Finite Group Databasebeta

← C11×#2457 #13065295

Subgroups — C11×#2457 #13065295

Order 1408.

596 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#123C211yesmaximal, characteristic, complemented
2C2×C4×D4×C11C211yesmaximal, characteristic, complemented
3C11×#400C211yesmaximal, characteristic, complemented
4C11×#396C211yesmaximal, characteristic, complemented
5C11×#394C211yesmaximal, characteristic, complemented
6C11×#392C211yesmaximal, characteristic
7C11×#388C211yesmaximal, characteristic, complemented
8C11×#388C211yesmaximal, characteristic, complemented
9C11×#387C211yesmaximal, characteristic, complemented
10C11×#386C211yesmaximal, characteristic, complemented
11C11×#386C211yesmaximal, characteristic, complemented
12C11×#386C211yesmaximal, characteristic, complemented
13C11×#381C211yesmaximal, characteristic, complemented
14C11×#380C211yesmaximal, characteristic, complemented
15C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×D4×C11C2211yescharacteristic
19C23×C4×C11C2211yescharacteristic
20C23×C4×C11C2211yescharacteristic
21C23×C4×C11C2211yescharacteristic
22C11×#123—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×C22⋊C4C2211yescharacteristic
30C2×C11×C22⋊C4C2211yescharacteristic
31C2×C11×C22⋊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×C11×C22⋊C4C2211yescharacteristic
41C2×C42×C11C2211yescharacteristic
42C2×C42×C11C2211yescharacteristic
43C11×#95C2211yescharacteristic
44C11×#95C2211yescharacteristic
45C11×#95C2211yescharacteristic
46C11×#95C2211yescharacteristic
47C11×#95C2211yescharacteristic
48C11×#95C2211yescharacteristic
49C11×#95C2211yescharacteristic
50C11×#95C2211yescharacteristic
51C11×#95C2211yescharacteristic
52C11×#95C2211yescharacteristic
53C24×C11C2311yescharacteristic
54C24×C11C2311yescharacteristic
55C24×C11C2311yescharacteristic
56C2×D4×C11—22no—
57C2×D4×C11—22no—
58C2×D4×C11—22no—
59C2×D4×C11—22no—
60C2×D4×C11—22no—
61C2×D4×C11—22no—
62C2×D4×C11—22no—
63C2×D4×C11—41no—
64C2×D4×C11—41no—
65C22×C4×C11—22no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
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—41no—
91C11×C22⋊C4—22no—
92C11×C22⋊C4—22no—
93C11×C22⋊C4—22no—
94C11×C22⋊C4—22no—
95C11×C22⋊C4—22no—
96C11×C22⋊C4—22no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4D414yescomplemented
103C42×C11—22no—
104C42×C11—41no—
105#2457C1111yesmaximal, characteristic, direct product factor, Sylow
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×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11C2×D412yes—
125C23×C11#4112yes—
126C23×C11#4112yes—
127C23×C11C2411yescharacteristic
128D4×C11—28no—
129D4×C11—44no—
130D4×C11—44no—
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—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—44no—
164C2×C4×C11—44no—
165C2×C4×C11—44no—
166C2×C4×C11C2×D412yes—
167C2×C4×C11C2×D412yes—
168C2×C4×C11#4112yes—
169C2×C4×C11#4112yes—
170C2×#123C2×C1111yescharacteristic, complemented
171C2×C4×D4C2×C1111yescharacteristic, complemented
172#400C2×C1111yescharacteristic, complemented
173#396C2×C1111yescharacteristic, complemented
174#394C2×C1111yescharacteristic, complemented
