Finite Group Databasebeta

← #14764986

Subgroups — #14764986

Order 2816.

1080 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×#10622840C211yesmaximal, characteristic
2#13071122C211yesmaximal, characteristic
3C2×#10622843C211yesmaximal, characteristic, complemented
4#13069494C212yesmaximal, complemented
5#13069303C212yesmaximal, complemented
6#13069260C212yesmaximal, complemented
7#13068947C212yesmaximal, complemented
8#13068931C211yesmaximal, characteristic
9#13068803C211yesmaximal, characteristic, complemented
10#13068380C211yesmaximal, characteristic, complemented
11C11×#1787C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C22×#4325C2212yes—
14C2×#66983C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×C4×Dic11C2211yescharacteristic
17C2×#66946C2211yescharacteristic
18C2×(C22⋊D11)⋊C4—21no—
19C2×C11×#103C2212yes—
20C2×C11×#103C2212yes—
21C2×C11×C22⋊C8C2211yescharacteristic
22C11×#380C2211yescharacteristic
23#10622843—21no—
24#10622843—21no—
25#10622843C2212yes—
26#10622843C2212yes—
27#10622840C418yescomplemented
28C2×#66899C2212yes—
29C2×C11⋊#95—21no—
30C2×C11⋊#95—21no—
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×#66885C2212yes—
33C2×#66879C2212yes—
34#10622601C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36#10622586C2211yescharacteristic
37C2×#66871C2212yes—
38#10622571—21no—
39#10622282—21no—
40#10622279—21no—
41#10622189C2212yes—
42#10622188C2212yes—
43#10622167C2212yes—
44C22×Q8×C11—21no—
45C22×Q8×C11—22no—
46C22×Q8×C11—42no—
47C22×Q8×C11—42no—
48C22×Q8×C11C2×C414yescomplemented
49C22×Q8×C11C2312yes—
50C23×C4×C11—21no—
51C23×C4×C11C2311yescharacteristic
52C22×C22⋊D11—21no—
53C23×Dic11—21no—
54C23×Dic11D411yescharacteristic
55C23×Dic11D411yescharacteristic
56C22×D44C2311yescharacteristic
57C22×C4×D11—21no—
58C22×C8×C11C2312yes—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C22⋊C4—21no—
62C2×#4325—42no—
63C2×#4325—42no—
64C2×#4325C2×C418yescomplemented
65#66983—22no—
66#66983C2×C414yes—
67C2×(C2×D11)⋊C4—21no—
68C2×(C2×D11)⋊C4—21no—
69C2×(C2×D11)⋊C4—21no—
70C2×(C2×D11)⋊C4—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—42no—
73C2×C4⋊Dic11C2312yes—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×Dic11⋊C4—21no—
76C2×C4×Dic11—21no—
77C2×C4×Dic11—42no—
78C2×C4×Dic11D411yescharacteristic
79C2×C4×Dic11D411yescharacteristic
80C2×C4×Dic11C2311yescharacteristic
81C2×C4×Dic11C2311yescharacteristic
82C22×C11⋊C8C2312yes—
83#66946—42no—
84(C22⋊D11)⋊C4—44no—
85C11×#103—42no—
86C11×#103—42no—
87C11×C22⋊C8—22no—
88C11×#95—21no—
89#66899C2×C418yescomplemented
90C11⋊#95—21no—
91C11⋊#95—21no—
92C11⋊#95—22no—
93C11⋊#95—22no—
94C11⋊#95—22no—
95C11⋊#95—22no—
96C22⋊(C11⋊C8)C2×C414yescomplemented
97#66885—42no—
98#66879—42no—
99#66871—42no—
100#22047—111nomaximal, Sylow
101C24×C11C2×D411yescharacteristic
102C23×D11—21no—
103C2×Q8×C11—24no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—48no—
110C2×Q8×C11—42no—
111C2×Q8×C11—42no—
112C2×Q8×C11—48no—
113C2×Q8×C11C22×C414yes—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—24no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11C22×C412yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11#4112yes—
125C22×C4×C11C2411yescharacteristic
126C2×C22⋊D11—24no—
127C2×C22⋊D11—42no—
128C2×C22⋊D11—42no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—21no—
133C22×Dic11—22no—
134C22×Dic11—41no—
135C22×Dic11—41no—
136C22×Dic11—41no—
137C22×Dic11—42no—
138C22×Dic11—42no—
139C22×Dic11—42no—
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
144C2×D44—21no—
145C2×D44—22no—
146C2×D44—22no—
147C2×D44C22×C412yes—
148C2×C4×D11—42no—
149C2×C4×D11—42no—
150C2×C4×D11—42no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C22⋊C4—42no—
157#4325—48no—
158(C2×D11)⋊C4—24no—
159(C2×D11)⋊C4—42no—
160(C2×D11)⋊C4—42no—
