Finite Group Databasebeta

← #14680676

Subgroups — #14680676

Order 2816.

1766 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622604C211yesmaximal, characteristic
2C2×#10622601C211yesmaximal, characteristic
3C2×#10622282C212yesmaximal, complemented
4C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
5#13066879C211yesmaximal, characteristic, complemented
6#13066862C212yesmaximal, complemented
7#13066860C212yesmaximal, complemented
8#13066856C211yesmaximal, characteristic
9#13066852C212yesmaximal, complemented
10#13066841C211yesmaximal, characteristic, complemented
11C11×#1441C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×C4⋊Dic11C2211yescharacteristic
22C22×Dic11⋊C4C2212yes—
23C22×C4×Dic11C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2212yes—
28C2×C11×#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35#10622604C418yescomplemented
36#10622601—24no—
37C4⋊C4×Dic11—24no—
38#10622282—28no—
39C24×D11C2312yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×Dic11C2312yes—
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C22×D44—22no—
51C22×D44—22no—
52C22×D44—42no—
53C22×D44—42no—
54C22×D44C2×C414yes—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—42no—
59C2×C11×C4⋊C4C2×C414yes—
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4—24no—
62C2×(C2×D11)⋊C4—24no—
63C2×(C2×D11)⋊C4—24no—
64C2×(C2×D11)⋊C4—24no—
65C2×(C2×D11)⋊C4—24no—
66C2×(C2×D11)⋊C4—24no—
67C2×(C2×D11)⋊C4—24no—
68C2×(C2×D11)⋊C4—42no—
69C2×(C2×D11)⋊C4—42no—
70C2×(C2×D11)⋊C4—42no—
71C2×(C2×D11)⋊C4—42no—
72C2×(C2×D11)⋊C4—42no—
73C2×(C2×D11)⋊C4—42no—
74C2×(C2×D11)⋊C4—42no—
75C2×(C2×D11)⋊C4—42no—
76C2×(C2×D11)⋊C4C2×C418yes—
77C2×(C2×D11)⋊C4C2×C418yes—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—22no—
81C2×Dic11⋊C4—24no—
82C2×Dic11⋊C4—42no—
83C2×Dic11⋊C4—42no—
84C2×C4×Dic11—22no—
85C2×C4×Dic11—22no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11—42no—
88C2×C4×Dic11—42no—
89C2×C4×Dic11D414yes—
90C2×C4×Dic11D414yescomplemented
91C11×#95—24no—
92C11×#95—22no—
93C11×#95—42no—
94C11⋊#95—22no—
95C11⋊#95—24no—
96C11⋊#95—22no—
97C11⋊#95—42no—
98C11⋊#95—42no—
99C11⋊#95C2×C414yes—
100#14312—111nomaximal, Sylow
101C24×C11C2411yescharacteristic
102C23×D11—22no—
103C23×D11—22no—
104C23×D11—22no—
105C23×D11—22no—
106C23×D11—22no—
107C23×D11—22no—
108C23×D11—22no—
109C23×D11—22no—
110C23×D11—22no—
111C23×D11—22no—
112C23×D11—22no—
113C23×D11—22no—
114C23×D11—22no—
115C23×D11—22no—
116C23×D11C22×C414yes—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11C22×C412yes—
142C22×C4×C11C22×C412yes—
143C22×C4×C11C22×C412yes—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11#4112yes—
147C22×C4×C11#4112yes—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—22no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11C22×C414yes—
169C22×Dic11C2×D412yes—
170C22×Dic11C2×D412yes—
171C22×Dic11C2×D412yes—
172C22×Dic11C2×D412yes—
173C22×Dic11#4112yes—
174C22×Dic11#4112yes—
175C2×D44—28no—
176C2×D44—48no—
177C2×D44—44no—
178C2×D44—44no—
179C2×D44—48no—
180C11×C4⋊C4—28no—
181C11×C4⋊C4—44no—
182(C2×D11)⋊C4—216no—
183(C2×D11)⋊C4—48no—
184(C2×D11)⋊C4—48no—
185(C2×D11)⋊C4—48no—
186(C2×D11)⋊C4—48no—
187(C2×D11)⋊C4—48no—
188C4⋊Dic11—28no—
189Dic11⋊C4—48no—
190C4×Dic11—28no—
191C4×Dic11—44no—
192C4×Dic11—44no—
193C2×#394—111no—
