Finite Group Databasebeta

← #14826471

Subgroups — #14826471

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#13071630C211yesmaximal, characteristic
2#13070030C211yesmaximal, characteristic, complemented
3#13070001C211yesmaximal, characteristic, complemented
4#13069805C211yesmaximal, characteristic
5#13069798C211yesmaximal, characteristic
6#13069382C211yesmaximal, characteristic, complemented
7#13069346C211yesmaximal, characteristic, complemented
8#13069224C211yesmaximal, characteristic, complemented
9#13069205C211yesmaximal, characteristic, complemented
10#13069194C211yesmaximal, characteristic, complemented
11#13068862C211yesmaximal, characteristic, complemented
12#13068803C211yesmaximal, characteristic, complemented
13#13068704C211yesmaximal, characteristic, complemented
14C4×#66873C211yesmaximal, characteristic, complemented
15C11×#2494C211yesmaximal, characteristic, complemented
16C2×#66983C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C2×(C22⋊D11)⋊C4—21no—
19C2×C4×D44C2211yescharacteristic
20C11×#401—21no—
21C11×#397—21no—
22C11×#389C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#388—21no—
25C11×#387—21no—
26C11×#382C2211yescharacteristic
27C11×#380C2211yescharacteristic
28C11×#380C2211yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic
30C4×C11×C22⋊C4C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×#66873C2211yescharacteristic
34C2×#66873C2211yescharacteristic
35C2×#66873C2211yescharacteristic
36C2×#66873C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622571—21no—
42#10622552C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44#10622541C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622283—21no—
48#10622281—21no—
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C23×Dic11—21no—
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4D411yescharacteristic
73C2×C11×C22⋊C4D411yescharacteristic
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77#66983—22no—
78#66983—22no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—41no—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—21no—
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95(C22⋊D11)⋊C4—44no—
96C4×D44—22no—
97C4×D44—41no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95—21no—
105C11×#95D411yescharacteristic
106C11×#95D411yescharacteristic
107C11⋊#95—21no—
108C11⋊#95—21no—
109C22⋊(C11⋊C8)—22no—
110C22⋊(C11⋊C8)—41no—
111#66873—22no—
112#66873—22no—
113#66873—22no—
114#66873—41no—
115#66872—22no—
116#66871—22no—
117#66871—22no—
118#66871—41no—
119C4⋊(C11⋊C8)—22no—
120C4×C11⋊C8—41no—
121#27033—111nomaximal, Sylow
122C24×C11C2×D411yescharacteristic
123C23×D11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C2×C22⋊D11—24no—
141C2×C22⋊D11—42no—
142C2×C22⋊D11—42no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—42no—
147C22×Dic11—42no—
148C22×Dic11—81no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44#4112yes—
155C2×C4×D11—42no—
156C2×C4×D11—42no—
157C2×C4×D11—81no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—42no—
167C11×C4⋊C4—81no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—42no—
171C11×C22⋊C4—81no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—81no—
177(C2×D11)⋊C4—24no—
178(C2×D11)⋊C4—42no—
179(C2×D11)⋊C4—42no—
180(C2×D11)⋊C4—81no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—42no—
186C4⋊Dic11#4112yes—
187C4⋊Dic11#4112yes—
188Dic11⋊C4—42no—
189C4×Dic11—42no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
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#2494D1111yescharacteristic, complemented
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#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#13512yes—
224C23×C11C22×D411yescharacteristic
225C22×D11—22no—
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—41no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
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—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
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×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×C11AGL(1,ℤ/8)12yes—
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11H(5,𝔽2)11yescharacteristic
268C2×C4×C112−1+411yescharacteristic
269C22⋊D11—48no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—84no—
280D44—22no—
281D44—22no—
282D44—41no—
283D44—41no—
284C4×D11—84no—
285C11⋊C8—22no—
286C11⋊C8—41no—
287C11⋊C8—41no—
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×#107—111no—
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—21no—
306#397—21no—
307#390—111no—
308#389—111no—
309#389C2×D1111yescharacteristic
310#389C2×D1111yescharacteristic
311#388—21no—
312#388—221no—
313#387—21no—
314#386—221no—
315#385—221no—
316#382C2×D1111yescharacteristic
317#380C2×D1111yescharacteristic
318#380C2×D1111yescharacteristic
319C4×C4⋊C4—111no—
320C4×C4⋊C4C2×D1111yescharacteristic
321C4×C22⋊C4C2×D1111yescharacteristic
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
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#52511yescharacteristic
340C22×C11#54611yescharacteristic
341C22×C11#54711yescharacteristic
342C22×C11C2×#13511yescharacteristic
343C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
