Finite Group Databasebeta

← C11×#9961 #14587154

Subgroups — C11×#9961 #14587154

Order 2816.

552 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3189C211yesmaximal, characteristic
2C2×C11×#483C211yesmaximal, characteristic
3C11×#2503C211yesmaximal, characteristic
4C11×#1996C211yesmaximal, characteristic
5C11×#1823C211yesmaximal, characteristic
6C11×#1520C211yesmaximal, characteristic
7C11×#1282C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C2×C11×C22⋊Q8C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C11×#484—21no—
12C11×#484—21no—
13C11×#483—22no—
14C11×#483—22no—
15C11×#467—22no—
16C11×#451—21no—
17C11×#451—21no—
18C2×C11×#106—21no—
19C2×C11×#103—21no—
20C2×C11×C22⋊C8C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C11×#400—22no—
23C11×#391—21no—
24C11×#382—21no—
25C11×#381—22no—
26C11×#380C2211yescharacteristic
27C4×C11×C22⋊C4C2211yescharacteristic
28C11×#342—22no—
29C11×#340—22no—
30C11×#328—22no—
31C22×Q8×C11D411yescharacteristic
32C22×Q8×C11D411yescharacteristic
33C23×C4×C11—21no—
34C23×C4×C11C2311yescharacteristic
35C2×C11×Q16—22no—
36C22×C8×C11—21no—
37C22×C8×C11D412yes—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C11×C22⋊Q8—21no—
44C11×C22⋊Q8—21no—
45C11×C22⋊Q8—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4D412yes—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4—21no—
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4D412yes—
61C2×C42×C11—21no—
62C11×#107—22no—
63C11×#106—24no—
64C11×#103—24no—
65C11×#103—22no—
66C11×#103—22no—
67C11×C22⋊C8—21no—
68C11×C22⋊C8—21no—
69C11×C22⋊C8—21no—
70C11×C22⋊C8D412yes—
71C11×#95—24no—
72C11×#95—24no—
73C11×#95—21no—
74C11×#95—21no—
75#9961C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11C2×D411yescharacteristic
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—42no—
82C2×Q8×C11—42no—
83C22×C4×C11—22no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—22no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—42no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11—41no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11#4111yescharacteristic
101C11×Q16—82no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11—42no—
105C2×C8×C11—42no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—21no—
112C11×C4⋊C4—42no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C22⋊C4—22no—
120C11×C22⋊C4—22no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—42no—
126C42×C11—42no—
127#3189C2×C1111yescharacteristic
128C2×#483C2×C1111yescharacteristic
129#2503C2×C1111yescharacteristic
130#1996C2×C1111yescharacteristic
131#1823C2×C1111yescharacteristic
132#1520C2×C1111yescharacteristic
133#1282C2×C1111yescharacteristic
134C23×C11—41no—
135C23×C11—41no—
136C23×C11#12011yescharacteristic
137C23×C11#12111yescharacteristic
138C23×C11#12711yescharacteristic
139C23×C11#13512yes—
140C23×C11#13712yes—
141Q8×C11—42no—
142Q8×C11—42no—
143Q8×C11—42no—
144Q8×C11—81no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—44no—
162C2×C4×C11—82no—
163C2×C4×C11—81no—
164C2×C4×C11—81no—
165C2×C4×C11—81no—
166C2×C4×C11—81no—
167C2×C4×C11—81no—
168C2×C4×C11—81no—
169C2×C4×C11—81no—
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11#12011yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C8×C11—42no—
175C8×C11—42no—
176C2×C22⋊Q8C22×C1111yescharacteristic
177C2×C22⋊Q8C22×C1111yescharacteristic
178C22×C4⋊C4C22×C1111yescharacteristic
179#484—21no—
180#484—21no—
181#483—22no—
182#483—22no—
183#467—22no—
184#451—21no—
185#451—21no—
186C2×#106—21no—
187C2×#103—21no—
188C2×C22⋊C8C22×C1111yescharacteristic
189C2×C22⋊C8C22×C1111yescharacteristic
190#400—22no—
