Finite Group Databasebeta

← C11×#24620 #14601813

Subgroups — C11×#24620 #14601813

Order 2816.

718 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
1C11×#3094C211yesmaximal, characteristic
2C2×C11×#480C211yesmaximal, characteristic
3C11×#2924C211yesmaximal, characteristic, complemented
4C2×C11×#428C211yesmaximal, characteristic, complemented
5C11×#2089C212yesmaximal, complemented
6C11×#2063C212yesmaximal, complemented
7C11×#1952C212yesmaximal, complemented
8C11×#1931C212yesmaximal, complemented
9C11×#1900C211yesmaximal, characteristic
10C11×#1855C211yesmaximal, characteristic, complemented
11C11×#1821C211yesmaximal, characteristic, complemented
12C22×C11×M16C2211yescharacteristic
13C2×C11×#121C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C11×#482—21no—
17C11×#482—21no—
18C11×#481—21no—
19C11×#480—21no—
20C11×#480—21no—
21C11×#480—21no—
22C11×#480—22no—
23C11×#433—22no—
24C11×#432—21no—
25C11×#431—21no—
26C2×C11×#108C2212yes—
27C11×#428—21no—
28C11×#428—21no—
29C11×#428C2212yes—
30C11×#428C2212yes—
31C11×#428C2211yescharacteristic
32C11×#428C2211yescharacteristic
33C2×C11×#107—21no—
34C2×C11×#107C2212yes—
35C2×C11×#106—21no—
36C11×#424C2212yes—
37C11×#418C2211yescharacteristic
38C11×#418C2211yescharacteristic
39C2×C11×#102C2212yes—
40C2×C11×#100C2212yes—
41C11×#407C2211yescharacteristic
42C11×#407C2211yescharacteristic
43C2×C11×C22⋊C8C2211yescharacteristic
44C11×#405C2212yes—
45C11×#343C2212yes—
46C11×#343C2212yes—
47C11×#343C2212yes—
48C11×#341C2212yes—
49C22×D4×C11—21no—
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11C2311yescharacteristic
53C2×C11×M16—21no—
54C2×C11×M16—24no—
55C2×C11×M16C2311yescharacteristic
56C2×C11×M16C2312yes—
57C2×C11×M16C2311yescharacteristic
58C2×C11×M16C2312yes—
59C22×C8×C11—21no—
60C22×C8×C11C2312yes—
61C11×#121—21no—
62C11×#121—21no—
63C11×#121—21no—
64C11×#121—21no—
65C11×#117—21no—
66C11×#117—21no—
67C11×#117D411yescharacteristic
68C11×#117D411yescharacteristic
69C11×#117C2311yescharacteristic
70C11×#117C2311yescharacteristic
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C42×C11—21no—
83C11×#108—24no—
84C11×#107—22no—
85C11×#107—22no—
86C11×#107—22no—
87C11×#107—22no—
88C11×#107—21no—
89C11×#107—21no—
90C11×#106—22no—
91C11×#106—22no—
92C11×#106—21no—
93C11×#106—21no—
94C11×C4⋊C8—22no—
95C11×C4⋊C8—22no—
96C11×#102—22no—
97C11×#102—22no—
98C11×#102—21no—
99C11×#102—21no—
100C11×#102—21no—
101C11×#102—21no—
102C11×#100—24no—
103C11×C22⋊C8—21no—
104C11×C22⋊C8—21no—
105C11×C22⋊C8—21no—
106C11×C22⋊C8—21no—
107C11×C22⋊C8D411yescharacteristic
108C11×C22⋊C8D411yescharacteristic
109C11×C22⋊C8D412yes—
110C11×#97—22no—
111C4×C8×C11—22no—
112#24620C1111yesmaximal, characteristic, direct product factor, Sylow
113C24×C11—21no—
114C24×C11#4111yescharacteristic
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—41no—
120C2×D4×C11—41no—
121C2×D4×C11—82no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—41no—
129C22×C4×C11—41no—
130C22×C4×C11—82no—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11#4111yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C11×M16—24no—
138C11×M16—22no—
139C11×M16—22no—
140C11×M16—22no—
141C11×M16—22no—
142C11×M16—22no—
143C11×M16#4114yes—
144C2×C8×C11—24no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11C2×D412yes—
152C2×C8×C11C2×D412yes—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—41no—
160C11×C4⋊C4—41no—
161C11×C4⋊C4C2×D411yescharacteristic
162C11×C4⋊C4C2×D411yescharacteristic
163C11×C4⋊C4C2×D411yescharacteristic
