Finite Group Databasebeta

← #14790151

Subgroups — #14790151

Order 2816.

1146 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
1C2×#10623261C211yesmaximal, characteristic, complemented
2C2×C4×#4323C211yesmaximal, characteristic
3#13073538C211yesmaximal, characteristic, complemented
4#13069956C212yesmaximal, complemented
5#13069760C212yesmaximal, complemented
6#13069578C211yesmaximal, characteristic, complemented
7#13069551C211yesmaximal, characteristic, complemented
8#13068961C212yesmaximal
9#13068874C212yesmaximal, complemented
10#13068617C211yesmaximal, characteristic, complemented
11C2×C11×#476C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66999—22no—
15C22×#4323C2211yescharacteristic
16C2×#66977—21no—
17#10623261—24no—
18#10623261—24no—
19C2×#66950—21no—
20C2×#66946C2212yes—
21C2×C4⋊C4×D11—21no—
22C2×#66943C2212yes—
23C2×C4×D44C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C11×#476—24no—
26C2×C11×#106C2212yes—
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×#102C2212yes—
29#10622834C2212yes—
30C2×#66896C2211yescharacteristic
31#10622825—21no—
32C2×#66885C2212yes—
33C4×#4323—24no—
34#10622586C2212yes—
35C2×#66873C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37#10622561—22no—
38#10622548C2211yescharacteristic
39C2×C4×C11⋊C8C2211yescharacteristic
40#10622189C2212yes—
41#10622188C2212yes—
42#10622188C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11—21no—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C22×D44C2311yescharacteristic
49C22×C4×D11—21no—
50C22×C4×D11—22no—
51C22×Dic22D411yescharacteristic
52C22×C8×C11C2312yes—
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8D414yes—
55C4×D4×C11—22no—
56C4×D4×C11—22no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C22⋊C4—21no—
61C2×C42×C11C2311yescharacteristic
62C2×C22⋊Dic11—22no—
63C2×C22⋊Dic11—22no—
64#66999—216no—
65C2×#4323—22no—
66C2×#4323—22no—
67C2×#4323Q814yescomplemented
68C2×(C2×D11)⋊C4—21no—
69C2×(C2×D11)⋊C4—22no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11D411yescharacteristic
74C2×C4⋊Dic11C2312yes—
75C2×C4⋊Dic11C2311yescharacteristic
76#66977—44no—
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—22no—
79C2×Dic11⋊C4D412yes—
80C2×C4×Dic11C2312yes—
81C22×C11⋊C8C2311yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83#66950—28no—
84#66946—24no—
85#66946—24no—
86C4⋊C4×D11—28no—
87#66943—24no—
88#66943—24no—
89C4×D44—22no—
90C4×D44D414yes—
91C4×Dic22—22no—
92C4×Dic22—22no—
93C11×#106—24no—
94C11×C4⋊C8—22no—
95C11×#102—24no—
96#66896—22no—
97C11⋊#95—22no—
98#66885—24no—
99#66873—22no—
100#66871—22no—
101C4×C11⋊C8—22no—
102#24327—111nomaximal, Sylow
103C24×C11—21no—
104C23×D11—21no—
105C2×Q8×C11—24no—
106C2×Q8×C11—81no—
107C2×Q8×C11—81no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11C2×Q812yes—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2411yescharacteristic
122C22×Dic11—21no—
123C22×Dic11—22no—
124C22×Dic11C2×D412yes—
125C22×Dic11C2×D412yes—
126C2×D44—21no—
127C2×D44—21no—
128C2×D44—21no—
129C2×D44C2×D412yes—
130C2×D44C2×Q812yes—
131C2×D44#4112yes—
132C2×C4×D11—28no—
133C2×C4×D11—24no—
134C2×C4×D11—42no—
135C2×C4×D11—42no—
136C2×C4×D11—82no—
137C2×C4×D11—82no—
138C2×Dic22—22no—
139C2×Dic22—22no—
140C2×Dic22—22no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4C2×D414yes—
149C11×C22⋊C4—42no—
150C42×C11C2×D412yes—
151C42×C11C2×D412yes—
152C22⋊Dic11—44no—
153C22⋊Dic11—82no—
154#4323—28no—
155(C2×D11)⋊C4—28no—
156(C2×D11)⋊C4—24no—
157C4⋊Dic11—28no—
158C4⋊Dic11—22no—
159C4⋊Dic11—21no—
160C4⋊Dic11—22no—
161C4⋊Dic11—22no—
162C4⋊Dic11—42no—
163C4⋊Dic11—81no—
164C4⋊Dic11C2×D412yes—
165Dic11⋊C4—28no—
166Dic11⋊C4—24no—
167Dic11⋊C4—44no—
168C4×Dic11—22no—
169C4×Dic11—22no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8C2×Q812yes—
176C2×#554—111no—
177C2×#476D1111yescharacteristic, complemented
