Finite Group Databasebeta

← #14769642

Subgroups — #14769642

Order 2816.

1450 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66965C211yesmaximal, characteristic
2C2×C4×Dic44C211yesmaximal, characteristic, complemented
3C2×#10622486C211yesmaximal, characteristic, complemented
4#13071455C212yesmaximal, complemented
5#13069483C211yesmaximal, characteristic, complemented
6#13068974C212yesmaximal, complemented
7#13068968C212yesmaximal, complemented
8#13068642C211yesmaximal, characteristic, complemented
9#13068553C212yesmaximal, complemented
10C8×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
11C11×#1970C211yesmaximal, characteristic, complemented
12C22×#4341C2212yes—
13C22×C11×D8C2211yescharacteristic
14C22×#4324C2212yes—
15C2×#66965—24no—
16C2×#66965—24no—
17C2×#66965C418yescomplemented
18C22×Dic44C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20C2×#66940C2212yes—
21C2×C4×Dic22C2212yes—
22C2×C11×#107C2211yescharacteristic
23C2×C11×#102C2212yes—
24C2×C4×C8×C11C2211yescharacteristic
25C11×#390C2212yes—
26#10622834C2212yes—
27C2×#66896C2212yes—
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66880C2212yes—
31C2×C8×Dic11C2211yescharacteristic
32#10622600C2212yes—
33C2×#66874C2212yes—
34#10622570—22no—
35#10622570—22no—
36#10622555—22no—
37C22⋊C4×Dic11—22no—
38C4×(C2×D11)⋊C4C2211yescharacteristic
39#10622486—24no—
40C4×Dic44—24no—
41#10622188C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2211yescharacteristic
44C22×D4×C11C2312yes—
45C22×C22⋊D11—22no—
46C23×Dic11—22no—
47C2×#4341—24no—
48C2×#4341—24no—
49C2×#4341—24no—
50C2×#4341—42no—
51C2×#4341—42no—
52C2×#4341C2×C418yes—
53C22×C4×D11C2311yescharacteristic
54C22×Dic22C2312yes—
55C2×C11×D8—22no—
56C2×C11×D8—22no—
57C2×C11×D8C2×C414yes—
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C2×C11×C4⋊C4C2312yes—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C42×C11C2311yescharacteristic
64C2×C22⋊Dic11—22no—
65C2×C22⋊Dic11—22no—
66C2×#4324—24no—
67C2×#4324—24no—
68C2×#4324C2×C418yes—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4D411yescharacteristic
71C2×(C2×D11)⋊C4D411yescharacteristic
72C2×C4⋊Dic11C2312yes—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—22no—
75C2×C4×Dic11—22no—
76C2×C4×Dic11—22no—
77C2×C4×Dic11C2311yescharacteristic
78C22×C11⋊C8C2311yescharacteristic
79C22×C11⋊C8C2311yescharacteristic
80#66965—232no—
81C2×Dic44C2×C414yes—
82C2×Dic44D414yes—
83C2×Dic44D414yes—
84C2×C8×D11—22no—
85C2×C8×D11—22no—
86C2×C8×D11C2×C414yes—
87#66940—24no—
88#66940—42no—
89C4×Dic22—24no—
90C4×Dic22—42no—
91C11×#107—22no—
92C11×#102—42no—
93C4×C8×C11—22no—
94#66896—42no—
95C11⋊#95—22no—
96C11⋊#95D411yescharacteristic
97C11⋊#95D411yescharacteristic
98(C2×D11)⋊C8—22no—
99#66882—22no—
100#66880—24no—
101C8×Dic11—22no—
102#66874—24no—
103#22451—111nomaximal, Sylow
104C24×C11—22no—
105C23×D11C2×D411yescharacteristic
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11C22×C414yes—
112C22×C4×C11—22no—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2411yescharacteristic
116C2×C22⋊D11—28no—
117C2×C22⋊D11—44no—
118C2×C22⋊D11—44no—
