Finite Group Databasebeta

← #14769611

Subgroups — #14769611

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×#66965C211yesmaximal, characteristic
2C2×D8×Dic11C211yesmaximal, characteristic, complemented
3#13071441C212yesmaximal, complemented
4#13069477C211yesmaximal, characteristic, complemented
5#13069475C211yesmaximal, characteristic, complemented
6#13068950C212yesmaximal, complemented
7#13068948C212yesmaximal, complemented
8#13068642C211yesmaximal, characteristic, complemented
9#13068553C212yesmaximal, complemented
10C8×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
11C2×C4×C11×D8C211yesmaximal, characteristic, complemented
12C22×#4341C2212yes—
13C22×C11×D8C2211yescharacteristic
14C2×C4×D4×C11C2212yes—
15C2×D4×Dic11C2212yes—
16C22×#4324C2212yes—
17C2×#66965—24no—
18C2×#66965—24no—
19C2×#66965C418yescomplemented
20C22×Dic44C2211yescharacteristic
21C22×C8×D11C2211yescharacteristic
22C4×C11×D8—24no—
23C2×C11×#107C2211yescharacteristic
24C2×C11×#102C2212yes—
25C2×C4×C8×C11C2211yescharacteristic
26C2×#66896C2212yes—
27#10622826—22no—
28C2×C11⋊#95—22no—
29D8×Dic11—24no—
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66880C2212yes—
33C2×C8×Dic11C2211yescharacteristic
34#10622600C2212yes—
35#10622587C2212yes—
36C2×#66874C2212yes—
37#10622571—22no—
38#10622556—22no—
39C4×(C2×D11)⋊C4C2211yescharacteristic
40#10622542C2212yes—
41#10622188C2211yescharacteristic
42#10622167C2212yes—
43#10622162C2211yescharacteristic
44C22×D4×C11C2312yes—
45C23×C4×C11—22no—
46C22×C22⋊D11—22no—
47C23×Dic11—22no—
48C23×Dic11—22no—
49C2×#4341—24no—
50C2×#4341—24no—
51C2×#4341—24no—
52C2×#4341—42no—
53C2×#4341—42no—
54C2×#4341C2×C418yescomplemented
55C22×C4×D11C2311yescharacteristic
56C22×Dic22C2312yes—
57C2×C11×D8C2×C414yes—
58C2×C11×D8D414yes—
59C2×C11×D8D414yes—
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C4×D4×C11—24no—
63C4×D4×C11—42no—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C22⋊C4—22no—
66C2×C42×C11C2311yescharacteristic
67C2×C22⋊Dic11—22no—
68D4×Dic11—24no—
69D4×Dic11—42no—
70C2×#4324—24no—
71C2×#4324—24no—
72C2×#4324C2×C418yescomplemented
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4D411yescharacteristic
75C2×(C2×D11)⋊C4D411yescharacteristic
76C2×C4⋊Dic11C2312yes—
77C2×C4×Dic11C2311yescharacteristic
78C22×C11⋊C8C2311yescharacteristic
79C22×C11⋊C8C2311yescharacteristic
80#66965—232no—
81C2×Dic44—22no—
82C2×Dic44—22no—
83C2×Dic44C2×C414yescomplemented
84C2×C8×D11—22no—
85C2×C8×D11—22no—
86C2×C8×D11C2×C414yescomplemented
87C11×#107—22no—
88C11×#102—24no—
89C4×C8×C11—22no—
90#66896—24no—
91C11⋊#95—22no—
92C11⋊#95—22no—
93C11⋊#95—22no—
94C11⋊#95—22no—
95C11⋊#95—22no—
96C11⋊#95D411yescharacteristic
97C11⋊#95D411yescharacteristic
98(C2×D11)⋊C8—22no—
99#66882—22no—
100#66880—42no—
101C8×Dic11—22no—
102#66874—42no—
103#22448—111nomaximal, Sylow
104C24×C11—22no—
105C23×D11C2×D411yescharacteristic
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11C22×C414yes—
110C2×D4×C11C2×D414yes—
