Finite Group Databasebeta

← #14675528

Subgroups — #14675528

Order 2816.

1790 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66940C211yesmaximal, characteristic
2C2×C4⋊C4×Dic11C211yesmaximal, characteristic
3C2×#10622261C211yesmaximal, characteristic
4#13066886C212yesmaximal
5#13066882C212yesmaximal
6#13066870C211yesmaximal, characteristic
7#13066869C211yesmaximal, characteristic
8#13066866C211yesmaximal, characteristic
9#95×Dic11C212yesmaximal
10#95×Dic11C212yesmaximal
11C11×#1441C211yesmaximal, characteristic
12C23×Dic22C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×Dic11⋊C4C2211yescharacteristic
17C22×Dic11⋊C4C2211yescharacteristic
18C22×C4×Dic11C2212yes—
19C22×C4×Dic11C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2212yes—
22C22×C4×Dic11C2211yescharacteristic
23C2×#66940—24no—
24C2×#66940—24no—
25C2×#66940C418yescomplemented
26C2×C11×#95C2212yes—
27C2×C11×#95C2212yes—
28C2×C11×#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C4⋊C4×Dic11—24no—
39#10622261—24no—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C22×Dic22—22no—
52C22×Dic22—22no—
53C22×Dic22—22no—
54C22×Dic22—22no—
55C22×Dic22—22no—
56C22×Dic22—22no—
57C22×Dic22C2×C414yes—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—24no—
62C2×C11×C4⋊C4C2×C414yes—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11—24no—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4C2×C414yes—
70C2×Dic11⋊C4C2×C414yes—
71C2×C4×Dic11—22no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11—22no—
74C2×C4×Dic11—22no—
75C2×C4×Dic11—24no—
76C2×C4×Dic11—24no—
77C2×C4×Dic11—24no—
78C2×C4×Dic11—24no—
79C2×C4×Dic11—24no—
80C2×C4×Dic11C2×C414yes—
81C2×C4×Dic11C2×C414yes—
82C2×C4×Dic11C2×C414yes—
83C2×C4×Dic11D414yes—
84C2×C4×Dic11D414yes—
85C2×C4×Dic11Q818yescomplemented
86#66940—232no—
87C11×#95—22no—
88C11×#95—24no—
89C11×#95—24no—
90C11⋊#95—22no—
91C11⋊#95—24no—
92C11⋊#95—24no—
93C11⋊#95—24no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96C11⋊#95—24no—
97C11⋊#95—24no—
98C11⋊#95—24no—
99#13850—111nomaximal, Sylow
100C24×C11C2411yescharacteristic
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11C22×C412yes—
124C22×C4×C11C22×C412yes—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×Q814yes—
129C22×C4×C11#4114yes—
130C22×C4×C11#4112yes—
131C22×C4×C11#4112yes—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11C22×C412yes—
157C22×Dic11C22×C412yes—
158C22×Dic11C22×C412yes—
159C22×Dic11C22×C412yes—
160C22×Dic11C2×D412yes—
161C22×Dic11C2×D412yes—
162C22×Dic11C2×D412yes—
163C22×Dic11C2×D412yes—
164C22×Dic11C2×Q814yes—
165C22×Dic11C2×Q814yes—
166C22×Dic11#4114yes—
167C22×Dic11#4112yes—
168C22×Dic11#4112yes—
169C22×Dic11#4114yes—
170C2×Dic22—28no—
171C2×Dic22—28no—
172C2×Dic22—28no—
173C2×Dic22—28no—
174C2×Dic22—28no—
175C2×Dic22—28no—
176C2×Dic22—28no—
177C11×C4⋊C4—28no—
178C11×C4⋊C4—28no—
179C4⋊Dic11—28no—
180Dic11⋊C4—28no—
181Dic11⋊C4—28no—
182C4×Dic11—28no—
183C4×Dic11—28no—
184C4×Dic11—216no—
185C4×Dic11—48no—
186C4×Dic11C22⋊C4116yes—
187C22×C4×Q8—111no—
188C2×C4×C4⋊C4—111no—
189C2×#376—111no—
190#1446—112no—
191#1445—112no—
192#1441—111no—
193#1441—111no—
194#1441—111no—
195#1441D1111yescharacteristic
196C4×#95—112no—
197C4×#95—112no—
198C23×C11C23×C411yescharacteristic
199C23×C11C22×D411yescharacteristic
200C23×C11C22×D411yescharacteristic
201C23×C11C22×Q812yes—
202C23×C11C2×#4111yescharacteristic
203C23×C11C2×#4112yes—
204C23×C11C2×#4111yescharacteristic
205C23×C11C2×#4111yescharacteristic
