Finite Group Databasebeta

← #14817157

Subgroups — #14817157

Order 2816.

858 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622407C211yesmaximal, characteristic, complemented
2C2×#10622430C211yesmaximal, characteristic
3#13072464C211yesmaximal, characteristic
4Q8×C4⋊Dic11C211yesmaximal, characteristic, complemented
5#13070143C211yesmaximal, characteristic
6#13070087C211yesmaximal, characteristic, complemented
7#13069985C211yesmaximal, characteristic
8#13069943C211yesmaximal, characteristic, complemented
9#13069360C211yesmaximal, characteristic, complemented
10#13069181C211yesmaximal, characteristic, complemented
11#13068971C211yesmaximal, characteristic
12#13068969C211yesmaximal, characteristic
13#13068872C211yesmaximal, characteristic, complemented
14#13068864C211yesmaximal, characteristic
15C11×#1865C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C2×#66950—21no—
21C2×#66946C2211yescharacteristic
22C2×#66941C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66879C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34#10622607—21no—
35#10622601C2211yescharacteristic
36#10622598—21no—
37#10622598—21no—
38#10622598C2211yescharacteristic
39#10622598C2211yescharacteristic
40#10622598C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622552C2211yescharacteristic
45#10622548—21no—
46#10622548C2211yescharacteristic
47C4×C4⋊Dic11—21no—
48C4×C4⋊Dic11C2211yescharacteristic
49#10622430—24no—
50#10622407—24no—
51#10622286—21no—
52#10622281—21no—
53C11×#340C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×Dic22—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76Q8×Dic11—22no—
77Q8×Dic11—22no—
78Q8×Dic11—41no—
79Q8×Dic11—41no—
80C2×#4325—22no—
81C2×#4325—22no—
82C2×#4325Q814yescomplemented
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11D411yescharacteristic
96C2×C4⋊Dic11D411yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×Dic11⋊C4—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11C2311yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107#66950—44no—
108#66946—22no—
109#66946—41no—
110#66941—22no—
111#66941—41no—
112C11×#106—22no—
113C11×#103—22no—
114C11×#103D414yes—
115C11×#95—21no—
116#66899—22no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95D411yescharacteristic
121C11⋊#95D411yescharacteristic
122#66885—22no—
123#66885—41no—
124#66882—22no—
125#66882—41no—
126#66879—22no—
127Dic11⋊C8—22no—
128#66873—22no—
129#66871—22no—
130#66871—22no—
131#26397—111nomaximal, Sylow
132C23×D11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11C2×D412yes—
137C2×Q8×C11C2×Q812yes—
138C2×Q8×C11#4112yes—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44C2×Q812yes—
159C2×C4×D11—42no—
160C2×C4×D11—42no—
161C2×C4×D11—81no—
162C2×Dic22—42no—
163C2×Dic22—42no—
164C2×Dic22—81no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11C2×D412yes—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—42no—
177C11×C4⋊C4C2×D412yes—
178C11×C4⋊C4#4112yes—
179C42×C11—24no—
180C42×C11—21no—
181C42×C11—21no—
182#4325—28no—
183(C2×D11)⋊C4—42no—
184(C2×D11)⋊C4—42no—
185(C2×D11)⋊C4—42no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—81no—
188C4⋊Dic11—22no—
189C4⋊Dic11—22no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—42no—
197C4⋊Dic11—42no—
198C4⋊Dic11—42no—
199C4⋊Dic11—42no—
200C4⋊Dic11—81no—
201C4⋊Dic11—81no—
202C4⋊Dic11—81no—
203Dic11⋊C4—42no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—42no—
209C4×Dic11—42no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8C2×Q812yes—
216C2×#477—111no—
217C2×#440—111no—
218#2452—111no—
219Q8×C4⋊C4—111no—
220#2093—111no—
221#2083—111no—
222#2065—111no—
223#2057—111no—
224#1944—111no—
225#1917—111no—
226#1880—111no—
227#1880—111no—
228#1865D1111yescharacteristic, complemented
