Finite Group Databasebeta

← C11×#24608 #14601801

Subgroups — C11×#24608 #14601801

Order 2816.

922 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#480C211yesmaximal, characteristic
2C2×C11×#432C211yesmaximal, characteristic, complemented
3C11×#2854C211yesmaximal, characteristic
4C2×C11×#389C211yesmaximal, characteristic, complemented
5C11×#2087C212yesmaximal, complemented
6C11×#2065C212yesmaximal, complemented
7C11×#1944C212yesmaximal, complemented
8C11×#1936C212yesmaximal, complemented
9C11×#1874C211yesmaximal, characteristic
10C11×#1853C211yesmaximal, characteristic, complemented
11C11×#1823C211yesmaximal, characteristic, complemented
12C2×C11×#123—21no—
13C2×C11×#121C2211yescharacteristic
14C22×C11×C4⋊C4—21no—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C11×#480—24no—
19C11×#432—24no—
20C2×C11×#107C2212yes—
21C2×C11×#106C2212yes—
22C2×C11×C4⋊C8C2212yes—
23C2×C11×#102C2212yes—
24C2×C11×#102C2212yes—
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C2×C11×#97C2212yes—
28C11×#390C2211yescharacteristic
29C11×#390C2211yescharacteristic
30C11×#389—21no—
31C11×#389—21no—
32C11×#389C2212yes—
33C11×#389C2211yescharacteristic
34C11×#389C2212yes—
35C11×#389C2211yescharacteristic
36C11×#388—21no—
37C11×#388—21no—
38C11×#386—21no—
39C11×#380C2211yescharacteristic
40C2×C11×#95—21no—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C22×D4×C11—21no—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11—21no—
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D411yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C22×C8×C11C2312yes—
53C22×C8×C11C2312yes—
54C11×#123—44no—
55C11×#121—22no—
56C11×#121—22no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—24no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—44no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C42×C11—22no—
79C2×C42×C11—22no—
80C2×C42×C11D411yescharacteristic
81C2×C42×C11D411yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C11×#107—24no—
85C11×#106—24no—
86C11×C4⋊C8—24no—
87C11×#102—24no—
88C11×#102—24no—
89C11×C22⋊C8—22no—
90C11×C22⋊C8D414yes—
91C11×#97—24no—
92C11×#95—22no—
93C11×#95—22no—
94C11×#95—21no—
95C11×#95—21no—
96C11×#95—21no—
97#24608C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11—21no—
99C24×C11C2×D411yescharacteristic
100C2×D4×C11—21no—
101C2×D4×C11—22no—
102C2×D4×C11—21no—
103C2×D4×C11—22no—
104C2×D4×C11—42no—
105C2×D4×C11—42no—
106C2×D4×C11—42no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—24no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—41no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11#4112yes—
133C22×C4×C11C2411yescharacteristic
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11C2×D414yes—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—44no—
149C11×C4⋊C4—44no—
150C11×C4⋊C4—42no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4—42no—
153C11×C4⋊C4#4114yes—
154C11×C22⋊C4—42no—
155C11×C22⋊C4—42no—
156C11×C22⋊C4—42no—
157C11×C22⋊C4—42no—
158C11×C22⋊C4—42no—
159C11×C22⋊C4—42no—
160C42×C11—22no—
161C42×C11—22no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—21no—
166C2×#480C2×C1111yescharacteristic
167C2×#432C2×C1111yescharacteristic, complemented
168#2854C2×C1111yescharacteristic
169C2×#389C2×C1111yescharacteristic, complemented
170#2087C2×C1112yescomplemented
171#2065C2×C1112yescomplemented
172#1944C2×C1112yescomplemented
173#1936C2×C1112yescomplemented
174#1874C2×C1111yescharacteristic
