Finite Group Databasebeta

← #14676652

Subgroups — #14676652

Order 2816.

2558 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66946C211yesmaximal, characteristic
2C2×#10622552C211yesmaximal, characteristic
3C2×#10622601C211yesmaximal, characteristic
4C2×#10622586C211yesmaximal, characteristic, complemented
5C2×#10622602C214yesmaximal, complemented
6#13066858C214yesmaximal, complemented
7#13066845C211yesmaximal, characteristic, complemented
8C4×C11⋊#95C211yesmaximal, characteristic, complemented
9C2×C11×#384C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C23×C4×D11C2212yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2214yes—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2214yes—
18C22×(C2×D11)⋊C4C2214yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C2×#66946—24no—
24C2×#66946—24no—
25C2×#66946—24no—
26C11×#384—24no—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31#10622602—216no—
32#10622601—24no—
33#10622586—24no—
34#10622552C418yescomplemented
35C24×D11C2312yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2312yes—
38C23×C4×C11C2312yes—
39C23×C4×C11C2311yescharacteristic
40C23×Dic11C2312yes—
41C23×Dic11C2311yescharacteristic
42C23×Dic11C2312yes—
43C23×Dic11C2311yescharacteristic
44C22×D44—22no—
45C22×D44—22no—
46C22×D44—22no—
47C22×D44—22no—
48C22×D44C2×C414yes—
49C22×D44D414yes—
50C22×D44Q814yes—
51C22×C4×D11—24no—
52C22×C4×D11—24no—
53C22×C4×D11—24no—
54C22×C4×D11—28no—
55C22×C4×D11—44no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—28no—
61C2×C11×C4⋊C4—28no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—44no—
64C2×C11×C4⋊C4D414yes—
65C2×C42×C11—22no—
66C2×C42×C11—22no—
67C2×C42×C11C2×C414yescomplemented
68C2×(C2×D11)⋊C4—24no—
69C2×(C2×D11)⋊C4—24no—
70C2×(C2×D11)⋊C4—28no—
71C2×(C2×D11)⋊C4—28no—
72C2×(C2×D11)⋊C4—24no—
73C2×(C2×D11)⋊C4—28no—
74C2×(C2×D11)⋊C4—28no—
75C2×(C2×D11)⋊C4—44no—
76C2×(C2×D11)⋊C4C2×C4116yescomplemented
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11C2×C414yescomplemented
80C2×Dic11⋊C4—24no—
81C2×Dic11⋊C4—28no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11—22no—
84C2×C4×Dic11—22no—
85C2×C4×Dic11—22no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11D414yes—
88#66946—232no—
89C11⋊#95—24no—
90C11⋊#95—24no—
91C11⋊#95—28no—
92C11⋊#95D418yescomplemented
93#13977—111nomaximal, Sylow
94C24×C11C2411yescharacteristic
95C23×D11—24no—
96C23×D11—22no—
97C23×D11—22no—
98C23×D11—24no—
99C23×D11—22no—
100C23×D11—22no—
101C23×D11—24no—
102C23×D11—24no—
103C23×D11C22×C414yes—
104C23×D11C2×D414yes—
105C23×D11C2×Q814yes—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—24no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—24no—
114C22×C4×C11—22no—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—24no—
119C22×C4×C11C22×C414yes—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C2×D414yes—
122C22×C4×C11C2×D414yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×Q812yes—
127C22×C4×C11#4114yes—
128C22×C4×C11#4112yes—
129C22×C4×C11#4112yes—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—22no—
133C22×Dic11—24no—
134C22×Dic11—21no—
135C22×Dic11—22no—
136C22×Dic11—21no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—24no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11C22×C414yes—
148C22×Dic11C2×D414yes—
149C22×Dic11C2×D412yes—
150C22×Dic11C2×D414yes—
