Finite Group Databasebeta

← #14682189

Subgroups — #14682189

Order 2816.

2118 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622601C211yesmaximal, characteristic
2C2×#10622278C212yesmaximal
3C2×#10622281C212yesmaximal, complemented
4C2×#10622602C212yesmaximal, complemented
5#13066869C211yesmaximal, characteristic, complemented
6#13066860C212yesmaximal, complemented
7#13066860C212yesmaximal, complemented
8Dic11⋊#95C212yesmaximal, complemented
9C11×#1441C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C23×C4×D11C2212yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4C2212yes—
21C22×Dic11⋊C4C2212yes—
22C22×C4×Dic11C2211yescharacteristic
23C2×C11×#95C2212yes—
24C2×C11×#95C2212yes—
25C2×C11×#95C2211yescharacteristic
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31#10622602—28no—
32#10622601C418yescomplemented
33#10622281—28no—
34#10622278—28no—
35C24×D11C2312yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×Dic11C2312yes—
42C23×Dic11C2312yes—
43C23×Dic11C2312yes—
44C22×D44—41no—
45C22×D44—41no—
46C22×D44—41no—
47C22×D44—41no—
48C22×D44C2×C414yes—
49C22×D44D414yes—
50C22×D44Q814yes—
51C22×C4×D11—24no—
52C22×C4×D11—24no—
53C22×C4×D11—24no—
54C22×C4×D11—42no—
55C22×C4×D11—42no—
56C22×C4×D11—42no—
57C22×C4×D11—42no—
58C2×C11×C4⋊C4—24no—
59C2×C11×C4⋊C4—41no—
60C2×C11×C4⋊C4—41no—
61C2×C11×C4⋊C4—41no—
62C2×C11×C4⋊C4C2×C414yescomplemented
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—24no—
69C2×(C2×D11)⋊C4—24no—
70C2×(C2×D11)⋊C4—24no—
71C2×(C2×D11)⋊C4—24no—
72C2×(C2×D11)⋊C4—42no—
73C2×(C2×D11)⋊C4—42no—
74C2×(C2×D11)⋊C4—42no—
75C2×(C2×D11)⋊C4—42no—
76C2×(C2×D11)⋊C4C2×C418yescomplemented
77C2×(C2×D11)⋊C4C2×C418yescomplemented
78C2×C4⋊Dic11—24no—
79C2×C4⋊Dic11—41no—
80C2×Dic11⋊C4—24no—
81C2×Dic11⋊C4—42no—
82C2×Dic11⋊C4—42no—
83C2×Dic11⋊C4—42no—
84C2×Dic11⋊C4—42no—
85C2×Dic11⋊C4D418yescomplemented
86C2×C4×Dic11—41no—
87C2×C4×Dic11—41no—
88C2×C4×Dic11C2×C414yescomplemented
89C11×#95—24no—
90C11×#95—24no—
91C11×#95—41no—
92C11⋊#95—24no—
93C11⋊#95—24no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96C11⋊#95—41no—
97#14440—111nomaximal, Sylow
98C24×C11C2411yescharacteristic
99C23×D11—22no—
100C23×D11—22no—
101C23×D11—22no—
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×D11C22×C414yes—
112C23×D11C2×D414yes—
113C23×D11C2×Q814yes—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
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×C11C22×C412yes—
140C22×C4×C11C22×C412yes—
141C22×C4×C11C22×C412yes—
142C22×C4×C11C2×D414yes—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×Q812yes—
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×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11C22×C414yes—
163C22×Dic11C2×D414yes—
164C22×Dic11C2×D414yes—
165C22×Dic11#4114yes—
166C2×D44—44no—
167C2×D44—44no—
168C2×D44—44no—
169C2×D44—44no—
170C2×D44—44no—
171C2×D44—44no—
172C2×D44C4⋊C4116yescomplemented
173C2×C4×D11—48no—
174C2×C4×D11—48no—
175C2×C4×D11—48no—
176C2×C4×D11—48no—
177C2×C4×D11—48no—
178C2×C4×D11—48no—
179C2×C4×D11—48no—
180C11×C4⋊C4—44no—
181C11×C4⋊C4—44no—
182(C2×D11)⋊C4—216no—
183(C2×D11)⋊C4—216no—
184(C2×D11)⋊C4—48no—
185(C2×D11)⋊C4—48no—
186(C2×D11)⋊C4—48no—
187C4⋊Dic11—44no—
188Dic11⋊C4—48no—
189Dic11⋊C4—48no—
190C4×Dic11—44no—
191C2×#390—111no—
192C2×#386—112no—
193C2×#385—112no—
194C2×#385—112no—
195#1441—111no—
196#1441D1111yescharacteristic, complemented
197#1439—112no—
198#1439—112no—
199C4⋊#95—112no—
200C23×C11C23×C411yescharacteristic
201C23×C11C22×D411yescharacteristic
202C23×C11C22×D412yes—
203C23×C11C22×Q811yescharacteristic
204C23×C11C2×#4112yes—
205C23×C11H(5,𝔽2)11yescharacteristic
