Finite Group Databasebeta

← #14775197

Subgroups — #14775197

Order 2816.

930 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622390C211yesmaximal, characteristic
2#13071637C211yesmaximal, characteristic
3#13071489C211yesmaximal, characteristic, complemented
4#13069357C211yesmaximal, characteristic, complemented
5#13069316C211yesmaximal, characteristic, complemented
6#13069199C211yesmaximal, characteristic, complemented
7#13069195C211yesmaximal, characteristic, complemented
8#13069041C211yesmaximal, characteristic
9#13068861C211yesmaximal, characteristic, complemented
10#13068802C211yesmaximal, characteristic, complemented
11#13068514C211yesmaximal, characteristic, complemented
12#13068443C211yesmaximal, characteristic, complemented
13#13068391C211yesmaximal, characteristic, complemented
14D11×#340C211yesmaximal, characteristic, complemented
15C11×#1925C211yesmaximal, characteristic, complemented
16C2×#66991C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19C2×C4⋊C4×D11C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×(C22⋊D11)⋊C4—21no—
22C2×C11×#107C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C11×#390C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32#10622600C2211yescharacteristic
33C4⋊C4×Dic11C2211yescharacteristic
34#10622586C2211yescharacteristic
35#10622586C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38#10622569—21no—
39#10622559—21no—
40#10622557—21no—
41C4×(C2×D11)⋊C4—21no—
42C4×(C2×D11)⋊C4C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44#10622546—21no—
45#10622541C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47#10622390C418yescomplemented
48#10622280—21no—
49#10622265—21no—
50C11×#340C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C23×Dic11—21no—
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C42×C11—21no—
74C2×C42×C11C2311yescharacteristic
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77#66991—22no—
78#66991C2×C414yes—
79D4×Dic11—22no—
80D4×Dic11—41no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4D411yescharacteristic
83C2×(C2×D11)⋊C4D411yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C2×C8×D11—22no—
99C2×C8×D11—22no—
100C2×C8×D11—41no—
101C4⋊C4×D11—22no—
102C4⋊C4×D11—22no—
103C4⋊C4×D11—41no—
104C4⋊C4×D11C2×C414yescomplemented
105(C22⋊D11)⋊C4—44no—
106C11×#107—41no—
107C11×#102—41no—
108C11×#102C2×C414yescomplemented
109C11×#95—21no—
110#66896—22no—
111#66896C2×C414yescomplemented
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95D411yescharacteristic
119C11⋊#95D411yescharacteristic
120(C2×D11)⋊C8C2×C414yescomplemented
121#66881C2×C414yescomplemented
122#66879—41no—
123#66872C2×C414yescomplemented
124#66871—22no—
125#66867—22no—
126#22936—111nomaximal, Sylow
127C24×C11—21no—
128C23×D11C2×D411yescharacteristic
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11C22×C412yes—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
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—42no—
149C22×Dic11—42no—
150C22×Dic11—81no—
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C2×C4×D11—24no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—42no—
160C2×C4×D11—42no—
161C2×C4×D11—81no—
162C2×C4×D11—81no—
163C2×C4×D11—81no—
164C2×C4×D11C22×C412yes—
165C2×C4×D11#4112yes—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11C22×C412yes—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4C22×C412yes—
178C11×C22⋊C4—42no—
179C11×C22⋊C4—81no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—81no—
183C22⋊Dic11—24no—
184C22⋊Dic11—42no—
185(C2×D11)⋊C4—22no—
186(C2×D11)⋊C4—22no—
187(C2×D11)⋊C4—42no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11C22×C412yes—
194C4⋊Dic11C22×C412yes—
195C4⋊Dic11#4112yes—
196Dic11⋊C4—24no—
197Dic11⋊C4—42no—
198Dic11⋊C4—42no—
199Dic11⋊C4—81no—
200Dic11⋊C4—81no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—42no—
204C4×Dic11—81no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8C22×C412yes—
210C2×C11⋊C8#4112yes—
211C8×D11—44no—
212C2×#481—111no—
213#2361—111no—
214#2345—111no—
215#1944—111no—
216#1936—111no—
217#1925D1111yescharacteristic, complemented
218#1920—111no—
219#1919—111no—
220#1893—111no—
