Finite Group Databasebeta

← #14822293

Subgroups — #14822293

Order 2816.

804 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073154C211yesmaximal, characteristic, complemented
2#13070029C211yesmaximal, characteristic, complemented
3#13070004C211yesmaximal, characteristic, complemented
4#13069847C211yesmaximal, characteristic
5#13069847C211yesmaximal, characteristic
6#13069302C211yesmaximal, characteristic, complemented
7#13069233C211yesmaximal, characteristic, complemented
8#13069208C211yesmaximal, characteristic, complemented
9#13069194C211yesmaximal, characteristic, complemented
10#13069175C211yesmaximal, characteristic, complemented
11#13068877C211yesmaximal, characteristic, complemented
12#13068877C211yesmaximal, characteristic, complemented
13#13068626C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic, complemented
15C11×#2366C211yesmaximal, characteristic
16C2×C11×#127C2211yescharacteristic
17C2×C4×D4×C11—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C11×#390—21no—
21C11×#390C2211yescharacteristic
22C11×#390C2211yescharacteristic
23C11×#386—21no—
24C11×#386—21no—
25C4×C11×C4⋊C4C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35#10622593—21no—
36#10622591—21no—
37C2×#66872C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39#10622549C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622271—21no—
48#10622263—21no—
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C11×#127—22no—
66C11×#127—22no—
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—41no—
70C4×D4×C11—41no—
71C4×D4×C11—44no—
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C11×#95—21no—
100C11×#95D411yescharacteristic
101C11×#95D411yescharacteristic
102#66896—22no—
103#66896—22no—
104#66896—22no—
105#66896—22no—
106#66896—22no—
107#66896—22no—
108#66896—41no—
109#66896—41no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117#66872—22no—
118#66871—22no—
119C4⋊(C11⋊C8)—41no—
120C4×C11⋊C8—41no—
121#26753—111nomaximal, Sylow
122C24×C11—21no—
123C24×C11—21no—
124C2×D4×C11—24no—
125C2×D4×C11—24no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11—81no—
139C2×D4×C11—81no—
140C2×D4×C11#4112yes—
141C2×D4×C11#4112yes—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11—81no—
149C22×C4×C11—81no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4#4112yes—
167C11×C22⋊C4—42no—
168C11×C22⋊C4—42no—
169C11×C22⋊C4—42no—
170C11×C22⋊C4—42no—
171C11×C22⋊C4—81no—
172C11×C22⋊C4—81no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—42no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11#4112yes—
188Dic11⋊C4—42no—
189Dic11⋊C4—81no—
190Dic11⋊C4—81no—
191Dic11⋊C4—81no—
192C4×Dic11—42no—
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—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205#2508—111no—
206#2366D1111yescharacteristic
207#2073—111no—
208#2067—111no—
209#2041—111no—
210#2041—111no—
211#1934—111no—
212#1925—111no—
213#1921—111no—
214#1919—111no—
215#1916—111no—
216#1864—111no—
217#1864—111no—
218#1804—111no—
219C4×#102—111no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11C22×D411yescharacteristic
235D4×C11—22no—
236D4×C11—22no—
237D4×C11—22no—
238D4×C11—22no—
239D4×C11—48no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—84no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—84no—
268C2×C4×C11—84no—
269C2×C4×C11#13512yes—
270C2×C4×C11AGL(1,ℤ/8)12yes—
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11H(5,𝔽2)11yescharacteristic
276C2×C4×C112−1+411yescharacteristic
277C2×Dic11—22no—
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—41no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C11⋊C8—41no—
293C2×#127C2×D1111yescharacteristic
294C2×C4×D4—21no—
295C2×C4×D4C2×D1111yescharacteristic
296C2×C4×D4C2×D1111yescharacteristic
297C2×#107—111no—
298C2×#106—111no—
299C2×C4⋊C8—111no—
300C2×#102—111no—
301C2×#102—111no—
302C2×#102—111no—
303C2×#102—111no—
304C2×#102—111no—
305C2×#102—111no—
306C2×#102—111no—
307C2×#102—111no—
308C2×C4×C8—111no—
309#400—221no—
310#398—221no—
311#390—21no—
312#390C2×D1111yescharacteristic
313#390C2×D1111yescharacteristic
314#389—111no—
315#389—111no—
316#389—111no—
317#389—111no—
318#387—221no—
319#386—21no—
320#386—21no—
321#382—111no—
322#382—221no—
323C4×C4⋊C4—111no—
324C4×C4⋊C4C2×D1111yescharacteristic
325C4×C4⋊C4C2×D1111yescharacteristic
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#340—111no—
331#340—111no—
332#336—111no—
333#336—111no—
334#336—111no—
335#336—111no—
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—42no—
341C22×C11—42no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11#52511yescharacteristic
351C22×C11#54611yescharacteristic
352C22×C11#54811yescharacteristic
353C22×C11C2×#13511yescharacteristic
354C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
355C22×C11#57611yescharacteristic
356C22×C11#57711yescharacteristic
