Finite Group Databasebeta

← #14765855

Subgroups — #14765855

Order 2816.

796 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622504C211yesmaximal, characteristic
2C4×#66943C211yesmaximal, characteristic, complemented
3#13071074C211yesmaximal, characteristic
4#13069570C211yesmaximal, characteristic, complemented
5#13069387C211yesmaximal, characteristic, complemented
6#13069350C211yesmaximal, characteristic, complemented
7#13069343C211yesmaximal, characteristic, complemented
8#13069300C211yesmaximal, characteristic
9#13069297C211yesmaximal, characteristic
10#13069243C211yesmaximal, characteristic
11#13069237C211yesmaximal, characteristic
12#13069198C211yesmaximal, characteristic, complemented
13#13068625C211yesmaximal, characteristic
14#13068464C211yesmaximal, characteristic, complemented
15C11×#1921C211yesmaximal, characteristic, complemented
16C2×#66946C2211yescharacteristic
17C2×#66945—21no—
18C2×#66943C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C11×#389C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×#66885C2211yescharacteristic
23C2×#66885C2211yescharacteristic
24C2×#66882C2211yescharacteristic
25C2×Dic11⋊C8C2211yescharacteristic
26C2×Dic11⋊C8C2211yescharacteristic
27C2×C8×Dic11C2211yescharacteristic
28C2×C8×Dic11C2211yescharacteristic
29#10622603—21no—
30#10622601C2211yescharacteristic
31#10622598C2211yescharacteristic
32#10622598C2211yescharacteristic
33#10622590C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35#10622586C2211yescharacteristic
36C2×#66873C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40#10622552C2211yescharacteristic
41C4×C4⋊Dic11—21no—
42C4×C4⋊Dic11C2211yescharacteristic
43C4×Dic11⋊C4—21no—
44C42×Dic11C2211yescharacteristic
45#10622504C418yescomplemented
46#10622283—21no—
47#10622279—21no—
48#10622268—21no—
49#10622267—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#336C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C42×C11—21no—
70C2×C42×C11C2311yescharacteristic
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×C4×Dic11—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11D411yescharacteristic
87C2×C4×Dic11D411yescharacteristic
88C2×C4×Dic11D411yescharacteristic
89C2×C4×Dic11D411yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94#66946—22no—
95#66946C2×C414yes—
96#66945—44no—
97#66943—22no—
98#66943C2×C414yes—
99C11×#107C2×C414yes—
100C11×#95—21no—
101C11×#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109#66885—41no—
110#66885C2×C414yes—
111#66882—41no—
112Dic11⋊C8—22no—
113Dic11⋊C8C2×C414yes—
114C8×Dic11—41no—
115C8×Dic11—41no—
116#66873—41no—
117#66873C2×C414yes—
118#66872—41no—
119#66872C2×C414yes—
120#22114—111nomaximal, Sylow
121C23×D11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44C22×C412yes—
142C2×C4×D11—24no—
143C2×C4×D11—42no—
144C2×C4×D11—42no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11C22×C412yes—
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—42no—
158C11×C4⋊C4C22×C412yes—
159C11×C4⋊C4C22×C412yes—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—42no—
163(C2×D11)⋊C4—24no—
164(C2×D11)⋊C4—42no—
165(C2×D11)⋊C4—42no—
166(C2×D11)⋊C4—42no—
167(C2×D11)⋊C4—42no—
168C4⋊Dic11—24no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—42no—
175C4⋊Dic11—42no—
176C4⋊Dic11C22×C412yes—
177Dic11⋊C4—24no—
178Dic11⋊C4—42no—
179C4×Dic11—22no—
180C4×Dic11—22no—
181C4×Dic11—22no—
182C4×Dic11—21no—
183C4×Dic11—21no—
184C4×Dic11—41no—
185C4×Dic11—42no—
186C4×Dic11—42no—
187C4×Dic11C22×C412yes—
