Finite Group Databasebeta

← #14909622

Subgroups — #14909622

Order 2816.

584 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078266C211yesmaximal, characteristic, complemented
2#13078265C211yesmaximal, characteristic
3#13070824C211yesmaximal, characteristic, complemented
4#13070810C211yesmaximal, characteristic, complemented
5#13070809C211yesmaximal, characteristic, complemented
6#13070732C211yesmaximal, characteristic, complemented
7#13070730C211yesmaximal, characteristic, complemented
8#13070715C211yesmaximal, characteristic, complemented
9#13070713C211yesmaximal, characteristic, complemented
10#13070547C211yesmaximal, characteristic, complemented
11#13070544C211yesmaximal, characteristic, complemented
12#13070534C211yesmaximal, characteristic, complemented
13#13070534C211yesmaximal, characteristic, complemented
14#13070228C211yesmaximal, characteristic, complemented
15C11×#2237C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic, complemented
17C22×D88C2211yescharacteristic
18C2×#66954C2211yescharacteristic
19#10623159—21no—
20#10623056—21no—
21C11×#467C2211yescharacteristic
22C11×#427C2211yescharacteristic
23#10622801C2211yescharacteristic, complemented
24C2×#66892C2211yescharacteristic
25C2×#66892C2211yescharacteristic
26#10622729C2211yescharacteristic
27#10622665—21no—
28#10622614—21no—
29C2×#66864C2211yescharacteristic
30C2×#66864C2211yescharacteristic
31C2×#66862C2211yescharacteristic, complemented
32C2×C16×D11C2211yescharacteristic, complemented
33#10622500C2211yescharacteristic, complemented
34#10622496C2211yescharacteristic
35#10622496C2211yescharacteristic
36#10622496C2211yescharacteristic
37#10622496C2211yescharacteristic
38#10622493C2211yescharacteristic, complemented
39#10622478—21no—
40#10622478—21no—
41#10622429—21no—
42#10622415—21no—
43C11×#367C2211yescharacteristic, complemented
44C11×#366C2211yescharacteristic, complemented
45C11×#358C2211yescharacteristic, complemented
46C11×#358C2211yescharacteristic, complemented
47C11×C22⋊C16C2211yescharacteristic
48C22⋊(C11⋊C16)C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622147C2211yescharacteristic
51(C2×D11)⋊C16C2211yescharacteristic, complemented
52(C2×D11)⋊C16C2211yescharacteristic, complemented
53#10622130C2211yescharacteristic, complemented
54#10622130C2211yescharacteristic, complemented
55#10622129C2211yescharacteristic
56#10622129C2211yescharacteristic
57#10622128C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C2×Q8×D11—21no—
60C2×#4339D411yescharacteristic
61C22×D44—21no—
62C2×C11×Q16C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×C22⋊Q8—21no—
65C11×#117—21no—
66#66999—21no—
67C2×#4326—21no—
68#66977—21no—
69C2×#4318D411yescharacteristic
70Q16×D11—41no—
71Q16×D11—41no—
72C2×Dic44C2311yescharacteristic
73C2×D88—21no—
74C2×D88—41no—
75C2×D88—41no—
76C2×D88C2311yescharacteristic
77C2×D88C2311yescharacteristic
78#66954—41no—
79#66954—41no—
80C2×#4313D411yescharacteristic
81C2×#4313D411yescharacteristic
82C2×C8×D11C2311yescharacteristic
83C2×C8×D11C2311yescharacteristic
84#66950—21no—
85#66948—21no—
86#66948—21no—
87#66948—21no—
88#66948—21no—
89#66947—41no—
90#66945—21no—
91#66941—41no—
92#66938—41no—
93#66936—41no—
94#66935—41no—
95#66935—41no—
96#66928—41no—
97#66927—41no—
98C2×C11×C16C2311yescharacteristic
99C2×C11×C16C2311yescharacteristic
100C11×#107C2311yescharacteristic
101C11×#107C2311yescharacteristic
102C11×#107C2311yescharacteristic
103C11×#106—21no—
104C11×#103—21no—
105#66899—21no—
106#66892—41no—
107#66892—41no—
108#66882C2311yescharacteristic
109#66880—21no—
110C2×C11⋊C16C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112#66874—21no—
113#66873—21no—
114#66873—21no—
115#66873—21no—
116#66873—21no—
117#66872—21no—
118#66864—41no—
119#66864—41no—
120#66862—41no—
121C16×D11—41no—
122#33766—111nomaximal, Sylow
123C23×D11—41no—
124C2×Q8×C11—21no—
125C22×C4×C11C2×D411yescharacteristic
126C2×C22⋊D11D811yescharacteristic
