Finite Group Databasebeta

← C11×#34956 #14612149

Subgroups — C11×#34956 #14612149

Order 2816.

3394 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C11C212yesmaximal, complemented
2C11×#2600C214yesmaximal, complemented
3C11×#2579C214yesmaximal, complemented
4C11×#2534C214yesmaximal, complemented
5C11×#2483C211yesmaximal, characteristic, complemented
6C11×#2405C212yesmaximal, complemented
7C11×#2403C211yesmaximal, characteristic
8C11×#2392C214yesmaximal, complemented
9C4×C11×#123C214yesmaximal, complemented
10C4×C11×#120C214yesmaximal, complemented
11C11×#2280C211yesmaximal, characteristic, complemented
12C23×D4×C11C2212yes—
13C24×C4×C11C2211yescharacteristic
14C24×C4×C11C2212yescomplemented
15C2×C11×#123C2214yes—
16C2×C11×#120C2214yes—
17C2×C4×D4×C11—216no—
18C2×C4×D4×C11C2214yes—
19C2×C4×D4×C11C2214yes—
20C2×C4×D4×C11C2214yescomplemented
21C2×C4×D4×C11C2214yescomplemented
22C2×C4×D4×C11C2214yescomplemented
23C2×C11×#117C2212yescomplemented
24C22×C11×C4⋊C4C2212yescomplemented
25C22×C11×C22⋊C4C2212yes—
26C22×C11×C22⋊C4C2212yescomplemented
27C22×C42×C11C2212yescomplemented
28C11×#398C2214yescomplemented
29C11×#397C2214yescomplemented
30C11×#396C2218yescomplemented
31C11×#394C2218yescomplemented
32C11×#394C2214yescomplemented
33C11×#392C2214yes—
34C11×#388C2218yescomplemented
35C11×#387C2218yescomplemented
36C11×#386C2214yes—
37C11×#386C2214yes—
38C11×#386C2218yescomplemented
39C11×#385C2214yescomplemented
40C11×#385C2214yescomplemented
41C11×#385C2218yescomplemented
42C11×#381C2214yescomplemented
43C11×#381C2212yescomplemented
44C11×#380C2214yescomplemented
45C11×#379C2211yescharacteristic
46C11×#379C2211yescharacteristic
47C11×#379C2214yescomplemented
48C4×C11×C4⋊C4C2214yescomplemented
49C4×C11×C22⋊C4C2218yescomplemented
50C4×C11×C22⋊C4C2214yescomplemented
51C25×C11C2312yes—
52C25×C11C2311yescharacteristic
53C22×D4×C11—28no—
54C22×D4×C11—216no—
55C22×D4×C11C2314yes—
56C22×D4×C11C2314yes—
57C22×D4×C11C2314yes—
58C23×C4×C11—28no—
59C23×C4×C11—44no—
60C23×C4×C11—48no—
61C23×C4×C11D418yescomplemented
62C23×C4×C11C2312yes—
63C23×C4×C11C2312yes—
64C23×C4×C11C2314yes—
65C23×C4×C11C2312yes—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2312yes—
68C23×C4×C11C2314yes—
69C23×C4×C11C2312yes—
70C23×C4×C11C2311yescharacteristic
71C11×#123—216no—
72C11×#120—216no—
73C4×D4×C11—216no—
74C4×D4×C11—216no—
75C4×D4×C11—216no—
76C4×D4×C11—216no—
77C4×D4×C11—48no—
78C11×#117—44no—
79C2×C11×C4⋊C4—28no—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C4⋊C4C2314yes—
82C2×C11×C4⋊C4C2318yes—
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C4⋊C4C2314yes—
85C2×C11×C22⋊C4—28no—
86C2×C11×C22⋊C4—28no—
87C2×C11×C22⋊C4C2314yes—
88C2×C11×C22⋊C4C2314yes—
89C2×C11×C22⋊C4C2314yes—
90C2×C11×C22⋊C4C2314yes—
91C2×C11×C22⋊C4C2314yes—
92C2×C11×C22⋊C4C2314yes—
