Finite Group Databasebeta

← #14803330

Subgroups — #14803330

Order 2816.

800 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622798C211yesmaximal, characteristic
2C2×C8×Dic22C211yesmaximal, characteristic, complemented
3#13074103C211yesmaximal, characteristic
4#13073980C211yesmaximal, characteristic, complemented
5#13069999C211yesmaximal, characteristic
6#13069997C211yesmaximal, characteristic, complemented
7#13069936C211yesmaximal, characteristic, complemented
8#13069931C211yesmaximal, characteristic
9#13069467C211yesmaximal, characteristic
10#13069424C211yesmaximal, characteristic
11#13069381C211yesmaximal, characteristic, complemented
12#13069299C211yesmaximal, characteristic
13#13069294C211yesmaximal, characteristic, complemented
14#103×Dic11C211yesmaximal, characteristic, complemented
15C11×#1969C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C2×#67000C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C11×#391C2211yescharacteristic
26C11×#391C2211yescharacteristic
27#10622843C2211yescharacteristic
28#10622843C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32#10622798—24no—
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38C2×C8×Dic11C2211yescharacteristic
39#10622601C2211yescharacteristic
40#10622598C2211yescharacteristic
41#10622590C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45#10622552C2211yescharacteristic
46#10622541C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C8×Dic22—24no—
49#10622288—21no—
50#10622286—21no—
51#10622283—21no—
52#10622282—21no—
53#10622273—21no—
54#10622269—21no—
55#10622268—21no—
56#10622267—21no—
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D44C2311yescharacteristic
64C22×Dic22D411yescharacteristic
65C2×C11×Q16—22no—
66C2×C11×Q16—22no—
67C2×C11×Q16—41no—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73#67000—22no—
74#67000—22no—
75Q8×Dic11—22no—
76Q8×Dic11—22no—
77C2×#4325—22no—
78C2×#4325—22no—
79C2×#4325—41no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11D411yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4D411yescharacteristic
94C2×Dic11⋊C4D411yescharacteristic
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C4×Dic22—22no—
102C4×Dic22—22no—
103C11×#107—41no—
104C11×#103—22no—
105C11×#103—22no—
106C4×C8×C11—22no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111#66899—22no—
112#66899—22no—
113#66899—41no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123#66885—22no—
124#66885—22no—
125Dic11⋊C8—22no—
126Dic11⋊C8D414yes—
127C8×Dic11—22no—
128C8×Dic11—22no—
129#66873—41no—
130#66872—41no—
131C4⋊(C11⋊C8)—22no—
132#25297—111nomaximal, Sylow
133C23×D11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11#4112yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×Dic22—22no—
167C2×Dic22—22no—
168C2×Dic22—22no—
169C11×Q16—44no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11C2×D412yes—
175C2×C8×C11#4112yes—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C42×C11—21no—
181C42×C11—21no—
182#4325—44no—
183(C2×D11)⋊C4—42no—
184(C2×D11)⋊C4—42no—
185(C2×D11)⋊C4—42no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—81no—
188(C2×D11)⋊C4—81no—
189C4⋊Dic11—22no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—42no—
197C4⋊Dic11—42no—
198Dic11⋊C4—22no—
199Dic11⋊C4—22no—
200Dic11⋊C4—42no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—42no—
204C4×Dic11—81no—
205C4×Dic11C2×D412yes—
206C4×Dic11#4112yes—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8C2×D412yes—
213C2×#464—111no—
214C2×C8×Q8—111no—
215#2592—111no—
