Finite Group Databasebeta

← C11×#19210 #14596403

Subgroups — C11×#19210 #14596403

Order 2816.

570 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3249C212yesmaximal
2C11×#3160C211yesmaximal, characteristic
3C11×#2960C211yesmaximal, characteristic
4C11×#1696C212yesmaximal, complemented
5C11×#1694C212yesmaximal, complemented
6C11×#1672C214yesmaximal, complemented
7C2×C11×#334C211yesmaximal, characteristic
8C11×#1550C212yesmaximal
9C11×#533C2212yes—
10C11×#533C2211yescharacteristic
11C11×#500C2211yescharacteristic
12C11×#500C2211yescharacteristic
13C11×#499—21no—
14C11×#499—21no—
15C11×#498C2212yes—
16C11×#477—22no—
17C11×#477C2214yes—
18C11×#467—24no—
19C11×#462—22no—
20C11×#462C2214yes—
21C11×#446—21no—
22C11×#446C2212yes—
23C8×Q8×C11—21no—
24C8×Q8×C11C2212yes—
25C11×#427—21no—
26C11×#427—21no—
27C11×#424—21no—
28C11×#423C2211yescharacteristic
29C2×C11×C4⋊C8C2212yes—
30C11×#405—21no—
31C2×C4×C8×C11C2211yescharacteristic
32C11×#334C2212yes—
33C11×#334C2212yes—
34C11×#333C2214yes—
35C11×#332C2214yes—
36C2×C11×Q16—24no—
37C2×C11×M16—21no—
38C22×C8×C11—22no—
39C22×C8×C11D411yescharacteristic
40C22×C8×C11D411yescharacteristic
41C11×C4⋊Q8D411yescharacteristic
42C11×C4⋊Q8D411yescharacteristic
43C11×C4⋊Q8C2312yes—
44C11×C4⋊Q8C2312yes—
45C11×#125—22no—
46C11×#125—21no—
47C11×C22⋊Q8—21no—
48C11×C22⋊Q8—22no—
49C11×C22⋊Q8—22no—
50C11×C22⋊Q8D412yes—
51C4×Q8×C11—21no—
52C4×Q8×C11—22no—
53C4×Q8×C11—22no—
54C4×Q8×C11C2312yes—
55C11×#117—21no—
56C11×#117—22no—
57C2×C42×C11C2311yescharacteristic
58C11×#107—21no—
59C11×#107—21no—
60C11×#107—21no—
61C11×#107—21no—
62C11×#107—24no—
63C11×#106—22no—
64C11×#106—22no—
65C11×C4⋊C8—22no—
66C11×C4⋊C8—22no—
67C11×C4⋊C8—22no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8C2312yes—
70C11×C4⋊C8C2314yes—
71C11×#103—24no—
72C11×#103—24no—
73C11×#97—22no—
74C4×C8×C11—22no—
75C4×C8×C11D411yescharacteristic
76C4×C8×C11D411yescharacteristic
77C4×C8×C11C2311yescharacteristic
78C4×C8×C11C2311yescharacteristic
79#19210C1111yesmaximal, characteristic, direct product factor, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11—22no—
82C2×Q8×C11—22no—
83C2×Q8×C11C2×D412yes—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11#4111yescharacteristic
87C11×Q16—84no—
88C11×M16—42no—
89C2×C8×C11—22no—
90C2×C8×C11—22no—
91C2×C8×C11—24no—
92C2×C8×C11—82no—
93C2×C8×C11Q1614yescomplemented
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2×D411yescharacteristic
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—42no—
108C11×C4⋊C4—42no—
109C11×C4⋊C4C2×D412yes—
110C11×C22⋊C4—22no—
111C11×C22⋊C4—42no—
112C42×C11—22no—
113C42×C11—42no—
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11#4111yescharacteristic
117C42×C11C2411yescharacteristic
118#3249C2×C1112yes—
119#3160C2×C1111yescharacteristic
120#2960C2×C1111yescharacteristic
121#1696C2×C1112yescomplemented
122#1694C2×C1112yescomplemented
123#1672C2×C1114yescomplemented
124C2×#334C2×C1111yescharacteristic
125#1550C2×C1112yes—
126C23×C11#12111yescharacteristic
127Q8×C11—24no—
128Q8×C11—42no—
129Q8×C11—42no—
130Q8×C11—42no—
131Q8×C11—82no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—41no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11#12111yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11C2×Q1612yes—
142C2×C4×C11#13712yes—
143C2×C4×C11C22×D411yescharacteristic
144C2×C4×C11C22×D411yescharacteristic
145C2×C4×C11C2×#4111yescharacteristic
146C8×C11—21no—
147C8×C11—21no—
148C8×C11—42no—
149C8×C11—44no—
150C8×C11C2×Q1612yes—
151C8×C11C2×Q1612yes—
152#533C22×C1112yes—
153#533C22×C1111yescharacteristic
154#500C22×C1111yescharacteristic
155#500C22×C1111yescharacteristic
156#499—21no—
157#499—21no—
158#498C22×C1112yes—
159#477—22no—
160#477C22×C1114yes—
161#467—24no—
162#462—22no—
163#462C22×C1114yes—
