Finite Group Databasebeta

← #14764917

Subgroups — #14764917

Order 2816.

1092 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622351C211yesmaximal, characteristic
2C4×#66983C211yesmaximal, characteristic
3C2×#10622542C211yesmaximal, characteristic, complemented
4#13069470C212yesmaximal, complemented
5#13069292C212yesmaximal, complemented
6#13069251C212yesmaximal, complemented
7#13068949C212yesmaximal, complemented
8#13068931C211yesmaximal, characteristic
9#13068811C211yesmaximal, characteristic, complemented
10#13068552C211yesmaximal, characteristic, complemented
11C4×C11×C22⋊C8C211yesmaximal, characteristic, complemented
12C23×Dic22C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C2×#66983C2211yescharacteristic
15C2×C4×C22⋊D11—21no—
16C22×C4⋊Dic11C2211yescharacteristic
17C22×#4314C2212yes—
18C2×C4×D44C2211yescharacteristic
19C2×C11×C22⋊C8C2211yescharacteristic
20C2×C11×C22⋊C8C2211yescharacteristic
21C2×C4×C8×C11C2212yes—
22#10622826—21no—
23#10622825C2211yescharacteristic
24C2×C11⋊#95—21no—
25C2×C11⋊#95—21no—
26C2×#66885C2212yes—
27C2×#66881C2212yes—
28C2×#66880C2212yes—
29C2×#66880C2212yes—
30C2×#66880C2212yes—
31#10622553—21no—
32#10622552C2211yescharacteristic
33C4×(C2×D11)⋊C4—21no—
34C4×C4⋊Dic11C2211yescharacteristic
35#10622542—21no—
36#10622542—21no—
37#10622542C2212yes—
38#10622542C2212yes—
39#10622541C2211yescharacteristic
40#10622351C418yescomplemented
41C11×#336C2212yes—
42#10622189C2212yes—
43#10622189C2212yes—
44C23×C4×C11D411yescharacteristic
45C23×C4×C11D411yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C22×C22⋊D11—21no—
48C23×Dic11—21no—
49C23×Dic11—21no—
50C22×D44C2311yescharacteristic
51C22×C4×D11—21no—
52C22×Dic22—21no—
53C22×Dic22—22no—
54C22×Dic22—42no—
55C22×Dic22—42no—
56C22×Dic22C2×C414yescomplemented
57C22×Dic22C2312yes—
58C22×C8×C11C2312yes—
59C22×C8×C11C2312yes—
60C2×C42×C11—42no—
61C2×C42×C11D411yescharacteristic
62C2×C42×C11D411yescharacteristic
63C2×C42×C11C2311yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×C22⋊Dic11—21no—
66#66983—22no—
67#66983C2×C414yes—
68C4×C22⋊D11—44no—
69C2×(C2×D11)⋊C4—21no—
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—42no—
75C2×C4⋊Dic11C2312yes—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×Dic11⋊C4—21no—
80C2×C4×Dic11—21no—
81C2×#4314—42no—
82C2×#4314—42no—
83C2×#4314C2×C418yescomplemented
84C4×D44—42no—
85C11×C22⋊C8—22no—
86C11×C22⋊C8C2×C414yescomplemented
87C4×C8×C11—42no—
88C11⋊#95—21no—
89C11⋊#95—22no—
90C11⋊#95—22no—
91C11⋊#95—22no—
92C11⋊#95—22no—
93C11⋊#95—21no—
94C11⋊#95—21no—
95#66885—42no—
96#66881—42no—
97#66880—42no—
98#66880—42no—
99#66880C2×C418yescomplemented
100#22041—111nomaximal, Sylow
101C24×C11C2×D411yescharacteristic
102C23×D11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—41no—
108C22×C4×C11—41no—
109C22×C4×C11—41no—
110C22×C4×C11SD1614yescomplemented
111C22×C4×C11C22×C412yes—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11#4112yes—
118C22×C4×C11C2411yescharacteristic