216#2581—111no—
217#2067—111no—
218#2066—111no—
219#2056—111no—
220#2055—111no—
221#1969D1111yescharacteristic, complemented
222#1968—111no—
223#1958—111no—
224#1949—111no—
225#1934—111no—
226#1933—111no—
227C4×#103—111no—
228C23×C11C22×D411yescharacteristic
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236Q8×C11—22no—
237Q8×C11—22no—
238Q8×C11—41no—
239Q8×C11—41no—
240Q8×C11—41no—
241Q8×C11—41no—
242Q8×C11—41no—
243Q8×C11—41no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
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#13512yes—
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C2×C4×C112−1+411yescharacteristic
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11#12112yes—
287C2×Dic11#12112yes—
288C2×Dic11#13512yes—
289D44—41no—
290D44—41no—
291D44—41no—
292D44—41no—
293Dic22—28no—
294C8×C11—22no—
295C8×C11—22no—
296C11⋊C8—22no—
297C11⋊C8—41no—
298C22×Q16C2×D1111yescharacteristic
299C22×SD16—111no—
300C2×#124—111no—
301C2×C4×Q8—111no—
302C2×C4×Q8—111no—
303#464—224no—
304C8×Q8—224no—
305C2×#107C2×D1111yescharacteristic
306C2×#106—111no—
307C2×C4⋊C8—111no—
308C2×C4⋊C8—111no—
309C2×C4⋊C8—111no—
310C2×#103—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#103C2×D1111yescharacteristic
314C2×#103C2×D1111yescharacteristic
315C2×#102—111no—
316C2×#102—111no—
317C2×#102—111no—
318C2×C4×C8—111no—
319C2×C4×C8—111no—
320C2×C4×C8C2×D1111yescharacteristic
321#400—221no—
322#397—221no—
323#395—221no—
324#393—221no—
325#391—111no—
326#391—111no—
327#391C2×D1111yescharacteristic
328#391C2×D1111yescharacteristic
329#390—111no—
330#390—111no—
331#389—111no—
332#389—111no—
333#388—221no—
334#388—221no—
335#387—221no—
336#387—221no—
337#382—111no—
338C4×C4⋊C4—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343C22×C11C2×#12111yescharacteristic
344C22×C11#54811yescharacteristic
345C22×C11#55011yescharacteristic
346C22×C11C2×#13511yescharacteristic
347C22×C11C2×#13511yescharacteristic
348C22×C11#57711yescharacteristic
349C22×C11#57811yescharacteristic
350C2×D11—81no—
351C2×D11—81no—
352C2×D11—81no—
353C2×D11—81no—
354C2×D11—81no—
355C2×D11—81no—
356C2×D11—81no—
357C4×C11—22no—
358C4×C11—42no—
359C4×C11—41no—
360C4×C11—81no—
361C4×C11—81no—
362C4×C11—81no—
363C4×C11#52911yescharacteristic
364C4×C11#54211yescharacteristic
365C4×C11#54611yescharacteristic
366C4×C11#54811yescharacteristic
367Dic11—22no—
368Dic11—22no—
369Dic11—22no—
370Dic11—41no—
371Dic11—81no—
372Dic11—81no—
373Dic11—81no—
374C22×Q8—111no—
375C22×Q8C22×D1111yescharacteristic
376C22×Q8C22×D1111yescharacteristic
377C22×D4—111no—
378C2×Q16—22no—
379C2×Q16—22no—
380C2×Q16—41no—
381C2×SD16—222no—
382C2×SD16—222no—
383C2×SD16—441no—
384C22×C8—111no—
385C22×C8—111no—
386C22×C8C22×D1111yescharacteristic
387C22×C8C22×D1111yescharacteristic
388#124—222no—
389#124—222no—
390C4×Q8—222no—
391C4×Q8—222no—
392C4×Q8—222no—
393C4×Q8—222no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4C22×D1111yescharacteristic
404C2×C4⋊C4C22×D1111yescharacteristic
405C2×C22⋊C4—221no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C42—111no—
412C2×C42—111no—
413C2×C42—221no—
414C2×C42—221no—
415C2×C42C22×D1111yescharacteristic
416#107—41no—
417#106—441no—
418C4⋊C8—114no—
419C4⋊C8—222no—
420C4⋊C8—222no—
421#103—22no—
422#103—22no—
423#103—222no—
424#103—222no—
425#103—441no—
426#102—222no—
427#102—222no—
428#102—441no—
429C4×C8—22no—
430C4×C8—222no—
431C4×C8—222no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445C2×C11#242611yescharacteristic
446C2×C11#305011yescharacteristic