206C23×C11C2×#4111yescharacteristic
207C23×C11C2×#4112yes—
208C23×C11C2×#4112yes—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—24no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—41no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—41no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11C2×C22⋊C414yes—
239C2×C4×C11#11714yes—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—41no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—41no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11C2×C22⋊C414yes—
272C2×Dic11C2×C22⋊C414yes—
273C2×Dic11#11714yes—
274C2×Dic11C4×Q818yes—
275C2×Dic11C22⋊Q818yes—
276C2×Dic11#12414yes—
277C2×Dic11C4⋊Q814yes—
278Dic22—232no—
279C23×Q8—111no—
280C2×C4×Q8—118no—
281C2×C4×Q8—224no—
282C2×C4×Q8—224no—
283C22×C4⋊C4—111no—
284C22×C4⋊C4—111no—
285C22×C4⋊C4—111no—
286C22×C4⋊C4C2×D1111yescharacteristic
287C22×C4⋊C4C2×D1111yescharacteristic
288C22×C42—111no—
289C22×C42—111no—
290C22×C42—111no—
291C22×C42—112no—
292C22×C42—112no—
293C4×C4⋊C4—224no—
294#376—224no—
295C2×#95—112no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95—112no—
301C2×#95—111no—
302C2×#95—112no—
303C2×#95—112no—
304C2×#95C2×D1112yes—
305C2×#95C2×D1112yes—
306C2×#95C2×D1111yescharacteristic
307C22×C11C22×C22⋊C411yescharacteristic
308C22×C11C2×#11711yescharacteristic
309C22×C11C2×#11711yescharacteristic
310C22×C11C2×C4×Q812yes—
311C22×C11C4×#4112yes—
312C22×C11C2×C22⋊Q812yes—
313C22×C11#52511yescharacteristic
314C22×C11#52511yescharacteristic
315C22×C11#52511yescharacteristic
316C22×C11#52511yescharacteristic
317C22×C11#52511yescharacteristic
318C22×C11#52511yescharacteristic
319C22×C11C2×#12411yescharacteristic
320C22×C11#52912yes—
321C22×C11#52912yes—
322C22×C11#52912yes—
323C22×C11#52912yes—
324C22×C11C2×C4⋊Q811yescharacteristic
325C22×C11#53212yes—
326C22×C11#53312yes—
327C22×C11#53312yes—
328C22×C11#53312yes—
329C22×C11#53312yes—
330C4×C11—24no—
331C4×C11—24no—
332C4×C11—44no—
333C4×C11—44no—
334C4×C11—42no—
335Dic11—24no—
336Dic11—24no—
337Dic11—44no—
338Dic11—44no—
339Dic11—42no—
340Dic11#39118yes—
341C22×Q8—114no—
342C22×Q8—222no—
343C22×Q8—222no—
344C22×Q8—222no—
345C22×Q8—222no—
346C22×Q8—222no—
347C22×Q8—222no—
348C23×C4—111no—
349C23×C4—111no—
350C23×C4—111no—
351C23×C4—111no—
352C23×C4—112no—
353C23×C4—112no—
354C23×C4C22×D1111yescharacteristic
355C23×C4C22×D1112yes—
356C23×C4C22×D1112yes—
357C23×C4C22×D1111yescharacteristic
358C23×C4C22×D1111yescharacteristic
359C4×Q8—2232no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—114no—
365C2×C4⋊C4—114no—
366C2×C4⋊C4—222no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—224no—
369C2×C4⋊C4—222no—
370C2×C4⋊C4—222no—
371C2×C4⋊C4—222no—
372C2×C4⋊C4C4×D1114yes—
373C2×C42—114no—
374C2×C42—114no—
375C2×C42—114no—
376C2×C42—114no—
377C2×C42—114no—
378C2×C42—118no—
379C2×C42—222no—
380C2×C42—222no—
381C2×C42—222no—
382C2×C42—222no—
383C2×C42—224no—
384C2×C42—224no—
385C2×C42—224no—
386C2×C42—224no—
387C2×C42—224no—
388#95—22no—
389#95—24no—
390#95—24no—
391#95—224no—
392#95—224no—
393#95—224no—
394#95—224no—
395#95—224no—
396#95—224no—
397#95—222no—
398#95—224no—
399#95—224no—
400C2×C11#228011yescharacteristic
401C2×C11C2×#39111yescharacteristic
402C2×C11#229512yes—
403C2×C11#229512yes—
404C2×C11#229711yescharacteristic
405C2×C11#239612yes—
406C2×C11#239612yes—
407C2×C11#239811yescharacteristic
408C2×C11#239811yescharacteristic
409C2×C11#239911yescharacteristic
410C2×C11#239911yescharacteristic
411C24C23×D1111yescharacteristic