119C22×Dic11—28no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—44no—
123C22×Dic11—44no—
124C22×Dic11C2×D411yescharacteristic
125C22×Dic11C2×D411yescharacteristic
126C22×Dic11C2×D411yescharacteristic
127#4341—216no—
128#4341—48no—
129#4341—48no—
130#4341—48no—
131C2×C4×D11—21no—
132C2×C4×D11—21no—
133C2×C4×D11—21no—
134C2×C4×D11—21no—
135C2×C4×D11C22×C412yes—
136C2×C4×D11#4112yes—
137C2×Dic22—22no—
138C2×Dic22—22no—
139C2×Dic22—22no—
140C2×Dic22C22×C414yes—
141C2×Dic22C2×D414yes—
142C2×Dic22C2×D414yes—
143C11×D8—28no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11C22×C412yes—
148C2×C8×C11C2×D412yes—
149C2×C8×C11C2×D412yes—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C22⋊C4—44no—
153C11×C22⋊C4—82no—
154C42×C11—21no—
155C42×C11—21no—
156C22⋊Dic11—44no—
157C22⋊Dic11—82no—
158#4324—216no—
159(C2×D11)⋊C4—22no—
160(C2×D11)⋊C4—22no—
161(C2×D11)⋊C4—82no—
162C4⋊Dic11—22no—
163C4⋊Dic11—22no—
164Dic11⋊C4—44no—
165Dic11⋊C4—44no—
166C4×Dic11—21no—
167C4×Dic11—21no—
168C4×Dic11—44no—
169C4×Dic11—44no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8C22×C412yes—
176Dic44C22⋊C4116yescomplemented
177C8×D11—28no—
178C22×#135—111no—
179C2×C4×Q16—111no—
180C2×C4×Q16—111no—
181#2341—112no—
182#1970—111no—
183#1970D1111yescharacteristic, complemented
184#1880—112no—
185#1880—112no—
186#1808—111no—
187#1788—112no—
188C8×C22⋊C4—111no—
189C23×C11—24no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11C22×D411yescharacteristic
197C22×D11—21no—
198C22×D11—21no—
199C22×D11—21no—
200C22×D11—21no—
201C22×D11—21no—
202C22×D11—21no—
203C22×D11C4×D412yes—
204D4×C11—24no—
205D4×C11—24no—
206D4×C11—42no—
207D4×C11—42no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11#13512yescomplemented
217C2×C4×C11C23×C411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11H(5,𝔽2)11yescharacteristic
222C2×C4×C11H(5,𝔽2)11yescharacteristic
223C22⋊D11—416no—
224C2×Dic11—24no—
225C2×Dic11—21no—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—21no—
229C2×Dic11—21no—
230C2×Dic11—21no—
231C2×Dic11—21no—
232C2×Dic11—21no—
233C2×Dic11—21no—
234C2×Dic11—416no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11C4×D412yes—
239C2×Dic11#13512yescomplemented
240C4×D11—22no—
241C4×D11—22no—
242C4×D11—22no—
243C4×D11—22no—
244Dic22—24no—
245Dic22—24no—
246Dic22—24no—
247Dic22C2×C22⋊C418yes—
248C8×C11—41no—
249C8×C11C2×C22⋊C414yes—
250C11⋊C8—22no—
251C11⋊C8—41no—
252C22×#41—112no—
253C2×#135—118no—
254C2×#135—224no—
255C2×#135—224no—
256C22×Q16—111no—
257C22×SD16—112no—
258C22×D8C2×D1111yescharacteristic
259C23×C8—111no—
260C2×C4×Q8—112no—
261C2×C4×Q8—112no—
262C4×Q16—224no—
263C4×Q16—224no—
264C2×#107—111no—
265C2×#107C2×D1111yescharacteristic
266C2×#103—112no—
267C2×#103—112no—
268C2×#102—112no—
269C2×#102C2×D1112yes—
270C2×C22⋊C8—111no—
271C2×C4×C8—111no—
272C2×C4×C8C2×D1111yescharacteristic
273#390—112no—
274#390—222no—
275#390—222no—
276#390C2×D1112yes—
277#380—112no—
278#380—222no—
279C4×C22⋊C4—111no—
280C4×C22⋊C4—222no—
281#340—112no—
282#336—111no—
283#336—111no—
284C22×C11—44no—
285C22×C11—44no—
286C22×C11—44no—
287C22×C11—82no—
288C22×C11—82no—
