Finite Group Databasebeta

← #14657100

Subgroups — #14657100

Order 2816.

716 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074720C211yesmaximal, characteristic
2#13068933C211yesmaximal, characteristic, complemented
3C2×#10622108C211yesmaximal, characteristic, complemented
4C2×#10622175C211yesmaximal, characteristic, complemented
5#13066875C211yesmaximal, characteristic, complemented
6#13066458C211yesmaximal, characteristic, complemented
7C11×#1874C211yesmaximal, characteristic, complemented
8C2×C11×#121C2211yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C2×#66992—21no—
11C2×#66992—21no—
12C2×#66983C2211yescharacteristic
13C2×C11×#102—21no—
14C2×C11×C22⋊C8C2211yescharacteristic
15#10622836—21no—
16C2×C11⋊#95—21no—
17C2×C11⋊#95—21no—
18C2×C11⋊#95C2211yescharacteristic
19C2×C11⋊#95C2211yescharacteristic
20C2×C22⋊(C11⋊C8)C2211yescharacteristic
21#10622605—21no—
22C2×#66873—21no—
23#10622573—21no—
24#10622562—21no—
25C11×#340—21no—
26#10622175—22no—
27#10622167—21no—
28#10622108—22no—
29C22×D4×C11—21no—
30C22×D4×C11D411yescharacteristic
31C23×C4×C11—21no—
32C23×C4×C11C2311yescharacteristic
33C22×C22⋊D11—21no—
34C22×C22⋊D11—21no—
35C22×C22⋊D11—21no—
36C23×Dic11—21no—
37C23×Dic11D411yescharacteristic
38C23×Dic11D411yescharacteristic
39C22×D44D411yescharacteristic
40C22×C8×C11—21no—
41C11×#121—21no—
42C11×#121—21no—
43C11×#121—21no—
44C11×#121—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—42no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C22⋊C4—21no—
50C2×C22⋊Dic11—21no—
51C2×C22⋊Dic11—21no—
52#66992—42no—
53#66992—42no—
54#66992—42no—
55#66992—42no—
56#66983—21no—
57#66983—21no—
58#66983—21no—
59#66983—21no—
60C2×(C2×D11)⋊C4—21no—
61C2×(C2×D11)⋊C4—21no—
62C2×(C2×D11)⋊C4—21no—
63C2×C4⋊Dic11D411yescharacteristic
64C2×Dic11⋊C4—21no—
65C2×Dic11⋊C4—21no—
66C22×C11⋊C8—21no—
67C11×#102—42no—
68C11×C22⋊C8—21no—
69C11×C22⋊C8—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C11⋊#95—42no—
74C11⋊#95—42no—
75C11⋊#95D412yescomplemented
76C22⋊(C11⋊C8)—21no—
77C22⋊(C11⋊C8)—21no—
78#66873—42no—
79#10403—111nomaximal, Sylow
80C24×C11—21no—
81C24×C11C2×D411yescharacteristic
82C23×D11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C22×C4×C11—22no—
94C22×C4×C11—21no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11#4111yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C2×C22⋊D11—42no—
110C2×C22⋊D11—42no—
111C2×C22⋊D11—41no—
112C2×C22⋊D11—41no—
113C2×C22⋊D11—41no—
114C2×C22⋊D11—41no—
115C2×C22⋊D11—41no—
116C2×C22⋊D11—41no—
117C2×C22⋊D11—81no—
118C2×C22⋊D11—81no—
119C2×C22⋊D11—81no—
120C2×C22⋊D11—81no—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—21no—
124C22×Dic11—22no—
125C22×Dic11—21no—
126C22×Dic11—21no—
127C22×Dic11—41no—
128C22×Dic11—41no—
129C22×Dic11—41no—
130C22×Dic11—41no—
131C22×Dic11—41no—
132C22×Dic11—41no—
133C22×Dic11—41no—
134C22×Dic11—41no—
135C22×Dic11—41no—
136C22×Dic11—41no—
137C22×Dic11D812yes—
138C22×Dic11SD1612yes—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44—41no—
142C2×D44—41no—
143C2×C8×C11—41no—
144C2×C8×C11—41no—
145C2×C8×C11—41no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—41no—
151C11×C4⋊C4—41no—
152C11×C22⋊C4—41no—
153C11×C22⋊C4—41no—
154C22⋊Dic11—42no—
155C22⋊Dic11—42no—
156(C2×D11)⋊C4—42no—
157(C2×D11)⋊C4—42no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162Dic11⋊C4—42no—
163Dic11⋊C4—42no—
164C2×C11⋊C8—41no—
165C2×C11⋊C8—41no—
166C2×C11⋊C8—41no—
167#2656—111no—
168#1874—111no—
169#1874D1111yescharacteristic, complemented
170C2×#327—111no—
171C2×#327—111no—
172#1442—111no—
173#1280—111no—
174C23×C11—21no—
175C23×C11—21no—
176C23×C11—21no—
177C23×C11—21no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11#12011yescharacteristic
186C23×C11#12111yescharacteristic
187C23×C11#12411yescharacteristic
188C23×C11C2×D811yescharacteristic
