Finite Group Databasebeta

← #14775322

Subgroups — #14775322

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#13071630C211yesmaximal, characteristic
3#13071507C211yesmaximal, characteristic, complemented
4#13069354C211yesmaximal, characteristic, complemented
5#13069299C211yesmaximal, characteristic, complemented
6#13069244C211yesmaximal, characteristic, complemented
7#13069202C211yesmaximal, characteristic, complemented
8#13069188C211yesmaximal, characteristic, complemented
9#13069054C211yesmaximal, characteristic
10#13068880C211yesmaximal, characteristic, complemented
11#13068811C211yesmaximal, characteristic, complemented
12C4×#66881C211yesmaximal, characteristic, complemented
13#13068442C211yesmaximal, characteristic, complemented
14#13068336C211yesmaximal, characteristic, complemented
15C11×#1753C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C2×(C22⋊D11)⋊C4—21no—
21C2×C4×D44C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23C2×C11×#97C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C4×C11×C22⋊C4C2211yescharacteristic
26#10622825C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35#10622571—21no—
36#10622558—21no—
37#10622558—21no—
38#10622552C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622350C418yescomplemented
46#10622283—21no—
47#10622281—21no—
48#10622264—21no—
49#10622262—21no—
50C11×#336C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C23×Dic11—21no—
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C2×C11×M16—22no—
66C2×C11×M16—22no—
67C2×C11×M16—41no—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C2×C11×C22⋊C4D411yescharacteristic
73C2×C11×C22⋊C4D411yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78#66983—22no—
79#66983C2×C414yes—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84#66979—22no—
85#66979C2×C414yescomplemented
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—41no—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103(C22⋊D11)⋊C4—44no—
104C4×D44—22no—
105C4×D44—41no—
106C11×C22⋊C8C2×C414yescomplemented
107C11×#97—41no—
108C4×C8×C11—22no—
109C11×#95D411yescharacteristic
110C11×#95D411yescharacteristic
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118#66885—22no—
119#66885—41no—
120#66885C2×C414yescomplemented
121#66885C2×C414yescomplemented
122#66882C2×C414yescomplemented
123#66881—22no—
124#66881—41no—
125#66881C2×C414yescomplemented
126#22944—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×C11C22×C412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11#4112yes—
140C22×C4×C11C2411yescharacteristic
141C2×C22⋊D11—24no—
142C2×C22⋊D11—42no—
143C2×C22⋊D11—42no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—42no—
152C22×Dic11—42no—
153C22×Dic11—81no—
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—
163C11×M16—44no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11C22×C412yes—
174C2×C8×C11C22×C412yes—
175C2×C8×C11#4112yes—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—41no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C22⋊Dic11—24no—
183C22⋊Dic11—81no—
184(C2×D11)⋊C4—24no—
185(C2×D11)⋊C4—42no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—81no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—42no—
199C4⋊Dic11C22×C412yes—
200C4⋊Dic11C22×C412yes—
201C4⋊Dic11C22×C412yes—
202C4⋊Dic11#4112yes—
203Dic11⋊C4—42no—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206C4×Dic11—24no—
207C4×Dic11—42no—
208C4×Dic11—81no—
209C4×Dic11—81no—
210C2×#482—111no—
211#2361—111no—
212#2347—111no—
213#1943—111no—
214#1934—111no—
215#1926—111no—
216#1920—111no—
217#1918—111no—
218#1895—111no—
219#1864—111no—
220#1853—111no—
221C4×#106—111no—
222#1762—111no—
223#1753D1111yescharacteristic, complemented
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—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11C4×D412yes—
258C2×C4×C11AGL(1,ℤ/8)12yes—
259C2×C4×C11C23×C411yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11H(5,𝔽2)11yescharacteristic
264C2×C4×C112−1+411yescharacteristic
265C22⋊D11—48no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—22no—
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—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—84no—
288D44—22no—
289D44—22no—
290D44—41no—
291D44—41no—
292C4×D11—84no—
293C8×C11—22no—
294C8×C11—22no—
295C8×C11—22no—
296C8×C11—41no—
297C22×M16C2×D1111yescharacteristic
298C2×#121—111no—
299C2×C4×D4—111no—
300C2×C4×D4—221no—
301C2×#117—111no—
302C22×C4⋊C4—111no—
303#482—118no—
304C2×#107—111no—
305C2×#106—111no—
306C2×#106—111no—
307C2×#106—111no—
308C2×#102—111no—
309C2×#102—111no—
310C2×#102—111no—
311C2×#102—111no—
312C2×C22⋊C8C2×D1111yescharacteristic
313C2×#97C2×D1111yescharacteristic
314C2×C4×C8C2×D1111yescharacteristic
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#383—221no—
325#380—111no—
326C4×C4⋊C4—111no—
327C4×C4⋊C4—111no—
328C4×C4⋊C4—111no—
329C4×C4⋊C4—221no—
330C4×C22⋊C4C2×D1111yescharacteristic
331#340—111no—
332#340—111no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#336C2×D1111yescharacteristic
340#336C2×D1111yescharacteristic
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#57711yescharacteristic
354C22×C11#57711yescharacteristic