175#392C2×C1111yescharacteristic
176#388C2×C1111yescharacteristic, complemented
177#388C2×C1111yescharacteristic, complemented
178#387C2×C1111yescharacteristic, complemented
179#386C2×C1111yescharacteristic, complemented
180#386C2×C1111yescharacteristic, complemented
181#386C2×C1111yescharacteristic, complemented
182#381C2×C1111yescharacteristic, complemented
183#380C2×C1111yescharacteristic, complemented
184C4×C22⋊C4C2×C1111yescharacteristic, complemented
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—22no—
188C22×C11—22no—
189C22×C11—22no—
190C22×C11—22no—
191C22×C11—22no—
192C22×C11—22no—
193C22×C11—22no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—41no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11—41no—
204C22×C11—41no—
205C22×C11—41no—
206C22×C11C22×D411yescharacteristic
207C22×C11C2×#4111yescharacteristic
208C22×C11C2×#4111yescharacteristic
209C22×C11C2×#4111yescharacteristic
210C22×C11C2×#4111yescharacteristic
211C22×C11H(5,𝔽2)11yescharacteristic
212C22×C11H(5,𝔽2)11yescharacteristic
213C4×C11—22no—
214C4×C11—22no—
215C4×C11—22no—
216C4×C11—22no—
217C4×C11—41no—
218C4×C11—41no—
219C4×C11—41no—
220C4×C11—41no—
221C4×C11—41no—
222C4×C11—41no—
223C4×C11—41no—
224C4×C11—41no—
225C22×D4C22×C1111yescharacteristic
226C22×D4C22×C1111yescharacteristic
227C22×D4C22×C1111yescharacteristic
228C23×C4C22×C1111yescharacteristic
229C23×C4C22×C1111yescharacteristic
230C23×C4C22×C1111yescharacteristic
231#123—24no—
232C4×D4—24no—
233C2×C4⋊C4C22×C1111yescharacteristic
234C2×C4⋊C4C22×C1111yescharacteristic
235C2×C4⋊C4C22×C1111yescharacteristic
236C2×C4⋊C4C22×C1111yescharacteristic
237C2×C4⋊C4C22×C1111yescharacteristic
238C2×C22⋊C4C22×C1111yescharacteristic
239C2×C22⋊C4C22×C1111yescharacteristic
240C2×C22⋊C4C22×C1111yescharacteristic
241C2×C22⋊C4C22×C1111yescharacteristic
242C2×C22⋊C4C22×C1111yescharacteristic
243C2×C22⋊C4C22×C1111yescharacteristic
244C2×C22⋊C4C22×C1111yescharacteristic
245C2×C22⋊C4C22×C1111yescharacteristic
246C2×C22⋊C4C22×C1111yescharacteristic
247C2×C22⋊C4C22×C1111yescharacteristic
248C2×C22⋊C4C22×C1111yescharacteristic
249C2×C22⋊C4C22×C1111yescharacteristic
250C2×C42C22×C1111yescharacteristic
251C2×C42C22×C1111yescharacteristic
252#95C22×C1111yescharacteristic
253#95C22×C1111yescharacteristic
254#95C22×C1111yescharacteristic
255#95C22×C1111yescharacteristic
256#95C22×C1111yescharacteristic
257#95C22×C1111yescharacteristic
258#95C22×C1111yescharacteristic
259#95C22×C1111yescharacteristic
260#95C22×C1111yescharacteristic
261#95C22×C1111yescharacteristic
262C2×C11—42no—
263C2×C11—42no—
264C2×C11—42no—
265C2×C11#52511yescharacteristic
266C2×C11#52911yescharacteristic
267C2×C11#54011yescharacteristic
268C2×C11#54611yescharacteristic
269C2×C11#54611yescharacteristic
270C2×C11#55111yescharacteristic
271C2×C11#55311yescharacteristic
272C24C23×C1111yescharacteristic
273C24C23×C1111yescharacteristic
274C24C23×C1111yescharacteristic
275C2×D4—22no—
276C2×D4—22no—
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4—22no—
281C2×D4—22no—
282C2×D4—41no—
283C2×D4—41no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4C23×C1111yescharacteristic
