Finite Group Databasebeta

← C11×#10061 #14587254

Subgroups — C11×#10061 #14587254

Order 2816.

534 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#487C211yesmaximal, characteristic
2C2×C11×#477C211yesmaximal, characteristic
3C11×#2568C211yesmaximal, characteristic
4C11×#1987C211yesmaximal, characteristic
5C2×C11×#332C211yesmaximal, characteristic
6C2×C11×Q8⋊C8C211yesmaximal, characteristic
7C11×#1279C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C11×#487—22no—
12C11×#487—22no—
13C11×#477—22no—
14C11×#477—22no—
15C2×C11×#107—21no—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#103—21no—
19C2×C11×#103—22no—
20C2×C4×C8×C11C2211yescharacteristic
21C11×#400—22no—
22C11×#391—21no—
23C11×#391—22no—
24C11×#382—21no—
25C4×C11×C4⋊C4C2211yescharacteristic
26C11×#340—22no—
27C11×#332—22no—
28C11×Q8⋊C8—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11—21no—
31C22×Q8×C11D411yescharacteristic
32C22×C8×C11—21no—
33C22×C8×C11—21no—
34C22×C8×C11—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8D412yes—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4D412yes—
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C11×C4⋊C4D412yes—
54C2×C42×C11—21no—
55C2×C42×C11—21no—
56C2×C42×C11C2311yescharacteristic
57C11×#107—24no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8D412yes—
62C11×#103—24no—
63C11×#103—28no—
64C4×C8×C11—21no—
65C4×C8×C11D412yes—
66C11×#95—24no—
67C11×#95—24no—
68C11×#95—21no—
69#10061C1111yesmaximal, characteristic, direct product factor, Sylow
70C2×Q8×C11—21no—
71C2×Q8×C11—21no—
72C2×Q8×C11—22no—
73C2×Q8×C11—21no—
74C2×Q8×C11—21no—
75C2×Q8×C11—21no—
76C2×Q8×C11—44no—
77C2×Q8×C11—41no—
78C2×Q8×C11—41no—
79C2×Q8×C11—41no—
80C2×Q8×C11—42no—
81C2×Q8×C11—42no—
82C2×Q8×C11Q1612yes—
83C22×C4×C11—21no—
84C22×C4×C11—22no—
85C22×C4×C11—21no—
86C22×C4×C11—22no—
87C22×C4×C11—41no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C2×C8×C11—22no—
92C2×C8×C11—22no—
93C2×C8×C11—42no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C2×C8×C11—42no—
97C2×C8×C11—41no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C42×C11—41no—
113C42×C11—41no—
114C42×C11—41no—
115C42×C11—41no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11#4111yescharacteristic
120C2×#487C2×C1111yescharacteristic
121C2×#477C2×C1111yescharacteristic
122#2568C2×C1111yescharacteristic
123#1987C2×C1111yescharacteristic
124C2×#332C2×C1111yescharacteristic
125C2×Q8⋊C8C2×C1111yescharacteristic
126#1279C2×C1111yescharacteristic
127C23×C11#12011yescharacteristic
128Q8×C11—22no—
129Q8×C11—22no—
130Q8×C11—44no—
131Q8×C11—41no—
132Q8×C11—41no—
133Q8×C11—82no—
134Q8×C11—82no—
135Q8×C11—81no—
136Q8×C11—81no—
137C2×C4×C11—22no—
138C2×C4×C11—22no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—44no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—82no—
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12711yescharacteristic
156C2×C4×C11C2×Q1611yescharacteristic
157C2×C4×C11#13511yescharacteristic
158C2×C4×C11#13512yes—
159C2×C4×C11#13711yescharacteristic
160C2×C4×C11#13711yescharacteristic
161C2×C4×C11#13712yes—
162C8×C11—42no—
163C8×C11—42no—
164C8×C11—81no—
165C2×C4⋊Q8C22×C1111yescharacteristic
166C2×C4⋊Q8C22×C1111yescharacteristic
167C2×C4×Q8C22×C1111yescharacteristic
168#487—22no—
169#487—22no—
170#477—22no—
171#477—22no—
172C2×#107—21no—
173C2×C4⋊C8C22×C1111yescharacteristic
174C2×C4⋊C8C22×C1111yescharacteristic
175C2×#103—21no—
176C2×#103—22no—
177C2×C4×C8C22×C1111yescharacteristic
178#400—22no—
179#391—21no—
180#391—22no—
181#382—21no—
182C4×C4⋊C4C22×C1111yescharacteristic
183#340—22no—
184#332—22no—
185Q8⋊C8—22no—
186C22×C11#39211yescharacteristic