164C11×C4⋊C4C2×D411yescharacteristic
165C11×C22⋊C4—21no—
166C11×C22⋊C4—21no—
167C11×C22⋊C4—21no—
168C11×C22⋊C4—21no—
169C11×C22⋊C4—41no—
170C11×C22⋊C4—41no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175#3094C2×C1111yescharacteristic
176C2×#480C2×C1111yescharacteristic
177#2924C2×C1111yescharacteristic, complemented
178C2×#428C2×C1111yescharacteristic, complemented
179#2089C2×C1112yescomplemented
180#2063C2×C1112yescomplemented
181#1952C2×C1112yescomplemented
182#1931C2×C1112yescomplemented
183#1900C2×C1111yescharacteristic
184#1855C2×C1111yescharacteristic, complemented
185#1821C2×C1111yescharacteristic, complemented
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—42no—
191C23×C11—81no—
192C23×C11—81no—
193C23×C11#12111yescharacteristic
194C23×C11#12111yescharacteristic
195C23×C11C2×#4111yescharacteristic
196D4×C11—41no—
197D4×C11—41no—
198D4×C11—42no—
199D4×C11—82no—
200D4×C11—82no—
201C2×C4×C11—22no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—81no—
216C2×C4×C11—82no—
217C2×C4×C11—82no—
218C2×C4×C11—82no—
219C2×C4×C11—81no—
220C2×C4×C11#12111yescharacteristic
221C2×C4×C11#12111yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C2×#4112yes—
225C2×C4×C112−1+412yes—
226C8×C11—24no—
227C8×C11—22no—
228C8×C11—22no—
229C8×C11—41no—
230C8×C11—41no—
231C8×C11—42no—
232C22×M16C22×C1111yescharacteristic
233C2×#121C22×C1111yescharacteristic
234C2×#117C22×C1111yescharacteristic
235C22×C4⋊C4C22×C1111yescharacteristic
236#482—21no—
237#482—21no—
238#481—21no—
239#480—21no—
240#480—21no—
241#480—21no—
242#480—22no—
243#433—22no—
244#432—21no—
245#431—21no—
246C2×#108C22×C1112yes—
247#428—21no—
248#428—21no—
249#428C22×C1112yes—
250#428C22×C1111yescharacteristic
251#428C22×C1111yescharacteristic
252#428C22×C1112yes—
253C2×#107—21no—
254C2×#107C22×C1112yes—
255C2×#106—21no—
256#424C22×C1112yes—
257#418C22×C1111yescharacteristic
258#418C22×C1111yescharacteristic
259C2×#102C22×C1112yes—
260C2×#100C22×C1112yes—
261#407C22×C1111yescharacteristic
262#407C22×C1111yescharacteristic
263C2×C22⋊C8C22×C1111yescharacteristic
264#405C22×C1112yes—
265#343C22×C1112yes—
266#343C22×C1112yes—
267#343C22×C1112yes—
268#341C22×C1112yes—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—21no—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11—21no—
276C22×C11—44no—
277C22×C11—81no—
278C22×C11—81no—
279C22×C11—81no—
280C22×C11—162no—
281C22×C11#47212yes—
282C22×C11C2×#12111yescharacteristic
283C22×C11#55212yes—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—41no—
287C4×C11—41no—
288C4×C11—41no—
289C4×C11—41no—
290C4×C11—82no—
291C4×C11—81no—
292C4×C11#52511yescharacteristic
293C4×C11#53611yescharacteristic
294C4×C11#54712yes—
295C22×D4—21no—
296C22×D4C23×C1111yescharacteristic
297C23×C4—21no—
298C23×C4C23×C1111yescharacteristic
299C2×M16—21no—
300C2×M16—24no—
301C2×M16C23×C1111yescharacteristic
302C2×M16C23×C1112yes—
303C2×M16C23×C1111yescharacteristic
304C2×M16C23×C1112yes—
305C22×C8—21no—
306C22×C8C23×C1112yes—
307#121—21no—
308#121—21no—
309#121—21no—
310#121—21no—
311#117—21no—
312#117—21no—
313#117D4×C1111yescharacteristic
314#117D4×C1111yescharacteristic
315#117C23×C1111yescharacteristic
316#117C23×C1111yescharacteristic
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4D4×C1111yescharacteristic
323C2×C4⋊C4D4×C1111yescharacteristic
324C2×C4⋊C4C23×C1112yes—
325C2×C4⋊C4C23×C1111yescharacteristic
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C42—21no—
329#108—24no—
330#107—22no—