151C22×Dic11C2×D412yes—
152C2×D44—28no—
153C2×D44—28no—
154C2×D44—28no—
155C2×D44—28no—
156C2×D44—28no—
157C2×D44—28no—
158C2×D44C4⋊C4116yescomplemented
159C2×C4×D11—216no—
160C2×C4×D11—416no—
161C2×C4×D11—416no—
162C2×C4×D11—48no—
163C2×C4×D11—48no—
164C11×C4⋊C4—28no—
165C11×C4⋊C4—416no—
166C11×C4⋊C4—44no—
167C42×C11—28no—
168(C2×D11)⋊C4—216no—
169(C2×D11)⋊C4—232no—
170(C2×D11)⋊C4—416no—
171C4⋊Dic11—28no—
172Dic11⋊C4—48no—
173C4×Dic11—28no—
174C4×Dic11—44no—
175C22×C4×D4—111no—
176C2×#390—111no—
177C2×#390—111no—
178C2×#389—111no—
179C2×#385—114no—
180C2×#384D1111yescharacteristic, complemented
181#1439—114no—
182C4⋊#95—111no—
183C4×#95—111no—
184C23×C11C23×C411yescharacteristic
185C23×C11C22×D411yescharacteristic
186C23×C11C22×D411yescharacteristic
187C23×C11C22×D412yes—
188C23×C11C22×D411yescharacteristic
189C23×C11C22×Q811yescharacteristic
190C23×C11C2×#4111yescharacteristic
191C23×C11C2×#4111yescharacteristic
192C23×C11C2×#4112yes—
193C23×C11H(5,𝔽2)12yes—
194C23×C112−1+412yes—
195C22×D11—28no—
196C22×D11—24no—
197C22×D11—24no—
198C22×D11—28no—
199C22×D11—24no—
200C22×D11—24no—
201C22×D11—24no—
202C22×D11—24no—
203C22×D11—28no—
204C22×D11—28no—
205C22×D11—28no—
206C22×D11—28no—
207C22×D11—42no—
208C22×D11—42no—
209C22×D11—44no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—44no—
213C22×D11—44no—
214C22×D11—44no—
215C22×D11—44no—
216C22×D11—44no—
217C22×D11C2×C4⋊C418yes—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—28no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—44no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—44no—
233C2×C4×C11—44no—
234C2×C4×C11C2×C4⋊C414yes—
235C2×C4×C11C4×D414yes—
236C2×C4×C11C4×D414yes—
237C2×C4×C11C4×D418yescomplemented
238C2×C4×C11#12014yes—
239C2×C4×C11C22⋊Q814yes—
240C2×C4×C11C22⋊Q814yes—
241C2×C4×C11#12314yes—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—28no—
248C2×Dic11—22no—
249C2×Dic11—24no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—44no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11#12714yes—
264D44—232no—
265C4×D11—432no—
266C23×D4—111no—
267C24×C4—112no—
268C2×C4×D4—224no—
269C2×C4×D4—224no—
270C2×C4×D4—224no—
271C22×C4⋊C4—111no—
272C22×C4⋊C4—112no—
273C22×C4⋊C4C2×D1111yescharacteristic
274C22×C4⋊C4C2×D1114yes—
275C22×C4⋊C4C2×D1111yescharacteristic
276C22×C22⋊C4—114no—
277C22×C22⋊C4—112no—
278C22×C22⋊C4—114no—
279C22×C42—111no—
280C22×C42—111no—
281C22×C42C2×D1111yescharacteristic
282#390—118no—
283#390—224no—
284#389—224no—
285#385—2216no—
286#384—24no—
287C2×#95—112no—
288C2×#95—112no—
289C2×#95—114no—
290C2×#95—112no—
291C22×C11C22×C4⋊C411yescharacteristic
292C22×C11C2×C4×D411yescharacteristic
293C22×C11C2×C4×D412yes—
294C22×C11C2×C4×D411yescharacteristic
295C22×C11#52012yes—
296C22×C11C2×#12011yescharacteristic
297C22×C11C2×C22⋊Q811yescharacteristic
298C22×C11C2×C22⋊Q811yescharacteristic
299C22×C11C2×#12311yescharacteristic
300C22×C11C2×#12711yescharacteristic
301C22×C11#53211yescharacteristic
302C22×C11#53212yes—
303C22×C11#53511yescharacteristic
304C22×C11#53611yescharacteristic
305C22×C11#54212yes—
306C22×C11D4212yes—
307C22×C11D4212yes—
308C22×C11#54712yes—
309C22×C11#54712yes—
310C22×C11#54812yes—
311C22×C11D4×Q812yes—
312C22×C11#55312yes—
313C22×C11#55412yes—
314C2×D11—216no—
315C2×D11—28no—
316C2×D11—44no—
317C2×D11—44no—
318C2×D11—44no—
319C2×D11—48no—