412C2×Q8—228no—
413C2×Q8—228no—
414C2×Q8—228no—
415C2×Q8—228no—
416C2×Q8—228no—
417C2×Q8—228no—
418C2×Q8—228no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—112no—
442C22×C4—112no—
443C22×C4—112no—
444C22×C4—114no—
445C22×C4—114no—
446C22×C4—112no—
447C22×C4—112no—
448C22×C4—112no—
449C22×C4—112no—
450C22×C4—112no—
451C22×C4—112no—
452C22×C4—112no—
453C22×C4—114no—
454C22×C4—114no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4C2×C4×D1112yes—
480C22×C4C2×C4×D1112yes—
481C22×C4C2×C4×D1112yes—
482C22×C4D4×D1112yes—
483C22×C4D4×D1112yes—
484C22×C4#434114yes—
485C22×C4#434112yes—
486C22×C4Q8×D1114yes—
487C22×C4#434312yes—
488C4⋊C4—28no—
489C4⋊C4—28no—
490C4⋊C4—228no—
491C4⋊C4—228no—
492C4⋊C4—228no—
493C42—1116no—
494C42—228no—
495C42—228no—
496C42—2216no—
497C42—448no—
498C11#1385011yescharacteristic, complemented, Sylow
499C23C22×C4×D1111yescharacteristic
500C23C2×D4×D1111yescharacteristic
501C23C2×D4×D1111yescharacteristic
502C23C2×#434112yes—
503C23C2×#434111yescharacteristic
504C23C2×Q8×D1112yes—
505C23C2×#434311yescharacteristic
506C23#41×D1111yescharacteristic
507C23#41×D1112yes—
508C23#41×D1112yes—
509C23#41×D1111yescharacteristic
510Q8—2232no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—114no—
541C2×C4—114no—
542C2×C4—118no—
543C2×C4—118no—
544C2×C4—114no—
545C2×C4—114no—
546C2×C4—114no—
547C2×C4—222no—
548C2×C4—222no—
549C2×C4—222no—
550C2×C4—222no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—222no—
555C2×C4—222no—
556C2×C4—222no—
557C2×C4—222no—
558C2×C4—222no—
559C2×C4—224no—
560C2×C4—224no—
561C2×C4—222no—
562C2×C4—224no—
563C2×C4—224no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—224no—
567C2×C4—442no—
568C2×C4—441no—
569C2×C4—442no—
570C2×C4—442no—
571C2×C4—442no—
572C2×C4—442no—
573C2×C4—442no—
574C2×C4—441no—
575C2×C4—442no—
576C2×C4—442no—
577C2×C4—442no—
578C2×C4C22⋊C4×D1114yes—
579C2×C4#6694514yes—
580C22C2×C22⋊C4×D1111yescharacteristic
581C22C2×#6694511yescharacteristic
582C22D11×#11711yescharacteristic
583C22C4×#434112yes—
584C22C4×Q8×D1112yes—
585C22#1062311711yescharacteristic
586C22#1062312712yes—
587C22#1062313112yes—
588C22#1062313711yescharacteristic
589C22#1062313711yescharacteristic
590C22#1062315312yes—
591C22#1062315312yes—
592C22D11×C22⋊Q812yes—
593C22#1062315811yescharacteristic
594C22#1062315811yescharacteristic
595C22#1062318012yes—
596C22#1062318711yescharacteristic
597C22D11×#12411yescharacteristic
598C22#1062321912yes—
599C22#1062322212yes—
600C22#1062323712yes—
601C22D11×C4⋊Q811yescharacteristic
602C22#1062325912yes—
603C4—24no—
604C4—24no—
605C4—44no—
606C4—44no—
607C4—42no—
608C4—118no—
609C4—224no—
610C4—224no—
611C4—444no—
612C4—444no—
613C4—442no—
614C2#1307099811yescharacteristic
615C2D11×#39111yescharacteristic
616C2#1307108712yes—
617C2#1307108912yes—
618C2#1307110111yescharacteristic
619C2#1307189112yes—
620C2#1307189312yes—
621C2#1307190411yescharacteristic
622C2#1307190511yescharacteristic
623C2#1307190611yescharacteristic
624C2#1307190811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1441C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1441D11
hypocenterC11#13850
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
25. C2×#66940C4semidirect
85. C2×C4×Dic11Q8semidirect
498. C11#13850semidirect

Maximal subgroups

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

subgroupindex
C22×#669402
C2×C4⋊C4×Dic112
C2×#106222612
#130668862
#130668822
#130668702
#130668692
#130668662
#95×Dic112
C11×#14412
#1385011