229#1863—111no—
230#1862—111no—
231C23×C11C22×D411yescharacteristic
232C22×D11—22no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239Q8×C11—22no—
240Q8×C11—22no—
241Q8×C11—22no—
242Q8×C11C22⋊Q814yescomplemented
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
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×C11AGL(1,ℤ/8)12yes—
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×Q811yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×C4×C112−1+411yescharacteristic
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
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#13712yes—
288D44—22no—
289D44—22no—
290D44—41no—
291D44—41no—
292C4×D11—84no—
293Dic22—84no—
294C8×C11—22no—
295C8×C11—41no—
296C11⋊C8—22no—
297C11⋊C8—41no—
298C22×SD16—111no—
299C2×C4⋊Q8—111no—
300C2×C22⋊Q8—221no—
301C2×C4×Q8—111no—
302C2×C4×Q8—111no—
303C2×C4×Q8C2×D1111yescharacteristic
304C2×C4×D4—111no—
305#477—224no—
306#440—224no—
307C2×#107—111no—
308C2×#107—111no—
309C2×#107—111no—
310C2×#107—111no—
311C2×#106C2×D1111yescharacteristic
312C2×C4⋊C8—111no—
313C2×#103—111no—
314C2×#103C2×D1111yescharacteristic
315C2×#103C2×D1111yescharacteristic
316C2×#102—111no—
317C2×#102—111no—
318C2×#102—111no—
319C2×#97—111no—
320#396—221no—
321#393—221no—
322#390—111no—
323#390—111no—
324#389—111no—
325#389—111no—
326#389—111no—
327#389—221no—
328#389—221no—
329#389C2×D1111yescharacteristic
330#385—221no—
331#384—111no—
332#384—221no—
333C4×C4⋊C4—111no—
334C4×C4⋊C4—221no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340C2×D1111yescharacteristic
339#336—111no—
340#336—111no—
341#336—111no—
342#336C2×D1111yescharacteristic
343C22×C11#52511yescharacteristic
344C22×C11D4211yescharacteristic
345C22×C11D4×Q811yescharacteristic
346C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
347C22×C11C2×#13711yescharacteristic
348C22×C11#57611yescharacteristic
349C22×C11#57811yescharacteristic
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—42no—
353C2×D11—81no—
354C2×D11—81no—
355C2×D11—81no—
356C2×D11—81no—
357C4×C11—22no—
358C4×C11—24no—
359C4×C11—41no—
360C4×C11—42no—
361C4×C11—42no—
362C4×C11—81no—
363C4×C11C2×C22⋊Q811yescharacteristic
364C4×C11#53911yescharacteristic
365C4×C11#54711yescharacteristic
366C4×C11#55411yescharacteristic
367Dic11—22no—
368Dic11—41no—
369Dic11—41no—
370Dic11—41no—
371Dic11—81no—
372Dic11—81no—
373Dic11—81no—
374C22×Q8—221no—
375C22×Q8C22×D1111yescharacteristic
376C22×D4—111no—
377C23×C4—221no—
378C2×SD16—114no—
379C2×SD16—222no—
380C2×SD16—222no—
381C22×C8—111no—
382C22×C8—111no—
383C22×C8C22×D1111yescharacteristic
384C22×C8C22×D1111yescharacteristic
385C4⋊Q8—222no—
386C4⋊Q8—441no—
387C22⋊Q8—444no—
388C4×Q8—22no—
389C4×Q8—22no—
390C4×Q8—222no—
391C4×Q8—222no—
392C4×Q8—441no—
393C4×Q8—441no—
394C4×D4—222no—
395C4×D4—441no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
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⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C4⋊C4C22×D1111yescharacteristic
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C42—21no—
420C2×C42—111no—
421C2×C42—111no—
422C2×C42—221no—
423C2×C42—221no—
424C2×C42C22×D1111yescharacteristic
425#107—222no—
426#107—222no—
427#107—222no—
428#107—441no—
429#106—22no—
430C4⋊C8—222no—
431#103—22no—
432#103—222no—
433#103D4414yes—
434#102—222no—
435#102—222no—
436#102—441no—
437#97—222no—
438#95—21no—
439#95—111no—
440#95—111no—
441#95—221no—
442#95—221no—
443#95—221no—
444C2×C11#244911yescharacteristic
445C2×C11#311211yescharacteristic
446C2×C11#312411yescharacteristic
447C2×C11#327011yescharacteristic
448C2×C11#327411yescharacteristic
449C2×C11#338511yescharacteristic
450C2×C11#338611yescharacteristic
451D11—82no—
