Finite Group Databasebeta

← #14770637

Subgroups — #14770637

Order 2816.

1054 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623099C211yesmaximal, characteristic
2C2×#10622441C211yesmaximal, characteristic, complemented
3#13071575C211yesmaximal, characteristic, complemented
4#13069546C211yesmaximal, characteristic
5#13069545C211yesmaximal, characteristic
6#13069537C211yesmaximal, characteristic, complemented
7#13069434C211yesmaximal, characteristic, complemented
8#13069430C211yesmaximal, characteristic
9#13069424C211yesmaximal, characteristic
10#13068630C211yesmaximal, characteristic, complemented
11#13068625C211yesmaximal, characteristic
12#13068446C211yesmaximal, characteristic, complemented
13#13068440C211yesmaximal, characteristic
14#13068435C211yesmaximal, characteristic, complemented
15C11×#1803C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#67000C2211yescharacteristic
18C2×#66997C2211yescharacteristic
19#10623099—24no—
20#10623099C418yescomplemented
21C2×#66951—21no—
22C2×#66949—21no—
23C2×#66946C2211yescharacteristic
24C2×#66940C2211yescharacteristic
25C2×#66929—21no—
26C2×#66928C2211yescharacteristic
27C2×#66925—21no—
28C2×C4×Dic22C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C11×#384C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66885C2211yescharacteristic
36C2×#66885C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39C2×#66879C2211yescharacteristic
40C2×Dic11⋊C8C2211yescharacteristic
41C2×Dic11⋊C8C2211yescharacteristic
42C2×C8×Dic11C2211yescharacteristic
43#10622591—21no—
44#10622591—21no—
45#10622590C2211yescharacteristic
46#10622590C2211yescharacteristic
47C4⋊C4×Dic11—21no—
48C4⋊C4×Dic11C2211yescharacteristic
49C4⋊C4×Dic11C2211yescharacteristic
50#10622587—21no—
51C2×#66874C2211yescharacteristic
52C2×#66874C2211yescharacteristic
53C2×#66873C2211yescharacteristic
54C2×#66873C2211yescharacteristic
55C4×C4⋊Dic11C2211yescharacteristic
56C2×#66867C2211yescharacteristic
57#10622441—24no—
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×Dic22D411yescharacteristic
66C22×Dic22C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C4×Q8×C11—22no—
70C4×Q8×C11C2×C414yes—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79#67000—22no—
80#67000C2×C414yes—
81#66997—22no—
82#66997C2×C414yes—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×C4⋊Dic11D411yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4D411yescharacteristic
95C2×Dic11⋊C4D411yescharacteristic
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104#66951—28no—
105#66949—28no—
106#66946—22no—
107#66946C2×C414yes—
108#66940—22no—
109#66940C2×C414yes—
110#66929—28no—
111#66928—22no—
112#66928C2×C414yes—
113#66925—28no—
114C4×Dic22C2×C414yes—
115C4×Dic22D414yes—
116C11×C4⋊C8—22no—
117C11×#103—41no—
118C11×#103—41no—
119#66899—22no—
120#66899—22no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128#66885—22no—
129#66885—41no—
130#66880—22no—
131#66880—41no—
132#66879—22no—
133Dic11⋊C8—22no—
134Dic11⋊C8—22no—
135C8×Dic11—22no—
136#66874—22no—
137#66874—41no—
138#66873—22no—
139#66873—41no—
140#66867—22no—
141#22548—111nomaximal, Sylow
142C23×D11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11C22×C412yes—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44C22×C412yes—
169C2×C4×D11—24no—
170C2×C4×D11—42no—
171C2×C4×D11—42no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—41no—
178C2×Dic22—41no—
179C2×Dic22C22⋊C414yes—
180C2×Dic22C22×C412yes—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—42no—
194C11×C4⋊C4—81no—
195C11×C4⋊C4C22×C412yes—
196C42×C11—24no—
197C42×C11C22×C412yes—
198C42×C11C2×D412yes—
199(C2×D11)⋊C4—24no—
200(C2×D11)⋊C4—24no—
201(C2×D11)⋊C4—24no—
202(C2×D11)⋊C4—24no—
203(C2×D11)⋊C4—24no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11C22⋊C414yes—
208C4⋊Dic11#4112yes—
209Dic11⋊C4—24no—
210Dic11⋊C4—24no—
211Dic11⋊C4—24no—
212Dic11⋊C4C22⋊C414yes—
213Dic11⋊C4C22⋊C414yes—
214C4×Dic11—24no—
215C4×Dic11—42no—
216C4×Dic11—81no—
217C4×Dic11—81no—
218C4×Dic11C22×C412yes—
219C4×Dic11C22×C412yes—
220C4×Dic11C2×D412yes—