194C2×#390—111no—
195C2×#388—112no—
196C2×C4×C4⋊C4—111no—
197#1444—111no—
198#1441D1111yescharacteristic, complemented
199#1439—112no—
200#1439—112no—
201#1438—111no—
202#1437—112no—
203#1434—111no—
204C23×C11C23×C411yescharacteristic
205C23×C11C22×D411yescharacteristic
206C23×C11C22×D411yescharacteristic
207C23×C11C2×#4111yescharacteristic
208C23×C11C2×#4111yescharacteristic
209C23×C11C2×#4111yescharacteristic
210C23×C11C2×#4111yescharacteristic
211C23×C11H(5,𝔽2)12yes—
212C23×C11H(5,𝔽2)12yes—
213C23×C11H(5,𝔽2)12yes—
214C23×C112−1+412yes—
215C22×D11—24no—
216C22×D11—24no—
217C22×D11—24no—
218C22×D11—24no—
219C22×D11—24no—
220C22×D11—24no—
221C22×D11—24no—
222C22×D11—42no—
223C22×D11—42no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11—42no—
227C22×D11—42no—
228C22×D11—42no—
229C22×D11—42no—
230C22×D11—42no—
231C22×D11—42no—
232C22×D11—42no—
233C22×D11—42no—
234C22×D11—42no—
235C22×D11—42no—
236C22×D11—42no—
237C22×D11—42no—
238C22×D11—42no—
239C22×D11—42no—
240C22×D11—42no—
241C22×D11—42no—
242C22×D11—42no—
243C22×D11—42no—
244C22×D11—42no—
245C22×D11—42no—
246C22×D11—42no—
247C22×D11—42no—
248C22×D11—42no—
249C22×D11—42no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—24no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—24no—
260C2×C4×C11—22no—
261C2×C4×C11—24no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—42no—
278C2×C4×C11—42no—
279C2×C4×C11C4×D414yes—
280C2×C4×C11C4×D414yes—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—24no—
284C2×Dic11—24no—
285C2×Dic11—24no—
286C2×Dic11—24no—
287C2×Dic11—24no—
288C2×Dic11—22no—
289C2×Dic11—22no—
290C2×Dic11—22no—
291C2×Dic11—22no—
292C2×Dic11—24no—
293C2×Dic11—22no—
294C2×Dic11—24no—
295C2×Dic11—41no—
296C2×Dic11—42no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—42no—
301C2×Dic11—42no—
302C2×Dic11—42no—
303C2×Dic11—42no—
304C2×Dic11—42no—
305C2×Dic11—42no—
306C2×Dic11—42no—
307C2×Dic11#12114yes—
308D44—416no—
309C23×D4—111no—
310C22×C4⋊C4—111no—
311C22×C4⋊C4—112no—
312C22×C4⋊C4C2×D1111yescharacteristic
313C22×C4⋊C4C2×D1111yescharacteristic
314C22×C22⋊C4—112no—
315C22×C22⋊C4—112no—
316C22×C22⋊C4—112no—
317C22×C22⋊C4—112no—
318C22×C22⋊C4—112no—
319C22×C22⋊C4—112no—
320C22×C42—111no—
321C22×C42—111no—
322C22×C42—111no—
323#394—118no—
324#390—224no—
325#388—228no—
326C4×C4⋊C4—224no—
327C2×#95—111no—
328C2×#95—112no—
329C2×#95—111no—
330C2×#95—111no—
331C2×#95—112no—
332C2×#95—112no—
333C2×#95C2×D1111yescharacteristic
334C2×#95C2×D1112yes—
335C2×#95C2×D1112yes—
336C22×C11C2×C4×D411yescharacteristic
337C22×C11C2×C4×D411yescharacteristic
338C22×C11C4×#4111yescharacteristic
339C22×C11#51812yes—
340C22×C11#52012yes—
341C22×C11C2×#12111yescharacteristic
342C22×C11#52511yescharacteristic
343C22×C11#52911yescharacteristic
344C22×C11#53211yescharacteristic
345C22×C11#53411yescharacteristic
346C22×C11#53511yescharacteristic
347C22×C11#53512yes—
348C22×C11#53511yescharacteristic
349C22×C11#53611yescharacteristic
350C22×C11#53712yes—
351C22×C11#53812yes—
352C22×C11#53812yes—
353C22×C11#53912yes—
354C22×C11#54012yes—
355C22×C11#54012yes—
356C22×C11#54212yes—
357C22×C11#54212yes—
358C22×C11#54212yes—
359C2×D11—44no—
360C2×D11—44no—
361C2×D11—44no—
362C2×D11—44no—
363C2×D11—44no—
364C2×D11—44no—
365C2×D11—44no—
366C2×D11—82no—
