Finite Group Databasebeta

← #14826482

Subgroups — #14826482

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#13073014C211yesmaximal, characteristic, complemented
2#13071634C211yesmaximal, characteristic
3#13070031C211yesmaximal, characteristic, complemented
4#13070001C211yesmaximal, characteristic, complemented
5#13069808C211yesmaximal, characteristic
6#13069801C211yesmaximal, characteristic
7#13069384C211yesmaximal, characteristic, complemented
8#13069348C211yesmaximal, characteristic, complemented
9#13069223C211yesmaximal, characteristic, complemented
10#13069197C211yesmaximal, characteristic, complemented
11#13068860C211yesmaximal, characteristic, complemented
12#13068802C211yesmaximal, characteristic, complemented
13#13068705C211yesmaximal, characteristic, complemented
14#13068430C211yesmaximal, characteristic, complemented
15C11×#1921C211yesmaximal, characteristic, complemented
16C2×#66948C2211yescharacteristic
17C2×#66946C2211yescharacteristic
18C2×C4⋊C4×D11C2211yescharacteristic
19C2×C4×D44—21no—
20C2×C11×#107C2211yescharacteristic
21C11×#389C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×#66885C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×(C2×D11)⋊C8C2211yescharacteristic
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×C8×Dic11C2211yescharacteristic
28#10622606—21no—
29#10622600C2211yescharacteristic
30#10622600C2211yescharacteristic
31#10622598C2211yescharacteristic
32#10622591—21no—
33C4⋊C4×Dic11C2211yescharacteristic
34#10622586C2211yescharacteristic
35C2×#66873C2211yescharacteristic
36C2×#66873C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622553—21no—
41#10622552C2211yescharacteristic
42C4×(C2×D11)⋊C4C2211yescharacteristic
43#10622549C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45#10622282—21no—
46#10622281—21no—
47#10622278—21no—
48C11⋊#401—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D44—21no—
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11—21no—
63C22×C4×D11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C42×C11—21no—
72C2×C42×C11C2311yescharacteristic
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4D411yescharacteristic
80C2×(C2×D11)⋊C4D411yescharacteristic
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91#66948—22no—
92#66948—22no—
93#66946—22no—
94#66946—41no—
95C4⋊C4×D11—22no—
96C4⋊C4×D11—41no—
97C4×D44—44no—
98C11×#107—22no—
99C11×#95—21no—
100C11×#95—21no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95D411yescharacteristic
109C11⋊#95D411yescharacteristic
110#66885—22no—
111#66885—22no—
112(C2×D11)⋊C8—22no—
113(C2×D11)⋊C8—41no—
114C8×Dic11—41no—
115#66873—22no—
116#66873—41no—
117#66872—22no—
118#66871—22no—
119#66871—41no—
120C4⋊(C11⋊C8)—22no—
121#27033—111nomaximal, Sylow
122C23×D11—21no—
123C23×D11C2×D411yescharacteristic
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2411yescharacteristic
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136C22×Dic11C2×D411yescharacteristic
137C2×D44—24no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44—42no—
144C2×D44—42no—
145C2×D44#4112yes—
146C2×C4×D11—21no—
147C2×C4×D11—21no—
148C2×C4×D11—21no—
149C2×C4×D11—21no—
150C2×C4×D11—21no—
151C2×C4×D11—21no—
152C2×C4×D11—42no—
153C2×C4×D11—42no—
154C2×C4×D11—42no—
155C2×C4×D11—42no—
156C2×C4×D11—81no—
157C2×C4×D11—81no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—81no—
171C11×C4⋊C4#4112yes—
172C11×C4⋊C4#4112yes—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—42no—
176(C2×D11)⋊C4—24no—
177(C2×D11)⋊C4—22no—
178(C2×D11)⋊C4—22no—
179(C2×D11)⋊C4—42no—
180(C2×D11)⋊C4—42no—
181(C2×D11)⋊C4—42no—
182(C2×D11)⋊C4—81no—
183(C2×D11)⋊C4—81no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—42no—
191Dic11⋊C4—42no—