447C2×C11#306311yescharacteristic
448C2×C11#336411yescharacteristic
449C2×C11#336511yescharacteristic
450C2×C11#339311yescharacteristic
451C2×C11#339411yescharacteristic
452D11—161no—
453C24—221no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—222no—
466C2×Q8—222no—
467C2×Q8—222no—
468C2×Q8#433912yes—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—221no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4D4×D1111yescharacteristic
487C22×C4D4×D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489Q16—44no—
490SD16—444no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—112no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8D4×D1112yes—
502C2×C8#434112yes—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—222no—
508C4⋊C4—222no—
509C4⋊C4—222no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—442no—
517C4⋊C4—442no—
518C4⋊C4—442no—
519C22⋊C4—442no—
520C22⋊C4—442no—
521C22⋊C4—442no—
522C22⋊C4—442no—
523C22⋊C4—881no—
524C22⋊C4—881no—
525C42—21no—
526C42—21no—
527C42—112no—
528C42—112no—
529C42—221no—
530C42—221no—
531C42—442no—
532C42—881no—
533C11#2529711yescharacteristic, complemented, Sylow
534C23—441no—
535C23—441no—
536C23—441no—
537C23—441no—
538C23—441no—
539C23—441no—
540C23—441no—
541C23C2×D4×D1111yescharacteristic
542Q8—22no—
543Q8—22no—
544Q8—41no—
545Q8—41no—
546Q8—41no—
547Q8—41no—
548Q8—41no—
549Q8—41no—
550Q8—228no—
551D4—441no—
552D4—441no—
553D4—441no—
554D4—441no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—112no—
573C2×C4—112no—
574C2×C4—112no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4#6697212yes—
594C2×C4C2×#433911yescharacteristic
595C2×C4C2×D4×D1111yescharacteristic
596C2×C4C2×#434111yescharacteristic
597C2×C4#6703711yescharacteristic
598C2×C4#41×D1111yescharacteristic
599C2×C4#6704311yescharacteristic
600C8—22no—
601C8—22no—
602C8—222no—
603C8—441no—
604C22—881no—
605C22—881no—
606C22—881no—
607C22—881no—
608C22—881no—
609C22—881no—
610C22—881no—
611C22#1062308311yescharacteristic
612C22D11×#12111yescharacteristic
613C22#1062324911yescharacteristic
614C22C2×#6697211yescharacteristic
615C22#1062329711yescharacteristic
616C22D11×#13511yescharacteristic
617C22#1062330111yescharacteristic
618C4—22no—
619C4—41no—
620C4—42no—
621C4—81no—
622C4—81no—
623C4—81no—
624C4—222no—
625C4—222no—
626C4—222no—
627C4—441no—
628C4—881no—
629C4—881no—
630C4—881no—
631C4#1062302111yescharacteristic
632C4#1062306911yescharacteristic
633C4#1062312911yescharacteristic
634C4#1062320011yescharacteristic
635C2—1761no—
636C2#1307217911yescharacteristic
637C2#1307819911yescharacteristic
638C2#1307830611yescharacteristic
639C2#1308130211yescharacteristic
640C2#1308131011yescharacteristic
641C2#1308160611yescharacteristic
642C2#1308160911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1969C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1969D11
hypocenterC11#25297
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1969

Complements

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

NH ≅ G/Ntype
2. C2×C8×Dic22C2semidirect
4. #13073980C2semidirect
6. #13069997C2semidirect
7. #13069936C2semidirect
11. #13069381C2semidirect
13. #13069294C2semidirect
14. #103×Dic11C2semidirect
15. C11×#1969C2semidirect
221. #1969D11semidirect
533. C11#25297semidirect

Maximal subgroups

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

subgroupindex
C2×#106227982
C2×C8×Dic222
#130741032
#130739802
#130699992
#130699972
#130699362
#130699312
#130694672
#130694242
#130693812
#130692992
#130692942
#103×Dic112
C11×#19692
#2529711