Finite Group Databasebeta

← C11×#9561 #14586754

Subgroups — C11×#9561 #14586754

Order 2816.

398 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#1988C211yesmaximal, characteristic
2C11×#1956C211yesmaximal, characteristic
3C11×#1947C211yesmaximal, characteristic
4C8×C11×C4⋊C4C211yesmaximal, characteristic
5C2×C11×#332C211yesmaximal, characteristic
6C11×#1296C211yesmaximal, characteristic
7C11×#1277C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#107—21no—
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C11×#103—21no—
14C2×C11×#103—21no—
15C2×C4×C8×C11—21no—
16C2×C4×C8×C11C2211yescharacteristic
17C11×#384C2211yescharacteristic
18C4×C11×C4⋊C4C2211yescharacteristic
19C11×#340—21no—
20C11×#340—21no—
21C11×#340—21no—
22C11×#336—21no—
23C11×#332C414yescomplemented
24C22×Q8×C11—21no—
25C22×C8×C11—21no—
26C22×C8×C11—21no—
27C22×C8×C11—21no—
28C22×C8×C11D411yescharacteristic
29C22×C8×C11D411yescharacteristic
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8C2×C412yes—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C42×C11—21no—
42C2×C42×C11C2311yescharacteristic
43C11×#107—42no—
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8C2×C412yes—
49C11×C4⋊C8C2×C412yes—
50C11×#103—42no—
51C11×#103—42no—
52C4×C8×C11—21no—
53C4×C8×C11—21no—
54C4×C8×C11—42no—
55C11×#95—21no—
56#9561C1111yesmaximal, characteristic, direct product factor, Sylow
57C2×Q8×C11—22no—
58C2×Q8×C11—41no—
59C2×Q8×C11—41no—
60C2×Q8×C11—41no—
61C2×Q8×C11—41no—
62C2×Q8×C11—41no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—41no—
66C22×C4×C11—41no—
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11#4111yescharacteristic
70C2×C8×C11—22no—
71C2×C8×C11—22no—
72C2×C8×C11—21no—
73C2×C8×C11—21no—
74C2×C8×C11—21no—
75C2×C8×C11—21no—
76C2×C8×C11—21no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C2×C8×C11—41no—
83C2×C8×C11—41no—
84C2×C8×C11D812yes—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—22no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—81no—
96C11×C4⋊C4SD1612yes—
97C11×C4⋊C4Q1612yes—
98C42×C11—41no—
99C42×C11—41no—
100C42×C11C22×C411yescharacteristic
101C42×C11#4111yescharacteristic
102C42×C11#4111yescharacteristic
103C42×C11#4111yescharacteristic
104#1988C2×C1111yescharacteristic
105#1956C2×C1111yescharacteristic
106#1947C2×C1111yescharacteristic
107C8×C4⋊C4C2×C1111yescharacteristic
108C2×#332C2×C1111yescharacteristic
109#1296C2×C1111yescharacteristic
110#1277C2×C1111yescharacteristic
111C23×C11#12111yescharacteristic
112Q8×C11—42no—
113Q8×C11—42no—
114Q8×C11—81no—
115Q8×C11—81no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—42no—
125C2×C4×C11—81no—
126C2×C4×C11—81no—
127C2×C4×C11—81no—
128C2×C4×C11—81no—
129C2×C4×C11—81no—
130C2×C4×C11#11711yescharacteristic
131C2×C4×C11C4×D411yescharacteristic
132C2×C4×C11C4×D411yescharacteristic
133C2×C4×C11#12311yescharacteristic
134C2×C4×C11#12411yescharacteristic
135C2×C4×C11#12611yescharacteristic
136C2×C4×C11C2×D811yescharacteristic
137C2×C4×C11C2×SD1611yescharacteristic
138C2×C4×C11C2×Q1611yescharacteristic
139C2×C4×C11#13511yescharacteristic
140C2×C4×C11#13511yescharacteristic
141C2×C4×C11#13511yescharacteristic
142C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C11#13711yescharacteristic
144C8×C11—22no—
145C8×C11—42no—
146C8×C11—42no—
147C8×C11—41no—
148C8×C11—81no—
149C2×C4⋊Q8C22×C1111yescharacteristic
150C2×#107—21no—
151C2×C4⋊C8C22×C1111yescharacteristic
152C2×C4⋊C8C22×C1111yescharacteristic
153C2×C4⋊C8C22×C1111yescharacteristic
154C2×#103—21no—
155C2×#103—21no—
156C2×C4×C8—21no—
157C2×C4×C8C22×C1111yescharacteristic
158#384C22×C1111yescharacteristic
159C4×C4⋊C4C22×C1111yescharacteristic
160#340—21no—
161#340—21no—
162#340—21no—
163#336—21no—
164#332C4×C1114yescomplemented
165C22×C11#38811yescharacteristic
166C22×C11#45911yescharacteristic
167C22×C11#46411yescharacteristic
168C22×C11#46511yescharacteristic
