Finite Group Databasebeta

← #14771020

Subgroups — #14771020

Order 2816.

982 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622384C211yesmaximal, characteristic
2#13071489C211yesmaximal, characteristic, complemented
3#13071455C211yesmaximal, characteristic
4#13069316C211yesmaximal, characteristic, complemented
5#13069296C211yesmaximal, characteristic, complemented
6#13069245C211yesmaximal, characteristic, complemented
7#13068887C211yesmaximal, characteristic, complemented
8#13068867C211yesmaximal, characteristic, complemented
9#13068701C211yesmaximal, characteristic, complemented
10#13068650C211yesmaximal, characteristic, complemented
11#13068553C211yesmaximal, characteristic
12#13068449C211yesmaximal, characteristic, complemented
13#13068435C211yesmaximal, characteristic, complemented
14#13068398C211yesmaximal, characteristic, complemented
15C11×#1925C211yesmaximal, characteristic, complemented
16C22×#4341C2211yescharacteristic
17C22×#4313C2211yescharacteristic
18C2×C4⋊C4×D11C2211yescharacteristic
19C2×#66940C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C11×#390C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26#10622834C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622600C2211yescharacteristic
35#10622600C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622586C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40#10622570—21no—
41#10622570—21no—
42#10622555—21no—
43C22⋊C4×Dic11—21no—
44C4×(C2×D11)⋊C4—21no—
45C4×(C2×D11)⋊C4C2211yescharacteristic
46#10622546—21no—
47#10622541C2211yescharacteristic
48C2×#66867C2211yescharacteristic
49#10622384C418yescomplemented
50#10622280—21no—
51#10622265—21no—
52C11×#340C2211yescharacteristic
53C11×#336C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C23×Dic11—21no—
63C2×#4341—22no—
64C2×#4341—22no—
65C2×#4341—22no—
66C2×#4341—41no—
67C2×#4341—41no—
68C2×#4341C2×C414yes—
69C22×C4×D11—21no—
70C22×C4×D11C2311yescharacteristic
71C22×Dic22C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4D411yescharacteristic
86C2×(C2×D11)⋊C4D411yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
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×Dic11—21no—
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C2×#4313—41no—
102C2×#4313—41no—
103C2×#4313C2×C414yes—
104C4⋊C4×D11—22no—
105C4⋊C4×D11C2×C414yes—
106#66940—22no—
107#66940—41no—
108C4×Dic22—22no—
109C4×Dic22—41no—
110C11×#107—41no—
111C11×#102—41no—
112C11×#102C2×C414yes—
113C11×#95—21no—
114#66896—41no—
115#66896C2×C414yes—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95D411yescharacteristic
122C11⋊#95D411yescharacteristic
123(C2×D11)⋊C8—22no—
124#66881—41no—
125#66880—22no—
126#66880C2×C414yes—
127C8×Dic11—41no—
128#66874—22no—
129#66874C2×C414yes—
130#66867—41no—
131#22579—111nomaximal, Sylow
132C24×C11—21no—
133C23×D11C2×D411yescharacteristic
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11C22×C412yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C2×C22⋊D11—24no—
147C2×C22⋊D11—42no—
148C2×C22⋊D11—42no—
149C22×Dic11—24no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—42no—
155C22×Dic11—42no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159#4341—28no—
160#4341—44no—
161#4341—44no—
162#4341—44no—
163C2×C4×D11—24no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—81no—
169C2×C4×D11—81no—
170C2×C4×D11C22×C412yes—
171C2×C4×D11#4112yes—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22C22×C412yes—
176C2×Dic22#4112yes—
177C2×Dic22#4112yes—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11C22×C412yes—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4C22×C412yes—
190C11×C22⋊C4—42no—
191C11×C22⋊C4—81no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—81no—
195C22⋊Dic11—42no—
196C22⋊Dic11—81no—
197(C2×D11)⋊C4—22no—
198(C2×D11)⋊C4—41no—
199(C2×D11)⋊C4—42no—
200(C2×D11)⋊C4—81no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11C22×C412yes—
207Dic11⋊C4—24no—
208Dic11⋊C4—42no—
209Dic11⋊C4—42no—
210Dic11⋊C4—81no—
211Dic11⋊C4—81no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—42no—
215C4×Dic11—42no—
216C4×Dic11—81no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8C22×C412yes—
223#4313—44no—
224C2×#417—111no—
225#2345—111no—