367C2×D11—82no—
368C2×D11—82no—
369C2×D11—82no—
370C2×D11—82no—
371C2×D11—82no—
372C2×D11—82no—
373C2×D11—82no—
374C4×C11—24no—
375C4×C11—24no—
376C4×C11—42no—
377C4×C11—82no—
378C4×C11—82no—
379Dic11—24no—
380Dic11—44no—
381Dic11—42no—
382Dic11—42no—
383Dic11—42no—
384C25—112no—
385C22×D4—114no—
386C22×D4—222no—
387C22×D4—222no—
388C22×D4—442no—
389C22×D4—442no—
390C23×C4—111no—
391C23×C4—111no—
392C23×C4—112no—
393C23×C4—111no—
394C23×C4—111no—
395C23×C4C22×D1112yes—
396C23×C4C22×D1112yes—
397C23×C4C22×D1111yescharacteristic
398C23×C4C22×D1111yescharacteristic
399C23×C4C22×D1111yescharacteristic
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—42no—
404C2×C4⋊C4—222no—
405C2×C4⋊C4—222no—
406C2×C4⋊C4—222no—
407C2×C4⋊C4—224no—
408C2×C4⋊C4—442no—
409C2×C4⋊C4—442no—
410C2×C4⋊C4C4×D1114yes—
411C2×C22⋊C4—118no—
412C2×C22⋊C4—118no—
413C2×C22⋊C4—224no—
414C2×C22⋊C4—224no—
415C2×C22⋊C4—224no—
416C2×C22⋊C4—224no—
417C2×C22⋊C4—224no—
418C2×C22⋊C4—224no—
419C2×C22⋊C4—224no—
420C2×C22⋊C4—224no—
421C2×C22⋊C4—442no—
422C2×C22⋊C4—442no—
423C2×C22⋊C4—442no—
424C2×C22⋊C4—442no—
425C2×C22⋊C4—442no—
426C2×C22⋊C4—442no—
427C2×C22⋊C4—442no—
428C2×C22⋊C4—442no—
429C2×C42—114no—
430C2×C42—114no—
431C2×C42—222no—
432C2×C42—222no—
433C2×C42—222no—
434C2×C42—442no—
435C2×C42—442no—
436#95—24no—
437#95—22no—
438#95—42no—
439#95—114no—
440#95—222no—
441#95—224no—
442#95—222no—
443#95—442no—
444#95—442no—
445C2×C11C4×#12111yescharacteristic
446C2×C11#232111yescharacteristic
447C2×C11#232412yes—
448C2×C11#232611yescharacteristic
449C2×C11#233512yes—
450C2×C11#261811yescharacteristic
451C2×C11#261911yescharacteristic
452C2×C11#263211yescharacteristic
453C2×C11#263511yescharacteristic
454C2×C11#265112yes—
455C2×C11#266212yes—
456D11—84no—
457C24—114no—
458C24—222no—
459C24—222no—
460C24—222no—
461C24—222no—
462C24—222no—
463C24—222no—
464C24—222no—
465C24—222no—
466C24—222no—
467C24—222no—
468C24—222no—
469C24—222no—
470C24—222no—
471C24—222no—
472C24C23×D1111yescharacteristic
473C2×D4—228no—
474C2×D4—448no—
475C2×D4—444no—
476C2×D4—448no—
477C2×D4—444no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—112no—
503C22×C4—112no—
504C22×C4—112no—
505C22×C4—114no—
506C22×C4—112no—
507C22×C4—112no—
508C22×C4—112no—
509C22×C4—222no—
510C22×C4—222no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—222no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—222no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—222no—
523C22×C4—222no—
524C22×C4—222no—
525C22×C4—222no—
526C22×C4—222no—
527C22×C4—222no—
528C22×C4—222no—
529C22×C4C2×C4×D1112yes—
530C22×C4C2×C4×D1112yes—
531C22×C4C2×C4×D1112yes—
532C22×C4D4×D1112yes—
533C22×C4D4×D1112yes—
534C22×C4#434112yes—
535C22×C4#434312yes—
536C4⋊C4—28no—
537C4⋊C4—44no—
538C4⋊C4—228no—
539C4⋊C4—448no—
540C22⋊C4—2216no—
541C22⋊C4—448no—
542C22⋊C4—448no—
543C22⋊C4—448no—
544C22⋊C4—448no—
545C22⋊C4—448no—
546C42—228no—
547C42—444no—
548C42—444no—
549C11#1431211yescharacteristic, complemented, Sylow
550C23—224no—
551C23—224no—
552C23—224no—
553C23—224no—
554C23—224no—
555C23—224no—
556C23—224no—
557C23—442no—
558C23—442no—
559C23—442no—
560C23—442no—
561C23—442no—
562C23—442no—
563C23—442no—
564C23—442no—
565C23—442no—
566C23—442no—
567C23—442no—
568C23—442no—
569C23—442no—
570C23—442no—
571C23—442no—
