Finite Group Databasebeta

← #14790142

Subgroups — #14790142

Order 2816.

1330 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623258C211yesmaximal, characteristic, complemented
2C2×#10622700C211yesmaximal, characteristic, complemented
3C2×C4×D88C211yesmaximal, characteristic
4#13073539C211yesmaximal, characteristic, complemented
5#13069943C212yesmaximal, complemented
6#13069751C212yesmaximal, complemented
7#13069552C211yesmaximal, characteristic, complemented
8#13068965C212yesmaximal
9#13068864C212yesmaximal, complemented
10#13068613C211yesmaximal, characteristic, complemented
11C11×#1990C211yesmaximal, characteristic, complemented
12C22×Q8×D11—21no—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#66999—21no—
15C22×D88C2211yescharacteristic
16#10623258—24no—
17#10623258—24no—
18C2×#66950—21no—
19C2×#66949—22no—
20C2×#66946C2212yes—
21C2×#66941C2212yes—
22C2×C4×D44C2211yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C11×#384C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30#10622700—24no—
31#10622607—22no—
32#10622601C2212yes—
33#10622600—21no—
34#10622598C2212yes—
35C2×#66873C2212yes—
36C2×#66873C2212yes—
37C2×#66871C2212yes—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39C4×D88—24no—
40C11×#340C2212yes—
41C11×#340C2212yes—
42#10622188C2212yes—
43#10622188C2212yes—
44#10622167C2212yes—
45C22×Q8×C11—21no—
46C2×Q8×D11—28no—
47C2×Q8×D11—44no—
48C2×Q8×D11—44no—
49C22×D44C2311yescharacteristic
50C22×D44C2311yescharacteristic
51C22×C4×D11—21no—
52C22×C4×D11—22no—
53C22×C4×D11—21no—
54C22×Dic22—22no—
55C22×Dic22D411yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C22×C8×C11C2311yescharacteristic
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8D414yes—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2312yes—
65C2×C42×C11C2311yescharacteristic
66#66999—28no—
67C2×(C2×D11)⋊C4—21no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—21no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11D411yescharacteristic
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4D412yes—
78C2×C4×Dic11C2312yes—
79C22×C11⋊C8C2312yes—
80C2×D88—22no—
81C2×D88—22no—
82C2×D88Q814yescomplemented
83#66950—44no—
84#66949—216no—
85#66946—24no—
86#66946—24no—
87#66941—24no—
88#66941—24no—
89C4×D44—22no—
90C4×D44—22no—
91C4×D44—22no—
92C4×D44D414yes—
93C4×Dic22—22no—
94C4×Dic22—22no—
95C4×C8×C11—22no—
96C11⋊#95—22no—
97#66885—22no—
98#66885—22no—
99#66882—22no—
100#66873—24no—
101#66873—24no—
102#66871—24no—
103C4⋊(C11⋊C8)—22no—
104#24326—111nomaximal, Sylow
105C23×D11—21no—
106C23×D11—21no—
107C2×Q8×C11—24no—
108C2×Q8×C11—42no—
109C2×Q8×C11—42no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2411yescharacteristic
115C22×Dic11—21no—
116C22×Dic11—21no—
117C22×Dic11C2×D412yes—
118C22×Dic11C2×D412yes—
119Q8×D11—432no—
120C2×D44—21no—
121C2×D44—21no—
122C2×D44—21no—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44—21no—
126C2×D44—21no—
127C2×D44—21no—
128C2×D44C2×D412yes—
129C2×D44C2×Q812yes—
130C2×D44C2×Q812yescomplemented
