Finite Group Databasebeta

← C11×#24744 #14601937

Subgroups — C11×#24744 #14601937

Order 2816.

1180 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#459C212yesmaximal, complemented
2C2×C11×#459C211yesmaximal, characteristic, complemented
3C2×C11×#442C211yesmaximal, characteristic, complemented
4C11×#2541C211yesmaximal, characteristic, complemented
5C11×#2349C211yesmaximal, characteristic, complemented
6C11×#2065C212yesmaximal, complemented
7C11×#2041C212yesmaximal, complemented
8C11×#1961C211yesmaximal, characteristic, complemented
9C11×#1940C211yesmaximal, characteristic, complemented
10C11×#1879C212yesmaximal, complemented
11C11×#1804C211yesmaximal, characteristic, complemented
12C22×C11×D8C2212yes—
13C22×C11×D8C2211yescharacteristic
14C2×C11×#127C2211yescharacteristic
15C2×C11×#127C2212yes—
16C2×C11×#121—22no—
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2212yes—
19C2×C4×D4×C11C2211yescharacteristic
20C11×#459—28no—
21C11×#459—24no—
22C11×#442—24no—
23C2×C11×#106C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2212yes—
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2212yes—
29C2×C11×#102C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×#102C2212yes—
32C2×C11×#97C2211yescharacteristic
33C11×#392—21no—
34C11×#392—21no—
35C11×#390C2212yes—
36C11×#389C2212yes—
37C11×#385—22no—
38C11×#382C2211yescharacteristic
39C11×#380—21no—
40C4×C11×C4⋊C4C2211yescharacteristic
41C2×C11×#95—21no—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C22×D4×C11—21no—
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11—21no—
48C22×D4×C11C2312yes—
49C22×D4×C11C2311yescharacteristic
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11—21no—
53C23×C4×C11—22no—
54C2×C11×D8—22no—
55C2×C11×D8—22no—
56C2×C11×D8—24no—
57C2×C11×D8—24no—
58C2×C11×D8—24no—
59C2×C11×D8D414yescomplemented
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2312yes—
62C22×C8×C11C2311yescharacteristic
63C11×#127—24no—
64C11×#127—22no—
65C11×#127—22no—
66C11×#127—42no—
67C11×#121—48no—
68C4×D4×C11—24no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11—42no—
73C4×D4×C11D414yescomplemented
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4D412yes—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C42×C11C2312yes—
85C2×C42×C11C2311yescharacteristic
86C11×#106—22no—
87C11×C4⋊C8—24no—
88C11×C4⋊C8—22no—
89C11×#102—22no—
90C11×#102—24no—
91C11×#102—24no—
92C11×#102—22no—
93C11×#102—24no—
94C11×#102—42no—
95C11×#97—22no—
96C11×#95—21no—
97C11×#95—22no—
98C11×#95—21no—
99C11×#95D411yescharacteristic
100C11×#95D411yescharacteristic
101#24744C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11—21no—
103C24×C11—21no—
104C24×C11—22no—
105C2×D4×C11—21no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—22no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—22no—
119C2×D4×C11—44no—
120C2×D4×C11—44no—
121C2×D4×C11—44no—
122C2×D4×C11—44no—
123C2×D4×C11—42no—
124C2×D4×C11—42no—
125C2×D4×C11—44no—
126C2×D4×C11—82no—
127C2×D4×C11—82no—
128C2×D4×C11—82no—
129C2×D4×C11C2×D412yes—
130C2×D4×C11C2×D412yes—
131C2×D4×C11C2×D412yes—
132C2×D4×C11#4112yes—
133C22×C4×C11—21no—
134C22×C4×C11—24no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—44no—
138C22×C4×C11—44no—
139C22×C4×C11—42no—
140C22×C4×C11—44no—
141C22×C4×C11—82no—
142C22×C4×C11—82no—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2411yescharacteristic
148C11×D8—28no—
149C11×D8—48no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—21no—
155C2×C8×C11—22no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11C2×D412yes—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—82no—
166C11×C4⋊C4C2×D412yes—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—44no—
169C11×C22⋊C4—44no—
170C11×C22⋊C4—42no—
171C11×C22⋊C4—44no—
172C42×C11—22no—
173C42×C11—22no—
174C42×C11C2×D412yes—
175C42×C11#4112yes—
176C2×#459C2×C1112yescomplemented
177C2×#459C2×C1111yescharacteristic, complemented
