Finite Group Databasebeta

← #14770442

Subgroups — #14770442

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×#10623221C211yesmaximal, characteristic
2C2×#10622444C211yesmaximal, characteristic, complemented
3#13071574C211yesmaximal, characteristic, complemented
4#13069587C211yesmaximal, characteristic, complemented
5#13069583C211yesmaximal, characteristic, complemented
6#13069582C211yesmaximal, characteristic, complemented
7#13069570C211yesmaximal, characteristic, complemented
8#13069566C211yesmaximal, characteristic, complemented
9#13068627C211yesmaximal, characteristic
10#13068625C211yesmaximal, characteristic
11#13068615C211yesmaximal, characteristic
12#13068440C211yesmaximal, characteristic
13#13068440C211yesmaximal, characteristic
14C4×#66873C211yesmaximal, characteristic
15C11×#1989C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17#10623221—24no—
18#10623221C418yescomplemented
19C2×#66950—21no—
20C2×#66949—21no—
21C2×#66949—21no—
22C2×#66946C2211yescharacteristic
23C2×#66946C2211yescharacteristic
24C2×C4⋊C4×D11—21no—
25C2×#66943C2211yescharacteristic
26C2×#66941C2211yescharacteristic
27C2×C4×D44C2211yescharacteristic
28C2×C4×Dic22C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×#66879C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37#10622590C2211yescharacteristic
38#10622589C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40C4⋊C4×Dic11C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43#10622549C2211yescharacteristic
44#10622546—21no—
45C4×Dic11⋊C4—21no—
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622444—24no—
48#10622267—21no—
49#10622259—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×Dic22—21no—
67C22×Dic22D411yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C11×#125—22no—
71C11×#125C2×C414yes—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11D411yescharacteristic
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⋊C4D411yescharacteristic
93C2×Dic11⋊C4D411yescharacteristic
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11C2311yescharacteristic
97C2×C4×Dic11C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100#66950—28no—
101#66949—28no—
102#66949—28no—
103#66946—22no—
104#66946—22no—
105#66946C2×C414yes—
106#66946C2×C414yes—
107C4⋊C4×D11—28no—
108#66943—22no—
109#66943C2×C414yes—
110#66941—22no—
111#66941C2×C414yes—
112C4×D44—22no—
113C4×D44C2×C414yes—
114C4×Dic22C2×C414yes—
115C4×Dic22D414yes—
116C11×C4⋊C8—22no—
117C11×#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124#66885—22no—
125#66885—22no—
126#66879—22no—
127#66879—22no—
128Dic11⋊C8—22no—
129Dic11⋊C8—22no—
130#66873—22no—
131#66873Q814yescomplemented
132C4×C11⋊C8—22no—
133#22526—111nomaximal, Sylow
134C23×D11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44C22×C412yes—
153C2×D44C2×Q812yes—
154C2×D44#4112yes—
155C2×C4×D11—24no—
156C2×C4×D11—24no—
157C2×C4×D11—24no—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×C4×D11—81no—
161C2×C4×D11—81no—
162C2×C4×D11—81no—
163C2×C4×D11—81no—
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—24no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4C22×C412yes—
184C11×C4⋊C4C22×C412yes—
185C11×C4⋊C4C2×Q812yes—
186C42×C11—81no—
187C42×C11C22×C412yes—
188C42×C11C2×D412yes—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—24no—
191(C2×D11)⋊C4—24no—
192C4⋊Dic11—24no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11C22⋊C414yes—
199C4⋊Dic11C22×C412yes—
200Dic11⋊C4—24no—
201Dic11⋊C4—24no—
