Finite Group Databasebeta

← C11×#13215 #14590408

Subgroups — C11×#13215 #14590408

Order 2816.

466 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3155C211yesmaximal, characteristic
2C2×C11×#361C211yesmaximal, characteristic, complemented
3C11×#2145C211yesmaximal, characteristic, complemented
4C11×#2143C211yesmaximal, characteristic, complemented
5C11×#2140C211yesmaximal, characteristic, complemented
6C11×#2110C211yesmaximal, characteristic, complemented
7C11×#1833C211yesmaximal, characteristic, complemented
8C2×C11×AGL(1,ℤ/8)—21no—
9C2×C11×#135C2211yescharacteristic
10C22×C11×D8C2211yescharacteristic
11C11×#535—21no—
12C2×C11×M32C2211yescharacteristic
13C2×C11×M32C2211yescharacteristic
14C11×#496—22no—
15C11×#495C412yescomplemented
16C11×#493C412yescomplemented
17C2×C11×#108C2211yescharacteristic
18C11×#427C2211yescharacteristic
19C11×#405C2211yescharacteristic
20C11×#361—22no—
21C11×#360—22no—
22C11×#359—22no—
23C11×#357—22no—
24C11×#347—22no—
25C11×#344—21no—
26C11×H(3,ℤ/4)—21no—
27C2×C11×#41—21no—
28C22×D4×C11—21no—
29C11×AGL(1,ℤ/8)—42no—
30C11×AGL(1,ℤ/8)—42no—
31C11×#135—21no—
32C11×#135—21no—
33C11×#135—21no—
34C11×#135—21no—
35C2×C11×Q16C2×C411yescharacteristic
36C2×C11×SD16—22no—
37C2×C11×SD16—21no—
38C2×C11×D8—22no—
39C2×C11×D8—21no—
40C2×C11×D8—21no—
41C2×C11×D8—21no—
42C2×C11×D8—21no—
43C2×C11×D8—21no—
44C2×C11×D8C2×C411yescharacteristic
45C2×C11×D8C2×C412yes—
46C2×C11×M16—21no—
47C2×C11×M16D411yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C11×#127—22no—
50C11×#124—22no—
51C11×#121—42no—
52C11×#120—42no—
53C11×#117—21no—
54C11×#117D411yescharacteristic
55C11×M32—21no—
56C11×M32—21no—
57C11×M32—21no—
58C11×M32D412yescomplemented
59C2×C11×C16—21no—
60C2×C11×C16D412yescomplemented
61C11×#108—21no—
62C11×#108—21no—
63C11×#107—21no—
64C11×#106—21no—
65C11×#97D412yes—
66C4×C8×C11C2×C412yes—
67#13215C1111yesmaximal, characteristic, direct product factor, Sylow
68C24×C11—41no—
69C11×#41—41no—
70C11×#41—41no—
71C11×#41—41no—
72C11×#41—41no—
73C2×Q8×C11—21no—
74C2×D4×C11—22no—
75C2×D4×C11—21no—
76C2×D4×C11—44no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11C2×D411yescharacteristic
85C11×Q16—21no—
86C11×Q16—21no—
87C11×SD16—44no—
88C11×SD16—41no—
89C11×SD16—41no—
90C11×D8—22no—
91C11×D8—22no—
92C11×D8—21no—
93C11×D8—21no—
94C11×D8—44no—
95C11×D8—41no—
96C11×D8—41no—
97C11×M16—21no—
98C11×M16—21no—
99C11×M16—41no—
100C11×M16—41no—
101C2×C8×C11—41no—
102C2×C8×C11C22⋊C412yes—
103C2×C8×C11C22×C411yescharacteristic
104C2×C8×C11C2×D411yescharacteristic
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11#4111yescharacteristic
108C2×C8×C11#4111yescharacteristic
109C11×C4⋊C4—21no—
110C11×C4⋊C4—41no—
111C11×C22⋊C4—21no—
112C11×C22⋊C4—44no—
113C11×C22⋊C4—41no—
114C42×C11—41no—
115C42×C11C22⋊C412yes—
116C11×C16—22no—
117C11×C16—22no—
118#3155C2×C1111yescharacteristic
119C2×#361C2×C1111yescharacteristic, complemented
