Finite Group Databasebeta

← C11×#13073 #14590266

Subgroups — C11×#13073 #14590266

Order 2816.

478 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#504C211yesmaximal, characteristic, complemented
2C2×C11×#472C211yesmaximal, characteristic
3C2×C11×#361C211yesmaximal, characteristic, complemented
4C2×C11×#357C211yesmaximal, characteristic, complemented
5C11×#1816C211yesmaximal, characteristic, complemented
6C11×#1387C211yesmaximal, characteristic, complemented
7C11×#1381C211yesmaximal, characteristic, complemented
8C2×C11×AGL(1,ℤ/8)—21no—
9C22×C11×D8C2211yescharacteristic
10C2×C11×#131C2211yescharacteristic
11C11×#504—22no—
12C11×#504—22no—
13C2×C11×M32—21no—
14C2×C11×M32C2211yescharacteristic
15C22×C11×C16—21no—
16C22×C11×C16C2211yescharacteristic
17C11×#472—22no—
18C11×#472C414yescomplemented
19C2×C11×#108C2211yescharacteristic
20C2×C11×#108C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C11×#417—21no—
23C2×C11×#100—21no—
24C11×#361—22no—
25C11×#357—21no—
26C11×#357—21no—
27C11×#343—21no—
28C2×C11×#41D411yescharacteristic
29C22×D4×C11—21no—
30C11×AGL(1,ℤ/8)—24no—
31C11×AGL(1,ℤ/8)—42no—
32C2×C11×SD16—41no—
33C2×C11×D8—21no—
34C2×C11×D8—21no—
35C2×C11×D8—21no—
36C2×C11×D8—21no—
37C2×C11×D8—21no—
38C2×C11×D8—41no—
39C2×C11×D8C2×C412yes—
40C11×#131—21no—
41C11×#131—21no—
42C11×#131C2×C412yes—
43C11×#131D412yes—
44C2×C11×M16—21no—
45C2×C11×M16—21no—
46C2×C11×M16—21no—
47C2×C11×M16D411yescharacteristic
48C22×C8×C11—21no—
49C22×C8×C11C2311yescharacteristic
50C2×C11×C4⋊C4—21no—
51C11×M32—24no—
52C11×M32—21no—
53C11×M32D412yes—
54C2×C11×C16—24no—
55C2×C11×C16—21no—
56C2×C11×C16—21no—
57C2×C11×C16—21no—
58C2×C11×C16D411yescharacteristic
59C2×C11×C16D411yescharacteristic
60C11×#108—21no—
61C11×#108—21no—
62C11×#108—21no—
63C11×#108C2×C412yes—
64C11×#107—21no—
65C11×#107—21no—
66C11×#103—41no—
67C11×#102—41no—
68C11×#100—24no—
69#13073C1111yesmaximal, characteristic, direct product factor, Sylow
70C24×C11—41no—
71C11×#41—21no—
72C11×#41—21no—
73C11×#41C22⋊C412yes—
74C11×#41SD1612yes—
75C2×Q8×C11D811yescharacteristic
76C2×D4×C11—21no—
77C2×D4×C11—22no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11D811yescharacteristic
84C22×C4×C11—21no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C11×SD16—44no—
88C11×D8—22no—
89C11×D8—22no—
90C11×D8—41no—
91C11×D8—41no—
92C11×D8—44no—
93C11×M16—22no—
94C11×M16—22no—
95C11×M16—22no—
96C11×M16—21no—
97C11×M16—41no—
98C11×M16—41no—
99C11×M16—41no—
100C11×M16C22⋊C412yes—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11—21no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C2×C8×C11C22×C411yescharacteristic
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11C2×D411yescharacteristic
109C2×C8×C11C2×D411yescharacteristic
110C2×C8×C11#4111yescharacteristic
111C2×C8×C11#4111yescharacteristic
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C16—21no—
115C11×C16—22no—
116C11×C16—21no—
117C2×#504C2×C1111yescharacteristic, complemented
