Finite Group Databasebeta

← #14795103

Subgroups — #14795103

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622372C211yesmaximal, characteristic, complemented
2C2×#10622333C211yesmaximal, characteristic, complemented
3#13074441C211yesmaximal, characteristic, complemented
4#13071311C211yesmaximal, characteristic
5#13070047C211yesmaximal, characteristic, complemented
6#13070039C211yesmaximal, characteristic, complemented
7#13069802C211yesmaximal, characteristic
8#13069562C211yesmaximal, characteristic, complemented
9#13069381C211yesmaximal, characteristic, complemented
10#13069358C211yesmaximal, characteristic, complemented
11#13069350C211yesmaximal, characteristic, complemented
12#13069315C211yesmaximal, characteristic, complemented
13#13069296C211yesmaximal, characteristic, complemented
14#13068624C211yesmaximal, characteristic, complemented
15C11×#2033C211yesmaximal, characteristic
16C2×C11×#121C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C2×#66941C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C11×#380C2211yescharacteristic
25#10622834—21no—
26#10622834C2211yescharacteristic
27#10622833—21no—
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30#10622825C2211yescharacteristic
31#10622825C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622598C2211yescharacteristic
40#10622590C2211yescharacteristic
41C4⋊C4×Dic11C2211yescharacteristic
42#10622586C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622564—21no—
46#10622563—21no—
47#10622562—21no—
48#10622560—21no—
49#10622372—24no—
50#10622333—24no—
51#10622273—21no—
52#10622269—21no—
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11—21no—
65C22×Dic22—21no—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×#121—22no—
69C11×#121—22no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11D411yescharacteristic
81C2×C22⋊Dic11D411yescharacteristic
82D4×Dic11—22no—
83D4×Dic11—22no—
84#66979—22no—
85#66979—22no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11D411yescharacteristic
89C2×C4⋊Dic11D411yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66941—22no—
102#66941—22no—
103C11×#107—22no—
104C11×#102—22no—
105C11×#102—22no—
106C11×C22⋊C8—22no—
107C11×#95—21no—
108#66896—22no—
109#66896—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—
118C22⋊(C11⋊C8)—22no—
119#66882—22no—
120#66879—22no—
121Dic11⋊C8—22no—
122Dic11⋊C8D414yescomplemented
123C8×Dic11—22no—
124#66872—22no—
125#66871—22no—
126#24712—111nomaximal, Sylow
127C24×C11—21no—
128C24×C11C2×D411yescharacteristic
129C2×D4×C11—24no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—81no—
136C2×D4×C11—81no—
137C2×D4×C11#4112yes—
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—21no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—42no—
154C22×Dic11—81no—
155C22×Dic11—81no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C2×Dic22—42no—
161C2×Dic22—81no—
162C2×Dic22—81no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11C2×D412yes—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4#4112yes—
175C11×C22⋊C4—24no—
176C11×C22⋊C4—81no—
177C22⋊Dic11—22no—
178C22⋊Dic11—22no—
179C22⋊Dic11—42no—
180C22⋊Dic11—81no—
181C22⋊Dic11—81no—
182C22⋊Dic11—81no—
183C22⋊Dic11—81no—
184C4⋊Dic11—22no—
185C4⋊Dic11—22no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—81no—
195C4⋊Dic11—81no—
196Dic11⋊C4—42no—
197Dic11⋊C4—81no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—81no—
201C4×Dic11C2×D412yes—
202C4×Dic11#4112yes—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8C2×D412yes—
209C2×#474—111no—
210C2×#433—111no—
211#2628—111no—
212#2324—111no—
213#2076—111no—
