Finite Group Databasebeta

← #14787693

Subgroups — #14787693

Order 2816.

1174 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622700C211yesmaximal, characteristic, complemented
2C2×C4×#4325C211yesmaximal, characteristic, complemented
3#13073529C211yesmaximal, characteristic
4#13069816C212yesmaximal, complemented
5#13069617C212yesmaximal, complemented
6#13069578C211yesmaximal, characteristic, complemented
7#13069411C211yesmaximal, characteristic, complemented
8#13068938C212yesmaximal, complemented
9#13068815C212yesmaximal, complemented
10#13068621C211yesmaximal, characteristic, complemented
11C2×C11×#556C211yesmaximal, characteristic, complemented
12C11×#556—24no—
13C11×#556—24no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#126—22no—
16C2×C11×#124—21no—
17C2×C11×C22⋊Q8C2212yes—
18C2×C4×Q8×C11—21no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#117C2212yes—
22C22×#4325C2211yescharacteristic
23C2×#66991—21no—
24C2×#66983C2212yes—
25C2×C4×D44C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66899C2212yes—
28#10622825C2212yes—
29C2×C22⋊(C11⋊C8)C2212yes—
30C2×C22⋊(C11⋊C8)C2212yes—
31#10622700—24no—
32C4×#4325—24no—
33#10622600—21no—
34C2×#66873C2212yes—
35C2×#66873C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66871C2212yes—
38#10622574—22no—
39#10622548C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11D411yescharacteristic
48C23×C4×C11C2312yes—
49C22×C22⋊D11—22no—
50C22×D44C2311yescharacteristic
51C22×C4×D11—21no—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8D414yescomplemented
54C11×#126—216no—
55C11×#124—28no—
56C11×C22⋊Q8—24no—
57C11×C22⋊Q8—24no—
58C4×Q8×C11—28no—
59C4×Q8×C11—22no—
60C4×Q8×C11D414yescomplemented
61C4×D4×C11—22no—
62C4×D4×C11—22no—
63C11×#117—24no—
64C11×#117—24no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4D412yes—
74C2×C42×C11—22no—
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—22no—
78C2×#4325—22no—
79C2×#4325—22no—
80C2×#4325—22no—
81#66991—44no—
82#66983—24no—
83#66983—42no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—22no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2312yes—
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2312yes—
92C22×C11⋊C8C2311yescharacteristic
93C4×D44—22no—
94C4×D44—22no—
95#66899—22no—
96#66899—42no—
97C11⋊#95—22no—
98C22⋊(C11⋊C8)—24no—
99C22⋊(C11⋊C8)—42no—
100#66873—22no—
101#66873—24no—
102#66872—22no—
103#66871—24no—
104C4⋊(C11⋊C8)—22no—
105C4×C11⋊C8—22no—
106#24119—111nomaximal, Sylow
107C24×C11C2×D412yes—
108C23×D11—21no—
109C2×Q8×C11—24no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—42no—
116C2×Q8×C11—42no—
117C2×Q8×C11C2×D412yes—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C2×C22⋊D11—44no—
135C2×C22⋊D11—44no—
136C2×C22⋊D11—82no—
137C22×Dic11—21no—
138C22×Dic11—22no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44#4112yes—
145C2×C4×D11—42no—
146C2×C4×D11—42no—
147C2×C4×D11—42no—
148C11×C4⋊C4—28no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4C2×D414yes—
155C11×C4⋊C4C2×D412yes—
156C11×C22⋊C4—28no—
157C11×C22⋊C4—28no—
158C11×C22⋊C4—24no—
159C42×C11—28no—
160C42×C11—24no—
161C42×C11C2×D412yes—
162C42×C11C2×D412yes—
163C22⋊Dic11—44no—
164#4325—28no—
165(C2×D11)⋊C4—44no—
166(C2×D11)⋊C4—42no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—22no—
170C4⋊Dic11—22no—
171C4⋊Dic11—42no—
172C4⋊Dic11—81no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8#4112yes—
182C2×#556D1111yescharacteristic, complemented
183C2×#474—111no—
184C2×C4×SD16—111no—
185#2537—111no—
186#2036—112no—
187#2000—112no—
188#1990—111no—
189#1954—111no—
190#1875—112no—
191#1854—112no—
192#1803—111no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11C22×D411yescharacteristic