118C2×#472C2×C1111yescharacteristic
119C2×#361C2×C1111yescharacteristic, complemented
120C2×#357C2×C1111yescharacteristic, complemented
121#1816C2×C1111yescharacteristic, complemented
122#1387C2×C1111yescharacteristic, complemented
123#1381C2×C1111yescharacteristic, complemented
124C23×C11—21no—
125C23×C11—42no—
126C23×C11—81no—
127C23×C11—81no—
128C23×C11—161no—
129C23×C11—161no—
130C23×C11#13511yescharacteristic
131Q8×C11—21no—
132Q8×C11#10212yes—
133D4×C11—22no—
134D4×C11—22no—
135D4×C11—21no—
136D4×C11—42no—
137D4×C11—42no—
138D4×C11—81no—
139D4×C11—81no—
140D4×C11#10212yes—
141C2×C4×C11—21no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—81no—
145C2×C4×C11—161no—
146C2×C4×C11C2×C22⋊C411yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11C2×D811yescharacteristic
150C2×C4×C11C2×SD1611yescharacteristic
151C2×C4×C11#13511yescharacteristic
152C8×C11—22no—
153C8×C11—42no—
154C8×C11—81no—
155C8×C11C4×D411yescharacteristic
156C8×C11C4×D411yescharacteristic
157C8×C11#12011yescharacteristic
158C8×C11#12311yescharacteristic
159C2×AGL(1,ℤ/8)—21no—
160C22×D8C22×C1111yescharacteristic
161C2×#131C22×C1111yescharacteristic
162#504—22no—
163#504—22no—
164C2×M32—21no—
165C2×M32C22×C1111yescharacteristic
166C22×C16—21no—
167C22×C16C22×C1111yescharacteristic
168#472—22no—
169#472C4×C1114yescomplemented
170C2×#108C22×C1111yescharacteristic
171C2×#108C22×C1111yescharacteristic
172C2×#107C22×C1111yescharacteristic
173#417—21no—
174C2×#100—21no—
175#361—22no—
176#357—21no—
177#357—21no—
178#343—21no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11—22no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—82no—
185C22×C11—162no—
186C22×C11—162no—
187C22×C11—161no—
188C22×C11—161no—
189C22×C11#41611yescharacteristic
190C22×C11#46511yescharacteristic
191C22×C11#46611yescharacteristic
192C4×C11—22no—
193C4×C11—161no—
194C4×C11#38611yescharacteristic
195C4×C11C2×#10211yescharacteristic
196C4×C11#46511yescharacteristic
197C4×C11#46611yescharacteristic
198C2×#41D4×C1111yescharacteristic
199C22×D4—21no—
200AGL(1,ℤ/8)—24no—
201AGL(1,ℤ/8)—42no—
202C2×SD16—41no—
203C2×D8—21no—
204C2×D8—21no—
205C2×D8—21no—
206C2×D8—21no—
207C2×D8—21no—
208C2×D8—41no—
209C2×D8C2×C4×C1112yes—
210#131—21no—
211#131—21no—
212#131C2×C4×C1112yes—
213#131D4×C1112yes—
214C2×M16—21no—
215C2×M16—21no—
216C2×M16—21no—
217C2×M16D4×C1111yescharacteristic
218C22×C8—21no—
219C22×C8C23×C1111yescharacteristic
220C2×C4⋊C4—21no—
221M32—24no—
222M32—21no—
223M32D4×C1112yes—
224C2×C16—24no—
225C2×C16—21no—
226C2×C16—21no—
227C2×C16—21no—
228C2×C16D4×C1111yescharacteristic
229C2×C16D4×C1111yescharacteristic
230#108—21no—
231#108—21no—
232#108—21no—
233#108C2×C4×C1112yes—
234#107—21no—
235#107—21no—
236#103—41no—
237#102—41no—
238#100—24no—
239C2×C11—21no—
240C2×C11—21no—
241C2×C11—42no—
242C2×C11—162no—
243C2×C11#189311yescharacteristic
244C2×C11#222111yescharacteristic
245C2×C11#222311yescharacteristic
246C24—41no—
