Finite Group Databasebeta

← #14765852

Subgroups — #14765852

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×#10622622C211yesmaximal, characteristic
2#13071171C211yesmaximal, characteristic, complemented
3#13071081C211yesmaximal, characteristic
4#13069571C211yesmaximal, characteristic, complemented
5#13069382C211yesmaximal, characteristic, complemented
6#13069348C211yesmaximal, characteristic, complemented
7#13069343C211yesmaximal, characteristic, complemented
8#13069296C211yesmaximal, characteristic
9#13069296C211yesmaximal, characteristic
10#13069246C211yesmaximal, characteristic
11#13069239C211yesmaximal, characteristic
12#13069211C211yesmaximal, characteristic, complemented
13#13069204C211yesmaximal, characteristic, complemented
14C4⋊C8×Dic11C211yesmaximal, characteristic, complemented
15C11×#1804C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66979—21no—
18C2×#66923C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C11×#382C2211yescharacteristic
23#10622834C2211yescharacteristic
24#10622834C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27C4×C22⋊Dic11—21no—
28C2×C8×Dic11C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30#10622622C418yescomplemented
31#10622598C2211yescharacteristic
32#10622598C2211yescharacteristic
33C4⋊C4×Dic11C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35#10622586C2211yescharacteristic
36#10622586C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622564—21no—
42#10622564—21no—
43C4×C4⋊Dic11C2211yescharacteristic
44C42×Dic11C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46#10622265—21no—
47#10622265—21no—
48#10622262—21no—
49#10622262—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C4×D4×C11—22no—
65C4×D4×C11C2×C414yes—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C42×C11C2311yescharacteristic
71C2×C22⋊Dic11—21no—
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75#66979—44no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11D411yescharacteristic
90C2×C4×Dic11D411yescharacteristic
91C2×C4×Dic11D411yescharacteristic
92C2×C4×Dic11D411yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97#66923—22no—
98#66923C2×C414yes—
99C11×C4⋊C8—22no—
100C11×#102—41no—
101C11×#102—41no—
102C11×#95—21no—
103C11×#95—21no—
104#66896C2×C414yes—
105#66896C2×C414yes—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C8×Dic11—41no—
114C8×Dic11—41no—
115#66872—41no—
116#66872C2×C414yes—
117#66871—41no—
118#66871C2×C414yes—
119C4⋊(C11⋊C8)C2×C414yes—
120#22114—111nomaximal, Sylow
121C24×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11C22×C412yes—
128C22×C4×C11—21no—
129C22×C4×C11—24no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
144C22×Dic11C2×D411yescharacteristic
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4C22×C412yes—
157C11×C22⋊C4—24no—
158C42×C11C22×C412yes—
159C42×C11#4112yes—
160C22⋊Dic11—42no—
161C22⋊Dic11—42no—
162C22⋊Dic11—42no—
163C22⋊Dic11—42no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—42no—
171C4⋊Dic11—42no—
172C4⋊Dic11C22×C412yes—
173C4⋊Dic11C22×C412yes—
174Dic11⋊C4—24no—
175Dic11⋊C4—24no—
176Dic11⋊C4—42no—
177Dic11⋊C4—42no—
178C4×Dic11—22no—
179C4×Dic11—22no—
180C4×Dic11—22no—
181C4×Dic11—21no—
182C4×Dic11—21no—
183C4×Dic11—21no—
184C4×Dic11—21no—
185C4×Dic11—41no—
186C4×Dic11—42no—
187C4×Dic11—42no—
188C4×Dic11—42no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8C22×C412yes—
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#1921—111no—
207#1920—111no—
208#1804D1111yescharacteristic
209C4×C4⋊C8—111no—
210C23×C11—22no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11C22×D411yescharacteristic
218D4×C11—22no—
219D4×C11—22no—
220D4×C11—41no—
221D4×C11—41no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—22no—
227C2×C4×C11—48no—
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—41no—
236C2×C4×C11C4×D412yes—
237C2×C4×C11C4×D412yes—
238C2×C4×C11C23×C411yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11H(5,𝔽2)11yescharacteristic
241C2×C4×C112−1+411yescharacteristic
242C2×C4×C112−1+411yescharacteristic
243C2×C4×C112−1+411yescharacteristic
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11#13512yes—
266C2×Dic11#13512yes—
267C2×Dic11AGL(1,ℤ/8)12yes—
268C8×C11—41no—
269C8×C11—41no—
270C11⋊C8—22no—
271C11⋊C8—22no—
272C2×#125—111no—
273C2×C4×D4C2×D1111yescharacteristic
274C2×#117—221no—
275#478—118no—
276C2×#107—111no—
277C2×#107—111no—
278C2×#106—111no—
279C2×#106—111no—
280C2×C4⋊C8—111no—
281C2×C4⋊C8C2×D1111yescharacteristic
282C2×#102—111no—
283C2×#102—111no—
284C2×#102C2×D1111yescharacteristic
285C2×#102C2×D1111yescharacteristic
286C2×C4×C8—111no—
287C2×C4×C8—111no—
288#390—111no—
289#390—111no—
290#389—111no—
291#389—111no—
292#389—111no—
293#389—111no—
294#388—221no—
295#388—221no—
296#387—221no—
297#387—221no—
298#382C2×D1111yescharacteristic
299C4×C4⋊C4—111no—
300C4×C4⋊C4—111no—
301C4×C4⋊C4—111no—
302C4×C4⋊C4—221no—
303C4×C4⋊C4—221no—
304C4×C22⋊C4—221no—
305C43—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#340—111no—
