Finite Group Databasebeta

← C11×#34943 #14612136

Subgroups — C11×#34943 #14612136

Order 2816.

2036 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2572C214yesmaximal, complemented
2C11×#2571C211yesmaximal, characteristic, complemented
3C11×#2563C212yesmaximal, complemented
4C11×#2537C211yesmaximal, characteristic
5C11×#2495C214yesmaximal, complemented
6C11×#2420C214yesmaximal, complemented
7C11×#2398C214yesmaximal, complemented
8C4×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
9C4×C11×#121C214yesmaximal, complemented
10C11×#2283C214yesmaximal, complemented
11C42×D4×C11C212yesmaximal, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×#121C2214yes—
14C2×C4×Q8×C11C2212yes—
15C2×C4×D4×C11C2212yes—
16C2×C4×D4×C11C2212yes—
17C2×C4×D4×C11C2212yes—
18C2×C4×D4×C11C2214yes—
19C22×C42×C11C2214yes—
20C11×#400C2214yes—
21C11×#400C2214yes—
22C11×#397C2218yes—
23C11×#394C2214yes—
24C11×#394C2214yes—
25C11×#393C2218yes—
26C11×#391C2212yes—
27C11×#390C2214yes—
28C11×#389C2214yes—
29C11×#389C2214yes—
30C11×#388C2218yes—
31C11×#386C2218yes—
32C11×#384C2211yescharacteristic
33C11×#383C2218yes—
34C11×#382C2214yes—
35C11×#382C2214yes—
36C11×#381C2218yes—
37C11×#380C2214yes—
38C11×#380C2214yes—
39C11×#380C2214yes—
40C4×C11×C4⋊C4C2212yes—
41C4×C11×C4⋊C4C2212yes—
42C4×C11×C4⋊C4C2212yes—
43C4×C11×C4⋊C4C2214yes—
44C4×C11×C22⋊C4C2214yes—
45C4×C11×C22⋊C4C2218yes—
46C4×C11×C22⋊C4C2214yes—
47C4×C11×C22⋊C4C2214yes—
48C11×#376C2214yes—
49C43×C11C2211yescharacteristic
50C22×Q8×C11C2312yes—
51C22×D4×C11C2314yes—
52C22×D4×C11C2312yes—
53C23×C4×C11C2314yes—
54C23×C4×C11C2314yes—
55C23×C4×C11C2314yes—
56C11×C4⋊Q8—24no—
57C11×#121—216no—
58C4×Q8×C11—44no—
59C4×D4×C11—28no—
60C4×D4×C11—28no—
61C4×D4×C11—28no—
62C4×D4×C11—48no—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2314yes—
67C2×C11×C4⋊C4C2314yes—
68C2×C11×C4⋊C4C2314yes—
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2314yes—
71C2×C11×C22⋊C4C2314yes—
72C2×C11×C22⋊C4C2314yes—
73C2×C11×C22⋊C4C2314yes—
74C2×C11×C22⋊C4C2318yes—
75C2×C11×C22⋊C4C2318yes—
76C2×C11×C22⋊C4C2318yes—
77C2×C42×C11—216no—
78C2×C42×C11C2314yes—
79C2×C42×C11C2314yes—
80C2×C42×C11C2312yes—
81C2×C42×C11C2314yes—
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2314yes—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2312yes—
87C11×#95C2314yes—
88C11×#95C2318yes—
89C11×#95C2314yes—
90C11×#95C2314yes—
91C11×#95C2314yes—
92C11×#95C2314yes—
93C11×#95C2318yes—
94C11×#95C2318yes—
95C11×#95C2318yes—
96#34943C1111yesmaximal, characteristic, direct product factor, Sylow
97C24×C11C2414yes—
98C2×Q8×C11—24no—
99C2×Q8×C11—42no—
100C2×Q8×C11—42no—
101C2×D4×C11—216no—
