Finite Group Databasebeta

← #14753869

Subgroups — #14753869

Order 2816.

1222 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623047C211yesmaximal, characteristic
2C2×#10622333C211yesmaximal, characteristic
3#13071223C211yesmaximal, characteristic
4#13068711C211yesmaximal, characteristic
5#13068630C211yesmaximal, characteristic, complemented
6#13068630C211yesmaximal, characteristic, complemented
7#13068620C211yesmaximal, characteristic, complemented
8#13068620C211yesmaximal, characteristic, complemented
9#13068552C211yesmaximal, characteristic
10#13068550C211yesmaximal, characteristic
11#13068445C211yesmaximal, characteristic, complemented
12#13068445C211yesmaximal, characteristic, complemented
13#13068435C211yesmaximal, characteristic, complemented
14#13068435C211yesmaximal, characteristic, complemented
15C11×#1825C211yesmaximal, characteristic
16C23×Dic22C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19#10623047—24no—
20#10623047C418yescomplemented
21C2×#66940C2211yescharacteristic
22C2×#66940C2211yescharacteristic
23C2×#66940C2211yescharacteristic
24C2×#66940C2211yescharacteristic
25C2×#66930—21no—
26C2×#66930—21no—
27C2×C4×Dic22—21no—
28C2×C4×Dic22—21no—
29C2×C11×C22⋊C8C2211yescharacteristic
30C11×#380C2211yescharacteristic
31#10622825C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66879C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40C2×C8×Dic11C2211yescharacteristic
41#10622590C2211yescharacteristic
42#10622589C2211yescharacteristic
43C4⋊C4×Dic11C2211yescharacteristic
44C4⋊C4×Dic11C2211yescharacteristic
45C2×#66874C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66874C2211yescharacteristic
49#10622558—21no—
50#10622557—21no—
51#10622333—24no—
52#10622267—21no—
53#10622266—21no—
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11—21no—
64C22×Dic22—21no—
65C22×Dic22—22no—
66C22×Dic22—22no—
67C22×Dic22—22no—
68C22×Dic22—22no—
69C22×Dic22—22no—
70C22×Dic22C2×C414yes—
71C22×Dic22C2311yescharacteristic
72C22×Dic22C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C11×#117—22no—
76C11×#117C2×C414yes—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C42×C11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11D411yescharacteristic
86C2×C22⋊Dic11D411yescharacteristic
87#66979C2×C414yes—
88#66979D414yes—
89C2×C4⋊Dic11D411yescharacteristic
90C2×C4⋊Dic11D411yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109#66940—22no—
110#66940—22no—
111#66940—22no—
112#66940—22no—
113#66940C2×C414yes—
114#66940C2×C414yes—
115#66940C2×C414yes—
116#66940C2×C414yes—
117#66930—28no—
118#66930—28no—
119C4×Dic22—28no—
120C4×Dic22—28no—
121C11×C22⋊C8—22no—
122C11×#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C22⋊(C11⋊C8)—22no—
129#66880—22no—
130#66880—22no—
131#66880—22no—
132#66880—22no—
133#66879—22no—
134Dic11⋊C8—22no—
135Dic11⋊C8—22no—
136C8×Dic11—22no—
137#66874—22no—
138#66874—22no—
139#66874—22no—
140#66874—22no—
141#20745—111nomaximal, Sylow
142C24×C11C2×D411yescharacteristic
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11C22×C412yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2411yescharacteristic
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—24no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C2×Dic22—24no—
167C2×Dic22—24no—
168C2×Dic22—28no—
169C2×Dic22—28no—
170C2×Dic22—28no—
171C2×Dic22—28no—
172C2×Dic22—24no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C2×Dic22C22×C412yes—
180C2×Dic22C22×C412yes—
181C2×Dic22#4112yes—
182C2×Dic22#4112yes—
183C2×Dic22#4112yes—
184C2×Dic22#4112yes—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4C22×C412yes—
198C11×C4⋊C4C22×C412yes—
199C11×C22⋊C4—24no—
200C11×C22⋊C4—81no—
201C42×C11—24no—
202C22⋊Dic11—81no—
203C22⋊Dic11C22⋊C414yes—
204C22⋊Dic11C22⋊C414yes—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11C22⋊C414yes—
210C4⋊Dic11C22⋊C414yes—
211Dic11⋊C4—24no—
212Dic11⋊C4—24no—
213Dic11⋊C4—24no—
214Dic11⋊C4—24no—
215Dic11⋊C4—81no—
216Dic11⋊C4—81no—
217C4×Dic11—24no—
218C4×Dic11—24no—
219C4×Dic11—24no—
220C4×Dic11—24no—
221C4×Dic11—81no—
222C4×Dic11—81no—
223C4×Dic11C22×C412yes—
