Finite Group Databasebeta

← #14826589

Subgroups — #14826589

Order 2816.

742 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073049C211yesmaximal, characteristic, complemented
2#13070019C211yesmaximal, characteristic, complemented
3#13070004C211yesmaximal, characteristic, complemented
4#13069795C211yesmaximal, characteristic
5#13069795C211yesmaximal, characteristic
6#13069374C211yesmaximal, characteristic, complemented
7#13069346C211yesmaximal, characteristic, complemented
8#13069224C211yesmaximal, characteristic, complemented
9#13069205C211yesmaximal, characteristic, complemented
10#13069194C211yesmaximal, characteristic, complemented
11#13068877C211yesmaximal, characteristic, complemented
12#13068815C211yesmaximal, characteristic, complemented
13#13068711C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic, complemented
15C11×#2363C211yesmaximal, characteristic
16C2×C11×#121C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C11×#390—21no—
20C11×#390C2211yescharacteristic
21C11×#389C2211yescharacteristic
22C11×#388—21no—
23C11×#386—21no—
24C4×C11×C4⋊C4C2211yescharacteristic
25C4×C11×C22⋊C4—21no—
26C4×C11×C22⋊C4C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31#10622825C2211yescharacteristic
32#10622825C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×#66872C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39#10622564—21no—
40#10622561—21no—
41#10622548C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622273—21no—
48#10622268—21no—
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C11×#121—22no—
64C11×#121—22no—
65C4×D4×C11—22no—
66C4×D4×C11—41no—
67C11×#117—22no—
68C11×#117—41no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4D411yescharacteristic
79C2×C11×C22⋊C4D411yescharacteristic
80C2×C42×C11—21no—
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
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×#95—21no—
101C11×#95D411yescharacteristic
102C11×#95D411yescharacteristic
103#66896—22no—
104#66896—22no—
105#66896—22no—
106#66896—41no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C22⋊(C11⋊C8)—22no—
113C22⋊(C11⋊C8)—41no—
114#66872—22no—
115#66871—22no—
116#66871—22no—
117#66871—41no—
118C4⋊(C11⋊C8)—22no—
119C4×C11⋊C8—41no—
120#27041—111nomaximal, Sylow
121C24×C11—21no—
122C24×C11C2×D411yescharacteristic
123C2×D4×C11—24no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—81no—
130C2×D4×C11—81no—
131C2×D4×C11#4112yes—
132C22×C4×C11—21no—
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—42no—
142C22×C4×C11—42no—
143C22×C4×C11—81no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—81no—
159C11×C4⋊C4#4112yes—
160C11×C4⋊C4#4112yes—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—42no—
165C11×C22⋊C4—42no—
166C11×C22⋊C4—42no—
167C11×C22⋊C4—81no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—42no—
173C42×C11—81no—
174C22⋊Dic11—81no—
175C22⋊Dic11—81no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—81no—
185C4⋊Dic11—81no—
186Dic11⋊C4—42no—
187Dic11⋊C4—81no—
188C4×Dic11—81no—
189C2×C11⋊C8—21no—
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#4112yes—
201#2497—111no—
202#2363D1111yescharacteristic
203#2071—111no—
204#2067—111no—
205#2033—111no—
206#2033—111no—
207#1947—111no—
208#1942—111no—
209#1923—111no—
210#1921—111no—
211#1919—111no—
212#1864—111no—
213#1854—111no—
214#1825—111no—
215C4×#102—111no—
216C23×C11—22no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11C22×D411yescharacteristic
231D4×C11—22no—
232D4×C11—22no—
233D4×C11—41no—
234D4×C11—41no—
235D4×C11—84no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
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—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×C11—84no—
263C2×C4×C11#13512yes—
264C2×C4×C11#13712yes—
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11H(5,𝔽2)11yescharacteristic
270C2×C4×C112−1+411yescharacteristic
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—41no—
283C11⋊C8—22no—
284C11⋊C8—41no—
285C11⋊C8—41no—
286C11⋊C8—41no—
287C2×#121C2×D1111yescharacteristic
288C2×C4×D4C2×D1111yescharacteristic
289C2×#117C2×D1111yescharacteristic
290C2×#107—111no—
291C2×#107—111no—
292C2×#107—111no—
293C2×#106—111no—
294C2×C4⋊C8—111no—
295C2×#102—111no—
296C2×#102—111no—
297C2×#102—111no—
298C2×#102—111no—
299C2×C22⋊C8—111no—
300C2×C22⋊C8—111no—
301C2×C4×C8—111no—
302#400—221no—
303#396—221no—
304#390—21no—
305#390C2×D1111yescharacteristic
306#389—111no—
307#389—111no—
308#389C2×D1111yescharacteristic
309#388—21no—
310#388—221no—
311#387—221no—
312#386—21no—
313#384—111no—
314#380—111no—
315#380—111no—
316C4×C4⋊C4—111no—
317C4×C4⋊C4C2×D1111yescharacteristic
318C4×C22⋊C4—21no—
319C4×C22⋊C4C2×D1111yescharacteristic
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#336—111no—
329#336—111no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—42no—
334C22×C11—41no—
335C22×C11—42no—
336C22×C11—41no—
337C22×C11—42no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11#52511yescharacteristic
345C22×C11#54611yescharacteristic
346C22×C11#54711yescharacteristic
347C22×C11C2×#13511yescharacteristic
348C22×C11C2×#13711yescharacteristic