161(C2×D11)⋊C4—42no—
162C4⋊Dic11—21no—
163C4⋊Dic11—22no—
164C4⋊Dic11—22no—
165C4⋊Dic11—42no—
166C4⋊Dic11C22×C412yes—
167Dic11⋊C4—42no—
168C4×Dic11—22no—
169C4×Dic11—22no—
170C4×Dic11—41no—
171C4×Dic11—41no—
172C4×Dic11—42no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8C22×C414yes—
176C2×#448—111no—
177C4×#121—111no—
178C2×#391—111no—
179#1973—112no—
180#1935—112no—
181#1928—112no—
182#1877—112no—
183#1874—111no—
184#1852—111no—
185#1787D1111yescharacteristic, complemented
186#1749—111no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—21no—
191C23×C11C4×D412yes—
192C23×C11AGL(1,ℤ/8)12yes—
193C23×C11#13712yes—
194C23×C11C22×D411yescharacteristic
195C22×D11—22no—
196C22×D11—41no—
197C22×D11—41no—
198C22×D11—41no—
199C22×D11—41no—
200C22×D11—41no—
201C22×D11—41no—
202Q8×C11—24no—
203Q8×C11—24no—
204Q8×C11—48no—
205Q8×C11—42no—
206Q8×C11—42no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—48no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11C4×D412yes—
222C2×C4×C11C23×C411yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11H(5,𝔽2)12yes—
225C2×C4×C11H(5,𝔽2)12yes—
226C22⋊D11—48no—
227C2×Dic11—21no—
228C2×Dic11—21no—
229C2×Dic11—22no—
230C2×Dic11—21no—
231C2×Dic11—21no—
232C2×Dic11—21no—
233C2×Dic11—21no—
234C2×Dic11—21no—
235C2×Dic11—21no—
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—44no—
240C2×Dic11—44no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—84no—
247C2×Dic11#13712yes—
248D44—24no—
249D44—42no—
250C4×D11—84no—
251C8×C11—42no—
252C11⋊C8—24no—
253C23×Q8C2×D1111yescharacteristic
254C22×SD16—112no—
255C2×#121—111no—
256C2×C4×D4—111no—
257C2×C4×D4—221no—
258C22×C4⋊C4—111no—
259C22×C42—111no—
260#448—118no—
261C2×#107—112no—
262C2×#103—112no—
263C2×#103C2×D1112yes—
264C2×#103C2×D1112yes—
265C2×#102—112no—
266C2×C22⋊C8—111no—
267C2×C22⋊C8C2×D1111yescharacteristic
268C2×#97—112no—
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#380C2×D1111yescharacteristic
278C4×C4⋊C4—111no—
279C4×C22⋊C4—221no—
280C2×#95—221no—
281C2×#95—221no—
282#340—112no—
283#340—112no—
284#336—112no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—22no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11#44014yes—
292C22×C11C2×C4×D411yescharacteristic
293C22×C11#53411yescharacteristic
294C22×C11#53511yescharacteristic
295C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
296C22×C11C2×#13711yescharacteristic
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—44no—
308C4×C11—81no—
309C4×C11—81no—
310C4×C11#51812yes—
311C4×C11#53812yes—
312Dic11—22no—
313Dic11—41no—
314Dic11—42no—
315Dic11—41no—
316Dic11—41no—
317Dic11—82no—
318C22×Q8—21no—
319C22×Q8—22no—
320C22×Q8—42no—
321C22×Q8—42no—
322C22×Q8C4×D1114yescomplemented
323C22×Q8C22×D1112yes—
324C22×D4—111no—
325C22×D4—221no—
326C23×C4—21no—
327C23×C4—111no—
328C23×C4—111no—
329C23×C4—221no—
330C23×C4—221no—
331C23×C4C22×D1111yescharacteristic
332C2×SD16—118no—
333C2×SD16—442no—
334C2×SD16—442no—
335C22×C8—112no—
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—221no—
344C2×C4⋊C4—221no—
345C2×C4⋊C4—442no—
346C2×C4⋊C4C22×D1111yescharacteristic
347C2×C4⋊C4C22×D1111yescharacteristic
348C2×C22⋊C4—21no—
349C2×C22⋊C4—221no—
350C2×C22⋊C4—221no—
351C2×C22⋊C4—221no—
352C2×C22⋊C4—221no—
353C2×C42—111no—
354C2×C42—111no—
355C2×C42—111no—
356C2×C42—111no—
357C2×C42—221no—
358C2×C42—442no—
359#107—442no—
360#103—42no—
361#103—42no—
362#103—118no—
363#102—442no—
364C22⋊C8—22no—
365C22⋊C8—114no—
366#97—442no—
367#95—21no—
368#95—222no—
369#95—222no—
370#95—222no—
371#95—222no—
372#95—221no—
373#95—221no—
374C2×C11—24no—
375C2×C11#232111yescharacteristic
376C2×C11C2×#44011yescharacteristic
377C2×C11C4×#13711yescharacteristic
378C2×C11#319311yescharacteristic
379C2×C11#319611yescharacteristic
380C2×C11#321311yescharacteristic