127C2×C22⋊D11D811yescharacteristic
128Q8×D11—42no—
129Q8×D11—42no—
130#4339—41no—
131#4339—41no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44—42no—
135C2×D44—42no—
136C2×D44—41no—
137C2×D44—41no—
138C2×D44—41no—
139C2×D44—41no—
140C2×D44—41no—
141C2×D44D811yescharacteristic
142C2×C4×D11—41no—
143C2×C4×D11C2×D411yescharacteristic
144C2×C4×D11C2×D411yescharacteristic
145C2×Dic22—21no—
146C2×Dic22—41no—
147C2×Dic22D811yescharacteristic
148C11×Q16—21no—
149C11×Q16—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11C2×D411yescharacteristic
153C2×C8×C11C2411yescharacteristic
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—41no—
158C11×C22⋊C4—41no—
159C11×C22⋊C4—41no—
160C42×C11—41no—
161C22⋊Dic11—41no—
162#4326—42no—
163(C2×D11)⋊C4—41no—
164(C2×D11)⋊C4—41no—
165(C2×D11)⋊C4—41no—
166(C2×D11)⋊C4—41no—
167(C2×D11)⋊C4—41no—
168(C2×D11)⋊C4—41no—
169(C2×D11)⋊C4—41no—
170C4⋊Dic11—21no—
171C4⋊Dic11—41no—
172Dic11⋊C4—41no—
173Dic11⋊C4—41no—
174C4×Dic11—41no—
175#4318—41no—
176C2×C11⋊C8C2×D411yescharacteristic
177C2×C11⋊C8C2×D411yescharacteristic
178Dic44—21no—
179Dic44—21no—
180D88—21no—
181D88—21no—
182D88—21no—
183D88—21no—
184D88—42no—
185#4313—41no—
186#4313—41no—
187C8×D11—21no—
188C8×D11—21no—
189C8×D11—21no—
190C8×D11—21no—
191C11×C16—21no—
192C11×C16—21no—
193C11⋊C16—21no—
194C11⋊C16—21no—
195#3059—111no—
196#3058—111no—
197#2237—111no—
198#2237D1111yescharacteristic, complemented
199#2234—111no—
200#2234—111no—
201#2220—111no—
202#2220—111no—
203#2217—111no—
204#2217—111no—
205#2187—111no—
206#2187—111no—
207#2185—111no—
208#2185—111no—
209#2113—111no—
210C23×C11C2×D811yescharacteristic
211C22×D11—41no—
212C22×D11—41no—
213C22×D11—82no—
214C22×D11—161no—
215C22×D11—161no—
216C22×D11C2×D811yescharacteristic
217C22×D11C2×D811yescharacteristic
218Q8×C11—41no—
219Q8×C11—41no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11C2×D811yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C22⋊D11—41no—
229C22⋊D11—41no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232C2×Dic11C2×D811yescharacteristic
233C2×Dic11C2×D811yescharacteristic
234D44—41no—
235D44—41no—
236D44—41no—
237D44—41no—
238D44—41no—
239D44—82no—
240D44—161no—
241D44—161no—
242D44—161no—
243D44—161no—
244C4×D11—21no—
245C4×D11—21no—
246C4×D11—21no—
247C4×D11—21no—
248C4×D11—82no—
249Dic22—41no—
250Dic22—41no—
251Dic22—41no—
252Dic22—82no—
253C8×C11—21no—
254C8×C11H(5,𝔽2)11yescharacteristic
255C8×C11H(5,𝔽2)11yescharacteristic
256C11⋊C8—21no—
257C11⋊C8—21no—
258C22×Q16—111no—
259C22×D8—111no—
260C2×#131—111no—
261#536—221no—
262#535—221no—
263C2×SD32—111no—
264C2×SD32—111no—
265C2×SD32—111no—
266C2×SD32—111no—
267C2×M32—111no—
268C22×C16—111no—
269#470—221no—
270#470—221no—
271#469—221no—
272#469—221no—
273#467—111no—
274#467—111no—
275#467—111no—
276#467C2×D1111yescharacteristic
277#466—111no—
278#466—111no—
279#466—111no—
280#466—111no—
281#427—111no—
282#427C2×D1111yescharacteristic
283#419—221no—
284#418—221no—
285#367—111no—
286#367C2×D1111yescharacteristic, complemented
287#366—111no—
288#366C2×D1111yescharacteristic, complemented
289#358—111no—
290#358—111no—
291#358C2×D1111yescharacteristic, complemented
292#358C2×D1111yescharacteristic, complemented
293#357—111no—
294#357—111no—
295#357—111no—
296#357—111no—
297C22⋊C16—111no—
298C22⋊C16—111no—
299C22⋊C16—111no—
300C22⋊C16C2×D1111yescharacteristic
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11C22×D811yescharacteristic
305C2×D11—21no—
306C2×D11—21no—
307C2×D11—21no—
308C2×D11—21no—
309C2×D11—21no—
310C2×D11—21no—
311C2×D11—81no—
312C2×D11—81no—
313C2×D11—81no—
314C2×D11—81no—
315C2×D11—81no—
316C2×D11—81no—
317C2×D11—164no—
318C4×C11—21no—
319C4×C11—81no—
320C4×C11—81no—
321C4×C11—81no—
322C4×C11—81no—
323C4×C11#53411yescharacteristic
324C4×C11#57511yescharacteristic
325Dic11—21no—
326Dic11—21no—
327Dic11—81no—
328Dic11—81no—
329C2×#41—111no—
330C22×Q8—221no—
331C22×D4—221no—
332C2×Q16—111no—
