Finite Group Databasebeta

← #14753872

Subgroups — #14753872

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×#10623103C211yesmaximal, characteristic
2C2×#10622322C211yesmaximal, characteristic
3#13071221C211yesmaximal, characteristic
4#13068710C211yesmaximal, characteristic
5#13068709C211yesmaximal, characteristic
6#13068630C211yesmaximal, characteristic, complemented
7#13068629C211yesmaximal, characteristic, complemented
8#13068620C211yesmaximal, characteristic, complemented
9#13068619C211yesmaximal, characteristic, complemented
10#13068549C211yesmaximal, characteristic
11#13068549C211yesmaximal, characteristic
12#13068447C211yesmaximal, characteristic, complemented
13C4×#66874C211yesmaximal, characteristic, complemented
14C4×#66899C211yesmaximal, characteristic, complemented
15C11×#1763C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19#10623103—24no—
20#10623103C418yescomplemented
21C2×#66945—21no—
22C2×#66945C2211yescharacteristic
23C2×#66940—21no—
24C2×#66940C2211yescharacteristic
25C2×#66925—21no—
26C2×#66925C2211yescharacteristic
27C2×C4×Dic22—21no—
28C2×C4×Dic22C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#97C2211yescharacteristic
32C4×C11×C4⋊C4C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40C2×Dic11⋊C8C2211yescharacteristic
41#10622600C2211yescharacteristic
42#10622600C2211yescharacteristic
43#10622590C2211yescharacteristic
44#10622589C2211yescharacteristic
45C2×#66874C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47#10622553—21no—
48C4×C4⋊Dic11C2211yescharacteristic
49#10622546—21no—
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622322—24no—
52#10622282—21no—
53#10622265—21no—
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C2×Q8×D11—22no—
64C2×Q8×D11—22no—
65C2×Q8×D11—22no—
66C2×Q8×D11—22no—
67C2×Q8×D11—22no—
68C2×Q8×D11C2×C414yes—
69C22×C4×D11—21no—
70C22×C4×D11C2311yescharacteristic
71C22×Dic22—21no—
72C22×Dic22C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C4×Q8×C11—22no—
76C4×Q8×C11C2×C414yes—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C42×C11—21no—
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84Q8×Dic11—22no—
85Q8×Dic11C2×C414yes—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4D411yescharacteristic
90C2×(C2×D11)⋊C4D411yescharacteristic
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4D411yescharacteristic
100C2×Dic11⋊C4D411yescharacteristic
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109#66945—22no—
110#66945—28no—
111#66945C2×C414yes—
112#66940—28no—
113#66940—22no—
114#66940C2×C414yes—
115#66925—28no—
116#66925C2×C414yes—
117#66925D414yes—
118C4×Dic22—22no—
119C4×Dic22—28no—
120C4×Dic22C2×C414yes—
121C11×#103—22no—
122C11×#103—22no—
123C11×#97—22no—
124C11×#95—21no—
125#66899—22no—
126#66899—22no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132(C2×D11)⋊C8—22no—
133(C2×D11)⋊C8—22no—
134#66880—22no—
135#66880—22no—
136Dic11⋊C8—22no—
137Dic11⋊C8—22no—
138#66874—22no—
139#66874—22no—
140C4×C11⋊C8—22no—
141#20745—111nomaximal, Sylow
142C23×D11C2×D411yescharacteristic
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11C22×C412yes—
147C2×Q8×C11#4112yes—
148C2×Q8×C11#4112yes—
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×Dic11—21no—
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163Q8×D11—28no—
164Q8×D11—28no—
165Q8×D11—28no—
166Q8×D11—28no—
167C2×C4×D11—24no—
168C2×C4×D11—24no—
169C2×C4×D11—24no—
170C2×C4×D11—21no—
171C2×C4×D11—21no—
172C2×C4×D11—21no—
173C2×C4×D11—21no—
174C2×C4×D11C22×C412yes—
175C2×C4×D11C2×D412yes—
176C2×Dic22—24no—
177C2×Dic22—24no—
178C2×Dic22—24no—
179C2×Dic22—21no—
180C2×Dic22—21no—
181C2×Dic22—21no—
182C2×Dic22C22×C412yes—
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—24no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4C22×C412yes—
198C42×C11—24no—
199C42×C11—81no—
200C42×C11C22×C412yes—
201C42×C11C2×D412yes—
202(C2×D11)⋊C4—24no—
203(C2×D11)⋊C4—81no—
204(C2×D11)⋊C4—81no—
205(C2×D11)⋊C4C22⋊C414yes—
206(C2×D11)⋊C4C22⋊C414yes—
207C4⋊Dic11—24no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11C22×C412yes—
