Finite Group Databasebeta

← C11×#19168 #14596361

Subgroups — C11×#19168 #14596361

Order 2816.

696 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3141C211yesmaximal, characteristic, complemented
2C11×#3100C211yesmaximal, characteristic
3C2×C11×#476C211yesmaximal, characteristic, complemented
4D4×C11×M16C211yesmaximal, characteristic, complemented
5C11×#1703C212yesmaximal, complemented
6C11×#1697C212yesmaximal, complemented
7C11×#1683C212yesmaximal, complemented
8C11×#1677C212yesmaximal, complemented
9C11×#1565C211yesmaximal, characteristic, complemented
10C11×#1548C211yesmaximal, characteristic, complemented
11C11×#1547C211yesmaximal, characteristic, complemented
12C22×C11×M16—21no—
13C11×#532C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C11×#489—22no—
17C11×#487C2212yescomplemented
18C11×#486C2212yescomplemented
19C11×#480—21no—
20C11×#476—21no—
21C11×#476—21no—
22C11×#476C2212yes—
23C11×#476C2212yes—
24C11×#474C2211yescharacteristic
25C11×#474C2211yescharacteristic
26C11×#459C2211yescharacteristic
27C11×#459C2211yescharacteristic
28C11×#447—21no—
29C4×C11×D8—21no—
30C4×C11×D8—21no—
31C11×#436C2212yes—
32C11×#435—22no—
33C8×D4×C11C2212yes—
34C11×#431C2211yescharacteristic
35C2×C11×#106—21no—
36C11×#423C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C11×#417—21no—
39C11×#417—21no—
40C2×C11×#102—21no—
41C11×#407—21no—
42C4×C11×M16C2211yescharacteristic
43C11×#335C2212yescomplemented
44C11×#334C2212yescomplemented
45C11×#333C2212yescomplemented
46C11×#333C2212yescomplemented
47C11×#332C2212yescomplemented
48C11×#331C2212yescomplemented
49C2×C11×#41—21no—
50C22×Q8×C11—21no—
51C22×D4×C11D411yescharacteristic
52C23×C4×C11—21no—
53C2×C11×D8—21no—
54C2×C11×D8—21no—
55C2×C11×M16—21no—
56C2×C11×M16—22no—
57C2×C11×M16—44no—
58C2×C11×M16D411yescharacteristic
59C2×C11×M16D411yescharacteristic
60C22×C8×C11—21no—
61C22×C8×C11—22no—
62C11×C4⋊Q8—21no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8—21no—
65C11×C4⋊Q8C2311yescharacteristic
66C11×C4⋊Q8C2312yes—
67C11×#127C2311yescharacteristic
68C11×#124—21no—
69C11×#121—21no—
70C11×#121—21no—
71C4×D4×C11—21no—
72C4×D4×C11—21no—
73C4×D4×C11—21no—
74C4×D4×C11—21no—
75C4×D4×C11D411yescharacteristic
76C4×D4×C11D411yescharacteristic
77C4×D4×C11C2311yescharacteristic
78C4×D4×C11C2311yescharacteristic
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C42×C11C2311yescharacteristic
84C11×#107—21no—
85C11×#107—21no—
86C11×#106—22no—
87C11×#106—22no—
88C11×C4⋊C8—21no—
89C11×C4⋊C8—21no—
90C11×C4⋊C8C2312yes—
91C11×C4⋊C8C2312yes—
92C11×C4⋊C8C2311yescharacteristic
93C11×C4⋊C8C2311yescharacteristic
94C11×#103—22no—
95C11×#103—22no—
96C11×#102—22no—
97C11×#102—22no—
98C11×#102—21no—
99C11×#102—21no—
100C11×#102—22no—
101C11×#102—22no—
102C11×#102—21no—
103C11×#102—21no—
104C11×C22⋊C8—21no—
105C11×C22⋊C8—22no—
106C11×C22⋊C8—22no—
107C11×#97D412yes—
108C4×C8×C11—21no—
109C4×C8×C11C2312yes—
110#19168C1111yesmaximal, characteristic, direct product factor, Sylow
111C24×C11—21no—
112C11×#41—42no—
113C11×#41—42no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—41no—
117C2×Q8×C11—82no—
118C2×D4×C11—22no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—41no—
124C2×D4×C11—41no—
125C2×D4×C11C2×D411yescharacteristic
126C2×D4×C11C2×D411yescharacteristic
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11—41no—
135C22×C4×C11—41no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11#4111yescharacteristic
139C11×D8—42no—
140C11×D8—42no—
141C11×M16—22no—
142C11×M16—22no—
143C11×M16—44no—
144C11×M16—42no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—42no—
150C2×C8×C11—44no—
151C2×C8×C11C2×D412yes—
152C2×C8×C11C2×D412yes—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—41no—
159C11×C4⋊C4—41no—
160C11×C4⋊C4C2×D411yescharacteristic
161C11×C4⋊C4C2×D411yescharacteristic
162C11×C22⋊C4—21no—
163C11×C22⋊C4—21no—
164C11×C22⋊C4—21no—
165C11×C22⋊C4—21no—
166C11×C22⋊C4—41no—
167C11×C22⋊C4—41no—
