Finite Group Databasebeta

← C11×#34273 #14611466

Subgroups — C11×#34273 #14611466

Order 2816.

3578 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#534C211yesmaximal, characteristic
2C2×C11×#518C212yesmaximal, complemented
3C11×#2359C218yesmaximal, complemented
4C11×#2358C218yesmaximal, complemented
5C11×#2325C214yesmaximal, complemented
6C11×#2315C211yesmaximal, characteristic, complemented
7C4×C11×#121C214yesmaximal, complemented
8C2×C11×#386C212yesmaximal, complemented
9C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
10C23×D4×C11C2212yes—
11C24×C4×C11C2211yescharacteristic
12C11×#534C4116yescomplemented
13C2×C11×#123C2214yes—
14C2×C11×#121C2214yes—
15C2×C11×#120C2214yes—
16C11×#518—216no—
17C2×C4×D4×C11C2218yes—
18C2×C4×D4×C11C2218yescomplemented
19C2×C4×D4×C11C2214yescomplemented
20C2×C11×#117C2214yescomplemented
21C22×C11×C22⋊C4C2212yes—
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2214yescomplemented
25C22×C11×C22⋊C4C2214yescomplemented
26C22×C42×C11C2212yescomplemented
27C11×#390C2214yescomplemented
28C11×#389C2214yescomplemented
29C11×#388C2218yescomplemented
30C11×#388C2218yescomplemented
31C11×#387C2218yescomplemented
32C11×#386C2218yes—
33C11×#386C2214yescomplemented
34C11×#386C2214yescomplemented
35C11×#386C2218yescomplemented
36C11×#385C2218yescomplemented
37C11×#385C2218yescomplemented
38C11×#380C2214yescomplemented
39C4×C11×C4⋊C4C2214yescomplemented
40C4×C11×C22⋊C4C2218yescomplemented
41C4×C11×C22⋊C4C2218yescomplemented
42C2×C11×#95C2212yescomplemented
43C2×C11×#95C2214yescomplemented
44C25×C11C2312yes—
45C25×C11C2311yescharacteristic
46C22×D4×C11—28no—
47C22×D4×C11—28no—
48C22×D4×C11C2×C4116yescomplemented
49C22×D4×C11C2314yes—
50C22×D4×C11C2314yes—
51C22×D4×C11C2314yes—
52C23×C4×C11—24no—
53C23×C4×C11—44no—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2314yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2314yes—
58C23×C4×C11C2318yes—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2312yes—
61C23×C4×C11C2312yes—
62C11×#123C2×C4132yescomplemented
63C11×#121C2×C4132yescomplemented
64C11×#120C2×C4132yescomplemented
65C4×D4×C11—232no—
66C4×D4×C11—232no—
67C4×D4×C11—48no—
68C11×#117—216no—
69C2×C11×C4⋊C4C2318yes—
70C2×C11×C4⋊C4C2314yes—
71C2×C11×C4⋊C4C2314yes—
72C2×C11×C4⋊C4C2314yes—
73C2×C11×C22⋊C4—28no—
74C2×C11×C22⋊C4—216no—
75C2×C11×C22⋊C4—48no—
76C2×C11×C22⋊C4C2×C418yescomplemented
77C2×C11×C22⋊C4D418yescomplemented
78C2×C11×C22⋊C4C2314yes—
79C2×C11×C22⋊C4C2314yes—
80C2×C11×C22⋊C4C2318yes—
81C2×C11×C22⋊C4C2318yes—
82C2×C11×C22⋊C4C2318yes—
83C2×C11×C22⋊C4C2314yes—
84C2×C11×C22⋊C4C2318yes—
85C2×C11×C22⋊C4C2314yes—
86C2×C42×C11—44no—
87C2×C42×C11C2314yes—
88C2×C42×C11C2318yes—
89C2×C42×C11C2314yes—
90C11×#95C2318yes—
91C11×#95C2318yes—
92C11×#95C2318yes—
93C11×#95C2318yes—
94#34273C1111yesmaximal, characteristic, direct product factor, Sylow
95C24×C11—24no—
96C24×C11—24no—
