Finite Group Databasebeta

← #14770410

Subgroups — #14770410

Order 2816.

1250 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic22C211yesmaximal, characteristic
2C2×#10622314C211yesmaximal, characteristic, complemented
3#13071574C211yesmaximal, characteristic, complemented
4#13069589C211yesmaximal, characteristic, complemented
5#13069587C211yesmaximal, characteristic, complemented
6#13069575C211yesmaximal, characteristic, complemented
7#13069566C211yesmaximal, characteristic, complemented
8#13069564C211yesmaximal, characteristic, complemented
9#13069562C211yesmaximal, characteristic, complemented
10#13068626C211yesmaximal, characteristic
11#13068624C211yesmaximal, characteristic
12#13068614C211yesmaximal, characteristic
13#13068443C211yesmaximal, characteristic
14#102×Dic11C211yesmaximal, characteristic
15C11×#1762C211yesmaximal, characteristic
16C23×Dic22—21no—
17C2×C4×D4×C11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C2×D4×Dic11C2211yescharacteristic
20C2×#66977—21no—
21D4×Dic22—24no—
22D4×Dic22C418yescomplemented
23C2×#66941C2211yescharacteristic
24C2×#66941C2211yescharacteristic
25C2×#66931—21no—
26C2×#66931—21no—
27C2×#66922C2211yescharacteristic
28C2×C4×Dic22C2211yescharacteristic
29C2×C11×#102C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#97C2211yescharacteristic
32C4×C11×C4⋊C4C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66879C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38C2×C8×Dic11C2211yescharacteristic
39#10622590C2211yescharacteristic
40#10622589C2211yescharacteristic
41C4⋊C4×Dic11C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43#10622549C2211yescharacteristic
44#10622546—21no—
45C4×Dic11⋊C4—21no—
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47#10622314—24no—
48#10622267—21no—
49#10622259—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×Dic11—21no—
65C23×Dic11—21no—
66C22×Dic22—21no—
67C22×Dic22—21no—
68C22×Dic22—21no—
69C22×Dic22—28no—
70C22×Dic22—44no—
71C22×Dic22—44no—
72C22×Dic22D411yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C4×D4×C11—22no—
76C4×D4×C11C2×C414yes—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85D4×Dic11—22no—
86D4×Dic11—22no—
87D4×Dic11C2×C414yes—
88D4×Dic11C2×C414yes—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11D411yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95#66977—28no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4D411yescharacteristic
101C2×Dic11⋊C4D411yescharacteristic
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11C2311yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108#66941—22no—
109#66941—22no—
110#66941C2×C414yes—
111#66941C2×C414yes—
112#66931—28no—
113#66931—28no—
114#66922—22no—
115#66922C2×C414yes—
116C4×Dic22C2×C414yes—
117C4×Dic22D414yes—
118C11×#102—22no—
119C11×#102Q814yescomplemented
120C11×#97—22no—
121C11×#95—21no—
122#66896—22no—
123#66896—22no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130#66879—22no—
131Dic11⋊C8—22no—
132Dic11⋊C8—22no—
133C8×Dic11—22no—
134C4⋊(C11⋊C8)—22no—
135#22523—111nomaximal, Sylow
136C24×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11C22×C412yes—
141C2×D4×C11C2×Q812yes—
142C2×D4×C11#4112yes—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—24no—
146C22×C4×C11—21no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—42no—
159C22×Dic11—42no—
160C22×Dic11—42no—
161C22×Dic11—42no—
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C2×Dic22—22no—
167C2×Dic22—22no—
168C2×Dic22—24no—
169C2×Dic22—24no—
170C2×Dic22—24no—
171C2×Dic22—42no—
172C2×Dic22—42no—
173C2×Dic22—432no—
174C2×Dic22—42no—
175C2×Dic22—42no—
176C2×Dic22—42no—
177C2×Dic22—42no—
178C2×Dic22C22⋊C414yes—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11C2×Q812yescomplemented
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4C22×C412yes—
190C11×C4⋊C4C2×Q812yescomplemented
191C11×C22⋊C4—24no—
192C42×C11—81no—
193C42×C11C22×C412yes—
194C42×C11C2×D412yes—
195C22⋊Dic11—24no—
196C22⋊Dic11—24no—
197C4⋊Dic11—24no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11C22⋊C414yes—
205C4⋊Dic11C22×C412yes—
206C4⋊Dic11C22×C412yes—
207Dic11⋊C4—24no—
208Dic11⋊C4—24no—
209Dic11⋊C4—42no—