289C22×C11—82no—
290C22×C11—82no—
291C22×C11C2×C4×D411yescharacteristic
292C22×C11D4211yescharacteristic
293C22×C11D4211yescharacteristic
294C22×C11C2×#13511yescharacteristic
295C22×C11C2×#13511yescharacteristic
296C22×C11#57611yescharacteristic
297C22×C11#57811yescharacteristic
298C2×D11—22no—
299C2×D11—22no—
300C2×D11—22no—
301C2×D11—41no—
302C2×D11—41no—
303C2×D11—41no—
304C2×D11—41no—
305C4×C11—22no—
306C4×C11—41no—
307C4×C11—82no—
308C4×C11C22×C22⋊C411yescharacteristic
309C4×C11#51811yescharacteristic
310C4×C11#54611yescharacteristic
311C4×C11#54611yescharacteristic
312Dic11—28no—
313Dic11—22no—
314Dic11—22no—
315Dic11—41no—
316Dic11—82no—
317C2×#41—118no—
318C2×#41—224no—
319C2×#41—224no—
320C2×#41—224no—
321C2×#41—442no—
322C2×#41—442no—
323C22×Q8—112no—
324C22×D4—222no—
325C22×D4C22×D1112yes—
326C23×C4—111no—
327C23×C4—222no—
328#135—2232no—
329C2×Q16—114no—
330C2×Q16—114no—
331C2×Q16—114no—
332C2×SD16—118no—
333C2×SD16—224no—
334C2×SD16—224no—
335C2×D8—22no—
336C2×D8—22no—
337C2×D8C4×D1114yes—
338C22×C8—111no—
339C22×C8—114no—
340C22×C8—111no—
341C22×C8—222no—
342C22×C8—222no—
343C22×C8C22×D1111yescharacteristic
344C22×C8C22×D1111yescharacteristic
345C4×Q8—224no—
346C4×Q8—224no—
347C4×Q8—442no—
348C4×Q8—442no—
349C2×C4⋊C4—112no—
350C2×C4⋊C4—222no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4C22×D1112yes—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—111no—
356C2×C22⋊C4—111no—
357C2×C22⋊C4—222no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—222no—
360C2×C42—111no—
361C2×C42—222no—
362C2×C42—222no—
363C2×C42C22×D1111yescharacteristic
364#107—22no—
365#107—222no—
366#103—224no—
367#103—224no—
368#102—42no—
369#102—442no—
370C22⋊C8—222no—
371C4×C8—22no—
372C4×C8—222no—
373#95—111no—
374#95—111no—
375#95—222no—
376C2×C11—84no—
377C2×C11D4×C22⋊C411yescharacteristic
378C2×C11C4×#13511yescharacteristic
379C2×C11#295111yescharacteristic
380C2×C11#328511yescharacteristic
381C2×C11#328511yescharacteristic
382C2×C11#328711yescharacteristic
383C2×C11#328711yescharacteristic
384D11—42no—
385C24—22no—
386C24—111no—
387#41—2216no—
388#41—448no—
389#41—448no—
390#41—448no—
391C2×Q8—114no—
392C2×Q8—114no—
393C2×Q8—114no—
394C2×Q8—222no—
395C2×Q8—222no—
396C2×Q8—222no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—228no—
403C2×D4—444no—
404C2×D4—444no—
405C2×D4C2×C4×D1114yes—
406C22×C4—22no—
407C22×C4—111no—
408C22×C4—111no—
409C22×C4—112no—
410C22×C4—112no—
411C22×C4—111no—
412C22×C4—228no—
413C22×C4—222no—
414C22×C4—221no—
415C22×C4—221no—
416C22×C4—221no—
417C22×C4—221no—
418C22×C4—222no—
419C22×C4—444no—
420C22×C4—444no—
421C22×C4D4×D1111yescharacteristic
422C22×C4D4×D1111yescharacteristic
423C22×C4C23×D1111yescharacteristic
424Q16—1116no—
425SD16—2216no—
426D8—28no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—112no—
431C2×C8—221no—
432C2×C8—221no—
433C2×C8—228no—
434C2×C8—221no—
435C2×C8—221no—
436C2×C8—221no—
437C2×C8C2×C4×D1112yes—
438C2×C8D4×D1112yes—
439C2×C8D4×D1112yes—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—222no—
443C4⋊C4—222no—
444C4⋊C4—444no—
445C4⋊C4—444no—
446C22⋊C4—44no—