214Dic11⋊C4—24no—
215Dic11⋊C4—24no—
216Dic11⋊C4—81no—
217Dic11⋊C4—81no—
218Dic11⋊C4C22⋊C414yes—
219Dic11⋊C4C22⋊C414yes—
220C4×Dic11—24no—
221C4×Dic11—24no—
222C4×Dic11—24no—
223C4×Dic11—24no—
224C4×Dic11—81no—
225C4×Dic11C22×C412yes—
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#1825—111no—
238#1805—111no—
239#1805—111no—
240#1803—111no—
241#1803—111no—
242#1787—111no—
243#1787—111no—
244#1763—111no—
245#1763D1111yescharacteristic, complemented
246C4×#103—111no—
247C4×#103—111no—
248C23×C11C22×D411yescharacteristic
249C22×D11—21no—
250C22×D11—21no—
251C22×D11—21no—
252C22×D11—21no—
253C22×D11—21no—
254C22×D11—21no—
255C22×D11C2×C22⋊C412yes—
256Q8×C11—22no—
257Q8×C11—22no—
258Q8×C11—22no—
259Q8×C11#11714yes—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—22no—
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×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11C2×C22⋊C412yes—
277C2×C4×C11C2×C22⋊C412yes—
278C2×C4×C11C23×C411yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×Dic11—22no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—22no—
294C2×Dic11—41no—
295C2×Dic11—41no—
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—
305C4×D11—216no—
306C4×D11—22no—
307C4×D11—22no—
308C4×D11—22no—
309C4×D11—22no—
310Dic22—216no—
311Dic22—22no—
312Dic22—22no—
313Dic22—22no—
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—221no—
326C2×C4×Q8—221no—
327C2×C4×Q8C2×D1111yescharacteristic
328C2×#117—111no—
329C2×#117—111no—
330C2×#117—221no—
331C2×#117—221no—
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×#103C2×D1111yescharacteristic
342C2×#103C2×D1111yescharacteristic
343C2×C22⋊C8—111no—
344C2×C22⋊C8—111no—
345C2×#97C2×D1111yescharacteristic
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#380—111no—
355C4×C4⋊C4—111no—
356C4×C4⋊C4C2×D1111yescharacteristic
357#340—111no—
358#340—111no—
359#340—111no—
360#340—111no—
361#340—111no—
362#340—111no—
363#340C2×D1111yescharacteristic
364#340C2×D1111yescharacteristic
365C22×C11C22×C22⋊C411yescharacteristic
366C22×C11#52511yescharacteristic
367C22×C11#52511yescharacteristic
368C22×C11#57711yescharacteristic
369C22×C11#57711yescharacteristic
370C22×C11#57811yescharacteristic
371C22×C11#57811yescharacteristic
372C2×D11—22no—
373C2×D11—22no—
374C2×D11—22no—
375C2×D11—41no—
376C2×D11—41no—
377C2×D11—41no—
378C2×D11—41no—
379C4×C11—22no—
380C4×C11—22no—
381C4×C11—24no—
382C4×C11—42no—
383C4×C11—81no—
384C4×C11—81no—
385C4×C11C2×#11711yescharacteristic
386C4×C11C2×#11711yescharacteristic
387C4×C11#52511yescharacteristic
388C4×C11#52511yescharacteristic
389Dic11—22no—
390Dic11—22no—
391Dic11—22no—
392Dic11—24no—
393Dic11—42no—
394Dic11—81no—
395Dic11—81no—
396C22×Q8—114no—
397C22×Q8—111no—
398C22×Q8—221no—
399C22×Q8—222no—
400C22×Q8—222no—
401C22×Q8—222no—
402C22×Q8—222no—
403C22×Q8—222no—
404C22×Q8C22×D1111yescharacteristic
405C23×C4—111no—
406C23×C4—221no—
407C22×C8—111no—
408C22×C8—111no—
409C22×C8C22×D1111yescharacteristic
410C22×C8C22×D1111yescharacteristic
411C4×Q8—22no—
412C4×Q8—114no—
413C4×Q8—114no—
414C4×Q8—114no—
415C4×Q8—228no—
416C4×Q8—222no—
417C4×Q8—222no—
418C4×Q8—228no—
419C4×Q8—222no—
420C4×Q8C4×D1114yes—
421#117—114no—
422#117—114no—
423#117—114no—
424#117—228no—
425#117—228no—
426#117—222no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—111no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4—221no—
437C2×C4⋊C4—221no—
438C2×C4⋊C4C22×D1111yescharacteristic
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C22⋊C4—111no—
442C2×C22⋊C4—111no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42—111no—
449C2×C42—221no—
450C2×C42—221no—
451C2×C42—221no—
452C2×C42—221no—
453C2×C42—221no—
454C2×C42C22×D1111yescharacteristic
455C4⋊C8—222no—
456C4⋊C8—222no—
457#103—22no—
458#103—22no—
459#103—222no—
460#103—222no—
461#103—222no—
462#103—222no—
463#103—222no—
464#103—222no—
465C22⋊C8—222no—
466C22⋊C8—222no—
467#97—22no—
468C4×C8—222no—
469#95—21no—
470#95—221no—
471#95—221no—
472#95—221no—
473#95—221no—
474#95—221no—