93C2×C11×C22⋊C4C2318yes—
94C2×C11×C22⋊C4C2318yes—
95C2×C11×C22⋊C4C2312yes—
96C2×C11×C22⋊C4C2312yes—
97C2×C11×C22⋊C4C2318yes—
98C2×C42×C11—28no—
99C2×C42×C11C2314yes—
100C2×C42×C11C2314yes—
101C2×C42×C11C2314yes—
102C11×#95C2318yes—
103C11×#95C2318yes—
104C11×#95C2318yes—
105C11×#95C2314yes—
106C11×#95C2314yes—
107#34956C1111yesmaximal, characteristic, direct product factor, Sylow
108C24×C11—24no—
109C24×C11—28no—
110C24×C11—28no—
111C24×C11—28no—
112C24×C11—42no—
113C24×C11—44no—
114C24×C11C2×D414yes—
115C24×C11C2411yescharacteristic
116C24×C11C2414yes—
117C24×C11C2412yes—
118C2×D4×C11—264no—
119C2×D4×C11—28no—
120C2×D4×C11—28no—
121C2×D4×C11—28no—
122C2×D4×C11—28no—
123C2×D4×C11—216no—
124C2×D4×C11—28no—
125C2×D4×C11—44no—
126C2×D4×C11#41116yes—
127C22×C4×C11—24no—
128C22×C4×C11—28no—
129C22×C4×C11—24no—
130C22×C4×C11—28no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—28no—
134C22×C4×C11—28no—
135C22×C4×C11—28no—
136C22×C4×C11—216no—
137C22×C4×C11—416no—
138C22×C4×C11—44no—
139C22×C4×C11—42no—
140C22×C4×C11—48no—
141C22×C4×C11—44no—
142C22×C4×C11—432no—
143C22×C4×C11C2×D418yes—
144C22×C4×C11C2×D414yes—
145C22×C4×C11C2×D418yes—
146C22×C4×C11C2×D414yes—
147C22×C4×C11C2414yes—
148C22×C4×C11C2414yes—
149C22×C4×C11C2414yes—
150C22×C4×C11C2414yes—
151C22×C4×C11C2412yes—
152C22×C4×C11C2411yescharacteristic
153C22×C4×C11C2414yes—
154C22×C4×C11C2411yescharacteristic
155C11×C4⋊C4—28no—
156C11×C4⋊C4—28no—
157C11×C4⋊C4—216no—
158C11×C4⋊C4—44no—
159C11×C4⋊C4—44no—
160C11×C22⋊C4—28no—
161C11×C22⋊C4—28no—
162C11×C22⋊C4—28no—
163C11×C22⋊C4—28no—
164C11×C22⋊C4—216no—
165C11×C22⋊C4—28no—
166C11×C22⋊C4—28no—
167C11×C22⋊C4—216no—
168C11×C22⋊C4—42no—
169C11×C22⋊C4—42no—
170C11×C22⋊C4—48no—
171C42×C11—28no—
172C42×C11—28no—
173C42×C11—28no—
174C22×C4×D4C2×C1112yescomplemented
175#2600C2×C1114yescomplemented
176#2579C2×C1114yescomplemented
177#2534C2×C1114yescomplemented
178#2483C2×C1111yescharacteristic, complemented
179#2405C2×C1112yescomplemented
180#2403C2×C1111yescharacteristic
181#2392C2×C1114yescomplemented
182C4×#123C2×C1114yescomplemented
183C4×#120C2×C1114yescomplemented
184#2280C2×C1111yescharacteristic, complemented
185C23×C11—24no—
186C23×C11—24no—
187C23×C11—216no—
188C23×C11—216no—
189C23×C11—24no—
190C23×C11—28no—
191C23×C11—24no—
192C23×C11—24no—
193C23×C11—22no—
194C23×C11—28no—
195C23×C11—44no—
196C23×C11—416no—
197C23×C11—432no—
198C23×C11—48no—
199C23×C11—48no—
200C23×C11C22×D412yes—
201C23×C11C22×D414yes—
202C23×C11C2×#4118yes—
203C23×C11C2×#4118yes—
204C23×C11C2511yescharacteristic
205D4×C11—232no—
206D4×C11—232no—
207D4×C11—416no—
208C2×C4×C11—216no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—22no—
212C2×C4×C11—24no—
213C2×C4×C11—216no—
214C2×C4×C11—28no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—28no—
218C2×C4×C11—28no—