189C23×C11C2×SD1611yescharacteristic
190C23×C11AGL(1,ℤ/8)11yescharacteristic
191C23×C11AGL(1,ℤ/8)11yescharacteristic
192C22×D11—41no—
193C22×D11—41no—
194C22×D11—41no—
195C22×D11—41no—
196C22×D11—41no—
197C22×D11—41no—
198C22×D11—41no—
199D4×C11—42no—
200D4×C11—81no—
201D4×C11—81no—
202D4×C11—81no—
203D4×C11—81no—
204D4×C11—81no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—81no—
220C2×C4×C11—81no—
221C2×C4×C11—81no—
222C2×C4×C11—81no—
223C2×C4×C11#12111yescharacteristic
224C2×C4×C11#12111yescharacteristic
225C2×C4×C11#12311yescharacteristic
226C2×C4×C11#12311yescharacteristic
227C22⋊D11—84no—
228C22⋊D11—84no—
229C22⋊D11—81no—
230C22⋊D11—81no—
231C22⋊D11—81no—
232C22⋊D11—81no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11—41no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—42no—
247C2×Dic11—81no—
248C2×Dic11—81no—
249C2×Dic11—81no—
250C2×Dic11—81no—
251C2×Dic11—81no—
252C2×Dic11—81no—
253D44—42no—
254D44—81no—
255C8×C11—81no—
256C11⋊C8—81no—
257C2×#121—111no—
258C2×#121—221no—
259C2×#121—221no—
260C2×#121C2×D1111yescharacteristic
261C22×C4⋊C4C2×D1111yescharacteristic
262C2×#102—21no—
263C2×#102—221no—
264C2×C22⋊C8—111no—
265C2×C22⋊C8C2×D1111yescharacteristic
266#399—221no—
267#399—221no—
268#392—221no—
269#392—221no—
270C2×#95—111no—
271C2×#95—111no—
272C2×#95—221no—
273C2×#95—221no—
274#340—21no—
275#340—221no—
276#327—222no—
277#327—222no—
278C22×C11—21no—
279C22×C11—21no—
280C22×C11—21no—
281C22×C11—21no—
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—21no—
285C22×C11—21no—
286C22×C11—21no—
287C22×C11—21no—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—81no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11—81no—
294C22×C11—81no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11#39411yescharacteristic
298C22×C11#44711yescharacteristic
299C22×C11#45011yescharacteristic
300C22×C11#45411yescharacteristic
301C22×C11#45511yescharacteristic
302C22×C11B(4,𝔽2)11yescharacteristic
303C22×C11#45811yescharacteristic
304C22×C11#45911yescharacteristic
305C22×C11#46011yescharacteristic
306C22×C11#48611yescharacteristic
307C22×C11#49011yescharacteristic
308C2×D11—81no—
309C2×D11—81no—
310C2×D11—81no—
311C2×D11—81no—
312C2×D11—81no—
313C2×D11—81no—
314C2×D11—81no—
315C4×C11—21no—
316C4×C11—21no—
317C4×C11—21no—
318C4×C11—21no—
319C4×C11—82no—
320C4×C11—81no—
321Dic11—42no—
322Dic11—42no—
323Dic11—82no—
324Dic11—81no—
325C22×D4—21no—
326C22×D4—111no—
327C22×D4—221no—
328C22×D4—221no—
329C22×D4—221no—
330C22×D4C22⋊D1111yescharacteristic
331C23×C4—21no—
332C23×C4—111no—
333C23×C4—111no—
334C23×C4—221no—
335C23×C4C22×D1111yescharacteristic
336C22×C8—21no—
337C22×C8—221no—
338#121—21no—
339#121—21no—
340#121—21no—
341#121—21no—
342#121—221no—
343#121—221no—
344#121—221no—
345#121—221no—
346#121—442no—
347#121—442no—
348#121—442no—
349#121—442no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—111no—
354C2×C4⋊C4—221no—
355C2×C4⋊C4—221no—
356C2×C4⋊C4C22⋊D1111yescharacteristic
357C2×C22⋊C4—21no—
358C2×C22⋊C4—221no—
359C2×C22⋊C4—221no—
360C2×C22⋊C4—221no—
361C2×C22⋊C4—221no—
362C2×C22⋊C4—221no—
363#102—42no—
364#102—442no—
365C22⋊C8—21no—
366C22⋊C8—21no—
367C22⋊C8—221no—
368C22⋊C8—221no—
369#95—112no—
370#95—221no—
371#95—221no—
372#95—221no—
373#95—442no—
374#95—442no—
375C2×C11—21no—
376C2×C11—21no—
377C2×C11—21no—
378C2×C11—21no—
379C2×C11—161no—
380C2×C11#159811yescharacteristic
381C2×C11#160111yescharacteristic
382C2×C11#160711yescharacteristic
383C2×C11#161611yescharacteristic
384C2×C11#204011yescharacteristic
385C2×C11#204111yescharacteristic
386C2×C11#204411yescharacteristic
387D11—161no—
388C24—21no—
389C24—221no—
390C24D4×D1111yescharacteristic
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—221no—
402C2×D4—221no—
403C2×D4—441no—
404C2×D4—441no—
405C2×D4—442no—
