Finite Group Databasebeta

← C11×#32701 #14609894

Subgroups — C11×#32701 #14609894

Order 2816.

628 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2104C212yesmaximal, complemented
2C11×#2032C212yesmaximal, complemented
3C11×#2030C211yesmaximal, characteristic, complemented
4C11×#2022C211yesmaximal, characteristic
5C11×#1913C212yesmaximal
6C11×#1899C212yesmaximal, complemented
7C11×#1890C212yesmaximal, complemented
8C11×#1828C212yesmaximal, complemented
9C11×#1820C211yesmaximal, characteristic, complemented
10C11×#543C2211yescharacteristic
11C11×#534C2211yescharacteristic
12C2×C11×#123C2212yes—
13C11×#518C2212yes—
14C2×C11×#117C2211yescharacteristic
15C2×C11×#99C2212yes—
16C2×C11×#99C2212yes—
17C2×C11×#99C2212yes—
18C2×C11×#99C2212yes—
19C11×#381C2211yescharacteristic
20C11×#381C2212yes—
21C11×#381C2211yescharacteristic
22C11×#342C2212yes—
23C11×#342C2212yes—
24C11×#342C2212yes—
25C11×#342C2212yes—
26C11×#342C2212yes—
27C11×#342C2212yes—
28C11×#342C2211yescharacteristic
29C11×#342C2211yescharacteristic
30C11×#342C2212yes—
31C22×D4×C11C2312yes—
32C23×C4×C11C2311yescharacteristic
33C11×#123—22no—
34C11×#123—22no—
35C11×#123—22no—
36C11×#123—42no—
37C11×C22⋊Q8—41no—
38C11×C22⋊Q8—42no—
39C11×#121—41no—
40C11×#120—22no—
41C4×D4×C11—42no—
42C4×D4×C11—42no—
43C11×#117—22no—
44C11×#117—41no—
45C11×#117—41no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C22⋊C4—22no—
49C2×C11×C22⋊C4—22no—
50C2×C11×C22⋊C4C2311yescharacteristic
51C2×C11×C22⋊C4C2312yes—
52C2×C11×C22⋊C4C2312yes—
53C2×C11×C22⋊C4C2312yes—
54C2×C11×C22⋊C4C2312yes—
55C2×C11×C22⋊C4C2312yes—
56C2×C11×C22⋊C4C2311yescharacteristic
57C2×C42×C11—21no—
58C11×#99—42no—
59C11×#99—42no—
60C11×#99—42no—
61C11×#99—42no—
62C11×#95—41no—
63C11×#95—41no—
64C11×#95—42no—
65#32701C1111yesmaximal, characteristic, direct product factor, Sylow
66C24×C11#4112yes—
67C24×C11C2411yescharacteristic
68C2×Q8×C11—41no—
69C2×D4×C11—22no—
70C2×D4×C11—22no—
71C2×D4×C11—22no—
72C2×D4×C11—22no—
73C2×D4×C11—22no—
74C2×D4×C11—22no—
75C2×D4×C11—41no—
76C22×C4×C11—22no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—22no—
87C22×C4×C11—42no—
88C22×C4×C11#4111yescharacteristic
89C22×C4×C11#4112yes—
90C22×C4×C11#4111yescharacteristic
91C11×C4⋊C4—42no—
92C11×C4⋊C4—42no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—42no—
95C11×C4⋊C4—42no—
96C11×C4⋊C4—43no—
97C11×C22⋊C4—22no—
98C11×C22⋊C4—22no—
99C11×C22⋊C4—22no—
100C11×C22⋊C4—22no—
101C11×C22⋊C4—22no—
102C11×C22⋊C4—22no—
103C11×C22⋊C4—22no—
104C11×C22⋊C4—22no—
105C11×C22⋊C4—22no—
106C11×C22⋊C4—22no—
107C11×C22⋊C4—22no—
108C11×C22⋊C4—22no—
109C11×C22⋊C4—42no—
110C11×C22⋊C4—42no—
111C11×C22⋊C4—42no—
112C11×C22⋊C4—42no—
113C42×C11—42no—
114C42×C11—42no—
115#2104C2×C1112yescomplemented
116#2032C2×C1112yescomplemented
117#2030C2×C1111yescharacteristic, complemented
118#2022C2×C1111yescharacteristic
119#1913C2×C1112yes—
120#1899C2×C1112yescomplemented
121#1890C2×C1112yescomplemented
122#1828C2×C1112yescomplemented
123#1820C2×C1111yescharacteristic, complemented
124C23×C11—22no—
125C23×C11—22no—
126C23×C11—22no—
127C23×C11—81no—
128C23×C11—82no—
129C23×C11C2×#4112yes—
130C23×C11C2×#4111yescharacteristic
131C23×C11H(5,𝔽2)11yescharacteristic
132C23×C11H(5,𝔽2)11yescharacteristic
133C23×C11H(5,𝔽2)12yes—
134Q8×C11—161no—
135D4×C11—42no—
136D4×C11—42no—
137D4×C11—42no—
138D4×C11—42no—
139D4×C11—161no—
140C2×C4×C11—21no—
141C2×C4×C11—22no—
142C2×C4×C11—21no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—42no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—41no—
155C2×C4×C11—42no—
156C2×C4×C11—41no—
157C2×C4×C11—82no—
158C2×C4×C11—82no—
159C2×C4×C11—82no—
160C2×C4×C11—82no—
161C2×C4×C11—81no—
162C2×C4×C11—82no—
163C2×C4×C11—81no—
164C2×C4×C11—162no—
165#543C22×C1111yescharacteristic
166#534C22×C1111yescharacteristic
167C2×#123C22×C1112yes—
168#518C22×C1112yes—
169C2×#117C22×C1111yescharacteristic
170C2×#99C22×C1112yes—
171C2×#99C22×C1112yes—
172C2×#99C22×C1112yes—
173C2×#99C22×C1112yes—
174#381C22×C1111yescharacteristic