169C22×C11#46711yescharacteristic
170C22×C11#47111yescharacteristic
171C22×C11#47311yescharacteristic
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—42no—
175C4×C11—42no—
176C4×C11—82no—
177C4×C11—161no—
178C4×C11C4×D811yescharacteristic
179C4×C11C4×SD1611yescharacteristic
180C4×C11C4×Q1611yescharacteristic
181C4×C11#44011yescharacteristic
182C4×C11#48011yescharacteristic
183C4×C11#48211yescharacteristic
184C4×C11#48711yescharacteristic
185C4×C11#48811yescharacteristic
186C22×Q8—21no—
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—21no—
190C22×C8D4×C1111yescharacteristic
191C22×C8D4×C1111yescharacteristic
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8C2×C4×C1112yes—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4D4×C1111yescharacteristic
202C2×C4⋊C4D4×C1111yescharacteristic
203C2×C42—21no—
204C2×C42C23×C1111yescharacteristic
205#107—42no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8C2×C4×C1112yes—
211C4⋊C8C2×C4×C1112yes—
212#103—42no—
213#103—42no—
214C4×C8—21no—
215C4×C8—21no—
216C4×C8—42no—
217#95—21no—
218C2×C11#166511yescharacteristic
219C2×C11#166911yescharacteristic
220C2×C11#168011yescharacteristic
221C2×C11#168411yescharacteristic
222C2×C11#192511yescharacteristic
223C2×C11#193011yescharacteristic
224C2×C11#193311yescharacteristic
225C2×Q8—22no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4C2×D4×C1111yescharacteristic
236C22×C4C2×D4×C1111yescharacteristic
237C22×C4C11×#4111yescharacteristic
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—22no—
241C2×C8—22no—
242C2×C8—21no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8C11×D812yes—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—81no—
264C4⋊C4C11×SD1612yes—
265C4⋊C4C11×Q1612yes—
266C42—41no—
267C42—41no—
268C42C22×C4×C1111yescharacteristic
269C42C11×#4111yescharacteristic
270C42C11×#4111yescharacteristic
271C42C11×#4111yescharacteristic
272C11#956111yescharacteristic, direct product factor, Sylow
273C23C11×#12111yescharacteristic
274Q8—42no—
275Q8—42no—
276Q8—81no—
277Q8—81no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4C11×#11711yescharacteristic
293C2×C4C4×D4×C1111yescharacteristic
294C2×C4C4×D4×C1111yescharacteristic
295C2×C4C11×#12311yescharacteristic
296C2×C4C11×#12411yescharacteristic
297C2×C4C11×#12611yescharacteristic
298C2×C4C2×C11×D811yescharacteristic
299C2×C4C2×C11×SD1611yescharacteristic
300C2×C4C2×C11×Q1611yescharacteristic
301C2×C4C11×#13511yescharacteristic
302C2×C4C11×#13511yescharacteristic
303C2×C4C11×#13511yescharacteristic
304C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
305C2×C4C11×#13711yescharacteristic
306C8—22no—
307C8—42no—
308C8—42no—
309C8—41no—
310C8—81no—
311C22C11×#38811yescharacteristic
312C22C11×#45911yescharacteristic
313C22C11×#46411yescharacteristic
314C22C11×#46511yescharacteristic
315C22C11×#46711yescharacteristic
316C22C11×#47111yescharacteristic
317C22C11×#47311yescharacteristic
318C4—21no—
319C4—21no—
320C4—42no—
321C4—42no—
322C4—82no—
323C4—161no—
324C4C4×C11×D811yescharacteristic
325C4C4×C11×SD1611yescharacteristic
326C4C4×C11×Q1611yescharacteristic
327C4C11×#44011yescharacteristic
328C4C11×#48011yescharacteristic
329C4C11×#48211yescharacteristic
330C4C11×#48711yescharacteristic
331C4C11×#48811yescharacteristic
332C2C11×#166511yescharacteristic
333C2C11×#166911yescharacteristic
334C2C11×#168011yescharacteristic
335C2C11×#168411yescharacteristic
336C2C11×#192511yescharacteristic
337C2C11×#193011yescharacteristic
338C2C11×#193311yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11#121
commutatorC42C22×C4×C11
Frattini, cosocleC2×C42C23×C11
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
23. C11×#332C4semidirect
56. #9561C11direct (N × H)
164. #332C4×C11semidirect
272. C11#9561direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#19882
C11×#19562
C11×#19472
C8×C11×C4⋊C42
C2×C11×#3322
C11×#12962
C11×#12772
#956111