Finite Group Databasebeta

← #14775658

Subgroups — #14775658

Order 2816.

886 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622374C211yesmaximal, characteristic
2#13071703C211yesmaximal, characteristic, complemented
3D4×Dic11⋊C4C211yesmaximal, characteristic
4#13069575C211yesmaximal, characteristic, complemented
5#13069373C211yesmaximal, characteristic, complemented
6#13069359C211yesmaximal, characteristic, complemented
7#13069358C211yesmaximal, characteristic, complemented
8#13069201C211yesmaximal, characteristic, complemented
9#13069200C211yesmaximal, characteristic, complemented
10#13068865C211yesmaximal, characteristic
11#13068863C211yesmaximal, characteristic
12#13068484C211yesmaximal, characteristic, complemented
13#13068443C211yesmaximal, characteristic
14#102×Dic11C211yesmaximal, characteristic
15C11×#1762C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C22×Dic11⋊C4—21no—
20C2×#66941C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#97C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27#10622823—21no—
28C2×#66882C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33#10622598C2211yescharacteristic
34#10622589C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622586C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622559—21no—
41#10622555—21no—
42C4×Dic11⋊C4—21no—
43C4×Dic11⋊C4C2211yescharacteristic
44#10622542—21no—
45#10622541C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622374C418yescomplemented
48#10622260—21no—
49#10622259—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×Dic11—21no—
63C23×Dic11—21no—
64C22×Dic22—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C4×D4×C11—22no—
68C4×D4×C11—41no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C42×C11—21no—
74C2×C42×C11C2311yescharacteristic
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77D4×Dic11—22no—
78D4×Dic11—22no—
79D4×Dic11—41no—
80D4×Dic11C2×C414yes—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—44no—
93C2×Dic11⋊C4D411yescharacteristic
94C2×Dic11⋊C4D411yescharacteristic
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66941—22no—
102#66941C2×C414yescomplemented
103C11×#102C2×C414yes—
104C11×#102Q814yescomplemented
105C11×#97—41no—
106C11×#95—21no—
107#66896—22no—
108#66896C2×C414yes—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95D411yescharacteristic
116C11⋊#95D411yescharacteristic
117#66882—41no—
118#66881C2×C414yescomplemented
119#66879—41no—
120Dic11⋊C8C2×C414yescomplemented
121C8×Dic11—22no—
122#66872C2×C414yescomplemented
123#66871—41no—
124#22969—111nomaximal, Sylow
125C24×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11C22×C412yes—
130C2×D4×C11C2×Q812yes—
131C2×D4×C11#4112yes—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
137C22×C4×C11—81no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C22×Dic11—24no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—42no—
147C22×Dic11—42no—
148C22×Dic11—42no—
149C22×Dic11—42no—
150C22×Dic11—81no—
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C2×Dic22—24no—
156C2×Dic22—81no—
157C2×Dic22—81no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11C22×C412yes—
163C2×C8×C11C2×Q812yes—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4C22×C412yes—
169C11×C4⋊C4C2×Q812yes—
170C11×C22⋊C4—42no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—81no—
174C22⋊Dic11—24no—
175C22⋊Dic11—42no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—81no—
183C4⋊Dic11C22×C412yes—
184C4⋊Dic11C22×C412yes—
185Dic11⋊C4—24no—
186Dic11⋊C4—22no—
187Dic11⋊C4—22no—
188Dic11⋊C4—42no—
189Dic11⋊C4—42no—
190Dic11⋊C4—42no—
191Dic11⋊C4—81no—
192Dic11⋊C4—81no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—42no—
196C4×Dic11—81no—
197C4×Dic11C22×C412yes—