168C42×C11C2×D411yescharacteristic
169C42×C11C2×D411yescharacteristic
170C42×C11#4111yescharacteristic
171C42×C11C2411yescharacteristic
172#3141C2×C1111yescharacteristic, complemented
173#3100C2×C1111yescharacteristic
174C2×#476C2×C1111yescharacteristic, complemented
175D4×M16C2×C1111yescharacteristic, complemented
176#1703C2×C1112yescomplemented
177#1697C2×C1112yescomplemented
178#1683C2×C1112yescomplemented
179#1677C2×C1112yescomplemented
180#1565C2×C1111yescharacteristic, complemented
181#1548C2×C1111yescharacteristic, complemented
182#1547C2×C1111yescharacteristic, complemented
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—42no—
186C23×C11—42no—
187C23×C11—41no—
188C23×C11—81no—
189C23×C11#12111yescharacteristic
190Q8×C11—41no—
191Q8×C11—41no—
192Q8×C11—82no—
193Q8×C11—82no—
194D4×C11—21no—
195D4×C11—21no—
196D4×C11—21no—
197D4×C11—42no—
198D4×C11—41no—
199D4×C11—41no—
200D4×C11—41no—
201D4×C11—41no—
202D4×C11—81no—
203D4×C11—82no—
204D4×C11#13712yes—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—82no—
220C2×C4×C11—82no—
221C2×C4×C11#12111yescharacteristic
222C2×C4×C11#12111yescharacteristic
223C2×C4×C11#12111yescharacteristic
224C2×C4×C11#13512yes—
225C2×C4×C11AGL(1,ℤ/8)12yes—
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C8×C11—22no—
230C8×C11—22no—
231C8×C11—42no—
232C8×C11—41no—
233C8×C11—42no—
234C8×C11—41no—
235C22×M16—21no—
236#532C22×C1111yescharacteristic
237C2×C4⋊Q8C22×C1111yescharacteristic
238C2×C4×D4C22×C1111yescharacteristic
239#489—22no—
240#487C22×C1112yescomplemented
241#486C22×C1112yescomplemented
242#480—21no—
243#476—21no—
244#476—21no—
245#476C22×C1112yes—
246#476C22×C1112yes—
247#474C22×C1111yescharacteristic
248#474C22×C1111yescharacteristic
249#459C22×C1111yescharacteristic
250#459C22×C1111yescharacteristic
251#447—21no—
252C4×D8—21no—
253C4×D8—21no—
254#436C22×C1112yes—
255#435—22no—
256C8×D4C22×C1112yes—
257#431C22×C1111yescharacteristic
258C2×#106—21no—
259#423C22×C1111yescharacteristic
260C2×C4⋊C8C22×C1111yescharacteristic
261#417—21no—
262#417—21no—
263C2×#102—21no—
264#407—21no—
265C4×M16C22×C1111yescharacteristic
266#335C22×C1112yescomplemented
267#334C22×C1112yescomplemented
268#333C22×C1112yescomplemented
269#333C22×C1112yescomplemented
270#332C22×C1112yescomplemented
271#331C22×C1112yescomplemented
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—22no—
275C22×C11—41no—
276C22×C11—41no—
277C22×C11—41no—
278C22×C11—41no—
279C22×C11—41no—
280C22×C11—84no—
281C22×C11—81no—
282C22×C11—81no—
283C22×C11—81no—
284C22×C11#46312yes—
285C22×C11C2×#12111yescharacteristic
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—41no—
290C4×C11—41no—
291C4×C11—81no—
292C4×C11—82no—
293C4×C11#46312yes—
294C4×C11C2×#13511yescharacteristic
295C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
296C4×C11C2×#13711yescharacteristic
297C4×C11#57511yescharacteristic
298C2×#41—21no—
299C22×Q8—21no—
300C22×D4D4×C1111yescharacteristic
301C23×C4—21no—
302C2×D8—21no—
303C2×D8—21no—
304C2×M16—21no—
305C2×M16—22no—
306C2×M16—44no—
307C2×M16D4×C1111yescharacteristic
308C2×M16D4×C1111yescharacteristic
309C22×C8—21no—
310C22×C8—22no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8C23×C1112yes—
315C4⋊Q8C23×C1111yescharacteristic
316#127C23×C1111yescharacteristic
317#124—21no—
318#121—21no—
319#121—21no—
320C4×D4—21no—
321C4×D4—21no—
322C4×D4—21no—
323C4×D4—21no—
324C4×D4D4×C1111yescharacteristic
325C4×D4D4×C1111yescharacteristic
326C4×D4C23×C1111yescharacteristic
327C4×D4C23×C1111yescharacteristic
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4D4×C1111yescharacteristic
331C2×C22⋊C4—21no—
332C2×C42C23×C1111yescharacteristic
333#107—21no—
334#107—21no—
335#106—22no—
336#106—22no—
337C4⋊C8—21no—
338C4⋊C8—21no—
339C4⋊C8C23×C1112yes—
340C4⋊C8C23×C1112yes—
341C4⋊C8C23×C1111yescharacteristic
342C4⋊C8C23×C1111yescharacteristic
343#103—22no—
344#103—22no—
345#102—22no—
346#102—22no—