452C24—221no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—442no—
457C2×Q8—442no—
458C2×Q8—881no—
459C2×Q8C2×D4412yes—
460C2×Q8#434112yes—
461C2×Q8Q8×D1112yes—
462C2×D4—112no—
463C2×D4—221no—
464C2×D4—221no—
465C2×D4—221no—
466C2×D4—221no—
467C2×D4—221no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—442no—
480C22×C4—442no—
481C22×C4—881no—
482C22×C4D4×D1111yescharacteristic
483C22×C4D4×D1111yescharacteristic
484C22×C4C23×D1111yescharacteristic
485SD16—228no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—112no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8C2×D4412yes—
498C4⋊C4—24no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—42no—
504C4⋊C4—222no—
505C4⋊C4—222no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—442no—
513C4⋊C4—442no—
514C4⋊C4—442no—
515C4⋊C4—442no—
516C4⋊C4—442no—
517C4⋊C4—881no—
518C4⋊C4—881no—
519C4⋊C4—881no—
520C4⋊C4C2×D4412yes—
521C4⋊C4#434112yes—
522C22⋊C4—442no—
523C22⋊C4—442no—
524C22⋊C4—442no—
525C22⋊C4—442no—
526C22⋊C4—881no—
527C42—24no—
528C42—21no—
529C42—21no—
530C42—221no—
531C42—221no—
532C42—221no—
533C42—221no—
534C42—442no—
535C42—442no—
536C11#2639711yescharacteristic, complemented, Sylow
537C23—222no—
538C23—441no—
539C23—441no—
540C23—441no—
541C23—441no—
542C23—441no—
543C23—441no—
544C23C2×D4×D1111yescharacteristic
545Q8—22no—
546Q8—22no—
547Q8—22no—
548Q8—884no—
549Q8#6695014yescomplemented
550D4—222no—
551D4—222no—
552D4—441no—
553D4—441no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—21no—
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—112no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
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—884no—
593C2×C4#6696712yes—
594C2×C4C22×D4411yescharacteristic
595C2×C4C2×#434111yescharacteristic
596C2×C4C2×#434111yescharacteristic
597C2×C4C2×Q8×D1111yescharacteristic
598C2×C4#6704211yescharacteristic
599C2×C4#6704311yescharacteristic
600C8—22no—
601C8—41no—
602C8—222no—
603C8—441no—
604C22—442no—
605C22—442no—
606C22—442no—
607C22—881no—
608C22—881no—
609C22—881no—
610C22—881no—
611C22D4×D4411yescharacteristic
612C22#1062311711yescharacteristic
613C22#1062316311yescharacteristic
614C22C2×#6696711yescharacteristic
615C22#1062330011yescharacteristic
616C22D11×#13711yescharacteristic
617C22#1062331011yescharacteristic
618C4—24no—
619C4—22no—
620C4—41no—
621C4—42no—
622C4—42no—
623C4—81no—
624C4—222no—
625C4—441no—
626C4—441no—
627C4—441no—
628C4—881no—
629C4—881no—
630C4—881no—
631C4C2×#6695011yescharacteristic
632C4#1062308611yescharacteristic
633C4#1062316611yescharacteristic
634C4#1062319611yescharacteristic
635C2—882no—
636C2#1307242311yescharacteristic
637C2#1307873311yescharacteristic
638C2#1307887911yescharacteristic
639C2#1308018811yescharacteristic
640C2#1308023711yescharacteristic
641C2#1308152911yescharacteristic
642C2#1308153611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1865C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1865D11
hypocenterC11#26397
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1865

Complements

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

NH ≅ G/Ntype
1. C2×#10622407C2semidirect
4. Q8×C4⋊Dic11C2semidirect
6. #13070087C2semidirect
8. #13069943C2semidirect
9. #13069360C2semidirect
10. #13069181C2semidirect
13. #13068872C2semidirect
15. C11×#1865C2semidirect
82. C2×#4325Q8semidirect
228. #1865D11semidirect
242. Q8×C11C22⋊Q8semidirect
536. C11#26397semidirect
549. Q8#66950semidirect

Maximal subgroups

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

subgroupindex
C2×#106224072
C2×#106224302
#130724642
Q8×C4⋊Dic112
#130701432
#130700872
#130699852
#130699432
#130693602
#130691812
#130689712
#130689692
#130688722
#130688642
C11×#18652
#2639711