102C2×D4×C11—24no—
103C2×D4×C11—24no—
104C2×D4×C11—44no—
105C2×D4×C11#4118yes—
106C22×C4×C11—28no—
107C22×C4×C11—28no—
108C22×C4×C11—28no—
109C22×C4×C11—28no—
110C22×C4×C11—28no—
111C22×C4×C11—28no—
112C22×C4×C11—28no—
113C22×C4×C11—28no—
114C22×C4×C11—44no—
115C22×C4×C11C2414yes—
116C22×C4×C11C2414yes—
117C22×C4×C11C2414yes—
118C22×C4×C11C2414yes—
119C22×C4×C11C2414yes—
120C22×C4×C11C2411yescharacteristic
121C22×C4×C11C2412yes—
122C22×C4×C11C2411yescharacteristic
123C22×C4×C11C2412yes—
124C22×C4×C11C2411yescharacteristic
125C11×C4⋊C4—24no—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—24no—
128C11×C4⋊C4—28no—
129C11×C4⋊C4—28no—
130C11×C4⋊C4—44no—
131C11×C4⋊C4—42no—
132C11×C4⋊C4—44no—
133C11×C22⋊C4—28no—
134C11×C22⋊C4—216no—
135C11×C22⋊C4—28no—
136C11×C22⋊C4—28no—
137C11×C22⋊C4—48no—
138C11×C22⋊C4—48no—
139C42×C11—28no—
140C42×C11—28no—
141C42×C11—28no—
142C42×C11—24no—
143C42×C11—28no—
144C42×C11—22no—
145C42×C11—41no—
146C42×C11#4118yes—
147C42×C11#4114yes—
148#2572C2×C1114yescomplemented
149#2571C2×C1111yescharacteristic, complemented
150#2563C2×C1112yescomplemented
151#2537C2×C1111yescharacteristic
152#2495C2×C1114yescomplemented
153#2420C2×C1114yescomplemented
154#2398C2×C1114yescomplemented
155C4×C4⋊Q8C2×C1111yescharacteristic, complemented
156C4×#121C2×C1114yescomplemented
157#2283C2×C1114yescomplemented
158C42×D4C2×C1112yescomplemented
159C23×C11—24no—
160C23×C11—24no—
161C23×C11—24no—
162C23×C11—24no—
163C23×C11—24no—
164C23×C11—24no—
165C23×C11C2×#4118yes—
166C23×C11C2511yescharacteristic
167Q8×C11—48no—
168D4×C11—216no—
169D4×C11—416no—
170C2×C4×C11—22no—
171C2×C4×C11—21no—
172C2×C4×C11—22no—
173C2×C4×C11—21no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
176C2×C4×C11—24no—
177C2×C4×C11—22no—
178C2×C4×C11—24no—
179C2×C4×C11—24no—
180C2×C4×C11—24no—
181C2×C4×C11—24no—
182C2×C4×C11—28no—
183C2×C4×C11—24no—
184C2×C4×C11—24no—
185C2×C4×C11—21no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—24no—
190C2×C4×C11—416no—
191C2×C4×C11—416no—
192C2×C4×C11—416no—
193C2×C4×C11C2×#4114yes—
194C2×C4×C11C2×#4112yes—
195C2×C4×C11C2×#4114yes—
196C2×C4×C11C2×#4114yes—
197C2×C4×C11C2×#4114yes—
198C2×C4×C11C2×#4114yes—
199C2×C4×C11H(5,𝔽2)12yes—
200C2×C4⋊Q8C22×C1111yescharacteristic
201C2×#121C22×C1114yes—
202C2×C4×Q8C22×C1112yes—
203C2×C4×D4C22×C1112yes—
204C2×C4×D4C22×C1112yes—
205C2×C4×D4C22×C1112yes—
206C2×C4×D4C22×C1114yes—
207C22×C42C22×C1114yes—
208#400C22×C1114yes—
209#400C22×C1114yes—
210#397C22×C1118yes—
211#394C22×C1114yes—
212#394C22×C1114yes—
213#393C22×C1118yes—
214#391C22×C1112yes—
215#390C22×C1114yes—
216#389C22×C1114yes—
217#389C22×C1114yes—
218#388C22×C1118yes—
