Finite Group Databasebeta

← C11×#23265 #14600458

Subgroups — C11×#23265 #14600458

Order 2816.

624 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C11×#125C211yesmaximal, characteristic
2C11×#1917C212yesmaximal
3C11×#1917C212yesmaximal
4C11×#1917C212yesmaximal
5C11×#1916C212yesmaximal
6C11×#1771C212yesmaximal
7C11×#1770C212yesmaximal
8C11×#1745C211yesmaximal, characteristic
9C11×#1745C211yesmaximal, characteristic
10C2×C11×#125C411yescharacteristic
11C2×C11×C4⋊C8C2212yes—
12C2×C11×C4⋊C8C2212yes—
13C2×C11×#97C2212yes—
14C2×C11×#97C2212yes—
15C2×C11×#97C2212yes—
16C2×C4×C8×C11C2212yes—
17C11×#389C411yescharacteristic
18C11×#389C411yescharacteristic
19C11×#387C412yes—
20C11×#387C412yes—
21C11×#382C411yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C4×C11×C4⋊C4C2212yes—
25C4×C11×C4⋊C4C2212yes—
26C43×C11C2211yescharacteristic
27C11×#336C2212yes—
28C11×#336C2212yes—
29C11×#336C2212yes—
30C11×#336C2212yes—
31C11×#336C2212yes—
32C11×#336C2211yescharacteristic
33C11×#336C2211yescharacteristic
34C11×#336C2212yes—
35C11×#336C2211yescharacteristic
36C11×#336C2211yescharacteristic
37C22×C8×C11C2312yes—
38C22×C8×C11C2312yes—
39C22×C8×C11C2312yes—
40C22×C8×C11C2312yes—
41C11×#125—24no—
42C2×C11×C4⋊C4C2×C412yes—
43C2×C11×C4⋊C4C2×C412yes—
44C2×C11×C4⋊C4C2×C411yescharacteristic
45C2×C11×C4⋊C4C2×C411yescharacteristic
46C2×C11×C4⋊C4C2×C411yescharacteristic
47C2×C11×C4⋊C4C2×C412yes—
48C2×C11×C4⋊C4C2×C412yes—
49C2×C11×C4⋊C4C2×C411yescharacteristic
50C2×C42×C11C2×C411yescharacteristic
51C2×C42×C11C2×C411yescharacteristic
52C2×C42×C11C2×C411yescharacteristic
53C2×C42×C11C2×C411yescharacteristic
54C2×C42×C11C2311yescharacteristic
55C2×C42×C11C2311yescharacteristic
56C2×C42×C11C2311yescharacteristic
57C2×C42×C11C2312yes—
58C2×C42×C11C2312yes—
59C11×C4⋊C8—24no—
60C11×C4⋊C8—24no—
61C11×#97—24no—
62C11×#97—24no—
63C11×#97—24no—
64C4×C8×C11—24no—
65C11×#95C2×C412yes—
66C11×#95C2×C412yes—
67C11×#95C2×C412yes—
68C11×#95C2×C412yes—
69C11×#95C2×C412yes—
70C11×#95C2×C412yes—
71#23265C1111yesmaximal, characteristic, direct product factor, Sylow
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C22×C412yes—
74C22×C4×C11C22×C412yes—
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C22×C412yes—
80C22×C4×C11C22×C412yes—
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C2411yescharacteristic
83C2×C8×C11—22no—
84C2×C8×C11—22no—
85C2×C8×C11—22no—
86C2×C8×C11—22no—
87C2×C8×C11—22no—
88C2×C8×C11—22no—
89C2×C8×C11—22no—
90C2×C8×C11—22no—
91C2×C8×C11—22no—
92C2×C8×C11—22no—
93C2×C8×C11#4114yes—
94C2×C8×C11#4114yes—
95C11×C4⋊C4—24no—
96C11×C4⋊C4—24no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—42no—
101C11×C4⋊C4—42no—
102C11×C4⋊C4M1614yes—
103C42×C11—22no—
104C42×C11—22no—
105C42×C11—22no—
106C42×C11—22no—
107C42×C11—22no—
108C42×C11—22no—
109C42×C11—22no—
110C42×C11—21no—
111C42×C11—21no—
112C42×C11—41no—
113C42×C11—41no—
114C42×C11—41no—
115C4×#125C2×C1111yescharacteristic
116#1917C2×C1112yes—
117#1917C2×C1112yes—
118#1917C2×C1112yes—
119#1916C2×C1112yes—
120#1771C2×C1112yes—
121#1770C2×C1112yes—
122#1745C2×C1111yescharacteristic
123#1745C2×C1111yescharacteristic
124C23×C11C23×C411yescharacteristic
125C2×C4×C11—22no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—22no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—22no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—22no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11C2×M1612yes—
154C2×C4×C11C2×M1614yes—
155C2×C4×C11C2×#4112yes—
156C2×C4×C11C2×#4112yes—
157C2×C4×C112−1+411yescharacteristic
158C2×C4×C112−1+411yescharacteristic
159C8×C11—24no—
160C8×C11—24no—
161C8×C11—42no—
162C8×C11—42no—
163C2×#125C4×C1111yescharacteristic
164C2×C4⋊C8C22×C1112yes—
165C2×C4⋊C8C22×C1112yes—
166C2×#97C22×C1112yes—
167C2×#97C22×C1112yes—
168C2×#97C22×C1112yes—
169C2×C4×C8C22×C1112yes—
170#389C4×C1111yescharacteristic
171#389C4×C1111yescharacteristic
172#387C4×C1112yes—
173#387C4×C1112yes—
174#382C4×C1111yescharacteristic
175C4×C4⋊C4C22×C1111yescharacteristic
176C4×C4⋊C4C22×C1111yescharacteristic
177C4×C4⋊C4C22×C1112yes—
178C4×C4⋊C4C22×C1112yes—