97C24×C11—42no—
98C24×C11—42no—
99C24×C11—44no—
100C24×C11—44no—
101C24×C11C22×C418yes—
102C24×C11C22×C414yes—
103C24×C11C2×D414yes—
104C24×C11#4114yes—
105C24×C11C2414yes—
106C24×C11C2412yes—
107C24×C11C2411yescharacteristic
108C2×D4×C11—264no—
109C2×D4×C11—28no—
110C2×D4×C11—28no—
111C2×D4×C11—28no—
112C2×D4×C11—28no—
113C2×D4×C11—44no—
114C2×D4×C11—44no—
115C2×D4×C11C22×C4116yes—
116C2×D4×C11C22×C4116yes—
117C2×D4×C11C22×C4116yescomplemented
118C22×C4×C11—24no—
119C22×C4×C11—22no—
120C22×C4×C11—24no—
121C22×C4×C11—24no—
122C22×C4×C11—28no—
123C22×C4×C11—22no—
124C22×C4×C11—28no—
125C22×C4×C11—28no—
126C22×C4×C11—216no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11—44no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11—44no—
134C22×C4×C11—48no—
135C22×C4×C11—48no—
136C22×C4×C11—44no—
137C22×C4×C11—416no—
138C22×C4×C11C22×C418yes—
139C22×C4×C11C22×C418yes—
140C22×C4×C11C2×D418yes—
141C22×C4×C11C2412yes—
142C22×C4×C11C2418yes—
143C22×C4×C11C2414yes—
144C22×C4×C11C2414yes—
145C22×C4×C11C2414yes—
146C22×C4×C11C2412yes—
147C11×C4⋊C4—216no—
148C11×C4⋊C4—44no—
149C11×C4⋊C4—44no—
150C11×C4⋊C4C22×C4116yescomplemented
151C11×C22⋊C4—28no—
152C11×C22⋊C4—28no—
153C11×C22⋊C4—216no—
154C11×C22⋊C4—216no—
155C11×C22⋊C4—48no—
156C11×C22⋊C4C22×C4116yes—
157C11×C22⋊C4C22×C4132yescomplemented
158C11×C22⋊C4C2×D4116yes—
159C42×C11—216no—
160C42×C11—28no—
161C42×C11—44no—
162C2×#534C2×C1111yescharacteristic
163C2×#518C2×C1112yescomplemented
164#2359C2×C1118yescomplemented
165#2358C2×C1118yescomplemented
166#2325C2×C1114yescomplemented
167#2315C2×C1111yescharacteristic, complemented
168C4×#121C2×C1114yescomplemented
169C2×#386C2×C1112yescomplemented
170C2×C4×C22⋊C4C2×C1111yescharacteristic, complemented
171C23×C11—22no—
172C23×C11—24no—
173C23×C11—22no—
174C23×C11—24no—
175C23×C11—24no—
176C23×C11—24no—
177C23×C11—28no—
178C23×C11—28no—
179C23×C11—216no—
180C23×C11—44no—
181C23×C11—48no—
182C23×C11—48no—
183C23×C11—44no—
184C23×C11—416no—
185C23×C11—84no—
186C23×C11—84no—
187C23×C11—88no—
188C23×C11C4×D4116yescomplemented
189C23×C11C23×C418yes—
190C23×C11C23×C414yes—
191C23×C11C23×C412yes—
192C23×C11C22×D412yes—
193C23×C11C22×D414yes—
194C23×C11C2×#4114yes—
195C23×C11C2×#4112yes—
196C23×C11C2511yescharacteristic
197D4×C11—232no—
198D4×C11—232no—
199D4×C11—416no—
200C2×C4×C11—28no—
201C2×C4×C11—216no—
202C2×C4×C11—24no—
203C2×C4×C11—22no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—22no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—28no—
211C2×C4×C11—22no—
212C2×C4×C11—28no—
213C2×C4×C11—24no—
214C2×C4×C11—28no—
215C2×C4×C11—48no—
216C2×C4×C11—48no—
217C2×C4×C11—416no—
218C2×C4×C11—44no—
219C2×C4×C11—816no—
220C2×C4×C11—88no—
221C2×C4×C11C23×C418yes—
222C2×C4×C11C23×C418yes—
223C2×C4×C11C22×D418yes—
224C2×C4×C11H(5,𝔽2)14yes—
225C23×D4C22×C1112yes—
226C24×C4C22×C1111yescharacteristic
227#534C4×C11116yescomplemented
