Finite Group Databasebeta

← #14821818

Subgroups — #14821818

Order 2816.

832 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072959C211yesmaximal, characteristic, complemented
2#13071632C211yesmaximal, characteristic
3#13069930C211yesmaximal, characteristic, complemented
4#13069799C211yesmaximal, characteristic
5#13069761C211yesmaximal, characteristic, complemented
6#13069617C211yesmaximal, characteristic
7#13069570C211yesmaximal, characteristic, complemented
8#13069289C211yesmaximal, characteristic, complemented
9#13069259C211yesmaximal, characteristic, complemented
10#13069225C211yesmaximal, characteristic, complemented
11#13069186C211yesmaximal, characteristic, complemented
12#13068947C211yesmaximal, characteristic, complemented
13#13068706C211yesmaximal, characteristic, complemented
14#13068430C211yesmaximal, characteristic, complemented
15C11×#1872C211yesmaximal, characteristic, complemented
16C2×C11×C22⋊Q8C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×#4325C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C2×C4×C22⋊D11—21no—
21C2×#66946C2211yescharacteristic
22C2×#66943C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26#10622843C2211yescharacteristic
27#10622843C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29#10622826—21no—
30#10622825C2211yescharacteristic
31C4×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic
35C2×#66882C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38#10622603—21no—
39#10622602—21no—
40#10622601C2211yescharacteristic
41#10622595—21no—
42#10622590—21no—
43C4⋊C4×Dic11C2211yescharacteristic
44C4⋊C4×Dic11C2211yescharacteristic
45#10622586C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47#10622566—21no—
48#10622558—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×C22⋊Q8—22no—
68C11×C22⋊Q8—41no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—41no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11D411yescharacteristic
79C2×C22⋊Dic11D411yescharacteristic
80C2×#4325—22no—
81C2×#4325—41no—
82C2×#4325—41no—
83#66983—22no—
84#66983—22no—
85C4×C22⋊D11—44no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2311yescharacteristic
99C2×C4×Dic11C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102#66946—22no—
103#66946—41no—
104#66943—22no—
105#66943—41no—
106C11×#103—22no—
107C11×#103—41no—
108C11×C22⋊C8—41no—
109#66899—22no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95D411yescharacteristic
119C11⋊#95D411yescharacteristic
120C22⋊(C11⋊C8)—41no—
121#66885—22no—
122#66885—41no—
123#66882—22no—
124Dic11⋊C8—41no—
125C8×Dic11—41no—
126#66873—22no—
127#26721—111nomaximal, Sylow
128C24×C11C2×D411yescharacteristic
129C23×D11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11—81no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C2×C22⋊D11—24no—
152C2×C22⋊D11—42no—
153C2×C22⋊D11—42no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44#4112yes—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×C4×D11—81no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4#4112yes—
183C11×C4⋊C4#4112yes—
184C11×C22⋊C4—42no—
185C22⋊Dic11—22no—
186C22⋊Dic11—22no—
187C22⋊Dic11—42no—
188#4325—44no—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—81no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—42no—
199C4⋊Dic11#4112yes—
200Dic11⋊C4—42no—
201Dic11⋊C4—42no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—42no—
207C4×Dic11—42no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214#2489—111no—
215#2361—111no—
216#2055—111no—
217#2033—111no—
218#2025—111no—
219#2000—111no—
220#1989—111no—
221#1933—111no—
222#1928—111no—