178C2×#442C2×C1111yescharacteristic, complemented
179#2541C2×C1111yescharacteristic, complemented
180#2349C2×C1111yescharacteristic, complemented
181#2065C2×C1112yescomplemented
182#2041C2×C1112yescomplemented
183#1961C2×C1111yescharacteristic, complemented
184#1940C2×C1111yescharacteristic, complemented
185#1879C2×C1112yescomplemented
186#1804C2×C1111yescharacteristic, complemented
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11C22×D411yescharacteristic
205D4×C11—22no—
206D4×C11—22no—
207D4×C11—22no—
208D4×C11—22no—
209D4×C11—22no—
210D4×C11—42no—
211D4×C11—41no—
212D4×C11—42no—
213D4×C11—42no—
214D4×C11—41no—
215D4×C11—42no—
216D4×C11—88no—
217D4×C11—84no—
218D4×C11—84no—
219D4×C11—88no—
220D4×C11#12114yescomplemented
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—42no—
230C2×C4×C11—41no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—84no—
236C2×C4×C11—88no—
237C2×C4×C11—84no—
238C2×C4×C11#12112yes—
239C2×C4×C11#12112yes—
240C2×C4×C11AGL(1,ℤ/8)14yes—
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11H(5,𝔽2)11yescharacteristic
246C2×C4×C112−1+411yescharacteristic
247C8×C11—22no—
248C8×C11—42no—
249C8×C11—41no—
250C22×D8C22×C1112yes—
251C22×D8C22×C1111yescharacteristic
252C2×#127C22×C1111yescharacteristic
253C2×#127C22×C1112yes—
254C2×#121—22no—
255C2×C4×D4C22×C1111yescharacteristic
256C2×C4×D4C22×C1112yes—
257C2×C4×D4C22×C1111yescharacteristic
258#459—28no—
259#459—24no—
260#442—24no—
261C2×#106C22×C1111yescharacteristic
262C2×C4⋊C8C22×C1111yescharacteristic
263C2×C4⋊C8C22×C1112yes—
264C2×#102C22×C1112yes—
265C2×#102C22×C1112yes—
266C2×#102C22×C1112yes—
267C2×#102C22×C1111yescharacteristic
268C2×#102C22×C1111yescharacteristic
269C2×#102C22×C1112yes—
270C2×#97C22×C1111yescharacteristic
271#392—21no—
272#392—21no—
273#390C22×C1112yes—
274#389C22×C1112yes—
275#385—22no—
276#382C22×C1111yescharacteristic
277#380—21no—
278C4×C4⋊C4C22×C1111yescharacteristic
279C2×#95—21no—
280#340C22×C1112yes—
281#336C22×C1112yes—
282C22×C11—24no—
283C22×C11—44no—
284C22×C11—44no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—44no—
289C22×C11—82no—
290C22×C11—81no—
291C22×C11—81no—
292C22×C11—82no—
293C22×C11—82no—
294C22×C11—82no—
295C22×C11—82no—
296C22×C11—82no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11C2×#12111yescharacteristic
300C22×C11D4211yescharacteristic
301C22×C11#54811yescharacteristic
302C22×C11C2×AGL(1,ℤ/8)12yes—
303C22×C11#57612yes—
304C4×C11—24no—
305C4×C11—22no—
306C4×C11—22no—
307C4×C11—42no—
308C4×C11—42no—
309C4×C11—82no—
310C4×C11—81no—
311C4×C11C2×#12111yescharacteristic
312C4×C11#53711yescharacteristic
313C4×C11#54711yescharacteristic
314C4×C11#55311yescharacteristic
315C22×D4—21no—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—21no—
319C22×D4C23×C1112yes—
320C22×D4C23×C1111yescharacteristic
321C22×D4C23×C1111yescharacteristic
322C23×C4—21no—
323C23×C4—21no—
324C23×C4—22no—
325C2×D8—22no—
326C2×D8—22no—
327C2×D8—24no—
328C2×D8—24no—
329C2×D8—24no—
330C2×D8D4×C1114yescomplemented
331C22×C8C23×C1112yes—
332C22×C8C23×C1111yescharacteristic
333C22×C8C23×C1111yescharacteristic
334#127—24no—
335#127—22no—
336#127—22no—
337#127—42no—
338#121—48no—
339C4×D4—24no—
340C4×D4—22no—
341C4×D4—22no—
342C4×D4—22no—
343C4×D4—42no—
344C4×D4D4×C1114yescomplemented
345C2×C4⋊C4—22no—
346C2×C4⋊C4D4×C1112yes—
347C2×C4⋊C4C23×C1111yescharacteristic
348C2×C4⋊C4C23×C1112yes—
349C2×C4⋊C4C23×C1111yescharacteristic
350C2×C22⋊C4—21no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C42C23×C1112yes—
356C2×C42C23×C1111yescharacteristic
357#106—22no—
358C4⋊C8—24no—
359C4⋊C8—22no—
360#102—22no—
361#102—24no—
362#102—24no—
363#102—22no—
364#102—24no—
365#102—42no—
366#97—22no—
367#95—21no—
368#95—22no—
369#95—21no—
370#95D4×C1111yescharacteristic
371#95D4×C1111yescharacteristic
372C2×C11—44no—
373C2×C11—82no—
374C2×C11—162no—
375C2×C11#241611yescharacteristic
