Finite Group Databasebeta

← C11×#18213 #14595406

Subgroups — C11×#18213 #14595406

Order 2816.

974 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3501C211yesmaximal, characteristic
2C11×#3104C212yesmaximal, complemented
3C11×#2580C211yesmaximal, characteristic
4C11×#1614C214yesmaximal, complemented
5C11×#1602C214yesmaximal, complemented
6C11×#1518C212yesmaximal, complemented
7C11×#1460C211yesmaximal, characteristic
8C11×#554—22no—
9C11×#554—24no—
10D4×Q8×C11—22no—
11C11×#544—21no—
12C11×#543C2214yes—
13C11×#533C2212yes—
14C2×C11×C22⋊Q8—22no—
15C11×#518—21no—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C11×#484C2214yes—
19C11×#477—22no—
20C11×#462—22no—
21C11×#451C2214yes—
22C4×C11×Q16—24no—
23C11×#431C2212yes—
24C11×#399C2212yes—
25C11×#393C2212yes—
26C11×#390—21no—
27C11×#389—21no—
28C11×#385—22no—
29C11×#382C2211yescharacteristic
30C11×#328C2218yes—
31C11×#323C2214yes—
32C22×Q8×C11—22no—
33C22×Q8×C11C2311yescharacteristic
34C22×D4×C11D411yescharacteristic
35C23×C4×C11D412yes—
36C2×C11×Q16—24no—
37C11×C4⋊Q8—24no—
38C11×C4⋊Q8D412yes—
39C11×C4⋊Q8D412yes—
40C11×#125—24no—
41C11×#125—22no—
42C11×C22⋊Q8—24no—
43C11×C22⋊Q8—24no—
44C11×C22⋊Q8—28no—
45C11×C22⋊Q8—22no—
46C11×C22⋊Q8—24no—
47C11×C22⋊Q8—28no—
48C11×C22⋊Q8C2314yes—
49C4×Q8×C11—22no—
50C4×Q8×C11—22no—
51C4×Q8×C11—22no—
52C4×Q8×C11D414yes—
53C4×D4×C11—24no—
54C4×D4×C11—24no—
55C4×D4×C11—22no—
56C4×D4×C11—22no—
57C11×#117—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—24no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4C2312yes—
69C2×C42×C11—21no—
70C2×C42×C11C2311yescharacteristic
71C11×#107—24no—
72C11×C4⋊C8—22no—
73C11×#103—24no—
74C11×#103—24no—
75C11×C22⋊C8C2314yes—
76C4×C8×C11—22no—
77C11×#95—21no—
78C11×#95—22no—
79C11×#95C2312yes—
80#18213C1111yesmaximal, characteristic, direct product factor, Sylow
81C24×C11C2×D412yes—
82C2×Q8×C11—24no—
83C2×Q8×C11—22no—
84C2×Q8×C11—22no—
85C2×Q8×C11—42no—
86C2×Q8×C11—84no—
87C2×Q8×C11C2×D414yes—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11Q1614yescomplemented
91C22×C4×C11—21no—
92C22×C4×C11—24no—
93C22×C4×C11—24no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—21no—
98C22×C4×C11—82no—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2411yescharacteristic
103C11×Q16—48no—
104C2×C8×C11—24no—
105C11×C4⋊C4—24no—
106C11×C4⋊C4—28no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—42no—
117C11×C4⋊C4—82no—
118C11×C4⋊C4C2×D414yes—
119C11×C22⋊C4—28no—
120C11×C22⋊C4—24no—
121C11×C22⋊C4—24no—
122C11×C22⋊C4—44no—
123C11×C22⋊C4—82no—
124C42×C11—24no—
125C42×C11—42no—
126C42×C11C2×D412yes—
127C42×C11C2×D412yes—
128#3501C2×C1111yescharacteristic
129#3104C2×C1112yescomplemented
130#2580C2×C1111yescharacteristic
131#1614C2×C1114yescomplemented
132#1602C2×C1114yescomplemented
133#1518C2×C1112yescomplemented
134#1460C2×C1111yescharacteristic
135C23×C11—22no—
136C23×C11—22no—
137C23×C11—42no—
138C23×C11—42no—
139C23×C11C2×Q1614yes—
140C23×C11C22×D411yescharacteristic
141Q8×C11—24no—
142Q8×C11—44no—
143Q8×C11—42no—
144Q8×C11—44no—
145Q8×C11—84no—
146D4×C11—28no—
147C2×C4×C11—22no—
148C2×C4×C11—24no—
149C2×C4×C11—24no—
150C2×C4×C11—22no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—44no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—82no—
164C2×C4×C11—84no—
165C2×C4×C11—84no—
166C2×C4×C11#12011yescharacteristic
167C2×C4×C11#12011yescharacteristic
168C2×C4×C11#12012yes—
169C2×C4×C11C2×Q1612yes—
170C2×C4×C11#13712yes—
171C2×C4×C11C22×D412yes—
172C8×C11—44no—
173#554—22no—
174#554—24no—
175D4×Q8—22no—
176#544—21no—
177#543C22×C1114yes—
178#533C22×C1112yes—
179C2×C22⋊Q8—22no—
180#518—21no—
181C2×C4×Q8C22×C1111yescharacteristic
182C2×C4×D4C22×C1111yescharacteristic
183#484C22×C1114yes—
184#477—22no—
185#462—22no—
186#451C22×C1114yes—
187C4×Q16—24no—
188#431C22×C1112yes—
189#399C22×C1112yes—
190#393C22×C1112yes—
191#390—21no—
192#389—21no—
193#385—22no—
194#382C22×C1111yescharacteristic