349C22×C11#57611yescharacteristic
350C22×C11#57611yescharacteristic
351C4×C11—22no—
352C4×C11—22no—
353C4×C11—41no—
354C4×C11—42no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11—42no—
358C4×C11—81no—
359C4×C11#52911yescharacteristic
360C4×C11#53911yescharacteristic
361C4×C11#55311yescharacteristic
362C4×C11#55611yescharacteristic
363Dic11—81no—
364Dic11—81no—
365Dic11—81no—
366Dic11—81no—
367C22×D4—21no—
368C22×D4C22×D1111yescharacteristic
369C23×C4—21no—
370C23×C4C22×D1111yescharacteristic
371C22×C8—111no—
372C22×C8—111no—
373C22×C8—111no—
374C22×C8—111no—
375#121—22no—
376#121—22no—
377C4×D4—22no—
378C4×D4—41no—
379#117—22no—
380#117—41no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C4⋊C4C22×D1111yescharacteristic
392C2×C4⋊C4C22×D1111yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—221no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4C22⋊D1111yescharacteristic
401C2×C22⋊C4C22⋊D1111yescharacteristic
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—221no—
405C2×C42C22×D1111yescharacteristic
406C2×C42C22×D1111yescharacteristic
407#107—222no—
408#107—222no—
409#107—441no—
410#106—222no—
411C4⋊C8—222no—
412#102—222no—
413#102—222no—
414#102—222no—
415#102—441no—
416C22⋊C8—222no—
417C22⋊C8—441no—
418C4×C8—441no—
419#95—21no—
420#95—21no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95C22⋊D1111yescharacteristic
427#95C22⋊D1111yescharacteristic
428C2×C11—81no—
429C2×C11—82no—
430C2×C11#246611yescharacteristic
431C2×C11#310711yescharacteristic
432C2×C11#312211yescharacteristic
433C2×C11#330511yescharacteristic
434C2×C11#331411yescharacteristic
435C2×C11#333911yescharacteristic
436C2×C11#335711yescharacteristic
437C24—21no—
438C24C2×C22⋊D1111yescharacteristic
439C2×D4—24no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—81no—
446C2×D4—81no—
447C2×D4#433912yes—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—81no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4C2×C22⋊D1111yescharacteristic
465C22×C4C2×C22⋊D1111yescharacteristic
466C22×C4C2×C22⋊D1111yescharacteristic
467C22×C4C2×C22⋊D1111yescharacteristic
468C22×C4C2×C22⋊D1111yescharacteristic
469C22×C4C23×D1111yescharacteristic
470C2×C8—112no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—81no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—442no—
496C4⋊C4—881no—
497C4⋊C4—881no—
498C4⋊C4—881no—
499C4⋊C4#433912yes—
500C4⋊C4#434112yes—
501C22⋊C4—24no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—42no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—81no—
508C22⋊C4—881no—
509C22⋊C4—881no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—42no—
515C42—81no—
516C42—881no—
517C11#2704111yescharacteristic, complemented, Sylow
518C23—22no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23C22×C22⋊D1111yescharacteristic
533D4—22no—
534D4—22no—
535D4—41no—
536D4—41no—
537D4—84no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
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—84no—
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#6700312yes—
578C2×C4#6700412yes—
579C2×C4C2×#433911yescharacteristic
580C2×C4C2×#433911yescharacteristic
581C2×C4C2×#434111yescharacteristic
582C2×C4#6703711yescharacteristic
583C2×C4#41×D1111yescharacteristic
584C2×C4#6704311yescharacteristic
585C8—222no—
586C8—441no—
587C8—441no—
588C8—441no—
589C22—41no—
590C22—42no—
591C22—41no—
592C22—42no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—42no—
597C22—41no—
598C22—41no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22#1062332211yescharacteristic
604C22#1062333711yescharacteristic
605C22C2×#6700311yescharacteristic
606C22C2×#6700411yescharacteristic
607C22#1062335511yescharacteristic
608C22#1062336611yescharacteristic
609C22#1062336611yescharacteristic
610C4—22no—
611C4—22no—
612C4—41no—
613C4—42no—
614C4—42no—
615C4—41no—
616C4—41no—
617C4—81no—
618C4—881no—
619C4—881no—
620C4—881no—
621C4—881no—
622C4#1062306911yescharacteristic
623C4#1062307311yescharacteristic
624C4#1062308911yescharacteristic
625C4#1062309511yescharacteristic
626C2—81no—
627C2—82no—
628C2#1307264611yescharacteristic
629C2#1307868711yescharacteristic
630C2#1307885911yescharacteristic
631C2#1308056611yescharacteristic
632C2#1308069711yescharacteristic
633C2#1308101211yescharacteristic
634C2#1308123611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2363C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#2363D11
hypocenterC11#27041
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2363

Complements

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

NH ≅ G/Ntype
1. #13073049C2semidirect
2. #13070019C2semidirect
3. #13070004C2semidirect
6. #13069374C2semidirect
7. #13069346C2semidirect
8. #13069224C2semidirect
9. #13069205C2semidirect
10. #13069194C2semidirect
11. #13068877C2semidirect
12. #13068815C2semidirect
13. #13068711C2semidirect
14. C4×#66896C2semidirect
517. C11#27041semidirect

Maximal subgroups

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

subgroupindex
#130730492
#130700192
#130700042
#130697952
#130693742
#130693462
#130692242
#130692052
#130691942
#130688772
#130688152
#130687112
C4×#668962
C11×#23632
#2704111