219#386C22×C1118yes—
220#384C22×C1111yescharacteristic
221#383C22×C1118yes—
222#382C22×C1114yes—
223#382C22×C1114yes—
224#381C22×C1118yes—
225#380C22×C1114yes—
226#380C22×C1114yes—
227#380C22×C1114yes—
228C4×C4⋊C4C22×C1114yes—
229C4×C4⋊C4C22×C1112yes—
230C4×C4⋊C4C22×C1112yes—
231C4×C4⋊C4C22×C1112yes—
232C4×C22⋊C4C22×C1114yes—
233C4×C22⋊C4C22×C1114yes—
234C4×C22⋊C4C22×C1118yes—
235C4×C22⋊C4C22×C1114yes—
236#376C22×C1114yes—
237C43C22×C1111yescharacteristic
238C22×C11—28no—
239C22×C11—28no—
240C22×C11—28no—
241C22×C11—44no—
242C22×C11—44no—
243C22×C11—44no—
244C22×C11—44no—
245C22×C11C22×#4111yescharacteristic
246C22×C11C22×#4112yes—
247C22×C11C22×#4112yes—
248C22×C11C2×H(5,𝔽2)11yescharacteristic
249C22×C11#58511yescharacteristic
250C4×C11—22no—
251C4×C11—24no—
252C4×C11—44no—
253C4×C11—44no—
254C4×C11—44no—
255C4×C11—44no—
256C4×C11—41no—
257C4×C11—44no—
258C4×C11#52918yes—
259C4×C11#55514yes—
260C22×Q8C23×C1112yes—
261C22×D4C23×C1114yes—
262C22×D4C23×C1112yes—
263C23×C4C23×C1114yes—
264C23×C4C23×C1114yes—
265C23×C4C23×C1114yes—
266C4⋊Q8—24no—
267#121—216no—
268C4×Q8—44no—
269C4×D4—28no—
270C4×D4—28no—
271C4×D4—28no—
272C4×D4—48no—
273C2×C4⋊C4C23×C1112yes—
274C2×C4⋊C4C23×C1112yes—
275C2×C4⋊C4C23×C1112yes—
276C2×C4⋊C4C23×C1114yes—
277C2×C4⋊C4C23×C1114yes—
278C2×C4⋊C4C23×C1114yes—
279C2×C4⋊C4C23×C1112yes—
280C2×C4⋊C4C23×C1114yes—
281C2×C22⋊C4C23×C1114yes—
282C2×C22⋊C4C23×C1114yes—
283C2×C22⋊C4C23×C1114yes—
284C2×C22⋊C4C23×C1118yes—
285C2×C22⋊C4C23×C1118yes—
286C2×C22⋊C4C23×C1118yes—
287C2×C42—216no—
288C2×C42C23×C1114yes—
289C2×C42C23×C1112yes—
290C2×C42C23×C1111yescharacteristic
291C2×C42C23×C1114yes—
292C2×C42C23×C1114yes—
293C2×C42C23×C1114yes—
294C2×C42C23×C1111yescharacteristic
295C2×C42C23×C1111yescharacteristic
296C2×C42C23×C1112yes—
297#95C23×C1114yes—
298#95C23×C1118yes—
299#95C23×C1114yes—
300#95C23×C1114yes—
301#95C23×C1114yes—
302#95C23×C1114yes—
303#95C23×C1118yes—
304#95C23×C1118yes—
305#95C23×C1118yes—
306C2×C11—48no—
307C2×C11C2×#52912yes—
308C2×C11#346011yescharacteristic
309C2×C11C2×#55511yescharacteristic
310C2×C11#347512yes—
311C2×C11#348111yescharacteristic
312C24C24×C1114yes—
313C2×Q8—24no—
314C2×Q8—42no—
315C2×Q8—42no—
316C2×D4—216no—
317C2×D4—24no—
318C2×D4—24no—
319C2×D4—44no—
320C2×D4C11×#4118yes—
321C22×C4—28no—
322C22×C4—28no—
323C22×C4—28no—
324C22×C4—28no—
325C22×C4—28no—
326C22×C4—28no—
327C22×C4—28no—
328C22×C4—28no—
329C22×C4—44no—
330C22×C4C24×C1114yes—
331C22×C4C24×C1114yes—
332C22×C4C24×C1114yes—
333C22×C4C24×C1114yes—
334C22×C4C24×C1114yes—
335C22×C4C24×C1111yescharacteristic
336C22×C4C24×C1112yes—
337C22×C4C24×C1111yescharacteristic