119C2×C22⋊D11—24no—
120C2×C22⋊D11—42no—
121C2×C22⋊D11—42no—
122C22×Dic11—24no—
123C22×Dic11—22no—
124C22×Dic11—21no—
125C22×Dic11—22no—
126C22×Dic11—21no—
127C22×Dic11—21no—
128C22×Dic11—42no—
129C22×Dic11—42no—
130C22×Dic11—42no—
131C22×Dic11—42no—
132C22×Dic11—42no—
133C2×D44—21no—
134C2×D44—22no—
135C2×D44—22no—
136C2×D44C22×C412yes—
137C2×C4×D11—42no—
138C2×C4×D11—42no—
139C2×C4×D11—42no—
140C2×Dic22—24no—
141C2×Dic22—22no—
142C2×Dic22—22no—
143C2×Dic22—22no—
144C2×Dic22—22no—
145C2×Dic22—22no—
146C2×Dic22—48no—
147C2×Dic22—42no—
148C2×Dic22—42no—
149C2×Dic22—48no—
150C2×Dic22C22×C414yes—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11C22×C414yes—
157C42×C11—22no—
158C42×C11—22no—
159C42×C11—41no—
160C42×C11—41no—
161C22⋊Dic11—42no—
162(C2×D11)⋊C4—24no—
163(C2×D11)⋊C4—42no—
164(C2×D11)⋊C4—42no—
165(C2×D11)⋊C4—42no—
166C4⋊Dic11—21no—
167C4⋊Dic11—22no—
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170C4⋊Dic11—22no—
171C4⋊Dic11—42no—
172C4⋊Dic11C22×C412yes—
173Dic11⋊C4—42no—
174C4×Dic11—42no—
175#4314—48no—
176C2×#448—111no—
177C4×#121—111no—
178C2×#391—111no—
179#1968—112no—
180#1933—112no—
181#1927—112no—
182#1877—112no—
183#1874—111no—
184#1853—111no—
185#1787—111no—
186C4×C22⋊C8D1111yescharacteristic, complemented
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—21no—
191C23×C11C4×D412yes—
192C23×C11C2×SD1612yes—
193C23×C11#13512yes—
194C23×C11C22×D411yescharacteristic
195C22×D11—22no—
196C22×D11—41no—
197C22×D11—41no—
198C22×D11—41no—
199C22×D11—41no—
200C22×D11—41no—
201C22×D11—41no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—44no—
216C2×C4×C11—44no—
217C2×C4×C11C4×D412yes—
218C2×C4×C11C2×SD1612yes—
219C2×C4×C11C2×SD1612yes—
220C2×C4×C11#13712yes—
221C2×C4×C11C23×C411yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C11H(5,𝔽2)12yes—
224C2×C4×C11H(5,𝔽2)12yes—
225C22⋊D11—48no—
226C2×Dic11—22no—
227C2×Dic11—24no—
228C2×Dic11—48no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—42no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11—42no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—42no—
242C2×Dic11—84no—
243D44—24no—
244D44—42no—
245C4×D11—84no—
246Dic22—24no—
247Dic22—24no—
248Dic22—48no—
249Dic22—42no—
250Dic22—42no—
251C8×C11—24no—
252C8×C11—42no—
253C23×Q8—111no—
254C22×SD16—112no—
255C2×#121—111no—
256C2×C4×D4—111no—
257C2×C4×D4—221no—
258C22×C4⋊C4—111no—
259C22×C42C2×D1111yescharacteristic
260#448—118no—
261C2×#106—112no—
262C2×#103—112no—
263C2×#103—112no—
264C2×#103—112no—
265C2×#102—112no—
266C2×C22⋊C8C2×D1111yescharacteristic
267C2×C22⋊C8C2×D1111yescharacteristic
268C2×C4×C8C2×D1112yes—
269#391—112no—
270#391—112no—
271#391—221no—
272#391—221no—
273#390—111no—
274#389—111no—
275#388—221no—
276#386—221no—
277#380—111no—
278C4×C4⋊C4—111no—
279C4×C22⋊C4—221no—
280C2×#95—221no—
281C2×#95—221no—
282#340—112no—
283#340—112no—
284#336C2×D1112yes—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11C4×SD1614yes—
292C22×C11C2×C4×D411yescharacteristic