175#1853C2×C1111yescharacteristic, complemented
176#1823C2×C1111yescharacteristic, complemented
177C23×C11—21no—
178C23×C11—21no—
179C23×C11—21no—
180C23×C11—21no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11—41no—
187C23×C11—41no—
188C23×C11#12112yes—
189C23×C11AGL(1,ℤ/8)12yes—
190C23×C11AGL(1,ℤ/8)12yes—
191C23×C11C22×D411yescharacteristic
192D4×C11—42no—
193D4×C11—42no—
194D4×C11—84no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—24no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—44no—
212C2×C4×C11—48no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—44no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—42no—
223C2×C4×C11—41no—
224C2×C4×C11—42no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—84no—
229C2×C4×C11#12112yes—
230C2×C4×C11#13712yes—
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C2×#4112yes—
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C112−1+412yes—
235C8×C11—24no—
236C8×C11—42no—
237C2×#123—21no—
238C2×#121C22×C1111yescharacteristic
239C22×C4⋊C4—21no—
240C22×C4⋊C4C22×C1111yescharacteristic
241C22×C4⋊C4C22×C1111yescharacteristic
242C22×C42C22×C1111yescharacteristic
243#480—24no—
244#432—24no—
245C2×#107C22×C1112yes—
246C2×#106C22×C1112yes—
247C2×C4⋊C8C22×C1112yes—
248C2×#102C22×C1112yes—
249C2×#102C22×C1112yes—
250C2×C22⋊C8C22×C1111yescharacteristic
251C2×C22⋊C8C22×C1111yescharacteristic
252C2×#97C22×C1112yes—
253#390C22×C1111yescharacteristic
254#390C22×C1111yescharacteristic
255#389—21no—
256#389—21no—
257#389C22×C1112yes—
258#389C22×C1111yescharacteristic
259#389C22×C1111yescharacteristic
260#389C22×C1112yes—
261#388—21no—
262#388—21no—
263#386—21no—
264#380C22×C1111yescharacteristic
265C2×#95—21no—
266#340C22×C1112yes—
267#340C22×C1112yes—
268#340C22×C1112yes—
269#340C22×C1112yes—
270C22×C11—22no—
271C22×C11—22no—
272C22×C11—22no—
273C22×C11—22no—
274C22×C11—22no—
275C22×C11—22no—
276C22×C11—81no—
277C22×C11—81no—
278C22×C11—81no—
279C22×C11—81no—
280C22×C11—81no—
281C22×C11—81no—
282C22×C11—81no—
283C22×C11#46914yes—
284C22×C11C2×#12111yescharacteristic
285C22×C11#52511yescharacteristic
286C22×C11#53611yescharacteristic
287C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
288C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
289C22×C11C2×#13711yescharacteristic
290C22×C11#57511yescharacteristic
291C4×C11—22no—
292C4×C11—22no—
293C4×C11—44no—
294C4×C11—41no—
295C4×C11—41no—
296C4×C11—41no—
297C4×C11—81no—
298C4×C11—81no—
299C4×C11—82no—
300C4×C11—81no—
301C4×C11#54712yes—
302C4×C11#55212yes—
303C22×D4—21no—
304C22×D4C23×C1111yescharacteristic
305C23×C4—21no—
306C23×C4—21no—
307C23×C4D4×C1111yescharacteristic
308C23×C4D4×C1111yescharacteristic
309C23×C4C23×C1111yescharacteristic
310C22×C8C23×C1112yes—
311C22×C8C23×C1112yes—
312#123—44no—
313#121—22no—
314#121—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4C23×C1112yes—
326C2×C4⋊C4C23×C1111yescharacteristic
327C2×C4⋊C4C23×C1111yescharacteristic
328C2×C4⋊C4C23×C1111yescharacteristic
329C2×C4⋊C4C23×C1112yes—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C42—22no—
337C2×C42—22no—
338C2×C42D4×C1111yescharacteristic
339C2×C42D4×C1111yescharacteristic
340C2×C42C23×C1111yescharacteristic
341C2×C42C23×C1111yescharacteristic
342#107—24no—
343#106—24no—
344C4⋊C8—24no—
345#102—24no—
346#102—24no—
347C22⋊C8—22no—
348C22⋊C8D4×C1114yes—
349#97—24no—
350#95—22no—
351#95—22no—
352#95—21no—
353#95—21no—
354#95—21no—
355C2×C11—24no—
356C2×C11—161no—