219C2×C4×C11—28no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—28no—
223C2×C4×C11—44no—
224C2×C4×C11—48no—
225C2×C4×C11—416no—
226C2×C4×C11—48no—
227C2×C4×C11—48no—
228C2×C4×C11—416no—
229C2×C4×C11C22×D414yes—
230C2×C4×C11C22×D412yes—
231C2×C4×C11C22×D412yes—
232C2×C4×C11C2×#4118yes—
233C2×C4×C11H(5,𝔽2)14yes—
234C23×D4C22×C1112yes—
235C24×C4C22×C1111yescharacteristic
236C24×C4C22×C1112yescomplemented
237C2×#123C22×C1114yes—
238C2×#120C22×C1114yes—
239C2×C4×D4—216no—
240C2×C4×D4C22×C1114yes—
241C2×C4×D4C22×C1114yes—
242C2×C4×D4C22×C1114yescomplemented
243C2×C4×D4C22×C1114yescomplemented
244C2×C4×D4C22×C1114yescomplemented
245C2×#117C22×C1112yescomplemented
246C22×C4⋊C4C22×C1112yescomplemented
247C22×C22⋊C4C22×C1112yes—
248C22×C22⋊C4C22×C1112yescomplemented
249C22×C42C22×C1112yescomplemented
250#398C22×C1114yescomplemented
251#397C22×C1114yescomplemented
252#396C22×C1118yescomplemented
253#394C22×C1118yescomplemented
254#394C22×C1114yescomplemented
255#392C22×C1114yes—
256#388C22×C1118yescomplemented
257#387C22×C1118yescomplemented
258#386C22×C1114yes—
259#386C22×C1114yes—
260#386C22×C1118yescomplemented
261#385C22×C1118yescomplemented
262#385C22×C1114yescomplemented
263#385C22×C1114yescomplemented
264#381C22×C1112yescomplemented
265#381C22×C1114yescomplemented
266#380C22×C1114yescomplemented
267#379C22×C1111yescharacteristic
268#379C22×C1111yescharacteristic
269#379C22×C1114yescomplemented
270C4×C4⋊C4C22×C1114yescomplemented
271C4×C22⋊C4C22×C1118yescomplemented
272C4×C22⋊C4C22×C1114yescomplemented
273C22×C11—24no—
274C22×C11—24no—
275C22×C11—216no—
276C22×C11—24no—
277C22×C11—28no—
278C22×C11—22no—
279C22×C11—216no—
280C22×C11—416no—
281C22×C11—432no—
282C22×C11—44no—
283C22×C11—44no—
284C22×C11—48no—
285C22×C11—44no—
286C22×C11#52518yes—
287C22×C11C23×D411yescharacteristic
288C22×C11C22×#4114yes—
289C22×C11C2×H(5,𝔽2)12yes—
290C4×C11—28no—
291C4×C11—24no—
292C4×C11—22no—
293C4×C11—44no—
294C4×C11—44no—
295C4×C11—44no—
296C4×C11—44no—
297C4×C11#53414yes—
298C25C23×C1112yes—
299C25C23×C1111yescharacteristic
300C22×D4—28no—
301C22×D4—216no—
302C22×D4C23×C1114yes—
303C22×D4C23×C1114yes—
304C22×D4C23×C1114yes—
305C23×C4—28no—
306C23×C4—44no—
307C23×C4—48no—
308C23×C4D4×C1118yescomplemented
309C23×C4C23×C1112yes—
310C23×C4C23×C1112yes—
311C23×C4C23×C1114yes—
312C23×C4C23×C1111yescharacteristic
313C23×C4C23×C1112yes—
314C23×C4C23×C1112yes—
315C23×C4C23×C1114yes—
316C23×C4C23×C1112yes—
317C23×C4C23×C1111yescharacteristic
318#123—216no—
319#120—216no—
320C4×D4—216no—
321C4×D4—216no—
322C4×D4—216no—
323C4×D4—216no—
324C4×D4—48no—
325#117—44no—
326C2×C4⋊C4—28no—
327C2×C4⋊C4C23×C1114yes—
328C2×C4⋊C4C23×C1114yes—
329C2×C4⋊C4C23×C1118yes—
330C2×C4⋊C4C23×C1114yes—
331C2×C4⋊C4C23×C1114yes—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4C23×C1114yes—