293C22×C11#53411yescharacteristic
294C22×C11#53511yescharacteristic
295C22×C11C22×SD1611yescharacteristic
296C22×C11C2×#13511yescharacteristic
297C22×C11C2×#13711yescharacteristic
298C22×C11#57511yescharacteristic
299C2×D11—42no—
300C2×D11—42no—
301C2×D11—42no—
302C2×D11—81no—
303C2×D11—81no—
304C2×D11—81no—
305C2×D11—81no—
306C4×C11—22no—
307C4×C11—22no—
308C4×C11—22no—
309C4×C11—22no—
310C4×C11—41no—
311C4×C11#51812yes—
312C4×C11#53812yes—
313Dic11—44no—
314Dic11—42no—
315Dic11—81no—
316Dic11—81no—
317Dic11—82no—
318C22×Q8—114no—
319C22×Q8—112no—
320C22×Q8—221no—
321C22×Q8—222no—
322C22×Q8—442no—
323C22×Q8—442no—
324C22×D4—111no—
325C22×D4—221no—
326C23×C4—221no—
327C23×C4—221no—
328C23×C4—221no—
329C23×C4D4411yescharacteristic
330C23×C4D4411yescharacteristic
331C23×C4C22×D1111yescharacteristic
332C2×SD16—118no—
333C2×SD16—442no—
334C2×SD16—442no—
335C22×C8C22×D1112yes—
336C22×C8C22×D1112yes—
337#121—114no—
338#121—222no—
339C4×D4—442no—
340C4×D4—444no—
341C2×C4⋊C4—111no—
342C2×C4⋊C4—112no—
343C2×C4⋊C4—111no—
344C2×C4⋊C4—111no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4—442no—
348C2×C22⋊C4—221no—
349C2×C22⋊C4—221no—
350C2×C22⋊C4—221no—
351C2×C22⋊C4—221no—
352C2×C22⋊C4—221no—
353C2×C42—42no—
354C2×C42—221no—
355C2×C42D4411yescharacteristic
356C2×C42D4411yescharacteristic
357C2×C42C22×D1111yescharacteristic
358C2×C42C22×D1111yescharacteristic
359#106—442no—
360#103—118no—
361#103—442no—
362#103—442no—
363#102—442no—
364C22⋊C8—22no—
365C22⋊C8C4×D1114yescomplemented
366C4×C8—42no—
367#95—222no—
368#95—222no—
369#95—222no—
370#95—222no—
371#95—221no—
372#95—221no—
373#95—221no—
374C2×C11—24no—
375C2×C11#232111yescharacteristic
376C2×C11C2×C4×SD1611yescharacteristic
377C2×C11C4×#13711yescharacteristic
378C2×C11#318711yescharacteristic
379C2×C11#319011yescharacteristic
380C2×C11#320611yescharacteristic
381C2×C11#321111yescharacteristic
382D11—82no—
383C24—221no—
384C24C2×D4411yescharacteristic
385C2×Q8—114no—
386C2×Q8—224no—
387C2×Q8—222no—
388C2×Q8—222no—
389C2×Q8—222no—
390C2×Q8—222no—
391C2×Q8—222no—
392C2×Q8—448no—
393C2×Q8—442no—
394C2×Q8—442no—
395C2×Q8—448no—
396C2×D4—112no—
397C2×D4—224no—
398C2×D4—221no—
399C2×D4—222no—
400C2×D4—222no—
401C2×D4—442no—
402C2×D4—442no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—224no—
411C22×C4—222no—
412C22×C4—221no—
413C22×C4—222no—
414C22×C4—221no—
415C22×C4—221no—
416C22×C4—442no—
417C22×C4—442no—
418C22×C4—442no—
419C22×C4—442no—
420C22×C4—442no—
421C22×C4—442no—
422C22×C4—442no—
423C22×C4—442no—
424C22×C4#431414yescomplemented
425C22×C4C2×C4×D1112yes—
426C22×C4C2×D4411yescharacteristic
427C22×C4C2×D4411yescharacteristic
428C22×C4C2×D4411yescharacteristic
429C22×C4C2×D4411yescharacteristic
430C22×C4C2×D4411yescharacteristic
431C22×C4#433912yes—
432C22×C4C23×D1111yescharacteristic
433SD16—448no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8C2×C4×D1114yes—
440C4⋊C4—112no—
441C4⋊C4—221no—
442C4⋊C4—222no—
443C4⋊C4—222no—
444C4⋊C4—222no—
445C4⋊C4—222no—
446C4⋊C4—442no—