406C2×D4—442no—
407C2×D4—441no—
408C2×D4—441no—
409C2×D4—441no—
410C2×D4—441no—
411C2×D4—441no—
412C2×D4—441no—
413C2×D4—881no—
414C2×D4—881no—
415C2×D4—881no—
416C2×D4—881no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—112no—
428C22×C4—112no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—222no—
434C22×C4—221no—
435C22×C4—441no—
436C22×C4—441no—
437C22×C4—441no—
438C22×C4—441no—
439C22×C4—441no—
440C22×C4—441no—
441C22×C4—441no—
442C22×C4—441no—
443C22×C4—441no—
444C22×C4—441no—
445C22×C4#433911yescharacteristic
446C22×C4#433911yescharacteristic
447C22×C4D4×D1111yescharacteristic
448C22×C4D4×D1111yescharacteristic
449C22×C4#434111yescharacteristic
450C22×C4C2×C22⋊D1111yescharacteristic
451C2×C8—41no—
452C2×C8—41no—
453C2×C8—41no—
454C2×C8—441no—
455C2×C8—441no—
456C2×C8—441no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—442no—
466C4⋊C4—442no—
467C22⋊C4—41no—
468C22⋊C4—41no—
469C22⋊C4—442no—
470C22⋊C4—442no—
471C22⋊C4—442no—
472C22⋊C4—442no—
473C22⋊C4—441no—
474C22⋊C4—441no—
475C11#1040311yescharacteristic, complemented, Sylow
476C23—21no—
477C23—21no—
478C23—21no—
479C23—21no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—441no—
488C23—441no—
489C23—441no—
490C23—441no—
491C23—441no—
492C23—441no—
493C23—441no—
494C23#6693711yescharacteristic
495C23#6693811yescharacteristic
496C23D8×D1111yescharacteristic
497C23#6696411yescharacteristic
498C23SD16×D1111yescharacteristic
499C23#6696711yescharacteristic
500C23#6699011yescharacteristic
501D4—42no—
502D4—81no—
503D4—81no—
504D4—81no—
505D4—81no—
506D4—81no—
507D4—442no—
508D4—881no—
509D4—884no—
510D4—884no—
511D4—881no—
512D4—881no—
513D4—881no—
514D4—881no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—81no—
530C2×C4—81no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—222no—
534C2×C4—222no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—442no—
540C2×C4—442no—
541C2×C4—442no—
542C2×C4—442no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—442no—
547C2×C4—881no—
548C2×C4—881no—
549C2×C4—881no—
550C2×C4—881no—
551C2×C4—881no—
552C2×C4—881no—
553C2×C4#6693611yescharacteristic
554C2×C4#6693711yescharacteristic
555C2×C4#6698211yescharacteristic
556C2×C4#6699211yescharacteristic
557C8—81no—
558C8—881no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—881no—
579C22—881no—
580C22—881no—
581C22—881no—
582C22—881no—
583C22—881no—
584C22—881no—
585C22#1062237311yescharacteristic
586C22#1062237511yescharacteristic
587C22#1062237711yescharacteristic
588C22#1062239911yescharacteristic
589C22#1062257211yescharacteristic
590C22#1062264511yescharacteristic
591C22#1062266611yescharacteristic
592C22#1062276911yescharacteristic
593C22#1062278211yescharacteristic
594C22#1062281411yescharacteristic
595C22#1062281511yescharacteristic
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—81no—
601C4—82no—
602C4—442no—
603C4—442no—
604C4—882no—
605C4—881no—
606C2—21no—
607C2—21no—
608C2—21no—
609C2—21no—
610C2—161no—
611C2—1761no—
612C2#1306754911yescharacteristic
613C2#1306756611yescharacteristic
614C2#1306760011yescharacteristic
615C2#1306765111yescharacteristic
616C2#1306984311yescharacteristic
617C2#1306984811yescharacteristic
618C2#1306986511yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1874C2
socleC23×C11#120
prime radical#13074720C2
hypercenter#1874D11
hypocenterC11#10403
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. #13068933C2semidirect
3. C2×#10622108C2semidirect
4. C2×#10622175C2semidirect
5. #13066875C2semidirect
6. #13066458C2semidirect
7. C11×#1874C2semidirect
75. C11⋊#95D4semidirect
169. #1874D11semidirect
475. C11#10403semidirect

Maximal subgroups

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

subgroupindex
#130747202
#130689332
C2×#106221082
C2×#106221752
#130668752
#130664582
C11×#18742
#1040311