226#2341—111no—
227#1936—111no—
228#1934—111no—
229#1926—111no—
230#1925D1111yescharacteristic, complemented
231#1865—111no—
232#1863—111no—
233#1823—111no—
234#1809—111no—
235#1788—111no—
236#1763—111no—
237C4×#103—111no—
238#1753—111no—
239C23×C11—22no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11C22×D411yescharacteristic
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—21no—
250C22×D11—21no—
251C22×D11—21no—
252C22×D11—21no—
253C22×D11C4×D412yes—
254D4×C11—22no—
255D4×C11—22no—
256D4×C11—41no—
257D4×C11—41no—
258C2×C4×C11—22no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11C23×C411yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11H(5,𝔽2)11yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C22⋊D11—48no—
280C2×Dic11—22no—
281C2×Dic11—21no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—22no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—48no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11C4×D412yes—
301C2×Dic11#13712yes—
302C4×D11—22no—
303C4×D11—22no—
304C4×D11—22no—
305C4×D11—22no—
306C4×D11—84no—
307Dic22—22no—
308Dic22—22no—
309Dic22—22no—
310Dic22#11714yes—
311C8×C11—22no—
312C8×C11—41no—
313C11⋊C8—22no—
314C11⋊C8—41no—
315C22×#41—111no—
316C22×M16—111no—
317C2×C4×Q8—111no—
318C2×C4×Q8—111no—
319C22×C4⋊C4—111no—
320C2×#107C2×D1111yescharacteristic
321C2×#106—111no—
322#417—118no—
323C2×#103—111no—
324C2×#103—111no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#102—111no—
328C2×#102—111no—
329C2×#102C2×D1111yescharacteristic
330C2×#102C2×D1111yescharacteristic
331C2×C22⋊C8—111no—
332C2×#97—111no—
333C2×C4×C8—111no—
334#390—111no—
335#390—221no—
336#390—221no—
337#390C2×D1111yescharacteristic
338#389—111no—
339#389—111no—
340#387—221no—
341#387—221no—
342#380—111no—
343#380—111no—
344#380—221no—
345#380—221no—
346C4×C4⋊C4—111no—
347C4×C4⋊C4C2×D1111yescharacteristic
348C4×C22⋊C4—111no—
349C4×C22⋊C4—221no—
350C4×C22⋊C4—221no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#340—111no—
356#340C2×D1111yescharacteristic
357#336—111no—
358#336C2×D1111yescharacteristic
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—42no—
362C22×C11—81no—
363C22×C11—81no—
364C22×C11—81no—
365C22×C11—81no—
366C22×C11C2×C4×D411yescharacteristic
367C22×C11#54611yescharacteristic
368C22×C11#54611yescharacteristic
369C22×C11C2×#13711yescharacteristic
370C22×C11#57511yescharacteristic
371C22×C11#57611yescharacteristic
372C22×C11#57711yescharacteristic
373C2×D11—22no—
374C2×D11—22no—
375C2×D11—22no—
376C2×D11—41no—
377C2×D11—41no—
378C2×D11—41no—
379C2×D11—41no—
380C4×C11—41no—
381C4×C11—42no—
382C4×C11—41no—
383C4×C11—81no—
384C4×C11—81no—
385C4×C11C2×#11711yescharacteristic
386C4×C11#51811yescharacteristic
387C4×C11#55111yescharacteristic
388C4×C11#55111yescharacteristic
389Dic11—24no—
390Dic11—22no—
391Dic11—22no—
392Dic11—42no—
393Dic11—41no—
394Dic11—81no—
395Dic11—81no—
396C2×#41—114no—
397C2×#41—222no—
398C2×#41—222no—
399C2×#41—222no—
400C2×#41—441no—
401C2×#41—441no—
402C22×Q8—111no—
403C22×D4—221no—
404C22×D4C22×D1111yescharacteristic
405C23×C4—111no—
406C23×C4—221no—
407C23×C4—221no—
408C2×M16—114no—
409C2×M16—441no—
410C2×M16—441no—
411C22×C8—111no—
412C22×C8—111no—
413C22×C8C22×D1111yescharacteristic
414C22×C8C22×D1111yescharacteristic
415C4×Q8—222no—
416C4×Q8—222no—
417C4×Q8—441no—
418C4×Q8—441no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—114no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—222no—
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—21no—
434C2×C22⋊C4—111no—
435C2×C22⋊C4—111no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C42—21no—
441C2×C42—111no—
442C2×C42—221no—
443C2×C42—221no—
444C2×C42—221no—
445C2×C42C22×D1111yescharacteristic
446#107—41no—
447#106—441no—
448#103—114no—
449#103—114no—
450#103—222no—
451#103—222no—
452#102—41no—
453#102—114no—
454#102—441no—
455#102C4×D1114yes—
456C22⋊C8—222no—
457#97—441no—
458C4×C8—441no—
459#95—21no—
460#95—111no—
461#95—111no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95—221no—
466#95—221no—
467C2×C11—82no—
468C2×C11#234211yescharacteristic
469C2×C11C4×#13711yescharacteristic
470C2×C11#294611yescharacteristic
471C2×C11#330911yescharacteristic
472C2×C11#331611yescharacteristic