344C22×C11#57611yescharacteristic
345C22×C11#57811yescharacteristic
346C2×D11—42no—
347C2×D11—42no—
348C2×D11—42no—
349C2×D11—81no—
350C2×D11—81no—
351C2×D11—81no—
352C2×D11—81no—
353C4×C11—22no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11—41no—
358C4×C11—81no—
359C4×C11—81no—
360C4×C11—81no—
361C4×C11—81no—
362C4×C11#52911yescharacteristic
363C4×C11#53911yescharacteristic
364C4×C11#55311yescharacteristic
365C4×C11#55611yescharacteristic
366Dic11—42no—
367Dic11—42no—
368Dic11—81no—
369C22×D4—111no—
370C22×D4—221no—
371C23×C4—221no—
372C23×C4—221no—
373C23×C4C22×D1111yescharacteristic
374C22×C8—111no—
375C22×C8—111no—
376C22×C8—111no—
377C22×C8—111no—
378#121—222no—
379#121—222no—
380C4×D4—222no—
381C4×D4—441no—
382C4×D4—444no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—222no—
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—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—221no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C22⋊C4C22⋊D1111yescharacteristic
403C2×C22⋊C4C22⋊D1111yescharacteristic
404C2×C42—21no—
405C2×C42—221no—
406C2×C42C22×D1111yescharacteristic
407C2×C42C22×D1111yescharacteristic
408#107—222no—
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—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—221no—
428#95—221no—
429#95C22⋊D1111yescharacteristic
430#95C22⋊D1111yescharacteristic
431C2×C11—42no—
432C2×C11#246611yescharacteristic
433C2×C11#310511yescharacteristic
434C2×C11#312411yescharacteristic
435C2×C11#330011yescharacteristic
436C2×C11#331811yescharacteristic
437C2×C11#333911yescharacteristic
438C2×C11#335311yescharacteristic
439D11—82no—
440C24—221no—
441C24C2×C22⋊D1111yescharacteristic
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—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—442no—
465C22×C4—442no—
466C22×C4—442no—
467C22×C4—442no—
468C22×C4—881no—
469C22×C4—881no—
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1111yescharacteristic
472C22×C4C2×C22⋊D1111yescharacteristic
473C22×C4C2×C22⋊D1111yescharacteristic
474C22×C4C2×C22⋊D1111yescharacteristic
475C22×C4C23×D1111yescharacteristic
476C2×C8—112no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
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—21no—
495C4⋊C4—21no—
496C4⋊C4—42no—
497C4⋊C4—81no—
498C4⋊C4—112no—
499C4⋊C4—112no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—442no—
505C4⋊C4—442no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—42no—
509C22⋊C4—81no—
510C22⋊C4—224no—
511C22⋊C4—442no—
512C22⋊C4—442no—
513C22⋊C4—881no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—81no—
519C42—442no—
520C11#2703311yescharacteristic, complemented, Sylow
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—222no—
528C23—441no—
529C23—441no—
530C23—441no—
531C23—441no—
532C23—441no—
533C23—441no—
534C23#6700312yes—
535C23C22×C22⋊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—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
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—222no—
572C2×C4—222no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—884no—
581C2×C4—884no—
582C2×C4#6700212yes—
583C2×C4#41×D1111yescharacteristic
584C2×C4#41×D1111yescharacteristic
585C2×C4#41×D1111yescharacteristic
586C2×C4#41×D1111yescharacteristic
587C2×C4#6704211yescharacteristic
588C2×C4#6704311yescharacteristic
589C8—222no—
590C8—441no—
591C8—441no—
592C8—441no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—442no—
601C22—442no—
602C22—442no—
603C22—881no—
604C22—881no—
605C22—881no—
606C22—881no—
607C22C2×#6700211yescharacteristic
608C22C2×#6700311yescharacteristic
609C22#1062335511yescharacteristic
610C22#1062335911yescharacteristic
611C22#1062336011yescharacteristic
612C22#1062336611yescharacteristic
613C22#1062336911yescharacteristic
614C4—22no—
615C4—41no—
616C4—41no—
617C4—41no—
618C4—41no—
619C4—81no—
620C4—81no—
621C4—81no—
622C4—81no—
623C4—442no—
624C4—442no—
625C4—881no—
626C4#1062323311yescharacteristic
627C4#1062323711yescharacteristic
628C4#1062323811yescharacteristic
629C4#1062324011yescharacteristic
630C2—42no—
631C2—882no—
632C2#1307264811yescharacteristic
633C2#1307865911yescharacteristic
634C2#1307887211yescharacteristic
635C2#1308049711yescharacteristic
636C2#1308075111yescharacteristic
637C2#1308101211yescharacteristic
638C2#1308119411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2494C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#2494D11
hypocenterC11#27033
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2494

Complements

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

NH ≅ G/Ntype
2. #13070030C2semidirect
3. #13070001C2semidirect
6. #13069382C2semidirect
7. #13069346C2semidirect
8. #13069224C2semidirect
9. #13069205C2semidirect
10. #13069194C2semidirect
11. #13068862C2semidirect
12. #13068803C2semidirect
13. #13068704C2semidirect
14. C4×#66873C2semidirect
15. C11×#2494C2semidirect
202. #2494D11semidirect
520. C11#27033semidirect

Maximal subgroups

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

subgroupindex
#130716302
#130700302
#130700012
#130698052
#130697982
#130693822
#130693462
#130692242
#130692052
#130691942
#130688622
#130688032
#130687042
C4×#668732
C11×#24942
#2703311