131C2×D44#4112yes—
132C2×C4×D11—28no—
133C2×C4×D11—24no—
134C2×C4×D11—44no—
135C2×C4×D11—44no—
136C2×C4×D11—42no—
137C2×C4×D11—42no—
138C2×C4×D11—42no—
139C2×C4×D11—42no—
140C2×C4×D11—42no—
141C2×Dic22—28no—
142C2×Dic22—22no—
143C2×Dic22—22no—
144C2×Dic22—44no—
145C2×Dic22—44no—
146C2×Dic22D814yescomplemented
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11C2×Q812yescomplemented
153C11×C4⋊C4—24no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4—81no—
159C11×C4⋊C4C2×D414yes—
160C42×C11C2×D412yes—
161C42×C11C2×D412yes—
162(C2×D11)⋊C4—28no—
163(C2×D11)⋊C4—24no—
164(C2×D11)⋊C4—44no—
165(C2×D11)⋊C4—42no—
166(C2×D11)⋊C4—82no—
167C4⋊Dic11—22no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—44no—
172C4⋊Dic11C2×D412yes—
173Dic11⋊C4—28no—
174Dic11⋊C4—24no—
175C4×Dic11—22no—
176C4×Dic11—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180D88—28no—
181C2×D4×Q8—111no—
182C2×#474—111no—
183C2×C4×D8—111no—
184#2538—111no—
185#2057—112no—
186#2023—112no—
187#1990D1111yescharacteristic, complemented
188#1984—111no—
189#1879—112no—
190#1862—112no—
191#1802—111no—
192C23×C11C22×D411yescharacteristic
193C22×D11—22no—
194C22×D11—22no—
195C22×D11—22no—
196C22×D11—22no—
197C22×D11—41no—
198C22×D11—41no—
199C22×D11—41no—
200C22×D11—41no—
201C22×D11—41no—
202C22×D11—41no—
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—41no—
206C22×D11—41no—
207Q8×C11—48no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—24no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11#12012yes—
217C2×C4×C11#12012yes—
218C2×C4×C11C2×D812yes—
219C2×C4×C11AGL(1,ℤ/8)12yes—
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C22×Q811yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C112−1+411yescharacteristic
225C2×C4×C112−1+411yescharacteristic
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11C2×D814yes—
238D44—22no—
239D44—22no—
240D44—22no—
241D44—22no—
242D44—22no—
243D44—41no—
244D44—41no—
245D44C22⋊Q814yescomplemented
246C4×D11—416no—
247C4×D11—48no—
248C4×D11—84no—
249Dic22—28no—
250Dic22—416no—
251C8×C11—22no—
252C8×C11—41no—
253C11⋊C8—42no—
254C23×Q8—221no—
255C22×D8—111no—
256D4×Q8—224no—
257D4×Q8—224no—
258C2×C4⋊Q8—112no—
259C2×C4⋊Q8C2×D1111yescharacteristic
260C2×C22⋊Q8—222no—
261C2×C22⋊Q8—221no—
262C2×C22⋊Q8—221no—
263C2×C4×Q8—111no—
264C2×C4×D4—112no—
265C2×C4×D4—111no—
266C2×C4×D4—111no—
267#474—224no—
268C4×D8—224no—
269C2×#107—111no—
270C2×#107—112no—
271C2×C4⋊C8—111no—
272C2×#102—111no—
273C2×#102—111no—
274C2×#102—112no—
275C2×#102—112no—
276C2×C4×C8C2×D1111yescharacteristic
277#396—222no—
278#390—112no—
279#389—112no—
280#384C2×D1111yescharacteristic
281#380—221no—
282#340—112no—
283#340C2×D1112yes—
284#340C2×D1112yes—
285#336—112no—
286#336—112no—
287C22×C11C2×#12011yescharacteristic
288C22×C11#54811yescharacteristic
289C22×C11D4×Q811yescharacteristic
290C22×C11C22×D811yescharacteristic
291C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
292C22×C11#57711yescharacteristic
293C22×C11#57811yescharacteristic
