Finite Group Databasebeta

← #14769615

Subgroups — #14769615

Order 2816.

1506 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
1C22×#66972C211yesmaximal, characteristic
2C2×C4×D88C211yesmaximal, characteristic, complemented
3C2×#10622485C211yesmaximal, characteristic, complemented
4#13071445C212yesmaximal, complemented
5#13069478C211yesmaximal, characteristic, complemented
6#13068953C212yesmaximal, complemented
7#13068947C212yesmaximal, complemented
8#13068642C211yesmaximal, characteristic, complemented
9#13068555C212yesmaximal, complemented
10C8×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
11C11×#1969C211yesmaximal, characteristic, complemented
12C22×#4343C2212yes—
13C22×C11×Q16C2211yescharacteristic
14C22×#4325C2212yes—
15C2×#66972—24no—
16C2×#66972—24no—
17C2×#66972C418yescomplemented
18C22×D88C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20C2×#66946C2212yes—
21C2×C4×D44C2212yes—
22C2×C11×#107C2211yescharacteristic
23C2×C11×#103C2212yes—
24C2×C4×C8×C11C2211yescharacteristic
25C11×#391C2212yes—
26#10622843C2212yes—
27C2×#66899C2212yes—
28C2×#66885C2212yes—
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32#10622600C2212yes—
33C2×#66873C2212yes—
34C4×(C2×D11)⋊C4C2211yescharacteristic
35#10622485—24no—
36C4×D88—24no—
37#10622278—22no—
38#10622278—22no—
39#10622277—22no—
40D11×#95—22no—
41#10622188C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2211yescharacteristic
44C22×Q8×C11C2312yes—
45C2×#4343—24no—
46C2×#4343—24no—
47C2×#4343—24no—
48C2×#4343—42no—
49C2×#4343—42no—
50C2×#4343C2×C418yescomplemented
51C22×D44—22no—
52C22×D44C2312yes—
53C22×C4×D11—22no—
54C22×C4×D11—22no—
55C22×C4×D11—22no—
56C22×C4×D11C2311yescharacteristic
57C2×C11×Q16—22no—
58C2×C11×Q16—22no—
59C2×C11×Q16C2×C414yescomplemented
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C2×C11×C4⋊C4C2312yes—
63C2×C42×C11C2311yescharacteristic
64C2×#4325—24no—
65C2×#4325—24no—
66C2×#4325C2×C418yescomplemented
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4D411yescharacteristic
71C2×(C2×D11)⋊C4D411yescharacteristic
72C2×C4⋊Dic11C2312yes—
73C2×C4×Dic11C2311yescharacteristic
74C22×C11⋊C8C2311yescharacteristic
75C22×C11⋊C8C2311yescharacteristic
76#66972—232no—
77C2×D88C2×C414yes—
78C2×D88D414yes—
79C2×D88D414yes—
80C2×C8×D11—22no—
81C2×C8×D11—22no—
82C2×C8×D11C2×C414yescomplemented
83#66946—24no—
84#66946—42no—
85C4×D44—24no—
86C4×D44—42no—
87C11×#107—22no—
88C11×#103—42no—
89C4×C8×C11—22no—
90C11×#95—22no—
91C11×#95—22no—
92#66899—42no—
93C11⋊#95—22no—
94C11⋊#95—22no—
95C11⋊#95—22no—
96C11⋊#95D411yescharacteristic
97C11⋊#95D411yescharacteristic
98#66885—24no—
99(C2×D11)⋊C8—22no—
100#66882—22no—
101C8×Dic11—22no—
102#66873—24no—
103#22448—111nomaximal, Sylow
104C23×D11—22no—
105C23×D11C2×D411yescharacteristic
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11C22×C414yes—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2411yescharacteristic
117C22×Dic11—22no—
118C22×Dic11C2×D411yescharacteristic
119C22×Dic11C2×D411yescharacteristic
120C22×Dic11C2×D411yescharacteristic
121#4343—216no—
122#4343—48no—
123#4343—48no—
124#4343—48no—
125C2×D44—28no—
