Finite Group Databasebeta

← #14775348

Subgroups — #14775348

Order 2816.

902 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622350C211yesmaximal, characteristic
2#13071632C211yesmaximal, characteristic
3#13071503C211yesmaximal, characteristic, complemented
4#13069357C211yesmaximal, characteristic, complemented
5#13069297C211yesmaximal, characteristic, complemented
6#13069235C211yesmaximal, characteristic, complemented
7#13069207C211yesmaximal, characteristic, complemented
8#13069200C211yesmaximal, characteristic, complemented
9#13069052C211yesmaximal, characteristic
10#13068860C211yesmaximal, characteristic, complemented
11#107×Dic11C211yesmaximal, characteristic, complemented
12#13068440C211yesmaximal, characteristic, complemented
13#13068402C211yesmaximal, characteristic, complemented
14#13068335C211yesmaximal, characteristic, complemented
15C11×#1852C211yesmaximal, characteristic, complemented
16C22×C11×C4⋊C4C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C2×C4×C22⋊D11—21no—
19C2×#66979C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C2×#66946C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C11×#380C2211yescharacteristic
26#10622826—21no—
27C4×C22⋊Dic11C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×#66879C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622603—21no—
35#10622602—21no—
36#10622601C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40#10622586C2211yescharacteristic
41#10622586C2211yescharacteristic
42#10622586C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45#10622558—21no—
46#10622558—21no—
47#10622350C418yescomplemented
48#10622263—21no—
49#10622261—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—41no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11D411yescharacteristic
77C2×C22⋊Dic11D411yescharacteristic
78#66983—22no—
79#66983C2×C414yes—
80C4×C22⋊D11—44no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85#66979—22no—
86#66979C2×C414yescomplemented
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—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C2×#4318—22no—
100C2×#4318—22no—
101C2×#4318—41no—
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104#66946—22no—
105#66946—41no—
106C11×#107—22no—
107C11×#107—41no—
108C11×C22⋊C8C2×C414yescomplemented
109C11×#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95D411yescharacteristic
117C11⋊#95D411yescharacteristic
118#66885C2×C414yescomplemented
119#66885C2×C414yescomplemented
120#66882C2×C414yescomplemented
121#66881C2×C414yescomplemented
122#66879—41no—
123C8×Dic11—22no—
124#66873—22no—
125#66873—41no—
126#22946—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C23×D11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11—81no—
140C22×C4×C11C22×C412yes—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11#4112yes—
143C22×C4×C11C2411yescharacteristic
144C2×C22⋊D11—24no—
145C2×C22⋊D11—42no—
146C2×C22⋊D11—42no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44C22×C412yes—
160C2×C4×D11—42no—
161C2×C4×D11—42no—
162C2×C4×D11—81no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11C22×C412yes—
168C2×C8×C11C22×C412yes—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—42no—
177C11×C4⋊C4#4112yes—
178C11×C22⋊C4—81no—
179C22⋊Dic11—22no—
180C22⋊Dic11—24no—
181C22⋊Dic11—41no—
182(C2×D11)⋊C4—24no—
183(C2×D11)⋊C4—42no—
184(C2×D11)⋊C4—42no—
185(C2×D11)⋊C4—81no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11C22×C412yes—
190C4⋊Dic11C22×C412yes—
191C4⋊Dic11C22×C412yes—
192Dic11⋊C4—42no—
193Dic11⋊C4—81no—
194Dic11⋊C4—81no—
195C4×Dic11—24no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—42no—
201C4×Dic11—42no—
202C4×Dic11—42no—
203#4318—44no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8#4112yes—
210C2×#482—111no—
211#2361—111no—
212#2346—111no—
213#1944—111no—