224C4×Dic11C22×C412yes—
225C4×Dic11C2×D412yes—
226C4×Dic11C2×D412yes—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×#519—111no—
234C2×#433—111no—
235#2314—111no—
236#1825—111no—
237#1825D1111yescharacteristic
238#1805—111no—
239#1805—111no—
240#1803—111no—
241#1803—111no—
242#1787—111no—
243#1787—111no—
244#1763—111no—
245#1763—111no—
246C4×#103—111no—
247C4×#103—111no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11C2×C22⋊C412yes—
255C23×C11C22×D411yescharacteristic
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
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×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11C2×C22⋊C412yes—
275C2×C4×C11C23×C411yescharacteristic
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×Dic11—216no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—22no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11C2×C22⋊C412yes—
303C2×Dic11C2×C22⋊C412yes—
304C2×Dic11C2×C22⋊C412yes—
305C2×Dic11C2×C22⋊C412yes—
306Dic22—216no—
307Dic22—22no—
308Dic22—22no—
309Dic22—22no—
310Dic22—22no—
311Dic22—22no—
312Dic22—22no—
313Dic22#11714yes—
314Dic22#11714yes—
315C8×C11—41no—
316C8×C11—41no—
317C11⋊C8—41no—
318C11⋊C8—41no—
319C23×Q8—111no—
320#519—118no—
321#519—224no—
322C2×C4×Q8—111no—
323C2×C4×Q8—111no—
324C2×C4×Q8—111no—
325C2×C4×Q8—111no—
326C2×C4×Q8—221no—
327C2×C4×Q8—221no—
328C2×#117—111no—
329C2×#117—221no—
330C2×#117—221no—
331C2×#117C2×D1111yescharacteristic
332#433—224no—
333C2×C4⋊C8—111no—
334C2×C4⋊C8—111no—
335C2×#103—111no—
336C2×#103—111no—
337C2×#103—111no—
338C2×#103—111no—
339C2×#103—111no—
340C2×#103—111no—
341C2×#103—111no—
342C2×#103—111no—
343C2×C22⋊C8—111no—
344C2×C22⋊C8C2×D1111yescharacteristic
345C2×#97—111no—
346C2×C4×C8—111no—
347#388—221no—
348#388—221no—
349#387—221no—
350#387—221no—
351#384—111no—
352#382—111no—
353#380—111no—
354#380C2×D1111yescharacteristic
355C4×C4⋊C4—111no—
356C4×C4⋊C4—111no—
357#340—111no—
358#340—111no—
359#340—111no—
360#340—111no—
361#340C2×D1111yescharacteristic
362#340C2×D1111yescharacteristic
363#340C2×D1111yescharacteristic
364#340C2×D1111yescharacteristic
365C22×C11—22no—
366C22×C11—22no—
367C22×C11—22no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11—41no—
371C22×C11—41no—
372C22×C11C22×C22⋊C411yescharacteristic
373C22×C11#52511yescharacteristic
374C22×C11#52511yescharacteristic
375C22×C11#57711yescharacteristic
376C22×C11#57711yescharacteristic
377C22×C11#57811yescharacteristic
378C22×C11#57811yescharacteristic
379C4×C11—22no—
380C4×C11—42no—
381C4×C11—42no—
382C4×C11—81no—
383C4×C11—81no—
384C4×C11C2×#11711yescharacteristic
385C4×C11C2×#11711yescharacteristic
386C4×C11#52511yescharacteristic
387C4×C11#52511yescharacteristic
388Dic11—22no—
389Dic11—22no—
390Dic11—22no—
391Dic11—22no—
392Dic11—24no—
393Dic11—24no—
394Dic11—81no—
395Dic11—81no—
396C22×Q8—114no—
397C22×Q8—111no—
398C22×Q8—111no—
399C22×Q8—222no—
400C22×Q8—222no—
401C22×Q8—222no—
402C22×Q8—222no—
403C22×Q8—221no—
404C22×Q8—222no—
405C23×C4—221no—
406C23×C4C22×D1111yescharacteristic
407C22×C8—111no—
408C22×C8—111no—
409C22×C8C22×D1111yescharacteristic
410C22×C8C22×D1111yescharacteristic
411C4×Q8—114no—
412C4×Q8—114no—
413C4×Q8—114no—
414C4×Q8—114no—
415C4×Q8—228no—
416C4×Q8—228no—
417C4×Q8—222no—
418C4×Q8—222no—
419C4×Q8—222no—
420C4×Q8—222no—
421#117—22no—
422#117—114no—
423#117—114no—
424#117—228no—
425#117—228no—
426#117C4×D1114yes—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4—221no—
437C2×C4⋊C4C22×D1111yescharacteristic
438C2×C4⋊C4C22×D1111yescharacteristic
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—111no—
444C2×C22⋊C4—111no—
445C2×C22⋊C4—221no—
446C2×C42—21no—
447C2×C42—111no—
448C2×C42—111no—
449C2×C42—221no—
450C2×C42—221no—
451C2×C42—221no—
452C2×C42—221no—
453C2×C42—221no—
454C2×C42—221no—
455C4⋊C8—222no—
456C4⋊C8—222no—
457#103—222no—
458#103—222no—
459#103—222no—
460#103—222no—
461#103—222no—
462#103—222no—
463#103—222no—
464#103—222no—
465C22⋊C8—22no—
466C22⋊C8—222no—
467#97—222no—
468C4×C8—222no—
469#95—21no—
470#95—221no—
471#95—221no—
472#95—221no—
473#95—221no—
474#95—221no—
475C2×C11—42no—
