Finite Group Databasebeta

← C11×#13144 #14590337

Subgroups — C11×#13144 #14590337

Order 2816.

334 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#361C211yesmaximal, characteristic
2C2×C11×#357C211yesmaximal, characteristic
3C11×#2108C211yesmaximal, characteristic, complemented
4C11×#1978C211yesmaximal, characteristic
5C11×#1952C211yesmaximal, characteristic, complemented
6C11×#1387C211yesmaximal, characteristic, complemented
7C11×#1381C211yesmaximal, characteristic, complemented
8C22×C11×D8C2211yescharacteristic
9C2×C11×M32C2211yescharacteristic
10C22×C11×C16C2211yescharacteristic
11C2×C11×#108C2211yescharacteristic
12C2×C11×#108C2211yescharacteristic
13C11×#428—21no—
14C2×C11×#107C2211yescharacteristic
15C11×#418—21no—
16C2×C11×#100—21no—
17C11×#405C2211yescharacteristic
18C11×#361C414yescomplemented
19C11×#357—21no—
20C11×#357—21no—
21C11×#346—21no—
22C4×C11×C16—21no—
23C11×#343—21no—
24C22×D4×C11—21no—
25C2×C11×D8—21no—
26C2×C11×D8—21no—
27C2×C11×D8—21no—
28C2×C11×D8—21no—
29C2×C11×D8—21no—
30C2×C11×D8C2×C412yes—
31C2×C11×M16—21no—
32C2×C11×M16—21no—
33C2×C11×M16D411yescharacteristic
34C22×C8×C11C2311yescharacteristic
35C11×#117D411yescharacteristic
36C2×C11×C4⋊C4—21no—
37C11×M32—21no—
38C11×M32C2×C412yes—
39C2×C11×C16—21no—
40C2×C11×C16—21no—
41C2×C11×C16—21no—
42C2×C11×C16D411yescharacteristic
43C2×C11×C16D411yescharacteristic
44C11×#108—21no—
45C11×#108—21no—
46C11×#108—21no—
47C11×#108C2×C412yes—
48C11×#107—21no—
49C11×#107—21no—
50C11×#107—41no—
51C11×#106—41no—
52C11×#102—41no—
53C11×#102—41no—
54C11×#100—42no—
55C11×#97—21no—
56C4×C8×C11—21no—
57#13144C1111yesmaximal, characteristic, direct product factor, Sylow
58C24×C11—41no—
59C2×D4×C11—22no—
60C2×D4×C11—41no—
61C2×D4×C11—41no—
62C2×D4×C11—41no—
63C2×D4×C11—41no—
64C2×D4×C11—41no—
65C22×C4×C11—41no—
66C22×C4×C11C2×D411yescharacteristic
67C11×D8—22no—
68C11×D8—22no—
69C11×D8—41no—
70C11×D8—41no—
71C11×M16—22no—
72C11×M16—21no—
73C11×M16—41no—
74C11×M16—41no—
75C11×M16—41no—
76C11×M16SD1612yes—
77C2×C8×C11—21no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C2×C8×C11C22×C411yescharacteristic
81C2×C8×C11C2×D411yescharacteristic
82C2×C8×C11#4111yescharacteristic
83C2×C8×C11#4111yescharacteristic
84C2×C8×C11#4111yescharacteristic
85C2×C8×C11#4111yescharacteristic
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4D811yescharacteristic
89C11×C4⋊C4D811yescharacteristic
90C11×C22⋊C4—21no—
91C42×C11—21no—
92C11×C16—22no—
93C11×C16—21no—
94C11×C16—21no—
95C2×#361C2×C1111yescharacteristic
96C2×#357C2×C1111yescharacteristic
97#2108C2×C1111yescharacteristic, complemented
98#1978C2×C1111yescharacteristic
99#1952C2×C1111yescharacteristic, complemented
100#1387C2×C1111yescharacteristic, complemented
101#1381C2×C1111yescharacteristic, complemented
102C23×C11—42no—
103C23×C11—81no—
104C23×C11—81no—
105C23×C11—161no—
106C23×C11—161no—
107C23×C11#13511yescharacteristic
108D4×C11—42no—
109D4×C11—42no—
110D4×C11—81no—
111D4×C11—81no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—81no—
115C2×C4×C11—161no—
116C2×C4×C11C4×D411yescharacteristic
117C2×C4×C11#12111yescharacteristic
118C2×C4×C11#12411yescharacteristic
119C2×C4×C11C2×D811yescharacteristic
120C2×C4×C11C2×SD1611yescharacteristic
121C2×C4×C11#13511yescharacteristic
122C8×C11—22no—
123C8×C11—42no—
124C8×C11—81no—
125C8×C11#11711yescharacteristic
126C8×C11C4×D411yescharacteristic
127C8×C11#12311yescharacteristic
128C8×C11#12611yescharacteristic
129C22×D8C22×C1111yescharacteristic
130C2×M32C22×C1111yescharacteristic
131C22×C16C22×C1111yescharacteristic
132C2×#108C22×C1111yescharacteristic
133C2×#108C22×C1111yescharacteristic
134#428—21no—
135C2×#107C22×C1111yescharacteristic
136#418—21no—
137C2×#100—21no—
138#405C22×C1111yescharacteristic
139#361C4×C1114yescomplemented
140#357—21no—
141#357—21no—