223#1923—111no—
224#1918—111no—
225#1877—111no—
226#1872D1111yescharacteristic, complemented
227#1824—111no—
228C4×#102—111no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11#13512yes—
236C23×C11C22×D411yescharacteristic
237C22×D11—22no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244Q8×C11—41no—
245Q8×C11—41no—
246Q8×C11—41no—
247Q8×C11—41no—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—84no—
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11H(5,𝔽2)11yescharacteristic
273C2×C4×C11H(5,𝔽2)11yescharacteristic
274C22⋊D11—48no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—22no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11AGL(1,ℤ/8)12yes—
296D44—22no—
297D44—22no—
298D44—41no—
299D44—41no—
300C4×D11—84no—
301C8×C11—41no—
302C8×C11—41no—
303C11⋊C8—41no—
304C11⋊C8—41no—
305C22×SD16—111no—
306C2×#125—111no—
307C2×C22⋊Q8C2×D1111yescharacteristic
308C2×#121—111no—
309C2×C4×D4—111no—
310C2×C4×D4—221no—
311C22×C4⋊C4C2×D1111yescharacteristic
312C2×#107—111no—
313C2×C4⋊C8—111no—
314C2×#103—111no—
315C2×#103C2×D1111yescharacteristic
316C2×#103C2×D1111yescharacteristic
317C2×#102—111no—
318C2×#102—111no—
319C2×#102—111no—
320C2×C22⋊C8—111no—
321C2×C22⋊C8C2×D1111yescharacteristic
322C2×C4×C8—111no—
323#400—221no—
324#397—221no—
325#391—111no—
326#391—111no—
327#390—111no—
328#389—111no—
329#388—221no—
330#388—221no—
331#386—221no—
332#385—221no—
333#382—221no—
334#380—111no—
335C4×C4⋊C4—111no—
336C4×C4⋊C4—111no—
337C4×C22⋊C4—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#340—111no—
344#340C2×D1111yescharacteristic
345#340C2×D1111yescharacteristic
346#336—111no—
347#336—111no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11#52511yescharacteristic
356C22×C11#54611yescharacteristic
357C22×C11#54611yescharacteristic
358C22×C11C2×#13511yescharacteristic
359C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
360C22×C11#57711yescharacteristic
361C22×C11#57811yescharacteristic
362C2×D11—42no—
363C2×D11—42no—
364C2×D11—42no—
365C2×D11—81no—
366C2×D11—81no—
367C2×D11—81no—
368C2×D11—81no—
369C4×C11—42no—
370C4×C11—41no—
371C4×C11—42no—
372C4×C11—81no—
373C4×C11—81no—
374C4×C11#52911yescharacteristic
375C4×C11#53811yescharacteristic
376C4×C11#55511yescharacteristic
377C4×C11#55911yescharacteristic
378Dic11—22no—
379Dic11—41no—
380Dic11—42no—
381Dic11—41no—
382Dic11—41no—
383Dic11—81no—
384Dic11—81no—
385C22×Q8C22×D1111yescharacteristic
386C22×D4—111no—
387C22×D4—221no—
388C23×C4—21no—
389C23×C4—221no—
390C23×C4C22×D1111yescharacteristic
391C2×SD16—222no—
392C2×SD16—441no—
393C2×SD16—441no—
394C22×C8—111no—
395C22×C8—111no—
396C22×C8C22×D1111yescharacteristic
397C22×C8C22×D1111yescharacteristic
398#125—222no—
399#125—441no—
400C22⋊Q8—22no—
401C22⋊Q8—41no—
402#121—222no—
403#121—222no—
404C4×D4—222no—
405C4×D4—441no—
406C4×D4—444no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—41no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C22⋊C4—21no—
421C2×C22⋊C4—111no—
422C2×C22⋊C4—111no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C42—111no—
429C2×C42—111no—
430C2×C42—221no—
431C2×C42—221no—
432#107—222no—
433C4⋊C8—441no—
434#103—22no—
435#103—41no—
436#103—222no—
437#102—222no—
438#102—222no—
439#102—441no—
440C22⋊C8—41no—
441C22⋊C8—441no—
442C4×C8—441no—
443#95—111no—
444#95—111no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95—221no—
452#95—221no—
453C2×C11—42no—
454C2×C11#245911yescharacteristic
455C2×C11#310511yescharacteristic
456C2×C11#312011yescharacteristic
457C2×C11#330011yescharacteristic
458C2×C11#330111yescharacteristic
459C2×C11#331011yescharacteristic