126C2×D44—22no—
127C2×D44—22no—
128C2×D44—22no—
129C2×D44—44no—
130C2×D44—44no—
131C2×D44C22×C414yes—
132C2×D44C2×D414yes—
133C2×D44C2×D414yes—
134C2×C4×D11—28no—
135C2×C4×D11—21no—
136C2×C4×D11—21no—
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11—44no—
140C2×C4×D11—44no—
141C2×C4×D11—44no—
142C2×C4×D11—44no—
143C2×C4×D11—44no—
144C2×C4×D11—44no—
145C2×C4×D11—82no—
146C2×C4×D11—82no—
147C2×C4×D11C22×C412yes—
148C2×C4×D11#4112yes—
149C11×Q16—28no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11C22×C412yes—
154C2×C8×C11C2×D412yes—
155C2×C8×C11C2×D412yes—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C42×C11—21no—
159C42×C11—21no—
160#4325—216no—
161(C2×D11)⋊C4—22no—
162(C2×D11)⋊C4—22no—
163(C2×D11)⋊C4—44no—
164(C2×D11)⋊C4—44no—
165(C2×D11)⋊C4—82no—
166C4⋊Dic11—22no—
167C4⋊Dic11—22no—
168C4×Dic11—21no—
169C4×Dic11—21no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8C22×C412yes—
176D88C22⋊C4116yescomplemented
177C8×D11—28no—
178C22×#135—111no—
179C2×C4×D8—111no—
180C2×C4×D8—111no—
181#2339—112no—
182#1969—111no—
183#1969D1111yescharacteristic, complemented
184#1877—112no—
185#1877—112no—
186#1808—111no—
187#1788—112no—
188C8×C22⋊C4—111no—
189C23×C11C22×D411yescharacteristic
190C22×D11—24no—
191C22×D11—24no—
192C22×D11—24no—
193C22×D11—21no—
194C22×D11—21no—
195C22×D11—21no—
196C22×D11—21no—
197C22×D11—21no—
198C22×D11—21no—
199C22×D11—42no—
200C22×D11—42no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11C4×D412yes—
204Q8×C11—24no—
205Q8×C11—24no—
206Q8×C11—42no—
207Q8×C11—42no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—24no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11#13512yescomplemented
220C2×C4×C11C23×C411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11H(5,𝔽2)11yescharacteristic
225C2×C4×C11H(5,𝔽2)11yescharacteristic
226C2×Dic11—21no—
227C2×Dic11—21no—
228C2×Dic11—21no—
229C2×Dic11—21no—
230C2×Dic11—21no—
231C2×Dic11—21no—
232C2×Dic11—21no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11C4×D412yes—
237C2×Dic11#13512yescomplemented
238D44—24no—
239D44—24no—
240D44—24no—
241D44—416no—
242D44C2×C22⋊C418yes—
243C4×D11—22no—
244C4×D11—22no—
245C4×D11—22no—
246C4×D11—22no—
247C4×D11—416no—
248C4×D11—88no—
249C4×D11—88no—
250C8×C11—41no—
251C8×C11C2×C22⋊C414yes—
252C11⋊C8—22no—
253C11⋊C8—41no—
254C22×#41—112no—
255C2×#135—118no—
256C2×#135—224no—
257C2×#135—224no—
258C22×Q16C2×D1111yescharacteristic
259C22×SD16—112no—
260C22×D8—111no—
261C23×C8—111no—
262C2×C4×D4—112no—
263C2×C4×D4—112no—
264C4×D8—224no—
265C4×D8—224no—
266C2×#107—111no—
267C2×#107C2×D1111yescharacteristic
268C2×#103—112no—
269C2×#103C2×D1112yes—
270C2×#102—112no—
271C2×#102—112no—
272C2×C22⋊C8—111no—
273C2×C4×C8—111no—
274C2×C4×C8C2×D1111yescharacteristic
275#391—112no—
276#391C2×D1112yes—
277#386—222no—
278#386—222no—
279#381—222no—
280#380—112no—
281C4×C22⋊C4—111no—
282C2×#95—222no—
283#340—112no—
284#336—111no—
285#336—111no—
286C22×C11C2×C4×D411yescharacteristic
287C22×C11D4211yescharacteristic
288C22×C11D4211yescharacteristic
289C22×C11C2×#13511yescharacteristic
290C22×C11C2×#13511yescharacteristic
291C22×C11#57611yescharacteristic
