Finite Group Databasebeta

← C11×#18295 #14595488

Subgroups — C11×#18295 #14595488

Order 2816.

940 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#544C211yesmaximal, characteristic
2C11×#3189C212yesmaximal
3C11×#2627C211yesmaximal, characteristic
4C11×#1617C214yesmaximal, complemented
5C11×#1605C214yesmaximal, complemented
6C11×#1520C212yesmaximal
7C2×C11×#324C211yesmaximal, characteristic
8C11×#544—24no—
9C11×#544—22no—
10C11×#544C2214yes—
11C2×C11×C4⋊Q8—22no—
12C2×C11×#125—22no—
13C2×C11×C22⋊Q8—21no—
14C2×C11×C22⋊Q8C2212yes—
15C2×C11×C22⋊Q8C2211yescharacteristic
16C2×C11×#117—21no—
17C22×C11×C4⋊C4C2211yescharacteristic
18C11×#484—22no—
19C11×#484C2214yes—
20C11×#467—24no—
21C11×#451—22no—
22C11×#451C2214yes—
23C2×C11×C22⋊C8C2212yes—
24C11×#400C2212yes—
25C11×#398—22no—
26C11×#395C2212yes—
27C11×#385—21no—
28C11×#381—21no—
29C11×#380C2211yescharacteristic
30C11×#328C2218yes—
31C11×#324C2214yes—
32C22×Q8×C11—21no—
33C22×Q8×C11D412yes—
34C22×Q8×C11C2311yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11D411yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C2×C11×Q16—24no—
39C22×C8×C11—22no—
40C11×C4⋊Q8—28no—
41C11×C4⋊Q8—28no—
42C11×#125—28no—
43C11×#125—28no—
44C11×C22⋊Q8—24no—
45C11×C22⋊Q8—24no—
46C11×C22⋊Q8—22no—
47C11×C22⋊Q8—22no—
48C11×C22⋊Q8—22no—
49C11×C22⋊Q8—22no—
50C11×C22⋊Q8D414yes—
51C11×C22⋊Q8C2314yes—
52C11×#117—24no—
53C11×#117—24no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4D412yes—
65C2×C11×C4⋊C4D412yes—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C42×C11—22no—
72C11×#107—24no—
73C11×#103—24no—
74C11×#103—24no—
75C11×C22⋊C8—22no—
76C11×C22⋊C8C2314yes—
77C11×#95—22no—
78C11×#95—22no—
79C11×#95—22no—
80C11×#95C2312yes—
81#18295C1111yesmaximal, characteristic, direct product factor, Sylow
82C24×C11C2×D411yescharacteristic
83C2×Q8×C11—24no—
84C2×Q8×C11—22no—
85C2×Q8×C11—22no—
86C2×Q8×C11—81no—
87C2×Q8×C11—82no—
88C2×Q8×C11—82no—
89C2×Q8×C11C2×D414yes—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—21no—
100C22×C4×C11—81no—
101C22×C4×C11—81no—
102C22×C4×C11Q1614yescomplemented
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2411yescharacteristic
109C11×Q16—84no—
110C2×C8×C11—24no—
111C2×C8×C11—82no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—24no—
114C11×C4⋊C4—24no—
115C11×C4⋊C4—28no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—24no—
120C11×C4⋊C4—24no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—42no—
123C11×C4⋊C4—81no—
124C11×C4⋊C4—82no—
125C11×C4⋊C4C2×D414yes—
126C11×C22⋊C4—24no—
127C11×C22⋊C4—24no—
128C11×C22⋊C4—41no—
129C11×C22⋊C4—41no—
130C11×C22⋊C4—42no—
131C42×C11—28no—
132C2×#544C2×C1111yescharacteristic
133#3189C2×C1112yes—
134#2627C2×C1111yescharacteristic
135#1617C2×C1114yescomplemented
136#1605C2×C1114yescomplemented
137#1520C2×C1112yes—
138C2×#324C2×C1111yescharacteristic
139C23×C11—41no—
140C23×C11—41no—
141C23×C11#12011yescharacteristic
142C23×C11#12011yescharacteristic
143C23×C11C2×Q1612yes—
144C23×C11#13712yes—
145C23×C11C22×D411yescharacteristic
146Q8×C11—44no—
147Q8×C11—44no—
148Q8×C11—82no—
149Q8×C11—84no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—24no—
153C2×C4×C11—24no—
154C2×C4×C11—24no—
155C2×C4×C11—24no—
156C2×C4×C11—22no—
157C2×C4×C11—41no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11—41no—
161C2×C4×C11—44no—
162C2×C4×C11—42no—
163C2×C4×C11—44no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11—42no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11—81no—
173C2×C4×C11#12012yes—
174C2×C4×C11C2×Q1614yes—
175C2×C4×C11C22×D412yes—
176C8×C11—44no—
177#544—24no—
178#544—22no—
179#544C22×C1114yes—
180C2×C4⋊Q8—22no—
181C2×#125—22no—
182C2×C22⋊Q8—21no—
183C2×C22⋊Q8C22×C1112yes—
184C2×C22⋊Q8C22×C1111yescharacteristic
185C2×#117—21no—
186C22×C4⋊C4C22×C1111yescharacteristic
187#484—22no—
188#484C22×C1114yes—
189#467—24no—
190#451—22no—
