Finite Group Databasebeta

← #14826470

Subgroups — #14826470

Order 2816.

784 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073012C211yesmaximal, characteristic, complemented
2#13071636C211yesmaximal, characteristic
3#13070032C211yesmaximal, characteristic, complemented
4#13070002C211yesmaximal, characteristic, complemented
5#13069802C211yesmaximal, characteristic
6#13069381C211yesmaximal, characteristic, complemented
7#13069350C211yesmaximal, characteristic, complemented
8#13069225C211yesmaximal, characteristic, complemented
9#13069207C211yesmaximal, characteristic, complemented
10#13069197C211yesmaximal, characteristic, complemented
11#13068865C211yesmaximal, characteristic, complemented
12#13068806C211yesmaximal, characteristic, complemented
13#13068704C211yesmaximal, characteristic, complemented
14#102×Dic11C211yesmaximal, characteristic, complemented
15C11×#2033C211yesmaximal, characteristic
16C2×C11×#121C2211yescharacteristic
17C2×D4×Dic11—21no—
18C2×D4×Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C11×#380C2211yescharacteristic
25#10622834C2211yescharacteristic
26#10622833—21no—
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29#10622825C2211yescharacteristic
30C4×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622598C2211yescharacteristic
38#10622590C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40C4⋊C4×Dic11C2211yescharacteristic
41#10622586C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43#10622565—21no—
44#10622564—21no—
45#10622564—21no—
46#10622563—21no—
47C11⋊#401—21no—
48#10622266—21no—
49C11×#340C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C23×Dic11—21no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×#121—22no—
67C11×#121—22no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11D411yescharacteristic
78C2×C22⋊Dic11D411yescharacteristic
79D4×Dic11—22no—
80D4×Dic11—41no—
81D4×Dic11—44no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—41no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11C2311yescharacteristic
95C2×C4×Dic11C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C11×#107—22no—
99C11×#102—22no—
100C11×#102—22no—
101C11×C22⋊C8—22no—
102C11×#95—21no—
103#66896—22no—
104#66896—41no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95D411yescharacteristic
114C11⋊#95D411yescharacteristic
115C22⋊(C11⋊C8)—41no—
116#66882—22no—
117#66882—41no—
118Dic11⋊C8—22no—
119C8×Dic11—41no—
120#66872—22no—
121#27033—111nomaximal, Sylow
122C24×C11—21no—
123C24×C11C2×D411yescharacteristic
124C2×D4×C11—24no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—42no—
131C2×D4×C11—42no—
132C2×D4×C11#4112yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×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×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—42no—
149C22×Dic11—42no—
150C22×Dic11—42no—
151C22×Dic11—42no—
152C22×Dic11—81no—
153C22×Dic11—81no—
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11#4112yes—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4#4112yes—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—42no—
172C22⋊Dic11—22no—
173C22⋊Dic11—22no—
174C22⋊Dic11—42no—
175C22⋊Dic11—42no—
176C22⋊Dic11—81no—
177C22⋊Dic11—81no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—42no—
186C4⋊Dic11—42no—
187C4⋊Dic11—42no—
188C4⋊Dic11#4112yes—
189Dic11⋊C4—81no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—42no—
195C4×Dic11—81no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202#2494—111no—
203#2361—111no—
204#2073—111no—
205#2067—111no—
206#2034—111no—
207#2033D1111yescharacteristic
208#1949—111no—
209#1942—111no—
210#1923—111no—
211#1921—111no—
212#1919—111no—
213#1862—111no—
214#1852—111no—
215#1824—111no—
216C4×#102—111no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—22no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11#13512yes—
231C23×C11C22×D411yescharacteristic
232D4×C11—22no—
233D4×C11—22no—
234D4×C11—48no—
235D4×C11—41no—
236D4×C11—41no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11H(5,𝔽2)11yescharacteristic
258C2×C4×C112−1+411yescharacteristic
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—22no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—84no—
283C2×Dic11—84no—
284C2×Dic11AGL(1,ℤ/8)12yes—
285C8×C11—22no—
286C8×C11—41no—
287C11⋊C8—41no—
288C11⋊C8—41no—
289C2×#121C2×D1111yescharacteristic
290C2×C4×D4—111no—
291C2×C4×D4—221no—
292C22×C4⋊C4—111no—
293C2×#107—111no—
294C2×#107—111no—
295C2×#107C2×D1111yescharacteristic
296C2×#106—111no—
297C2×C4⋊C8—111no—
298C2×#102—111no—
299C2×#102—111no—
300C2×#102C2×D1111yescharacteristic
301C2×#102C2×D1111yescharacteristic
302C2×C22⋊C8—111no—
303C2×C22⋊C8C2×D1111yescharacteristic
304C2×C4×C8—111no—
305#401—221no—
306#397—221no—
307#390—111no—
308#389—111no—
309#389—111no—
310#389—111no—
311#388—221no—
312#388—221no—
313#387—221no—
314#386—221no—
315#385—221no—
316#382—111no—
317#380—111no—
318#380C2×D1111yescharacteristic
319C4×C4⋊C4—111no—
320C4×C4⋊C4—111no—
321C4×C22⋊C4—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#340C2×D1111yescharacteristic
330#336—111no—
331#336—111no—
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—42no—