198C4×Dic11#4112yes—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8C22×C412yes—
205C2×#476—111no—
206#2369—111no—
207D4×C4⋊C4—111no—
208#1990—111no—
209#1947—111no—
210#1944—111no—
211#1944—111no—
212#1920—111no—
213#1920—111no—
214#1862—111no—
215#1862—111no—
216#1770—111no—
217#1762—111no—
218#1762D1111yescharacteristic
219C4×#102—111no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11C22×D411yescharacteristic
228D4×C11—22no—
229D4×C11—22no—
230D4×C11—22no—
231D4×C11C4×Q814yes—
232C2×C4×C11—22no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—84no—
248C2×C4×C11C23×C411yescharacteristic
249C2×C4×C11C22×Q811yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11H(5,𝔽2)11yescharacteristic
253C2×C4×C112−1+411yescharacteristic
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—48no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—84no—
276C2×Dic11C4×D412yes—
277C2×Dic11C4×D412yes—
278C2×Dic11AGL(1,ℤ/8)12yes—
279C2×Dic11#13712yes—
280Dic22—84no—
281C8×C11—22no—
282C8×C11—22no—
283C11⋊C8—22no—
284C11⋊C8—41no—
285C2×C4⋊Q8—111no—
286C2×C4×D4—111no—
287C2×C4×D4—111no—
288C2×C4×D4C2×D1111yescharacteristic
289C22×C4⋊C4—221no—
290#476—118no—
291C2×#107—111no—
292C2×#107—111no—
293C2×#106—111no—
294C2×#106—111no—
295C2×C4⋊C8—111no—
296C2×#102—111no—
297C2×#102—111no—
298C2×#102C2×D1111yescharacteristic
299C2×#102C2×D1111yescharacteristic
300C2×#97—111no—
301C2×#97C2×D1111yescharacteristic
302C2×C4×C8—111no—
303#391—221no—
304#391—221no—
305#389—111no—
306#389—111no—
307#389—111no—
308#389—111no—
309#389—221no—
310#385—221no—
311#385—221no—
312#384—111no—
313#380—221no—
314C4×C4⋊C4—111no—
315C4×C4⋊C4—111no—
316C4×C4⋊C4—111no—
317C4×C4⋊C4—221no—
318C4×C4⋊C4C2×D1111yescharacteristic
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340C2×D1111yescharacteristic
326#340C2×D1111yescharacteristic
327#336—111no—
328#336—111no—
329C22×C11—24no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11C2×C4×D411yescharacteristic
337C22×C11#54611yescharacteristic
338C22×C11D4×Q811yescharacteristic
339C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
340C22×C11C2×#13711yescharacteristic
341C22×C11#57611yescharacteristic
342C22×C11#57711yescharacteristic
343C4×C11—41no—
344C4×C11—42no—
345C4×C11—42no—
346C4×C11—41no—
347C4×C11—81no—
348C4×C11C2×C4×Q811yescharacteristic
349C4×C11#52011yescharacteristic
350C4×C11#55211yescharacteristic
351C4×C11#55411yescharacteristic
352Dic11—22no—
353Dic11—41no—
354Dic11—42no—
355Dic11—42no—
356Dic11—41no—
357Dic11—81no—
358Dic11—81no—
359Dic11#44014yes—
360C22×Q8—221no—
361C22×D4C22×D1111yescharacteristic
362C23×C4—21no—
363C23×C4—221no—
364C23×C4—221no—
365C22×C8—111no—
366C22×C8—111no—
367C22×C8C22×D1111yescharacteristic
368C22×C8C22×D1111yescharacteristic
369C4⋊Q8—114no—
370C4⋊Q8—222no—
371C4×D4—22no—
372C4×D4—41no—
373C4×D4—114no—
374C4×D4—222no—
375C4×D4—222no—
376C4×D4—441no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—444no—
391C2×C4⋊C4C22×D1111yescharacteristic
392C2×C4⋊C4C22×D1111yescharacteristic
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C22⋊C4—21no—
395C2×C22⋊C4—221no—
396C2×C22⋊C4—221no—
397C2×C42—21no—
398C2×C42—111no—
399C2×C42—111no—
400C2×C42—221no—
401C2×C42—221no—
402C2×C42C22×D1111yescharacteristic
403#107—441no—
404#107—441no—
405#106—114no—
406#106—114no—
407C4⋊C8—114no—
408#102—114no—
409#102—222no—
410#102Dic2214yescomplemented
411#102C4×D1114yes—
412#97—41no—
413#97—441no—
414C4×C8—222no—
415#95—21no—
416#95—111no—
417#95—111no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424C2×C11—44no—
425C2×C11#236011yescharacteristic
426C2×C11C2×#44011yescharacteristic
427C2×C11#294611yescharacteristic
428C2×C11#332511yescharacteristic
429C2×C11#333111yescharacteristic