214#1934—111no—
215#1925—111no—
216#1921—111no—
217#1920—111no—
218#1895—111no—
219#1862—111no—
220#1852D1111yescharacteristic, complemented
221C4×#107—111no—
222#1762—111no—
223#1753—111no—
224#1736—111no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11C4×D412yes—
232C23×C11C22×D411yescharacteristic
233C22×D11—22no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
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—84no—
259C2×C4×C11C4×D412yes—
260C2×C4×C11C23×C411yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C2×C4×C112−1+411yescharacteristic
266C22⋊D11—48no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11AGL(1,ℤ/8)12yes—
288D44—22no—
289D44—22no—
290D44—41no—
291D44—41no—
292C4×D11—84no—
293C8×C11—22no—
294C8×C11—22no—
295C11⋊C8—22no—
296C11⋊C8—41no—
297C22×M16—111no—
298C2×#121—111no—
299C2×C4×D4—111no—
300C2×C4×D4—221no—
301C2×#117—111no—
302C22×C4⋊C4C2×D1111yescharacteristic
303#482—118no—
304C2×#107—111no—
305C2×#107C2×D1111yescharacteristic
306C2×#107C2×D1111yescharacteristic
307C2×#106—111no—
308C2×#102—111no—
309C2×#102—111no—
310C2×#102—111no—
311C2×#102—111no—
312C2×C22⋊C8C2×D1111yescharacteristic
313C2×#97—111no—
314C2×C4×C8—111no—
315#390—111no—
316#389—111no—
317#389—111no—
318#389—111no—
319#388—221no—
320#388—221no—
321#388—221no—
322#386—221no—
323#385—221no—
324#382—221no—
325#380C2×D1111yescharacteristic
326C4×C4⋊C4—111no—
327C4×C4⋊C4—111no—
328C4×C4⋊C4—111no—
329C4×C22⋊C4—111no—
330#376—221no—
331#340—111no—
332#340—111no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340C2×D1111yescharacteristic
338#340C2×D1111yescharacteristic
339#336—111no—
340#336—111no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—22no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11C2×C4×D411yescharacteristic
349C22×C11#54611yescharacteristic
350C22×C11#54711yescharacteristic
351C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
352C22×C11#57511yescharacteristic
353C22×C11#57611yescharacteristic
354C22×C11#57811yescharacteristic
355C2×D11—42no—
356C2×D11—42no—
357C2×D11—42no—
358C2×D11—81no—
359C2×D11—81no—
360C2×D11—81no—
361C2×D11—81no—
362C4×C11—22no—
363C4×C11—42no—
364C4×C11—81no—
365C4×C11—81no—
366C4×C11—81no—
367C4×C11C4×#4111yescharacteristic
368C4×C11#52011yescharacteristic
369C4×C11#55111yescharacteristic
370C4×C11#55211yescharacteristic
371Dic11—22no—
372Dic11—41no—
373Dic11—42no—
374Dic11—42no—
375Dic11—42no—
376Dic11—41no—
377Dic11—41no—
378C22×D4—111no—
379C22×D4—221no—
380C23×C4—21no—
381C23×C4—221no—
382C23×C4C22×D1111yescharacteristic
383C2×M16—222no—
384C2×M16—222no—
385C2×M16—441no—
386C22×C8—111no—
387C22×C8—111no—
388C22×C8C22×D1111yescharacteristic
389C22×C8C22×D1111yescharacteristic
390#121—114no—
391#121—222no—
392C4×D4—222no—
393C4×D4—441no—
394C4×D4—444no—
395#117—114no—
396#117—222no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—41no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C22⋊C4—21no—
411C2×C22⋊C4—111no—
412C2×C22⋊C4—111no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C42—111no—
419C2×C42—111no—
420C2×C42—221no—
421C2×C42—221no—
422C2×C42—221no—
423C2×C42—221no—
424#107—22no—
425#107—41no—
426#107—114no—
427#106—114no—
428#102—114no—
429#102—114no—
430#102—222no—
431#102—441no—
432C22⋊C8C4×D1114yescomplemented
433#97—441no—
434C4×C8—222no—
435#95—21no—
436#95—111no—
437#95—111no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444C2×C11—42no—
445C2×C11#235911yescharacteristic
446C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
447C2×C11#295111yescharacteristic
448C2×C11#332511yescharacteristic
449C2×C11#332711yescharacteristic
450C2×C11#334311yescharacteristic
451C2×C11#334711yescharacteristic
452D11—82no—
453C24—221no—
454C24D4×D1111yescharacteristic
455C2×D4—112no—
456C2×D4—224no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4—221no—