221#1862—111no—
222#1852—111no—
223#1776—111no—
224#1762—111no—
225#1752—111no—
226C2×#340—111no—
227C23×C11—22no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11C22×D411yescharacteristic
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239C22×D11C4×D412yes—
240C22×D11AGL(1,ℤ/8)12yes—
241C22×D11#13712yes—
242D4×C11—22no—
243D4×C11—22no—
244D4×C11—41no—
245D4×C11—41no—
246C2×C4×C11—22no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
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×C11—41no—
261C2×C4×C11C23×C411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×C4×C112−1+411yescharacteristic
267C22⋊D11—48no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—22no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
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—41no—
288C2×Dic11—84no—
289C2×Dic11C4×D412yes—
290C4×D11—22no—
291C4×D11—22no—
292C4×D11—22no—
293C4×D11—22no—
294C4×D11—84no—
295C4×D11—84no—
296C8×C11—22no—
297C8×C11—41no—
298C11⋊C8—22no—
299C11⋊C8—22no—
300C23×C8—111no—
301C2×#121—111no—
302C2×C4×D4—111no—
303C2×C4×D4—221no—
304C22×C4⋊C4—111no—
305C22×C4⋊C4—111no—
306#481—118no—
307C2×#107—111no—
308C2×#107C2×D1111yescharacteristic
309C2×#106—111no—
310C2×#106—111no—
311C2×#102—111no—
312C2×#102—111no—
313C2×#102C2×D1111yescharacteristic
314C2×#102C2×D1111yescharacteristic
315C2×C22⋊C8—111no—
316C2×#97—111no—
317C2×#97—111no—
318#390C2×D1111yescharacteristic
319#389—111no—
320#389—111no—
321#389—111no—
322#388—221no—
323#387—221no—
324#387—221no—
325#386—221no—
326#385—221no—
327#380—111no—
328#380—221no—
329C4×C4⋊C4—111no—
330C4×C4⋊C4—111no—
331C4×C4⋊C4C2×D1111yescharacteristic
332C4×C22⋊C4—111no—
333C4×C22⋊C4—221no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340C2×D1111yescharacteristic
342#336—111no—
343#336C2×D1111yescharacteristic
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11C2×C4×D411yescharacteristic
352C22×C11#54611yescharacteristic
353C22×C11#54711yescharacteristic
354C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
355C22×C11C2×#13711yescharacteristic
356C22×C11#57611yescharacteristic
357C22×C11#57711yescharacteristic
358C2×D11—22no—
359C2×D11—22no—
360C2×D11—22no—
361C2×D11—22no—
362C2×D11—22no—
363C2×D11—22no—
364C2×D11#44014yes—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11—42no—
368C4×C11—81no—
369C4×C11—81no—
370C4×C11C4×#4111yescharacteristic
371C4×C11#52011yescharacteristic
372C4×C11#55111yescharacteristic
373C4×C11#55211yescharacteristic
374Dic11—22no—
375Dic11—42no—
376Dic11—42no—
377Dic11—41no—
378Dic11—42no—
379Dic11—41no—
380Dic11—81no—
381C22×D4—221no—
382C22×D4C22×D1111yescharacteristic
383C23×C4—111no—
384C23×C4—221no—
385C23×C4—221no—
386C23×C4—221no—
387C22×C8—111no—
388C22×C8—111no—
389C22×C8—222no—
390C22×C8—222no—
391C22×C8—441no—
392C22×C8C22×D1111yescharacteristic
393C22×C8C22×D1111yescharacteristic
394#121—114no—
395#121—222no—
396C4×D4—222no—
397C4×D4—441no—
398C4×D4—444no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—114no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—222no—
405C2×C4⋊C4—222no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—441no—
412C2×C4⋊C4C22×D1111yescharacteristic
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—111no—
418C2×C22⋊C4—111no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C42—21no—
423C2×C42—111no—
424C2×C42—221no—
425C2×C42—221no—
426C2×C42C22×D1111yescharacteristic
427#107—41no—
428#107—222no—
429#106—114no—
430#106—114no—
431#102—41no—
432#102—114no—
433#102—222no—
434#102C4×D1114yescomplemented
435C22⋊C8—114no—
436#97—222no—
437#97—441no—
438#95—21no—
439#95—111no—
440#95—111no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447C2×C11—82no—
448C2×C11#235911yescharacteristic
449C2×C11C2×#44011yescharacteristic
450C2×C11#294611yescharacteristic
451C2×C11#331611yescharacteristic
452C2×C11#331811yescharacteristic
453C2×C11#334511yescharacteristic
454C2×C11#334611yescharacteristic
455D11—24no—
456C24—21no—
457C24—111no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—224no—
464C2×D4—442no—
465C2×D4—442no—
466C2×D4C2×C4×D1112yes—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—111no—