292C22×C11#57811yescharacteristic
293C2×D11—28no—
294C2×D11—22no—
295C2×D11—22no—
296C2×D11—22no—
297C2×D11—44no—
298C2×D11—44no—
299C2×D11—41no—
300C2×D11—41no—
301C2×D11—44no—
302C2×D11—44no—
303C2×D11—41no—
304C2×D11—41no—
305C2×D11—44no—
306C2×D11—44no—
307C4×C11—22no—
308C4×C11—44no—
309C4×C11—41no—
310C4×C11—82no—
311C4×C11C22×C22⋊C411yescharacteristic
312C4×C11#51811yescharacteristic
313C4×C11#54611yescharacteristic
314C4×C11#54611yescharacteristic
315Dic11—22no—
316Dic11—22no—
317Dic11—41no—
318Dic11—82no—
319C2×#41—118no—
320C2×#41—224no—
321C2×#41—224no—
322C2×#41—224no—
323C2×#41—442no—
324C2×#41—442no—
325C22×Q8C22×D1112yes—
326C22×D4—112no—
327C22×D4—222no—
328C23×C4—111no—
329C23×C4—222no—
330C23×C4—222no—
331C23×C4—222no—
332#135—2232no—
333C2×Q16—22no—
334C2×Q16—22no—
335C2×Q16C4×D1114yescomplemented
336C2×SD16—118no—
337C2×SD16—224no—
338C2×SD16—224no—
339C2×D8—114no—
340C2×D8—114no—
341C2×D8—114no—
342C22×C8—111no—
343C22×C8—114no—
344C22×C8—111no—
345C22×C8—222no—
346C22×C8—222no—
347C22×C8C22×D1111yescharacteristic
348C22×C8C22×D1111yescharacteristic
349C4×D4—224no—
350C4×D4—224no—
351C4×D4—442no—
352C4×D4—442no—
353C2×C4⋊C4—112no—
354C2×C4⋊C4C22×D1112yes—
355C2×C22⋊C4—111no—
356C2×C22⋊C4—111no—
357C2×C22⋊C4—222no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—222no—
360C2×C42—111no—
361C2×C42C22×D1111yescharacteristic
362#107—22no—
363#107—222no—
364#103—42no—
365#103—442no—
366#102—224no—
367#102—224no—
368C22⋊C8—222no—
369C4×C8—22no—
370C4×C8—222no—
371#95—22no—
372#95—22no—
373#95—111no—
374#95—111no—
375#95—222no—
376#95—222no—
377#95—222no—
378C2×C11D4×C22⋊C411yescharacteristic
379C2×C11C4×#13511yescharacteristic
380C2×C11#295111yescharacteristic
381C2×C11#328011yescharacteristic
382C2×C11#328011yescharacteristic
383C2×C11#328311yescharacteristic
384C2×C11#328311yescharacteristic
385D11—42no—
386D11—48no—
387C24—111no—
388C24—222no—
389#41—2216no—
390#41—448no—
391#41—448no—
392#41—448no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8C2×C4×D1114yes—
399C2×D4—114no—
400C2×D4—114no—
401C2×D4—114no—
402C2×D4—228no—
403C2×D4—222no—
404C2×D4—222no—
405C2×D4—222no—
406C2×D4—444no—
407C2×D4—444no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—111no—
411C22×C4—111no—
412C22×C4—112no—
413C22×C4—112no—
414C22×C4—111no—
415C22×C4—228no—
416C22×C4—221no—
417C22×C4—221no—
418C22×C4—221no—
419C22×C4—221no—
420C22×C4—222no—
421C22×C4—444no—
422C22×C4—444no—
423C22×C4—444no—
424C22×C4—444no—
425C22×C4—444no—
426C22×C4—444no—
427C22×C4—882no—
428C22×C4—882no—
429C22×C4D4×D1111yescharacteristic
430C22×C4D4×D1111yescharacteristic
431C22×C4C23×D1111yescharacteristic
432Q16—28no—
433SD16—2216no—
434D8—1116no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—112no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—228no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8C2×C4×D1112yes—
446C2×C8D4×D1112yes—
447C2×C8D4×D1112yes—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—222no—
451C4⋊C4—222no—
452C22⋊C4—222no—
453C22⋊C4—222no—
454C22⋊C4—444no—
455C22⋊C4—444no—
456C22⋊C4—882no—
457C42—21no—
458C42—21no—
459C42—221no—