340C22×C11—42no—
341C22×C11—42no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11#52511yescharacteristic
347C22×C11#54611yescharacteristic
348C22×C11#54711yescharacteristic
349C22×C11C2×#13511yescharacteristic
350C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
351C22×C11#57611yescharacteristic
352C22×C11#57811yescharacteristic
353C4×C11—42no—
354C4×C11—41no—
355C4×C11—81no—
356C4×C11—81no—
357C4×C11#52911yescharacteristic
358C4×C11#53911yescharacteristic
359C4×C11#55311yescharacteristic
360C4×C11#55611yescharacteristic
361Dic11—22no—
362Dic11—41no—
363Dic11—41no—
364Dic11—41no—
365Dic11—42no—
366Dic11—81no—
367Dic11—81no—
368Dic11—81no—
369C22×D4—21no—
370C22×D4C22×D1111yescharacteristic
371C23×C4—221no—
372C23×C4—221no—
373C23×C4C22×D1111yescharacteristic
374C22×C8—111no—
375C22×C8—111no—
376C22×C8C22×D1111yescharacteristic
377C22×C8C22×D1111yescharacteristic
378#121—22no—
379#121—22no—
380C4×D4—222no—
381C4×D4—441no—
382C4×D4—444no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—222no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—441no—
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—111no—
399C2×C22⋊C4—111no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C22⋊C4—221no—
403C2×C22⋊C4—221no—
404C2×C42—111no—
405C2×C42—111no—
406C2×C42—221no—
407C2×C42—221no—
408#107—22no—
409#107—222no—
410#107—441no—
411#106—222no—
412C4⋊C8—222no—
413#102—22no—
414#102—22no—
415#102—222no—
416#102—441no—
417C22⋊C8—22no—
418C22⋊C8—441no—
419C4×C8—441no—
420#95—21no—
421#95—111no—
422#95—111no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431C2×C11—42no—
432C2×C11—82no—
433C2×C11#246611yescharacteristic
434C2×C11#310511yescharacteristic
435C2×C11#312411yescharacteristic
436C2×C11#330011yescharacteristic
437C2×C11#331811yescharacteristic
438C2×C11#333911yescharacteristic
439C2×C11#335311yescharacteristic
440C24—21no—
441C24D4×D1111yescharacteristic
442C2×D4—24no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4#434112yes—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—111no—
461C22×C4—111no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—442no—
469C22×C4—442no—
470C22×C4—442no—
471C22×C4—442no—
472C22×C4—881no—
473C22×C4—881no—
474C22×C4D4×D1111yescharacteristic
475C22×C4C23×D1111yescharacteristic
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8#434112yes—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—112no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—442no—
502C4⋊C4—442no—
503C4⋊C4—442no—
504C4⋊C4—881no—
505C4⋊C4#434112yes—
506C22⋊C4—24no—
507C22⋊C4—42no—
508C22⋊C4—222no—
509C22⋊C4—222no—
510C22⋊C4—442no—
511C22⋊C4—442no—
512C22⋊C4—881no—
513C22⋊C4—881no—
514C42—221no—
515C42—221no—
516C42—221no—
517C42—221no—
518C42—442no—
519C42—881no—
520C11#2703311yescharacteristic, complemented, Sylow
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—22no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23#6696512yes—
535C23C2×D4×D1111yescharacteristic
536D4—22no—
537D4—22no—
538D4—48no—
539D4—41no—
540D4—41no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—112no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—222no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—884no—
582C2×C4—884no—
583C2×C4C2×#434111yescharacteristic
584C2×C4C2×#434111yescharacteristic
585C2×C4C2×#434111yescharacteristic
586C2×C4#41×D1111yescharacteristic
587C2×C4#6704211yescharacteristic
588C2×C4#6704311yescharacteristic
589C8—22no—
590C8—41no—
591C8—441no—
592C8—441no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22#1062311711yescharacteristic
608C22#1062314211yescharacteristic
609C22#1062318511yescharacteristic
610C22C2×#6696511yescharacteristic
611C22#1062330011yescharacteristic
612C22D11×AGL(1,ℤ/8)11yescharacteristic
613C22#1062331011yescharacteristic
614C4—41no—
615C4—42no—
616C4—81no—
617C4—81no—
618C4—222no—
619C4—441no—
620C4—441no—
621C4—442no—
622C4—441no—
623C4—881no—
624C4—881no—
625C4—881no—
626C4#1062313111yescharacteristic
627C4#1062314911yescharacteristic
628C4#1062319611yescharacteristic
629C4#1062320211yescharacteristic
630C2—42no—
631C2—82no—
632C2#1307264711yescharacteristic
633C2#1307865811yescharacteristic
634C2#1307887911yescharacteristic
635C2#1308050111yescharacteristic
636C2#1308076011yescharacteristic
637C2#1308102111yescharacteristic
638C2#1308119511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2033C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#2033D11
hypocenterC11#27033
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. #13073012C2semidirect
3. #13070032C2semidirect
4. #13070002C2semidirect
6. #13069381C2semidirect
7. #13069350C2semidirect
8. #13069225C2semidirect
9. #13069207C2semidirect
10. #13069197C2semidirect
11. #13068865C2semidirect
12. #13068806C2semidirect
13. #13068704C2semidirect
14. #102×Dic11C2semidirect
520. C11#27033semidirect

Maximal subgroups

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

subgroupindex
#130730122
#130716362
#130700322
#130700022
#130698022
#130693812
#130693502
#130692252
#130692072
#130691972
#130688652
#130688062
#130687042
#102×Dic112
C11×#20332
#2703311