Finite Group Databasebeta

← C11×#2450 #13065288

Subgroups — C11×#2450 #13065288

Order 1408.

584 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C4×D4×C11C211yesmaximal, characteristic
3C11×#400C211yesmaximal, characteristic, complemented
4C11×#398C211yesmaximal, characteristic, complemented
5C11×#396C211yesmaximal, characteristic, complemented
6C11×#393C211yesmaximal, characteristic, complemented
7C11×#391C211yesmaximal, characteristic, complemented
8C11×#387C211yesmaximal, characteristic, complemented
9C11×#386C211yesmaximal, characteristic
10C11×#386C211yesmaximal, characteristic
11C11×#385C211yesmaximal, characteristic, complemented
12C11×#385C211yesmaximal, characteristic, complemented
13C11×#385C211yesmaximal, characteristic, complemented
14C11×#380C211yesmaximal, characteristic, complemented
15C2×C11×#95C211yesmaximal, characteristic, complemented
16C22×Q8×C11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C23×C4×C11C2211yescharacteristic
19C23×C4×C11C2211yescharacteristic
20C23×C4×C11C2211yescharacteristic
21C23×C4×C11C2211yescharacteristic
22C11×C22⋊Q8—24no—
23C4×D4×C11—24no—
24C2×C11×C4⋊C4C2211yescharacteristic
25C2×C11×C4⋊C4C2211yescharacteristic
26C2×C11×C4⋊C4C2211yescharacteristic
27C2×C11×C4⋊C4C2211yescharacteristic
28C2×C11×C4⋊C4C2211yescharacteristic
29C2×C11×C4⋊C4C2211yescharacteristic
30C2×C11×C4⋊C4C2211yescharacteristic
31C2×C11×C4⋊C4C2211yescharacteristic
32C2×C11×C22⋊C4C2211yescharacteristic
33C2×C11×C22⋊C4C2211yescharacteristic
34C2×C11×C22⋊C4C2211yescharacteristic
35C2×C11×C22⋊C4C2211yescharacteristic
36C2×C11×C22⋊C4C2211yescharacteristic
37C2×C11×C22⋊C4C2211yescharacteristic
38C2×C11×C22⋊C4C2211yescharacteristic
39C2×C11×C22⋊C4C2211yescharacteristic
40C2×C42×C11C2211yescharacteristic
41C11×#95C2211yescharacteristic
42C11×#95C2211yescharacteristic
43C11×#95C2211yescharacteristic
44C11×#95C2211yescharacteristic
45C11×#95C2211yescharacteristic
46C11×#95C2211yescharacteristic
47C11×#95C2211yescharacteristic
48C11×#95C2211yescharacteristic
49C11×#95C2211yescharacteristic
50C11×#95C2211yescharacteristic
51C11×#95C2211yescharacteristic
52C11×#95C2211yescharacteristic
53C24×C11C2311yescharacteristic
54C24×C11C2311yescharacteristic
55C2×Q8×C11—22no—
56C2×Q8×C11—22no—
57C2×Q8×C11—41no—
58C2×D4×C11—22no—
59C2×D4×C11—22no—
60C2×D4×C11Q814yescomplemented
61C22×C4×C11—22no—
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—41no—
69C22×C4×C11—41no—
70C22×C4×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11C2311yescharacteristic
74C22×C4×C11C2311yescharacteristic
75C22×C4×C11C2311yescharacteristic
76C22×C4×C11C2311yescharacteristic
77C22×C4×C11C2311yescharacteristic
78C22×C4×C11C2311yescharacteristic
79C22×C4×C11C2311yescharacteristic
80C22×C4×C11C2311yescharacteristic
81C22×C4×C11C2311yescharacteristic
82C22×C4×C11C2311yescharacteristic
83C22×C4×C11C2311yescharacteristic
84C22×C4×C11C2311yescharacteristic
85C22×C4×C11C2311yescharacteristic
86C11×C4⋊C4—22no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—22no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C22⋊C4—22no—
95C11×C22⋊C4—22no—
96C11×C22⋊C4—22no—
97C11×C22⋊C4—22no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4D414yes—
102C42×C11—22no—
103#2450C1111yesmaximal, characteristic, direct product factor, Sylow