320C2×D11—48no—
321C2×D11—44no—
322C2×D11—44no—
323C2×D11—48no—
324C2×D11—44no—
325C4×C11—28no—
326C4×C11—44no—
327C4×C11—82no—
328C4×C11#38518yescomplemented
329Dic11—24no—
330Dic11—44no—
331Dic11—44no—
332Dic11—42no—
333C25—112no—
334C22×D4—114no—
335C22×D4—114no—
336C22×D4—114no—
337C22×D4—222no—
338C22×D4—222no—
339C22×D4—222no—
340C22×D4—222no—
341C23×C4—111no—
342C23×C4—112no—
343C23×C4—112no—
344C23×C4—111no—
345C23×C4—224no—
346C23×C4—228no—
347C23×C4—224no—
348C23×C4—224no—
349C23×C4—444no—
350C23×C4C22×D1112yes—
351C23×C4C22×D1112yes—
352C23×C4C22×D1112yes—
353C23×C4C22×D1111yescharacteristic
354C4×D4—2232no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—28no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—28no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—114no—
364C2×C4⋊C4—222no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—228no—
367C2×C4⋊C4—224no—
368C2×C4⋊C4C22⋊D1114yes—
369C2×C22⋊C4—1116no—
370C2×C22⋊C4—224no—
371C2×C22⋊C4—224no—
372C2×C22⋊C4—228no—
373C2×C22⋊C4—228no—
374C2×C22⋊C4—224no—
375C2×C22⋊C4—228no—
376C2×C22⋊C4—228no—
377C2×C22⋊C4—444no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—114no—
381C2×C42—222no—
382C2×C42—222no—
383C2×C42—222no—
384C2×C42—222no—
385C2×C42—222no—
386C2×C42C4×D1114yescomplemented
387#95—118no—
388#95—228no—
389#95—224no—
390#95—224no—
391C2×C11C2×#38511yescharacteristic
392C2×C11C4×#12711yescharacteristic
393C2×C11#232611yescharacteristic
394C2×C11D4×C4⋊C412yes—
395C2×C11#236112yes—
396C2×C11#242212yes—
397C2×C11#243211yescharacteristic
398C2×C11#243311yescharacteristic
399C2×C11#245212yes—
400C2×C11#254211yescharacteristic
401C2×C11#256611yescharacteristic
402D11—48no—
403C24—114no—
404C24—114no—
405C24—114no—
406C24—222no—
407C24—224no—
408C24—222no—
409C24—224no—
410C24—224no—
411C24—222no—
412C24—224no—
413C24—222no—
414C24C23×D1111yescharacteristic
415C2×D4—1116no—
416C2×D4—228no—
417C2×D4—228no—
418C2×D4—228no—
419C2×D4—228no—
420C2×D4—228no—
421C2×D4—228no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—114no—
436C22×C4—112no—
437C22×C4—114no—
438C22×C4—114no—
439C22×C4—112no—
440C22×C4—2216no—
441C22×C4—221no—
442C22×C4—222no—
443C22×C4—221no—
444C22×C4—222no—
445C22×C4—224no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—221no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—224no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—221no—
458C22×C4—4416no—
459C22×C4—448no—
460C22×C4—4416no—
461C22×C4—448no—
462C22×C4C2×C4×D1114yes—
463C22×C4C2×C4×D1112yes—
464C22×C4#433912yes—
465C22×C4D4×D1114yes—
466C22×C4D4×D1112yes—
467C22×C4D4×D1112yes—
468C22×C4Q8×D1112yes—
469C22×C4#434314yes—
470C22×C4#434312yes—
471C22×C4C2×C22⋊D1114yes—
472C22×C4C2×C22⋊D1112yes—
473C4⋊C4—28no—
474C4⋊C4—416no—
475C4⋊C4—44no—
476C4⋊C4—228no—
477C4⋊C4—448no—
478C22⋊C4—2216no—
479C22⋊C4—2232no—
480C22⋊C4—4416no—
481C42—28no—
482C42—228no—
483C42—444no—
484C11#1397711yescharacteristic, complemented, Sylow
485C23—118no—
486C23—228no—
487C23—228no—
488C23—228no—
489C23—228no—
490C23—228no—
491C23—224no—
492C23—228no—
493C23—224no—
494C23—224no—
495C23—224no—
496C23—224no—
497C23—224no—
498C23—442no—
499C23—442no—
500C23—442no—
501C23—444no—
502C23—442no—
503C23—444no—
504C23—444no—
505C23—444no—
506C23—444no—
507C23—444no—
508C23C22×C4×D1111yescharacteristic
509C23C2×#433911yescharacteristic