381C2×C11#321811yescharacteristic
382D11—82no—
383C24—221no—
384C24D4×D1111yescharacteristic
385C2×Q8—24no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—48no—
392C2×Q8—42no—
393C2×Q8—42no—
394C2×Q8—48no—
395C2×Q8C2×C4×D1114yes—
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—24no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—111no—
412C22×C4—111no—
413C22×C4—111no—
414C22×C4—111no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—221no—
419C22×C4—222no—
420C22×C4—442no—
421C22×C4—442no—
422C22×C4—442no—
423C22×C4—441no—
424C22×C4—441no—
425C22×C4—441no—
426C22×C4—442no—
427C22×C4—442no—
428C22×C4—442no—
429C22×C4C2×C4×D1112yes—
430C22×C4D4×D1111yescharacteristic
431C22×C4#434112yes—
432C22×C4C23×D1111yescharacteristic
433SD16—448no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—114no—
438C2×C8—222no—
439C2×C8—222no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—112no—
443C4⋊C4—221no—
444C4⋊C4—222no—
445C4⋊C4—222no—
446C4⋊C4—442no—
447C4⋊C4—442no—
448C22⋊C4—42no—
449C22⋊C4—224no—
450C22⋊C4—442no—
451C22⋊C4—442no—
452C22⋊C4—442no—
453C42—222no—
454C42—222no—
455C42—441no—
456C42—441no—
457C42—442no—
458C11#2204711yescharacteristic, complemented, Sylow
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—222no—
464C23—441no—
465C23—441no—
466C23—441no—
467C23—441no—
468C23—441no—
469C23—441no—
470C23(C22⋊D11)⋊C412yes—
471C23#6696712yes—
472C23#6697112yes—
473C23C2×D4×D1111yescharacteristic
474Q8—24no—
475Q8—24no—
476Q8—48no—
477Q8—42no—
478Q8—42no—
479D4—224no—
480D4—448no—
481D4—442no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—48no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—112no—
497C2×C4—221no—
498C2×C4—221no—
499C2×C4—222no—
500C2×C4—221no—
501C2×C4—221no—
502C2×C4—221no—
503C2×C4—221no—
504C2×C4—221no—
505C2×C4—221no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—444no—
510C2×C4—444no—
511C2×C4—441no—
512C2×C4—441no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—884no—
517C2×C4—884no—
518C2×C4(C22⋊D11)⋊C412yes—
519C2×C4C22×C4×D1111yescharacteristic
520C2×C4C2×#434111yescharacteristic
521C2×C4#6703712yes—
522C2×C4#6703712yes—
523C8—42no—
524C8—224no—
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—
538C22#1062243014yes—
539C22C2×(C22⋊D11)⋊C411yescharacteristic
540C22#1062312011yescharacteristic
541C22#1062312311yescharacteristic
542C22C2×#6696711yescharacteristic
543C22C2×#6697111yescharacteristic
544C22D11×#13711yescharacteristic
545C22#1062330811yescharacteristic
546C4—22no—
547C4—44no—
548C4—81no—
549C4—81no—
550C4—222no—
551C4—441no—
552C4—442no—
553C4—441no—
554C4—441no—
555C4—882no—
556C4#1062301712yes—
557C4#1062312412yes—
558C2—24no—
559C2—882no—
560C2#1307127111yescharacteristic
561C2C2×#1062243011yescharacteristic
562C2#1307743111yescharacteristic
563C2#1307942011yescharacteristic
564C2#1307944911yescharacteristic
565C2#1307960211yescharacteristic
566C2#1307964611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1787C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
cosocleC22×C4×C11C24
hypercenter#1787D11
hypocenterC11#22047
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
3. C2×#10622843C2semidirect
4. #13069494C2semidirect
5. #13069303C2semidirect
6. #13069260C2semidirect
7. #13068947C2semidirect
9. #13068803C2semidirect
10. #13068380C2semidirect
11. C11×#1787C2semidirect
27. #10622840C4semidirect
48. C22×Q8×C11C2×C4semidirect
64. C2×#4325C2×C4semidirect
89. #66899C2×C4semidirect
96. C22⋊(C11⋊C8)C2×C4semidirect
185. #1787D11semidirect
322. C22×Q8C4×D11semidirect
458. C11#22047semidirect

Maximal subgroups

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

subgroupindex
C2×#106228402
#130711222
C2×#106228432
#130694942
#130693032
#130692602
#130689472
#130689312
#130688032
#130683802
C11×#17872
#2204711