210Dic11⋊C4—81no—
211Dic11⋊C4C22⋊C414yes—
212Dic11⋊C4C22⋊C414yes—
213C4×Dic11—42no—
214C4×Dic11—81no—
215C4×Dic11C22×C412yes—
216C4×Dic11C22×C412yes—
217C4×Dic11C2×D412yes—
218C4×Dic11C2×D412yes—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×D4×Q8—111no—
226C2×#446—111no—
227#2355—111no—
228#1993—111no—
229#1993—111no—
230#1990—111no—
231#1988—111no—
232#1987—111no—
233#1987—111no—
234#1804—111no—
235#1804—111no—
236#1802—111no—
237#1762—111no—
238#1762D1111yescharacteristic
239C4×#102—111no—
240C23×C11—22no—
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11C22×D411yescharacteristic
248D4×C11—22no—
249D4×C11—22no—
250D4×C11—22no—
251D4×C11C4×Q814yes—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—48no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11C2×C22⋊C412yes—
267C2×C4×C11C2×C22⋊C412yes—
268C2×C4×C11C23×C411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×Q811yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C112−1+411yescharacteristic
273C2×C4×C112−1+411yescharacteristic
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—48no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—48no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11C2×C22⋊C412yes—
295C2×Dic11C2×C22⋊C412yes—
296C2×Dic11C2×C22⋊C412yes—
297C2×Dic11C2×C22⋊C412yes—
298C2×Dic11AGL(1,ℤ/8)12yes—
299C2×Dic11AGL(1,ℤ/8)12yes—
300Dic22—28no—
301Dic22—48no—
302Dic22—48no—
303Dic22—48no—
304C8×C11—22no—
305C8×C11—41no—
306C11⋊C8—41no—
307C11⋊C8—41no—
308C23×Q8—221no—
309D4×Q8—118no—
310D4×Q8—224no—
311C2×C4⋊Q8—111no—
312C2×C4⋊Q8—111no—
313C2×C4⋊Q8—111no—
314C2×C22⋊Q8—221no—
315C2×C22⋊Q8—221no—
316C2×C22⋊Q8—221no—
317C2×C4×Q8—111no—
318C2×C4×D4—111no—
319C2×C4×D4—111no—
320C2×C4×D4C2×D1111yescharacteristic
321#446—224no—
322C2×C4⋊C8—111no—
323C2×C4⋊C8—111no—
324C2×C4⋊C8—111no—
325C2×#102—111no—
326C2×#102—111no—
327C2×#102C2×D1111yescharacteristic
328C2×#102C2×D1111yescharacteristic
329C2×#97—111no—
330C2×#97C2×D1111yescharacteristic
331C2×C4×C8—111no—
332#391—221no—
333#387—221no—
334#387—221no—
335#384—111no—
336#382—111no—
337#382—111no—
338C4×C4⋊C4—111no—
339C4×C4⋊C4—111no—
340C4×C4⋊C4—221no—
341C4×C4⋊C4C2×D1111yescharacteristic
342#340—111no—
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340C2×D1111yescharacteristic
353#340C2×D1111yescharacteristic
354C22×C11—24no—
355C22×C11—42no—
356C22×C11—42no—
357C22×C11—42no—
358C22×C11—42no—
359C22×C11—42no—
360C22×C11—42no—
361C22×C11C22×C22⋊C411yescharacteristic
362C22×C11#54811yescharacteristic
363C22×C11D4×Q811yescharacteristic
364C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
365C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
366C22×C11#57711yescharacteristic
367C22×C11#57811yescharacteristic
368C4×C11—22no—
369C4×C11—22no—
370C4×C11—42no—
371C4×C11—42no—
372C4×C11—81no—
373C4×C11C2×C4×Q811yescharacteristic
374C4×C11#51911yescharacteristic
375C4×C11#54811yescharacteristic
376C4×C11D4×Q811yescharacteristic
377Dic11—22no—
378Dic11—22no—
379Dic11—22no—
380Dic11—42no—
381Dic11—42no—
382Dic11—81no—
383Dic11—81no—
384Dic11#41814yes—
385C22×Q8—111no—
386C22×Q8—221no—
387C22×Q8—221no—
388C22×Q8—228no—
389C22×Q8—221no—
390C22×Q8—444no—
391C22×Q8—444no—
392C22×D4C22×D1111yescharacteristic
393C23×C4—21no—
394C23×C4—221no—
395C23×C4—221no—
396C22×C8—111no—
397C22×C8—111no—
398C22×C8C22×D1111yescharacteristic
399C22×C8C22×D1111yescharacteristic
400C4⋊Q8—114no—
401C4⋊Q8—114no—
402C4⋊Q8—114no—
403C4⋊Q8—222no—
404C4⋊Q8—222no—
405C4⋊Q8—222no—
406C22⋊Q8—228no—
407C22⋊Q8—228no—
408C22⋊Q8—228no—
409C4×Q8—114no—
410C4×Q8—114no—
411C4×D4—22no—
412C4×D4—114no—
413C4×D4—114no—
414C4×D4—222no—
415C4×D4—222no—
416C4×D4C4×D1114yes—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4C22×D1111yescharacteristic
430C2×C4⋊C4C22×D1111yescharacteristic
431C2×C4⋊C4C22×D1111yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C42—21no—
436C2×C42—111no—
437C2×C42—111no—
438C2×C42—221no—
439C2×C42—221no—
440C2×C42C22×D1111yescharacteristic
441C4⋊C8—222no—
442C4⋊C8—222no—
443C4⋊C8—222no—
444#102—22no—
445#102—222no—
446#102—222no—
447#102Dic2214yescomplemented
448#97—22no—
449#97—222no—
450C4×C8—222no—