228C2×#123C22×C1114yes—
229C2×#121C22×C1114yes—
230C2×#120C22×C1114yes—
231#518—216no—
232C2×C4×D4C22×C1118yes—
233C2×C4×D4C22×C1118yescomplemented
234C2×C4×D4C22×C1114yescomplemented
235C2×#117C22×C1114yescomplemented
236C22×C22⋊C4C22×C1112yes—
237C22×C22⋊C4C22×C1111yescharacteristic
238C22×C22⋊C4C22×C1111yescharacteristic
239C22×C22⋊C4C22×C1114yescomplemented
240C22×C22⋊C4C22×C1114yescomplemented
241C22×C42C22×C1112yescomplemented
242#390C22×C1114yescomplemented
243#389C22×C1114yescomplemented
244#388C22×C1118yescomplemented
245#388C22×C1118yescomplemented
246#387C22×C1118yescomplemented
247#386C22×C1118yes—
248#386C22×C1114yescomplemented
249#386C22×C1118yescomplemented
250#386C22×C1114yescomplemented
251#385C22×C1118yescomplemented
252#385C22×C1118yescomplemented
253#380C22×C1114yescomplemented
254C4×C4⋊C4C22×C1114yescomplemented
255C4×C22⋊C4C22×C1118yescomplemented
256C4×C22⋊C4C22×C1118yescomplemented
257C2×#95C22×C1112yescomplemented
258C2×#95C22×C1114yescomplemented
259C22×C11—24no—
260C22×C11—28no—
261C22×C11—22no—
262C22×C11—24no—
263C22×C11—24no—
264C22×C11—22no—
265C22×C11—24no—
266C22×C11—28no—
267C22×C11—28no—
268C22×C11—216no—
269C22×C11—416no—
270C22×C11—44no—
271C22×C11—44no—
272C22×C11—48no—
273C22×C11—816no—
274C22×C11C2×C4×D418yes—
275C22×C11C2×C4×D414yes—
276C22×C11C24×C411yescharacteristic
277C22×C11C23×D411yescharacteristic
278C22×C11C22×#4111yescharacteristic
279C22×C11C2×H(5,𝔽2)12yes—
280C22×C11#58512yes—
281C4×C11—28no—
282C4×C11—28no—
283C4×C11—24no—
284C4×C11—28no—
285C4×C11—42no—
286C4×C11—48no—
287C25C23×C1112yes—
288C25C23×C1111yescharacteristic
289C22×D4—28no—
290C22×D4—28no—
291C22×D4C2×C4×C11116yescomplemented
292C22×D4C23×C1114yes—
293C22×D4C23×C1114yes—
294C22×D4C23×C1114yes—
295C23×C4—24no—
296C23×C4—44no—
297C23×C4C23×C1111yescharacteristic
298C23×C4C23×C1114yes—
299C23×C4C23×C1112yes—
300C23×C4C23×C1114yes—
301C23×C4C23×C1118yes—
302C23×C4C23×C1111yescharacteristic
303C23×C4C23×C1112yes—
304C23×C4C23×C1112yes—
305#123C2×C4×C11132yescomplemented
306#121C2×C4×C11132yescomplemented
307#120C2×C4×C11132yescomplemented
308C4×D4—232no—
309C4×D4—232no—
310C4×D4—48no—
311#117—216no—
312C2×C4⋊C4C23×C1118yes—
313C2×C4⋊C4C23×C1114yes—
314C2×C4⋊C4C23×C1114yes—
315C2×C4⋊C4C23×C1114yes—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—216no—
318C2×C22⋊C4—48no—
319C2×C22⋊C4C2×C4×C1118yescomplemented
320C2×C22⋊C4D4×C1118yescomplemented
321C2×C22⋊C4C23×C1114yes—
322C2×C22⋊C4C23×C1114yes—
323C2×C22⋊C4C23×C1118yes—
324C2×C22⋊C4C23×C1118yes—
325C2×C22⋊C4C23×C1118yes—
326C2×C22⋊C4C23×C1114yes—
327C2×C22⋊C4C23×C1118yes—
328C2×C22⋊C4C23×C1114yes—
329C2×C42—44no—
330C2×C42C23×C1118yes—
331C2×C42C23×C1114yes—
332C2×C42C23×C1114yes—
333#95C23×C1118yes—
334#95C23×C1118yes—
335#95C23×C1118yes—
336#95C23×C1118yes—
337C2×C11—28no—
338C2×C11—24no—
339C2×C11—48no—
340C2×C11C22×C4×D411yescharacteristic
341C2×C11C4×H(5,𝔽2)12yes—
