Finite Group Databasebeta

← #14790144

Subgroups — #14790144

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×D4×Dic22C211yesmaximal, characteristic, complemented
2C2×#10622620C211yesmaximal, characteristic, complemented
3#13073538C211yesmaximal, characteristic, complemented
4#13069942C212yesmaximal, complemented
5#13069750C212yesmaximal, complemented
6#13069577C211yesmaximal, characteristic, complemented
7#13069552C211yesmaximal, characteristic, complemented
8#13068966C212yesmaximal
9#13068861C212yesmaximal, complemented
10#13068616C211yesmaximal, characteristic, complemented
11C2×C4×C11×D8C211yesmaximal, characteristic
12C23×Dic22—21no—
13C22×C11×D8C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×D4×Dic11C2212yes—
17C2×#66977—21no—
18C2×#66977—21no—
19D4×Dic22—24no—
20D4×Dic22—24no—
21C2×#66941C2212yes—
22C2×#66931—22no—
23C2×#66922C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C4×C11×D8—24no—
26C2×C11×#107C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C2×C4×C8×C11C2211yescharacteristic
30#10622834C2212yes—
31C2×#66896C2212yes—
32C2×#66896C2212yes—
33#10622825—21no—
34#10622620—24no—
35#10622586C2212yes—
36C2×#66871C2212yes—
37#10622561—22no—
38#10622548C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40#10622189C2212yes—
41#10622189C2212yes—
42#10622188C2212yes—
43#10622188C2212yes—
44#10622167C2212yes—
45C22×D4×C11C2311yescharacteristic
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11—21no—
49C23×Dic11—22no—
50C22×Dic22—28no—
51C22×Dic22—21no—
52C22×Dic22—22no—
53C22×Dic22—44no—
54C22×Dic22—44no—
55C22×Dic22D411yescharacteristic
56C2×C11×D8—22no—
57C2×C11×D8—22no—
58C2×C11×D8Q814yescomplemented
59C22×C8×C11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C4×D4×C11—22no—
62C4×D4×C11—22no—
63C4×D4×C11—22no—
64C4×D4×C11D414yes—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C42×C11C2311yescharacteristic
70C2×C22⋊Dic11—22no—
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11—22no—
73D4×Dic11—24no—
74D4×Dic11—24no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11D411yescharacteristic
79C2×C4⋊Dic11C2312yes—
80C2×C4⋊Dic11C2312yes—
81#66977—28no—
82#66977—44no—
83C2×Dic11⋊C4—22no—
84C2×Dic11⋊C4—22no—
85C2×Dic11⋊C4D412yes—
86C2×C4×Dic11C2312yes—
87C22×C11⋊C8C2312yes—
88#66941—24no—
89#66941—24no—
90#66931—216no—
91#66922—22no—
92#66922D414yes—
93C4×Dic22—22no—
94C4×Dic22—22no—
95C11×#107—22no—
96C11×#102—22no—
97C11×#102—22no—
98C4×C8×C11—22no—
99#66896—24no—
100#66896—24no—
101C11⋊#95—22no—
102#66871—24no—
103C4⋊(C11⋊C8)—22no—
104#24326—111nomaximal, Sylow
105C24×C11—21no—
106C24×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11C2×D412yes—
116C2×D4×C11C2×Q812yes—
117C2×D4×C11C2×Q812yescomplemented
118C2×D4×C11#4112yes—
119C22×C4×C11—21no—
120C22×C4×C11—24no—
121C22×C4×C11—21no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2411yescharacteristic
130C22×Dic11—28no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—44no—
134C22×Dic11—44no—
135C22×Dic11C2×D412yes—
136C22×Dic11C2×D412yes—
137C2×Dic22—28no—
138C2×Dic22—22no—
139C2×Dic22—24no—
140C2×Dic22—22no—
141C2×Dic22—432no—
142C2×Dic22—44no—
143C2×Dic22—44no—
144C2×Dic22—42no—
145C2×Dic22—42no—
146C2×Dic22D814yescomplemented
147C11×D8—28no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11C2×Q812yescomplemented
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4C2×D412yes—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—42no—
160C42×C11C2×D412yes—
161C42×C11C2×D412yes—
162C22⋊Dic11—28no—
163C22⋊Dic11—44no—
164C22⋊Dic11—82no—
165C4⋊Dic11—22no—
166C4⋊Dic11—24no—
167C4⋊Dic11—22no—
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170C4⋊Dic11—42no—
171C4⋊Dic11—81no—
172C4⋊Dic11C2×D414yes—
173Dic11⋊C4—28no—
174Dic11⋊C4—24no—
175Dic11⋊C4—44no—
176C4×Dic11—22no—
177C4×Dic11—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×D4×Q8—111no—
182C2×#474—111no—
