Finite Group Databasebeta

← C11×#13216 #14590409

Subgroups — C11×#13216 #14590409

Order 2816.

434 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3156C211yesmaximal, characteristic
2C2×C11×#362C211yesmaximal, characteristic, complemented
3C11×#2145C211yesmaximal, characteristic
4C11×#2143C211yesmaximal, characteristic
5C11×#2141C211yesmaximal, characteristic, complemented
6C11×#2110C211yesmaximal, characteristic, complemented
7C11×#1833C211yesmaximal, characteristic, complemented
8C2×C11×#137—21no—
9C2×C11×#135C2211yescharacteristic
10C22×C11×Q16C2211yescharacteristic
11C11×#536—21no—
12C2×C11×M32C2211yescharacteristic
13C2×C11×M32C2211yescharacteristic
14C11×#497—22no—
15C11×#495C412yescomplemented
16C11×#494C412yescomplemented
17C2×C11×#108C2211yescharacteristic
18C11×#427C2211yescharacteristic
19C11×#405C2211yescharacteristic
20C11×#362—22no—
21C11×#360—22no—
22C11×#359—22no—
23C11×#358—22no—
24C11×#347—22no—
25C11×#344—21no—
26C11×H(3,ℤ/4)—21no—
27C2×C11×#41—21no—
28C22×Q8×C11—21no—
29C11×#137—42no—
30C11×#137—42no—
31C11×#135—21no—
32C11×#135—21no—
33C11×#135—21no—
34C11×#135—21no—
35C2×C11×Q16—22no—
36C2×C11×Q16—21no—
37C2×C11×Q16—21no—
38C2×C11×Q16—21no—
39C2×C11×Q16—21no—
40C2×C11×Q16—21no—
41C2×C11×Q16C2×C411yescharacteristic
42C2×C11×Q16C2×C412yes—
43C2×C11×SD16—22no—
44C2×C11×SD16—21no—
45C2×C11×D8C2×C411yescharacteristic
46C2×C11×M16—21no—
47C2×C11×M16D411yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C11×C4⋊Q8—22no—
50C11×#124—22no—
51C11×#123—42no—
52C11×C22⋊Q8—42no—
53C11×#117—21no—
54C11×#117D411yescharacteristic
55C11×M32—21no—
56C11×M32—21no—
57C11×M32—21no—
58C11×M32D412yes—
59C2×C11×C16—21no—
60C2×C11×C16D412yes—
61C11×#108—21no—
62C11×#108—21no—
63C11×#107—21no—
64C11×#106—21no—
65C11×#97D412yes—
66C4×C8×C11C2×C412yes—
67#13216C1111yesmaximal, characteristic, direct product factor, Sylow
68C11×#41—41no—
69C11×#41—41no—
70C11×#41—41no—
71C11×#41—41no—
72C2×Q8×C11—22no—
73C2×Q8×C11—21no—
74C2×Q8×C11—41no—
75C2×Q8×C11—41no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×D4×C11—21no—
80C2×D4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11C2×D411yescharacteristic
84C11×Q16—22no—
85C11×Q16—22no—
86C11×Q16—21no—
87C11×Q16—21no—
88C11×Q16—44no—
89C11×Q16—41no—
90C11×Q16—41no—
91C11×SD16—44no—
92C11×SD16—41no—
93C11×SD16—41no—
94C11×D8—21no—
95C11×D8—21no—
96C11×M16—21no—
97C11×M16—21no—
98C11×M16—41no—
99C11×M16—41no—
100C2×C8×C11—41no—
101C2×C8×C11C22⋊C412yes—
102C2×C8×C11C22×C411yescharacteristic
103C2×C8×C11C2×D411yescharacteristic
104C2×C8×C11C2×D411yescharacteristic
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11#4111yescharacteristic
107C2×C8×C11#4111yescharacteristic
108C11×C4⋊C4—21no—
109C11×C4⋊C4—44no—
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#3156C2×C1111yescharacteristic
119C2×#362C2×C1111yescharacteristic, complemented
120#2145C2×C1111yescharacteristic
121#2143C2×C1111yescharacteristic
122#2141C2×C1111yescharacteristic, complemented
123#2110C2×C1111yescharacteristic, complemented
124#1833C2×C1111yescharacteristic, complemented
125C23×C11—41no—
126C23×C11AGL(1,ℤ/8)11yescharacteristic
127Q8×C11—41no—
128Q8×C11—42no—
129Q8×C11—42no—
130Q8×C11—41no—
131Q8×C11—81no—
132Q8×C11—81no—
133D4×C11—41no—
134D4×C11—41no—
135D4×C11—81no—
136D4×C11—81no—
137C2×C4×C11—22no—
138C2×C4×C11—42no—
139C2×C4×C11—41no—
140C2×C4×C11—81no—
141C2×C4×C11—81no—
142C2×C4×C11—81no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11C2×C22⋊C411yescharacteristic
146C2×C4×C11#12411yescharacteristic
147C2×C4×C11#12711yescharacteristic
148C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
151C8×C11—22no—
152C8×C11—81no—
153C8×C11C4×D411yescharacteristic
154C8×C11C4×D411yescharacteristic
155C8×C11#12111yescharacteristic
156C8×C11#12111yescharacteristic
157C2×#137—21no—
158C2×#135C22×C1111yescharacteristic
159C22×Q16C22×C1111yescharacteristic
160#536—21no—
161C2×M32C22×C1111yescharacteristic
162C2×M32C22×C1111yescharacteristic
163#497—22no—
164#495C4×C1112yescomplemented
165#494C4×C1112yescomplemented