221C4×Dic11C2×D412yes—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8#4112yes—
228C2×#556—111no—
229C2×#446—111no—
230#2355—111no—
231#1983—111no—
232#1983—111no—
233#1981—111no—
234#1960—111no—
235#1959—111no—
236#1958—111no—
237#1805—111no—
238#1804—111no—
239#1803D1111yescharacteristic, complemented
240#1763—111no—
241#1762—111no—
242C4×#103—111no—
243C23×C11C22×D411yescharacteristic
244C22×D11—22no—
245C22×D11—41no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251Q8×C11—22no—
252Q8×C11—22no—
253Q8×C11—41no—
254Q8×C11—41no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
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×C11C2×C22⋊C412yes—
272C2×C4×C11C2×C22⋊C412yes—
273C2×C4×C11C23×C411yescharacteristic
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11H(5,𝔽2)11yescharacteristic
278C2×C4×C112−1+411yescharacteristic
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11C2×C22⋊C412yes—
297C2×Dic11C2×C22⋊C412yes—
298C2×Dic11C2×C22⋊C412yes—
299C2×Dic11C2×C22⋊C412yes—
300D44—22no—
301D44—22no—
302D44—41no—
303D44—41no—
304C4×D11—48no—
305Dic22—22no—
306Dic22—22no—
307Dic22—44no—
308Dic22—41no—
309Dic22—41no—
310C8×C11—41no—
311C8×C11—41no—
312C11⋊C8—22no—
313C11⋊C8—41no—
314#556—118no—
315#556—224no—
316C2×C4⋊Q8—111no—
317C2×#126—221no—
318C2×#126—221no—
319C2×#124—111no—
320C2×#124—111no—
321C2×C22⋊Q8—221no—
322C2×C4×Q8—111no—
323C2×C4×Q8—111no—
324C2×C4×Q8C2×D1111yescharacteristic
325C2×C4×D4—111no—
326C2×#117—221no—
327#446—224no—
328C2×C4⋊C8—111no—
329C2×C4⋊C8—111no—
330C2×C4⋊C8C2×D1111yescharacteristic
331C2×#103—111no—
332C2×#103—111no—
333C2×#103—111no—
334C2×#103—111no—
335C2×#103—111no—
336C2×#103—111no—
337C2×#103C2×D1111yescharacteristic
338C2×#103C2×D1111yescharacteristic
339C2×#102—111no—
340C2×#102—111no—
341C2×#102—111no—
342C2×#102—111no—
343C2×#97—111no—
344C2×#97—111no—
345C2×C4×C8—111no—
346#391—221no—
347#387—221no—
348#387—221no—
349#384C2×D1111yescharacteristic
350#382—111no—
351#382—111no—
352C4×C4⋊C4—111no—
353C4×C4⋊C4—111no—
354C4×C4⋊C4—111no—
355C4×C4⋊C4—221no—
356#340—111no—
357#340—111no—
358#340C2×D1111yescharacteristic
359#340C2×D1111yescharacteristic
360C22×C11C22×C22⋊C411yescharacteristic
361C22×C11#54811yescharacteristic
362C22×C11#55011yescharacteristic
363C22×C11#57511yescharacteristic
364C22×C11#57511yescharacteristic
365C22×C11#57711yescharacteristic
366C22×C11#57811yescharacteristic
367C2×D11—42no—
368C2×D11—42no—
369C2×D11—42no—
370C2×D11—81no—
371C2×D11—81no—
372C2×D11—81no—
373C2×D11—81no—
374C4×C11—22no—
375C4×C11—22no—
376C4×C11—42no—
377C4×C11—42no—
378C4×C11—81no—
379C4×C11—81no—
380C4×C11C4×#4111yescharacteristic
381C4×C11#52011yescharacteristic
382C4×C11#54811yescharacteristic
383C4×C11#55011yescharacteristic
384Dic11—22no—
385Dic11—22no—
386Dic11—22no—
387Dic11—22no—
388Dic11—42no—
389Dic11—42no—
390Dic11—81no—
391C22×Q8—111no—
392C22×Q8—111no—
393C22×Q8C22×D1111yescharacteristic
394C22×D4—111no—
395C23×C4—221no—
396C22×C8—111no—
397C22×C8—111no—
398C22×C8C22×D1111yescharacteristic
399C22×C8C22×D1111yescharacteristic
400C4⋊Q8—114no—
401C4⋊Q8—222no—
402#126—228no—
403#126—228no—
404#124—114no—
405#124—114no—
406#124—222no—
407#124—222no—
408C22⋊Q8—228no—
409C4×Q8—22no—
410C4×Q8—114no—
411C4×Q8—114no—
412C4×Q8—114no—
413C4×Q8—222no—
414C4×Q8C4×D1114yes—
415C4×D4—114no—
416C4×D4—222no—
417#117—228no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
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—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C42—21no—
438C2×C42—111no—
439C2×C42—111no—
440C2×C42—221no—
441C2×C42—221no—
442C2×C42—221no—
443C2×C42—221no—
444C2×C42C22×D1111yescharacteristic
445C4⋊C8—22no—
446C4⋊C8—222no—
447C4⋊C8—222no—
448#103—41no—
449#103—41no—
450#103—222no—
451#103—222no—
452#103—222no—
453#103—222no—
454#103—441no—
455#103—441no—
456#102—222no—
457#102—222no—
458#102—441no—
459#102—441no—
460#97—222no—
461#97—222no—
462C4×C8—222no—
463#95—221no—
464#95—221no—
465#95—221no—
466#95—221no—
467#95—221no—
468#95—221no—
469#95—221no—
470C2×C11#234111yescharacteristic
471C2×C11#289611yescharacteristic
472C2×C11#289811yescharacteristic