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—22no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11C4×#4111yescharacteristic
368C4×C11#52011yescharacteristic
369C4×C11#55111yescharacteristic
370C4×C11#55211yescharacteristic
371Dic11—42no—
372Dic11—42no—
373Dic11—42no—
374Dic11—42no—
375Dic11—81no—
376Dic11—81no—
377Dic11—81no—
378C22×D4—111no—
379C22×D4—221no—
380C23×C4—221no—
381C23×C4—221no—
382C23×C4C22×D1111yescharacteristic
383C2×M16—22no—
384C2×M16—22no—
385C2×M16—41no—
386C22×C8C22×D1111yescharacteristic
387C22×C8C22×D1111yescharacteristic
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—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—222no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—441no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4D4411yescharacteristic
417C2×C22⋊C4D4411yescharacteristic
418C2×C42—221no—
419C2×C42—221no—
420C2×C42—221no—
421C2×C42—221no—
422C2×C42C22×D1111yescharacteristic
423C2×C42C22×D1111yescharacteristic
424#107—114no—
425#106—114no—
426#106—222no—
427#106—441no—
428#102—114no—
429#102—114no—
430#102—222no—
431#102—441no—
432C22⋊C8C4×D1114yescomplemented
433#97—41no—
434C4×C8—22no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95D4411yescharacteristic
443#95D4411yescharacteristic
444C2×C11—42no—
445C2×C11#235911yescharacteristic
446C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
447C2×C11#295211yescharacteristic
448C2×C11#332411yescharacteristic
449C2×C11#332611yescharacteristic
450C2×C11#334511yescharacteristic
451C2×C11#335011yescharacteristic
452D11—82no—
453C24—221no—
454C24C2×D4411yescharacteristic
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—221no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—442no—
476C22×C4—442no—
477C22×C4—442no—
478C22×C4—442no—
479C22×C4—881no—
480C22×C4—881no—
481C22×C4C2×C4×D1112yes—
482C22×C4C2×D4411yescharacteristic
483C22×C4C2×D4411yescharacteristic
484C22×C4C2×D4411yescharacteristic
485C22×C4C2×D4411yescharacteristic
486C22×C4C2×D4411yescharacteristic
487C22×C4#433912yes—
488C22×C4C23×D1111yescharacteristic
489M16—44no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8C2×C4×D1112yes—
500C2×C8C2×C4×D1112yes—
501C2×C8#434112yes—
502C4⋊C4—112no—
503C4⋊C4—112no—
504C4⋊C4—112no—
505C4⋊C4—112no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—442no—
517C4⋊C4—442no—
518C4⋊C4—442no—
519C4⋊C4—442no—
520C22⋊C4—22no—
521C22⋊C4—41no—
522C22⋊C4—224no—
523C22⋊C4—224no—
524C22⋊C4—442no—
525C22⋊C4—442no—
526C22⋊C4—881no—
527C22⋊C4—881no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—224no—
533C42—442no—
534C42—881no—
535C42—881no—
536C11#2294411yescharacteristic, 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—
550C23C4×D4412yes—
551C23C22×D4411yescharacteristic
552D4—222no—
553D4—222no—
554D4—448no—
555D4—441no—
556D4—441no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—222no—
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—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—884no—
596C2×C4—884no—
597C2×C4C4×D4412yes—
598C2×C4#6696112yes—
599C2×C4C22×C4×D1111yescharacteristic
600C2×C4C2×#433911yescharacteristic
601C2×C4C2×#434111yescharacteristic
602C2×C4#6703711yescharacteristic
603C2×C4#41×D1111yescharacteristic
604C2×C4#6704311yescharacteristic
605C8—22no—
606C8—22no—
607C8—22no—
608C8—41no—
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×C4×D4411yescharacteristic
624C22#1062308511yescharacteristic
625C22#1062308611yescharacteristic
626C22C2×#6696111yescharacteristic
627C22#1062327911yescharacteristic
628C22#1062328211yescharacteristic
629C22#1062328211yescharacteristic
630C4—22no—
631C4—22no—
632C4—41no—
633C4—41no—
634C4—41no—
635C4—442no—
636C4—442no—
637C4—442no—
638C4—442no—
639C4—881no—
640C4—881no—
641C4—881no—
642C4#1062302611yescharacteristic
643C4#1062306211yescharacteristic
644C4C4×#434111yescharacteristic
645C4#1062307711yescharacteristic
646C2—42no—
647C2—882no—
648C2#1307161011yescharacteristic
649C2C4×#6696111yescharacteristic
650C2#1307750111yescharacteristic
651C2#1308084811yescharacteristic
652C2#1308087111yescharacteristic
653C2#1308108811yescharacteristic
654C2#1308116311yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1753C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
cosocleC22×C4×C11C24
hypercenter#1753D11
hypocenterC11#22944
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
3. #13071507C2semidirect
4. #13069354C2semidirect
5. #13069299C2semidirect
6. #13069244C2semidirect
7. #13069202C2semidirect
8. #13069188C2semidirect
10. #13068880C2semidirect
11. #13068811C2semidirect
12. C4×#66881C2semidirect
13. #13068442C2semidirect
14. #13068336C2semidirect
15. C11×#1753C2semidirect
45. #10622350C4semidirect
85. #66979C2×C4semidirect
106. C11×C22⋊C8C2×C4semidirect
120. #66885C2×C4semidirect
121. #66885C2×C4semidirect
122. #66882C2×C4semidirect
125. #66881C2×C4semidirect
223. #1753D11semidirect
432. C22⋊C8C4×D11semidirect
536. C11#22944semidirect

Maximal subgroups

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

subgroupindex
C2×#106223502
#130716302
#130715072
#130693542
#130692992
#130692442
#130692022
#130691882
#130690542
#130688802
#130688112
C4×#668812
#130684422
#130683362
C11×#17532
#2294411