120#2145C2×C1111yescharacteristic, complemented
121#2143C2×C1111yescharacteristic, complemented
122#2140C2×C1111yescharacteristic, complemented
123#2110C2×C1111yescharacteristic, complemented
124#1833C2×C1111yescharacteristic, complemented
125C23×C11—42no—
126C23×C11—41no—
127C23×C11—81no—
128C23×C11—81no—
129C23×C11—162no—
130C23×C11AGL(1,ℤ/8)11yescharacteristic
131Q8×C11—41no—
132Q8×C11—41no—
133D4×C11—42no—
134D4×C11—41no—
135D4×C11—41no—
136D4×C11—42no—
137D4×C11—81no—
138D4×C11—81no—
139D4×C11—81no—
140D4×C11—81no—
141D4×C11—164no—
142C2×C4×C11—22no—
143C2×C4×C11—41no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11—81no—
147C2×C4×C11C2×C22⋊C411yescharacteristic
148C2×C4×C11#12411yescharacteristic
149C2×C4×C11#12711yescharacteristic
150C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C8×C11—22no—
154C8×C11—81no—
155C8×C11C4×D411yescharacteristic
156C8×C11C4×D411yescharacteristic
157C8×C11#12111yescharacteristic
158C8×C11#12111yescharacteristic
159C2×AGL(1,ℤ/8)—21no—
160C2×#135C22×C1111yescharacteristic
161C22×D8C22×C1111yescharacteristic
162#535—21no—
163C2×M32C22×C1111yescharacteristic
164C2×M32C22×C1111yescharacteristic
165#496—22no—
166#495C4×C1112yescomplemented
167#493C4×C1112yescomplemented
168C2×#108C22×C1111yescharacteristic
169#427C22×C1111yescharacteristic
170#405C22×C1111yescharacteristic
171#361—22no—
172#360—22no—
173#359—22no—
174#357—22no—
175#347—22no—
176#344—21no—
177H(3,ℤ/4)—21no—
178C22×C11—41no—
179C22×C11—82no—
180C22×C11—84no—
181C22×C11—81no—
182C22×C11—82no—
183C22×C11—162no—
184C22×C11—162no—
185C22×C11#41811yescharacteristic
186C22×C11#49011yescharacteristic
187C22×C11#49611yescharacteristic
188C4×C11—42no—
189C4×C11—81no—
190C4×C11—161no—
191C4×C11#39011yescharacteristic
192C4×C11#41811yescharacteristic
193C4×C11#49011yescharacteristic
194C4×C11#49611yescharacteristic
195C2×#41—21no—
196C22×D4—21no—
197AGL(1,ℤ/8)—42no—
198AGL(1,ℤ/8)—42no—
199#135—21no—
200#135—21no—
201#135—21no—
202#135—21no—
203C2×Q16C2×C4×C1111yescharacteristic
204C2×SD16—22no—
205C2×SD16—21no—
206C2×D8—22no—
207C2×D8—21no—
208C2×D8—21no—
209C2×D8—21no—
210C2×D8—21no—
211C2×D8—21no—
212C2×D8C2×C4×C1112yes—
213C2×D8C2×C4×C1111yescharacteristic
214C2×M16—21no—
215C2×M16D4×C1111yescharacteristic
216C22×C8C23×C1111yescharacteristic
217#127—22no—
218#124—22no—
219#121—42no—
220#120—42no—
221#117—21no—
222#117D4×C1111yescharacteristic
223M32—21no—
224M32—21no—
225M32—21no—
226M32D4×C1112yescomplemented
227C2×C16—21no—
228C2×C16D4×C1112yescomplemented
229#108—21no—
230#108—21no—
231#107—21no—
232#106—21no—
233#97D4×C1112yes—
234C4×C8C2×C4×C1112yes—
235C2×C11—21no—
236C2×C11—21no—
237C2×C11—21no—
238C2×C11—161no—
239C2×C11—162no—
240C2×C11#196111yescharacteristic
241C24—41no—
242#41—41no—
243#41—41no—
244#41—41no—
245#41—41no—
246C2×Q8—21no—
247C2×D4—22no—
248C2×D4—21no—
249C2×D4—44no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—41no—