188C4×Dic11#4112yes—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8C22×C412yes—
195C2×#478—111no—
196C4×#125—111no—
197#2293—111no—
198#1989—111no—
199#1949—111no—
200#1942—111no—
201#1941—111no—
202#1934—111no—
203#1934—111no—
204#1926—111no—
205#1925—111no—
206#1921D1111yescharacteristic, complemented
207#1920—111no—
208#1804—111no—
209C4×C4⋊C8—111no—
210C23×C11C22×D411yescharacteristic
211C22×D11—22no—
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
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×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11#13512yes—
236C2×C4×C11C23×C411yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11H(5,𝔽2)11yescharacteristic
239C2×C4×C112−1+411yescharacteristic
240C2×C4×C112−1+411yescharacteristic
241C2×C4×C112−1+411yescharacteristic
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—22no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11C4×D412yes—
260C2×Dic11C4×D412yes—
261C2×Dic11#13512yes—
262C2×Dic11AGL(1,ℤ/8)12yes—
263D44—22no—
264D44—22no—
265D44—41no—
266D44—41no—
267C4×D11—48no—
268C8×C11—22no—
269C8×C11—41no—
270C11⋊C8—22no—
271C11⋊C8—41no—
272C2×#125—111no—
273C2×C4×D4—111no—
274C2×#117—221no—
275#478—118no—
276C2×#107—111no—
277C2×#107C2×D1111yescharacteristic
278C2×#106—111no—
279C2×#106—111no—
280C2×C4⋊C8—111no—
281C2×C4⋊C8—111no—
282C2×#102—111no—
283C2×#102—111no—
284C2×#102—111no—
285C2×#102—111no—
286C2×C4×C8—111no—
287C2×C4×C8—111no—
288#390—111no—
289#390—111no—
290#389—111no—
291#389—111no—
292#389—111no—
293#389C2×D1111yescharacteristic
294#388—221no—
295#388—221no—
296#387—221no—
297#387—221no—
298#382—111no—
299C4×C4⋊C4—111no—
300C4×C4⋊C4—111no—
301C4×C4⋊C4—221no—
302C4×C4⋊C4—221no—
303C4×C4⋊C4C2×D1111yescharacteristic
304C4×C22⋊C4—221no—
305C43—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#340C2×D1111yescharacteristic
312#340C2×D1111yescharacteristic
313#340C2×D1111yescharacteristic
314#336—111no—
315#336C2×D1111yescharacteristic
316C22×C11C2×C4×D411yescharacteristic
317C22×C11#53611yescharacteristic
318C22×C11#53711yescharacteristic
319C22×C11C2×#13511yescharacteristic
320C22×C11C2×#13511yescharacteristic
321C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
322C22×C11#57511yescharacteristic
323C2×D11—42no—
324C2×D11—42no—
325C2×D11—42no—
326C2×D11—81no—
327C2×D11—81no—
328C2×D11—81no—
329C2×D11—81no—
330C4×C11—22no—
331C4×C11—42no—
332C4×C11—42no—
333C4×C11—41no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11#51911yescharacteristic
337C4×C11#52011yescharacteristic
338C4×C11#54111yescharacteristic
339C4×C11#54211yescharacteristic
340Dic11—22no—
341Dic11—22no—
342Dic11—22no—
343Dic11—22no—
344Dic11—42no—
345Dic11—81no—
346Dic11—81no—
347C22×D4—111no—
348C23×C4—221no—
349C22×C8—111no—
350C22×C8—111no—
351C22×C8C22×D1111yescharacteristic
352C22×C8C22×D1111yescharacteristic
353#125—114no—
354#125—222no—
355C4×D4—114no—
356C4×D4—222no—
357#117—444no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4C22×D1111yescharacteristic
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C22⋊C4—221no—
372C2×C22⋊C4—221no—
373C2×C22⋊C4—221no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—221no—
376C2×C42—21no—
377C2×C42—111no—
378C2×C42—111no—
379C2×C42—111no—
380C2×C42—111no—
381C2×C42—111no—
382C2×C42—111no—
383C2×C42—221no—
384C2×C42—221no—
385C2×C42C22×D1111yescharacteristic
386#107—441no—
387#107C4×D1114yes—
388#106—114no—
389#106—441no—
390C4⋊C8—114no—
391C4⋊C8—222no—