447C4⋊C4—442no—
448C22⋊C4—224no—
449C22⋊C4—442no—
450C22⋊C4—442no—
451C22⋊C4—442no—
452C22⋊C4—442no—
453C42—22no—
454C42—22no—
455C42—41no—
456C42—41no—
457C42—442no—
458C11#2204111yescharacteristic, complemented, Sylow
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—222no—
464C23—441no—
465C23—441no—
466C23—441no—
467C23—441no—
468C23—441no—
469C23—441no—
470C23C4×D4412yes—
471C23C2×#431412yes—
472C23#6695712yes—
473C23C22×D4411yescharacteristic
474Q8—224no—
475Q8—224no—
476Q8—448no—
477Q8—442no—
478Q8—442no—
479D4—224no—
480D4—448no—
481D4—442no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—44no—
496C2×C4—44no—
497C2×C4—222no—
498C2×C4—224no—
499C2×C4—448no—
500C2×C4—441no—
501C2×C4—441no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—441no—
505C2×C4—441no—
506C2×C4—442no—
507C2×C4—441no—
508C2×C4—442no—
509C2×C4—441no—
510C2×C4—441no—
511C2×C4—442no—
512C2×C4—441no—
513C2×C4—884no—
514C2×C4—884no—
515C2×C4C4×D4412yes—
516C2×C4C2×#431412yes—
517C2×C4C2×#431412yes—
518C2×C4#6696212yes—
519C2×C4C22×C4×D1111yescharacteristic
520C2×C4C2×#433911yescharacteristic
521C2×C4#6703712yes—
522C2×C4#6704212yes—
523C8—24no—
524C8—42no—
525C22—22no—
526C22—22no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—442no—
532C22—442no—
533C22—442no—
534C22—881no—
535C22—881no—
536C22—881no—
537C22—881no—
538C22C4×#431414yes—
539C22C2×C4×D4411yescharacteristic
540C22#1062302411yescharacteristic
541C22#1062305611yescharacteristic
542C22C22×#431411yescharacteristic
543C22C2×#6695711yescharacteristic
544C22C2×#6696211yescharacteristic
545C22#1062327911yescharacteristic
546C4—22no—
547C4—22no—
548C4—22no—
549C4—22no—
550C4—41no—
551C4—442no—
552C4—444no—
553C4—882no—
554C4—881no—
555C4—881no—
556C4#1062307612yes—
557C4#1062309112yes—
558C2—24no—
559C2—882no—
560C2#1307127611yescharacteristic
561C2C2×C4×#431411yescharacteristic
562C2C4×#6696211yescharacteristic
563C2#1307937411yescharacteristic
564C2#1307939911yescharacteristic
565C2#1307954311yescharacteristic
566C2#1307958311yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×C22⋊C8C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
cosocleC22×C4×C11C24
hypercenterC4×C22⋊C8D11
hypocenterC11#22041
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. C2×#10622542C2semidirect
4. #13069470C2semidirect
5. #13069292C2semidirect
6. #13069251C2semidirect
7. #13068949C2semidirect
9. #13068811C2semidirect
10. #13068552C2semidirect
11. C4×C11×C22⋊C8C2semidirect
40. #10622351C4semidirect
56. C22×Dic22C2×C4semidirect
83. C2×#4314C2×C4semidirect
86. C11×C22⋊C8C2×C4semidirect
99. #66880C2×C4semidirect
110. C22×C4×C11SD16semidirect
186. C4×C22⋊C8D11semidirect
365. C22⋊C8C4×D11semidirect
424. C22×C4#4314semidirect
458. C11#22041semidirect

Maximal subgroups

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

subgroupindex
C2×#106223512
C4×#669832
C2×#106225422
#130694702
#130692922
#130692512
#130689492
#130689312
#130688112
#130685522
C4×C11×C22⋊C82
#2204111