255C2×D4—41no—
256C22×C4—41no—
257C22×C4C2×D4×C1111yescharacteristic
258Q16—21no—
259Q16—21no—
260SD16—44no—
261SD16—41no—
262SD16—41no—
263D8—22no—
264D8—22no—
265D8—21no—
266D8—21no—
267D8—44no—
268D8—41no—
269D8—41no—
270M16—21no—
271M16—21no—
272M16—41no—
273M16—41no—
274C2×C8—41no—
275C2×C8C11×C22⋊C412yes—
276C2×C8C22×C4×C1111yescharacteristic
277C2×C8C2×D4×C1111yescharacteristic
278C2×C8C2×D4×C1111yescharacteristic
279C2×C8C2×D4×C1111yescharacteristic
280C2×C8C11×#4111yescharacteristic
281C2×C8C11×#4111yescharacteristic
282C4⋊C4—21no—
283C4⋊C4—41no—
284C22⋊C4—21no—
285C22⋊C4—44no—
286C22⋊C4—41no—
287C42—41no—
288C42C11×C22⋊C412yes—
289C16—22no—
290C16—22no—
291C11#1321511yescharacteristic, direct product factor, Sylow
292C23—42no—
293C23—41no—
294C23—81no—
295C23—81no—
296C23—162no—
297C23C11×AGL(1,ℤ/8)11yescharacteristic
298Q8—41no—
299Q8—41no—
300D4—42no—
301D4—41no—
302D4—41no—
303D4—42no—
304D4—81no—
305D4—81no—
306D4—81no—
307D4—81no—
308D4—164no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4C2×C11×C22⋊C411yescharacteristic
315C2×C4C11×#12411yescharacteristic
316C2×C4C11×#12711yescharacteristic
317C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
318C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
319C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
320C8—22no—
321C8—81no—
322C8C4×D4×C1111yescharacteristic
323C8C4×D4×C1111yescharacteristic
324C8C11×#12111yescharacteristic
325C8C11×#12111yescharacteristic
326C22—41no—
327C22—82no—
328C22—84no—
329C22—81no—
330C22—82no—
331C22—162no—
332C22—162no—
333C22C11×#41811yescharacteristic
334C22C11×#49011yescharacteristic
335C22C11×#49611yescharacteristic
336C4—42no—
337C4—81no—
338C4—161no—
339C4C11×#39011yescharacteristic
340C4C11×#41811yescharacteristic
341C4C11×#49011yescharacteristic
342C4C11×#49611yescharacteristic
343C2—21no—
344C2—21no—
345C2—21no—
346C2—162no—
347C2—161no—
348C2C11×#196111yescharacteristic
subgroupG/H
center, socleC2×C11#1961
commutatorC2×C8C22×C4×C11
Frattini, cosocleC22×C8C23×C11
prime radicalC11×#3155C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C22×C4×C11 ◁ C11×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#361C2semidirect
3. C11×#2145C2semidirect
4. C11×#2143C2semidirect
5. C11×#2140C2semidirect
6. C11×#2110C2semidirect
7. C11×#1833C2semidirect
15. C11×#495C4semidirect
16. C11×#493C4semidirect
58. C11×M32D4semidirect
60. C2×C11×C16D4semidirect
67. #13215C11direct (N × H)
119. C2×#361C2×C11semidirect
120. #2145C2×C11semidirect
121. #2143C2×C11semidirect
122. #2140C2×C11semidirect
123. #2110C2×C11semidirect
124. #1833C2×C11semidirect
166. #495C4×C11semidirect
167. #493C4×C11semidirect
226. M32D4×C11semidirect
228. C2×C16D4×C11semidirect
291. C11#13215direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31552
C2×C11×#3612
C11×#21452
C11×#21432
C11×#21402
C11×#21102
C11×#18332
#1321511