Finite Group Databasebeta

← #14812744

Subgroups — #14812744

Order 2816.

714 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073857C211yesmaximal, characteristic, complemented
2#13071561C211yesmaximal, characteristic
3#13070136C211yesmaximal, characteristic
4#13070134C211yesmaximal, characteristic
5#13070005C211yesmaximal, characteristic
6#13070001C211yesmaximal, characteristic
7#13069384C211yesmaximal, characteristic, complemented
8#13069383C211yesmaximal, characteristic, complemented
9#13069378C211yesmaximal, characteristic, complemented
10#13069333C211yesmaximal, characteristic, complemented
11#13069207C211yesmaximal, characteristic, complemented
12#13068774C211yesmaximal, characteristic, complemented
13#13068615C211yesmaximal, characteristic
14#13068430C211yesmaximal, characteristic
15C11×#1921C211yesmaximal, characteristic, complemented
16C2×#66946C2211yescharacteristic
17C2×#66925—21no—
18C2×C11×#107C2211yescharacteristic
19C11×#389C2211yescharacteristic
20C4×C11×C4⋊C4C2211yescharacteristic
21C2×#66885C2211yescharacteristic
22C2×#66885C2211yescharacteristic
23C2×#66882C2211yescharacteristic
24C2×#66881C2211yescharacteristic
25C2×Dic11⋊C8C2211yescharacteristic
26C2×Dic11⋊C8C2211yescharacteristic
27C2×C8×Dic11C2211yescharacteristic
28#10622601C2211yescharacteristic
29#10622595—21no—
30#10622590C2211yescharacteristic
31#10622589C2211yescharacteristic
32#10622589C2211yescharacteristic
33C4⋊C4×Dic11C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35#10622586C2211yescharacteristic
36#10622585—21no—
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42#10622553—21no—
43#10622552C2211yescharacteristic
44#10622549C2211yescharacteristic
45C4×Dic11⋊C4C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47#10622282—21no—
48#10622280—21no—
49#10622271—21no—
50#10622263—21no—
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C42×C11—21no—
69C2×C42×C11C2311yescharacteristic
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4D411yescharacteristic
84C2×Dic11⋊C4D411yescharacteristic
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11C2311yescharacteristic
88C2×C4×Dic11C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91#66946—22no—
92#66946Q814yes—
93#66925—44no—
94C11×#107—22no—
95C11×#95—21no—
96C11×#95—21no—
97C11⋊#95—21no—
98C11⋊#95—21no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95D411yescharacteristic
105C11⋊#95D411yescharacteristic
106#66885—22no—
107#66885—41no—
108#66882—22no—
109#66881—41no—
110Dic11⋊C8—22no—
111Dic11⋊C8—22no—
112C8×Dic11—22no—
113#66873—22no—
114#66873—41no—
115#66872—41no—
116#66871—41no—
117#66871—41no—
118C4⋊(C11⋊C8)—22no—
119#26087—111nomaximal, Sylow
120C23×D11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11C2×D411yescharacteristic
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44C2×Q812yes—
141C2×C4×D11—24no—
142C2×C4×D11—42no—
143C2×C4×D11—42no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11#4112yes—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—81no—
158C11×C4⋊C4C2×Q812yes—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11—42no—
162(C2×D11)⋊C4—24no—
163(C2×D11)⋊C4—42no—
164(C2×D11)⋊C4—42no—
165(C2×D11)⋊C4—81no—
166(C2×D11)⋊C4—81no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173Dic11⋊C4—22no—
174Dic11⋊C4—22no—
175Dic11⋊C4—42no—
176Dic11⋊C4—42no—
177Dic11⋊C4—81no—
178Dic11⋊C4—81no—
179Dic11⋊C4—81no—
180C4×Dic11—21no—
181C4×Dic11—21no—
182C4×Dic11—42no—
183C4×Dic11—42no—
184C4×Dic11C2×Q812yes—
185C4×Dic11#4112yes—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8#4112yes—
192#2571—111no—