111C2×D4×C11C2×D414yes—
112C22×C4×C11—22no—
113C22×C4×C11—44no—
114C22×C4×C11—44no—
115C22×C4×C11—82no—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2411yescharacteristic
119C2×C22⋊D11—28no—
120C2×C22⋊D11—44no—
121C2×C22⋊D11—44no—
122C22×Dic11—28no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—44no—
126C22×Dic11—44no—
127C22×Dic11—44no—
128C22×Dic11—44no—
129C22×Dic11—82no—
130C22×Dic11C2×D411yescharacteristic
131C22×Dic11C2×D411yescharacteristic
132C22×Dic11C2×D411yescharacteristic
133#4341—216no—
134#4341—48no—
135#4341—48no—
136#4341—48no—
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11—21no—
140C2×C4×D11—21no—
141C2×C4×D11C22×C412yes—
142C2×C4×D11#4112yes—
143C2×Dic22—22no—
144C2×Dic22—22no—
145C2×Dic22—22no—
146C2×Dic22—22no—
147C2×Dic22—22no—
148C2×Dic22C22×C414yes—
149C11×D8C22⋊C4116yescomplemented
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—
158C11×C22⋊C4—44no—
159C42×C11—21no—
160C42×C11—21no—
161C22⋊Dic11—44no—
162#4324—216no—
163(C2×D11)⋊C4—22no—
164(C2×D11)⋊C4—22no—
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—
176Dic44—28no—
177C8×D11—28no—
178C22×#135—111no—
179C2×C4×D8—111no—
180C2×C4×D8D1111yescharacteristic, complemented
181#2339—112no—
182#1969—111no—
183#1969—111no—
184#1877—112no—
185#1877—112no—
186#1808—111no—
187#1788—112no—
188C8×C22⋊C4—111no—
189C23×C11—24no—
190C23×C11—24no—
191C23×C11—24no—
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—24no—
207D4×C11C2×C22⋊C418yes—
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—88no—
217C2×C4×C11#13512yescomplemented
218C2×C4×C11C23×C411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11H(5,𝔽2)11yescharacteristic
223C2×C4×C11H(5,𝔽2)11yescharacteristic
224C22⋊D11—416no—
225C2×Dic11—21no—
226C2×Dic11—21no—
227C2×Dic11—21no—
228C2×Dic11—21no—
229C2×Dic11—24no—
230C2×Dic11—21no—
231C2×Dic11—21no—
232C2×Dic11—21no—
233C2×Dic11—416no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—88no—
240C2×Dic11C4×D412yes—
241C2×Dic11#13512yescomplemented
242C4×D11—22no—
243C4×D11—22no—
244C4×D11—22no—
245C4×D11—22no—
246Dic22—24no—
247Dic22—24no—
248Dic22—42no—
249Dic22—42no—
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×Q16—111no—
259C22×SD16—112no—
260C22×D8C2×D1111yescharacteristic
261C23×C8—111no—
262C2×C4×D4—112no—
263C2×C4×D4C2×D1112yes—
264C4×D8—24no—
265C4×D8—224no—
266C2×#107—111no—
267C2×#107C2×D1111yescharacteristic
268C2×#103—112no—
269C2×#103—112no—
270C2×#102—112no—
271C2×#102C2×D1112yes—
272C2×C22⋊C8—111no—
273C2×C4×C8—111no—
274C2×C4×C8C2×D1111yescharacteristic
275#391—112no—
276#391—112no—
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×C11—28no—
287C22×C11—44no—
288C22×C11—44no—
289C22×C11—44no—
290C22×C11—44no—
291C22×C11—44no—
292C22×C11—44no—
293C22×C11C2×C4×D411yescharacteristic
294C22×C11D4211yescharacteristic
295C22×C11D4211yescharacteristic
296C22×C11C2×#13511yescharacteristic
297C22×C11C2×#13511yescharacteristic
298C22×C11#57611yescharacteristic