294C22×C4C23×C1111yescharacteristic
295C22×C4C23×C1111yescharacteristic
296C22×C4C23×C1111yescharacteristic
297C22×C4C23×C1111yescharacteristic
298C22×C4C23×C1111yescharacteristic
299C22×C4C23×C1111yescharacteristic
300C22×C4C23×C1111yescharacteristic
301C22×C4C23×C1111yescharacteristic
302C22×C4C23×C1111yescharacteristic
303C22×C4C23×C1111yescharacteristic
304C22×C4C23×C1111yescharacteristic
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—41no—
310C22⋊C4—22no—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—22no—
314C22⋊C4—22no—
315C22⋊C4—22no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4D4×C1114yescomplemented
322C42—22no—
323C42—41no—
324C11#245711yescharacteristic, direct product factor, Sylow
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23C2×D4×C1112yes—
344C23C11×#4112yes—
345C23C11×#4112yes—
346C23C24×C1111yescharacteristic
347D4—28no—
348D4—44no—
349D4—44no—
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—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—44no—
383C2×C4—44no—
384C2×C4—44no—
385C2×C4C2×D4×C1112yes—
386C2×C4C2×D4×C1112yes—
387C2×C4C11×#4112yes—
388C2×C4C11×#4112yes—
389C22—22no—
390C22—22no—
391C22—22no—
392C22—22no—
393C22—22no—
394C22—22no—
395C22—22no—
396C22—22no—
397C22—22no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22C22×D4×C1111yescharacteristic
411C22C2×C11×#4111yescharacteristic
412C22C2×C11×#4111yescharacteristic
413C22C2×C11×#4111yescharacteristic
414C22C2×C11×#4111yescharacteristic
415C22C11×H(5,𝔽2)11yescharacteristic
416C22C11×H(5,𝔽2)11yescharacteristic
417C4—22no—
418C4—22no—
419C4—22no—
420C4—22no—
421C4—41no—
422C4—41no—
423C4—41no—
424C4—41no—
425C4—41no—
426C4—41no—
427C4—41no—
428C4—41no—
429C2—42no—
430C2—42no—
431C2—42no—
432C2C11×#52511yescharacteristic
433C2C11×#52911yescharacteristic
434C2C11×#54011yescharacteristic
435C2C11×#54611yescharacteristic
436C2C11×#54611yescharacteristic
437C2C11×#55111yescharacteristic
438C2C11×#55311yescharacteristic
subgroupG/H
center, socleC23×C11C24
commutator, Frattini, cosocleC23C24×C11
prime radicalC11×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#123C2semidirect
2. C2×C4×D4×C11C2semidirect
3. C11×#400C2semidirect
4. C11×#396C2semidirect
5. C11×#394C2semidirect
7. C11×#388C2semidirect
8. C11×#388C2semidirect
9. C11×#387C2semidirect
10. C11×#386C2semidirect
11. C11×#386C2semidirect
12. C11×#386C2semidirect
13. C11×#381C2semidirect
14. C11×#380C2semidirect
15. C4×C11×C22⋊C4C2semidirect
102. C11×C22⋊C4D4semidirect
105. #2457C11direct (N × H)
170. C2×#123C2×C11semidirect
171. C2×C4×D4C2×C11semidirect
172. #400C2×C11semidirect
173. #396C2×C11semidirect
174. #394C2×C11semidirect
176. #388C2×C11semidirect
177. #388C2×C11semidirect
178. #387C2×C11semidirect
179. #386C2×C11semidirect
180. #386C2×C11semidirect
181. #386C2×C11semidirect
182. #381C2×C11semidirect
183. #380C2×C11semidirect
184. C4×C22⋊C4C2×C11semidirect
321. C22⋊C4D4×C11semidirect
324. C11#2457direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#1232
C2×C4×D4×C112
C11×#4002
C11×#3962
C11×#3942
C11×#3922
C11×#3882
C11×#3872
C11×#3862
C11×#3812
C11×#3802
C4×C11×C22⋊C42
#245711