108—21no—
58C11×#107D412yes—
59C11×#106—21no—
60C11×C4⋊C8—42no—
61C4×C8×C11—21no—
62C4×C8×C11—21no—
63#13414C1111yesmaximal, characteristic, direct product factor, Sylow
64C24×C11—41no—
65C2×Q8×C11—22no—
66C2×Q8×C11—41no—
67C2×Q8×C11—41no—
68C2×Q8×C11—41no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C2×D4×C11—22no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C22×C4×C11—21no—
78C22×C4×C11—41no—
79C22×C4×C11C2×D411yescharacteristic
80C11×Q16—22no—
81C11×Q16—22no—
82C11×Q16—41no—
83C11×Q16—41no—
84C11×SD16—48no—
85C11×D8—22no—
86C11×D8—22no—
87C11×D8—41no—
88C11×D8—41no—
89C11×M16—41no—
90C11×M16—41no—
91C2×C8×C11—21no—
92C2×C8×C11—21no—
93C2×C8×C11—41no—
94C2×C8×C11D812yes—
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11#4111yescharacteristic
99C2×C8×C11#4111yescharacteristic
100C2×C8×C11#4111yescharacteristic
101C11×C4⋊C4—22no—
102C11×C22⋊C4—48no—
103C11×C22⋊C4—41no—
104C42×C11—21no—
105C42×C11—41no—
106C42×C11SD1612yes—
107C11×C16—41no—
108C11×C16—41no—
109C2×#495C2×C1111yescharacteristic
110C2×#362C2×C1111yescharacteristic, complemented
111C2×#361C2×C1111yescharacteristic
112#2141C2×C1111yescharacteristic, complemented
113#2140C2×C1111yescharacteristic
114#1945C2×C1111yescharacteristic, complemented
115#1376C2×C1111yescharacteristic, complemented
116C23×C11—42no—
117C23×C11—84no—
118C23×C11—81no—
119C23×C11—81no—
120C23×C11AGL(1,ℤ/8)11yescharacteristic
121Q8×C11—42no—
122Q8×C11—42no—
123Q8×C11—81no—
124Q8×C11—81no—
125D4×C11—42no—
126D4×C11—42no—
127D4×C11—81no—
128D4×C11—81no—
129C2×C4×C11—22no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—81no—
134C2×C4×C11—81no—
135C2×C4×C11#12011yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12411yescharacteristic
138C2×C4×C11C2×D811yescharacteristic
139C2×C4×C11C2×SD1611yescharacteristic
140C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
141C8×C11—22no—
142C8×C11—81no—
143C8×C11#12111yescharacteristic
144C8×C11#12111yescharacteristic
145C8×C11#12311yescharacteristic
146C8×C11#12311yescharacteristic
147C22×Q16C22×C1111yescharacteristic
148C22×SD16—21no—
149C22×D8C22×C1111yescharacteristic
150C2×#124—21no—
151C2×M32C22×C1111yescharacteristic
152C2×M32C22×C1111yescharacteristic
153#495—22no—
154#495—22no—
155C2×#108C22×C1111yescharacteristic
156#427C22×C1111yescharacteristic
157#424—21no—
158C2×C4×C8C22×C1111yescharacteristic
159#362—22no—
160#361—22no—
161#358—22no—
162#357—22no—
163#339—21no—
164C22×C11—22no—
165C22×C11—84no—
166C22×C11—82no—
167C22×C11—162no—
168C22×C11—162no—
169C22×C11#45011yescharacteristic
170C22×C11#45911yescharacteristic
171C22×C11#49011yescharacteristic
172C4×C11—42no—
173C4×C11—82no—
174C4×C11—82no—
175C4×C11#39411yescharacteristic
176C4×C11#44711yescharacteristic
177C4×C11#46011yescharacteristic
178C4×C11#48611yescharacteristic
179C22×Q8—21no—
180C22×D4—21no—
181C2×Q16—21no—
182C2×Q16—21no—
183C2×Q16—21no—
184C2×Q16—21no—
185C2×Q16—21no—
186C2×Q16D4×C1112yes—
187C2×SD16—24no—
188C2×SD16—42no—
189C2×SD16—42no—
190C2×D8—21no—
191C2×D8—21no—
192C2×D8—21no—
