Finite Group Databasebeta

← C11×#9553 #14586746

Subgroups — C11×#9553 #14586746

Order 2816.

414 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#1984C211yesmaximal, characteristic
2C11×#1939C211yesmaximal, characteristic
3C4×C11×#103C211yesmaximal, characteristic
4C2×C11×Q8⋊C8C211yesmaximal, characteristic
5C2×C82×C11C211yesmaximal, characteristic
6C11×#1279C211yesmaximal, characteristic
7C11×#1277C211yesmaximal, characteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C2×C11×C4⋊C8—21no—
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×#103C411yescharacteristic
13C2×C11×#103C411yescharacteristic
14C2×C4×C8×C11C2211yescharacteristic
15C2×C4×C8×C11C2211yescharacteristic
16C2×C4×C8×C11C2211yescharacteristic
17C4×C11×C4⋊C4C2211yescharacteristic
18C11×#340C411yescharacteristic
19C11×#340C411yescharacteristic
20C11×#336—21no—
21C11×#336—21no—
22C11×#336—21no—
23C11×Q8⋊C8—22no—
24C82×C11—22no—
25C22×Q8×C11C2×C411yescharacteristic
26C22×C8×C11—21no—
27C22×C8×C11—21no—
28C22×C8×C11—21no—
29C22×C8×C11C2×C411yescharacteristic
30C22×C8×C11C2×C411yescharacteristic
31C22×C8×C11D411yescharacteristic
32C22×C8×C11D411yescharacteristic
33C4×Q8×C11—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4C2×C411yescharacteristic
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C4⋊C4C2×C411yescharacteristic
41C2×C42×C11—21no—
42C2×C42×C11—21no—
43C2×C42×C11C2311yescharacteristic
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—42no—
49C11×#103—22no—
50C11×#103C814yescomplemented
51C4×C8×C11—21no—
52C4×C8×C11—21no—
53C4×C8×C11—21no—
54C4×C8×C11—21no—
55C4×C8×C11—21no—
56C4×C8×C11D412yes—
57C11×#95—21no—
58#9553C1111yesmaximal, characteristic, direct product factor, Sylow
59C2×Q8×C11—21no—
60C2×Q8×C11—21no—
61C2×Q8×C11—21no—
62C2×Q8×C11—21no—
63C2×Q8×C11—21no—
64C2×Q8×C11C2×C812yes—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11#4111yescharacteristic
72C2×C8×C11—22no—
73C2×C8×C11—22no—
74C2×C8×C11—21no—
75C2×C8×C11—21no—
76C2×C8×C11—21no—
77C2×C8×C11—21no—
78C2×C8×C11—22no—
79C2×C8×C11—21no—
80C2×C8×C11—21no—
81C2×C8×C11—21no—
82C2×C8×C11—21no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C2×C8×C11—41no—
89C2×C8×C11C2×C812yes—
90C2×C8×C11M1612yes—
91C2×C8×C11SD1612yes—
92C2×C8×C11Q1612yes—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4C2×C812yes—
101C42×C11—41no—
102C42×C11—41no—
103C42×C11—41no—
104C42×C11—41no—
105C42×C11C2×D411yescharacteristic
106C42×C11#4111yescharacteristic
107C42×C11#4111yescharacteristic
108C42×C11#4111yescharacteristic
109#1984C2×C1111yescharacteristic
110#1939C2×C1111yescharacteristic
111C4×#103C2×C1111yescharacteristic
112C2×Q8⋊C8C2×C1111yescharacteristic
113C2×C82C2×C1111yescharacteristic
114#1279C2×C1111yescharacteristic
115#1277C2×C1111yescharacteristic
116C23×C11C4×D411yescharacteristic
117Q8×C11—22no—
118Q8×C11—22no—
119Q8×C11—41no—
120Q8×C11—41no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—22no—
124C2×C4×C11—22no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11#11711yescharacteristic
136C2×C4×C11C4×D411yescharacteristic
137C2×C4×C11#12111yescharacteristic
138C2×C4×C11#12311yescharacteristic
139C2×C4×C11#12411yescharacteristic
140C2×C4×C11#12611yescharacteristic
141C2×C4×C11C22×C811yescharacteristic
142C2×C4×C11C2×M1611yescharacteristic
143C2×C4×C11#13111yescharacteristic
144C2×C4×C11#13111yescharacteristic
145C2×C4×C11C2×SD1611yescharacteristic
146C2×C4×C11C2×Q1611yescharacteristic
147C2×C4×C11#13511yescharacteristic
148C2×C4×C11#13511yescharacteristic
149C8×C11—24no—
150C8×C11—22no—
151C8×C11—22no—
152C8×C11—22no—
153C8×C11—22no—
154C8×C11—81no—
155C8×C11—81no—
156C2×C4×Q8C22×C1111yescharacteristic
157C2×C4⋊C8—21no—
158C2×C4⋊C8C22×C1111yescharacteristic
159C2×C4⋊C8C22×C1111yescharacteristic
160C2×#103C4×C1111yescharacteristic
161C2×#103C4×C1111yescharacteristic
162C2×C4×C8C22×C1111yescharacteristic
163C2×C4×C8C22×C1111yescharacteristic
164C2×C4×C8C22×C1111yescharacteristic
165C4×C4⋊C4C22×C1111yescharacteristic
166#340C4×C1111yescharacteristic
167#340C4×C1111yescharacteristic
168#336—21no—
169#336—21no—
170#336—21no—
171Q8⋊C8—22no—
172C82—22no—
173C22×C11#38811yescharacteristic
174C22×C11C8×D411yescharacteristic
175C22×C11#43611yescharacteristic
176C22×C11C4×SD1611yescharacteristic