179C43C22×C1111yescharacteristic
180#336C22×C1112yes—
181#336C22×C1112yes—
182#336C22×C1112yes—
183#336C22×C1112yes—
184#336C22×C1112yes—
185#336C22×C1111yescharacteristic
186#336C22×C1111yescharacteristic
187#336C22×C1112yes—
188#336C22×C1111yescharacteristic
189#336C22×C1111yescharacteristic
190C22×C11C4×#4111yescharacteristic
191C22×C11C4×#4111yescharacteristic
192C22×C11#51911yescharacteristic
193C22×C11C22×M1611yescharacteristic
194C22×C11#56811yescharacteristic
195C22×C11#56811yescharacteristic
196C22×C11#56811yescharacteristic
197C4×C11—24no—
198C4×C11—22no—
199C4×C11—41no—
200C4×C11—41no—
201C4×C11—42no—
202C4×C11—42no—
203C4×C11—41no—
204C4×C11—41no—
205C4×C11—42no—
206C4×C11—41no—
207C4×C11#55212yes—
208C4×C11#55212yes—
209C22×C8C23×C1112yes—
210C22×C8C23×C1112yes—
211C22×C8C23×C1112yes—
212C22×C8C23×C1112yes—
213#125—24no—
214C2×C4⋊C4C2×C4×C1112yes—
215C2×C4⋊C4C2×C4×C1112yes—
216C2×C4⋊C4C2×C4×C1111yescharacteristic
217C2×C4⋊C4C2×C4×C1111yescharacteristic
218C2×C4⋊C4C2×C4×C1111yescharacteristic
219C2×C4⋊C4C2×C4×C1112yes—
220C2×C4⋊C4C2×C4×C1112yes—
221C2×C4⋊C4C2×C4×C1111yescharacteristic
222C2×C42C2×C4×C1111yescharacteristic
223C2×C42C2×C4×C1111yescharacteristic
224C2×C42C2×C4×C1111yescharacteristic
225C2×C42C2×C4×C1111yescharacteristic
226C2×C42C23×C1111yescharacteristic
227C2×C42C23×C1111yescharacteristic
228C2×C42C23×C1111yescharacteristic
229C2×C42C23×C1112yes—
230C2×C42C23×C1112yes—
231C4⋊C8—24no—
232C4⋊C8—24no—
233#97—24no—
234#97—24no—
235#97—24no—
236C4×C8—24no—
237#95C2×C4×C1112yes—
238#95C2×C4×C1112yes—
239#95C2×C4×C1112yes—
240#95C2×C4×C1112yes—
241#95C2×C4×C1112yes—
242#95C2×C4×C1112yes—
243C2×C11#237111yescharacteristic
244C2×C11#296711yescharacteristic
245C2×C11#296711yescharacteristic
246C2×C11#297011yescharacteristic
247C2×C11#297111yescharacteristic
248C2×C11#298311yescharacteristic
249C2×C11#298711yescharacteristic
250C22×C4C22×C4×C1111yescharacteristic
251C22×C4C22×C4×C1112yes—
252C22×C4C22×C4×C1112yes—
253C22×C4C22×C4×C1111yescharacteristic
254C22×C4C22×C4×C1111yescharacteristic
255C22×C4C22×C4×C1111yescharacteristic
256C22×C4C22×C4×C1111yescharacteristic
257C22×C4C22×C4×C1112yes—
258C22×C4C22×C4×C1112yes—
259C22×C4C22×C4×C1111yescharacteristic
260C22×C4C24×C1111yescharacteristic
261C2×C8—22no—
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—22no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—22no—
271C2×C8C11×#4114yes—
272C2×C8C11×#4114yes—
273C4⋊C4—24no—
274C4⋊C4—24no—
275C4⋊C4—22no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—42no—
279C4⋊C4—42no—
280C4⋊C4C11×M1614yes—
281C42—22no—
282C42—22no—
283C42—22no—
284C42—22no—
285C42—22no—
286C42—22no—
287C42—22no—
288C42—21no—
289C42—21no—
290C42—41no—
291C42—41no—
292C42—41no—
293C11#2326511yescharacteristic, direct product factor, Sylow
294C23C23×C4×C1111yescharacteristic
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4C2×C11×M1612yes—
324C2×C4C2×C11×M1614yes—
325C2×C4C2×C11×#4112yes—
326C2×C4C2×C11×#4112yes—
327C2×C4C11×2−1+411yescharacteristic
328C2×C4C11×2−1+411yescharacteristic
329C8—24no—
330C8—24no—
331C8—42no—
332C8—42no—
333C22C4×C11×#4111yescharacteristic
334C22C4×C11×#4111yescharacteristic
335C22C11×#51911yescharacteristic
336C22C22×C11×M1611yescharacteristic
337C22C11×#56811yescharacteristic
338C22C11×#56811yescharacteristic
339C22C11×#56811yescharacteristic
340C4—24no—
341C4—22no—
342C4—41no—
343C4—41no—
344C4—42no—
345C4—42no—
346C4—41no—
347C4—41no—
348C4—42no—
349C4—41no—
350C4C11×#55212yes—
351C4C11×#55212yes—
352C2C11×#237111yescharacteristic
353C2C11×#296711yescharacteristic
354C2C11×#296711yescharacteristic
355C2C11×#297011yescharacteristic
356C2C11×#297111yescharacteristic
357C2C11×#298311yescharacteristic
358C2C11×#298711yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC22×C4C24×C11
socle, prime radicalC23×C11C23×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
71. #23265C11direct (N × H)
293. C11#23265direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C11×#1252
C11×#19172
C11×#19162
C11×#17712
C11×#17702
C11×#17452
#2326511