175#381C22×C1111yescharacteristic
176#381C22×C1112yes—
177#342C22×C1112yes—
178#342C22×C1112yes—
179#342C22×C1111yescharacteristic
180#342C22×C1112yes—
181#342C22×C1112yes—
182#342C22×C1111yescharacteristic
183#342C22×C1112yes—
184#342C22×C1112yes—
185#342C22×C1112yes—
186C22×C11—41no—
187C22×C11—42no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—42no—
191C22×C11—42no—
192C22×C11—82no—
193C22×C11—82no—
194C22×C11—82no—
195C22×C11#53811yescharacteristic
196C22×C11#53812yes—
197C22×C11#55112yes—
198C22×C11#55111yescharacteristic
199C22×C11#56011yescharacteristic
200C4×C11—41no—
201C4×C11—41no—
202C4×C11—42no—
203C4×C11—82no—
204C4×C11—82no—
205C4×C11—82no—
206C4×C11—82no—
207C4×C11—81no—
208C4×C11—82no—
209C4×C11—81no—
210C22×D4C23×C1112yes—
211C23×C4C23×C1111yescharacteristic
212#123—22no—
213#123—22no—
214#123—22no—
215#123—42no—
216C22⋊Q8—41no—
217C22⋊Q8—42no—
218#121—41no—
219#120—22no—
220C4×D4—42no—
221C4×D4—42no—
222#117—22no—
223#117—41no—
224#117—41no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—22no—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4C23×C1112yes—
230C2×C22⋊C4C23×C1112yes—
231C2×C22⋊C4C23×C1112yes—
232C2×C22⋊C4C23×C1112yes—
233C2×C22⋊C4C23×C1111yescharacteristic
234C2×C22⋊C4C23×C1111yescharacteristic
235C2×C22⋊C4C23×C1112yes—
236C2×C42—21no—
237#99—42no—
238#99—42no—
239#99—42no—
240#99—42no—
241#95—41no—
242#95—41no—
243#95—42no—
244C2×C11—21no—
245C2×C11—22no—
246C2×C11—21no—
247C2×C11—21no—
248C2×C11—22no—
249C2×C11—82no—
250C2×C11#276011yescharacteristic
251C24C11×#4112yes—
252C24C24×C1111yescharacteristic
253C2×Q8—41no—
254C2×D4—22no—
255C2×D4—22no—
256C2×D4—22no—
257C2×D4—22no—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—41no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—42no—
273C22×C4C11×#4111yescharacteristic
274C22×C4C11×#4112yes—
275C22×C4C11×#4111yescharacteristic
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—41no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—43no—
282C22⋊C4—22no—
283C22⋊C4—22no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—22no—
289C22⋊C4—22no—
290C22⋊C4—22no—
291C22⋊C4—22no—
292C22⋊C4—22no—
293C22⋊C4—22no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—42no—
298C42—42no—
299C42—42no—
300C11#3270111yescharacteristic, direct product factor, Sylow
301C23—22no—
302C23—22no—
303C23—22no—
304C23—81no—
305C23—82no—
306C23C2×C11×#4112yes—
307C23C2×C11×#4111yescharacteristic
308C23C11×H(5,𝔽2)11yescharacteristic
309C23C11×H(5,𝔽2)11yescharacteristic
310C23C11×H(5,𝔽2)12yes—
311Q8—161no—
312D4—42no—
313D4—42no—
314D4—42no—
315D4—42no—
316D4—161no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—42no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—81no—
337C2×C4—82no—
338C2×C4—81no—
339C2×C4—82no—
340C2×C4—82no—
341C2×C4—162no—
342C22—41no—
343C22—42no—
344C22—41no—
345C22—41no—
346C22—42no—
347C22—42no—
348C22—82no—
349C22—82no—
350C22—82no—
351C22C11×#53811yescharacteristic
352C22C11×#53812yes—
353C22C11×#55112yes—
354C22C11×#55111yescharacteristic
355C22C11×#56011yescharacteristic
356C4—41no—
357C4—41no—
358C4—42no—
359C4—82no—
360C4—82no—
361C4—81no—
362C4—82no—
363C4—81no—
364C4—82no—
365C4—82no—
366C2—21no—
367C2—22no—
368C2—21no—
369C2—21no—
370C2—22no—
371C2—82no—
372C2C11×#276011yescharacteristic
subgroupG/H
center, socleC2×C11#2760
commutator, Frattini, cosocleC24C24×C11
prime radicalC11×#534C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2104C2semidirect
2. C11×#2032C2semidirect
3. C11×#2030C2semidirect
6. C11×#1899C2semidirect
7. C11×#1890C2semidirect
8. C11×#1828C2semidirect
9. C11×#1820C2semidirect
65. #32701C11direct (N × H)
115. #2104C2×C11semidirect
116. #2032C2×C11semidirect
117. #2030C2×C11semidirect
120. #1899C2×C11semidirect
121. #1890C2×C11semidirect
122. #1828C2×C11semidirect
123. #1820C2×C11semidirect
300. C11#32701direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#21042
C11×#20322
C11×#20302
C11×#20222
C11×#19132
C11×#18992
C11×#18902
C11×#18282
C11×#18202
#3270111