202Dic11⋊C4—42no—
203Dic11⋊C4—81no—
204Dic11⋊C4C22⋊C414yes—
205Dic11⋊C4C22⋊C414yes—
206C4×Dic11—42no—
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#1989D1111yescharacteristic, complemented
226#1988—111no—
227#1804—111no—
228#1804—111no—
229#1802—111no—
230#1762—111no—
231#1762—111no—
232C4×#102—111no—
233C23×C11C22×D411yescharacteristic
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—22no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
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×C11C2×C22⋊C412yes—
258C2×C4×C11C2×C22⋊C412yes—
259C2×C4×C11C23×C411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×Q811yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C112−1+411yescharacteristic
264C2×C4×C112−1+411yescharacteristic
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—22no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11C2×C22⋊C412yes—
283C2×Dic11C2×C22⋊C412yes—
284C2×Dic11C2×C22⋊C412yes—
285C2×Dic11C2×C22⋊C412yes—
286D44—22no—
287D44—22no—
288D44—22no—
289D44C4×Q814yes—
290C4×D11—48no—
291C4×D11—84no—
292C4×D11—84no—
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×#125C2×D1111yescharacteristic
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×D4—111no—
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×#102—111no—
319C2×#102—111no—
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#382—111no—
329C4×C4⋊C4—111no—
330C4×C4⋊C4—111no—
331C4×C4⋊C4—221no—
332C4×C4⋊C4C2×D1111yescharacteristic
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#340C2×D1111yescharacteristic
342#340C2×D1111yescharacteristic
343#340C2×D1111yescharacteristic
344#340C2×D1111yescharacteristic
345C22×C11C22×C22⋊C411yescharacteristic
346C22×C11#54811yescharacteristic
347C22×C11D4×Q811yescharacteristic
348C22×C11#57511yescharacteristic
349C22×C11#57511yescharacteristic
350C22×C11#57611yescharacteristic
351C22×C11#57711yescharacteristic
352C2×D11—24no—
353C2×D11—42no—
354C2×D11—42no—
355C2×D11—42no—
356C2×D11—42no—
357C2×D11—42no—
358C2×D11—42no—
359C4×C11—22no—
360C4×C11—22no—
361C4×C11—42no—
362C4×C11—42no—
363C4×C11—42no—
364C4×C11—81no—
365C4×C11C2×C4×Q811yescharacteristic
366C4×C11#51911yescharacteristic
367C4×C11#54811yescharacteristic
368C4×C11D4×Q811yescharacteristic
369Dic11—22no—
370Dic11—22no—
371Dic11—22no—
372Dic11—22no—
373Dic11—42no—
374Dic11—81no—
375Dic11—81no—
376C22×Q8—111no—
377C22×Q8—221no—
378C22×D4—111no—
379C23×C4—221no—
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—22no—
389#125—114no—
390#125—222no—
391#125C4×D1114yes—
392C22⋊Q8—228no—
393C22⋊Q8—228no—
394C22⋊Q8—228no—
395C4×Q8—114no—
396C4×Q8—114no—
397C4×D4—114no—
398C4×D4—114no—
399C4×D4—114no—
400C4×D4—222no—
401C4×D4—222no—
402C4×D4—222no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—228no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C42—21no—
425C2×C42—111no—
426C2×C42—111no—
427C2×C42—221no—
428C2×C42—221no—
429C2×C42C22×D1111yescharacteristic
430C4⋊C8—22no—
431C4⋊C8—222no—
432C4⋊C8—222no—
433#102—114no—
434#102—222no—
435#102—222no—
436#102—222no—
437#97—222no—
438#97—222no—
439C4×C8—222no—
440#95—21no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447C2×C11Q8×C22⋊C411yescharacteristic
448C2×C11#289611yescharacteristic
449C2×C11#289711yescharacteristic
450C2×C11#337011yescharacteristic
451C2×C11#337611yescharacteristic
452C2×C11#338811yescharacteristic
453C2×C11#338911yescharacteristic
454D11—44no—
455C24—221no—
456C2×Q8—114no—
457C2×Q8—224no—
458C2×Q8—441no—
459C2×Q8—441no—