460C2×C11#333011yescharacteristic
461D11—82no—
462C24—221no—
463C24D4×D1111yescharacteristic
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×D4—112no—
471C2×D4—224no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—221no—
475C2×D4—221no—
476C2×D4—221no—
477C2×D4—442no—
478C2×D4—442no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—81no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—111no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—442no—
500C22×C4—442no—
501C22×C4—881no—
502C22×C4D4×D1111yescharacteristic
503C22×C4C23×D1111yescharacteristic
504SD16—444no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—42no—
522C4⋊C4—42no—
523C4⋊C4—112no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—442no—
530C4⋊C4—442no—
531C4⋊C4—442no—
532C4⋊C4#433912yes—
533C4⋊C4#434112yes—
534C22⋊C4—42no—
535C22⋊C4—224no—
536C22⋊C4—222no—
537C22⋊C4—222no—
538C22⋊C4—442no—
539C22⋊C4—442no—
540C22⋊C4—442no—
541C22⋊C4—881no—
542C42—221no—
543C42—221no—
544C42—221no—
545C42—221no—
546C42—442no—
547C42—442no—
548C11#2672111yescharacteristic, complemented, Sylow
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—222no—
556C23—441no—
557C23—441no—
558C23—441no—
559C23—441no—
560C23—441no—
561C23—441no—
562C23#6697212yes—
563C23C2×D4×D1111yescharacteristic
564Q8—41no—
565Q8—41no—
566Q8—41no—
567Q8—41no—
568D4—222no—
569D4—222no—
570D4—448no—
571D4—441no—
572D4—441no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—84no—
593C2×C4—112no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—222no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—884no—
615C2×C4C2×#433911yescharacteristic
616C2×C4C2×#434111yescharacteristic
617C2×C4#6703711yescharacteristic
618C2×C4#6703711yescharacteristic
619C2×C4#41×D1111yescharacteristic
620C2×C4#41×D1111yescharacteristic
621C8—41no—
622C8—41no—
623C8—441no—
624C8—441no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—442no—
633C22—442no—
634C22—442no—
635C22—881no—
636C22—881no—
637C22—881no—
638C22—881no—
639C22#1062302111yescharacteristic
640C22#1062312211yescharacteristic
641C22#1062318711yescharacteristic
642C22#1062329311yescharacteristic
643C22C2×#6697211yescharacteristic
644C22D11×AGL(1,ℤ/8)11yescharacteristic
645C22#1062331011yescharacteristic
646C4—42no—
647C4—42no—
648C4—41no—
649C4—81no—
650C4—81no—
651C4—222no—
652C4—441no—
653C4—442no—
654C4—441no—
655C4—441no—
656C4—881no—
657C4—881no—
658C4#1062308811yescharacteristic
659C4#1062309011yescharacteristic
660C4#1062314411yescharacteristic
661C4#1062314711yescharacteristic
662C2—42no—
663C2—882no—
664C2#1307255211yescharacteristic
665C2#1307866611yescharacteristic
666C2#1307883311yescharacteristic
667C2#1308050711yescharacteristic
668C2#1308051411yescharacteristic
669C2#1308063011yescharacteristic
670C2#1308091711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1872C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1872D11
hypocenterC11#26721
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
1. #13072959C2semidirect
3. #13069930C2semidirect
5. #13069761C2semidirect
7. #13069570C2semidirect
8. #13069289C2semidirect
9. #13069259C2semidirect
10. #13069225C2semidirect
11. #13069186C2semidirect
12. #13068947C2semidirect
13. #13068706C2semidirect
14. #13068430C2semidirect
15. C11×#1872C2semidirect
226. #1872D11semidirect
548. C11#26721semidirect

Maximal subgroups

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

subgroupindex
#130729592
#130716322
#130699302
#130697992
#130697612
#130696172
#130695702
#130692892
#130692592
#130692252
#130691862
#130689472
#130687062
#130684302
C11×#18722
#2672111