Finite Group Databasebeta

← #14770448

Subgroups — #14770448

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623070C211yesmaximal, characteristic
2C2×#10622444C211yesmaximal, characteristic, complemented
3#13071568C211yesmaximal, characteristic, complemented
4#13069587C211yesmaximal, characteristic, complemented
5#13069583C211yesmaximal, characteristic, complemented
6#13069580C211yesmaximal, characteristic, complemented
7#13069572C211yesmaximal, characteristic, complemented
8#13069571C211yesmaximal, characteristic, complemented
9#13069566C211yesmaximal, characteristic, complemented
10#13068624C211yesmaximal, characteristic
11#13068614C211yesmaximal, characteristic
12#13068443C211yesmaximal, characteristic
13#13068443C211yesmaximal, characteristic
14C4×#66896C211yesmaximal, characteristic
15C11×#1804C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C2×#66977—21no—
20C22×Dic11⋊C4—21no—
21#10623070—24no—
22#10623070C418yescomplemented
23C2×#66943C2211yescharacteristic
24C2×#66941C2211yescharacteristic
25C2×#66931—21no—
26C2×#66931—21no—
27C2×#66923C2211yescharacteristic
28C2×C4×Dic22C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#102C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C11×#382C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66879C2211yescharacteristic
36C2×#66879C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39#10622590C2211yescharacteristic
40#10622589C2211yescharacteristic
41C4⋊C4×Dic11C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622444—24no—
46#10622266—21no—
47#10622265—21no—
48#10622262—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×Dic22D411yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C4×D4×C11—22no—
71C4×D4×C11C2×C414yes—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79D4×Dic11—22no—
80D4×Dic11—22no—
81D4×Dic11C2×C414yes—
82D4×Dic11C2×C414yes—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11D411yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89#66977—28no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—28no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4D411yescharacteristic
98C2×Dic11⋊C4D411yescharacteristic
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106#66943—22no—
107#66943C2×C414yes—
108#66941—22no—
109#66941C2×C414yes—
110#66931—28no—
111#66931—28no—
112#66923—22no—
113#66923C2×C414yes—
114C4×Dic22C2×C414yes—
115C4×Dic22D414yes—
116C11×C4⋊C8—22no—
117C11×#102—22no—
118C11×#102—22no—
119C11×#95—21no—
120C11×#95—21no—
121#66896—22no—
122#66896Q814yescomplemented
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128#66879—22no—
129#66879—22no—
130Dic11⋊C8—22no—
131Dic11⋊C8—22no—
132C4×C11⋊C8—22no—
133#22526—111nomaximal, Sylow
134C24×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11C22×C412yes—
139C2×D4×C11C2×Q812yes—
140C2×D4×C11#4112yes—
141C22×C4×C11—21no—
142C22×C4×C11—24no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—81no—
146C22×C4×C11—81no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—42no—
157C22×Dic11—42no—
158C22×Dic11—81no—
159C22×Dic11—81no—
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C2×Dic22—24no—
165C2×Dic22—41no—
166C2×Dic22—41no—
167C2×Dic22—81no—
168C2×Dic22—81no—
169C2×Dic22C22⋊C414yes—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4C22×C412yes—
182C11×C22⋊C4—24no—
183C42×C11C22×C412yes—
184C42×C11C2×D412yes—
185C22⋊Dic11—24no—
186C22⋊Dic11—24no—
187C4⋊Dic11—24no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11C22⋊C414yes—
194C4⋊Dic11C22×C412yes—
195C4⋊Dic11C22×C412yes—
196C4⋊Dic11C2×Q812yes—
197Dic11⋊C4—24no—
198Dic11⋊C4—24no—
199Dic11⋊C4—24no—
200Dic11⋊C4—24no—
201Dic11⋊C4—42no—
202Dic11⋊C4—81no—
203Dic11⋊C4C22⋊C414yes—
204Dic11⋊C4C22⋊C414yes—
205C4×Dic11—42no—
206C4×Dic11—81no—
207C4×Dic11—81no—
208C4×Dic11C22×C412yes—
209C4×Dic11C22×C412yes—