335C2×C22⋊C4C23×C1114yes—
336C2×C22⋊C4C23×C1114yes—
337C2×C22⋊C4C23×C1114yes—
338C2×C22⋊C4C23×C1114yes—
339C2×C22⋊C4C23×C1118yes—
340C2×C22⋊C4C23×C1114yes—
341C2×C22⋊C4C23×C1118yes—
342C2×C22⋊C4C23×C1112yes—
343C2×C22⋊C4C23×C1112yes—
344C2×C22⋊C4C23×C1118yes—
345C2×C42—28no—
346C2×C42C23×C1114yes—
347C2×C42C23×C1114yes—
348C2×C42C23×C1114yes—
349#95C23×C1118yes—
350#95C23×C1118yes—
351#95C23×C1118yes—
352#95C23×C1114yes—
353#95C23×C1114yes—
354C2×C11—28no—
355C2×C11—42no—
356C2×C11—48no—
357C2×C11C2×#52512yes—
358C2×C11C2×#53411yescharacteristic
359C2×C11#348114yes—
360C24—24no—
361C24—28no—
362C24—28no—
363C24—28no—
364C24—42no—
365C24—44no—
366C24C2×D4×C1114yes—
367C24C24×C1111yescharacteristic
368C24C24×C1114yes—
369C24C24×C1112yes—
370C2×D4—264no—
371C2×D4—28no—
372C2×D4—28no—
373C2×D4—28no—
374C2×D4—28no—
375C2×D4—216no—
376C2×D4—28no—
377C2×D4—44no—
378C2×D4C11×#41116yes—
379C22×C4—24no—
380C22×C4—28no—
381C22×C4—24no—
382C22×C4—28no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—28no—
386C22×C4—28no—
387C22×C4—28no—
388C22×C4—216no—
389C22×C4—416no—
390C22×C4—44no—
391C22×C4—42no—
392C22×C4—48no—
393C22×C4—44no—
394C22×C4—432no—
395C22×C4C2×D4×C1118yes—
396C22×C4C2×D4×C1114yes—
397C22×C4C2×D4×C1118yes—
398C22×C4C2×D4×C1114yes—
399C22×C4C24×C1114yes—
400C22×C4C24×C1114yes—
401C22×C4C24×C1114yes—
402C22×C4C24×C1114yes—
403C22×C4C24×C1112yes—
404C22×C4C24×C1111yescharacteristic
405C22×C4C24×C1114yes—
406C22×C4C24×C1111yescharacteristic
407C4⋊C4—28no—
408C4⋊C4—28no—
409C4⋊C4—216no—
410C4⋊C4—44no—
411C4⋊C4—44no—
412C22⋊C4—28no—
413C22⋊C4—28no—
414C22⋊C4—28no—
415C22⋊C4—28no—
416C22⋊C4—216no—
417C22⋊C4—28no—
418C22⋊C4—28no—
419C22⋊C4—216no—
420C22⋊C4—42no—
421C22⋊C4—42no—
422C22⋊C4—48no—
423C42—28no—
424C42—28no—
425C42—28no—
426C11#3495611yescharacteristic, direct product factor, Sylow
427C23—24no—
428C23—24no—
429C23—216no—
430C23—216no—
431C23—24no—
432C23—28no—
433C23—24no—
434C23—24no—
435C23—22no—
436C23—28no—
437C23—44no—
438C23—416no—
439C23—432no—
440C23—48no—
441C23—48no—
442C23C22×D4×C1112yes—
443C23C22×D4×C1114yes—
444C23C2×C11×#4118yes—
445C23C2×C11×#4118yes—
446C23C25×C1111yescharacteristic
447D4—232no—
448D4—232no—
449D4—416no—
450C2×C4—216no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—216no—
456C2×C4—28no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—28no—
460C2×C4—28no—
461C2×C4—28no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—28no—
465C2×C4—44no—
466C2×C4—48no—
467C2×C4—416no—
468C2×C4—48no—
469C2×C4—48no—
470C2×C4—416no—
471C2×C4C22×D4×C1114yes—
472C2×C4C22×D4×C1112yes—
473C2×C4C22×D4×C1112yes—
474C2×C4C2×C11×#4118yes—
475C2×C4C11×H(5,𝔽2)14yes—
476C22—24no—
477C22—24no—
478C22—216no—
479C22—24no—
480C22—28no—
481C22—22no—
482C22—216no—
483C22—416no—
484C22—432no—
485C22—44no—
486C22—44no—
487C22—48no—
