Finite Group Databasebeta

← C11×#16297 #14593490

Subgroups — C11×#16297 #14593490

Order 2816.

2894 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#393C213yesmaximal, complemented
2C2×C11×#379C213yesmaximal
3C11×#1439C216yesmaximal, complemented
4C11×#1439C213yesmaximal, complemented
5C26×C11C2211yescharacteristic
6C23×Q8×C11C2211yescharacteristic, complemented
7C22×C11×C4⋊C4C2213yescomplemented
8C22×C11×C22⋊C4C2216yes—
9C22×C11×C22⋊C4C2216yes—
10C22×C11×C22⋊C4C2213yes—
11C22×C11×C22⋊C4C2213yes—
12C11×#393—212no—
13C11×#379—212no—
14C2×C11×#95C2213yescomplemented
15C2×C11×#95C2216yescomplemented
16C2×C11×#95C2212yescomplemented
17C2×C11×#95C2211yescharacteristic, complemented
18C25×C11—26no—
19C25×C11—26no—
20C25×C11—43no—
21C25×C11—43no—
22C25×C11—41no—
23C25×C11—41no—
24C25×C11Q814yescomplemented
25C25×C11C2313yes—
26C22×Q8×C11—26no—
27C22×Q8×C11—43no—
28C22×Q8×C11—41no—
29C23×C4×C11C2316yes—
30C23×C4×C11C2313yes—
31C23×C4×C11C2313yes—
32C2×C11×C4⋊C4—43no—
33C2×C11×C4⋊C4—46no—
34C2×C11×C22⋊C4—26no—
35C2×C11×C22⋊C4—212no—
36C2×C11×C22⋊C4—212no—
37C2×C11×C22⋊C4—212no—
38C2×C11×C22⋊C4—212no—
39C2×C11×C22⋊C4—43no—
40C2×C11×C22⋊C4—43no—
41C2×C11×C22⋊C4—46no—
42C2×C11×C22⋊C4—46no—
43C2×C11×C22⋊C4—43no—
44C2×C11×C22⋊C4—43no—
45C2×C11×C22⋊C4D4112yes—
46C11×#95—212no—
47C11×#95—26no—
48C11×#95—41no—
49C11×#95—42no—
50#16297C1111yesmaximal, characteristic, direct product factor, Sylow
51C24×C11—26no—
52C24×C11—26no—
53C24×C11—23no—
54C24×C11—23no—
55C24×C11—23no—
56C24×C11—23no—
57C24×C11—26no—
58C24×C11—26no—
59C24×C11—224no—
60C24×C11—412no—
61C24×C11—44no—
62C24×C11—412no—
63C24×C11—424no—
64C24×C11—412no—
65C24×C11—412no—
66C24×C11—412no—
67C24×C11—412no—
68C24×C11—412no—
69C24×C11—412no—
70C24×C11—44no—
71C24×C11C2×D416yes—
72C24×C11C2×Q816yes—
73C24×C11#4116yes—
74C24×C11C2411yescharacteristic
75C2×Q8×C11—412no—
76C2×Q8×C11—412no—
77C2×Q8×C11—44no—
78C22×C4×C11—26no—
79C22×C4×C11—26no—
80C22×C4×C11—23no—
81C22×C4×C11—23no—
82C22×C4×C11—26no—
83C22×C4×C11—23no—
84C22×C4×C11—23no—
85C22×C4×C11—26no—
86C22×C4×C11—26no—
87C22×C4×C11—26no—
88C22×C4×C11—26no—
89C22×C4×C11—26no—
90C22×C4×C11—26no—
91C22×C4×C11—26no—
92C22×C4×C11—26no—
93C22×C4×C11C2×D416yes—
94C22×C4×C11C2×D416yes—
95C11×C4⋊C4—412no—
96C11×C22⋊C4—412no—
97C11×C22⋊C4—424no—
98C11×C22⋊C4—424no—
99C11×C22⋊C4—412no—
100C2×#393C2×C1113yescomplemented
101C2×#379C2×C1113yes—
102#1439C2×C1116yescomplemented
103#1439C2×C1113yescomplemented
104C23×C11—212no—
105C23×C11—26no—
106C23×C11—26no—
107C23×C11—26no—
108C23×C11—26no—
109C23×C11—26no—
110C23×C11—26no—
111C23×C11—212no—
112C23×C11—212no—
113C23×C11—212no—
114C23×C11—212no—
115C23×C11—212no—
116C23×C11—448no—
117C23×C11—448no—
118C23×C11—416no—
119C23×C11—448no—
120C23×C11—416no—
121C23×C11—448no—
122C23×C11—416no—
123C23×C11—46no—
124C23×C11—46no—
125C23×C11—46no—