460C2×D4—221no—
461C2×D4—221no—
462C2×D4—442no—
463C2×D4—442no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—81no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—442no—
483C22×C4—442no—
484C22×C4—881no—
485C22×C4C2×C4×D1112yes—
486C22×C4D4×D1111yescharacteristic
487C22×C4#434312yes—
488C22×C4C23×D1111yescharacteristic
489M16—444no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—112no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8C2×C4×D1112yes—
501C2×C8C2×C4×D1112yes—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—42no—
510C4⋊C4—112no—
511C4⋊C4—112no—
512C4⋊C4—112no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—442no—
517C4⋊C4—881no—
518C4⋊C4—881no—
519C4⋊C4#434112yes—
520C22⋊C4—81no—
521C22⋊C4—222no—
522C22⋊C4—224no—
523C22⋊C4—224no—
524C22⋊C4—442no—
525C22⋊C4—442no—
526C22⋊C4—441no—
527C22⋊C4—881no—
528C42—224no—
529C42—221no—
530C42—221no—
531C42—221no—
532C42—221no—
533C42—442no—
534C42—442no—
535C42—442no—
536C11#2294611yescharacteristic, complemented, Sylow
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—222no—
544C23—441no—
545C23—441no—
546C23—441no—
547C23—441no—
548C23—441no—
549C23—441no—
550C23#6694612yes—
551C23C2×D4×D1111yescharacteristic
552D4—222no—
553D4—222no—
554D4—448no—
555D4—441no—
556D4—441no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—84no—
576C2×C4—112no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—222no—
582C2×C4—222no—
583C2×C4—222no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—884no—
598C2×C4#6694612yes—
599C2×C4C22×C4×D1111yescharacteristic
600C2×C4C2×#434111yescharacteristic
601C2×C4#6703711yescharacteristic
602C2×C4C2×#434311yescharacteristic
603C2×C4#41×D1111yescharacteristic
604C2×C4#6704311yescharacteristic
605C8—22no—
606C8—22no—
607C8—222no—
608C8—441no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—442no—
617C22—442no—
618C22—442no—
619C22—881no—
620C22—881no—
621C22—881no—
622C22—881no—
623C22C2×#6694611yescharacteristic
624C22#1062312211yescharacteristic
625C22#1062318611yescharacteristic
626C22#1062328811yescharacteristic
627C22#1062329711yescharacteristic
628C22D11×AGL(1,ℤ/8)11yescharacteristic
629C22#1062330811yescharacteristic
630C4—22no—
631C4—42no—
632C4—81no—
633C4—81no—
634C4—81no—
635C4—222no—
636C4—441no—
637C4—441no—
638C4—441no—
639C4—442no—
640C4—442no—
641C4—442no—
642C4C4×#434111yescharacteristic
643C4#1062307711yescharacteristic
644C4#1062316811yescharacteristic
645C4#1062317311yescharacteristic
646C2—42no—
647C2—882no—
648C2#1307160611yescharacteristic
649C2#1307742311yescharacteristic
650C2#1307749011yescharacteristic
651C2#1308085111yescharacteristic
652C2#1308088811yescharacteristic
653C2#1308105911yescharacteristic
654C2#1308111911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1852C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
cosocleC22×C4×C11C24
hypercenter#1852D11
hypocenterC11#22946
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
3. #13071503C2semidirect
4. #13069357C2semidirect
5. #13069297C2semidirect
6. #13069235C2semidirect
7. #13069207C2semidirect
8. #13069200C2semidirect
10. #13068860C2semidirect
11. #107×Dic11C2semidirect
12. #13068440C2semidirect
13. #13068402C2semidirect
14. #13068335C2semidirect
15. C11×#1852C2semidirect
47. #10622350C4semidirect
86. #66979C2×C4semidirect
108. C11×C22⋊C8C2×C4semidirect
118. #66885C2×C4semidirect
119. #66885C2×C4semidirect
120. #66882C2×C4semidirect
121. #66881C2×C4semidirect
220. #1852D11semidirect
432. C22⋊C8C4×D11semidirect
536. C11#22946semidirect

Maximal subgroups

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

subgroupindex
C2×#106223502
#130716322
#130715032
#130693572
#130692972
#130692352
#130692072
#130692002
#130690522
#130688602
#107×Dic112
#130684402
#130684022
#130683352
C11×#18522
#2294611