299C22×C11#57811yescharacteristic
300C2×D11—22no—
301C2×D11—22no—
302C2×D11—22no—
303C2×D11—41no—
304C2×D11—41no—
305C2×D11—41no—
306C2×D11—41no—
307C4×C11—22no—
308C4×C11—41no—
309C4×C11—82no—
310C4×C11C22×C22⋊C411yescharacteristic
311C4×C11#51811yescharacteristic
312C4×C11#54611yescharacteristic
313C4×C11#54611yescharacteristic
314Dic11—22no—
315Dic11—22no—
316Dic11—44no—
317Dic11—41no—
318Dic11—82no—
319C2×#41—118no—
320C2×#41—224no—
321C2×#41—224no—
322C2×#41—224no—
323C2×#41—442no—
324C2×#41—442no—
325C22×Q8—112no—
326C22×D4—222no—
327C22×D4C22×D1112yes—
328C23×C4—22no—
329C23×C4—111no—
330C23×C4—222no—
331C23×C4—222no—
332#135—2232no—
333C2×Q16—114no—
334C2×Q16—222no—
335C2×Q16—222no—
336C2×SD16—118no—
337C2×SD16—224no—
338C2×SD16—224no—
339C2×D8C4×D1114yes—
340C2×D8D4414yes—
341C2×D8C22⋊D1114yes—
342C22×C8—111no—
343C22×C8—114no—
344C22×C8—111no—
345C22×C8—222no—
346C22×C8—222no—
347C22×C8C22×D1111yescharacteristic
348C22×C8C22×D1111yescharacteristic
349C4×D4—24no—
350C4×D4—42no—
351C4×D4—224no—
352C4×D4—442no—
353C2×C4⋊C4—112no—
354C2×C4⋊C4C22×D1112yes—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—111no—
357C2×C22⋊C4—111no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4—222no—
360C2×C42—111no—
361C2×C42C22×D1111yescharacteristic
362#107—22no—
363#107—222no—
364#103—442no—
365#103—442no—
366#102—24no—
367#102—224no—
368C22⋊C8—222no—
369C4×C8—22no—
370C4×C8—222no—
371#95—111no—
372#95—111no—
373#95—222no—
374#95—222no—
375#95—222no—
376#95—222no—
377#95—222no—
378C2×C11—48no—
379C2×C11D4×C22⋊C411yescharacteristic
380C2×C11C4×#13511yescharacteristic
381C2×C11#295111yescharacteristic
382C2×C11#328011yescharacteristic
383C2×C11#328011yescharacteristic
384C2×C11#328311yescharacteristic
385C2×C11#328311yescharacteristic
386D11—42no—
387C24—22no—
388C24—111no—
389#41—2216no—
390#41—448no—
391#41—448no—
392#41—448no—
393C2×Q8—114no—
394C2×Q8—222no—
395C2×Q8—222no—
396C2×Q8—222no—
397C2×Q8—222no—
398C2×Q8—222no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—228no—
403C2×D4—444no—
404C2×D4—444no—
405C2×D4C2×C4×D1114yes—
406C2×D4C2×D4414yes—
407C2×D4C2×C22⋊D1114yes—
408C22×C4—22no—
409C22×C4—44no—
410C22×C4—44no—
411C22×C4—82no—
412C22×C4—111no—
413C22×C4—111no—
414C22×C4—112no—
415C22×C4—112no—
416C22×C4—111no—
417C22×C4—228no—
418C22×C4—221no—
419C22×C4—221no—
420C22×C4—221no—
421C22×C4—221no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—444no—
425C22×C4—444no—
426C22×C4—444no—
427C22×C4—444no—
428C22×C4—882no—
429C22×C4D4×D1111yescharacteristic
430C22×C4D4×D1111yescharacteristic
431C22×C4C23×D1111yescharacteristic
432Q16—228no—
433SD16—2216no—
434D8(C2×D11)⋊C4116yescomplemented
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×C8C2×D4412yes—
447C2×C8C2×C22⋊D1112yes—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—222no—
451C4⋊C4—222no—
452C22⋊C4—44no—
453C22⋊C4—222no—
454C22⋊C4—222no—
455C22⋊C4—444no—
456C22⋊C4—882no—
457C42—21no—
458C42—21no—
459C42—221no—
460C42—221no—