376C2×C11#303811yescharacteristic
377C2×C11#304111yescharacteristic
378C2×C11#326412yes—
379C2×C11#336612yes—
380C24—21no—
381C24—21no—
382C24—22no—
383C2×D4—21no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—22no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—22no—
397C2×D4—44no—
398C2×D4—44no—
399C2×D4—44no—
400C2×D4—44no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—44no—
404C2×D4—82no—
405C2×D4—82no—
406C2×D4—82no—
407C2×D4C2×D4×C1112yes—
408C2×D4C2×D4×C1112yes—
409C2×D4C2×D4×C1112yes—
410C2×D4C11×#4112yes—
411C22×C4—21no—
412C22×C4—24no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—44no—
416C22×C4—44no—
417C22×C4—42no—
418C22×C4—44no—
419C22×C4—82no—
420C22×C4—82no—
421C22×C4C2×D4×C1112yes—
422C22×C4C2×D4×C1111yescharacteristic
423C22×C4C2×D4×C1111yescharacteristic
424C22×C4C2×D4×C1112yes—
425C22×C4C24×C1111yescharacteristic
426D8—28no—
427D8—48no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8C2×D4×C1112yes—
437C4⋊C4—24no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—22no—
443C4⋊C4—82no—
444C4⋊C4C2×D4×C1112yes—
445C22⋊C4—24no—
446C22⋊C4—44no—
447C22⋊C4—44no—
448C22⋊C4—42no—
449C22⋊C4—44no—
450C42—22no—
451C42—22no—
452C42C2×D4×C1112yes—
453C42C11×#4112yes—
454C11#2474411yescharacteristic, direct product factor, Sylow
455C23—22no—
456C23—22no—
457C23—22no—
458C23—22no—
459C23—42no—
460C23—42no—
461C23—41no—
462C23—41no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23C22×D4×C1111yescharacteristic
473D4—22no—
474D4—22no—
475D4—22no—
476D4—22no—
477D4—22no—
478D4—42no—
479D4—41no—
480D4—42no—
481D4—42no—
482D4—41no—
483D4—42no—
484D4—88no—
485D4—84no—
486D4—84no—
487D4—88no—
488D4C11×#12114yescomplemented
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—84no—
504C2×C4—88no—
505C2×C4—84no—
506C2×C4C11×#12112yes—
507C2×C4C11×#12112yes—
508C2×C4C11×AGL(1,ℤ/8)14yes—
509C2×C4C22×D4×C1111yescharacteristic
510C2×C4C22×D4×C1111yescharacteristic
511C2×C4C2×C11×#4111yescharacteristic
512C2×C4C2×C11×#4111yescharacteristic
513C2×C4C11×H(5,𝔽2)11yescharacteristic
514C2×C4C11×2−1+411yescharacteristic
515C8—22no—
516C8—42no—
517C8—41no—
518C22—24no—
519C22—44no—
520C22—42no—
521C22—42no—
522C22—44no—
523C22—42no—
524C22—44no—
525C22—81no—
526C22—81no—
527C22—82no—
528C22—82no—
529C22—82no—
530C22—82no—
531C22—82no—
532C22—82no—
533C22—82no—
534C22—82no—
535C22C2×C11×#12111yescharacteristic
536C22D42×C1111yescharacteristic
537C22C11×#54811yescharacteristic
538C22C2×C11×AGL(1,ℤ/8)12yes—
539C22C11×#57612yes—
540C4—24no—
541C4—22no—
542C4—22no—
543C4—42no—
544C4—42no—
545C4—82no—
546C4—81no—
547C4C2×C11×#12111yescharacteristic
548C4C11×#53711yescharacteristic
549C4C11×#54711yescharacteristic
550C4C11×#55311yescharacteristic
551C2—44no—
552C2—82no—
553C2—162no—
554C2C11×#241611yescharacteristic
555C2C11×#303811yescharacteristic
556C2C11×#304111yescharacteristic
557C2C11×#326412yes—
558C2C11×#336612yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#459C2semidirect
2. C2×C11×#459C2semidirect
3. C2×C11×#442C2semidirect
4. C11×#2541C2semidirect
5. C11×#2349C2semidirect
6. C11×#2065C2semidirect
7. C11×#2041C2semidirect
8. C11×#1961C2semidirect
9. C11×#1940C2semidirect
10. C11×#1879C2semidirect
11. C11×#1804C2semidirect
59. C2×C11×D8D4semidirect
73. C4×D4×C11D4semidirect
101. #24744C11direct (N × H)
176. C2×#459C2×C11semidirect
177. C2×#459C2×C11semidirect
178. C2×#442C2×C11semidirect
179. #2541C2×C11semidirect
180. #2349C2×C11semidirect
181. #2065C2×C11semidirect
182. #2041C2×C11semidirect
183. #1961C2×C11semidirect
184. #1940C2×C11semidirect
185. #1879C2×C11semidirect
186. #1804C2×C11semidirect
220. D4×C11#121semidirect
330. C2×D8D4×C11semidirect
344. C4×D4D4×C11semidirect
454. C11#24744direct (N × H)
488. D4C11×#121semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4592
C2×C11×#4422
C11×#25412
C11×#23492
C11×#20652
C11×#20412
C11×#19612
C11×#19402
C11×#18792
C11×#18042
#2474411