460C42—221no—
461C11#2244811yescharacteristic, complemented, Sylow
462C23—112no—
463C23—224no—
464C23—221no—
465C23—221no—
466C23—221no—
467C23—221no—
468C23—221no—
469C23—224no—
470C23—224no—
471C23—221no—
472C23—442no—
473C23—442no—
474C23—442no—
475C23—442no—
476C23C2×D4×D1111yescharacteristic
477Q8—24no—
478Q8—24no—
479Q8—42no—
480Q8—42no—
481D4—118no—
482D4—224no—
483D4—224no—
484D4—224no—
485D4—4416no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—24no—
491C2×C4—21no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—112no—
498C2×C4—112no—
499C2×C4—221no—
500C2×C4—221no—
501C2×C4—221no—
502C2×C4—221no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—4416no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—888no—
515C2×C4—888no—
516C2×C4#6697212yescomplemented
517C2×C4C22×C4×D1111yescharacteristic
518C2×C4C2×D4×D1111yescharacteristic
519C2×C4C2×D4×D1111yescharacteristic
520C2×C4#6703711yescharacteristic
521C2×C4#41×D1111yescharacteristic
522C2×C4#6704211yescharacteristic
523C8—41no—
524C8—222no—
525C8—441no—
526C8C22⋊C4×D1114yes—
527C22—222no—
528C22—228no—
529C22—222no—
530C22—222no—
531C22—441no—
532C22—444no—
533C22—441no—
534C22—444no—
535C22—444no—
536C22—444no—
537C22—441no—
538C22—444no—
539C22—441no—
540C22—444no—
541C22C4×D4×D1111yescharacteristic
542C22#1062314011yescharacteristic
543C22#1062324811yescharacteristic
544C22C2×#6697211yescharacteristic
545C22#1062329711yescharacteristic
546C22D11×#13511yescharacteristic
547C22#1062330011yescharacteristic
548C4—22no—
549C4—41no—
550C4—44no—
551C4—82no—
552C4—222no—
553C4—222no—
554C4—441no—
555C4—882no—
556C4C2×C22⋊C4×D1111yescharacteristic
557C4#1062307611yescharacteristic
558C4#1062314311yescharacteristic
559C4#1062320711yescharacteristic
560C2—442no—
561C2—448no—
562C2#1307143711yescharacteristic
563C2C4×#6697211yescharacteristic
564C2#1307749111yescharacteristic
565C2#1308029811yescharacteristic
566C2#1308030011yescharacteristic
567C2#1308033511yescharacteristic
568C2#1308033611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1969C2
socleC23×C11C22×D4
prime radicalC22×#66972C2
cosocleC22×C4×C11C24
hypercenter#1969D11
hypocenterC11#22448
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1969

Complements

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

NH ≅ G/Ntype
2. C2×C4×D88C2semidirect
3. C2×#10622485C2semidirect
4. #13071445C2semidirect
5. #13069478C2semidirect
6. #13068953C2semidirect
7. #13068947C2semidirect
8. #13068642C2semidirect
9. #13068555C2semidirect
10. C8×(C2×D11)⋊C4C2semidirect
11. C11×#1969C2semidirect
17. C2×#66972C4semidirect
50. C2×#4343C2×C4semidirect
59. C2×C11×Q16C2×C4semidirect
66. C2×#4325C2×C4semidirect
82. C2×C8×D11C2×C4semidirect
176. D88C22⋊C4semidirect
183. #1969D11semidirect
219. C2×C4×C11#135semidirect
237. C2×Dic11#135semidirect
335. C2×Q16C4×D11semidirect
461. C11#22448semidirect
516. C2×C4#66972semidirect

Maximal subgroups

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

subgroupindex
C22×#669722
C2×C4×D882
C2×#106224852
#130714452
#130694782
#130689532
#130689472
#130686422
#130685552
C8×(C2×D11)⋊C42
C11×#19692
#2244811