294C2×D11—24no—
295C2×D11—42no—
296C2×D11—42no—
297C2×D11—42no—
298C2×D11—42no—
299C2×D11—42no—
300C2×D11—42no—
301C2×D11—42no—
302C2×D11—42no—
303C2×D11—42no—
304C2×D11—81no—
305C2×D11—81no—
306C2×D11—81no—
307C2×D11—81no—
308C4×C11—22no—
309C4×C11—44no—
310C4×C11—82no—
311C4×C11#44714yes—
312C4×C11C2×C22⋊Q811yescharacteristic
313C4×C11#53611yescharacteristic
314C4×C11#54811yescharacteristic
315C4×C11D4×Q811yescharacteristic
316Dic11—24no—
317Dic11—42no—
318Dic11—42no—
319Dic11—81no—
320C22×Q8—21no—
321C22×Q8—111no—
322C22×Q8—222no—
323C22×Q8—228no—
324C22×Q8—444no—
325C22×Q8—444no—
326C22×D4—111no—
327C22×D4—111no—
328C23×C4—222no—
329C23×C4—221no—
330C23×C4—221no—
331C2×D8—114no—
332C2×D8—222no—
333C2×D8—222no—
334C22×C8—112no—
335C22×C8C22×D1111yescharacteristic
336C22×C8C22×D1111yescharacteristic
337C4⋊Q8—22no—
338C4⋊Q8—224no—
339C4⋊Q8—224no—
340C4⋊Q8D4414yes—
341C22⋊Q8—2216no—
342C22⋊Q8—228no—
343C22⋊Q8—444no—
344C4×Q8—222no—
345C4×Q8—222no—
346C4×D4—114no—
347C4×D4—224no—
348C4×D4—224no—
349C4×D4—222no—
350C4×D4—222no—
351C4×D4—222no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—112no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—222no—
360C2×C4⋊C4—222no—
361C2×C4⋊C4C22×D1112yes—
362C2×C4⋊C4C22×D1112yes—
363C2×C22⋊C4—222no—
364C2×C22⋊C4—221no—
365C2×C22⋊C4—222no—
366C2×C22⋊C4—221no—
367C2×C22⋊C4—222no—
368C2×C42—112no—
369C2×C42C22×D1111yescharacteristic
370#107—222no—
371#107—224no—
372C4⋊C8—222no—
373#102—224no—
374#102—222no—
375#102—222no—
376#102—224no—
377C4×C8—22no—
378#95—222no—
379C2×C11#240911yescharacteristic
380C2×C11C2×#44711yescharacteristic
381C2×C11#301311yescharacteristic
382C2×C11#335811yescharacteristic
383C2×C11#336711yescharacteristic
384C2×C11Q8×D811yescharacteristic
385C2×C11#338411yescharacteristic
386D11—44no—
387D11—82no—
388C24—221no—
389C24—221no—
390C2×Q8—24no—
391C2×Q8—42no—
392C2×Q8—42no—
393C2×Q8—114no—
394C2×Q8—228no—
395C2×Q8—222no—
396C2×Q8—222no—
397C2×Q8—444no—
398C2×Q8—444no—
399C2×Q8—4432no—
400C2×D4—112no—
401C2×D4—112no—
402C2×D4—112no—
403C2×D4—112no—
404C2×D4—221no—
405C2×D4—221no—
406C2×D4—221no—
407C2×D4—221no—
408C2×D4—221no—
409C2×D4—221no—
410C2×D4—221no—
411C2×D4—221no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—112no—
415C22×C4—112no—
416C22×C4—228no—
417C22×C4—221no—
418C22×C4—224no—
419C22×C4—221no—
420C22×C4—444no—
421C22×C4—444no—
422C22×C4—442no—
423C22×C4—442no—
424C22×C4—442no—
425C22×C4—442no—
426C22×C4—442no—
427C22×C4D4×D1111yescharacteristic
428C22×C4D4×D1111yescharacteristic
429C22×C4C23×D1111yescharacteristic
430D8—228no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—222no—
437C2×C8—222no—
438C2×C8—222no—
439C2×C8Q8×D1112yescomplemented
440C4⋊C4—24no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—42no—
445C4⋊C4—81no—
446C4⋊C4—112no—
447C4⋊C4—228no—
448C4⋊C4—224no—
449C4⋊C4—222no—
450C4⋊C4—221no—
451C4⋊C4—221no—
452C4⋊C4—221no—
453C4⋊C4—444no—
454C4⋊C4C2×D4414yes—
455C22⋊C4—228no—
456C22⋊C4—224no—
457C22⋊C4—444no—