357C2×C11#241311yescharacteristic
358C2×C11C2×#46911yescharacteristic
359C2×C11#305611yescharacteristic
360C2×C11#311211yescharacteristic
361C2×C11#311411yescharacteristic
362C2×C11#323411yescharacteristic
363C2×C11#323811yescharacteristic
364C24—21no—
365C24C2×D4×C1111yescharacteristic
366C2×D4—21no—
367C2×D4—22no—
368C2×D4—21no—
369C2×D4—22no—
370C2×D4—42no—
371C2×D4—42no—
372C2×D4—42no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—24no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—41no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4C2×D4×C1111yescharacteristic
393C22×C4C2×D4×C1111yescharacteristic
394C22×C4C2×D4×C1111yescharacteristic
395C22×C4C2×D4×C1111yescharacteristic
396C22×C4C2×D4×C1112yes—
397C22×C4C2×D4×C1111yescharacteristic
398C22×C4C11×#4112yes—
399C22×C4C24×C1111yescharacteristic
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8C2×D4×C1114yes—
406C4⋊C4—24no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—21no—
413C4⋊C4—22no—
414C4⋊C4—44no—
415C4⋊C4—44no—
416C4⋊C4—42no—
417C4⋊C4—42no—
418C4⋊C4—42no—
419C4⋊C4C11×#4114yes—
420C22⋊C4—42no—
421C22⋊C4—42no—
422C22⋊C4—42no—
423C22⋊C4—42no—
424C22⋊C4—42no—
425C22⋊C4—42no—
426C42—22no—
427C42—22no—
428C42—21no—
429C42—21no—
430C42—21no—
431C42—21no—
432C11#2460811yescharacteristic, direct product factor, Sylow
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23C11×#12112yes—
445C23C11×AGL(1,ℤ/8)12yes—
446C23C11×AGL(1,ℤ/8)12yes—
447C23C22×D4×C1111yescharacteristic
448D4—42no—
449D4—42no—
450D4—84no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—24no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—44no—
468C2×C4—48no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—44no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—84no—
485C2×C4C11×#12112yes—
486C2×C4C11×#13712yes—
487C2×C4C22×D4×C1111yescharacteristic
488C2×C4C2×C11×#4112yes—
489C2×C4C2×C11×#4111yescharacteristic
490C2×C4C11×2−1+412yes—
491C8—24no—
492C8—42no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22C11×#46914yes—
507C22C2×C11×#12111yescharacteristic
508C22C11×#52511yescharacteristic
509C22C11×#53611yescharacteristic
510C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
511C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
512C22C2×C11×#13711yescharacteristic
513C22C11×#57511yescharacteristic
514C4—22no—
515C4—22no—
516C4—41no—
517C4—41no—
518C4—41no—
519C4—44no—
520C4—81no—
521C4—82no—
522C4—81no—
523C4—81no—
524C4C11×#54712yes—
525C4C11×#55212yes—
526C2—24no—
527C2—161no—
528C2C11×#241311yescharacteristic
529C2C2×C11×#46911yescharacteristic
530C2C11×#305611yescharacteristic
531C2C11×#311211yescharacteristic
532C2C11×#311411yescharacteristic
533C2C11×#323411yescharacteristic
534C2C11×#323811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#432C2semidirect
4. C2×C11×#389C2semidirect
5. C11×#2087C2semidirect
6. C11×#2065C2semidirect
7. C11×#1944C2semidirect
8. C11×#1936C2semidirect
10. C11×#1853C2semidirect
11. C11×#1823C2semidirect
97. #24608C11direct (N × H)
167. C2×#432C2×C11semidirect
169. C2×#389C2×C11semidirect
170. #2087C2×C11semidirect
171. #2065C2×C11semidirect
172. #1944C2×C11semidirect
173. #1936C2×C11semidirect
175. #1853C2×C11semidirect
176. #1823C2×C11semidirect
432. C11#24608direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4802
C2×C11×#4322
C11×#28542
C2×C11×#3892
C11×#20872
C11×#20652
C11×#19442
C11×#19362
C11×#18742
C11×#18532
C11×#18232
#2460811