166C2×#108C22×C1111yescharacteristic
167#427C22×C1111yescharacteristic
168#405C22×C1111yescharacteristic
169#362—22no—
170#360—22no—
171#359—22no—
172#358—22no—
173#347—22no—
174#344—21no—
175H(3,ℤ/4)—21no—
176C22×C11—41no—
177C22×C11—82no—
178C22×C11—81no—
179C22×C11#41811yescharacteristic
180C22×C11#49011yescharacteristic
181C22×C11#49611yescharacteristic
182C4×C11—42no—
183C4×C11—81no—
184C4×C11—82no—
185C4×C11—161no—
186C4×C11#39011yescharacteristic
187C4×C11#41811yescharacteristic
188C4×C11#49011yescharacteristic
189C4×C11#49611yescharacteristic
190C2×#41—21no—
191C22×Q8—21no—
192#137—42no—
193#137—42no—
194#135—21no—
195#135—21no—
196#135—21no—
197#135—21no—
198C2×Q16—22no—
199C2×Q16—21no—
200C2×Q16—21no—
201C2×Q16—21no—
202C2×Q16—21no—
203C2×Q16—21no—
204C2×Q16C2×C4×C1112yes—
205C2×Q16C2×C4×C1111yescharacteristic
206C2×SD16—22no—
207C2×SD16—21no—
208C2×D8C2×C4×C1111yescharacteristic
209C2×M16—21no—
210C2×M16D4×C1111yescharacteristic
211C22×C8C23×C1111yescharacteristic
212C4⋊Q8—22no—
213#124—22no—
214#123—42no—
215C22⋊Q8—42no—
216#117—21no—
217#117D4×C1111yescharacteristic
218M32—21no—
219M32—21no—
220M32—21no—
221M32D4×C1112yes—
222C2×C16—21no—
223C2×C16D4×C1112yes—
224#108—21no—
225#108—21no—
226#107—21no—
227#106—21no—
228#97D4×C1112yes—
229C4×C8C2×C4×C1112yes—
230C2×C11—21no—
231C2×C11—21no—
232C2×C11—21no—
233C2×C11—161no—
234C2×C11#196111yescharacteristic
235#41—41no—
236#41—41no—
237#41—41no—
238#41—41no—
239C2×Q8—22no—
240C2×Q8—21no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×D4—21no—
247C2×D4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4C2×D4×C1111yescharacteristic
251Q16—22no—
252Q16—22no—
253Q16—21no—
254Q16—21no—
255Q16—44no—
256Q16—41no—
257Q16—41no—
258SD16—44no—
259SD16—41no—
260SD16—41no—
261D8—21no—
262D8—21no—
263M16—21no—
264M16—21no—
265M16—41no—
266M16—41no—
267C2×C8—41no—
268C2×C8C11×C22⋊C412yes—
269C2×C8C22×C4×C1111yescharacteristic
270C2×C8C2×D4×C1111yescharacteristic
271C2×C8C2×D4×C1111yescharacteristic
272C2×C8C2×D4×C1111yescharacteristic
273C2×C8C11×#4111yescharacteristic
274C2×C8C11×#4111yescharacteristic
275C4⋊C4—21no—
276C4⋊C4—44no—
277C4⋊C4—41no—
278C22⋊C4—21no—
279C22⋊C4—44no—
280C22⋊C4—41no—
281C42—41no—
282C42C11×C22⋊C412yes—
283C16—22no—
284C16—22no—
285C11#1321611yescharacteristic, direct product factor, Sylow
286C23—41no—
287C23C11×AGL(1,ℤ/8)11yescharacteristic
288Q8—41no—
289Q8—42no—
290Q8—42no—
291Q8—41no—
292Q8—81no—
293Q8—81no—
294D4—41no—
295D4—41no—
296D4—81no—
297D4—81no—
298C2×C4—22no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4C2×C11×C22⋊C411yescharacteristic
307C2×C4C11×#12411yescharacteristic
308C2×C4C11×#12711yescharacteristic
309C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
310C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
311C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
312C8—22no—
313C8—81no—
314C8C4×D4×C1111yescharacteristic
315C8C4×D4×C1111yescharacteristic
316C8C11×#12111yescharacteristic
317C8C11×#12111yescharacteristic
318C22—41no—
319C22—82no—
320C22—81no—
321C22C11×#41811yescharacteristic
322C22C11×#49011yescharacteristic
323C22C11×#49611yescharacteristic
324C4—42no—
325C4—81no—
326C4—82no—
327C4—161no—
328C4C11×#39011yescharacteristic
329C4C11×#41811yescharacteristic
330C4C11×#49011yescharacteristic
331C4C11×#49611yescharacteristic
332C2—21no—
333C2—21no—
334C2—21no—
335C2—161no—
336C2C11×#196111yescharacteristic
subgroupG/H
center, socleC2×C11#1961
commutatorC2×C8C22×C4×C11
Frattini, cosocleC22×C8C23×C11
prime radicalC2×C11×#135C22
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×#362C2semidirect
5. C11×#2141C2semidirect
6. C11×#2110C2semidirect
7. C11×#1833C2semidirect
15. C11×#495C4semidirect
16. C11×#494C4semidirect
67. #13216C11direct (N × H)
119. C2×#362C2×C11semidirect
122. #2141C2×C11semidirect
123. #2110C2×C11semidirect
124. #1833C2×C11semidirect
164. #495C4×C11semidirect
165. #494C4×C11semidirect
285. C11#13216direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31562
C2×C11×#3622
C11×#21452
C11×#21432
C11×#21412
C11×#21102
C11×#18332
#1321611