191#391—21no—
192#382—21no—
193#381—22no—
194#380C22×C1111yescharacteristic
195C4×C22⋊C4C22×C1111yescharacteristic
196#342—22no—
197#340—22no—
198#328—22no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—42no—
206C22×C11—42no—
207C22×C11#39211yescharacteristic
208C22×C11#45212yes—
209C22×C11#46412yes—
210C22×C11#49511yescharacteristic
211C22×C11#49711yescharacteristic
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—82no—
216C4×C11—81no—
217C4×C11—81no—
218C4×C11—82no—
219C4×C11—81no—
220C4×C11—81no—
221C4×C11—161no—
222C4×C11#45812yes—
223C22×Q8D4×C1111yescharacteristic
224C22×Q8D4×C1111yescharacteristic
225C23×C4—21no—
226C23×C4C23×C1111yescharacteristic
227C2×Q16—22no—
228C22×C8—21no—
229C22×C8D4×C1112yes—
230C22⋊Q8—21no—
231C22⋊Q8—21no—
232C22⋊Q8—21no—
233C22⋊Q8—21no—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4D4×C1112yes—
247C2×C4⋊C4D4×C1111yescharacteristic
248C2×C4⋊C4D4×C1111yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4D4×C1112yes—
253C2×C42—21no—
254#107—22no—
255#106—24no—
256#103—24no—
257#103—22no—
258#103—22no—
259C22⋊C8—21no—
260C22⋊C8—21no—
261C22⋊C8—21no—
262C22⋊C8D4×C1112yes—
263#95—24no—
264#95—24no—
265#95—21no—
266#95—21no—
267C2×C11—22no—
268C2×C11—21no—
269C2×C11—22no—
270C2×C11—21no—
271C2×C11#200911yescharacteristic
272C2×C11#201511yescharacteristic
273C2×C11#202211yescharacteristic
274C24C2×D4×C1111yescharacteristic
275C2×Q8—21no—
276C2×Q8—21no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8—42no—
280C2×Q8—42no—
281C22×C4—22no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—42no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—41no—
293C22×C4C2×D4×C1111yescharacteristic
294C22×C4C2×D4×C1111yescharacteristic
295C22×C4C2×D4×C1111yescharacteristic
296C22×C4C2×D4×C1111yescharacteristic
297C22×C4C2×D4×C1111yescharacteristic
298C22×C4C11×#4111yescharacteristic
299Q16—82no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—42no—
303C2×C8—42no—
304C4⋊C4—22no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—22no—
309C4⋊C4—21no—
310C4⋊C4—42no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C22⋊C4—22no—
318C22⋊C4—22no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—42no—
324C42—42no—
325C11#996111yescharacteristic, direct product factor, Sylow
326C23—41no—
327C23—41no—
328C23C11×#12011yescharacteristic
329C23C11×#12111yescharacteristic
330C23C11×#12711yescharacteristic
331C23C11×#13512yes—
332C23C11×#13712yes—
333Q8—42no—
334Q8—42no—
335Q8—42no—
336Q8—81no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—44no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—82no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4C11×#12011yescharacteristic
363C2×C4C11×#12011yescharacteristic
364C2×C4C11×#12111yescharacteristic
365C2×C4C11×#12111yescharacteristic
366C8—42no—
367C8—42no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—42no—
375C22—42no—
376C22C11×#39211yescharacteristic
377C22C11×#45212yes—
378C22C11×#46412yes—
379C22C11×#49511yescharacteristic
380C22C11×#49711yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—82no—
385C4—81no—
386C4—81no—
387C4—82no—
388C4—81no—
389C4—81no—
390C4—161no—
391C4C11×#45812yes—
392C2—22no—
393C2—21no—
394C2—21no—
395C2—22no—
396C2C11×#200911yescharacteristic
397C2C11×#201511yescharacteristic
398C2C11×#202211yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC23×C4C23×C11
prime radicalC24×C11C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
75. #9961C11direct (N × H)
325. C11#9961direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31892
C2×C11×#4832
C11×#25032
C11×#19962
C11×#18232
C11×#15202
C11×#12822
#996111