126C23×C11—46no—
127C23×C11—43no—
128C23×C11—46no—
129C23×C11—43no—
130C23×C11—46no—
131C23×C11—43no—
132C23×C11—43no—
133C23×C11C22⋊Q8112yes—
134C23×C11C22×D413yes—
135C23×C11C22×Q811yescharacteristic
136C23×C11C2×#4113yes—
137C23×C11H(5,𝔽2)11yescharacteristic
138C23×C11H(5,𝔽2)13yes—
139C23×C11H(5,𝔽2)11yescharacteristic
140C23×C11H(5,𝔽2)13yes—
141Q8×C11—416no—
142C2×C4×C11—26no—
143C2×C4×C11—26no—
144C2×C4×C11—212no—
145C2×C4×C11—212no—
146C2×C4×C11—46no—
147C2×C4×C11—46no—
148C2×C4×C11—43no—
149C2×C4×C11—43no—
150C2×C4×C11—43no—
151C2×C4×C11—43no—
152C2×C4×C11—46no—
153C2×C4×C11—46no—
154C2×C4×C11—46no—
155C2×C4×C11—46no—
156C2×C4×C11—46no—
157C2×C4×C11—46no—
158C2×C4×C11—46no—
159C26C22×C1111yescharacteristic
160C23×Q8C22×C1111yescharacteristic, complemented
161C22×C4⋊C4C22×C1113yescomplemented
162C22×C22⋊C4C22×C1116yes—
163C22×C22⋊C4C22×C1116yes—
164C22×C22⋊C4C22×C1113yes—
165C22×C22⋊C4C22×C1113yes—
166#393—212no—
167#379—212no—
168C2×#95C22×C1113yescomplemented
169C2×#95C22×C1116yescomplemented
170C2×#95C22×C1112yescomplemented
171C2×#95C22×C1111yescharacteristic, complemented
172C22×C11—212no—
173C22×C11—224no—
174C22×C11—464no—
175C22×C11—46no—
176C22×C11—412no—
177C22×C11—412no—
178C22×C11—46no—
179C22×C11—46no—
180C22×C11—46no—
181C22×C11—412no—
182C22×C11—46no—
183C22×C11—46no—
184C22×C11C2×C22⋊Q813yes—
185C22×C11#53413yes—
186C22×C11#53513yes—
187C22×C11#53813yes—
188C22×C11#53813yes—
189C22×C11#54313yes—
190C22×C11#54311yescharacteristic
191C22×C11D4213yes—
192C22×C11#54616yes—
193C22×C11#55113yes—
194C22×C11H(3,𝔽4)13yes—
195C22×C11H(3,𝔽4)11yescharacteristic
196C4×C11—46no—
197C4×C11—46no—
198C4×C11—86no—
199C25—26no—
200C25—26no—
201C25—43no—
202C25—43no—
203C25—41no—
204C25—41no—
205C25Q8×C1114yescomplemented
206C25C23×C1113yes—
207C22×Q8—26no—
208C22×Q8—43no—
209C22×Q8—41no—
210C23×C4C23×C1116yes—
211C23×C4C23×C1113yes—
212C23×C4C23×C1113yes—
213C2×C4⋊C4—43no—
214C2×C4⋊C4—46no—
215C2×C22⋊C4—26no—
216C2×C22⋊C4—212no—
217C2×C22⋊C4—212no—
218C2×C22⋊C4—212no—
219C2×C22⋊C4—212no—
220C2×C22⋊C4—43no—
221C2×C22⋊C4—43no—
222C2×C22⋊C4—46no—
223C2×C22⋊C4—46no—
224C2×C22⋊C4—43no—
225C2×C22⋊C4—43no—
226C2×C22⋊C4D4×C11112yes—
227#95—212no—
228#95—26no—
229#95—41no—
230#95—42no—
231C2×C11—412no—
232C2×C11#243713yes—
233C2×C11#262613yes—
234C2×C11#267013yes—
235C2×C11#267911yescharacteristic
236C2×C11#268413yes—
237C2×C11#273611yescharacteristic
238C2×C11#284011yescharacteristic
239C24—26no—
240C24—26no—
241C24—23no—
242C24—23no—
243C24—23no—
244C24—23no—
245C24—26no—
246C24—26no—
247C24—224no—
248C24—412no—
249C24—44no—
250C24—412no—
251C24—424no—
252C24—412no—
253C24—412no—
254C24—412no—
255C24—412no—
256C24—412no—
257C24—412no—
258C24—44no—
259C24C2×D4×C1116yes—
260C24C2×Q8×C1116yes—
261C24C11×#4116yes—
262C24C24×C1111yescharacteristic
263C2×Q8—412no—
264C2×Q8—412no—