195#328C22×C1118yes—
196#323C22×C1114yes—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—24no—
200C22×C11—44no—
201C22×C11—42no—
202C22×C11—42no—
203C22×C11—82no—
204C22×C11C2×#12011yescharacteristic
205C22×C11C22×Q1611yescharacteristic
206C22×C11C2×#13711yescharacteristic
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—22no—
210C4×C11—42no—
211C4×C11—44no—
212C4×C11—42no—
213C4×C11—44no—
214C4×C11—82no—
215C4×C11—81no—
216C4×C11#45114yes—
217C22×Q8—22no—
218C22×Q8C23×C1111yescharacteristic
219C22×D4D4×C1111yescharacteristic
220C23×C4D4×C1112yes—
221C2×Q16—24no—
222C4⋊Q8—24no—
223C4⋊Q8D4×C1112yes—
224C4⋊Q8D4×C1112yes—
225#125—24no—
226#125—22no—
227C22⋊Q8—24no—
228C22⋊Q8—24no—
229C22⋊Q8—28no—
230C22⋊Q8—22no—
231C22⋊Q8—24no—
232C22⋊Q8—28no—
233C22⋊Q8C23×C1114yes—
234C4×Q8—22no—
235C4×Q8—22no—
236C4×Q8—22no—
237C4×Q8D4×C1114yes—
238C4×D4—24no—
239C4×D4—24no—
240C4×D4—22no—
241C4×D4—22no—
242#117—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—24no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4D4×C1111yescharacteristic
249C2×C4⋊C4C23×C1111yescharacteristic
250C2×C22⋊C4—24no—
251C2×C22⋊C4—22no—
252C2×C22⋊C4—22no—
253C2×C22⋊C4C23×C1112yes—
254C2×C42—21no—
255C2×C42C23×C1111yescharacteristic
256#107—24no—
257C4⋊C8—22no—
258#103—24no—
259#103—24no—
260C22⋊C8C23×C1114yes—
261C4×C8—22no—
262#95—21no—
263#95—22no—
264#95C23×C1112yes—
265C2×C11—21no—
266C2×C11—21no—
267C2×C11—44no—
268C2×C11C2×#45111yescharacteristic
269C2×C11#301911yescharacteristic
270C2×C11#302511yescharacteristic
271C24C2×D4×C1112yes—
272C2×Q8—24no—
273C2×Q8—22no—
274C2×Q8—22no—
275C2×Q8—42no—
276C2×Q8—84no—
277C2×Q8C2×D4×C1114yes—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4C11×Q1614yescomplemented
281C22×C4—21no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—21no—
288C22×C4—82no—
289C22×C4C2×D4×C1112yes—
290C22×C4C2×D4×C1111yescharacteristic
291C22×C4C2×D4×C1111yescharacteristic
292C22×C4C24×C1111yescharacteristic
293Q16—48no—
294C2×C8—24no—
295C4⋊C4—24no—
296C4⋊C4—28no—
297C4⋊C4—22no—
298C4⋊C4—24no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—24no—
303C4⋊C4—22no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—42no—
307C4⋊C4—82no—
308C4⋊C4C2×D4×C1114yes—
309C22⋊C4—28no—
310C22⋊C4—24no—
311C22⋊C4—24no—
312C22⋊C4—44no—
313C22⋊C4—82no—
314C42—24no—
315C42—42no—
316C42C2×D4×C1112yes—
317C42C2×D4×C1112yes—
318C11#1821311yescharacteristic, direct product factor, Sylow
319C23—22no—
320C23—22no—
321C23—42no—
322C23—42no—
323C23C2×C11×Q1614yes—
324C23C22×D4×C1111yescharacteristic
325Q8—24no—
326Q8—44no—
327Q8—42no—
328Q8—44no—
329Q8—84no—
330D4—28no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—44no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—82no—
348C2×C4—84no—
349C2×C4—84no—
350C2×C4C11×#12011yescharacteristic
351C2×C4C11×#12011yescharacteristic
352C2×C4C11×#12012yes—
353C2×C4C2×C11×Q1612yes—
354C2×C4C11×#13712yes—
355C2×C4C22×D4×C1112yes—
356C8—44no—
357C22—21no—
358C22—21no—
359C22—24no—
360C22—44no—
361C22—42no—
362C22—42no—
363C22—82no—
364C22C2×C11×#12011yescharacteristic
365C22C22×C11×Q1611yescharacteristic
366C22C2×C11×#13711yescharacteristic
367C4—21no—
368C4—21no—
369C4—22no—
370C4—42no—
371C4—44no—
372C4—42no—
373C4—44no—
374C4—82no—
375C4—81no—
376C4C11×#45114yes—
377C2—21no—
378C2—21no—
379C2—44no—
380C2C2×C11×#45111yescharacteristic
381C2C11×#301911yescharacteristic
382C2C11×#302511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3104C2semidirect
4. C11×#1614C2semidirect
5. C11×#1602C2semidirect
6. C11×#1518C2semidirect
80. #18213C11direct (N × H)
90. C2×D4×C11Q16semidirect
129. #3104C2×C11semidirect
131. #1614C2×C11semidirect
132. #1602C2×C11semidirect
133. #1518C2×C11semidirect
280. C2×D4C11×Q16semidirect
318. C11#18213direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35012
C11×#31042
C11×#25802
C11×#16142
C11×#16022
C11×#15182
C11×#14602
#1821311