331#107—22no—
332#107—22no—
333#107—22no—
334#107—21no—
335#107—21no—
336#106—22no—
337#106—22no—
338#106—21no—
339#106—21no—
340C4⋊C8—22no—
341C4⋊C8—22no—
342#102—22no—
343#102—22no—
344#102—21no—
345#102—21no—
346#102—21no—
347#102—21no—
348#100—24no—
349C22⋊C8—21no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8D4×C1111yescharacteristic
354C22⋊C8D4×C1111yescharacteristic
355C22⋊C8D4×C1112yes—
356#97—22no—
357C4×C8—22no—
358C2×C11—22no—
359C2×C11—22no—
360C2×C11—41no—
361C2×C11—161no—
362C2×C11#241311yescharacteristic
363C2×C11C2×#47211yescharacteristic
364C2×C11#306911yescharacteristic
365C24—21no—
366C24C11×#4111yescharacteristic
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—82no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—82no—
383C22×C4C2×D4×C1111yescharacteristic
384C22×C4C2×D4×C1111yescharacteristic
385C22×C4C2×D4×C1111yescharacteristic
386C22×C4C2×D4×C1111yescharacteristic
387C22×C4C11×#4111yescharacteristic
388C22×C4C24×C1111yescharacteristic
389M16—24no—
390M16—22no—
391M16—22no—
392M16—22no—
393M16—22no—
394M16—22no—
395M16C11×#4114yes—
396C2×C8—24no—
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8C2×D4×C1112yes—
404C2×C8C2×D4×C1112yes—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—41no—
412C4⋊C4—41no—
413C4⋊C4C2×D4×C1111yescharacteristic
414C4⋊C4C2×D4×C1111yescharacteristic
415C4⋊C4C2×D4×C1111yescharacteristic
416C4⋊C4C2×D4×C1111yescharacteristic
417C22⋊C4—21no—
418C22⋊C4—21no—
419C22⋊C4—21no—
420C22⋊C4—21no—
421C22⋊C4—41no—
422C22⋊C4—41no—
423C42—21no—
424C42—21no—
425C42—21no—
426C42—21no—
427C11#2462011yescharacteristic, direct product factor, Sylow
428C23—22no—
429C23—22no—
430C23—41no—
431C23—41no—
432C23—42no—
433C23—81no—
434C23—81no—
435C23C11×#12111yescharacteristic
436C23C11×#12111yescharacteristic
437C23C2×C11×#4111yescharacteristic
438D4—41no—
439D4—41no—
440D4—42no—
441D4—82no—
442D4—82no—
443C2×C4—22no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—81no—
458C2×C4—82no—
459C2×C4—82no—
460C2×C4—82no—
461C2×C4—81no—
462C2×C4C11×#12111yescharacteristic
463C2×C4C11×#12111yescharacteristic
464C2×C4C22×D4×C1111yescharacteristic
465C2×C4C22×D4×C1111yescharacteristic
466C2×C4C2×C11×#4112yes—
467C2×C4C11×2−1+412yes—
468C8—24no—
469C8—22no—
470C8—22no—
471C8—41no—
472C8—41no—
473C8—42no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—44no—
482C22—81no—
483C22—81no—
484C22—81no—
485C22—162no—
486C22C11×#47212yes—
487C22C2×C11×#12111yescharacteristic
488C22C11×#55212yes—
489C4—21no—
490C4—21no—
491C4—41no—
492C4—41no—
493C4—41no—
494C4—41no—
495C4—82no—
496C4—81no—
497C4C11×#52511yescharacteristic
498C4C11×#53611yescharacteristic
499C4C11×#54712yes—
500C2—22no—
501C2—22no—
502C2—41no—
503C2—161no—
504C2C11×#241311yescharacteristic
505C2C2×C11×#47211yescharacteristic
506C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2924C2semidirect
4. C2×C11×#428C2semidirect
5. C11×#2089C2semidirect
6. C11×#2063C2semidirect
7. C11×#1952C2semidirect
8. C11×#1931C2semidirect
10. C11×#1855C2semidirect
11. C11×#1821C2semidirect
112. #24620C11direct (N × H)
177. #2924C2×C11semidirect
178. C2×#428C2×C11semidirect
179. #2089C2×C11semidirect
180. #2063C2×C11semidirect
181. #1952C2×C11semidirect
182. #1931C2×C11semidirect
184. #1855C2×C11semidirect
185. #1821C2×C11semidirect
427. C11#24620direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30942
C2×C11×#4802
C11×#29242
C2×C11×#4282
C11×#20892
C11×#20632
C11×#19522
C11×#19312
C11×#19002
C11×#18552
C11×#18212
#2462011