178C2×C4×D8—111no—
179#2538—111no—
180#2059—112no—
181#2025—112no—
182#1990—111no—
183#1984—111no—
184#1879—112no—
185#1864—112no—
186#1802—111no—
187C23×C11—22no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11C22×D411yescharacteristic
195C22×D11—22no—
196C22×D11—22no—
197C22×D11—22no—
198C22×D11—41no—
199C22×D11—41no—
200C22×D11—41no—
201C22×D11—41no—
202Q8×C11—84no—
203D4×C11—22no—
204D4×C11—22no—
205D4×C11—41no—
206D4×C11—41no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—24no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—84no—
216C2×C4×C11#12012yes—
217C2×C4×C11#12012yes—
218C2×C4×C11#13512yes—
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—22no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238D44—22no—
239D44—22no—
240D44—22no—
241D44C22⋊Q814yescomplemented
242C4×D11—48no—
243C4×D11—88no—
244Dic22—44no—
245C8×C11—42no—
246C11⋊C8—22no—
247C11⋊C8—41no—
248C22×D8—111no—
249#554—224no—
250#554—224no—
251C2×C4⋊Q8C2×D1111yescharacteristic
252C2×#125—112no—
253C2×C22⋊Q8—221no—
254C2×C22⋊Q8—222no—
255C2×C22⋊Q8—221no—
256C2×C4×Q8—111no—
257C2×C4×D4—112no—
258C2×C4×D4—111no—
259C2×C4×D4C2×D1111yescharacteristic
260C22×C4⋊C4—221no—
261#476—24no—
262C4×D8—224no—
263C2×#107—111no—
264C2×#106C2×D1112yes—
265C2×C4⋊C8C2×D1111yescharacteristic
266C2×#102—111no—
267C2×#102—112no—
268C2×#102—111no—
269C2×#102C2×D1112yes—
270C2×C4×C8—111no—
271#396—222no—
272#390—112no—
273#389—112no—
274#384—111no—
275#380—221no—
276#340—112no—
277#340—112no—
278#340—112no—
279#336—112no—
280#336—112no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—81no—
285C22×C11—81no—
286C22×C11—81no—
287C22×C11—81no—
288C22×C11C2×#12011yescharacteristic
289C22×C11#54811yescharacteristic
290C22×C11D4×Q811yescharacteristic
291C22×C11C2×#13511yescharacteristic
292C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
293C22×C11#57611yescharacteristic
294C22×C11#57711yescharacteristic
295C2×D11—24no—
296C2×D11—42no—
297C2×D11—42no—
298C2×D11—42no—
299C2×D11—42no—
300C2×D11—42no—
301C2×D11—42no—
302C4×C11—22no—
303C4×C11—44no—
304C4×C11—81no—
305C4×C11#44914yes—
306C4×C11C2×C22⋊Q811yescharacteristic
307C4×C11#53611yescharacteristic
308C4×C11#54811yescharacteristic
309C4×C11D4×Q811yescharacteristic
310Dic11—42no—
311Dic11—42no—
312Dic11—42no—
313Dic11—82no—
314C22×Q8—21no—
315C22×Q8—111no—
316C22×D4—111no—
317C22×D4C22×D1111yescharacteristic
318C23×C4—21no—
319C23×C4—222no—
320C23×C4—221no—
321C2×D8—114no—
322C2×D8—222no—
323C2×D8—222no—
324C22×C8—111no—
325C22×C8—111no—
326C22×C8C22×D1112yes—
327C4⋊Q8—22no—
328C4⋊Q8C22⋊D1114yes—
329#125—224no—
330#125—224no—
331C22⋊Q8—228no—
332C22⋊Q8—2216no—
333C22⋊Q8—444no—
334C4×Q8—222no—
335C4×Q8—222no—
336C4×D4—22no—
337C4×D4—22no—
338C4×D4—114no—
339C4×D4—224no—
340C4×D4—224no—
341C4×D4—222no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—111no—
344C2×C4⋊C4—111no—
345C2×C4⋊C4—112no—
346C2×C4⋊C4—112no—
347C2×C4⋊C4—228no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4—222no—
351C2×C4⋊C4—221no—
352C2×C4⋊C4—221no—
353C2×C4⋊C4C22×D1111yescharacteristic
354C2×C4⋊C4C22×D1112yes—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—222no—
357C2×C22⋊C4—221no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—222no—
360C2×C42—112no—
361C2×C42C22×D1111yescharacteristic
362#107—222no—
363#106—24no—
364C4⋊C8—22no—
365#102—24no—
366#102—222no—
367#102—222no—
368#102—224no—
369C4×C8—222no—
370#95—222no—
371C2×C11—82no—
372C2×C11#240911yescharacteristic
373C2×C11C2×#44911yescharacteristic
374C2×C11#301211yescharacteristic
375C2×C11#336011yescharacteristic
376C2×C11#336611yescharacteristic
377C2×C11#338011yescharacteristic
378C2×C11#338411yescharacteristic
379D11—44no—
380C24—21no—
381C24—221no—
382C2×Q8—24no—
383C2×Q8—81no—
384C2×Q8—81no—
385C2×Q8—222no—
386C2×Q8—222no—
