Finite Group Databasebeta

← #14826473

Subgroups — #14826473

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#13073016C211yesmaximal, characteristic, complemented
2#13071630C211yesmaximal, characteristic
3#13070031C211yesmaximal, characteristic, complemented
4#13070003C211yesmaximal, characteristic, complemented
5#13069806C211yesmaximal, characteristic
6#13069799C211yesmaximal, characteristic
7#13069386C211yesmaximal, characteristic, complemented
8#13069349C211yesmaximal, characteristic, complemented
9#13069209C211yesmaximal, characteristic, complemented
10#13069195C211yesmaximal, characteristic, complemented
11#13068866C211yesmaximal, characteristic, complemented
12#13068806C211yesmaximal, characteristic, complemented
13#13068707C211yesmaximal, characteristic, complemented
14C4×#66885C211yesmaximal, characteristic, complemented
15C11×#1923C211yesmaximal, characteristic, complemented
16C2×#66983C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C2×(C22⋊D11)⋊C4—21no—
19C2×C4×D44C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C4×C11×C22⋊C4C2211yescharacteristic
25#10622825C2211yescharacteristic
26#10622825C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35#10622571—21no—
36#10622565—21no—
37#10622558—21no—
38#10622552C2211yescharacteristic
39#10622549C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622283—21no—
46#10622281—21no—
47C11⋊#401—21no—
48#10622265—21no—
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C23×Dic11—21no—
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C22⋊C4D411yescharacteristic
69C2×C11×C22⋊C4D411yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74#66983—22no—
75#66983—22no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—41no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
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×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95(C22⋊D11)⋊C4—44no—
96C4×D44—22no—
97C4×D44—41no—
98C11×C4⋊C8—22no—
99C11×C22⋊C8—22no—
100C11×C22⋊C8—41no—
101C4×C8×C11—41no—
102C11×#95D411yescharacteristic
103C11×#95D411yescharacteristic
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113#66885—22no—
114#66885—22no—
115#66885—22no—
116#66885—41no—
117#66882—22no—
118#66882—22no—
119#66882—41no—
120#66881—22no—
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×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C2×C22⋊D11—24no—
137C2×C22⋊D11—42no—
138C2×C22⋊D11—42no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
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—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11#4112yes—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—22no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C22⋊Dic11—42no—
177C22⋊Dic11—81no—
178(C2×D11)⋊C4—24no—
179(C2×D11)⋊C4—42no—
180(C2×D11)⋊C4—42no—
181(C2×D11)⋊C4—81no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
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—42no—
195C4⋊Dic11#4112yes—
196C4⋊Dic11#4112yes—
197Dic11⋊C4—42no—
198Dic11⋊C4—42no—
199Dic11⋊C4—81no—
200C4×Dic11—42no—
201C4×Dic11—81no—
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#1923D1111yescharacteristic, complemented
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×C11AGL(1,ℤ/8)12yes—
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11H(5,𝔽2)11yescharacteristic
256C2×C4×C112−1+411yescharacteristic
257C22⋊D11—48no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
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×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—
285C8×C11—22no—
286C8×C11—41no—
287C8×C11—41no—
288C8×C11—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⋊C8C2×D1111yescharacteristic
298C2×#102—111no—
299C2×#102—111no—
300C2×#102—111no—
301C2×#102—111no—
302C2×C22⋊C8C2×D1111yescharacteristic
303C2×C22⋊C8C2×D1111yescharacteristic
304C2×C4×C8C2×D1111yescharacteristic
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#380—111no—
319C4×C4⋊C4—111no—
320C4×C4⋊C4—111no—
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#336C2×D1111yescharacteristic
331#336C2×D1111yescharacteristic
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#52911yescharacteristic
359C4×C11#53911yescharacteristic
360C4×C11#55311yescharacteristic