460C2×Q8—881no—
461C2×Q8—881no—
462C2×D4—112no—
463C2×D4—112no—
464C2×D4—112no—
465C2×D4—221no—
466C2×D4—221no—
467C2×D4—221no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—224no—
477C22×C4—224no—
478C22×C4—221no—
479C22×C4—224no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—442no—
483C22×C4—442no—
484C22×C4—881no—
485C22×C4—881no—
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—24no—
504C4⋊C4—24no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—114no—
511C4⋊C4—114no—
512C4⋊C4—114no—
513C4⋊C4—112no—
514C4⋊C4—224no—
515C4⋊C4—224no—
516C4⋊C4—224no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—442no—
523C4⋊C4—881no—
524C4⋊C4C2×C4×D1112yes—
525C4⋊C4C2×C4×D1112yes—
526C4⋊C4Q8×D1112yes—
527C22⋊C4—224no—
528C22⋊C4—224no—
529C22⋊C4—224no—
530C42—81no—
531C42—112no—
532C42—112no—
533C42—112no—
534C42—112no—
535C42—442no—
536C42—881no—
537C42C2×C4×D1112yes—
538C42D4×D1112yes—
539C11#2252611yescharacteristic, complemented, Sylow
540C23—222no—
541C23—222no—
542C23—222no—
543C23—441no—
544C23—441no—
545C23—441no—
546C23—441no—
547C23C2×D4×D1111yescharacteristic
548Q8—444no—
549Q8—884no—
550D4—114no—
551D4—222no—
552D4—222no—
553D4—222no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—112no—
571C2×C4—112no—
572C2×C4—112no—
573C2×C4—112no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—221no—
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—884no—
593C2×C4—884no—
594C2×C4C22⋊C4×D1112yes—
595C2×C4C22⋊C4×D1112yes—
596C2×C4C22×C4×D1111yescharacteristic
597C2×C4C2×D4×D1111yescharacteristic
598C2×C4C2×Q8×D1111yescharacteristic
599C2×C4#6704011yescharacteristic
600C2×C4#41×D1111yescharacteristic
601C2×C4#6704311yescharacteristic
602C8—41no—
603C8—41no—
604C8—222no—
605C8—441no—
606C22—224no—
607C22—442no—
608C22—442no—
609C22—442no—
610C22—442no—
611C22—442no—
612C22—442no—
613C22C2×C22⋊C4×D1111yescharacteristic
614C22#1062316311yescharacteristic
615C22#1062316411yescharacteristic
616C22#1062329911yescharacteristic
617C22#1062329911yescharacteristic
618C22#1062330511yescharacteristic
619C22#1062330911yescharacteristic
620C4—22no—
621C4—22no—
622C4—42no—
623C4—42no—
624C4—42no—
625C4—81no—
626C4—222no—
627C4—222no—
628C4—222no—
629C4—222no—
630C4—442no—
631C4—881no—
632C4—881no—
633C4C4×Q8×D1111yescharacteristic
634C4#1062310311yescharacteristic
635C4#1062320811yescharacteristic
636C4#1062325811yescharacteristic
637C2—444no—
638C2#1307145011yescharacteristic
639C2#1307713111yescharacteristic
640C2#1307714011yescharacteristic
641C2#1308136711yescharacteristic
642C2#1308144111yescharacteristic
643C2#1308155911yescharacteristic
644C2#1308157411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1989C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1989D11
hypocenterC11#22526
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1989

Complements

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

NH ≅ G/Ntype
2. C2×#10622444C2semidirect
3. #13071574C2semidirect
4. #13069587C2semidirect
5. #13069583C2semidirect
6. #13069582C2semidirect
7. #13069570C2semidirect
8. #13069566C2semidirect
15. C11×#1989C2semidirect
18. #10623221C4semidirect
131. #66873Q8semidirect
225. #1989D11semidirect
539. C11#22526semidirect

Maximal subgroups

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

subgroupindex
C2×#106232212
C2×#106224442
#130715742
#130695872
#130695832
#130695822
#130695702
#130695662
#130686272
#130686252
#130686152
#130684402
C4×#668732
C11×#19892
#2252611