Finite Group Databasebeta

← C11×#10578 #14587771

Subgroups — C11×#10578 #14587771

Order 2816.

390 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2571C211yesmaximal, characteristic
2C11×#1948C211yesmaximal, characteristic
3C11×#1947C211yesmaximal, characteristic
4C11×#1834C211yesmaximal, characteristic
5C11×#1296C211yesmaximal, characteristic
6C11×#1279C211yesmaximal, characteristic
7C11×#1279C211yesmaximal, characteristic
8C2×C11×#107—21no—
9C2×C11×#106—21no—
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C4×C8×C11C2211yescharacteristic
13C11×#400—22no—
14C11×#389—21no—
15C11×#389—21no—
16C11×#384C2211yescharacteristic
17C11×#384C2211yescharacteristic
18C11×#382—21no—
19C11×#382—21no—
20C4×C11×C4⋊C4C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C11×#340—21no—
23C11×#340—21no—
24C11×#340—22no—
25C22×C8×C11—21no—
26C22×C8×C11—21no—
27C22×C8×C11—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—22no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C11×C4⋊C4D412yes—
39C2×C42×C11—21no—
40C2×C42×C11—21no—
41C2×C42×C11C2311yescharacteristic
42C11×#107—42no—
43C11×#106—42no—
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8Q812yes—
47C11×C4⋊C8Q812yes—
48C4×C8×C11—21no—
49C4×C8×C11Q812yes—
50C11×#95—22no—
51C11×#95—22no—
52C11×#95—22no—
53C11×#95—21no—
54C11×#95—21no—
55#10578C1111yesmaximal, characteristic, direct product factor, Sylow
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—22no—
61C22×C4×C11—41no—
62C22×C4×C11C2×D411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C2×C8×C11—22no—
66C2×C8×C11—22no—
67C2×C8×C11—22no—
68C2×C8×C11—41no—
69C2×C8×C11—41no—
70C2×C8×C11—41no—
71C2×C8×C11—41no—
72C2×C8×C11—41no—
73C2×C8×C11—41no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4—21no—
76C11×C4⋊C4—21no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—42no—
83C11×C4⋊C4—42no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—82no—
93C42×C11—41no—
94C42×C11—41no—
95C42×C11—41no—
96C42×C11—41no—
97C42×C11C2×Q811yescharacteristic
98C42×C11C2×Q811yescharacteristic
99C42×C11C2×Q811yescharacteristic
100C42×C11#4111yescharacteristic
101#2571C2×C1111yescharacteristic
102#1948C2×C1111yescharacteristic
103#1947C2×C1111yescharacteristic
104#1834C2×C1111yescharacteristic
105#1296C2×C1111yescharacteristic
106#1279C2×C1111yescharacteristic
107#1279C2×C1111yescharacteristic
108C23×C11#12011yescharacteristic
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—42no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—42no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—42no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—81no—
127C2×C4×C11—81no—
128C2×C4×C11—81no—
129C2×C4×C11C22⋊Q811yescharacteristic
130C2×C4×C11C22⋊Q811yescharacteristic
131C2×C4×C11C22⋊Q811yescharacteristic
132C2×C4×C11C4⋊Q811yescharacteristic
133C2×C4×C11C4⋊Q811yescharacteristic
134C2×C4×C11C4⋊Q811yescharacteristic
135C2×C4×C11#13511yescharacteristic
136C2×C4×C11#13511yescharacteristic
137C2×C4×C11#13511yescharacteristic
138C2×C4×C11#13511yescharacteristic
139C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C11#13711yescharacteristic
142C2×C4×C11#13711yescharacteristic
143C8×C11—42no—
144C8×C11—42no—
145C8×C11—42no—
146C2×#107—21no—
147C2×#106—21no—
148C2×C4⋊C8C22×C1111yescharacteristic
149C2×C4⋊C8C22×C1111yescharacteristic
150C2×C4×C8C22×C1111yescharacteristic
151#400—22no—
152#389—21no—
153#389—21no—
154#384C22×C1111yescharacteristic
155#384C22×C1111yescharacteristic
156#382—21no—
157#382—21no—
158C4×C4⋊C4C22×C1111yescharacteristic
159C4×C4⋊C4C22×C1111yescharacteristic
160#340—22no—
161#340—21no—
162#340—21no—
163C22×C11#39511yescharacteristic
164C22×C11#44911yescharacteristic