361C4×C11#55611yescharacteristic
362Dic11—42no—
363Dic11—42no—
364Dic11—81no—
365Dic11—81no—
366Dic11—81no—
367Dic11—81no—
368Dic11—81no—
369C22×D4—111no—
370C22×D4—221no—
371C23×C4—221no—
372C23×C4—221no—
373C23×C4C22×D1111yescharacteristic
374C22×C8C22×D1111yescharacteristic
375C22×C8C22×D1111yescharacteristic
376C22×C8C22×D1111yescharacteristic
377C22×C8C22×D1111yescharacteristic
378#121—222no—
379#121—222no—
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—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—441no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4—221no—
398C2×C22⋊C4—221no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C22⋊C4D4411yescharacteristic
403C2×C22⋊C4D4411yescharacteristic
404C2×C42—221no—
405C2×C42—221no—
406C2×C42C22×D1111yescharacteristic
407C2×C42C22×D1111yescharacteristic
408#107—222no—
409#107—222no—
410#107—441no—
411#106—222no—
412C4⋊C8—22no—
413#102—222no—
414#102—222no—
415#102—222no—
416#102—441no—
417C22⋊C8—22no—
418C22⋊C8—41no—
419C4×C8—41no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95D4411yescharacteristic
430#95D4411yescharacteristic
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×D4411yescharacteristic
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—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
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×D4411yescharacteristic
471C22×C4C2×D4411yescharacteristic
472C22×C4C2×D4411yescharacteristic
473C22×C4C2×D4411yescharacteristic
474C22×C4C2×D4411yescharacteristic
475C22×C4C23×D1111yescharacteristic
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8#434112yes—
488C4⋊C4—112no—
489C4⋊C4—112no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—442no—
503C4⋊C4—442no—
504C4⋊C4—442no—
505C4⋊C4—881no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—224no—
509C22⋊C4—442no—
510C22⋊C4—442no—
511C22⋊C4—442no—
512C22⋊C4—881no—
513C22⋊C4—881no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—442no—
519C42—881no—
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#6695712yes—
535C23C22×D4411yescharacteristic
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—222no—
560C2×C4—222no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
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—884no—
581C2×C4—884no—
582C2×C4#6696112yes—
583C2×C4C2×#434111yescharacteristic
584C2×C4#6703711yescharacteristic
585C2×C4#41×D1111yescharacteristic
586C2×C4#41×D1111yescharacteristic
587C2×C4#41×D1111yescharacteristic
588C2×C4#6704311yescharacteristic
589C8—22no—
590C8—41no—
591C8—41no—
592C8—41no—
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—
607C22#1062305511yescharacteristic
608C22#1062308511yescharacteristic
609C22#1062308611yescharacteristic
610C22C2×#6695711yescharacteristic
611C22C2×#6696111yescharacteristic
612C22#1062328311yescharacteristic
613C22#1062328411yescharacteristic
614C4—22no—
615C4—41no—
616C4—41no—
617C4—41no—
618C4—41no—
619C4—442no—
620C4—442no—
621C4—881no—
622C4—881no—
623C4—881no—
624C4—881no—
625C4—881no—
626C4#1062313211yescharacteristic
627C4#1062319111yescharacteristic
628C4#1062321111yescharacteristic
629C4#1062323311yescharacteristic
630C2—42no—
631C2—882no—
632C2#1307265011yescharacteristic
633C2#1307866511yescharacteristic
634C2#1307888011yescharacteristic
635C2#1308050511yescharacteristic
636C2#1308075911yescharacteristic
637C2#1308101911yescharacteristic
638C2#1308120111yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1923C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1923D11
hypocenterC11#27033
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. #13073016C2semidirect
3. #13070031C2semidirect
4. #13070003C2semidirect
7. #13069386C2semidirect
8. #13069349C2semidirect
9. #13069209C2semidirect
10. #13069195C2semidirect
11. #13068866C2semidirect
12. #13068806C2semidirect
13. #13068707C2semidirect
14. C4×#66885C2semidirect
15. C11×#1923C2semidirect
210. #1923D11semidirect
520. C11#27033semidirect

Maximal subgroups

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

subgroupindex
#130730162
#130716302
#130700312
#130700032
#130698062
#130697992
#130693862
#130693492
#130692092
#130691952
#130688662
#130688062
#130687072
C4×#668852
C11×#19232
#2703311