210C4×Dic11C2×D412yes—
211C4×Dic11C2×D412yes—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8C2×Q812yes—
218C2×#554—111no—
219C2×#446—111no—
220#2355—111no—
221#1993—111no—
222#1992—111no—
223#1991—111no—
224#1989—111no—
225#1989—111no—
226#1988—111no—
227#1804—111no—
228#1804D1111yescharacteristic
229#1802—111no—
230#1762—111no—
231#1762—111no—
232C4×#102—111no—
233C23×C11—22no—
234C23×C11—22no—
235C23×C11—22no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11C22×D411yescharacteristic
241D4×C11—22no—
242D4×C11—22no—
243D4×C11—22no—
244D4×C11C4×Q814yes—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—84no—
259C2×C4×C11C2×C22⋊C412yes—
260C2×C4×C11C2×C22⋊C412yes—
261C2×C4×C11C23×C411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×Q811yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C112−1+411yescharacteristic
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—22no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—48no—
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×Dic11C2×C22⋊C412yes—
290C2×Dic11C2×C22⋊C412yes—
291C2×Dic11C2×C22⋊C412yes—
292C2×Dic11C2×C22⋊C412yes—
293Dic22—44no—
294Dic22—84no—
295C8×C11—41no—
296C8×C11—41no—
297C11⋊C8—22no—
298C11⋊C8—41no—
299#554—118no—
300#554—224no—
301C2×C4⋊Q8—111no—
302C2×#125—111no—
303C2×#125—111no—
304C2×C22⋊Q8—221no—
305C2×C22⋊Q8—221no—
306C2×C22⋊Q8—221no—
307C2×C4×Q8—111no—
308C2×C4×D4—111no—
309C2×C4×D4—111no—
310C2×C4×D4C2×D1111yescharacteristic
311C22×C4⋊C4—221no—
312#446—224no—
313C2×C4⋊C8—111no—
314C2×C4⋊C8—111no—
315C2×C4⋊C8C2×D1111yescharacteristic
316C2×#102—111no—
317C2×#102—111no—
318C2×#102C2×D1111yescharacteristic
319C2×#102C2×D1111yescharacteristic
320C2×#97—111no—
321C2×#97—111no—
322C2×C4×C8—111no—
323#391—221no—
324#387—221no—
325#387—221no—
326#384—111no—
327#382—111no—
328#382C2×D1111yescharacteristic
329C4×C4⋊C4—111no—
330C4×C4⋊C4—111no—
331C4×C4⋊C4—111no—
332C4×C4⋊C4—221no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#340C2×D1111yescharacteristic
344#340C2×D1111yescharacteristic
345C22×C11—24no—
346C22×C11—42no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11—42no—
350C22×C11—42no—
351C22×C11—42no—
352C22×C11C22×C22⋊C411yescharacteristic
353C22×C11#54811yescharacteristic
354C22×C11D4×Q811yescharacteristic
355C22×C11#57511yescharacteristic
356C22×C11#57511yescharacteristic
357C22×C11#57611yescharacteristic
358C22×C11#57711yescharacteristic
359C4×C11—22no—
360C4×C11—22no—
361C4×C11—42no—
362C4×C11—81no—
363C4×C11—81no—
364C4×C11C2×C4×Q811yescharacteristic
365C4×C11#51911yescharacteristic
366C4×C11#54811yescharacteristic
367C4×C11D4×Q811yescharacteristic
368Dic11—22no—
369Dic11—22no—
370Dic11—22no—
371Dic11—22no—
372Dic11—42no—
373Dic11—42no—
374Dic11—42no—
375Dic11—81no—
376C22×Q8—111no—
377C22×Q8—221no—
378C22×D4C22×D1111yescharacteristic
379C23×C4—21no—
380C23×C4—221no—
381C23×C4—221no—
382C22×C8—111no—
383C22×C8—111no—
384C22×C8C22×D1111yescharacteristic
385C22×C8C22×D1111yescharacteristic
386C4⋊Q8—114no—
387C4⋊Q8—222no—
388#125—114no—
389#125—114no—
390#125—222no—
391#125—222no—
392C22⋊Q8—228no—
393C22⋊Q8—228no—
394C22⋊Q8—228no—
395C4×Q8—114no—
396C4×Q8—114no—
397C4×D4—22no—
398C4×D4—114no—
399C4×D4—114no—
400C4×D4—222no—
401C4×D4—222no—
402C4×D4C4×D1114yes—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—228no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C42—111no—
425C2×C42—111no—
426C2×C42—221no—
427C2×C42—221no—
428C2×C42—221no—
429C2×C42C22×D1111yescharacteristic
430C4⋊C8—22no—
431C4⋊C8—222no—
432C4⋊C8—222no—
433#102—22no—
434#102—22no—
435#102—114no—
436#102—222no—
437#97—222no—
438#97—222no—
439C4×C8—222no—
440#95—21no—
441#95—21no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447C2×C11—44no—
448C2×C11Q8×C22⋊C411yescharacteristic
449C2×C11#289611yescharacteristic