458C22⋊C4—442no—
459C22⋊C4—882no—
460C42—222no—
461C42—222no—
462C42C2×D4412yes—
463C42D4×D1112yes—
464C11#2432611yescharacteristic, complemented, Sylow
465C23—222no—
466C23—222no—
467C23—222no—
468C23—222no—
469C23—441no—
470C23—441no—
471C23—441no—
472C23—441no—
473C23—441no—
474C23—441no—
475C23—441no—
476C23—441no—
477C23—441no—
478C23—441no—
479C23C2×D4×D1111yescharacteristic
480Q8—48no—
481Q8—228no—
482Q8—4416no—
483D4—114no—
484D4—222no—
485D4—222no—
486D4—222no—
487D4—222no—
488D4—222no—
489D4—441no—
490D4—441no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—24no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—114no—
500C2×C4—222no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—4416no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—448no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4—441no—
513C2×C4—884no—
514C2×C4#6693512yes—
515C2×C4#6693512yes—
516C2×C4D8×D1112yes—
517C2×C4#6696712yes—
518C2×C4C22×D4411yescharacteristic
519C2×C4C2×D4×D1111yescharacteristic
520C2×C4C2×Q8×D1111yescharacteristic
521C2×C4#6704011yescharacteristic
522C2×C4#41×D1111yescharacteristic
523C2×C4#6704311yescharacteristic
524C8—22no—
525C8—41no—
526C8—442no—
527C22—224no—
528C22—442no—
529C22—442no—
530C22—442no—
531C22—442no—
532C22—442no—
533C22—442no—
534C22—442no—
535C22—442no—
536C22—442no—
537C22—881no—
538C22—881no—
539C22—881no—
540C22—881no—
541C22C2×#6693511yescharacteristic
542C22#1062320811yescharacteristic
543C22#1062325811yescharacteristic
544C22C2×D8×D1111yescharacteristic
545C22C2×#6696711yescharacteristic
546C22#1062329311yescharacteristic
547C22#1062329711yescharacteristic
548C4—22no—
549C4—44no—
550C4—82no—
551C4—224no—
552C4—442no—
553C4—442no—
554C4—881no—
555C4#1062238614yes—
556C4Q8×D4411yescharacteristic
557C4#1062310711yescharacteristic
558C4D11×C22⋊Q811yescharacteristic
559C4#1062315911yescharacteristic
560C2—444no—
561C2—882no—
562C2#1307197911yescharacteristic
563C2C2×#1062238611yescharacteristic
564C2#1307793611yescharacteristic
565C2#1308124811yescharacteristic
566C2#1308133911yescharacteristic
567C2#1308146811yescharacteristic
568C2#1308152011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1990C2
socleC23×C11C22×D4
prime radicalC22×D88C22
hypercenter#1990D11
hypocenterC11#24326
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
1. C2×#10623258C2semidirect
2. C2×#10622700C2semidirect
4. #13073539C2semidirect
5. #13069943C2semidirect
6. #13069751C2semidirect
7. #13069552C2semidirect
9. #13068864C2semidirect
10. #13068613C2semidirect
11. C11×#1990C2semidirect
82. C2×D88Q8semidirect
130. C2×D44C2×Q8semidirect
146. C2×Dic22D8semidirect
152. C2×C8×C11C2×Q8semidirect
187. #1990D11semidirect
245. D44C22⋊Q8semidirect
439. C2×C8Q8×D11semidirect
464. C11#24326semidirect

Maximal subgroups

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

subgroupindex
C2×#106232582
C2×#106227002
C2×C4×D882
#130735392
#130699432
#130697512
#130695522
#130689652
#130688642
#130686132
C11×#19902
#2432611