193#2354—111no—
194#2092—111no—
195#2092—111no—
196#2067—111no—
197#2067—111no—
198#1949—111no—
199#1949—111no—
200#1948—111no—
201#1939—111no—
202#1921—111no—
203#1921D1111yescharacteristic, complemented
204#1845—111no—
205#1802—111no—
206C4×#102—111no—
207C23×C11C22×D411yescharacteristic
208C22×D11—22no—
209C22×D11—41no—
210C22×D11—41no—
211C22×D11—41no—
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—41no—
215C2×C4×C11—22no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11C22×Q811yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11H(5,𝔽2)11yescharacteristic
238C2×C4×C112−1+411yescharacteristic
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11C22⋊Q812yes—
257C2×Dic11C22⋊Q812yes—
258C2×Dic11#13512yes—
259C2×Dic11AGL(1,ℤ/8)12yes—
260D44—22no—
261D44—22no—
262D44—41no—
263D44—41no—
264C4×D11—48no—
265C8×C11—22no—
266C8×C11—41no—
267C11⋊C8—22no—
268C11⋊C8—41no—
269C2×C4×D4—111no—
270C2×#117—221no—
271C2×#107—111no—
272C2×#107—111no—
273C2×#107—111no—
274C2×#107C2×D1111yescharacteristic
275C2×#106—111no—
276C2×#106—111no—
277C2×C4⋊C8—111no—
278C2×C4⋊C8—111no—
279C2×C4⋊C8—111no—
280C2×#102—111no—
281C2×#102—111no—
282C2×#102—111no—
283C2×#102—111no—
284C2×C4×C8—111no—
285#400—221no—
286#400—221no—
287#390—111no—
288#390—111no—
289#389—111no—
290#389—221no—
291#389C2×D1111yescharacteristic
292#388—221no—
293#388—221no—
294#384—111no—
295#384—111no—
296#382—111no—
297#382—111no—
298#382—221no—
299#380—221no—
300C4×C4⋊C4—111no—
301C4×C4⋊C4—111no—
302C4×C4⋊C4—111no—
303C4×C4⋊C4C2×D1111yescharacteristic
304#340—111no—
305#340—111no—
306#340—111no—
307#340C2×D1111yescharacteristic
308#340C2×D1111yescharacteristic
309#340C2×D1111yescharacteristic
310#336—111no—
311#336C2×D1111yescharacteristic
312C22×C11C2×C22⋊Q811yescharacteristic
313C22×C11#54711yescharacteristic
314C22×C11#55011yescharacteristic
315C22×C11C2×#13511yescharacteristic
316C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
317C22×C11#57611yescharacteristic
318C22×C11#57811yescharacteristic
319C2×D11—42no—
320C2×D11—42no—
321C2×D11—42no—
322C2×D11—81no—
323C2×D11—81no—
324C2×D11—81no—
325C2×D11—81no—
326C4×C11—42no—
327C4×C11—41no—
328C4×C11—41no—
329C4×C11—81no—
330C4×C11—81no—
331C4×C11—81no—
332C4×C11#53311yescharacteristic
333C4×C11#54411yescharacteristic
334C4×C11#55211yescharacteristic
335C4×C11#55311yescharacteristic
336Dic11—22no—
337Dic11—41no—
338Dic11—41no—
339Dic11—81no—
340Dic11—81no—
341Dic11—81no—
342Dic11#47814yes—
343C22×D4—111no—
344C23×C4—221no—
345C22×C8—111no—
346C22×C8—111no—
347C22×C8C22×D1111yescharacteristic
348C22×C8C22×D1111yescharacteristic
349C4×D4—114no—
350C4×D4—222no—
351#117—444no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—111no—
354C2×C4⋊C4—111no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—221no—
359C2×C4⋊C4—221no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4C22×D1111yescharacteristic
364C2×C4⋊C4C22×D1111yescharacteristic
365C2×C4⋊C4C22×D1111yescharacteristic
366C2×C4⋊C4C22×D1111yescharacteristic
367C2×C22⋊C4—221no—
368C2×C22⋊C4—221no—
369C2×C22⋊C4—221no—
370C2×C22⋊C4—221no—
371C2×C22⋊C4—221no—
372C2×C42—21no—
373C2×C42—111no—
374C2×C42—111no—
375C2×C42—221no—
376C2×C42—221no—
377C2×C42C22×D1111yescharacteristic
378#107—22no—
379#107—222no—
380#107—441no—
381#107—441no—
382#106—441no—
383#106—441no—
384C4⋊C8—222no—
385C4⋊C8—222no—
386C4⋊C8—222no—
387#102—222no—
388#102—222no—
389#102—441no—
390#102—441no—
391C4×C8—222no—
392#95—21no—
393#95—21no—
394#95—111no—
395#95—111no—
396#95—221no—
397#95—221no—
398#95—221no—
399#95—221no—
400#95—221no—
401#95—221no—
