Finite Group Databasebeta

← #14765978

Subgroups — #14765978

Order 2816.

740 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622483C211yesmaximal, characteristic
2#13071363C211yesmaximal, characteristic, complemented
3#13071255C211yesmaximal, characteristic
4#13069566C211yesmaximal, characteristic, complemented
5#13069385C211yesmaximal, characteristic, complemented
6#13069356C211yesmaximal, characteristic, complemented
7#13069312C211yesmaximal, characteristic
8#13069299C211yesmaximal, characteristic
9#13069242C211yesmaximal, characteristic
10#13069234C211yesmaximal, characteristic
11#13069204C211yesmaximal, characteristic, complemented
12#13069196C211yesmaximal, characteristic, complemented
13#13068625C211yesmaximal, characteristic
14#13068474C211yesmaximal, characteristic, complemented
15C11×#1941C211yesmaximal, characteristic, complemented
16C2×#66946C2211yescharacteristic
17C2×#66941C2211yescharacteristic
18C2×C11×#106C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20C2×C4×C8×C11C2211yescharacteristic
21C11×#389C2211yescharacteristic
22C11×#389C2211yescharacteristic
23C2×#66885C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×Dic11⋊C8C2211yescharacteristic
26C2×Dic11⋊C8C2211yescharacteristic
27#10622603—21no—
28#10622601C2211yescharacteristic
29#10622600—21no—
30#10622598C2211yescharacteristic
31#10622591—21no—
32#10622590C2211yescharacteristic
33C4⋊C4×Dic11C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36#10622587—21no—
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622552C2211yescharacteristic
42#10622545C2211yescharacteristic
43#10622541C2211yescharacteristic
44C2×#66867C2211yescharacteristic
45#10622483C418yescomplemented
46#10622283—21no—
47#10622277—21no—
48#10622265—21no—
49#10622259—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×Dic22—21no—
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×C4×Dic11—21no—
84C2×C4×Dic11—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11C2311yescharacteristic
87C2×C4×Dic11C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90#66946—22no—
91#66946C2×C414yes—
92#66941—22no—
93#66941C2×C414yes—
94C11×#106—41no—
95C11×#106C2×C414yes—
96C4×C8×C11—41no—
97C11×#95—21no—
98C11×#95—21no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95D411yescharacteristic
107C11⋊#95D411yescharacteristic
108C11⋊#95D411yescharacteristic
109C11⋊#95D411yescharacteristic
110#66885—41no—
111#66885C2×C414yes—
112Dic11⋊C8—22no—
113Dic11⋊C8C2×C414yes—
114#66873—41no—
115#66873C2×C414yes—
116#66872C2×C414yes—
117#66871—41no—
118#66867—41no—
119#22123—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×D44C22×C412yes—
141C2×C4×D11—24no—
142C2×C4×D11—81no—
143C2×C4×D11—81no—
144C2×Dic22—24no—
145C2×Dic22—81no—
146C2×Dic22—81no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11C22×C412yes—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—81no—
160C11×C4⋊C4—81no—
161C11×C4⋊C4C22×C412yes—
162C11×C4⋊C4C22×C412yes—
163C42×C11—21no—
164C42×C11—21no—
165(C2×D11)⋊C4—24no—
166(C2×D11)⋊C4—81no—
167(C2×D11)⋊C4—81no—
168(C2×D11)⋊C4—81no—
169(C2×D11)⋊C4—81no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—81no—
176C4⋊Dic11C22×C412yes—
177Dic11⋊C4—24no—
178Dic11⋊C4—81no—
179C4×Dic11—21no—
180C4×Dic11—21no—
181C4×Dic11—81no—
182C4×Dic11—81no—
183C4×Dic11—81no—
184C4×Dic11C22×C412yes—
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⋊C8C22×C412yes—
192C2×#476—111no—
193#2331—111no—
194#2319—111no—
195#1988—111no—
196#1949—111no—
197#1944—111no—
198#1941D1111yescharacteristic, complemented