201C22×D11—22no—
202C22×D11—41no—
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—41no—
206C22×D11—41no—
207C22×D11—41no—
208Q8×C11—22no—
209Q8×C11—22no—
210Q8×C11—41no—
211Q8×C11—41no—
212Q8×C11—48no—
213D4×C11—44no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11#12012yes—
233C2×C4×C11#12012yes—
234C2×C4×C11#13512yes—
235C2×C4×C11AGL(1,ℤ/8)12yes—
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11H(5,𝔽2)11yescharacteristic
241C2×C4×C112−1+411yescharacteristic
242C22⋊D11—88no—
243C2×Dic11—41no—
244C2×Dic11—42no—
245C2×Dic11—41no—
246C2×Dic11—42no—
247C2×Dic11—41no—
248C2×Dic11—42no—
249D44—22no—
250D44—22no—
251D44—41no—
252D44—41no—
253C4×D11—84no—
254C11⋊C8—22no—
255C11⋊C8—41no—
256C11⋊C8—42no—
257C22×SD16—111no—
258#556—24no—
259#556—24no—
260C2×C4⋊Q8C2×D1111yescharacteristic
261C2×#126—22no—
262C2×#124—21no—
263C2×C22⋊Q8C2×D1112yes—
264C2×#121—112no—
265C2×#121—221no—
266C2×C4×Q8—21no—
267C2×C4×Q8C2×D1111yescharacteristic
268C2×C4×D4—111no—
269C2×C4×D4C2×D1111yescharacteristic
270C2×#117C2×D1112yes—
271#474—224no—
272C4×SD16—224no—
273C2×#107—112no—
274C2×#106—111no—
275C2×C4⋊C8—111no—
276C2×#103—111no—
277C2×#103—112no—
278C2×#102—111no—
279C2×#102—112no—
280C2×C22⋊C8—112no—
281C2×C22⋊C8—112no—
282C2×C4×C8—111no—
283#394—222no—
284#384—111no—
285#380—112no—
286#380—221no—
287#340—112no—
288#340—112no—
289#340—112no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11C2×#12011yescharacteristic
298C22×C11#54611yescharacteristic
299C22×C11#54711yescharacteristic
300C22×C11C2×#13511yescharacteristic
301C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
302C22×C11#57711yescharacteristic
303C22×C11#57811yescharacteristic
304C2×D11—42no—
305C2×D11—42no—
306C2×D11—42no—
307C2×D11—81no—
308C2×D11—81no—
309C2×D11—81no—
310C2×D11—81no—
311C4×C11—22no—
312C4×C11—42no—
313C4×C11—42no—
314C4×C11—44no—
315C4×C11—42no—
316C4×C11#44914yes—
317C4×C11#52511yescharacteristic
318C4×C11#53711yescharacteristic
319C4×C11#54811yescharacteristic
320C4×C11#55011yescharacteristic
321Dic11—81no—
322Dic11—82no—
323C22×Q8—21no—
324C22×Q8C22×D1111yescharacteristic
325C22×D4—111no—
326C22×D4—222no—
327C22×D4C22⋊D1111yescharacteristic
328C23×C4—221no—
329C23×C4C22×D1112yes—
330C2×SD16—222no—
331C2×SD16—222no—
332C2×SD16—222no—
333C22×C8—111no—
334C22×C8—111no—
335C22×C8—112no—
336C4⋊Q8—22no—
337C4⋊Q8C22⋊D1114yescomplemented
338#126—216no—
339#124—28no—
340C22⋊Q8—24no—
341C22⋊Q8—24no—
342#121—224no—
343#121—442no—
344#121—444no—
345C4×Q8—28no—
346C4×Q8—22no—
347C4×Q8C22⋊D1114yescomplemented
348C4×D4—22no—
349C4×D4—22no—
350C4×D4—222no—
351C4×D4—222no—
352#117—24no—
353#117—24no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—112no—
359C2×C4⋊C4—221no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4C22⋊D1111yescharacteristic
362C2×C4⋊C4C22×D1111yescharacteristic
363C2×C4⋊C4C22×D1112yes—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—222no—
367C2×C22⋊C4—221no—
368C2×C22⋊C4—222no—
369C2×C22⋊C4C22⋊D1112yes—
370C2×C42—22no—
371C2×C42—21no—
372C2×C42C22×D1111yescharacteristic
373#107—224no—
374#106—222no—
375C4⋊C8—222no—
376#103—222no—
377#103—442no—
378#102—222no—
379#102—224no—
380C22⋊C8—224no—
381C22⋊C8—442no—
382C4×C8—222no—
383#95—222no—
384C2×C11—82no—
385C2×C11#240711yescharacteristic
386C2×C11C2×#44911yescharacteristic
387C2×C11#301311yescharacteristic
388C2×C11#330211yescharacteristic
389C2×C11#332411yescharacteristic
390C2×C11#334011yescharacteristic
391C2×C11#335311yescharacteristic
392D11—82no—
393C24—221no—
394C24C2×C22⋊D1112yes—
395C2×Q8—24no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—42no—
402C2×Q8—42no—
403C2×Q8C2×C22⋊D1112yes—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—112no—