247#41—21no—
248#41—21no—
249#41C11×C22⋊C412yes—
250#41C11×SD1612yes—
251C2×Q8C11×D811yescharacteristic
252C2×D4—21no—
253C2×D4—22no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4C11×D811yescharacteristic
260C22×C4—21no—
261C22×C4—41no—
262C22×C4C2×D4×C1111yescharacteristic
263SD16—44no—
264D8—22no—
265D8—22no—
266D8—44no—
267D8—41no—
268D8—41no—
269M16—21no—
270M16—22no—
271M16—22no—
272M16—22no—
273M16—41no—
274M16—41no—
275M16—41no—
276M16C11×C22⋊C412yes—
277C2×C8—21no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8C22×C4×C1111yescharacteristic
283C2×C8C2×D4×C1111yescharacteristic
284C2×C8C2×D4×C1111yescharacteristic
285C2×C8C2×D4×C1111yescharacteristic
286C2×C8C11×#4111yescharacteristic
287C2×C8C11×#4111yescharacteristic
288C4⋊C4—41no—
289C4⋊C4—41no—
290C16—21no—
291C16—22no—
292C16—21no—
293C11#1307311yescharacteristic, direct product factor, Sylow
294C23—21no—
295C23—42no—
296C23—81no—
297C23—81no—
298C23—161no—
299C23—161no—
300C23C11×#13511yescharacteristic
301Q8—21no—
302Q8C11×#10212yes—
303D4—22no—
304D4—22no—
305D4—21no—
306D4—42no—
307D4—42no—
308D4—81no—
309D4—81no—
310D4C11×#10212yes—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—81no—
315C2×C4—161no—
316C2×C4C2×C11×C22⋊C411yescharacteristic
317C2×C4C11×#12111yescharacteristic
318C2×C4C11×#12111yescharacteristic
319C2×C4C2×C11×D811yescharacteristic
320C2×C4C2×C11×SD1611yescharacteristic
321C2×C4C11×#13511yescharacteristic
322C8—22no—
323C8—42no—
324C8—81no—
325C8C4×D4×C1111yescharacteristic
326C8C4×D4×C1111yescharacteristic
327C8C11×#12011yescharacteristic
328C8C11×#12311yescharacteristic
329C22—21no—
330C22—21no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—82no—
335C22—162no—
336C22—162no—
337C22—161no—
338C22—161no—
339C22C11×#41611yescharacteristic
340C22C11×#46511yescharacteristic
341C22C11×#46611yescharacteristic
342C4—22no—
343C4—161no—
344C4C11×#38611yescharacteristic
345C4C2×C11×#10211yescharacteristic
346C4C11×#46511yescharacteristic
347C4C11×#46611yescharacteristic
348C2—21no—
349C2—21no—
350C2—42no—
351C2—162no—
352C2C11×#189311yescharacteristic
353C2C11×#222111yescharacteristic
354C2C11×#222311yescharacteristic
subgroupG/H
center, socleC22×C11#466
commutatorC2×C8C22×C4×C11
Frattini, cosocleC22×C8C23×C11
prime radicalC2×C11×#472C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C11×#131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#504C2semidirect
3. C2×C11×#361C2semidirect
4. C2×C11×#357C2semidirect
5. C11×#1816C2semidirect
6. C11×#1387C2semidirect
7. C11×#1381C2semidirect
18. C11×#472C4semidirect
69. #13073C11direct (N × H)
117. C2×#504C2×C11semidirect
119. C2×#361C2×C11semidirect
120. C2×#357C2×C11semidirect
121. #1816C2×C11semidirect
122. #1387C2×C11semidirect
123. #1381C2×C11semidirect
169. #472C4×C11semidirect
293. C11#13073direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5042
C2×C11×#4722
C2×C11×#3612
C2×C11×#3572
C11×#18162
C11×#13872
C11×#13812
#1307311