199#1936—111no—
200#1934—111no—
201#1926—111no—
202#1925—111no—
203#1920—111no—
204#1919—111no—
205#1804—111no—
206#1768—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—22no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
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×C11C23×C411yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11H(5,𝔽2)11yescharacteristic
236C2×C4×C112−1+411yescharacteristic
237C2×C4×C112−1+411yescharacteristic
238C2×C4×C112−1+411yescharacteristic
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—22no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11C4×D412yes—
259C2×Dic11C4×D412yes—
260D44—22no—
261D44—22no—
262D44—41no—
263D44—41no—
264C4×D11—84no—
265Dic22—84no—
266C8×C11—22no—
267C8×C11—41no—
268C11⋊C8—22no—
269C11⋊C8—41no—
270C2×C4⋊Q8—111no—
271C2×C4×D4—111no—
272#476—118no—
273C2×#107—111no—
274C2×#106—111no—
275C2×#106C2×D1111yescharacteristic
276C2×#106C2×D1111yescharacteristic
277C2×C4⋊C8—111no—
278C2×C4⋊C8—111no—
279C2×#102—111no—
280C2×#102—111no—
281C2×#102—111no—
282C2×#102—111no—
283C2×#97—111no—
284C2×C4×C8C2×D1111yescharacteristic
285#391—221no—
286#391—221no—
287#390—111no—
288#390—111no—
289#389—111no—
290#389—111no—
291#389C2×D1111yescharacteristic
292#389C2×D1111yescharacteristic
293#388—221no—
294#388—221no—
295#387—221no—
296#387—221no—
297#382—111no—
298#381—221no—
299#380—221no—
300C4×C4⋊C4—111no—
301C4×C4⋊C4—111no—
302C4×C4⋊C4—111no—
303#376—111no—
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340C2×D1111yescharacteristic
311#340C2×D1111yescharacteristic
312#336—111no—
313#336—111no—
314C22×C11C2×C4×D411yescharacteristic
315C22×C11#53611yescharacteristic
316C22×C11#53711yescharacteristic
317C22×C11#57611yescharacteristic
318C22×C11#57711yescharacteristic
319C22×C11#57711yescharacteristic
320C22×C11#57711yescharacteristic
321C2×D11—42no—
322C2×D11—42no—
323C2×D11—42no—
324C2×D11—81no—
325C2×D11—81no—
326C2×D11—81no—
327C2×D11—81no—
328C4×C11—42no—
329C4×C11—42no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—81no—
333C4×C11—81no—
334C4×C11#51911yescharacteristic
335C4×C11#52011yescharacteristic
336C4×C11#54111yescharacteristic
337C4×C11#54211yescharacteristic
338Dic11—22no—
339Dic11—22no—
340Dic11—42no—
341Dic11—41no—
342Dic11—41no—
343Dic11—81no—
344Dic11—81no—
345C22×Q8—221no—
346C22×D4—111no—
347C23×C4—221no—
348C22×C8—111no—
349C22×C8—111no—
350C22×C8C22×D1111yescharacteristic
351C22×C8C22×D1111yescharacteristic
352C4⋊Q8—114no—
353C4⋊Q8—222no—
354C4×D4—114no—
355C4×D4—222no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4C22×D1111yescharacteristic
365C2×C4⋊C4C22×D1111yescharacteristic
366C2×C4⋊C4C22×D1111yescharacteristic
367C2×C4⋊C4C22×D1111yescharacteristic
368C2×C22⋊C4—221no—
369C2×C22⋊C4—221no—
370C2×C22⋊C4—221no—
371C2×C22⋊C4—221no—
372C2×C22⋊C4—221no—
373C2×C42—111no—
374C2×C42—111no—
375C2×C42—221no—
376C2×C42—221no—
377C2×C42—221no—
378C2×C42C22×D1111yescharacteristic
379#107—441no—
380#106—41no—
381#106—114no—
382#106C4×D1114yes—
383C4⋊C8—114no—
384C4⋊C8—222no—
385#102—114no—
386#102—114no—
387#102—441no—
388#102—441no—
389#97—441no—
390C4×C8—41no—
391#95—21no—
392#95—21no—
393#95—111no—
394#95—111no—
395#95—111no—
396#95—111no—
397#95—221no—
398#95—221no—
399#95—221no—
400#95—221no—
401#95—221no—
402#95—221no—
403#95—221no—
404C2×C11#232311yescharacteristic
405C2×C11#294611yescharacteristic
406C2×C11#294911yescharacteristic
407C2×C11#324111yescharacteristic
408C2×C11#324411yescharacteristic
409C2×C11#325711yescharacteristic