187C22×C11#45111yescharacteristic
188C22×C11#45212yes—
189C22×C11#45211yescharacteristic
190C22×C11#45412yes—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—42no—
194C4×C11—82no—
195C4×C11—81no—
196C4×C11—82no—
197C4×C11—82no—
198C4×C11#45111yescharacteristic
199C4×C11#45211yescharacteristic
200C4×C11#46412yes—
201C4×C11#46711yescharacteristic
202C4×C11#47011yescharacteristic
203C4×C11#49511yescharacteristic
204C4×C11#49711yescharacteristic
205C22×Q8—21no—
206C22×Q8—21no—
207C22×Q8D4×C1111yescharacteristic
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8D4×C1112yes—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×Q8—21no—
222C4×Q8—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4D4×C1111yescharacteristic
228C2×C4⋊C4D4×C1112yes—
229C2×C4⋊C4D4×C1112yes—
230C2×C42—21no—
231C2×C42—21no—
232C2×C42C23×C1111yescharacteristic
233#107—24no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8D4×C1112yes—
238#103—24no—
239#103—28no—
240C4×C8—21no—
241C4×C8D4×C1112yes—
242#95—24no—
243#95—24no—
244#95—21no—
245C2×C11#163612yes—
246C2×C11#163812yes—
247C2×C11#200111yescharacteristic
248C2×C11#200311yescharacteristic
249C2×C11#201511yescharacteristic
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—22no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—44no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—42no—
261C2×Q8—42no—
262C2×Q8C11×Q1612yes—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—21no—
266C22×C4—22no—
267C22×C4—41no—
268C22×C4C2×D4×C1111yescharacteristic
269C22×C4C2×D4×C1111yescharacteristic
270C22×C4C2×D4×C1111yescharacteristic
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—42no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—42no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—21no—
281C4⋊C4—22no—
282C4⋊C4—21no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C42—41no—
293C42—41no—
294C42—41no—
295C42—41no—
296C42C2×D4×C1111yescharacteristic
297C42C2×D4×C1111yescharacteristic
298C42C2×D4×C1111yescharacteristic
299C42C11×#4111yescharacteristic
300C11#1006111yescharacteristic, direct product factor, Sylow
301C23C11×#12011yescharacteristic
302Q8—22no—
303Q8—22no—
304Q8—44no—
305Q8—41no—
306Q8—41no—
307Q8—82no—
308Q8—81no—
309Q8—81no—
310Q8—82no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—44no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—82no—
324C2×C4C11×#12011yescharacteristic
325C2×C4C11×#12011yescharacteristic
326C2×C4C11×#12111yescharacteristic
327C2×C4C11×#12111yescharacteristic
328C2×C4C11×#12111yescharacteristic
329C2×C4C11×#12711yescharacteristic
330C2×C4C2×C11×Q1611yescharacteristic
331C2×C4C11×#13512yes—
332C2×C4C11×#13511yescharacteristic
333C2×C4C11×#13712yes—
334C2×C4C11×#13711yescharacteristic
335C2×C4C11×#13711yescharacteristic
336C8—42no—
337C8—42no—
338C8—81no—
339C22C11×#39211yescharacteristic
340C22C11×#45111yescharacteristic
341C22C11×#45212yes—
342C22C11×#45211yescharacteristic
343C22C11×#45412yes—
344C4—21no—
345C4—21no—
346C4—42no—
347C4—82no—
348C4—81no—
349C4—82no—
350C4—82no—
351C4C11×#45111yescharacteristic
352C4C11×#45211yescharacteristic
353C4C11×#46412yes—
354C4C11×#46711yescharacteristic
355C4C11×#47011yescharacteristic
356C4C11×#49511yescharacteristic
357C4C11×#49711yescharacteristic
358C2C11×#163612yes—
359C2C11×#163812yes—
360C2C11×#200111yescharacteristic
361C2C11×#200311yescharacteristic
362C2C11×#201511yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
69. #10061C11direct (N × H)
300. C11#10061direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4872
C2×C11×#4772
C11×#25682
C11×#19872
C2×C11×#3322
C2×C11×Q8⋊C82
C11×#12792
#1006111