447C22⋊C4—82no—
448C22⋊C4—222no—
449C22⋊C4—222no—
450C22⋊C4—444no—
451C22⋊C4—882no—
452C22⋊C4—882no—
453C42—21no—
454C42—21no—
455C42—221no—
456C42—221no—
457C42—444no—
458C42—444no—
459C11#2245111yescharacteristic, complemented, Sylow
460C23—24no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—112no—
468C23—221no—
469C23—221no—
470C23—221no—
471C23—221no—
472C23—221no—
473C23—221no—
474C23C2×D4×D1111yescharacteristic
475Q8—118no—
476Q8—224no—
477Q8—224no—
478Q8—224no—
479D4—24no—
480D4—24no—
481D4—42no—
482D4—42no—
483D4—4416no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—112no—
493C2×C4—112no—
494C2×C4—221no—
495C2×C4—224no—
496C2×C4—221no—
497C2×C4—221no—
498C2×C4—224no—
499C2×C4—224no—
500C2×C4—221no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—221no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—4416no—
509C2×C4—442no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4#6696512yescomplemented
513C2×C4C22×C4×D1111yescharacteristic
514C2×C4C2×D4×D1111yescharacteristic
515C2×C4C2×D4×D1111yescharacteristic
516C2×C4#6703711yescharacteristic
517C2×C4#41×D1111yescharacteristic
518C2×C4#6704211yescharacteristic
519C8—41no—
520C8—222no—
521C8—441no—
522C8C22⋊C4×D1114yes—
523C22—44no—
524C22—44no—
525C22—44no—
526C22—82no—
527C22—82no—
528C22—82no—
529C22—82no—
530C22—222no—
531C22—222no—
532C22—222no—
533C22—441no—
534C22—441no—
535C22—441no—
536C22—441no—
537C22C4×D4×D1111yescharacteristic
538C22#1062314011yescharacteristic
539C22#1062324811yescharacteristic
540C22C2×#6696511yescharacteristic
541C22#1062328811yescharacteristic
542C22D11×#13511yescharacteristic
543C22#1062330211yescharacteristic
544C4—22no—
545C4—41no—
546C4—82no—
547C4—222no—
548C4—222no—
549C4—228no—
550C4—441no—
551C4—882no—
552C4C2×C22⋊C4×D1111yescharacteristic
553C4#1062307611yescharacteristic
554C4#1062314311yescharacteristic
555C4#1062320711yescharacteristic
556C2—84no—
557C2—442no—
558C2#1307143711yescharacteristic
559C2C4×#6696511yescharacteristic
560C2#1307748611yescharacteristic
561C2#1308035411yescharacteristic
562C2#1308035611yescharacteristic
563C2#1308037311yescharacteristic
564C2#1308037411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1970C2
socleC23×C11C22×D4
prime radicalC22×#66965C2
cosocleC22×C4×C11C24
hypercenter#1970D11
hypocenterC11#22451
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1970

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic44C2semidirect
3. C2×#10622486C2semidirect
4. #13071455C2semidirect
5. #13069483C2semidirect
6. #13068974C2semidirect
7. #13068968C2semidirect
8. #13068642C2semidirect
9. #13068553C2semidirect
10. C8×(C2×D11)⋊C4C2semidirect
11. C11×#1970C2semidirect
17. C2×#66965C4semidirect
176. Dic44C22⋊C4semidirect
183. #1970D11semidirect
216. C2×C4×C11#135semidirect
239. C2×Dic11#135semidirect
459. C11#22451semidirect
512. C2×C4#66965semidirect

Maximal subgroups

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

subgroupindex
C22×#669652
C2×C4×Dic442
C2×#106224862
#130714552
#130694832
#130689742
#130689682
#130686422
#130685532
C8×(C2×D11)⋊C42
C11×#19702
#2245111