473C2×C11#337611yescharacteristic
474C2×C11#337711yescharacteristic
475C2×C11#340111yescharacteristic
476C2×C11#340211yescharacteristic
477D11—82no—
478C24—221no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—114no—
485C2×Q8—112no—
486C2×Q8—221no—
487C2×Q8—221no—
488C2×Q8—221no—
489C2×Q8—221no—
490C2×Q8—221no—
491C2×Q8—441no—
492C2×Q8—441no—
493C2×Q8C2×C4×D1112yes—
494C2×D4—112no—
495C2×D4—221no—
496C2×D4—221no—
497C2×D4—221no—
498C2×D4—221no—
499C2×D4—221no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—111no—
505C22×C4—111no—
506C22×C4—111no—
507C22×C4—111no—
508C22×C4—224no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—442no—
513C22×C4—442no—
514C22×C4D4×D1111yescharacteristic
515C22×C4D4×D1111yescharacteristic
516C22×C4C23×D1111yescharacteristic
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—112no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8—221no—
529C4⋊C4—24no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—42no—
536C4⋊C4—81no—
537C4⋊C4—114no—
538C4⋊C4—114no—
539C4⋊C4—114no—
540C4⋊C4—112no—
541C4⋊C4—224no—
542C4⋊C4—224no—
543C4⋊C4—224no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4C2×C4×D1112yes—
548C22⋊C4—224no—
549C22⋊C4—224no—
550C22⋊C4—224no—
551C22⋊C4—224no—
552C22⋊C4—224no—
553C42—24no—
554C42—112no—
555C42—112no—
556C42—112no—
557C42—112no—
558C42—224no—
559C42—442no—
560C42—881no—
561C42—881no—
562C42C2×C4×D1112yes—
563C42D4×D1112yes—
564C11#2254811yescharacteristic, complemented, Sylow
565C23—222no—
566C23—441no—
567C23—441no—
568C23—441no—
569C23—441no—
570C23—441no—
571C23—441no—
572C23C2×D4×D1111yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
577Q8—222no—
578Q8—222no—
579Q8—444no—
580Q8—441no—
581Q8—441no—
582D4—222no—
583D4—222no—
584D4—441no—
585D4—441no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—112no—
603C2×C4—112no—
604C2×C4—112no—
605C2×C4—112no—
606C2×C4—221no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—221no—
610C2×C4—221no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—221no—
614C2×C4—222no—
615C2×C4—222no—
616C2×C4—448no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4C22⋊C4×D1112yes—
625C2×C4C22⋊C4×D1112yes—
626C2×C4C22×C4×D1111yescharacteristic
627C2×C4C2×D4×D1111yescharacteristic
628C2×C4#6703711yescharacteristic
629C2×C4#6704011yescharacteristic
630C2×C4#41×D1111yescharacteristic
631C2×C4#41×D1111yescharacteristic
632C8—41no—
633C8—41no—
634C8—222no—
635C8—441no—
636C22—442no—
637C22—442no—
638C22—442no—
639C22—881no—
640C22—881no—
641C22—881no—
642C22—881no—
643C22C2×C22⋊C4×D1111yescharacteristic
644C22#1062313011yescharacteristic
645C22#1062316411yescharacteristic
646C22#1062329311yescharacteristic
647C22#1062329711yescharacteristic
648C22#1062330411yescharacteristic
649C22#1062330811yescharacteristic
650C4—22no—
651C4—22no—
652C4—42no—
653C4—42no—
654C4—81no—
655C4—81no—
656C4—222no—
657C4—222no—
658C4—222no—
659C4—222no—
660C4—442no—
661C4—442no—
662C4—881no—
663C4#1062303511yescharacteristic
664C4#1062305311yescharacteristic
665C4#1062313011yescharacteristic
666C4#1062316411yescharacteristic
667C2—882no—
668C2#1307145311yescharacteristic
669C2#1307713211yescharacteristic
670C2#1307714411yescharacteristic
671C2#1308145011yescharacteristic
672C2#1308146511yescharacteristic
673C2#1308167511yescharacteristic
674C2#1308169011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1803C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1803D11
hypocenterC11#22548
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
2. C2×#10622441C2semidirect
3. #13071575C2semidirect
6. #13069537C2semidirect
7. #13069434C2semidirect
10. #13068630C2semidirect
12. #13068446C2semidirect
14. #13068435C2semidirect
15. C11×#1803C2semidirect
20. #10623099C4semidirect
239. #1803D11semidirect
564. C11#22548semidirect

Maximal subgroups

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

subgroupindex
C2×#106230992
C2×#106224412
#130715752
#130695462
#130695452
#130695372
#130694342
#130694302
#130694242
#130686302
#130686252
#130684462
#130684402
#130684352
C11×#18032
#2254811