142#346—21no—
143C4×C16—21no—
144#343—21no—
145C22×C11—21no—
146C22×C11—21no—
147C22×C11—82no—
148C22×C11—162no—
149C22×C11—162no—
150C22×C11—161no—
151C22×C11—161no—
152C22×C11C4×SD1611yescharacteristic
153C22×C11#46611yescharacteristic
154C22×C11#48811yescharacteristic
155C4×C11—41no—
156C4×C11—41no—
157C4×C11—161no—
158C4×C11#38811yescharacteristic
159C4×C11C4×D811yescharacteristic
160C4×C11#46511yescharacteristic
161C4×C11#48611yescharacteristic
162C22×D4—21no—
163C2×D8—21no—
164C2×D8—21no—
165C2×D8—21no—
166C2×D8—21no—
167C2×D8—21no—
168C2×D8C2×C4×C1112yes—
169C2×M16—21no—
170C2×M16—21no—
171C2×M16D4×C1111yescharacteristic
172C22×C8C23×C1111yescharacteristic
173#117D4×C1111yescharacteristic
174C2×C4⋊C4—21no—
175M32—21no—
176M32C2×C4×C1112yes—
177C2×C16—21no—
178C2×C16—21no—
179C2×C16—21no—
180C2×C16D4×C1111yescharacteristic
181C2×C16D4×C1111yescharacteristic
182#108—21no—
183#108—21no—
184#108—21no—
185#108C2×C4×C1112yes—
186#107—21no—
187#107—21no—
188#107—41no—
189#106—41no—
190#102—41no—
191#102—41no—
192#100—42no—
193#97—21no—
194C4×C8—21no—
195C2×C11—21no—
196C2×C11—21no—
197C2×C11—162no—
198C2×C11#193411yescharacteristic
199C2×C11#222111yescharacteristic
200C2×C11#222311yescharacteristic
201C24—41no—
202C2×D4—22no—
203C2×D4—41no—
204C2×D4—41no—
205C2×D4—41no—
206C2×D4—41no—
207C2×D4—41no—
208C22×C4—41no—
209C22×C4C2×D4×C1111yescharacteristic
210D8—22no—
211D8—22no—
212D8—41no—
213D8—41no—
214M16—21no—
215M16—22no—
216M16—41no—
217M16—41no—
218M16—41no—
219M16C11×SD1612yes—
220C2×C8—21no—
221C2×C8—41no—
222C2×C8—41no—
223C2×C8C22×C4×C1111yescharacteristic
224C2×C8C2×D4×C1111yescharacteristic
225C2×C8C11×#4111yescharacteristic
226C2×C8C11×#4111yescharacteristic
227C2×C8C11×#4111yescharacteristic
228C2×C8C11×#4111yescharacteristic
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4C11×D811yescharacteristic
232C4⋊C4C11×D811yescharacteristic
233C22⋊C4—21no—
234C42—21no—
235C16—22no—
236C16—21no—
237C16—21no—
238C11#1314411yescharacteristic, direct product factor, Sylow
239C23—42no—
240C23—81no—
241C23—81no—
242C23—161no—
243C23—161no—
244C23C11×#13511yescharacteristic
245D4—42no—
246D4—42no—
247D4—81no—
248D4—81no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—81no—
252C2×C4—161no—
253C2×C4C4×D4×C1111yescharacteristic
254C2×C4C11×#12111yescharacteristic
255C2×C4C11×#12411yescharacteristic
256C2×C4C2×C11×D811yescharacteristic
257C2×C4C2×C11×SD1611yescharacteristic
258C2×C4C11×#13511yescharacteristic
259C8—22no—
260C8—42no—
261C8—81no—
262C8C11×#11711yescharacteristic
263C8C4×D4×C1111yescharacteristic
264C8C11×#12311yescharacteristic
265C8C11×#12611yescharacteristic
266C22—21no—
267C22—21no—
268C22—82no—
269C22—162no—
270C22—162no—
271C22—161no—
272C22—161no—
273C22C4×C11×SD1611yescharacteristic
274C22C11×#46611yescharacteristic
275C22C11×#48811yescharacteristic
276C4—41no—
277C4—41no—
278C4—161no—
279C4C11×#38811yescharacteristic
280C4C4×C11×D811yescharacteristic
281C4C11×#46511yescharacteristic
282C4C11×#48611yescharacteristic
283C2—21no—
284C2—21no—
285C2—162no—
286C2C11×#193411yescharacteristic
287C2C11×#222111yescharacteristic
288C2C11×#222311yescharacteristic
subgroupG/H
center, socleC22×C11#466
commutatorC2×C8C22×C4×C11
Frattini, cosocleC22×C8C23×C11
prime radicalC22×C11×D8C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C11×#405 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2108C2semidirect
5. C11×#1952C2semidirect
6. C11×#1387C2semidirect
7. C11×#1381C2semidirect
18. C11×#361C4semidirect
57. #13144C11direct (N × H)
97. #2108C2×C11semidirect
99. #1952C2×C11semidirect
100. #1387C2×C11semidirect
101. #1381C2×C11semidirect
139. #361C4×C11semidirect
238. C11#13144direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3612
C2×C11×#3572
C11×#21082
C11×#19782
C11×#19522
C11×#13872
C11×#13812
#1314411