408C2×D4—221no—
409C2×D4—221no—
410C2×D4—221no—
411C2×D4—221no—
412C2×D4—221no—
413C2×D4—444no—
414C2×D4—444no—
415C2×D4—882no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—221no—
426C22×C4—222no—
427C22×C4—442no—
428C22×C4—442no—
429C22×C4—442no—
430C22×C4C2×C22⋊D1112yes—
431C22×C4C2×C22⋊D1111yescharacteristic
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C23×D1111yescharacteristic
434SD16—228no—
435C2×C8—112no—
436C2×C8—221no—
437C2×C8—221no—
438C2×C8—222no—
439C2×C8—221no—
440C2×C8—222no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—222no—
444C4⋊C4—28no—
445C4⋊C4—24no—
446C4⋊C4—24no—
447C4⋊C4—22no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—222no—
451C4⋊C4—222no—
452C4⋊C4—221no—
453C4⋊C4—221no—
454C4⋊C4—442no—
455C4⋊C4—881no—
456C4⋊C4C2×C22⋊D1112yes—
457C4⋊C4C2×C22⋊D1114yes—
458C22⋊C4—28no—
459C22⋊C4—28no—
460C22⋊C4—24no—
461C22⋊C4—444no—
462C22⋊C4—444no—
463C22⋊C4—442no—
464C42—28no—
465C42—24no—
466C42C2×C22⋊D1112yes—
467C42C2×C22⋊D1112yes—
468C11#2411911yescharacteristic, complemented, Sylow
469C23—22no—
470C23—22no—
471C23—22no—
472C23—22no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—222no—
477C23—441no—
478C23—441no—
479C23—441no—
480C23—441no—
481C23—441no—
482C23—441no—
483C23C22×C22⋊D1111yescharacteristic
484Q8—22no—
485Q8—22no—
486Q8—41no—
487Q8—48no—
488Q8—41no—
489D4—44no—
490D4—222no—
491D4—222no—
492D4—441no—
493D4—441no—
494D4—888no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—441no—
514C2×C4—442no—
515C2×C4—441no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4—441no—
519C2×C4—884no—
520C2×C4#6700212yes—
521C2×C4#6700312yes—
522C2×C4#6700612yes—
523C2×C4#6700612yes—
524C2×C4#41×D1111yescharacteristic
525C2×C4#41×D1111yescharacteristic
526C2×C4#6704211yescharacteristic
527C2×C4#6704311yescharacteristic
528C2×C4C22×C22⋊D1111yescharacteristic
529C2×C4C22×C22⋊D1111yescharacteristic
530C8—222no—
531C8—441no—
532C8—442no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—442no—
541C22—442no—
542C22—442no—
543C22—881no—
544C22—881no—
545C22—881no—
546C22—881no—
547C22C2×#6700211yescharacteristic
548C22C2×#6700311yescharacteristic
549C22#1062335511yescharacteristic
550C22#1062336011yescharacteristic
551C22#1062336811yescharacteristic
552C22#1062336911yescharacteristic
553C22C2×#6700611yescharacteristic
554C4—22no—
555C4—44no—
556C4—42no—
557C4—42no—
558C4—42no—
559C4—882no—
560C4—881no—
561C4#1062285114yes—
562C4#1062335911yescharacteristic
563C4#1062336211yescharacteristic
564C4#1062336411yescharacteristic
565C4#1062336511yescharacteristic
566C2—82no—
567C2—882no—
568C2#1307195511yescharacteristic
569C2C2×#1062285111yescharacteristic
570C2#1307793111yescharacteristic
571C2#1308052711yescharacteristic
572C2#1308084111yescharacteristic
573C2#1308102311yescharacteristic
574C2#1308119411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#556C2
socleC23×C11C22×D4
prime radical#13073529C2
hypercenterC2×#556D11
hypocenterC11#24119
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#10622700C2semidirect
2. C2×C4×#4325C2semidirect
4. #13069816C2semidirect
5. #13069617C2semidirect
6. #13069578C2semidirect
7. #13069411C2semidirect
8. #13068938C2semidirect
9. #13068815C2semidirect
10. #13068621C2semidirect
11. C2×C11×#556C2semidirect
53. C11×C4⋊Q8D4semidirect
60. C4×Q8×C11D4semidirect
182. C2×#556D11semidirect
337. C4⋊Q8C22⋊D11semidirect
347. C4×Q8C22⋊D11semidirect
468. C11#24119semidirect

Maximal subgroups

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

subgroupindex
C2×#106227002
C2×C4×#43252
#130735292
#130698162
#130696172
#130695782
#130694112
#130689382
#130688152
#130686212
C2×C11×#5562
#2411911