177C22×C11C4×Q1611yescharacteristic
178C22×C11#44311yescharacteristic
179C22×C11#44311yescharacteristic
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—42no—
183C4×C11—42no—
184C4×C11—81no—
185C4×C11—81no—
186C4×C11#43111yescharacteristic
187C4×C11#43311yescharacteristic
188C4×C11C8×D411yescharacteristic
189C4×C11#43511yescharacteristic
190C4×C11#46511yescharacteristic
191C4×C11#46711yescharacteristic
192C4×C11#48711yescharacteristic
193C4×C11#48811yescharacteristic
194C22×Q8C2×C4×C1111yescharacteristic
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—21no—
198C22×C8C2×C4×C1111yescharacteristic
199C22×C8C2×C4×C1111yescharacteristic
200C22×C8D4×C1111yescharacteristic
201C22×C8D4×C1111yescharacteristic
202C4×Q8—21no—
203C4×Q8—21no—
204C4×Q8—21no—
205C4×Q8—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4C2×C4×C1111yescharacteristic
208C2×C4⋊C4C2×C4×C1111yescharacteristic
209C2×C4⋊C4C2×C4×C1111yescharacteristic
210C2×C42—21no—
211C2×C42—21no—
212C2×C42C23×C1111yescharacteristic
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—42no—
218#103—22no—
219#103C8×C1114yescomplemented
220C4×C8—21no—
221C4×C8—21no—
222C4×C8—21no—
223C4×C8—21no—
224C4×C8—21no—
225C4×C8D4×C1112yes—
226#95—21no—
227C2×C11C8×SD1611yescharacteristic
228C2×C11C8×Q1611yescharacteristic
229C2×C11#159011yescharacteristic
230C2×C11#159111yescharacteristic
231C2×C11#192311yescharacteristic
232C2×C11#193311yescharacteristic
233C2×C11#193711yescharacteristic
234C2×Q8—21no—
235C2×Q8—21no—
236C2×Q8—21no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×Q8C2×C8×C1112yes—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4C22×C4×C1111yescharacteristic
245C22×C4C2×D4×C1111yescharacteristic
246C22×C4C11×#4111yescharacteristic
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—22no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8C2×C8×C1112yes—
265C2×C8C11×M1612yes—
266C2×C8C11×SD1612yes—
267C2×C8C11×Q1612yes—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4C2×C8×C1112yes—
276C42—41no—
277C42—41no—
278C42—41no—
279C42—41no—
280C42C2×D4×C1111yescharacteristic
281C42C11×#4111yescharacteristic
282C42C11×#4111yescharacteristic
283C42C11×#4111yescharacteristic
284C11#955311yescharacteristic, direct product factor, Sylow
285C23C4×D4×C1111yescharacteristic
286Q8—22no—
287Q8—22no—
288Q8—41no—
289Q8—41no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4C11×#11711yescharacteristic
305C2×C4C4×D4×C1111yescharacteristic
306C2×C4C11×#12111yescharacteristic
307C2×C4C11×#12311yescharacteristic
308C2×C4C11×#12411yescharacteristic
309C2×C4C11×#12611yescharacteristic
310C2×C4C22×C8×C1111yescharacteristic
311C2×C4C2×C11×M1611yescharacteristic
312C2×C4C11×#13111yescharacteristic
313C2×C4C11×#13111yescharacteristic
314C2×C4C2×C11×SD1611yescharacteristic
315C2×C4C2×C11×Q1611yescharacteristic
316C2×C4C11×#13511yescharacteristic
317C2×C4C11×#13511yescharacteristic
318C8—24no—
319C8—22no—
320C8—22no—
321C8—22no—
322C8—22no—
323C8—81no—
324C8—81no—
325C22C11×#38811yescharacteristic
326C22C8×D4×C1111yescharacteristic
327C22C11×#43611yescharacteristic
328C22C4×C11×SD1611yescharacteristic
329C22C4×C11×Q1611yescharacteristic
330C22C11×#44311yescharacteristic
331C22C11×#44311yescharacteristic
332C4—21no—
333C4—21no—
334C4—42no—
335C4—42no—
336C4—81no—
337C4—81no—
338C4C11×#43111yescharacteristic
339C4C11×#43311yescharacteristic
340C4C8×D4×C1111yescharacteristic
341C4C11×#43511yescharacteristic
342C4C11×#46511yescharacteristic
343C4C11×#46711yescharacteristic
344C4C11×#48711yescharacteristic
345C4C11×#48811yescharacteristic
346C2C8×C11×SD1611yescharacteristic
347C2C8×C11×Q1611yescharacteristic
348C2C11×#159011yescharacteristic
349C2C11×#159111yescharacteristic
350C2C11×#192311yescharacteristic
351C2C11×#193311yescharacteristic
352C2C11×#193711yescharacteristic
subgroupG/H
centerC22×C4×C11C2×D4
commutatorC2×C4C22×C8×C11
Frattini, cosocleC2×C42C23×C11
socle, prime radicalC23×C11C4×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ C2×C4×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
50. C11×#103C8semidirect
58. #9553C11direct (N × H)
219. #103C8×C11semidirect
284. C11#9553direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#19842
C11×#19392
C4×C11×#1032
C2×C11×Q8⋊C82
C2×C82×C112
C11×#12792
C11×#12772
#955311