165C22×C11#44911yescharacteristic
166C22×C11#45211yescharacteristic
167C22×C11#45211yescharacteristic
168C22×C11#45411yescharacteristic
169C22×C11#45511yescharacteristic
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—81no—
173C4×C11—81no—
174C4×C11—82no—
175C4×C11—81no—
176C4×C11—81no—
177C4×C11—161no—
178C4×C11#47811yescharacteristic
179C4×C11#47811yescharacteristic
180C4×C11#47911yescharacteristic
181C4×C11#47911yescharacteristic
182C4×C11#49911yescharacteristic
183C4×C11#49911yescharacteristic
184C4×C11#50111yescharacteristic
185C4×C11#50111yescharacteristic
186C22×C8—21no—
187C22×C8—21no—
188C22×C8—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4D4×C1111yescharacteristic
196C2×C4⋊C4D4×C1111yescharacteristic
197C2×C4⋊C4D4×C1111yescharacteristic
198C2×C4⋊C4D4×C1111yescharacteristic
199C2×C4⋊C4D4×C1112yes—
200C2×C42—21no—
201C2×C42—21no—
202C2×C42C23×C1111yescharacteristic
203#107—42no—
204#106—42no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8Q8×C1112yes—
208C4⋊C8Q8×C1112yes—
209C4×C8—21no—
210C4×C8Q8×C1112yes—
211#95—22no—
212#95—22no—
213#95—22no—
214#95—21no—
215#95—21no—
216C2×C11#162811yescharacteristic
217C2×C11#163811yescharacteristic
218C2×C11#164011yescharacteristic
219C2×C11#164611yescharacteristic
220C2×C11#205911yescharacteristic
221C2×C11#205911yescharacteristic
222C2×C11#206111yescharacteristic
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—22no—
228C22×C4—41no—
229C22×C4C2×D4×C1111yescharacteristic
230C22×C4C2×D4×C1111yescharacteristic
231C22×C4C2×D4×C1111yescharacteristic
232C2×C8—22no—
233C2×C8—22no—
234C2×C8—22no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—82no—
260C42—41no—
261C42—41no—
262C42—41no—
263C42—41no—
264C42C2×Q8×C1111yescharacteristic
265C42C2×Q8×C1111yescharacteristic
266C42C2×Q8×C1111yescharacteristic
267C42C11×#4111yescharacteristic
268C11#1057811yescharacteristic, direct product factor, Sylow
269C23C11×#12011yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—42no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4C11×C22⋊Q811yescharacteristic
291C2×C4C11×C22⋊Q811yescharacteristic
292C2×C4C11×C22⋊Q811yescharacteristic
293C2×C4C11×C4⋊Q811yescharacteristic
294C2×C4C11×C4⋊Q811yescharacteristic
295C2×C4C11×C4⋊Q811yescharacteristic
296C2×C4C11×#13511yescharacteristic
297C2×C4C11×#13511yescharacteristic
298C2×C4C11×#13511yescharacteristic
299C2×C4C11×#13511yescharacteristic
300C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
301C2×C4C11×AGL(1,ℤ/8)11yescharacteristic
302C2×C4C11×#13711yescharacteristic
303C2×C4C11×#13711yescharacteristic
304C8—42no—
305C8—42no—
306C8—42no—
307C22C11×#39511yescharacteristic
308C22C11×#44911yescharacteristic
309C22C11×#44911yescharacteristic
310C22C11×#45211yescharacteristic
311C22C11×#45211yescharacteristic
312C22C11×#45411yescharacteristic
313C22C11×#45511yescharacteristic
314C4—21no—
315C4—21no—
316C4—81no—
317C4—81no—
318C4—82no—
319C4—81no—
320C4—81no—
321C4—161no—
322C4C11×#47811yescharacteristic
323C4C11×#47811yescharacteristic
324C4C11×#47911yescharacteristic
325C4C11×#47911yescharacteristic
326C4C11×#49911yescharacteristic
327C4C11×#49911yescharacteristic
328C4C11×#50111yescharacteristic
329C4C11×#50111yescharacteristic
330C2C11×#162811yescharacteristic
331C2C11×#163811yescharacteristic
332C2C11×#164011yescharacteristic
333C2C11×#164611yescharacteristic
334C2C11×#205911yescharacteristic
335C2C11×#205911yescharacteristic
336C2C11×#206111yescharacteristic
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
55. #10578C11direct (N × H)
268. C11#10578direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25712
C11×#19482
C11×#19472
C11×#18342
C11×#12962
C11×#12792
#1057811