450C2×C11#289711yescharacteristic
451C2×C11#337011yescharacteristic
452C2×C11#337611yescharacteristic
453C2×C11#338811yescharacteristic
454C2×C11#338911yescharacteristic
455C24—21no—
456C2×Q8—114no—
457C2×Q8—224no—
458C2×Q8—441no—
459C2×Q8—441no—
460C2×Q8—881no—
461C2×Q8—881no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4C2×C4×D1112yes—
466C2×D4#434112yes—
467C2×D4Q8×D1112yes—
468C22×C4—21no—
469C22×C4—24no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—81no—
473C22×C4—81no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—224no—
479C22×C4—224no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—442no—
485C22×C4—442no—
486C22×C4—881no—
487C22×C4—881no—
488C22×C4D4×D1111yescharacteristic
489C22×C4D4×D1111yescharacteristic
490C22×C4C23×D1111yescharacteristic
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—112no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—114no—
509C4⋊C4—114no—
510C4⋊C4—114no—
511C4⋊C4—112no—
512C4⋊C4—112no—
513C4⋊C4—112no—
514C4⋊C4—224no—
515C4⋊C4—224no—
516C4⋊C4—224no—
517C4⋊C4—224no—
518C4⋊C4—224no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—442no—
525C4⋊C4—881no—
526C4⋊C4C2×C4×D1112yes—
527C22⋊C4—24no—
528C22⋊C4—224no—
529C22⋊C4—224no—
530C42—112no—
531C42—112no—
532C42—112no—
533C42—112no—
534C42—442no—
535C42—881no—
536C42—881no—
537C42C2×C4×D1112yes—
538C42D4×D1112yes—
539C11#2252611yescharacteristic, complemented, Sylow
540C23—22no—
541C23—22no—
542C23—22no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23C2×D4×D1111yescharacteristic
548Q8—444no—
549Q8—884no—
550D4—22no—
551D4—22no—
552D4—22no—
553D4#6694014yes—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—84no—
568C2×C4—112no—
569C2×C4—112no—
570C2×C4—112no—
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—222no—
581C2×C4—222no—
582C2×C4—222no—
583C2×C4—448no—
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—441no—
593C2×C4—884no—
594C2×C4C22⋊C4×D1112yes—
595C2×C4C22⋊C4×D1112yes—
596C2×C4C22×C4×D1111yescharacteristic
597C2×C4C2×D4×D1111yescharacteristic
598C2×C4C2×#434111yescharacteristic
599C2×C4C2×Q8×D1111yescharacteristic
600C2×C4#6704311yescharacteristic
601C2×C4#6704311yescharacteristic
602C8—41no—
603C8—41no—
604C8—222no—
605C8—441no—
606C22—24no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22C2×C22⋊C4×D1111yescharacteristic
614C22#1062312911yescharacteristic
615C22#1062316311yescharacteristic
616C22#1062329911yescharacteristic
617C22#1062329911yescharacteristic
618C22#1062330511yescharacteristic
619C22#1062330611yescharacteristic
620C4—22no—
621C4—22no—
622C4—42no—
623C4—81no—
624C4—81no—
625C4—222no—
626C4—222no—
627C4—222no—
628C4—222no—
629C4—442no—
630C4—442no—
631C4—442no—
632C4—881no—
633C4C2×#6694011yescharacteristic
634C4#1062304711yescharacteristic
635C4#1062312911yescharacteristic
636C4#1062316311yescharacteristic
637C2—44no—
638C2#1307144811yescharacteristic
639C2#1307713111yescharacteristic
640C2#1307714111yescharacteristic
641C2#1308137311yescharacteristic
642C2#1308144711yescharacteristic
643C2#1308156511yescharacteristic
644C2#1308157411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1804C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#1804D11
hypocenterC11#22526
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
2. C2×#10622444C2semidirect
3. #13071568C2semidirect
4. #13069587C2semidirect
5. #13069583C2semidirect
6. #13069580C2semidirect
7. #13069572C2semidirect
8. #13069571C2semidirect
9. #13069566C2semidirect
22. #10623070C4semidirect
122. #66896Q8semidirect
539. C11#22526semidirect

Maximal subgroups

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

subgroupindex
C2×#106230702
C2×#106224442
#130715682
#130695872
#130695832
#130695802
#130695722
#130695712
#130695662
#130686242
#130686142
#130684432
C4×#668962
C11×#18042
#2252611