214#2075—111no—
215#2034—111no—
216#2033D1111yescharacteristic
217#1987—111no—
218#1949—111no—
219#1944—111no—
220#1942—111no—
221#1936—111no—
222#1934—111no—
223#1804—111no—
224C23×C11—21no—
225C23×C11—22no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11C22×D411yescharacteristic
239D4×C11—22no—
240D4×C11—22no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—84no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—22no—
247C2×C4×C11—21no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
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×C11C22×D411yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C112−1+411yescharacteristic
265C2×C4×C112−1+411yescharacteristic
266C2×Dic11—21no—
267C2×Dic11—21no—
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—41no—
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—41no—
287C2×Dic11—41no—
288C2×Dic11—84no—
289C2×Dic11#12112yes—
290C2×Dic11#12112yes—
291Dic22—84no—
292C8×C11—22no—
293C8×C11—41no—
294C11⋊C8—22no—
295C11⋊C8—41no—
296C2×C4⋊Q8—111no—
297C2×#121C2×D1111yescharacteristic
298C2×C4×D4—111no—
299C2×#117—111no—
300#474—224no—
301#433—224no—
302C2×#107—111no—
303C2×#107—111no—
304C2×#107C2×D1111yescharacteristic
305C2×#106—111no—
306C2×C4⋊C8—111no—
307C2×C4⋊C8—111no—
308C2×#102—111no—
309C2×#102—111no—
310C2×#102C2×D1111yescharacteristic
311C2×#102C2×D1111yescharacteristic
312C2×C22⋊C8—111no—
313C2×C22⋊C8C2×D1111yescharacteristic
314C2×#97—111no—
315C2×C4×C8—111no—
316#400—221no—
317#399—221no—
318#395—221no—
319#393—221no—
320#390—111no—
321#390—221no—
322#389—111no—
323#389—111no—
324#389—111no—
325#388—221no—
326#386—221no—
327#385—221no—
328#382—111no—
329#380—111no—
330#380—111no—
331#380C2×D1111yescharacteristic
332C4×C4⋊C4—111no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340C2×D1111yescharacteristic
341C22×C11—41no—
342C22×C11—42no—
343C22×C11—41no—
344C22×C11—42no—
345C22×C11—41no—
346C22×C11—42no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—81no—
352C22×C11—81no—
353C22×C11—81no—
354C22×C11—81no—
355C22×C11C2×#12111yescharacteristic
356C22×C11#52511yescharacteristic
357C22×C11#53611yescharacteristic
358C22×C11#57611yescharacteristic
359C22×C11#57611yescharacteristic
360C22×C11#57711yescharacteristic
361C22×C11#57811yescharacteristic
362C4×C11—42no—
363C4×C11—41no—
364C4×C11—81no—
365C4×C11—81no—
366C4×C11#54711yescharacteristic
367C4×C11#54811yescharacteristic
368C4×C11#55211yescharacteristic
369C4×C11#55611yescharacteristic
370Dic11—22no—
371Dic11—22no—
372Dic11—41no—
373Dic11—41no—
374Dic11—81no—
375Dic11—81no—
376Dic11—81no—
377Dic11—81no—
378C22×Q8—221no—
379C22×D4—21no—
380C22×D4C22×D1111yescharacteristic
381C23×C4—221no—
382C23×C4C22×D1111yescharacteristic
383C22×C8—111no—
384C22×C8—111no—
385C22×C8C22×D1111yescharacteristic
386C22×C8C22×D1111yescharacteristic
387C4⋊Q8—222no—
388C4⋊Q8—222no—
389#121—22no—
390#121—22no—
391C4×D4—222no—
392C4×D4—222no—
393#117—222no—
394#117—222no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—111no—
411C2×C22⋊C4—111no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C42—111no—
418C2×C42—111no—
419C2×C42—221no—
420#107—22no—
421#107—222no—
422#107—222no—
423#106—222no—
424C4⋊C8—114no—
425C4⋊C8—222no—
426#102—22no—
427#102—22no—
428#102—222no—
429#102—222no—
430C22⋊C8—22no—
431C22⋊C8—222no—
432#97—222no—
433C4×C8—222no—
434#95—21no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443C2×C11—81no—
444C2×C11—82no—
445C2×C11#241511yescharacteristic
446C2×C11#305811yescharacteristic
447C2×C11#306311yescharacteristic
448C2×C11#311811yescharacteristic
449C2×C11#312411yescharacteristic