410C2×C11#326311yescharacteristic
411D11—82no—
412C24—221no—
413C2×Q8—224no—
414C2×Q8—881no—
415C2×Q8—881no—
416C2×D4—112no—
417C2×D4—221no—
418C2×D4—221no—
419C2×D4—221no—
420C2×D4—221no—
421C2×D4—221no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—224no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—881no—
435C22×C4—881no—
436C22×C4D4×D1111yescharacteristic
437C22×C4D4×D1111yescharacteristic
438C22×C4C23×D1111yescharacteristic
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—112no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8C2×C4×D1112yes—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—81no—
458C4⋊C4—81no—
459C4⋊C4—112no—
460C4⋊C4—224no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—881no—
467C4⋊C4—881no—
468C4⋊C4C2×C4×D1112yes—
469C4⋊C4C2×C4×D1112yes—
470C22⋊C4—224no—
471C22⋊C4—881no—
472C22⋊C4—881no—
473C22⋊C4—881no—
474C22⋊C4—881no—
475C42—21no—
476C42—21no—
477C42—112no—
478C42—112no—
479C42—221no—
480C42—221no—
481C42—881no—
482C42—881no—
483C42—881no—
484C11#2212311yescharacteristic, complemented, Sylow
485C23—222no—
486C23—441no—
487C23—441no—
488C23—441no—
489C23—441no—
490C23—441no—
491C23—441no—
492C23C2×D4×D1111yescharacteristic
493Q8—884no—
494D4—222no—
495D4—222no—
496D4—441no—
497D4—441no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
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—41no—
515C2×C4—41no—
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—221no—
527C2×C4—221no—
528C2×C4—222no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—884no—
538C2×C4C22×C4×D1111yescharacteristic
539C2×C4#6703711yescharacteristic
540C2×C4#6704011yescharacteristic
541C2×C4#6704011yescharacteristic
542C2×C4#41×D1111yescharacteristic
543C2×C4#6704311yescharacteristic
544C8—22no—
545C8—41no—
546C8—222no—
547C8—441no—
548C22—442no—
549C22—442no—
550C22—442no—
551C22—881no—
552C22—881no—
553C22—881no—
554C22—881no—
555C22C4×D4×D1111yescharacteristic
556C22#1062312811yescharacteristic
557C22#1062325511yescharacteristic
558C22#1062329311yescharacteristic
559C22#1062329311yescharacteristic
560C22#1062330011yescharacteristic
561C22#1062330111yescharacteristic
562C4—41no—
563C4—42no—
564C4—42no—
565C4—41no—
566C4—81no—
567C4—81no—
568C4—222no—
569C4—222no—
570C4—441no—
571C4—441no—
572C4—442no—
573C4—881no—
574C4—881no—
575C4#1062303511yescharacteristic
576C4#1062310311yescharacteristic
577C4#1062317111yescharacteristic
578C4#1062322711yescharacteristic
579C2—882no—
580C2#1307129311yescharacteristic
581C2#1307744311yescharacteristic
582C2#1307747011yescharacteristic
583C2#1307987211yescharacteristic
584C2#1307991711yescharacteristic
585C2#1308003011yescharacteristic
586C2#1308008011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1941C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1941D11
hypocenterC11#22123
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1941

Complements

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

NH ≅ G/Ntype
2. #13071363C2semidirect
4. #13069566C2semidirect
5. #13069385C2semidirect
6. #13069356C2semidirect
11. #13069204C2semidirect
12. #13069196C2semidirect
14. #13068474C2semidirect
15. C11×#1941C2semidirect
45. #10622483C4semidirect
198. #1941D11semidirect
484. C11#22123semidirect

Maximal subgroups

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

subgroupindex
C2×#106224832
#130713632
#130712552
#130695662
#130693852
#130693562
#130693122
#130692992
#130692422
#130692342
#130692042
#130691962
#130686252
#130684742
C11×#19412
#2212311