192Dic11⋊C4—42no—
193C4×Dic11—21no—
194C4×Dic11—21no—
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#4112yes—
202#2494—111no—
203#2361—111no—
204#2073—111no—
205#2067—111no—
206#2034—111no—
207#2033—111no—
208#1949—111no—
209#1942—111no—
210#1923—111no—
211#1921D1111yescharacteristic, complemented
212#1919—111no—
213#1862—111no—
214#1852—111no—
215#1824—111no—
216C4×#102—111no—
217C23×C11C22×D411yescharacteristic
218C22×D11—21no—
219C22×D11—21no—
220C22×D11—21no—
221C22×D11—21no—
222C22×D11—21no—
223C22×D11—21no—
224C22×D11—22no—
225C22×D11—41no—
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—41no—
231C22×D11#13512yes—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—41no—
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×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11H(5,𝔽2)11yescharacteristic
255C2×C4×C112−1+411yescharacteristic
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11AGL(1,ℤ/8)12yes—
274D44—22no—
275D44—22no—
276D44—48no—
277D44—41no—
278D44—41no—
279C4×D11—41no—
280C4×D11—41no—
281C4×D11—41no—
282C4×D11—41no—
283C4×D11—84no—
284C4×D11—84no—
285C8×C11—41no—
286C8×C11—41no—
287C11⋊C8—22no—
288C11⋊C8—41no—
289C2×#121—111no—
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×#102—111no—
301C2×#102—111no—
302C2×C22⋊C8—111no—
303C2×C22⋊C8—111no—
304C2×C4×C8—111no—
305#401—221no—
306#397—221no—
307#390—111no—
308#389—111no—
309#389—111no—
310#389C2×D1111yescharacteristic
311#388—221no—
312#388—221no—
313#387—221no—
314#386—221no—
315#385—221no—
316#382—111no—
317#380—111no—
318#380—111no—
319C4×C4⋊C4—111no—
320C4×C4⋊C4C2×D1111yescharacteristic
321C4×C22⋊C4—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340C2×D1111yescharacteristic
328#340C2×D1111yescharacteristic
329#340C2×D1111yescharacteristic
330#336—111no—
331#336C2×D1111yescharacteristic
332C22×C11#52511yescharacteristic
333C22×C11#54611yescharacteristic
334C22×C11#54711yescharacteristic
335C22×C11C2×#13511yescharacteristic
336C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
337C22×C11#57611yescharacteristic
338C22×C11#57811yescharacteristic
339C2×D11—22no—
340C2×D11—22no—
341C2×D11—22no—
342C2×D11—41no—
343C2×D11—41no—
344C2×D11—41no—
345C2×D11—41no—
346C2×D11—42no—
347C2×D11—42no—
348C2×D11—42no—
349C2×D11—81no—
350C2×D11—81no—
351C2×D11—81no—
352C2×D11—81no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—42no—
356C4×C11—42no—
357C4×C11—81no—
358C4×C11—81no—
359C4×C11#52911yescharacteristic
360C4×C11#53911yescharacteristic
361C4×C11#55311yescharacteristic
362C4×C11#55611yescharacteristic
363Dic11—22no—
364Dic11—41no—
365Dic11—41no—
366Dic11—81no—
367Dic11—81no—
368Dic11—81no—
369C22×D4—111no—
370C22×D4—221no—
371C23×C4—111no—
372C23×C4—221no—
373C23×C4—221no—
374C22×C8—111no—
375C22×C8—111no—
376C22×C8C22×D1111yescharacteristic
377C22×C8C22×D1111yescharacteristic
378#121—222no—
379#121—222no—
380C4×D4—222no—
381C4×D4—444no—
382C4×D4—441no—
383C2×C4⋊C4—21no—
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—441no—
392C2×C4⋊C4C22×D1111yescharacteristic
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C22⋊C4—111no—
397C2×C22⋊C4—111no—
398C2×C22⋊C4—221no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C22⋊C4—221no—
403C2×C22⋊C4—221no—
404C2×C42—21no—
405C2×C42—111no—
406C2×C42—221no—
407C2×C42C22×D1111yescharacteristic
408#107—22no—
409#107—222no—
410#107—441no—
411#106—222no—
412C4⋊C8—222no—
413#102—222no—
414#102—222no—
415#102—222no—
416#102—441no—
417C22⋊C8—222no—
418C22⋊C8—441no—
419C4×C8—441no—
420#95—21no—
421#95—21no—
422#95—111no—
423#95—111no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431C2×C11#246611yescharacteristic
432C2×C11#310511yescharacteristic
433C2×C11#312411yescharacteristic
