Finite Group Databasebeta

← #14775718

Subgroups — #14775718

Order 2816.

870 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622622C211yesmaximal, characteristic
2#13071712C211yesmaximal, characteristic, complemented
3D4×C4⋊Dic11C211yesmaximal, characteristic
4#13069585C211yesmaximal, characteristic, complemented
5#13069374C211yesmaximal, characteristic, complemented
6#13069358C211yesmaximal, characteristic, complemented
7#13069348C211yesmaximal, characteristic, complemented
8#13069211C211yesmaximal, characteristic, complemented
9#13069197C211yesmaximal, characteristic, complemented
10#13068861C211yesmaximal, characteristic
11#13068861C211yesmaximal, characteristic
12#13068488C211yesmaximal, characteristic, complemented
13#13068443C211yesmaximal, characteristic
14#102×Dic11C211yesmaximal, characteristic
15C11×#1762C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C22×C4⋊Dic11—21no—
20C2×#66923C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#97C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27#10622825—21no—
28C2×#66879C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30#10622622C418yescomplemented
31#10622598C2211yescharacteristic
32#10622598C2211yescharacteristic
33C4⋊C4×Dic11C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35#10622586C2211yescharacteristic
36#10622586C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622563—21no—
42#10622563—21no—
43#10622548C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45#10622546—21no—
46C4×Dic11⋊C4—21no—
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48#10622268—21no—
49#10622260—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×Dic11—21no—
63C23×Dic11—21no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C4×D4×C11—22no—
67C4×D4×C11C2×C414yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C42×C11—21no—
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76D4×Dic11—22no—
77D4×Dic11—22no—
78D4×Dic11—41no—
79D4×Dic11—41no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—44no—
85C2×C4⋊Dic11D411yescharacteristic
86C2×C4⋊Dic11D411yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66923—22no—
102#66923C2×C414yescomplemented
103C11×#102—22no—
104C11×#102Q814yes—
105C11×#97—22no—
106C11×#95—21no—
107#66896C2×C414yes—
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#66879—41no—
118C8×Dic11—41no—
119#66872C2×C414yescomplemented
120#66871—41no—
121#66871—41no—
122#66871C2×C414yescomplemented
123C4⋊(C11⋊C8)C2×C414yescomplemented
124#22974—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—24no—
135C22×C4×C11—21no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—42no—
146C22×Dic11—42no—
147C22×Dic11—42no—
148C22×Dic11—42no—
149C22×Dic11—81no—
150C22×Dic11—81no—
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11C2×Q812yes—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4C22×C412yes—
166C11×C4⋊C4C2×Q812yes—
167C11×C22⋊C4—24no—
168C42×C11—81no—
169C42×C11C22×C412yes—
170C42×C11#4112yes—
171C22⋊Dic11—42no—
172C22⋊Dic11—42no—
173C4⋊Dic11—22no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—41no—
181C4⋊Dic11—42no—
182C4⋊Dic11—42no—
183C4⋊Dic11—42no—
184C4⋊Dic11—81no—
185C4⋊Dic11C22×C412yes—
186C4⋊Dic11C22×C412yes—
187Dic11⋊C4—24no—
188Dic11⋊C4—24no—
189Dic11⋊C4—42no—
190Dic11⋊C4—81no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—42no—
196C4×Dic11—81no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8C22×C412yes—
202C2×C11⋊C8C22×C412yes—
203C2×#478—111no—
204#2370—111no—
205D4×C4⋊C4—111no—
206#1992—111no—
207#1947—111no—
208#1944—111no—