572C23—442no—
573C23—442no—
574C23—442no—
575C23—442no—
576C23—442no—
577C23—442no—
578C23—442no—
579C23—442no—
580C23—442no—
581C23—442no—
582C23—442no—
583C23—442no—
584C23—442no—
585C23C22×C4×D1111yescharacteristic
586C23C2×D4×D1111yescharacteristic
587C23C2×D4×D1111yescharacteristic
588C23C2×#434111yescharacteristic
589C23#6703712yes—
590C23C2×#434311yescharacteristic
591C23#6704012yes—
592C23#41×D1111yescharacteristic
593C23#41×D1111yescharacteristic
594C23#6704212yes—
595C23#6704212yes—
596D4—4416no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—24no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—24no—
609C2×C4—41no—
610C2×C4—42no—
611C2×C4—41no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—114no—
627C2×C4—222no—
628C2×C4—224no—
629C2×C4—222no—
630C2×C4—224no—
631C2×C4—224no—
632C2×C4—224no—
633C2×C4—224no—
634C2×C4—224no—
635C2×C4—222no—
636C2×C4—224no—
637C2×C4—222no—
638C2×C4—222no—
639C2×C4—222no—
640C2×C4—222no—
641C2×C4—442no—
642C2×C4—442no—
643C2×C4—441no—
644C2×C4—442no—
645C2×C4—442no—
646C2×C4—441no—
647C2×C4—442no—
648C2×C4—441no—
649C2×C4—441no—
650C2×C4—442no—
651C2×C4—442no—
652C2×C4—442no—
653C2×C4(C22⋊D11)⋊C414yes—
654C2×C4#6694614yes—
655C22—444no—
656C22—444no—
657C22—444no—
658C22—444no—
659C22—444no—
660C22—444no—
661C22—444no—
662C22—882no—
663C22—882no—
664C22—882no—
665C22—882no—
666C22—882no—
667C22—882no—
668C22—882no—
669C22—882no—
670C22C2×(C22⋊D11)⋊C411yescharacteristic
671C22C2×#6694611yescharacteristic
672C22#1062305311yescharacteristic
673C22#1062307612yes—
674C22#1062310512yes—
675C22#1062312311yescharacteristic
676C22#1062312711yescharacteristic
677C22D11×#12111yescharacteristic
678C22#1062313812yes—
679C22#1062314812yes—
680C22#1062315511yescharacteristic
681C22#1062315811yescharacteristic
682C22#1062316012yes—
683C22#1062317112yes—
684C22#1062317412yes—
685C22#1062318411yescharacteristic
686C22#1062319412yes—
687C22#1062320511yescharacteristic
688C22#1062322312yes—
689C22#1062322912yes—
690C22#1062323512yes—
691C22#1062325511yescharacteristic
692C22#1062326412yes—
693C4—24no—
694C4—24no—
695C4—42no—
696C4—82no—
697C4—82no—
698C4—224no—
699C4—442no—
700C4—442no—
701C4—442no—
702C4—444no—
703C2—884no—
704C2#1307112211yescharacteristic
705C2#1307127911yescharacteristic
706C2#1307130712yes—
707C2#1307133011yescharacteristic
708C2#1307141212yes—
709C2#1307435911yescharacteristic
710C2#1307436811yescharacteristic
711C2#1307448211yescharacteristic
712C2#1307450911yescharacteristic
713C2#1307465212yes—
714C2#1307475412yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1441C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1441D11
hypocenterC11#14312
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
3. C2×#10622282C2semidirect
4. C2×C4⋊C4×Dic11C2semidirect
5. #13066879C2semidirect
6. #13066862C2semidirect
7. #13066860C2semidirect
9. #13066852C2semidirect
10. #13066841C2semidirect
11. C11×#1441C2semidirect
35. #10622604C4semidirect
90. C2×C4×Dic11D4semidirect
198. #1441D11semidirect
549. C11#14312semidirect

Maximal subgroups

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

subgroupindex
C2×#106226042
C2×#106226012
C2×#106222822
C2×C4⋊C4×Dic112
#130668792
#130668622
#130668602
#130668562
#130668522
#130668412
C11×#14412
#1431211