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11C2×D412yes—
115C23×C11C2×Q812yes—
116C23×C11C2×Q812yes—
117C23×C11#4112yes—
118C23×C11C2411yescharacteristic
119Q8×C11—44no—
120D4×C11—28no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
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—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—44no—
156C2×C4×C11—44no—
157C2×C4×C11—44no—
158C2×C4×C11—44no—
159C2×C4×C11C2×D412yes—
160C2×C4×C11C2×D412yes—
161C2×C4×C11C2×Q812yes—
162C2×C4×C11#4112yes—
163C2×C4×C11#4112yes—
164C2×C22⋊Q8C2×C1111yescharacteristic, complemented
165C2×C4×D4C2×C1111yescharacteristic
166#400C2×C1111yescharacteristic, complemented
167#398C2×C1111yescharacteristic, complemented
168#396C2×C1111yescharacteristic, complemented
169#393C2×C1111yescharacteristic, complemented
170#391C2×C1111yescharacteristic, complemented
171#387C2×C1111yescharacteristic, complemented
172#386C2×C1111yescharacteristic
173#386C2×C1111yescharacteristic
174#385C2×C1111yescharacteristic, complemented
175#385C2×C1111yescharacteristic, complemented
176#385C2×C1111yescharacteristic, complemented
177#380C2×C1111yescharacteristic, complemented
178C2×#95C2×C1111yescharacteristic, complemented
179C22×C11—22no—
180C22×C11—22no—
181C22×C11—22no—
182C22×C11—22no—
183C22×C11—22no—
184C22×C11—22no—
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—22no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11C22⋊Q814yes—
193C22×C11C22×D411yescharacteristic
194C22×C11C22×Q811yescharacteristic
195C22×C11C2×#4111yescharacteristic
196C22×C11C2×#4111yescharacteristic
197C22×C11C2×#4111yescharacteristic
198C22×C11H(5,𝔽2)11yescharacteristic
199C22×C11H(5,𝔽2)11yescharacteristic
200C4×C11—22no—
201C4×C11—22no—
202C4×C11—22no—
203C4×C11—22no—
204C4×C11—22no—
205C4×C11—41no—
206C4×C11—41no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11—41no—
210C4×C11—41no—
211C4×C11—41no—
212C4×C11—41no—
213C22×Q8C22×C1111yescharacteristic
214C22×D4C22×C1111yescharacteristic
215C23×C4C22×C1111yescharacteristic
216C23×C4C22×C1111yescharacteristic
217C23×C4C22×C1111yescharacteristic
218C23×C4C22×C1111yescharacteristic
219C22⋊Q8—24no—
220C4×D4—24no—
221C2×C4⋊C4C22×C1111yescharacteristic
222C2×C4⋊C4C22×C1111yescharacteristic
223C2×C4⋊C4C22×C1111yescharacteristic
224C2×C4⋊C4C22×C1111yescharacteristic
225C2×C4⋊C4C22×C1111yescharacteristic
226C2×C4⋊C4C22×C1111yescharacteristic
227C2×C4⋊C4C22×C1111yescharacteristic
228C2×C4⋊C4C22×C1111yescharacteristic
229C2×C22⋊C4C22×C1111yescharacteristic
230C2×C22⋊C4C22×C1111yescharacteristic
231C2×C22⋊C4C22×C1111yescharacteristic
232C2×C22⋊C4C22×C1111yescharacteristic
233C2×C22⋊C4C22×C1111yescharacteristic
234C2×C22⋊C4C22×C1111yescharacteristic
235C2×C22⋊C4C22×C1111yescharacteristic
236C2×C22⋊C4C22×C1111yescharacteristic
237C2×C42C22×C1111yescharacteristic
238#95C22×C1111yescharacteristic
239#95C22×C1111yescharacteristic
240#95C22×C1111yescharacteristic
241#95C22×C1111yescharacteristic
242#95C22×C1111yescharacteristic
243#95C22×C1111yescharacteristic
244#95C22×C1111yescharacteristic
245#95C22×C1111yescharacteristic
246#95C22×C1111yescharacteristic
247#95C22×C1111yescharacteristic
248#95C22×C1111yescharacteristic
249#95C22×C1111yescharacteristic
250C2×C11—24no—
251C2×C11—42no—
252C2×C11C2×C22⋊Q811yescharacteristic
253C2×C11#52911yescharacteristic