342C2×C11#349011yescharacteristic
343C2×C11#349111yescharacteristic
344C2×C11#349612yes—
345C24—24no—
346C24—24no—
347C24—42no—
348C24—42no—
349C24—44no—
350C24—44no—
351C24C22×C4×C1118yes—
352C24C22×C4×C1114yes—
353C24C2×D4×C1114yes—
354C24C11×#4114yes—
355C24C24×C1114yes—
356C24C24×C1112yes—
357C24C24×C1111yescharacteristic
358C2×D4—264no—
359C2×D4—28no—
360C2×D4—28no—
361C2×D4—28no—
362C2×D4—28no—
363C2×D4—44no—
364C2×D4—44no—
365C2×D4C22×C4×C11116yes—
366C2×D4C22×C4×C11116yes—
367C2×D4C22×C4×C11116yescomplemented
368C22×C4—24no—
369C22×C4—22no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—28no—
373C22×C4—22no—
374C22×C4—28no—
375C22×C4—28no—
376C22×C4—216no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—44no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—44no—
384C22×C4—48no—
385C22×C4—48no—
386C22×C4—44no—
387C22×C4—416no—
388C22×C4C22×C4×C1118yes—
389C22×C4C22×C4×C1118yes—
390C22×C4C2×D4×C1118yes—
391C22×C4C24×C1112yes—
392C22×C4C24×C1118yes—
393C22×C4C24×C1114yes—
394C22×C4C24×C1114yes—
395C22×C4C24×C1114yes—
396C22×C4C24×C1112yes—
397C4⋊C4—216no—
398C4⋊C4—44no—
399C4⋊C4—44no—
400C4⋊C4C22×C4×C11116yescomplemented
401C22⋊C4—28no—
402C22⋊C4—28no—
403C22⋊C4—216no—
404C22⋊C4—216no—
405C22⋊C4—48no—
406C22⋊C4C22×C4×C11116yes—
407C22⋊C4C22×C4×C11132yescomplemented
408C22⋊C4C2×D4×C11116yes—
409C42—216no—
410C42—28no—
411C42—44no—
412C11#3427311yescharacteristic, direct product factor, Sylow
413C23—22no—
414C23—24no—
415C23—22no—
416C23—24no—
417C23—24no—
418C23—24no—
419C23—28no—
420C23—28no—
421C23—216no—
422C23—44no—
423C23—48no—
424C23—48no—
425C23—44no—
426C23—416no—
427C23—84no—
428C23—84no—
429C23—88no—
430C23C4×D4×C11116yescomplemented
431C23C23×C4×C1118yes—
432C23C23×C4×C1114yes—
433C23C23×C4×C1112yes—
434C23C22×D4×C1112yes—
435C23C22×D4×C1114yes—
436C23C2×C11×#4114yes—
437C23C2×C11×#4112yes—
438C23C25×C1111yescharacteristic
439D4—232no—
440D4—232no—
441D4—416no—
442C2×C4—28no—
443C2×C4—216no—
444C2×C4—24no—
445C2×C4—22no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—22no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—28no—
453C2×C4—22no—
454C2×C4—28no—
455C2×C4—24no—
456C2×C4—28no—
457C2×C4—48no—
458C2×C4—48no—
459C2×C4—416no—
460C2×C4—44no—
461C2×C4—816no—
462C2×C4—88no—
463C2×C4C23×C4×C1118yes—
464C2×C4C23×C4×C1118yes—
465C2×C4C22×D4×C1118yes—
466C2×C4C11×H(5,𝔽2)14yes—
467C22—24no—
468C22—28no—
469C22—22no—
470C22—24no—
471C22—24no—
472C22—22no—
473C22—24no—
474C22—28no—
475C22—28no—
476C22—216no—
477C22—416no—
478C22—44no—
479C22—44no—
480C22—48no—
481C22—816no—
482C22C2×C4×D4×C1118yes—
483C22C2×C4×D4×C1114yes—
484C22C24×C4×C1111yescharacteristic
485C22C23×D4×C1111yescharacteristic
486C22C22×C11×#4111yescharacteristic
487C22C2×C11×H(5,𝔽2)12yes—
488C22C11×#58512yes—
489C4—28no—
490C4—28no—
491C4—24no—
492C4—28no—
493C4—42no—
494C4—48no—
495C2—28no—
496C2—24no—
497C2—48no—