430C2×C11#338411yescharacteristic
431C2×C11#338511yescharacteristic
432C24—21no—
433C2×Q8—224no—
434C2×Q8—881no—
435C2×Q8—881no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4C2×Dic2212yes—
440C2×D4C2×C4×D1112yes—
441C2×D4#433912yes—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—81no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4—224no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—442no—
458C22×C4—442no—
459C22×C4—442no—
460C22×C4—442no—
461C22×C4—881no—
462C22×C4D4×D1111yescharacteristic
463C22×C4D4×D1111yescharacteristic
464C22×C4C23×D1111yescharacteristic
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—112no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8C2×Dic2212yes—
476C2×C8C2×C4×D1112yes—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—112no—
482C4⋊C4—112no—
483C4⋊C4—222no—
484C4⋊C4—222no—
485C4⋊C4—224no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—442no—
493C4⋊C4—442no—
494C4⋊C4—442no—
495C4⋊C4—881no—
496C4⋊C4—881no—
497C4⋊C4—881no—
498C4⋊C4C2×Dic2212yes—
499C4⋊C4C2×C4×D1112yes—
500C22⋊C4—42no—
501C22⋊C4—224no—
502C22⋊C4—442no—
503C42—21no—
504C42—21no—
505C42—81no—
506C42—112no—
507C42—112no—
508C42—221no—
509C42—221no—
510C42—442no—
511C42—881no—
512C11#2296911yescharacteristic, complemented, Sylow
513C23—22no—
514C23—22no—
515C23—22no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23C2×D4×D1111yescharacteristic
521Q8—884no—
522D4—22no—
523D4—22no—
524D4—22no—
525D4C4×Dic2214yes—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—84no—
542C2×C4—112no—
543C2×C4—112no—
544C2×C4—112no—
545C2×C4—112no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—222no—
555C2×C4—222no—
556C2×C4—448no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—884no—
568C2×C4C22×Dic2211yescharacteristic
569C2×C4C22×C4×D1111yescharacteristic
570C2×C4C2×#433911yescharacteristic
571C2×C4#6703711yescharacteristic
572C2×C4#41×D1111yescharacteristic
573C2×C4#6704311yescharacteristic
574C8—22no—
575C8—22no—
576C8—222no—
577C8—441no—
578C22—24no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22#1062302111yescharacteristic
586C22D4×Dic2211yescharacteristic
587C22C4×D4×D1111yescharacteristic
588C22D11×AGL(1,ℤ/8)11yescharacteristic
589C22#1062330511yescharacteristic
590C22#1062330611yescharacteristic
591C22D11×#13711yescharacteristic
592C4—41no—
593C4—41no—
594C4—42no—
595C4—42no—
596C4—81no—
597C4—114no—
598C4—222no—
599C4—441no—
600C4—441no—
601C4—442no—
602C4—442no—
603C4—881no—
604C4—881no—
605C4C2×C4×Dic2211yescharacteristic
606C4#1062306211yescharacteristic
607C4#1062307011yescharacteristic
608C4#1062307711yescharacteristic
609C2—44no—
610C2#1307162211yescharacteristic
611C2D11×#44011yescharacteristic
612C2#1307744511yescharacteristic
613C2#1308085411yescharacteristic
614C2#1308092811yescharacteristic
615C2#1308151611yescharacteristic
616C2#1308152711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1762C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#1762D11
hypocenterC11#22969
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. #13071703C2semidirect
4. #13069575C2semidirect
5. #13069373C2semidirect
6. #13069359C2semidirect
7. #13069358C2semidirect
8. #13069201C2semidirect
9. #13069200C2semidirect
12. #13068484C2semidirect
47. #10622374C4semidirect
102. #66941C2×C4semidirect
104. C11×#102Q8semidirect
118. #66881C2×C4semidirect
120. Dic11⋊C8C2×C4semidirect
122. #66872C2×C4semidirect
410. #102Dic22semidirect
512. C11#22969semidirect

Maximal subgroups

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

subgroupindex
C2×#106223742
#130717032
D4×Dic11⋊C42
#130695752
#130693732
#130693592
#130693582
#130692012
#130692002
#130688652
#130688632
#130684842
#130684432
#102×Dic112
C11×#17622
#2296911