451#95—21no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458C2×C11—44no—
459C2×C11Q8×C22⋊C411yescharacteristic
460C2×C11C2×#41811yescharacteristic
461C2×C11#289811yescharacteristic
462C2×C11#336711yescharacteristic
463C2×C11#337311yescharacteristic
464C2×C11#338411yescharacteristic
465C2×C11#338611yescharacteristic
466C24—21no—
467C2×Q8—114no—
468C2×Q8—222no—
469C2×Q8—222no—
470C2×Q8—224no—
471C2×Q8—224no—
472C2×Q8—224no—
473C2×Q8—442no—
474C2×Q8—442no—
475C2×Q8—442no—
476C2×Q8—442no—
477C2×Q8—442no—
478C2×Q8—442no—
479C2×Q8—4432no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4C2×Dic2212yes—
484C2×D4C2×C4×D1112yes—
485C2×D4#433912yes—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—24no—
489C22×C4—21no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—111no—
496C22×C4—224no—
497C22×C4—224no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—442no—
503C22×C4—442no—
504C22×C4—442no—
505C22×C4—442no—
506C22×C4D4×D1111yescharacteristic
507C22×C4D4×D1111yescharacteristic
508C22×C4C23×D1111yescharacteristic
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8C2×Dic2212yescomplemented
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—114no—
526C4⋊C4—114no—
527C4⋊C4—114no—
528C4⋊C4—112no—
529C4⋊C4—112no—
530C4⋊C4—224no—
531C4⋊C4—224no—
532C4⋊C4—224no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—442no—
540C4⋊C4—881no—
541C4⋊C4C2×Dic2212yescomplemented
542C4⋊C4C2×C4×D1112yes—
543C22⋊C4—24no—
544C22⋊C4—224no—
545C22⋊C4—224no—
546C42—81no—
547C42—112no—
548C42—112no—
549C42—112no—
550C42—112no—
551C42—442no—
552C42—881no—
553C42C2×C4×D1112yes—
554C42D4×D1112yes—
555C11#2252311yescharacteristic, complemented, Sylow
556C23—22no—
557C23—22no—
558C23—22no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23C2×D4×D1111yescharacteristic
564Q8—228no—
565Q8—448no—
566Q8—448no—
567Q8—448no—
568D4—22no—
569D4—22no—
570D4—22no—
571D4C4×Dic2214yes—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—48no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—112no—
587C2×C4—112no—
588C2×C4—112no—
589C2×C4—112no—
590C2×C4—112no—
591C2×C4—112no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—448no—
601C2×C4—448no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4C22⋊C4×D1112yes—
613C2×C4C22⋊C4×D1112yes—
614C2×C4C22×Dic2211yescharacteristic
615C2×C4C22×C4×D1111yescharacteristic
616C2×C4C2×#433911yescharacteristic
617C2×C4C2×D4×D1111yescharacteristic
618C2×C4#6704311yescharacteristic
619C2×C4#6704311yescharacteristic
620C8—22no—
621C8—41no—
622C8—441no—
623C8—441no—
624C22—24no—
625C22—42no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22C2×C22⋊C4×D1111yescharacteristic
632C22D4×Dic2211yescharacteristic
633C22#1062308311yescharacteristic
634C22D11×AGL(1,ℤ/8)11yescharacteristic
635C22D11×AGL(1,ℤ/8)11yescharacteristic
636C22#1062330611yescharacteristic
637C22#1062331011yescharacteristic
638C4—22no—
639C4—22no—
640C4—42no—
641C4—42no—
642C4—81no—
643C4—114no—
644C4—222no—
645C4—222no—
646C4—222no—
647C4—442no—
648C4—442no—
649C4—881no—
650C4—881no—
651C4C2×C4×Dic2211yescharacteristic
652C4#1062304711yescharacteristic
653C4D4×Dic2211yescharacteristic
654C4#1062308311yescharacteristic
655C2—44no—
656C2C22⋊C4×Dic2211yescharacteristic
657C2D11×#41811yescharacteristic
658C2#1307714711yescharacteristic
659C2#1308133511yescharacteristic
660C2#1308140911yescharacteristic
661C2#1308151611yescharacteristic
662C2#1308153811yescharacteristic
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#22523
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. C2×#10622314C2semidirect
3. #13071574C2semidirect
4. #13069589C2semidirect
5. #13069587C2semidirect
6. #13069575C2semidirect
7. #13069566C2semidirect
8. #13069564C2semidirect
9. #13069562C2semidirect
22. D4×Dic22C4semidirect
119. C11×#102Q8semidirect
184. C2×C8×C11C2×Q8semidirect
190. C11×C4⋊C4C2×Q8semidirect
447. #102Dic22semidirect
520. C2×C8C2×Dic22semidirect
541. C4⋊C4C2×Dic22semidirect
555. C11#22523semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic222
C2×#106223142
#130715742
#130695892
#130695872
#130695752
#130695662
#130695642
#130695622
#130686262
#130686242
#130686142
#130684432
#102×Dic112
C11×#17622
#2252311