498C2C22×C4×D4×C1111yescharacteristic
499C2C4×C11×H(5,𝔽2)12yes—
500C2C11×#349011yescharacteristic
501C2C11×#349111yescharacteristic
502C2C11×#349612yes—
subgroupG/H
center, socleC23×C11C25
commutatorC22C24×C4×C11
Frattini, cosocleC23C25×C11
prime radicalC2×C11×#534C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#518C2semidirect
3. C11×#2359C2semidirect
4. C11×#2358C2semidirect
5. C11×#2325C2semidirect
6. C11×#2315C2semidirect
7. C4×C11×#121C2semidirect
8. C2×C11×#386C2semidirect
9. C2×C4×C11×C22⋊C4C2semidirect
12. C11×#534C4semidirect
18. C2×C4×D4×C11C22semidirect
19. C2×C4×D4×C11C22semidirect
20. C2×C11×#117C22semidirect
24. C22×C11×C22⋊C4C22semidirect
25. C22×C11×C22⋊C4C22semidirect
26. C22×C42×C11C22semidirect
27. C11×#390C22semidirect
28. C11×#389C22semidirect
29. C11×#388C22semidirect
30. C11×#388C22semidirect
31. C11×#387C22semidirect
33. C11×#386C22semidirect
34. C11×#386C22semidirect
35. C11×#386C22semidirect
36. C11×#385C22semidirect
37. C11×#385C22semidirect
38. C11×#380C22semidirect
39. C4×C11×C4⋊C4C22semidirect
40. C4×C11×C22⋊C4C22semidirect
41. C4×C11×C22⋊C4C22semidirect
42. C2×C11×#95C22semidirect
43. C2×C11×#95C22semidirect
48. C22×D4×C11C2×C4semidirect
62. C11×#123C2×C4semidirect
63. C11×#121C2×C4semidirect
64. C11×#120C2×C4semidirect
76. C2×C11×C22⋊C4C2×C4semidirect
77. C2×C11×C22⋊C4D4semidirect
94. #34273C11direct (N × H)
117. C2×D4×C11C22×C4semidirect
150. C11×C4⋊C4C22×C4semidirect
157. C11×C22⋊C4C22×C4semidirect
163. C2×#518C2×C11semidirect
164. #2359C2×C11semidirect
165. #2358C2×C11semidirect
166. #2325C2×C11semidirect
167. #2315C2×C11semidirect
168. C4×#121C2×C11semidirect
169. C2×#386C2×C11semidirect
170. C2×C4×C22⋊C4C2×C11semidirect
188. C23×C11C4×D4semidirect
227. #534C4×C11semidirect
233. C2×C4×D4C22×C11semidirect
234. C2×C4×D4C22×C11semidirect
235. C2×#117C22×C11semidirect
239. C22×C22⋊C4C22×C11semidirect
240. C22×C22⋊C4C22×C11semidirect
241. C22×C42C22×C11semidirect
242. #390C22×C11semidirect
243. #389C22×C11semidirect
244. #388C22×C11semidirect
245. #388C22×C11semidirect
246. #387C22×C11semidirect
248. #386C22×C11semidirect
249. #386C22×C11semidirect
250. #386C22×C11semidirect
251. #385C22×C11semidirect
252. #385C22×C11semidirect
253. #380C22×C11semidirect
254. C4×C4⋊C4C22×C11semidirect
255. C4×C22⋊C4C22×C11semidirect
256. C4×C22⋊C4C22×C11semidirect
257. C2×#95C22×C11semidirect
258. C2×#95C22×C11semidirect
291. C22×D4C2×C4×C11semidirect
305. #123C2×C4×C11semidirect
306. #121C2×C4×C11semidirect
307. #120C2×C4×C11semidirect
319. C2×C22⋊C4C2×C4×C11semidirect
320. C2×C22⋊C4D4×C11semidirect
367. C2×D4C22×C4×C11semidirect
400. C4⋊C4C22×C4×C11semidirect
407. C22⋊C4C22×C4×C11semidirect
412. C11#34273direct (N × H)
430. C23C4×D4×C11semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5342
C2×C11×#5182
C11×#23592
C11×#23582
C11×#23252
C11×#23152
C4×C11×#1212
C2×C11×#3862
C2×C4×C11×C22⋊C42
#3427311