183C2×C4×D8D1111yescharacteristic
184#2538—111no—
185#2057—112no—
186#2023—112no—
187#1990—111no—
188#1984—111no—
189#1879—112no—
190#1862—112no—
191#1802—111no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11C22×D411yescharacteristic
207D4×C11—22no—
208D4×C11—22no—
209D4×C11—22no—
210D4×C11—22no—
211D4×C11—22no—
212D4×C11—41no—
213D4×C11—41no—
214D4×C11C22⋊Q814yescomplemented
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—22no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—48no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—84no—
225C2×C4×C11#12012yes—
226C2×C4×C11#12012yes—
227C2×C4×C11C2×D812yes—
228C2×C4×C11AGL(1,ℤ/8)12yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×Q811yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C112−1+411yescharacteristic
234C2×C4×C112−1+411yescharacteristic
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—24no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—416no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11C2×D814yes—
248Dic22—28no—
249Dic22—416no—
250Dic22—48no—
251C8×C11—22no—
252C8×C11—41no—
253C11⋊C8—42no—
254C23×Q8—221no—
255C22×D8C2×D1111yescharacteristic
256D4×Q8—224no—
257D4×Q8—224no—
258C2×C4⋊Q8—112no—
259C2×C4⋊Q8—111no—
260C2×C22⋊Q8—222no—
261C2×C22⋊Q8—221no—
262C2×C22⋊Q8—221no—
263C2×C4×Q8—111no—
264C2×C4×D4—112no—
265C2×C4×D4C2×D1111yescharacteristic
266C2×C4×D4C2×D1111yescharacteristic
267#474—224no—
268C4×D8—24no—
269C2×#107—112no—
270C2×#107C2×D1111yescharacteristic
271C2×C4⋊C8—111no—
272C2×#102—112no—
273C2×#102—112no—
274C2×#102C2×D1111yescharacteristic
275C2×#102C2×D1111yescharacteristic
276C2×C4×C8C2×D1111yescharacteristic
277#396—222no—
278#390—112no—
279#389—112no—
280#384—111no—
281#380—221no—
282#340—112no—
283#340—112no—
284#340—112no—
285#336—112no—
286#336—112no—
287C22×C11—24no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11—81no—
300C22×C11—81no—
301C22×C11C2×#12011yescharacteristic
302C22×C11#54811yescharacteristic
303C22×C11D4×Q811yescharacteristic
304C22×C11C22×D811yescharacteristic
305C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
306C22×C11#57711yescharacteristic
307C22×C11#57811yescharacteristic
308C4×C11—22no—
309C4×C11—42no—
310C4×C11—81no—
311C4×C11#44714yes—
312C4×C11C2×C22⋊Q811yescharacteristic
313C4×C11#53611yescharacteristic
314C4×C11#54811yescharacteristic
315C4×C11D4×Q811yescharacteristic
316Dic11—24no—
317Dic11—44no—
318Dic11—42no—
319Dic11—82no—
320C22×Q8—111no—
321C22×Q8—222no—
322C22×Q8—228no—
323C22×Q8—221no—
324C22×Q8—444no—
325C22×Q8—444no—
326C22×D4C22×D1111yescharacteristic
327C22×D4C22×D1111yescharacteristic
328C23×C4—21no—
329C23×C4—21no—
330C23×C4—222no—
331C2×D8—22no—
332C2×D8—22no—
333C2×D8Dic2214yescomplemented
334C22×C8—112no—
335C22×C8C22×D1111yescharacteristic
336C22×C8C22×D1111yescharacteristic
337C4⋊Q8—114no—
338C4⋊Q8—224no—
339C4⋊Q8—224no—
340C4⋊Q8—222no—
341C22⋊Q8—2216no—
342C22⋊Q8—228no—
343C22⋊Q8—444no—
344C4×Q8—222no—
345C4×Q8—222no—
346C4×D4—22no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—224no—
350C4×D4—224no—
351C4×D4C22⋊D1114yes—
352C2×C4⋊C4—112no—
353C2×C4⋊C4—111no—
354C2×C4⋊C4—112no—
355C2×C4⋊C4—112no—
356C2×C4⋊C4—222no—
357C2×C4⋊C4—221no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4—221no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4C22×D1111yescharacteristic
362C2×C4⋊C4C22×D1111yescharacteristic
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—222no—
366C2×C22⋊C4—222no—
367C2×C22⋊C4—222no—
368C2×C42—112no—
369C2×C42C22×D1111yescharacteristic
370#107—22no—
371#107—224no—
372C4⋊C8—222no—
373#102—22no—
374#102—22no—
375#102—224no—
376#102—224no—
377C4×C8—22no—
378#95—222no—
379C2×C11—44no—
380C2×C11—82no—
381C2×C11#240911yescharacteristic
382C2×C11C2×#44711yescharacteristic
383C2×C11#301311yescharacteristic
384C2×C11#335811yescharacteristic
385C2×C11#336711yescharacteristic