254C2×C11#53811yescharacteristic
255C2×C11#54611yescharacteristic
256C2×C11#54611yescharacteristic
257C2×C11#55411yescharacteristic
258C2×C11#55411yescharacteristic
259C24C23×C1111yescharacteristic
260C24C23×C1111yescharacteristic
261C2×Q8—22no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×D4—22no—
265C2×D4—22no—
266C2×D4Q8×C1114yescomplemented
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4C23×C1111yescharacteristic
280C22×C4C23×C1111yescharacteristic
281C22×C4C23×C1111yescharacteristic
282C22×C4C23×C1111yescharacteristic
283C22×C4C23×C1111yescharacteristic
284C22×C4C23×C1111yescharacteristic
285C22×C4C23×C1111yescharacteristic
286C22×C4C23×C1111yescharacteristic
287C22×C4C23×C1111yescharacteristic
288C22×C4C23×C1111yescharacteristic
289C22×C4C23×C1111yescharacteristic
290C22×C4C23×C1111yescharacteristic
291C22×C4C23×C1111yescharacteristic
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C22⋊C4—22no—
301C22⋊C4—22no—
302C22⋊C4—22no—
303C22⋊C4—22no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4D4×C1114yes—
308C42—22no—
309C11#245011yescharacteristic, direct product factor, Sylow
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23C2×D4×C1112yes—
321C23C2×Q8×C1112yes—
322C23C2×Q8×C1112yes—
323C23C11×#4112yes—
324C23C24×C1111yescharacteristic
325Q8—44no—
326D4—28no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—44no—
362C2×C4—44no—
363C2×C4—44no—
364C2×C4—44no—
365C2×C4C2×D4×C1112yes—
366C2×C4C2×D4×C1112yes—
367C2×C4C2×Q8×C1112yes—
368C2×C4C11×#4112yes—
369C2×C4C11×#4112yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22C11×C22⋊Q814yes—
384C22C22×D4×C1111yescharacteristic
385C22C22×Q8×C1111yescharacteristic
386C22C2×C11×#4111yescharacteristic
387C22C2×C11×#4111yescharacteristic
388C22C2×C11×#4111yescharacteristic
389C22C11×H(5,𝔽2)11yescharacteristic
390C22C11×H(5,𝔽2)11yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—22no—
395C4—22no—
396C4—41no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—41no—
403C4—41no—
404C2—24no—
405C2—42no—
406C2C2×C11×C22⋊Q811yescharacteristic
407C2C11×#52911yescharacteristic
408C2C11×#53811yescharacteristic
409C2C11×#54611yescharacteristic
410C2C11×#54611yescharacteristic
411C2C11×#55411yescharacteristic
412C2C11×#55411yescharacteristic
subgroupG/H
center, socleC23×C11C24
commutator, Frattini, cosocleC23C24×C11
prime radicalC22×D4×C11C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×C22⋊Q8C2semidirect
3. C11×#400C2semidirect
4. C11×#398C2semidirect
5. C11×#396C2semidirect
6. C11×#393C2semidirect
7. C11×#391C2semidirect
8. C11×#387C2semidirect
11. C11×#385C2semidirect
12. C11×#385C2semidirect
13. C11×#385C2semidirect
14. C11×#380C2semidirect
15. C2×C11×#95C2semidirect
60. C2×D4×C11Q8semidirect
103. #2450C11direct (N × H)
164. C2×C22⋊Q8C2×C11semidirect
166. #400C2×C11semidirect
167. #398C2×C11semidirect
168. #396C2×C11semidirect
169. #393C2×C11semidirect
170. #391C2×C11semidirect
171. #387C2×C11semidirect
174. #385C2×C11semidirect
175. #385C2×C11semidirect
176. #385C2×C11semidirect
177. #380C2×C11semidirect
178. C2×#95C2×C11semidirect
266. C2×D4Q8×C11semidirect
309. C11#2450direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×C22⋊Q82
C2×C4×D4×C112
C11×#4002
C11×#3982
C11×#3962
C11×#3932
C11×#3912
C11×#3872
C11×#3862
C11×#3852
C11×#3802
C2×C11×#952
#245011