333C2×Q16—221no—
334C2×Q16—441no—
335C2×Q16—441no—
336C2×Q16C22×D1111yescharacteristic
337C2×D8—111no—
338C2×D8—111no—
339C2×D8—221no—
340C2×D8—441no—
341C2×D8—441no—
342#131—441no—
343#131—441no—
344C2×M16—111no—
345C2×M16—111no—
346C2×M16—111no—
347C22×C8—111no—
348C22×C8—111no—
349C22×C8C22×D1111yescharacteristic
350C4⋊Q8—441no—
351#127—441no—
352#124—441no—
353#124—441no—
354#123—441no—
355#123—441no—
356C22⋊Q8—21no—
357C22⋊Q8—221no—
358C22⋊Q8—221no—
359C22⋊Q8—221no—
360#121—221no—
361#121—221no—
362#121—221no—
363#121—221no—
364#120—441no—
365#120—441no—
366#117—21no—
367#117—221no—
368SD32—441no—
369SD32—441no—
370SD32—441no—
371SD32—441no—
372M32—441no—
373C2×C16—111no—
374C2×C16—111no—
375C2×C16—441no—
376C2×C16C22×D1111yescharacteristic
377C2×C16C22×D1111yescharacteristic
378#107—111no—
379#107C22×D1111yescharacteristic
380#107C22×D1111yescharacteristic
381#107C22×D1111yescharacteristic
382#106—21no—
383#106—221no—
384#103—21no—
385#103—221no—
386#103—221no—
387#103—221no—
388#102—221no—
389#102—221no—
390#102—221no—
391#102—221no—
392C2×C11—41no—
393C2×C11#318611yescharacteristic
394C2×C11#341611yescharacteristic
395C2×C11#341611yescharacteristic
396D11—41no—
397D11—41no—
398D11—161no—
399D11—161no—
400C24—441no—
401#41—441no—
402#41—441no—
403C2×Q8—21no—
404C2×Q8—111no—
405C2×Q8—221no—
406C2×Q8—441no—
407C2×Q8—442no—
408C2×Q8—442no—
409C2×D4—111no—
410C2×D4—111no—
411C2×D4—111no—
412C2×D4—221no—
413C2×D4—221no—
414C2×D4—442no—
415C2×D4—442no—
416C2×D4—441no—
417C2×D4—441no—
418C2×D4—441no—
419C2×D4—441no—
420C2×D4—441no—
421C22×C4—111no—
422C22×C4—111no—
423C22×C4—441no—
424C22×C4D4×D1111yescharacteristic
425Q16—21no—
426Q16—21no—
427Q16—221no—
428Q16—221no—
429Q16—442no—
430D8—221no—
431D8—221no—
432D8—221no—
433D8—221no—
434D8—442no—
435M16—441no—
436M16—441no—
437M16—441no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—111no—
441C2×C8—111no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8D4×D1111yescharacteristic
447C2×C8C23×D1111yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—41no—
452C4⋊C4—221no—
453C4⋊C4—441no—
454C4⋊C4—441no—
455C4⋊C4—441no—
456C22⋊C4—41no—
457C22⋊C4—41no—
458C22⋊C4—441no—
459C22⋊C4—441no—
460C22⋊C4—441no—
461C22⋊C4—441no—
462C22⋊C4—441no—
463C22⋊C4—441no—
464C22⋊C4—441no—
465C22⋊C4—441no—
466C42—41no—
467C42—441no—
468C16—21no—
469C16—21no—
470C16—221no—
471C16—221no—
472C11#3376611yescharacteristic, complemented, Sylow
473C23—111no—
474C23—111no—
475C23—441no—
476C23—441no—
477C23—882no—
478C23—1761no—
479C23—1761no—
480C23D8×D1111yescharacteristic
481Q8—41no—
482Q8—41no—
483Q8—441no—
484Q8—441no—
485Q8—441no—
486Q8—882no—
487D4—441no—
488D4—441no—
489D4—441no—
490D4—441no—
491D4—441no—
492D4—441no—
493D4—441no—
494D4—882no—
495D4—1761no—
496D4—1761no—
497D4—1761no—
498D4—1761no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—111no—
506C2×C4—111no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—441no—
512C2×C4—441no—
513C2×C4—882no—
514C2×C4D8×D1111yescharacteristic
515C2×C4C2×D4×D1111yescharacteristic
516C8—21no—
517C8—221no—
518C8—221no—
519C8#6704211yescharacteristic
520C8#6704211yescharacteristic
521C22—21no—
522C22—21no—
523C22—21no—
524C22—221no—
525C22—221no—
526C22—221no—
527C22—221no—
528C22—221no—
529C22—221no—
530C22—881no—
531C22—881no—
532C22—881no—
533C22—881no—
534C22—881no—
535C22—881no—
536C22—1764no—
537C22C2×D8×D1111yescharacteristic
538C4—21no—
539C4—81no—
540C4—81no—
541C4—81no—
542C4—81no—
543C4—221no—
544C4—221no—
545C4—881no—
546C4—881no—
547C4#1062318411yescharacteristic
548C4#1062330811yescharacteristic
549C2—41no—
550C2—441no—
551C2—441no—
552C2—1761no—
553C2—1761no—
554C2#1307936611yescharacteristic
555C2#1308175911yescharacteristic
556C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2237C2
socleC22×C11C22×D8
prime radical#13078265C2
hypercenter#2237D11
hypocenterC11#33766
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2237