392#102—114no—
393#102—114no—
394#102—441no—
395#102—441no—
396C4×C8—441no—
397C4×C8—441no—
398#95—21no—
399#95—21no—
400#95—221no—
401#95—221no—
402#95—221no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407C2×C11#232311yescharacteristic
408C2×C11C4×#13511yescharacteristic
409C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
410C2×C11#322811yescharacteristic
411C2×C11#323211yescharacteristic
412C2×C11#324711yescharacteristic
413C2×C11#325011yescharacteristic
414D11—82no—
415C24—221no—
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—442no—
435C22×C4—442no—
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—42no—
458C4⋊C4—112no—
459C4⋊C4—224no—
460C4⋊C4—224no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—442no—
467C4⋊C4—442no—
468C4⋊C4—442no—
469C4⋊C4C2×C4×D1112yes—
470C4⋊C4C2×C4×D1112yes—
471C22⋊C4—224no—
472C22⋊C4—442no—
473C22⋊C4—442no—
474C22⋊C4—442no—
475C22⋊C4—442no—
476C42—21no—
477C42—21no—
478C42—42no—
479C42—112no—
480C42—112no—
481C42—222no—
482C42—222no—
483C42—222no—
484C42—221no—
485C42—221no—
486C42—441no—
487C42—442no—
488C42—442no—
489C11#2211411yescharacteristic, complemented, Sylow
490C23—222no—
491C23—441no—
492C23—441no—
493C23—441no—
494C23—441no—
495C23—441no—
496C23—441no—
497C23C2×D4×D1111yescharacteristic
498D4—222no—
499D4—222no—
500D4—441no—
501D4—441no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—112no—
520C2×C4—112no—
521C2×C4—112no—
522C2×C4—112no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—222no—
532C2×C4—448no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4#6697212yes—
542C2×C4C22×C4×D1111yescharacteristic
543C2×C4#6704011yescharacteristic
544C2×C4#41×D1111yescharacteristic
545C2×C4#6704211yescharacteristic
546C2×C4#6704311yescharacteristic
547C2×C4#6704311yescharacteristic
548C8—22no—
549C8—41no—
550C8—222no—
551C8—441no—
552C22—442no—
553C22—442no—
554C22—442no—
555C22—881no—
556C22—881no—
557C22—881no—
558C22—881no—
559C22C4×D4×D1111yescharacteristic
560C22#1062316011yescharacteristic
561C22#1062317911yescharacteristic
562C22C2×#6697211yescharacteristic
563C22D11×#13511yescharacteristic
564C22D11×AGL(1,ℤ/8)11yescharacteristic
565C22#1062330411yescharacteristic
566C4—22no—
567C4—42no—
568C4—42no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4—222no—
573C4—222no—
574C4—222no—
575C4—222no—
576C4—442no—
577C4—881no—
578C4—881no—
579C4#1062305411yescharacteristic
580C4#1062310311yescharacteristic
581C4#1062322711yescharacteristic
582C4#1062324111yescharacteristic
583C2—882no—
584C2#1307129711yescharacteristic
585C2C4×#6697211yescharacteristic
586C2#1307742711yescharacteristic
587C2#1307975011yescharacteristic
588C2#1307978911yescharacteristic
589C2#1307994511yescharacteristic
590C2#1307996711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1921C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1921D11
hypocenterC11#22114
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
2. C4×#66943C2semidirect
4. #13069570C2semidirect
5. #13069387C2semidirect
6. #13069350C2semidirect
7. #13069343C2semidirect
12. #13069198C2semidirect
14. #13068464C2semidirect
15. C11×#1921C2semidirect
45. #10622504C4semidirect
206. #1921D11semidirect
489. C11#22114semidirect

Maximal subgroups

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

subgroupindex
C2×#106225042
C4×#669432
#130710742
#130695702
#130693872
#130693502
#130693432
#130693002
#130692972
#130692432
#130692372
#130691982
#130686252
#130684642
C11×#19212
#2211411