338C22×C4C24×C1112yes—
339C22×C4C24×C1111yescharacteristic
340C4⋊C4—24no—
341C4⋊C4—24no—
342C4⋊C4—24no—
343C4⋊C4—28no—
344C4⋊C4—28no—
345C4⋊C4—44no—
346C4⋊C4—42no—
347C4⋊C4—44no—
348C22⋊C4—28no—
349C22⋊C4—216no—
350C22⋊C4—28no—
351C22⋊C4—28no—
352C22⋊C4—48no—
353C22⋊C4—48no—
354C42—28no—
355C42—28no—
356C42—28no—
357C42—24no—
358C42—28no—
359C42—22no—
360C42—41no—
361C42C11×#4118yes—
362C42C11×#4114yes—
363C11#3494311yescharacteristic, direct product factor, Sylow
364C23—24no—
365C23—24no—
366C23—24no—
367C23—24no—
368C23—24no—
369C23—24no—
370C23C2×C11×#4118yes—
371C23C25×C1111yescharacteristic
372Q8—48no—
373D4—216no—
374D4—416no—
375C2×C4—22no—
376C2×C4—21no—
377C2×C4—22no—
378C2×C4—21no—
379C2×C4—24no—
380C2×C4—24no—
381C2×C4—24no—
382C2×C4—22no—
383C2×C4—24no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—24no—
387C2×C4—28no—
388C2×C4—24no—
389C2×C4—24no—
390C2×C4—21no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—416no—
396C2×C4—416no—
397C2×C4—416no—
398C2×C4C2×C11×#4114yes—
399C2×C4C2×C11×#4112yes—
400C2×C4C2×C11×#4114yes—
401C2×C4C2×C11×#4114yes—
402C2×C4C2×C11×#4114yes—
403C2×C4C2×C11×#4114yes—
404C2×C4C11×H(5,𝔽2)12yes—
405C22—28no—
406C22—28no—
407C22—28no—
408C22—44no—
409C22—44no—
410C22—44no—
411C22—44no—
412C22C22×C11×#4111yescharacteristic
413C22C22×C11×#4112yes—
414C22C22×C11×#4112yes—
415C22C2×C11×H(5,𝔽2)11yescharacteristic
416C22C11×#58511yescharacteristic
417C4—22no—
418C4—24no—
419C4—44no—
420C4—44no—
421C4—44no—
422C4—44no—
423C4—44no—
424C4—41no—
425C4C11×#52918yes—
426C4C11×#55514yes—
427C2—48no—
428C2C2×C11×#52912yes—
429C2C11×#346011yescharacteristic
430C2C2×C11×#55511yescharacteristic
431C2C11×#347512yes—
432C2C11×#348111yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutator, Frattini, cosocleC23C25×C11
socleC23×C11C25
prime radicalC11×#2537C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2572C2semidirect
2. C11×#2571C2semidirect
3. C11×#2563C2semidirect
5. C11×#2495C2semidirect
6. C11×#2420C2semidirect
7. C11×#2398C2semidirect
8. C4×C11×C4⋊Q8C2semidirect
9. C4×C11×#121C2semidirect
10. C11×#2283C2semidirect
11. C42×D4×C11C2semidirect
96. #34943C11direct (N × H)
148. #2572C2×C11semidirect
149. #2571C2×C11semidirect
150. #2563C2×C11semidirect
152. #2495C2×C11semidirect
153. #2420C2×C11semidirect
154. #2398C2×C11semidirect
155. C4×C4⋊Q8C2×C11semidirect
156. C4×#121C2×C11semidirect
157. #2283C2×C11semidirect
158. C42×D4C2×C11semidirect
363. C11#34943direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25722
C11×#25712
C11×#25632
C11×#25372
C11×#24952
C11×#24202
C11×#23982
C4×C11×C4⋊Q82
C4×C11×#1212
C11×#22832
C42×D4×C112
#3494311