386C2×C11Q8×D811yescharacteristic
387C2×C11#338411yescharacteristic
388C24—21no—
389C24—21no—
390C2×Q8—114no—
391C2×Q8—228no—
392C2×Q8—222no—
393C2×Q8—222no—
394C2×Q8—224no—
395C2×Q8—444no—
396C2×Q8—444no—
397C2×Q8—4432no—
398C2×Q8—442no—
399C2×Q8—442no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4C2×Dic2212yes—
409C2×D4C2×Dic2212yescomplemented
410C2×D4#433912yes—
411C2×D4C2×C22⋊D1112yes—
412C22×C4—21no—
413C22×C4—24no—
414C22×C4—21no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—112no—
421C22×C4—112no—
422C22×C4—228no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—444no—
426C22×C4—444no—
427C22×C4D4×D1111yescharacteristic
428C22×C4D4×D1111yescharacteristic
429C22×C4C23×D1111yescharacteristic
430D8—28no—
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×C8C2×Dic2212yescomplemented
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—114no—
444C4⋊C4—228no—
445C4⋊C4—224no—
446C4⋊C4—222no—
447C4⋊C4—224no—
448C4⋊C4—222no—
449C4⋊C4—222no—
450C4⋊C4—222no—
451C4⋊C4—444no—
452C4⋊C4—442no—
453C4⋊C4—881no—
454C4⋊C4C2×C22⋊D1112yes—
455C22⋊C4—24no—
456C22⋊C4—42no—
457C22⋊C4—228no—
458C22⋊C4—444no—
459C22⋊C4—882no—
460C42—222no—
461C42—222no—
462C42D4×D1112yes—
463C42C2×C22⋊D1112yes—
464C11#2432611yescharacteristic, complemented, Sylow
465C23—22no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23C2×D4×D1111yescharacteristic
480Q8—228no—
481Q8—4416no—
482Q8—448no—
483D4—22no—
484D4—22no—
485D4—22no—
486D4—22no—
487D4—22no—
488D4—41no—
489D4—41no—
490D4#6697714yescomplemented
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—48no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—84no—
501C2×C4—114no—
502C2×C4—222no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—224no—
508C2×C4—4416no—
509C2×C4—442no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4D8×D1112yes—
515C2×C4#6696412yes—
516C2×C4#6699012yes—
517C2×C4#6699012yes—
518C2×C4C22×Dic2211yescharacteristic
519C2×C4C2×#433911yescharacteristic
520C2×C4C2×D4×D1111yescharacteristic
521C2×C4#6704311yescharacteristic
522C2×C4#6704311yescharacteristic
523C2×C4C22×C22⋊D1111yescharacteristic
524C8—22no—
525C8—41no—
526C8—442no—
527C22—24no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22D4×Dic2211yescharacteristic
542C22#1062308311yescharacteristic
543C22C2×D8×D1111yescharacteristic
544C22C2×#6696411yescharacteristic
545C22#1062330111yescharacteristic
546C22#1062330211yescharacteristic
547C22C2×#6699011yescharacteristic
548C4—22no—
549C4—42no—
550C4—81no—
551C4—224no—
552C4—444no—
553C4—442no—
554C4—882no—
555C4#1062276914yes—
556C4D4×Dic2211yescharacteristic
557C4#1062308311yescharacteristic
558C4C2×#6697711yescharacteristic
559C4#1062335611yescharacteristic
560C2—44no—
561C2—82no—
562C2#1307198111yescharacteristic
563C2C2×#1062276911yescharacteristic
564C2#1307792711yescharacteristic
565C2#1308124911yescharacteristic
566C2#1308133211yescharacteristic
567C2D8×Dic2211yescharacteristic
568C2#1308151311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C4×C11×D8C2
socleC23×C11C22×D4
prime radicalC22×C11×D8C22
hypercenterC2×C4×D8D11
hypocenterC11#24326
LCSG ▷ C22×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
1. C2×D4×Dic22C2semidirect
2. C2×#10622620C2semidirect
3. #13073538C2semidirect
4. #13069942C2semidirect
5. #13069750C2semidirect
6. #13069577C2semidirect
7. #13069552C2semidirect
9. #13068861C2semidirect
10. #13068616C2semidirect
58. C2×C11×D8Q8semidirect
117. C2×D4×C11C2×Q8semidirect
146. C2×Dic22D8semidirect
153. C2×C8×C11C2×Q8semidirect
214. D4×C11C22⋊Q8semidirect
333. C2×D8Dic22semidirect
409. C2×D4C2×Dic22semidirect
439. C2×C8C2×Dic22semidirect
464. C11#24326semidirect
490. D4#66977semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic222
C2×#106226202
#130735382
#130699422
#130697502
#130695772
#130695522
#130689662
#130688612
#130686162
C2×C4×C11×D82
#2432611