265C2×Q8—44no—
266C22×C4—26no—
267C22×C4—26no—
268C22×C4—23no—
269C22×C4—23no—
270C22×C4—26no—
271C22×C4—23no—
272C22×C4—23no—
273C22×C4—26no—
274C22×C4—26no—
275C22×C4—26no—
276C22×C4—26no—
277C22×C4—26no—
278C22×C4—26no—
279C22×C4—26no—
280C22×C4—26no—
281C22×C4C2×D4×C1116yes—
282C22×C4C2×D4×C1116yes—
283C4⋊C4—412no—
284C22⋊C4—412no—
285C22⋊C4—424no—
286C22⋊C4—424no—
287C22⋊C4—412no—
288C11#1629711yescharacteristic, direct product factor, Sylow
289C23—212no—
290C23—26no—
291C23—26no—
292C23—26no—
293C23—26no—
294C23—212no—
295C23—26no—
296C23—26no—
297C23—212no—
298C23—212no—
299C23—212no—
300C23—212no—
301C23—448no—
302C23—448no—
303C23—448no—
304C23—416no—
305C23—448no—
306C23—416no—
307C23—416no—
308C23—46no—
309C23—46no—
310C23—46no—
311C23—46no—
312C23—43no—
313C23—46no—
314C23—43no—
315C23—46no—
316C23—43no—
317C23—43no—
318C23C11×C22⋊Q8112yes—
319C23C22×D4×C1113yes—
320C23C22×Q8×C1111yescharacteristic
321C23C2×C11×#4113yes—
322C23C11×H(5,𝔽2)11yescharacteristic
323C23C11×H(5,𝔽2)13yes—
324C23C11×H(5,𝔽2)11yescharacteristic
325C23C11×H(5,𝔽2)13yes—
326Q8—416no—
327C2×C4—26no—
328C2×C4—26no—
329C2×C4—212no—
330C2×C4—212no—
331C2×C4—46no—
332C2×C4—46no—
333C2×C4—43no—
334C2×C4—43no—
335C2×C4—43no—
336C2×C4—43no—
337C2×C4—46no—
338C2×C4—46no—
339C2×C4—46no—
340C2×C4—46no—
341C2×C4—46no—
342C2×C4—46no—
343C2×C4—46no—
344C22—224no—
345C22—212no—
346C22—464no—
347C22—412no—
348C22—46no—
349C22—46no—
350C22—46no—
351C22—412no—
352C22—46no—
353C22—46no—
354C22—46no—
355C22—412no—
356C22C2×C11×C22⋊Q813yes—
357C22C11×#53413yes—
358C22C11×#53513yes—
359C22C11×#53813yes—
360C22C11×#53813yes—
361C22C11×#54313yes—
362C22C11×#54311yescharacteristic
363C22D42×C1113yes—
364C22C11×#54616yes—
365C22C11×#55113yes—
366C22C11×H(3,𝔽4)13yes—
367C22C11×H(3,𝔽4)11yescharacteristic
368C4—46no—
369C4—46no—
370C4—86no—
371C2—412no—
372C2C11×#243713yes—
373C2C11×#262613yes—
374C2C11×#267013yes—
375C2C11×#267911yescharacteristic
376C2C11×#268413yes—
377C2C11×#273611yescharacteristic
378C2C11×#284011yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC24C24×C11
prime radicalC26×C11C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#393C2semidirect
3. C11×#1439C2semidirect
4. C11×#1439C2semidirect
6. C23×Q8×C11C22semidirect
7. C22×C11×C4⋊C4C22semidirect
14. C2×C11×#95C22semidirect
15. C2×C11×#95C22semidirect
16. C2×C11×#95C22semidirect
17. C2×C11×#95C22semidirect
24. C25×C11Q8semidirect
50. #16297C11direct (N × H)
100. C2×#393C2×C11semidirect
102. #1439C2×C11semidirect
103. #1439C2×C11semidirect
160. C23×Q8C22×C11semidirect
161. C22×C4⋊C4C22×C11semidirect
168. C2×#95C22×C11semidirect
169. C2×#95C22×C11semidirect
170. C2×#95C22×C11semidirect
171. C2×#95C22×C11semidirect
205. C25Q8×C11semidirect
288. C11#16297direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3932
C2×C11×#3792
C11×#14392
#1629711