510C23C2×D4×D1111yescharacteristic
511C23C2×D4×D1112yes—
512C23C2×D4×D1111yescharacteristic
513C23#6703712yes—
514C23C2×Q8×D1111yescharacteristic
515C23C2×#434312yes—
516C23C2×#434311yescharacteristic
517C23#6704012yes—
518C23C22×C22⋊D1111yescharacteristic
519D4—2232no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—28no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—44no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—44no—
534C2×C4—42no—
535C2×C4—44no—
536C2×C4—114no—
537C2×C4—222no—
538C2×C4—224no—
539C2×C4—222no—
540C2×C4—224no—
541C2×C4—224no—
542C2×C4—222no—
543C2×C4—224no—
544C2×C4—222no—
545C2×C4—228no—
546C2×C4—224no—
547C2×C4—224no—
548C2×C4—222no—
549C2×C4—4432no—
550C2×C4—442no—
551C2×C4—444no—
552C2×C4—442no—
553C2×C4—442no—
554C2×C4—442no—
555C2×C4—442no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4—442no—
559C2×C4C4⋊C4×D1114yes—
560C2×C4#6694614yes—
561C2×C4#6694618yescomplemented
562C2×C4#6694714yes—
563C2×C4#6694914yes—
564C2×C4C4×C22⋊D1114yes—
565C2×C4#6699014yes—
566C2×C4#6699914yes—
567C22—2216no—
568C22—228no—
569C22—448no—
570C22—448no—
571C22—444no—
572C22—448no—
573C22—444no—
574C22—444no—
575C22—444no—
576C22—444no—
577C22—444no—
578C22C2×C4⋊C4×D1111yescharacteristic
579C22C2×#6694612yes—
580C22C2×#6694611yescharacteristic
581C22#1062303512yes—
582C22C2×#6694711yescharacteristic
583C22#1062303812yes—
584C22C2×#6694911yescharacteristic
585C22#1062304512yes—
586C22D11×#12711yescharacteristic
587C22#1062324611yescharacteristic
588C22#1062324812yes—
589C22#1062325511yescharacteristic
590C22#1062325612yes—
591C22#1062325611yescharacteristic
592C22#1062325712yes—
593C22#1062325812yes—
594C22#1062326112yes—
595C22#1062326412yes—
596C22C2×C4×C22⋊D1111yescharacteristic
597C22C2×#6699011yescharacteristic
598C22D4×C22⋊D1112yes—
599C22C2×#6699911yescharacteristic
600C22#1062334812yes—
601C4—28no—
602C4—44no—
603C4—82no—
604C4—224no—
605C4—444no—
606C4—444no—
607C4—442no—
608C4#1062260218yescomplemented
609C2—448no—
610C2C2×#1062260211yescharacteristic
611C2#1307117811yescharacteristic
612C2#1307132411yescharacteristic
613C2#1307151612yes—
614C2#1307163212yes—
615C2#1307213312yes—
616C2#1307224111yescharacteristic
617C2#1307225011yescharacteristic
618C2#1307246212yes—
619C2#1307356811yescharacteristic
620C2#1307381311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#384C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#384D11
hypocenterC11#13977
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#384

Complements

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

NH ≅ G/Ntype
4. C2×#10622586C2semidirect
5. C2×#10622602C2semidirect
6. #13066858C2semidirect
7. #13066845C2semidirect
8. C4×C11⋊#95C2semidirect
9. C2×C11×#384C2semidirect
34. #10622552C4semidirect
67. C2×C42×C11C2×C4semidirect
76. C2×(C2×D11)⋊C4C2×C4semidirect
79. C2×C4⋊Dic11C2×C4semidirect
92. C11⋊#95D4semidirect
158. C2×D44C4⋊C4semidirect
180. C2×#384D11semidirect
237. C2×C4×C11C4×D4semidirect
328. C4×C11#385semidirect
386. C2×C42C4×D11semidirect
484. C11#13977semidirect
561. C2×C4#66946semidirect
608. C4#10622602semidirect

Maximal subgroups

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

subgroupindex
C22×#669462
C2×#106225522
C2×#106226012
C2×#106225862
C2×#106226022
#130668582
#130668452
C4×C11⋊#952
C2×C11×#3842
#1397711