209#1942—111no—
210#1921—111no—
211#1919—111no—
212#1862—111no—
213#1862—111no—
214#1771—111no—
215#1762—111no—
216#1762D1111yescharacteristic
217C4×#102—111no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11C22×D411yescharacteristic
226D4×C11—22no—
227D4×C11—22no—
228D4×C11—22no—
229D4×C11C4×Q814yes—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—48no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11C4×D412yes—
245C2×C4×C11C4×D412yes—
246C2×C4×C11C23×C411yescharacteristic
247C2×C4×C11C22×Q811yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11H(5,𝔽2)11yescharacteristic
251C2×C4×C112−1+411yescharacteristic
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—84no—
276C2×Dic11—84no—
277C2×Dic11AGL(1,ℤ/8)12yes—
278C8×C11—22no—
279C8×C11—41no—
280C11⋊C8—22no—
281C11⋊C8—22no—
282C2×#125—111no—
283C2×C4×D4—111no—
284C2×C4×D4—111no—
285C2×C4×D4C2×D1111yescharacteristic
286C22×C4⋊C4—221no—
287#478—118no—
288C2×#107—111no—
289C2×#107—111no—
290C2×#107—111no—
291C2×#106—111no—
292C2×C4⋊C8—111no—
293C2×#102—111no—
294C2×#102—111no—
295C2×#102C2×D1111yescharacteristic
296C2×#102C2×D1111yescharacteristic
297C2×#97—111no—
298C2×#97C2×D1111yescharacteristic
299C2×C4×C8—111no—
300#389—111no—
301#389—111no—
302#389—111no—
303#389—111no—
304#389—221no—
305#387—221no—
306#387—221no—
307#385—221no—
308#385—221no—
309#384—111no—
310#380—221no—
311C4×C4⋊C4—111no—
312C4×C4⋊C4—111no—
313C4×C4⋊C4—111no—
314C4×C4⋊C4—221no—
315C4×C4⋊C4C2×D1111yescharacteristic
316#340—111no—
317#340—111no—
318#340—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340C2×D1111yescharacteristic
323#340C2×D1111yescharacteristic
324#336—111no—
325#336—111no—
326C22×C11—24no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11C2×C4×D411yescharacteristic
334C22×C11#54611yescharacteristic
335C22×C11D4×Q811yescharacteristic
336C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
337C22×C11#57511yescharacteristic
338C22×C11#57611yescharacteristic
339C22×C11#57811yescharacteristic
340C4×C11—22no—
341C4×C11—22no—
342C4×C11—42no—
343C4×C11—42no—
344C4×C11—81no—
345C4×C11C2×C4×Q811yescharacteristic
346C4×C11#52011yescharacteristic
347C4×C11#55211yescharacteristic
348C4×C11#55411yescharacteristic
349Dic11—22no—
350Dic11—42no—
351Dic11—42no—
352Dic11—41no—
353Dic11—41no—
354Dic11—41no—
355Dic11—81no—
356Dic11—81no—
357C22×D4C22×D1111yescharacteristic
358C23×C4—21no—
359C23×C4—221no—
360C23×C4—221no—
361C22×C8—111no—
362C22×C8—111no—
363C22×C8C22×D1111yescharacteristic
364C22×C8C22×D1111yescharacteristic
365#125—114no—
366#125—222no—
367C4×D4—22no—
368C4×D4—222no—
369C4×D4—222no—
370C4×D4—441no—
371C4×D4—441no—
372C4×D4C4×D1114yes—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—444no—
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C42—21no—
395C2×C42—111no—
396C2×C42—111no—
397C2×C42—221no—
398C2×C42—221no—
399C2×C42C22×D1111yescharacteristic
400#107—114no—
401#107—441no—
402#107—441no—
403#106—114no—
404C4⋊C8—114no—
405#102—22no—
406#102—114no—
407#102—114no—
408#102Dic2214yes—
409#97—22no—
410#97—441no—
411C4×C8—441no—
412#95—21no—
413#95—111no—
414#95—111no—
415#95—221no—
416#95—221no—
417#95—221no—
418#95—221no—
419#95—221no—
420#95—221no—
421C2×C11—44no—
422C2×C11#236011yescharacteristic
423C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
424C2×C11#295111yescharacteristic
425C2×C11#331511yescharacteristic
426C2×C11#331811yescharacteristic
427C2×C11#338611yescharacteristic
428C2×C11#338911yescharacteristic
429C24—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4C2×Dic2212yes—