402#95—221no—
403C2×C11#244111yescharacteristic
404C2×C11C2×#47811yescharacteristic
405C2×C11#308311yescharacteristic
406C2×C11#334111yescharacteristic
407C2×C11#335311yescharacteristic
408C2×C11#339311yescharacteristic
409C2×C11#339911yescharacteristic
410D11—82no—
411C24—221no—
412C2×D4—112no—
413C2×D4—221no—
414C2×D4—221no—
415C2×D4—221no—
416C2×D4—221no—
417C2×D4—221no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—111no—
423C22×C4—111no—
424C22×C4—111no—
425C22×C4—111no—
426C22×C4—224no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—442no—
431C22×C4—442no—
432C22×C4D4×D1111yescharacteristic
433C22×C4D4×D1111yescharacteristic
434C22×C4C23×D1111yescharacteristic
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—112no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8#433912yes—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—81no—
455C4⋊C4—222no—
456C4⋊C4—222no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—442no—
464C4⋊C4—442no—
465C4⋊C4—881no—
466C4⋊C4—881no—
467C4⋊C4—881no—
468C4⋊C4Q8×D1112yes—
469C22⋊C4—224no—
470C22⋊C4—442no—
471C22⋊C4—442no—
472C22⋊C4—881no—
473C22⋊C4—881no—
474C42—21no—
475C42—21no—
476C42—42no—
477C42—112no—
478C42—112no—
479C42—221no—
480C42—221no—
481C42—442no—
482C42—442no—
483C11#2608711yescharacteristic, complemented, Sylow
484C23—222no—
485C23—441no—
486C23—441no—
487C23—441no—
488C23—441no—
489C23—441no—
490C23—441no—
491C23C2×D4×D1111yescharacteristic
492D4—222no—
493D4—222no—
494D4—441no—
495D4—441no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—112no—
515C2×C4—112no—
516C2×C4—112no—
517C2×C4—112no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—448no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4C2×#433911yescharacteristic
537C2×C4C2×Q8×D1111yescharacteristic
538C2×C4#41×D1111yescharacteristic
539C2×C4#41×D1111yescharacteristic
540C2×C4#6704211yescharacteristic
541C2×C4#6704311yescharacteristic
542C8—22no—
543C8—41no—
544C8—222no—
545C8—441no—
546C22—442no—
547C22—442no—
548C22—442no—
549C22—881no—
550C22—881no—
551C22—881no—
552C22—881no—
553C22#1062308411yescharacteristic
554C22D11×C22⋊Q811yescharacteristic
555C22#1062318611yescharacteristic
556C22#1062329711yescharacteristic
557C22D11×#13511yescharacteristic
558C22D11×AGL(1,ℤ/8)11yescharacteristic
559C22#1062330511yescharacteristic
560C4—42no—
561C4—41no—
562C4—41no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4—114no—
567C4—222no—
568C4—441no—
569C4—441no—
570C4—881no—
571C4—881no—
572C4—881no—
573C4#1062306211yescharacteristic
574C4#1062310911yescharacteristic
575C4#1062322011yescharacteristic
576C4#1062324011yescharacteristic
577C2—882no—
578C2#1307232811yescharacteristic
579C2D11×#47811yescharacteristic
580C2#1307846411yescharacteristic
581C2#1308103311yescharacteristic
582C2#1308119311yescharacteristic
583C2#1308160411yescharacteristic
584C2#1308165911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1921C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1921D11
hypocenterC11#26087
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
1. #13073857C2semidirect
7. #13069384C2semidirect
8. #13069383C2semidirect
9. #13069378C2semidirect
10. #13069333C2semidirect
11. #13069207C2semidirect
12. #13068774C2semidirect
15. C11×#1921C2semidirect
203. #1921D11semidirect
483. C11#26087semidirect

Maximal subgroups

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

subgroupindex
#130738572
#130715612
#130701362
#130701342
#130700052
#130700012
#130693842
#130693832
#130693782
#130693332
#130692072
#130687742
#130686152
#130684302
C11×#19212
#2608711