461C11#2244811yescharacteristic, complemented, Sylow
462C23—24no—
463C23—24no—
464C23—24no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23—112no—
470C23—221no—
471C23—221no—
472C23—221no—
473C23—221no—
474C23—221no—
475C23—221no—
476C23C2×D4×D1111yescharacteristic
477Q8—224no—
478Q8—224no—
479Q8—442no—
480Q8—442no—
481D4—24no—
482D4—24no—
483D4—24no—
484D4—4416no—
485D4C2×(C2×D11)⋊C418yes—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—88no—
495C2×C4—112no—
496C2×C4—112no—
497C2×C4—221no—
498C2×C4—221no—
499C2×C4—221no—
500C2×C4—221no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—221no—
506C2×C4—221no—
507C2×C4—224no—
508C2×C4—221no—
509C2×C4—4416no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—888no—
516C2×C4#6696512yescomplemented
517C2×C4C22×C4×D1111yescharacteristic
518C2×C4C22×D4411yescharacteristic
519C2×C4#6703711yescharacteristic
520C2×C4#41×D1111yescharacteristic
521C2×C4#6704211yescharacteristic
522C2×C4C22×C22⋊D1111yescharacteristic
523C8—41no—
524C8—222no—
525C8—441no—
526C8C2×(C2×D11)⋊C414yes—
527C22—28no—
528C22—44no—
529C22—44no—
530C22—44no—
531C22—44no—
532C22—44no—
533C22—44no—
534C22—222no—
535C22—222no—
536C22—222no—
537C22—441no—
538C22—441no—
539C22—441no—
540C22—441no—
541C22C4×D4×D1111yescharacteristic
542C22D4×D4411yescharacteristic
543C22C2×#6696511yescharacteristic
544C22#1062328811yescharacteristic
545C22D11×#13511yescharacteristic
546C22#1062330211yescharacteristic
547C22D4×C22⋊D1111yescharacteristic
548C4—22no—
549C4—41no—
550C4—82no—
551C4—222no—
552C4—222no—
553C4—441no—
554C4—444no—
555C4—882no—
556C4#1062307611yescharacteristic
557C4#1062308511yescharacteristic
558C4C22×(C2×D11)⋊C411yescharacteristic
559C4#1062336011yescharacteristic
560C2—48no—
561C2—442no—
562C2D4×(C2×D11)⋊C411yescharacteristic
563C2C4×#6696511yescharacteristic
564C2#1307748611yescharacteristic
565C2#1308030111yescharacteristic
566C2#1308030211yescharacteristic
567C2#1308033211yescharacteristic
568C2#1308033711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C4×C11×D8C2
socleC23×C11C22×D4
prime radicalC22×#66965C2
cosocleC22×C4×C11C24
hypercenterC2×C4×D8D11
hypocenterC11#22448
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
2. C2×D8×Dic11C2semidirect
3. #13071441C2semidirect
4. #13069477C2semidirect
5. #13069475C2semidirect
6. #13068950C2semidirect
7. #13068948C2semidirect
8. #13068642C2semidirect
9. #13068553C2semidirect
10. C8×(C2×D11)⋊C4C2semidirect
11. C2×C4×C11×D8C2semidirect
19. C2×#66965C4semidirect
54. C2×#4341C2×C4semidirect
72. C2×#4324C2×C4semidirect
83. C2×Dic44C2×C4semidirect
86. C2×C8×D11C2×C4semidirect
149. C11×D8C22⋊C4semidirect
180. C2×C4×D8D11semidirect
217. C2×C4×C11#135semidirect
241. C2×Dic11#135semidirect
434. D8(C2×D11)⋊C4semidirect
461. C11#22448semidirect
516. 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×D8×Dic112
#130714412
#130694772
#130694752
#130689502
#130689482
#130686422
#130685532
C8×(C2×D11)⋊C42
C2×C4×C11×D82
#2244811