347#102—21no—
348#102—21no—
349#102—22no—
350#102—22no—
351#102—21no—
352#102—21no—
353C22⋊C8—21no—
354C22⋊C8—22no—
355C22⋊C8—22no—
356#97D4×C1112yes—
357C4×C8—21no—
358C4×C8C23×C1112yes—
359C2×C11—22no—
360C2×C11—42no—
361C2×C11—81no—
362C2×C11—161no—
363C2×C11C2×#46311yescharacteristic
364C2×C11#305611yescharacteristic
365C2×C11#306811yescharacteristic
366C24—21no—
367#41—42no—
368#41—42no—
369C2×Q8—21no—
370C2×Q8—22no—
371C2×Q8—41no—
372C2×Q8—82no—
373C2×D4—22no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4C2×D4×C1111yescharacteristic
381C2×D4C2×D4×C1111yescharacteristic
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4C2×D4×C1111yescharacteristic
392C22×C4C2×D4×C1111yescharacteristic
393C22×C4C11×#4111yescharacteristic
394D8—42no—
395D8—42no—
396M16—22no—
397M16—22no—
398M16—44no—
399M16—42no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—44no—
405C2×C8—42no—
406C2×C8C2×D4×C1112yes—
407C2×C8C2×D4×C1112yes—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—41no—
414C4⋊C4—41no—
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—
423C42C2×D4×C1111yescharacteristic
424C42C2×D4×C1111yescharacteristic
425C42C11×#4111yescharacteristic
426C42C24×C1111yescharacteristic
427C11#1916811yescharacteristic, direct product factor, Sylow
428C23—21no—
429C23—21no—
430C23—42no—
431C23—42no—
432C23—41no—
433C23—81no—
434C23C11×#12111yescharacteristic
435Q8—41no—
436Q8—41no—
437Q8—82no—
438Q8—82no—
439D4—21no—
440D4—21no—
441D4—21no—
442D4—42no—
443D4—41no—
444D4—41no—
445D4—41no—
446D4—41no—
447D4—81no—
448D4—82no—
449D4C11×#13712yes—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—41no—
463C2×C4—42no—
464C2×C4—82no—
465C2×C4—82no—
466C2×C4C11×#12111yescharacteristic
467C2×C4C11×#12111yescharacteristic
468C2×C4C11×#12111yescharacteristic
469C2×C4C11×#13512yes—
470C2×C4C11×AGL(1,ℤ/8)12yes—
471C2×C4C22×D4×C1111yescharacteristic
472C2×C4C22×D4×C1111yescharacteristic
473C2×C4C2×C11×#4111yescharacteristic
474C8—22no—
475C8—22no—
476C8—42no—
477C8—41no—
478C8—42no—
479C8—41no—
480C22—21no—
481C22—21no—
482C22—22no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—84no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22C11×#46312yes—
493C22C2×C11×#12111yescharacteristic
494C4—21no—
495C4—21no—
496C4—21no—
497C4—41no—
498C4—41no—
499C4—81no—
500C4—82no—
501C4C11×#46312yes—
502C4C2×C11×#13511yescharacteristic
503C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
504C4C2×C11×#13711yescharacteristic
505C4C11×#57511yescharacteristic
506C2—22no—
507C2—42no—
508C2—81no—
509C2—161no—
510C2C2×C11×#46311yescharacteristic
511C2C11×#305611yescharacteristic
512C2C11×#306811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3100C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3141C2semidirect
3. C2×C11×#476C2semidirect
4. D4×C11×M16C2semidirect
5. C11×#1703C2semidirect
6. C11×#1697C2semidirect
7. C11×#1683C2semidirect
8. C11×#1677C2semidirect
9. C11×#1565C2semidirect
10. C11×#1548C2semidirect
11. C11×#1547C2semidirect
17. C11×#487C22semidirect
18. C11×#486C22semidirect
43. C11×#335C22semidirect
44. C11×#334C22semidirect
45. C11×#333C22semidirect
46. C11×#333C22semidirect
47. C11×#332C22semidirect
48. C11×#331C22semidirect
110. #19168C11direct (N × H)
172. #3141C2×C11semidirect
174. C2×#476C2×C11semidirect
175. D4×M16C2×C11semidirect
176. #1703C2×C11semidirect
177. #1697C2×C11semidirect
178. #1683C2×C11semidirect
179. #1677C2×C11semidirect
180. #1565C2×C11semidirect
181. #1548C2×C11semidirect
182. #1547C2×C11semidirect
240. #487C22×C11semidirect
241. #486C22×C11semidirect
266. #335C22×C11semidirect
267. #334C22×C11semidirect
268. #333C22×C11semidirect
269. #333C22×C11semidirect
270. #332C22×C11semidirect
271. #331C22×C11semidirect
427. C11#19168direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31412
C11×#31002
C2×C11×#4762
D4×C11×M162
C11×#17032
C11×#16972
C11×#16832
C11×#16772
C11×#15652
C11×#15482
C11×#15472
#1916811