312#340C2×D1111yescharacteristic
313#340C2×D1111yescharacteristic
314#336—111no—
315#336—111no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11—81no—
322C22×C11—81no—
323C22×C11C2×C4×D411yescharacteristic
324C22×C11#53611yescharacteristic
325C22×C11#53711yescharacteristic
326C22×C11C2×#13511yescharacteristic
327C22×C11C2×#13511yescharacteristic
328C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
329C22×C11#57511yescharacteristic
330C4×C11—22no—
331C4×C11—22no—
332C4×C11—42no—
333C4×C11—81no—
334C4×C11—81no—
335C4×C11#51911yescharacteristic
336C4×C11#52011yescharacteristic
337C4×C11#54111yescharacteristic
338C4×C11#54211yescharacteristic
339Dic11—22no—
340Dic11—22no—
341Dic11—22no—
342Dic11—42no—
343Dic11—42no—
344Dic11—41no—
345Dic11—81no—
346Dic11—81no—
347C22×D4C22×D1111yescharacteristic
348C23×C4—21no—
349C22×C8—111no—
350C22×C8—111no—
351C22×C8C22×D1111yescharacteristic
352C22×C8C22×D1111yescharacteristic
353#125—114no—
354#125—222no—
355C4×D4—22no—
356C4×D4C4×D1114yes—
357#117—444no—
358C2×C4⋊C4—111no—
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⋊C4—221no—
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—221no—
373C2×C22⋊C4—221no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—221no—
376C2×C42—111no—
377C2×C42—111no—
378C2×C42—111no—
379C2×C42—111no—
380C2×C42—111no—
381C2×C42—111no—
382C2×C42—221no—
383C2×C42—221no—
384C2×C42—221no—
385C2×C42C22×D1111yescharacteristic
386#107—114no—
387#107—441no—
388#106—114no—
389#106—441no—
390C4⋊C8—22no—
391C4⋊C8—114no—
392#102—41no—
393#102—41no—
394#102—114no—
395#102—114no—
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—82no—
408C2×C11#232311yescharacteristic
409C2×C11C4×#13511yescharacteristic
410C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
411C2×C11#322811yescharacteristic
412C2×C11#323211yescharacteristic
413C2×C11#324711yescharacteristic
414C2×C11#325011yescharacteristic
415C24—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4C2×C4×D1112yes—
422C22×C4—21no—
423C22×C4—24no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
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—21no—
445C2×C8—112no—
446C2×C8—112no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—112no—
457C4⋊C4—112no—
458C4⋊C4—224no—
459C4⋊C4—224no—
460C4⋊C4—221no—
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⋊C4—442no—
470C4⋊C4C2×C4×D1112yes—
471C22⋊C4—24no—
472C22⋊C4—442no—
473C22⋊C4—442no—
474C22⋊C4—442no—
475C22⋊C4—442no—
476C42—222no—
477C42—222no—
478C42—222no—
479C42—221no—
480C42—221no—
481C42—221no—
482C42—221no—
483C42—441no—
484C42—442no—
485C42—442no—
486C42—442no—
487C42C2×C4×D1112yes—
488C42#434112yes—
489C11#2211411yescharacteristic, complemented, Sylow
490C23—22no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23C2×D4×D1111yescharacteristic
498D4—22no—
499D4—22no—
500D4—41no—
501D4—41no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—48no—
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—112no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—222no—
526C2×C4—222no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4(C22⋊D11)⋊C412yes—
541C2×C4(C22⋊D11)⋊C412yes—
542C2×C4C22×C4×D1111yescharacteristic
543C2×C4C2×#434111yescharacteristic
544C2×C4#6703711yescharacteristic
545C2×C4#6704011yescharacteristic
546C2×C4#6704311yescharacteristic
547C2×C4#6704311yescharacteristic
548C8—41no—
549C8—41no—
550C8—222no—
551C8—222no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22C2×(C22⋊D11)⋊C411yescharacteristic
560C22#1062313911yescharacteristic
561C22#1062315911yescharacteristic
562C22D11×#13511yescharacteristic
563C22D11×#13511yescharacteristic
564C22D11×AGL(1,ℤ/8)11yescharacteristic
565C22#1062330411yescharacteristic
566C4—22no—
567C4—22no—
568C4—42no—
569C4—81no—
570C4—81no—
571C4—222no—
572C4—222no—
573C4—222no—
574C4—442no—
575C4—442no—
576C4—441no—
577C4—881no—
578C4—881no—
579C4#1062303511yescharacteristic
580C4#1062304711yescharacteristic
581C4#1062313411yescharacteristic
582C4#1062315611yescharacteristic
583C2—82no—
584C2#1307129411yescharacteristic
585C2#1307738411yescharacteristic
586C2#1307742011yescharacteristic
587C2#1307975111yescharacteristic
588C2#1307978211yescharacteristic
589C2#1307993911yescharacteristic
590C2#1307996511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1804C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#1804D11
hypocenterC11#22114
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
2. #13071171C2semidirect
4. #13069571C2semidirect
5. #13069382C2semidirect
6. #13069348C2semidirect
7. #13069343C2semidirect
12. #13069211C2semidirect
13. #13069204C2semidirect
14. C4⋊C8×Dic11C2semidirect
30. #10622622C4semidirect
489. C11#22114semidirect

Maximal subgroups

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

subgroupindex
C2×#106226222
#130711712
#130710812
#130695712
#130693822
#130693482
#130693432
#130692962
#130692462
#130692392
#130692112
#130692042
C4⋊C8×Dic112
C11×#18042
#2211411