Complements

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

NH ≅ G/Ntype
1. #13078266C2semidirect
3. #13070824C2semidirect
4. #13070810C2semidirect
5. #13070809C2semidirect
6. #13070732C2semidirect
7. #13070730C2semidirect
8. #13070715C2semidirect
9. #13070713C2semidirect
10. #13070547C2semidirect
11. #13070544C2semidirect
12. #13070534C2semidirect
13. #13070534C2semidirect
14. #13070228C2semidirect
15. C11×#2237C2semidirect
16. C2×Q16×D11C22semidirect
23. #10622801C22semidirect
31. C2×#66862C22semidirect
32. C2×C16×D11C22semidirect
33. #10622500C22semidirect
38. #10622493C22semidirect
43. C11×#367C22semidirect
44. C11×#366C22semidirect
45. C11×#358C22semidirect
46. C11×#358C22semidirect
51. (C2×D11)⋊C16C22semidirect
52. (C2×D11)⋊C16C22semidirect
53. #10622130C22semidirect
54. #10622130C22semidirect
57. #10622128C22semidirect
58. #10622127C22semidirect
198. #2237D11semidirect
286. #367C2×D11semidirect
288. #366C2×D11semidirect
291. #358C2×D11semidirect
292. #358C2×D11semidirect
472. C11#33766semidirect

Maximal subgroups

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

subgroupindex
#130782662
#130782652
#130708242
#130708102
#130708092
#130707322
#130707302
#130707152
#130707132
#130705472
#130705442
#130705342
#130702282
C11×#22372
#3376611