473C2×C11#332611yescharacteristic
474C2×C11#333311yescharacteristic
475D11—42no—
476C24—21no—
477C24—111no—
478#41—228no—
479#41—444no—
480#41—444no—
481#41—444no—
482C2×Q8—112no—
483C2×Q8—112no—
484C2×Q8—112no—
485C2×Q8—221no—
486C2×Q8—221no—
487C2×Q8—221no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—224no—
494C2×D4—442no—
495C2×D4—442no—
496C2×D4C2×C4×D1112yes—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—111no—
501C22×C4—111no—
502C22×C4—112no—
503C22×C4—112no—
504C22×C4—111no—
505C22×C4—224no—
506C22×C4—224no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—442no—
516C22×C4—442no—
517C22×C4—881no—
518C22×C4—881no—
519C22×C4D4×D1111yescharacteristic
520C22×C4D4×D1111yescharacteristic
521C22×C4C23×D1111yescharacteristic
522M16—444no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—112no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8C2×C4×D1112yes—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—112no—
541C4⋊C4—224no—
542C4⋊C4—221no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—442no—
548C4⋊C4—442no—
549C4⋊C4—881no—
550C4⋊C4—881no—
551C4⋊C4C2×C4×D1112yes—
552C22⋊C4—42no—
553C22⋊C4—81no—
554C22⋊C4—222no—
555C22⋊C4—441no—
556C22⋊C4—442no—
557C22⋊C4—442no—
558C22⋊C4—881no—
559C22⋊C4—881no—
560C42—21no—
561C42—21no—
562C42—81no—
563C42—221no—
564C42—221no—
565C42—442no—
566C42—442no—
567C42—881no—
568C11#2257911yescharacteristic, complemented, Sylow
569C23—22no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—112no—
577C23—221no—
578C23—221no—
579C23—221no—
580C23—221no—
581C23—221no—
582C23—221no—
583C23C2×D4×D1111yescharacteristic
584Q8—114no—
585Q8—222no—
586Q8—222no—
587Q8—222no—
588D4—22no—
589D4—22no—
590D4—41no—
591D4—41no—
592D4—448no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—112no—
609C2×C4—112no—
610C2×C4—221no—
611C2×C4—222no—
612C2×C4—221no—
613C2×C4—222no—
614C2×C4—221no—
615C2×C4—222no—
616C2×C4—221no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—221no—
622C2×C4—221no—
623C2×C4—222no—
624C2×C4—221no—
625C2×C4—448no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—884no—
635C2×C4C22×C4×D1111yescharacteristic
636C2×C4#6703711yescharacteristic
637C2×C4#41×D1111yescharacteristic
638C2×C4#41×D1111yescharacteristic
639C2×C4#41×D1111yescharacteristic
640C2×C4#6704211yescharacteristic
641C8—22no—
642C8—41no—
643C8—222no—
644C8—441no—
645C22—42no—
646C22—42no—
647C22—42no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—222no—
653C22—222no—
654C22—222no—
655C22—441no—
656C22—441no—
657C22—441no—
658C22—441no—
659C22C4×D4×D1111yescharacteristic
660C22#1062314311yescharacteristic
661C22#1062318511yescharacteristic
662C22#1062328811yescharacteristic
663C22#1062330111yescharacteristic
664C22#1062330411yescharacteristic
665C22D11×#13711yescharacteristic
666C4—41no—
667C4—41no—
668C4—42no—
669C4—81no—
670C4—81no—
671C4—222no—
672C4—224no—
673C4—222no—
674C4—441no—
675C4—442no—
676C4—881no—
677C4—881no—
678C4D11×#11711yescharacteristic
679C4#1062307611yescharacteristic
680C4#1062321011yescharacteristic
681C4#1062323611yescharacteristic
682C2—82no—
683C2—442no—
684C2#1307146011yescharacteristic
685C2#1307743811yescharacteristic
686C2#1307744111yescharacteristic
687C2#1308062911yescharacteristic
688C2#1308073411yescharacteristic
689C2#1308086711yescharacteristic
690C2#1308095211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1925C2
socleC23×C11C22×D4
prime radicalC22×#4341C22
cosocleC22×C4×C11C24
hypercenter#1925D11
hypocenterC11#22579
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
2. #13071489C2semidirect
4. #13069316C2semidirect
5. #13069296C2semidirect
6. #13069245C2semidirect
7. #13068887C2semidirect
8. #13068867C2semidirect
9. #13068701C2semidirect
10. #13068650C2semidirect
12. #13068449C2semidirect
13. #13068435C2semidirect
14. #13068398C2semidirect
15. C11×#1925C2semidirect
49. #10622384C4semidirect
230. #1925D11semidirect
568. C11#22579semidirect

Maximal subgroups

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

subgroupindex
C2×#106223842
#130714892
#130714552
#130693162
#130692962
#130692452
#130688872
#130688672
#130687012
#130686502
#130685532
#130684492
#130684352
#130683982
C11×#19252
#2257911