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11—42no—
364C4×C11—81no—
365C4×C11#52911yescharacteristic
366C4×C11#53911yescharacteristic
367C4×C11#55211yescharacteristic
368C4×C11#55311yescharacteristic
369Dic11—42no—
370Dic11—81no—
371Dic11—81no—
372Dic11—81no—
373C22×D4—21no—
374C22×D4—21no—
375C22×D4C22×D1111yescharacteristic
376C22×D4C22×D1111yescharacteristic
377C23×C4—21no—
378C23×C4—21no—
379C22×C8—111no—
380C22×C8—111no—
381C22×C8—111no—
382C22×C8—111no—
383#127—22no—
384#127—22no—
385C4×D4—22no—
386C4×D4—22no—
387C4×D4—41no—
388C4×D4—41no—
389C4×D4—44no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4C22⋊D1111yescharacteristic
399C2×C4⋊C4C22⋊D1111yescharacteristic
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C42—21no—
409C2×C42—221no—
410C2×C42C22×D1111yescharacteristic
411C2×C42C22×D1111yescharacteristic
412C2×C42C22×D1111yescharacteristic
413#107—222no—
414#106—222no—
415C4⋊C8—441no—
416#102—222no—
417#102—222no—
418#102—222no—
419#102—222no—
420#102—222no—
421#102—222no—
422#102—441no—
423#102—441no—
424C4×C8—441no—
425#95—21no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95—221no—
433#95C22⋊D1111yescharacteristic
434#95C22⋊D1111yescharacteristic
435C2×C11—82no—
436C2×C11—82no—
437C2×C11#246011yescharacteristic
438C2×C11#310511yescharacteristic
439C2×C11#311811yescharacteristic
440C2×C11#330511yescharacteristic
441C2×C11#331011yescharacteristic
442C2×C11#336511yescharacteristic
443C2×C11#336611yescharacteristic
444C24—21no—
445C24—21no—
446C2×D4—24no—
447C2×D4—24no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—42no—
459C2×D4—42no—
460C2×D4—81no—
461C2×D4—81no—
462C2×D4#433912yes—
463C2×D4#433912yes—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—81no—
471C22×C4—81no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4C2×C22⋊D1111yescharacteristic
477C22×C4C2×C22⋊D1111yescharacteristic
478C22×C4C2×C22⋊D1111yescharacteristic
479C22×C4C2×C22⋊D1111yescharacteristic
480C22×C4C2×C22⋊D1111yescharacteristic
481C22×C4C2×C22⋊D1111yescharacteristic
482C22×C4C23×D1111yescharacteristic
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—112no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—442no—
509C4⋊C4—881no—
510C4⋊C4—881no—
511C4⋊C4—881no—
512C4⋊C4#434112yes—
513C22⋊C4—42no—
514C22⋊C4—42no—
515C22⋊C4—42no—
516C22⋊C4—42no—
517C22⋊C4—81no—
518C22⋊C4—81no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—42no—
526C42—442no—
527C11#2675311yescharacteristic, complemented, Sylow
528C23—22no—
529C23—22no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23C22×C22⋊D1111yescharacteristic
543D4—22no—
544D4—22no—
545D4—22no—
546D4—22no—
547D4—48no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—84no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—84no—
576C2×C4—84no—
577C2×C4—222no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4#6698512yes—
590C2×C4#6700312yes—
591C2×C4C2×#433911yescharacteristic
592C2×C4C2×#433911yescharacteristic
593C2×C4C2×#434111yescharacteristic
594C2×C4#6703711yescharacteristic
595C2×C4#41×D1111yescharacteristic
596C2×C4#6704311yescharacteristic
597C8—441no—
598C8—441no—
599C8—441no—
600C8—441no—
601C22—42no—
602C22—42no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22#1062332211yescharacteristic
616C22C2×#6698511yescharacteristic
617C22#1062333711yescharacteristic
618C22C2×#6700311yescharacteristic
619C22#1062336211yescharacteristic
620C22#1062336611yescharacteristic
621C22#1062336711yescharacteristic
622C4—22no—
623C4—22no—
624C4—41no—
625C4—41no—
626C4—42no—
627C4—41no—
628C4—41no—
629C4—81no—
630C4—442no—
631C4—881no—
632C4—881no—
633C4—881no—
634C4#1062306911yescharacteristic
635C4#1062307111yescharacteristic
636C4#1062307211yescharacteristic
637C4#1062309511yescharacteristic
638C2—82no—
639C2—82no—
640C2#1307256211yescharacteristic
641C2#1307866311yescharacteristic
642C2#1307880011yescharacteristic
643C2#1308056611yescharacteristic
644C2#1308063711yescharacteristic
645C2#1308130811yescharacteristic
646C2#1308131911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2366C2
socleC23×C11C22×D4
prime radicalC2×C11×#127C22
hypercenter#2366D11
hypocenterC11#26753
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2366

Complements

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

NH ≅ G/Ntype
1. #13073154C2semidirect
2. #13070029C2semidirect
3. #13070004C2semidirect
6. #13069302C2semidirect
7. #13069233C2semidirect
8. #13069208C2semidirect
9. #13069194C2semidirect
10. #13069175C2semidirect
11. #13068877C2semidirect
12. #13068877C2semidirect
13. #13068626C2semidirect
14. C4×#66896C2semidirect
527. C11#26753semidirect

Maximal subgroups

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

subgroupindex
#130731542
#130700292
#130700042
#130698472
#130693022
#130692332
#130692082
#130691942
#130691752
#130688772
#130686262
C4×#668962
C11×#23662
#2675311