164#446—21no—
165#446C22×C1112yes—
166C8×Q8—21no—
167C8×Q8C22×C1112yes—
168#427—21no—
169#427—21no—
170#424—21no—
171#423C22×C1111yescharacteristic
172C2×C4⋊C8C22×C1112yes—
173#405—21no—
174C2×C4×C8C22×C1111yescharacteristic
175#334C22×C1112yes—
176#334C22×C1112yes—
177#333C22×C1114yes—
178#332C22×C1114yes—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11#46212yes—
182C22×C11C2×#12111yescharacteristic
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—42no—
187C4×C11—42no—
188C4×C11—82no—
189C4×C11—82no—
190C4×C11#46212yes—
191C4×C11C22×Q1611yescharacteristic
192C4×C11C2×#13711yescharacteristic
193C4×C11#57712yes—
194C2×Q16—24no—
195C2×M16—21no—
196C22×C8—22no—
197C22×C8D4×C1111yescharacteristic
198C22×C8D4×C1111yescharacteristic
199C4⋊Q8D4×C1111yescharacteristic
200C4⋊Q8D4×C1111yescharacteristic
201C4⋊Q8C23×C1112yes—
202C4⋊Q8C23×C1112yes—
203#125—22no—
204#125—21no—
205C22⋊Q8—21no—
206C22⋊Q8—22no—
207C22⋊Q8—22no—
208C22⋊Q8D4×C1112yes—
209C4×Q8—21no—
210C4×Q8—22no—
211C4×Q8—22no—
212C4×Q8C23×C1112yes—
213#117—21no—
214#117—22no—
215C2×C42C23×C1111yescharacteristic
216#107—21no—
217#107—21no—
218#107—21no—
219#107—21no—
220#107—24no—
221#106—22no—
222#106—22no—
223C4⋊C8—22no—
224C4⋊C8—22no—
225C4⋊C8—22no—
226C4⋊C8—21no—
227C4⋊C8C23×C1112yes—
228C4⋊C8C23×C1114yes—
229#103—24no—
230#103—24no—
231#97—22no—
232C4×C8—22no—
233C4×C8D4×C1111yescharacteristic
234C4×C8D4×C1111yescharacteristic
235C4×C8C23×C1111yescharacteristic
236C4×C8C23×C1111yescharacteristic
237C2×C11—22no—
238C2×C11C2×#46211yescharacteristic
239C2×C11#306011yescharacteristic
240C2×C11#306711yescharacteristic
241C2×Q8—21no—
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8C2×D4×C1112yes—
245C22×C4C2×D4×C1111yescharacteristic
246C22×C4C2×D4×C1111yescharacteristic
247C22×C4C11×#4111yescharacteristic
248Q16—84no—
249M16—42no—
250C2×C8—22no—
251C2×C8—22no—
252C2×C8—24no—
253C2×C8—82no—
254C2×C8C11×Q1614yescomplemented
255C2×C8C2×D4×C1111yescharacteristic
256C2×C8C2×D4×C1111yescharacteristic
257C2×C8C2×D4×C1111yescharacteristic
258C2×C8C2×D4×C1111yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4C2×D4×C1112yes—
271C22⋊C4—22no—
272C22⋊C4—42no—
273C42—22no—
274C42—42no—
275C42C2×D4×C1111yescharacteristic
276C42C2×D4×C1111yescharacteristic
277C42C11×#4111yescharacteristic
278C42C24×C1111yescharacteristic
279C11#1921011yescharacteristic, direct product factor, Sylow
280C23C11×#12111yescharacteristic
281Q8—24no—
282Q8—42no—
283Q8—42no—
284Q8—42no—
285Q8—82no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4C11×#12111yescharacteristic
293C2×C4C11×#12111yescharacteristic
294C2×C4C11×#12111yescharacteristic
295C2×C4C2×C11×Q1612yes—
296C2×C4C11×#13712yes—
297C2×C4C22×D4×C1111yescharacteristic
298C2×C4C22×D4×C1111yescharacteristic
299C2×C4C2×C11×#4111yescharacteristic
300C8—21no—
301C8—21no—
302C8—42no—
303C8—44no—
304C8C2×C11×Q1612yes—
305C8C2×C11×Q1612yes—
306C22—21no—
307C22—21no—
308C22C11×#46212yes—
309C22C2×C11×#12111yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—42no—
314C4—42no—
315C4—82no—
316C4—82no—
317C4C11×#46212yes—
318C4C22×C11×Q1611yescharacteristic
319C4C2×C11×#13711yescharacteristic
320C4C11×#57712yes—
321C2—22no—
322C2C2×C11×#46211yescharacteristic
323C2C11×#306011yescharacteristic
324C2C11×#306711yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC23×C11#121
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1696C2semidirect
5. C11×#1694C2semidirect
6. C11×#1672C2semidirect
79. #19210C11direct (N × H)
93. C2×C8×C11Q16semidirect
121. #1696C2×C11semidirect
122. #1694C2×C11semidirect
123. #1672C2×C11semidirect
254. C2×C8C11×Q16semidirect
279. C11#19210direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32492
C11×#31602
C11×#29602
C11×#16962
C11×#16942
C11×#16722
C2×C11×#3342
C11×#15502
#1921011