387C2×Q8—222no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—112no—
394C2×D4—112no—
395C2×D4—112no—
396C2×D4—221no—
397C2×D4—221no—
398C2×D4—221no—
399C2×D4Q8×D1112yes—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—112no—
406C22×C4—112no—
407C22×C4—228no—
408C22×C4—221no—
409C22×C4—224no—
410C22×C4—222no—
411C22×C4—442no—
412C22×C4—442no—
413C22×C4—882no—
414C22×C4—882no—
415C22×C4D4×D1111yescharacteristic
416C22×C4D4×D1111yescharacteristic
417C22×C4C23×D1111yescharacteristic
418D8—228no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—112no—
423C2×C8—221no—
424C2×C8—221no—
425C2×C8—221no—
426C2×C8—221no—
427C2×C8—221no—
428C4⋊C4—24no—
429C4⋊C4—22no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—112no—
433C4⋊C4—228no—
434C4⋊C4—228no—
435C4⋊C4—222no—
436C4⋊C4—224no—
437C4⋊C4—221no—
438C4⋊C4—222no—
439C4⋊C4—222no—
440C4⋊C4—444no—
441C4⋊C4—442no—
442C4⋊C4—881no—
443C4⋊C4C2×C22⋊D1114yes—
444C22⋊C4—42no—
445C22⋊C4—228no—
446C22⋊C4—224no—
447C22⋊C4—444no—
448C22⋊C4—882no—
449C42—222no—
450C42—222no—
451C42D4×D1112yes—
452C42C2×C22⋊D1112yes—
453C11#2432711yescharacteristic, complemented, Sylow
454C23—22no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—222no—
462C23—222no—
463C23—222no—
464C23—441no—
465C23—441no—
466C23—441no—
467C23—441no—
468C23C2×D4×D1111yescharacteristic
469Q8—84no—
470Q8—444no—
471D4—22no—
472D4—22no—
473D4—41no—
474D4—41no—
475D4—114no—
476D4—222no—
477D4—222no—
478D4—222no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—24no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—84no—
488C2×C4—222no—
489C2×C4—222no—
490C2×C4—222no—
491C2×C4—222no—
492C2×C4—222no—
493C2×C4—222no—
494C2×C4—222no—
495C2×C4—441no—
496C2×C4—441no—
497C2×C4—448no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—888no—
502C2×C4#6696712yes—
503C2×C4#6696912yes—
504C2×C4#6699012yes—
505C2×C4#6699012yes—
506C2×C4C2×D4×D1111yescharacteristic
507C2×C4C2×Q8×D1111yescharacteristic
508C2×C4#6704011yescharacteristic
509C2×C4#41×D1111yescharacteristic
510C2×C4#6704311yescharacteristic
511C2×C4C22×C22⋊D1111yescharacteristic
512C8—42no—
513C8—222no—
514C8—441no—
515C22—42no—
516C22—42no—
517C22—42no—
518C22—81no—
519C22—81no—
520C22—81no—
521C22—81no—
522C22—224no—
523C22—442no—
524C22—442no—
525C22—442no—
526C22—442no—
527C22—442no—
528C22—442no—
529C22#1062316311yescharacteristic
530C22#1062316411yescharacteristic
531C22C2×#6696711yescharacteristic
532C22C2×#6696911yescharacteristic
533C22#1062330511yescharacteristic
534C22#1062330611yescharacteristic
535C22C2×#6699011yescharacteristic
536C4—22no—
537C4—44no—
538C4—81no—
539C4—442no—
540C4—442no—
541C4—442no—
542C4—882no—
543C4#1062278514yes—
544C4D11×C22⋊Q811yescharacteristic
545C4#1062315911yescharacteristic
546C4Q8×C22⋊D1111yescharacteristic
547C4#1062336211yescharacteristic
548C2—82no—
549C2—444no—
550C2#1307197711yescharacteristic
551C2C2×#1062278511yescharacteristic
552C2#1307791911yescharacteristic
553C2#1308126411yescharacteristic
554C2#1308132211yescharacteristic
555C2#1308148211yescharacteristic
556C2#1308151411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#476C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterC2×#476D11
hypocenterC11#24327
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#10623261C2semidirect
3. #13073538C2semidirect
4. #13069956C2semidirect
5. #13069760C2semidirect
6. #13069578C2semidirect
7. #13069551C2semidirect
9. #13068874C2semidirect
10. #13068617C2semidirect
11. C2×C11×#476C2semidirect
67. C2×#4323Q8semidirect
177. C2×#476D11semidirect
241. D44C22⋊Q8semidirect
453. C11#24327semidirect

Maximal subgroups

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

subgroupindex
C2×#106232612
C2×C4×#43232
#130735382
#130699562
#130697602
#130695782
#130695512
#130689612
#130688742
#130686172
C2×C11×#4762
#2432711