475C2×C11#228011yescharacteristic
476C2×C11#289811yescharacteristic
477C2×C11#289811yescharacteristic
478C2×C11#312111yescharacteristic
479C2×C11#312111yescharacteristic
480C2×C11#312611yescharacteristic
481C2×C11#312711yescharacteristic
482D11—42no—
483C24—111no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—112no—
488C2×Q8—112no—
489C2×Q8—112no—
490C2×Q8—224no—
491C2×Q8—224no—
492C2×Q8—224no—
493C2×Q8—228no—
494C2×Q8—228no—
495C2×Q8—228no—
496C2×Q8—228no—
497C2×Q8—221no—
498C2×Q8—221no—
499C2×Q8—221no—
500C2×Q8C2×C4×D1112yes—
501C2×Q8#433912yes—
502C2×Q8#433912yes—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—111no—
508C22×C4—111no—
509C22×C4—111no—
510C22×C4—112no—
511C22×C4—112no—
512C22×C4—224no—
513C22×C4—224no—
514C22×C4—224no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4D4×D1111yescharacteristic
524C22×C4D4×D1111yescharacteristic
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—24no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—114no—
545C4⋊C4—114no—
546C4⋊C4—112no—
547C4⋊C4—224no—
548C4⋊C4—224no—
549C4⋊C4—224no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—221no—
555C4⋊C4—881no—
556C4⋊C4—881no—
557C4⋊C4C2×C4×D1112yes—
558C22⋊C4—114no—
559C22⋊C4—114no—
560C22⋊C4—224no—
561C22⋊C4—881no—
562C22⋊C4—881no—
563C42—24no—
564C42—81no—
565C42—112no—
566C42—112no—
567C42—224no—
568C42—224no—
569C42—224no—
570C42—224no—
571C42—881no—
572C42C2×C4×D1112yes—
573C42D4×D1112yes—
574C11#2074511yescharacteristic, complemented, Sylow
575C23—112no—
576C23—221no—
577C23—221no—
578C23—221no—
579C23—221no—
580C23—221no—
581C23—221no—
582C23C2×D4×D1111yescharacteristic
583Q8—22no—
584Q8—22no—
585Q8—22no—
586Q8—114no—
587Q8—2216no—
588Q8—222no—
589Q8—222no—
590Q8—222no—
591Q8#6692514yes—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
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—112no—
609C2×C4—112no—
610C2×C4—112no—
611C2×C4—2216no—
612C2×C4—222no—
613C2×C4—221no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—222no—
622C2×C4—222no—
623C2×C4—222no—
624C2×C4—222no—
625C2×C4—222no—
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×C4C22⋊C4×D1112yes—
635C2×C4C22⋊C4×D1112yes—
636C2×C4C22×C4×D1111yescharacteristic
637C2×C4C2×#433911yescharacteristic
638C2×C4C2×#433911yescharacteristic
639C2×C4C2×D4×D1111yescharacteristic
640C2×C4#41×D1111yescharacteristic
641C2×C4#41×D1111yescharacteristic
642C8—41no—
643C8—41no—
644C8—441no—
645C8—441no—
646C22—222no—
647C22—222no—
648C22—222no—
649C22—441no—
650C22—441no—
651C22—441no—
652C22—441no—
653C22C2×C22⋊C4×D1111yescharacteristic
654C22#1062307811yescharacteristic
655C22#1062307811yescharacteristic
656C22#1062330611yescharacteristic
657C22#1062330911yescharacteristic
658C22#1062331011yescharacteristic
659C22#1062331011yescharacteristic
660C4—24no—
661C4—22no—
662C4—22no—
663C4—42no—
664C4—81no—
665C4—81no—
666C4—222no—
667C4—224no—
668C4—222no—
669C4—222no—
670C4—442no—
671C4—881no—
672C4—881no—
673C4C2×#6692511yescharacteristic
674C4D11×#11711yescharacteristic
675C4#1062307811yescharacteristic
676C4#1062307811yescharacteristic
677C2—442no—
678C2#1307099711yescharacteristic
679C2#1307714711yescharacteristic
680C2#1307714811yescharacteristic
681C2#1307884311yescharacteristic
682C2#1307884911yescharacteristic
683C2#1307890611yescharacteristic
684C2#1307891511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1763C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1763D11
hypocenterC11#20745
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
6. #13068630C2semidirect
7. #13068629C2semidirect
8. #13068620C2semidirect
9. #13068619C2semidirect
12. #13068447C2semidirect
13. C4×#66874C2semidirect
14. C4×#66899C2semidirect
15. C11×#1763C2semidirect
20. #10623103C4semidirect
245. #1763D11semidirect
574. C11#20745semidirect

Maximal subgroups

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

subgroupindex
C2×#106231032
C2×#106223222
#130712212
#130687102
#130687092
#130686302
#130686292
#130686202
#130686192
#130685492
#130684472
C4×#668742
C4×#668992
C11×#17632
#2074511