450C2×C11#324111yescharacteristic
451C2×C11#324311yescharacteristic
452C24—21no—
453C24D4×D1111yescharacteristic
454C2×Q8—442no—
455C2×Q8—881no—
456C2×Q8—881no—
457C2×D4—24no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—81no—
464C2×D4—81no—
465C2×D4#434112yes—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—442no—
484C22×C4—881no—
485C22×C4—881no—
486C22×C4D4×D1111yescharacteristic
487C22×C4C23×D1111yescharacteristic
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—112no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8D4×D1112yes—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—222no—
506C4⋊C4—222no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—442no—
516C4⋊C4—881no—
517C4⋊C4—881no—
518C4⋊C4—881no—
519C4⋊C4#434112yes—
520C22⋊C4—24no—
521C22⋊C4—81no—
522C22⋊C4—222no—
523C22⋊C4—222no—
524C22⋊C4—442no—
525C22⋊C4—881no—
526C22⋊C4—881no—
527C22⋊C4—881no—
528C22⋊C4—881no—
529C42—112no—
530C42—112no—
531C42—221no—
532C42—221no—
533C42—881no—
534C11#2471211yescharacteristic, complemented, Sylow
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—22no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23C2×D4×D1111yescharacteristic
550Q8—884no—
551D4—22no—
552D4—22no—
553D4—41no—
554D4—41no—
555D4—84no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
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—221no—
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—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—884no—
597C2×C4C2×D4×D1111yescharacteristic
598C2×C4C2×#434111yescharacteristic
599C2×C4C2×#434111yescharacteristic
600C2×C4#41×D1111yescharacteristic
601C2×C4#6704311yescharacteristic
602C2×C4#6704311yescharacteristic
603C8—22no—
604C8—41no—
605C8—222no—
606C8—441no—
607C22—41no—
608C22—42no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—42no—
614C22—41no—
615C22—42no—
616C22—41no—
617C22—81no—
618C22—81no—
619C22—81no—
620C22—81no—
621C22#1062311711yescharacteristic
622C22D11×#12111yescharacteristic
623C22#1062317911yescharacteristic
624C22#1062328811yescharacteristic
625C22#1062330011yescharacteristic
626C22#1062330611yescharacteristic
627C22#1062331011yescharacteristic
628C4—42no—
629C4—41no—
630C4—81no—
631C4—81no—
632C4—222no—
633C4—222no—
634C4—441no—
635C4—441no—
636C4—881no—
637C4—881no—
638C4—881no—
639C4—881no—
640C4#1062312911yescharacteristic
641C4#1062314211yescharacteristic
642C4#1062318111yescharacteristic
643C4#1062320211yescharacteristic
644C2—81no—
645C2—82no—
646C2#1307203811yescharacteristic
647C2#1307825911yescharacteristic
648C2#1307830211yescharacteristic
649C2#1307879311yescharacteristic
650C2#1307887911yescharacteristic
651C2#1307987511yescharacteristic
652C2#1307989511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2033C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#2033D11
hypocenterC11#24712
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2033

Complements

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

NH ≅ G/Ntype
1. C2×#10622372C2semidirect
2. C2×#10622333C2semidirect
3. #13074441C2semidirect
5. #13070047C2semidirect
6. #13070039C2semidirect
8. #13069562C2semidirect
9. #13069381C2semidirect
10. #13069358C2semidirect
11. #13069350C2semidirect
12. #13069315C2semidirect
13. #13069296C2semidirect
14. #13068624C2semidirect
122. Dic11⋊C8D4semidirect
534. C11#24712semidirect

Maximal subgroups

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

subgroupindex
C2×#106223722
C2×#106223332
#130744412
#130713112
#130700472
#130700392
#130698022
#130695622
#130693812
#130693582
#130693502
#130693152
#130692962
#130686242
C11×#20332
#2471211