434C2×C11#330011yescharacteristic
435C2×C11#331811yescharacteristic
436C2×C11#333911yescharacteristic
437C2×C11#335311yescharacteristic
438D11—42no—
439D11—82no—
440C24—111no—
441C24—221no—
442C2×D4—112no—
443C2×D4—224no—
444C2×D4—221no—
445C2×D4—221no—
446C2×D4—221no—
447C2×D4—221no—
448C2×D4—221no—
449C2×D4—442no—
450C2×D4—442no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—442no—
468C22×C4—442no—
469C22×C4—442no—
470C22×C4—442no—
471C22×C4—881no—
472C22×C4—881no—
473C22×C4D4×D1111yescharacteristic
474C22×C4D4×D1111yescharacteristic
475C22×C4C23×D1111yescharacteristic
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—112no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—81no—
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#433912yes—
505C4⋊C4#434312yes—
506C22⋊C4—222no—
507C22⋊C4—222no—
508C22⋊C4—224no—
509C22⋊C4—442no—
510C22⋊C4—442no—
511C22⋊C4—442no—
512C22⋊C4—881no—
513C22⋊C4—881no—
514C42—21no—
515C42—21no—
516C42—42no—
517C42—221no—
518C42—221no—
519C42—881no—
520C11#2703311yescharacteristic, complemented, Sylow
521C23—112no—
522C23—221no—
523C23—221no—
524C23—221no—
525C23—221no—
526C23—221no—
527C23—221no—
528C23—222no—
529C23—441no—
530C23—441no—
531C23—441no—
532C23—441no—
533C23—441no—
534C23—441no—
535C23C2×D4×D1111yescharacteristic
536D4—222no—
537D4—222no—
538D4—448no—
539D4—441no—
540D4—441no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
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—41no—
558C2×C4—41no—
559C2×C4—112no—
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—441no—
569C2×C4—441no—
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×#433911yescharacteristic
584C2×C4C2×#434311yescharacteristic
585C2×C4#41×D1111yescharacteristic
586C2×C4#41×D1111yescharacteristic
587C2×C4#6704211yescharacteristic
588C2×C4#6704311yescharacteristic
589C8—41no—
590C8—41no—
591C8—222no—
592C8—441no—
593C22—222no—
594C22—222no—
595C22—222no—
596C22—441no—
597C22—441no—
598C22—441no—
599C22—441no—
600C22—442no—
601C22—442no—
602C22—442no—
603C22—881no—
604C22—881no—
605C22—881no—
606C22—881no—
607C22#1062308111yescharacteristic
608C22#1062315811yescharacteristic
609C22#1062318611yescharacteristic
610C22#1062329711yescharacteristic
611C22D11×#13511yescharacteristic
612C22D11×AGL(1,ℤ/8)11yescharacteristic
613C22#1062330511yescharacteristic
614C4—41no—
615C4—42no—
616C4—41no—
617C4—42no—
618C4—81no—
619C4—81no—
620C4—222no—
621C4—441no—
622C4—441no—
623C4—881no—
624C4—881no—
625C4—881no—
626C4#1062305911yescharacteristic
627C4#1062311511yescharacteristic
628C4#1062322611yescharacteristic
629C4#1062323811yescharacteristic
630C2—442no—
631C2—882no—
632C2#1307265911yescharacteristic
633C2#1307866811yescharacteristic
634C2#1307888511yescharacteristic
635C2#1308050811yescharacteristic
636C2#1308076211yescharacteristic
637C2#1308101111yescharacteristic
638C2#1308119311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1921C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenter#1921D11
hypocenterC11#27033
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
1. #13073014C2semidirect
3. #13070031C2semidirect
4. #13070001C2semidirect
7. #13069384C2semidirect
8. #13069348C2semidirect
9. #13069223C2semidirect
10. #13069197C2semidirect
11. #13068860C2semidirect
12. #13068802C2semidirect
13. #13068705C2semidirect
14. #13068430C2semidirect
15. C11×#1921C2semidirect
211. #1921D11semidirect
520. C11#27033semidirect

Maximal subgroups

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

subgroupindex
#130730142
#130716342
#130700312
#130700012
#130698082
#130698012
#130693842
#130693482
#130692232
#130691972
#130688602
#130688022
#130687052
#130684302
C11×#19212
#2703311