471C22×C4—112no—
472C22×C4—112no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—224no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—442no—
485C22×C4—442no—
486C22×C4—442no—
487C22×C4—442no—
488C22×C4—881no—
489C22×C4—881no—
490C22×C4—881no—
491C22×C4—881no—
492C22×C4D4×D1111yescharacteristic
493C22×C4D4×D1111yescharacteristic
494C22×C4C23×D1111yescharacteristic
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—112no—
501C2×C8—112no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—444no—
507C2×C8C2×C4×D1112yes—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—112no—
514C4⋊C4—112no—
515C4⋊C4—112no—
516C4⋊C4—224no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—442no—
523C4⋊C4—442no—
524C4⋊C4—881no—
525C4⋊C4—881no—
526C4⋊C4C2×C4×D1112yes—
527C22⋊C4—42no—
528C22⋊C4—81no—
529C22⋊C4—222no—
530C22⋊C4—222no—
531C22⋊C4—224no—
532C22⋊C4—442no—
533C22⋊C4—442no—
534C42—21no—
535C42—21no—
536C42—81no—
537C42—221no—
538C42—221no—
539C42—442no—
540C42—881no—
541C11#2293611yescharacteristic, complemented, Sylow
542C23—22no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—112no—
550C23—112no—
551C23—112no—
552C23—221no—
553C23—221no—
554C23—221no—
555C23—221no—
556C23C2×D4×D1111yescharacteristic
557D4—22no—
558D4—22no—
559D4—41no—
560D4—41no—
561D4—448no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—112no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—222no—
581C2×C4—222no—
582C2×C4—222no—
583C2×C4—222no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—222no—
589C2×C4—222no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—222no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—884no—
603C2×C4—884no—
604C2×C4—884no—
605C2×C4C22×C4×D1111yescharacteristic
606C2×C4#6703711yescharacteristic
607C2×C4#41×D1111yescharacteristic
608C2×C4#41×D1111yescharacteristic
609C2×C4#41×D1111yescharacteristic
610C2×C4#6704311yescharacteristic
611C8—22no—
612C8—41no—
613C8—222no—
614C8—222no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—81no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22—114no—
623C22—222no—
624C22—222no—
625C22—222no—
626C22—222no—
627C22—222no—
628C22—222no—
629C22C4×D4×D1111yescharacteristic
630C22#1062314311yescharacteristic
631C22#1062318611yescharacteristic
632C22#1062328811yescharacteristic
633C22#1062330111yescharacteristic
634C22D11×AGL(1,ℤ/8)11yescharacteristic
635C22D11×#13711yescharacteristic
636C4—41no—
637C4—41no—
638C4—42no—
639C4—81no—
640C4—81no—
641C4—222no—
642C4—442no—
643C4—441no—
644C4—441no—
645C4—442no—
646C4—442no—
647C4—881no—
648C4#1062305311yescharacteristic
649C4#1062307711yescharacteristic
650C4#1062321011yescharacteristic
651C4#1062323911yescharacteristic
652C2—82no—
653C2—224no—
654C2#1307160511yescharacteristic
655C2D11×#44011yescharacteristic
656C2#1307744111yescharacteristic
657C2#1308073411yescharacteristic
658C2#1308076411yescharacteristic
659C2#1308108911yescharacteristic
660C2#1308110411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1925C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
cosocleC22×C4×C11C24
hypercenter#1925D11
hypocenterC11#22936
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1925

Complements

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

NH ≅ G/Ntype
3. #13071489C2semidirect
4. #13069357C2semidirect
5. #13069316C2semidirect
6. #13069199C2semidirect
7. #13069195C2semidirect
9. #13068861C2semidirect
10. #13068802C2semidirect
11. #13068514C2semidirect
12. #13068443C2semidirect
13. #13068391C2semidirect
14. D11×#340C2semidirect
15. C11×#1925C2semidirect
47. #10622390C4semidirect
104. C4⋊C4×D11C2×C4semidirect
108. C11×#102C2×C4semidirect
111. #66896C2×C4semidirect
120. (C2×D11)⋊C8C2×C4semidirect
121. #66881C2×C4semidirect
123. #66872C2×C4semidirect
217. #1925D11semidirect
434. #102C4×D11semidirect
541. C11#22936semidirect

Maximal subgroups

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

subgroupindex
C2×#106223902
#130716372
#130714892
#130693572
#130693162
#130691992
#130691952
#130690412
#130688612
#130688022
#130685142
#130684432
#130683912
D11×#3402
C11×#19252
#2293611