193C2×D8—21no—
194C2×D8—21no—
195C2×D8D4×C1112yes—
196C2×M16—21no—
197C22×C8D4×C1111yescharacteristic
198C22×C8C23×C1111yescharacteristic
199#124—24no—
200#124—42no—
201#117—21no—
202C2×C22⋊C4—42no—
203C2×C42D4×C1111yescharacteristic
204M32—21no—
205M32—21no—
206M32—21no—
207M32—21no—
208C2×C16—21no—
209C2×C16—21no—
210#108—21no—
211#108—21no—
212#107D4×C1112yes—
213#106—21no—
214C4⋊C8—42no—
215C4×C8—21no—
216C4×C8—21no—
217C2×C11—21no—
218C2×C11—21no—
219C2×C11—162no—
220C2×C11#204111yescharacteristic
221C2×C11#221212yes—
222C24—41no—
223C2×Q8—22no—
224C2×Q8—41no—
225C2×Q8—41no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×D4—22no—
230C2×D4—41no—
231C2×D4—41no—
232C2×D4—41no—
233C2×D4—41no—
234C2×D4—41no—
235C22×C4—21no—
236C22×C4—41no—
237C22×C4C2×D4×C1111yescharacteristic
238Q16—22no—
239Q16—22no—
240Q16—41no—
241Q16—41no—
242SD16—48no—
243D8—22no—
244D8—22no—
245D8—41no—
246D8—41no—
247M16—41no—
248M16—41no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—41no—
252C2×C8C11×D812yes—
253C2×C8C2×D4×C1111yescharacteristic
254C2×C8C2×D4×C1111yescharacteristic
255C2×C8C2×D4×C1111yescharacteristic
256C2×C8C11×#4111yescharacteristic
257C2×C8C11×#4111yescharacteristic
258C2×C8C11×#4111yescharacteristic
259C4⋊C4—22no—
260C22⋊C4—48no—
261C22⋊C4—41no—
262C42—21no—
263C42—41no—
264C42C11×SD1612yes—
265C16—41no—
266C16—41no—
267C11#1341411yescharacteristic, direct product factor, Sylow
268C23—42no—
269C23—84no—
270C23—81no—
271C23—81no—
272C23C11×AGL(1,ℤ/8)11yescharacteristic
273Q8—42no—
274Q8—42no—
275Q8—81no—
276Q8—81no—
277D4—42no—
278D4—42no—
279D4—81no—
280D4—81no—
281C2×C4—22no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4C11×#12011yescharacteristic
288C2×C4C11×#12111yescharacteristic
289C2×C4C11×#12411yescharacteristic
290C2×C4C2×C11×D811yescharacteristic
291C2×C4C2×C11×SD1611yescharacteristic
292C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
293C8—22no—
294C8—81no—
295C8C11×#12111yescharacteristic
296C8C11×#12111yescharacteristic
297C8C11×#12311yescharacteristic
298C8C11×#12311yescharacteristic
299C22—22no—
300C22—84no—
301C22—82no—
302C22—162no—
303C22—162no—
304C22C11×#45011yescharacteristic
305C22C11×#45911yescharacteristic
306C22C11×#49011yescharacteristic
307C4—42no—
308C4—82no—
309C4—82no—
310C4C11×#39411yescharacteristic
311C4C11×#44711yescharacteristic
312C4C11×#46011yescharacteristic
313C4C11×#48611yescharacteristic
314C2—21no—
315C2—21no—
316C2—162no—
317C2C11×#204111yescharacteristic
318C2C11×#221212yes—
subgroupG/H
center, socleC22×C11#459
commutator, Frattini, cosocleC22×C8C23×C11
prime radicalC22×C11×D8C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#362C2semidirect
4. C11×#2141C2semidirect
6. C11×#1945C2semidirect
7. C11×#1376C2semidirect
63. #13414C11direct (N × H)
110. C2×#362C2×C11semidirect
112. #2141C2×C11semidirect
114. #1945C2×C11semidirect
115. #1376C2×C11semidirect
267. C11#13414direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4952
C2×C11×#3622
C2×C11×#3612
C11×#21412
C11×#21402
C11×#19452
C11×#13762
#1341411