476C2×C11#228011yescharacteristic
477C2×C11#289811yescharacteristic
478C2×C11#289811yescharacteristic
479C2×C11#312111yescharacteristic
480C2×C11#312111yescharacteristic
481C2×C11#312611yescharacteristic
482C2×C11#312711yescharacteristic
483C24D4×D1111yescharacteristic
484C2×Q8—112no—
485C2×Q8—112no—
486C2×Q8—112no—
487C2×Q8—112no—
488C2×Q8—112no—
489C2×Q8—112no—
490C2×Q8—228no—
491C2×Q8—228no—
492C2×Q8—224no—
493C2×Q8—224no—
494C2×Q8—228no—
495C2×Q8—228no—
496C2×Q8—224no—
497C2×Q8—221no—
498C2×Q8—221no—
499C2×Q8—221no—
500C2×Q8—221no—
501C2×Q8—221no—
502C2×Q8—221no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—111no—
512C22×C4—111no—
513C22×C4—111no—
514C22×C4—111no—
515C22×C4—224no—
516C22×C4—224no—
517C22×C4—224no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4C2×C4×D1112yes—
523C22×C4D4×D1111yescharacteristic
524C22×C4D4×D1112yes—
525C22×C4C23×D1111yescharacteristic
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8—221no—
536C2×C8—221no—
537C2×C8—221no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—114no—
545C4⋊C4—114no—
546C4⋊C4—224no—
547C4⋊C4—224no—
548C4⋊C4—224no—
549C4⋊C4—224no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—881no—
555C4⋊C4—881no—
556C4⋊C4C2×C4×D1112yes—
557C4⋊C4C2×C4×D1112yes—
558C22⋊C4—24no—
559C22⋊C4—81no—
560C22⋊C4—114no—
561C22⋊C4—114no—
562C22⋊C4—881no—
563C42—24no—
564C42—112no—
565C42—112no—
566C42—112no—
567C42—112no—
568C42—224no—
569C42—224no—
570C42—224no—
571C42—224no—
572C42—881no—
573C42—881no—
574C11#2074511yescharacteristic, complemented, Sylow
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23C22⋊C4×D1112yes—
582C23C2×D4×D1111yescharacteristic
583Q8—114no—
584Q8—114no—
585Q8—2216no—
586Q8—222no—
587Q8—222no—
588Q8—222no—
589Q8—222no—
590Q8—222no—
591Q8—222no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
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—41no—
609C2×C4—41no—
610C2×C4—112no—
611C2×C4—112no—
612C2×C4—112no—
613C2×C4—112no—
614C2×C4—2216no—
615C2×C4—222no—
616C2×C4—222no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—221no—
622C2×C4—221no—
623C2×C4—221no—
624C2×C4—221no—
625C2×C4—222no—
626C2×C4—222no—
627C2×C4—222no—
628C2×C4—222no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4C22⋊C4×D1112yes—
636C2×C4C22×C4×D1111yescharacteristic
637C2×C4C2×D4×D1111yescharacteristic
638C2×C4#41×D1111yescharacteristic
639C2×C4#41×D1111yescharacteristic
640C2×C4#41×D1111yescharacteristic
641C2×C4#41×D1111yescharacteristic
642C8—41no—
643C8—41no—
644C8—441no—
645C8—441no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22C2×C22⋊C4×D1111yescharacteristic
654C22#1062318711yescharacteristic
655C22#1062318711yescharacteristic
656C22#1062330111yescharacteristic
657C22#1062330211yescharacteristic
658C22#1062330611yescharacteristic
659C22#1062331011yescharacteristic
660C4—22no—
661C4—42no—
662C4—42no—
663C4—81no—
664C4—81no—
665C4—224no—
666C4—224no—
667C4—222no—
668C4—222no—
669C4—222no—
670C4—222no—
671C4—881no—
672C4—881no—
673C4D11×#11711yescharacteristic
674C4D11×#11711yescharacteristic
675C4#1062318711yescharacteristic
676C4#1062318711yescharacteristic
677C2—42no—
678C2#1307099611yescharacteristic
679C2#1307714511yescharacteristic
680C2#1307714711yescharacteristic
681C2#1307884011yescharacteristic
682C2#1307884811yescharacteristic
683C2#1307890311yescharacteristic
684C2#1307891211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1825C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1825D11
hypocenterC11#20745
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1825

Complements

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

NH ≅ G/Ntype
5. #13068630C2semidirect
6. #13068630C2semidirect
7. #13068620C2semidirect
8. #13068620C2semidirect
11. #13068445C2semidirect
12. #13068445C2semidirect
13. #13068435C2semidirect
14. #13068435C2semidirect
20. #10623047C4semidirect
574. C11#20745semidirect

Maximal subgroups

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

subgroupindex
C2×#106230472
C2×#106223332
#130712232
#130687112
#130686302
#130686202
#130685522
#130685502
#130684452
#130684352
C11×#18252
#2074511