434C2×D4C2×C4×D1112yes—
435C2×D4#433912yes—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—24no—
439C22×C4—21no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—111no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—442no—
451C22×C4—442no—
452C22×C4—442no—
453C22×C4—442no—
454C22×C4—881no—
455C22×C4—881no—
456C22×C4D4×D1111yescharacteristic
457C22×C4D4×D1111yescharacteristic
458C22×C4C23×D1111yescharacteristic
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—112no—
465C2×C8—112no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8C2×Dic2212yes—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—112no—
476C4⋊C4—112no—
477C4⋊C4—222no—
478C4⋊C4—224no—
479C4⋊C4—224no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—441no—
487C4⋊C4—442no—
488C4⋊C4—442no—
489C4⋊C4—442no—
490C4⋊C4—442no—
491C4⋊C4—881no—
492C4⋊C4—881no—
493C4⋊C4C2×Dic2212yes—
494C4⋊C4C2×C4×D1112yes—
495C22⋊C4—24no—
496C22⋊C4—442no—
497C22⋊C4—442no—
498C42—81no—
499C42—221no—
500C42—221no—
501C42—221no—
502C42—221no—
503C42—442no—
504C42—881no—
505C42C2×C4×D1112yes—
506C42#434112yes—
507C11#2297411yescharacteristic, complemented, Sylow
508C23—22no—
509C23—22no—
510C23—22no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23C2×D4×D1111yescharacteristic
516D4—22no—
517D4—22no—
518D4—22no—
519D4C4×Dic2214yes—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—48no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—112no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—222no—
538C2×C4—222no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—884no—
559C2×C4—884no—
560C2×C4(C22⋊D11)⋊C412yes—
561C2×C4(C22⋊D11)⋊C412yes—
562C2×C4C22×Dic2211yescharacteristic
563C2×C4C22×C4×D1111yescharacteristic
564C2×C4C2×#433911yescharacteristic
565C2×C4C2×#434111yescharacteristic
566C2×C4#6704211yescharacteristic
567C2×C4#6704311yescharacteristic
568C8—22no—
569C8—41no—
570C8—222no—
571C8—222no—
572C22—24no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22C2×(C22⋊D11)⋊C411yescharacteristic
580C22D4×Dic2211yescharacteristic
581C22#1062308111yescharacteristic
582C22D11×AGL(1,ℤ/8)11yescharacteristic
583C22#1062330411yescharacteristic
584C22#1062330511yescharacteristic
585C22#1062331011yescharacteristic
586C4—22no—
587C4—22no—
588C4—42no—
589C4—42no—
590C4—81no—
591C4—222no—
592C4—441no—
593C4—441no—
594C4—442no—
595C4—441no—
596C4—442no—
597C4—881no—
598C4—881no—
599C4C2×C4×Dic2211yescharacteristic
600C4#1062305411yescharacteristic
601C4#1062307211yescharacteristic
602C4#1062307411yescharacteristic
603C2—44no—
604C2#1307161911yescharacteristic
605C2#1307742011yescharacteristic
606C2#1307748711yescharacteristic
607C2#1308071711yescharacteristic
608C2#1308076211yescharacteristic
609C2#1308153811yescharacteristic
610C2#1308157511yescharacteristic
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#22974
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. #13071712C2semidirect
4. #13069585C2semidirect
5. #13069374C2semidirect
6. #13069358C2semidirect
7. #13069348C2semidirect
8. #13069211C2semidirect
9. #13069197C2semidirect
12. #13068488C2semidirect
30. #10622622C4semidirect
102. #66923C2×C4semidirect
119. #66872C2×C4semidirect
122. #66871C2×C4semidirect
123. C4⋊(C11⋊C8)C2×C4semidirect
507. C11#22974semidirect

Maximal subgroups

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

subgroupindex
C2×#106226222
#130717122
D4×C4⋊Dic112
#130695852
#130693742
#130693582
#130693482
#130692112
#130691972
#130688612
#130684882
#130684432
#102×Dic112
C11×#17622
#2297411