488C22—44no—
489C22C11×#52518yes—
490C22C23×D4×C1111yescharacteristic
491C22C22×C11×#4114yes—
492C22C2×C11×H(5,𝔽2)12yes—
493C4—28no—
494C4—24no—
495C4—22no—
496C4—44no—
497C4—44no—
498C4—44no—
499C4—44no—
500C4C11×#53414yes—
501C2—28no—
502C2—42no—
503C2—48no—
504C2C2×C11×#52512yes—
505C2C2×C11×#53411yescharacteristic
506C2C11×#348114yes—
subgroupG/H
centerC22×C4×C11C24
commutator, Frattini, cosocleC23C25×C11
socleC23×C11C25
prime radicalC11×#2403C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C4×D4×C11C2semidirect
2. C11×#2600C2semidirect
3. C11×#2579C2semidirect
4. C11×#2534C2semidirect
5. C11×#2483C2semidirect
6. C11×#2405C2semidirect
8. C11×#2392C2semidirect
9. C4×C11×#123C2semidirect
10. C4×C11×#120C2semidirect
11. C11×#2280C2semidirect
14. C24×C4×C11C22semidirect
20. C2×C4×D4×C11C22semidirect
21. C2×C4×D4×C11C22semidirect
22. C2×C4×D4×C11C22semidirect
23. C2×C11×#117C22semidirect
24. C22×C11×C4⋊C4C22semidirect
26. C22×C11×C22⋊C4C22semidirect
27. C22×C42×C11C22semidirect
28. C11×#398C22semidirect
29. C11×#397C22semidirect
30. C11×#396C22semidirect
31. C11×#394C22semidirect
32. C11×#394C22semidirect
34. C11×#388C22semidirect
35. C11×#387C22semidirect
38. C11×#386C22semidirect
39. C11×#385C22semidirect
40. C11×#385C22semidirect
41. C11×#385C22semidirect
42. C11×#381C22semidirect
43. C11×#381C22semidirect
44. C11×#380C22semidirect
47. C11×#379C22semidirect
48. C4×C11×C4⋊C4C22semidirect
49. C4×C11×C22⋊C4C22semidirect
50. C4×C11×C22⋊C4C22semidirect
61. C23×C4×C11D4semidirect
107. #34956C11direct (N × H)
174. C22×C4×D4C2×C11semidirect
175. #2600C2×C11semidirect
176. #2579C2×C11semidirect
177. #2534C2×C11semidirect
178. #2483C2×C11semidirect
179. #2405C2×C11semidirect
181. #2392C2×C11semidirect
182. C4×#123C2×C11semidirect
183. C4×#120C2×C11semidirect
184. #2280C2×C11semidirect
236. C24×C4C22×C11semidirect
242. C2×C4×D4C22×C11semidirect
243. C2×C4×D4C22×C11semidirect
244. C2×C4×D4C22×C11semidirect
245. C2×#117C22×C11semidirect
246. C22×C4⋊C4C22×C11semidirect
248. C22×C22⋊C4C22×C11semidirect
249. C22×C42C22×C11semidirect
250. #398C22×C11semidirect
251. #397C22×C11semidirect
252. #396C22×C11semidirect
253. #394C22×C11semidirect
254. #394C22×C11semidirect
256. #388C22×C11semidirect
257. #387C22×C11semidirect
260. #386C22×C11semidirect
261. #385C22×C11semidirect
262. #385C22×C11semidirect
263. #385C22×C11semidirect
264. #381C22×C11semidirect
265. #381C22×C11semidirect
266. #380C22×C11semidirect
269. #379C22×C11semidirect
270. C4×C4⋊C4C22×C11semidirect
271. C4×C22⋊C4C22×C11semidirect
272. C4×C22⋊C4C22×C11semidirect
308. C23×C4D4×C11semidirect
426. C11#34956direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D4×C112
C11×#26002
C11×#25792
C11×#25342
C11×#24832
C11×#24052
C11×#24032
C11×#23922
C4×C11×#1232
C4×C11×#1202
C11×#22802
#3495611