191#451C22×C1114yes—
192C2×C22⋊C8C22×C1112yes—
193#400C22×C1112yes—
194#398—22no—
195#395C22×C1112yes—
196#385—21no—
197#381—21no—
198#380C22×C1111yescharacteristic
199#328C22×C1118yes—
200#324C22×C1114yes—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—42no—
208C22×C11—42no—
209C22×C11#45112yes—
210C22×C11#45112yes—
211C22×C11C2×#12011yescharacteristic
212C22×C11C22×Q1611yescharacteristic
213C22×C11C2×#13711yescharacteristic
214C4×C11—24no—
215C4×C11—22no—
216C4×C11—22no—
217C4×C11—44no—
218C4×C11—42no—
219C4×C11—44no—
220C4×C11—82no—
221C4×C11—81no—
222C4×C11—81no—
223C22×Q8—21no—
224C22×Q8D4×C1112yes—
225C22×Q8C23×C1111yescharacteristic
226C23×C4D4×C1111yescharacteristic
227C23×C4D4×C1111yescharacteristic
228C23×C4C23×C1111yescharacteristic
229C2×Q16—24no—
230C22×C8—22no—
231C4⋊Q8—28no—
232C4⋊Q8—28no—
233#125—28no—
234#125—28no—
235C22⋊Q8—24no—
236C22⋊Q8—24no—
237C22⋊Q8—22no—
238C22⋊Q8—22no—
239C22⋊Q8—22no—
240C22⋊Q8—22no—
241C22⋊Q8D4×C1114yes—
242C22⋊Q8C23×C1114yes—
243#117—24no—
244#117—24no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4D4×C1112yes—
256C2×C4⋊C4D4×C1112yes—
257C2×C4⋊C4C23×C1111yescharacteristic
258C2×C4⋊C4C23×C1112yes—
259C2×C22⋊C4—22no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C42—22no—
263#107—24no—
264#103—24no—
265#103—24no—
266C22⋊C8—22no—
267C22⋊C8C23×C1114yes—
268#95—22no—
269#95—22no—
270#95—22no—
271#95C23×C1112yes—
272C2×C11—21no—
273C2×C11—21no—
274C2×C11—22no—
275C2×C11—22no—
276C2×C11C2×#45111yescharacteristic
277C2×C11#302011yescharacteristic
278C2×C11#302611yescharacteristic
279C24C2×D4×C1111yescharacteristic
280C2×Q8—24no—
281C2×Q8—22no—
282C2×Q8—22no—
283C2×Q8—81no—
284C2×Q8—82no—
285C2×Q8—82no—
286C2×Q8C2×D4×C1114yes—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—22no—
296C22×C4—21no—
297C22×C4—81no—
298C22×C4—81no—
299C22×C4C11×Q1614yescomplemented
300C22×C4C2×D4×C1112yes—
301C22×C4C2×D4×C1112yes—
302C22×C4C2×D4×C1111yescharacteristic
303C22×C4C2×D4×C1112yes—
304C22×C4C2×D4×C1112yes—
305C22×C4C24×C1111yescharacteristic
306Q16—84no—
307C2×C8—24no—
308C2×C8—82no—
309C4⋊C4—24no—
310C4⋊C4—24no—
311C4⋊C4—24no—
312C4⋊C4—28no—
313C4⋊C4—24no—
314C4⋊C4—24no—
315C4⋊C4—22no—
316C4⋊C4—24no—
317C4⋊C4—24no—
318C4⋊C4—22no—
319C4⋊C4—42no—
320C4⋊C4—81no—
321C4⋊C4—82no—
322C4⋊C4C2×D4×C1114yes—
323C22⋊C4—24no—
324C22⋊C4—24no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—42no—
328C42—28no—
329C11#1829511yescharacteristic, direct product factor, Sylow
330C23—41no—
331C23—41no—
332C23C11×#12011yescharacteristic
333C23C11×#12011yescharacteristic
334C23C2×C11×Q1612yes—
335C23C11×#13712yes—
336C23C22×D4×C1111yescharacteristic
337Q8—44no—
338Q8—44no—
339Q8—82no—
340Q8—84no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—24no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—44no—
353C2×C4—42no—
354C2×C4—44no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—81no—
364C2×C4C11×#12012yes—
365C2×C4C2×C11×Q1614yes—
366C2×C4C22×D4×C1112yes—
367C8—44no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—42no—
375C22—42no—
376C22C11×#45112yes—
377C22C11×#45112yes—
378C22C2×C11×#12011yescharacteristic
379C22C22×C11×Q1611yescharacteristic
380C22C2×C11×#13711yescharacteristic
381C4—24no—
382C4—22no—
383C4—22no—
384C4—44no—
385C4—42no—
386C4—44no—
387C4—82no—
388C4—81no—
389C4—81no—
390C2—21no—
391C2—21no—
392C2—22no—
393C2—22no—
394C2C2×C11×#45111yescharacteristic
395C2C11×#302011yescharacteristic
396C2C11×#302611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#1617C2semidirect
5. C11×#1605C2semidirect
81. #18295C11direct (N × H)
102. C22×C4×C11Q16semidirect
135. #1617C2×C11semidirect
136. #1605C2×C11semidirect
299. C22×C4C11×Q16semidirect
329. C11#18295direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5442
C11×#31892
C11×#26272
C11×#16172
C11×#16052
C11×#15202
C2×C11×#3242
#1829511