206C23×C11H(5,𝔽2)11yescharacteristic
207C23×C11H(5,𝔽2)11yescharacteristic
208C23×C11H(5,𝔽2)11yescharacteristic
209C23×C11H(5,𝔽2)12yes—
210C23×C112−1+412yes—
211C22×D11—24no—
212C22×D11—24no—
213C22×D11—24no—
214C22×D11—24no—
215C22×D11—24no—
216C22×D11—24no—
217C22×D11—24no—
218C22×D11—24no—
219C22×D11—24no—
220C22×D11—24no—
221C22×D11—24no—
222C22×D11—24no—
223C22×D11—24no—
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—24no—
227C22×D11—24no—
228C22×D11—24no—
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×D11C2×C4⋊C418yes—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—24no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
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×C11C2×C4⋊C414yes—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—24no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—24no—
283C2×Dic11—24no—
284C2×Dic11—24no—
285C2×Dic11—24no—
286C2×Dic11—42no—
287C2×Dic11—42no—
288C2×Dic11—42no—
289C2×Dic11—42no—
290C2×Dic11—42no—
291C2×Dic11—42no—
292C2×Dic11—42no—
293C2×Dic11—42no—
294C2×Dic11—42no—
295C2×Dic11—42no—
296C2×Dic11—42no—
297C2×Dic11C4×D418yes—
298D44—416no—
299C4×D11—432no—
300C23×D4—111no—
301C24×C4—112no—
302C22×C4⋊C4—112no—
303C22×C4⋊C4—111no—
304C22×C4⋊C4—112no—
305C22×C4⋊C4C2×D1111yescharacteristic
306C22×C4⋊C4C2×D1111yescharacteristic
307C22×C22⋊C4—112no—
308C22×C22⋊C4—112no—
309C22×C22⋊C4—112no—
310C22×C22⋊C4—112no—
311C22×C22⋊C4—112no—
312C22×C42—111no—
313#390—118no—
314#386—228no—
315#385—228no—
316#385—228no—
317C2×#95—112no—
318C2×#95—112no—
319C2×#95—112no—
320C2×#95—112no—
321C2×#95—111no—
322C2×#95C2×D1112yes—
323C2×#95C2×D1112yes—
324C2×#95C2×D1111yescharacteristic
325C22×C11C22×C4⋊C411yescharacteristic
326C22×C11C2×C4×D412yes—
327C22×C11#51811yescharacteristic
328C22×C11#51811yescharacteristic
329C22×C11#52012yes—
330C22×C11#53411yescharacteristic
331C22×C11#53411yescharacteristic
332C22×C11#53412yes—
333C22×C11#53712yes—
334C22×C11#53812yes—
335C22×C11#53912yes—
336C22×C11#54311yescharacteristic
337C22×C11#54311yescharacteristic
338C22×C11D4211yescharacteristic
339C22×C11D4212yes—
340C22×C11#54712yes—
341C22×C11D4×Q812yes—
342C22×C11#55012yes—
343C22×C11#55412yes—
344C22×C11#55911yescharacteristic
345C22×C11H(3,𝔽4)11yescharacteristic
346C22×C11#56212yes—
347C22×C11#56311yescharacteristic
348C2×D11—28no—
349C2×D11—28no—
350C2×D11—28no—
351C2×D11—44no—
352C2×D11—44no—
353C2×D11—44no—
354C2×D11—44no—
355C2×D11—44no—
356C2×D11—44no—
357C2×D11—44no—
358C2×D11—44no—
359C2×D11—44no—
360C2×D11—44no—
361C2×D11—44no—
362C2×D11—44no—
363C4×C11—24no—
364C4×C11—42no—
365C4×C11—42no—
366C4×C11—44no—
367C4×C11—82no—
368Dic11—28no—
369Dic11—44no—
370Dic11—82no—
371C25—112no—
372C22×D4—114no—
373C22×D4—114no—
374C22×D4—114no—
375C22×D4—441no—
376C22×D4—441no—
377C22×D4—441no—
378C22×D4—441no—
379C23×C4—112no—
380C23×C4—112no—
381C23×C4—112no—
382C23×C4—224no—
383C23×C4—224no—
384C23×C4—224no—
385C23×C4—442no—
386C23×C4—442no—
387C23×C4—442no—
388C23×C4—442no—
389C23×C4C22×D1112yes—
390C23×C4C22×D1111yescharacteristic
391C23×C4C22×D1111yescharacteristic
392C23×C4C22×D1112yes—
393C23×C4C22×D1111yescharacteristic
394C2×C4⋊C4—24no—
395C2×C4⋊C4—41no—
396C2×C4⋊C4—41no—
397C2×C4⋊C4—41no—
398C2×C4⋊C4—118no—
399C2×C4⋊C4—224no—
400C2×C4⋊C4—224no—
401C2×C4⋊C4—442no—
402C2×C4⋊C4—442no—
403C2×C4⋊C4—442no—
404C2×C4⋊C4—442no—
405C2×C4⋊C4—441no—
406C2×C4⋊C4C4×D1114yescomplemented
407C2×C22⋊C4—118no—
408C2×C22⋊C4—118no—
409C2×C22⋊C4—224no—
410C2×C22⋊C4—224no—
411C2×C22⋊C4—224no—
412C2×C22⋊C4—224no—
413C2×C22⋊C4—224no—
414C2×C22⋊C4—224no—
415C2×C22⋊C4—224no—
416C2×C22⋊C4—224no—
417C2×C22⋊C4—224no—
418C2×C22⋊C4—442no—
419C2×C22⋊C4—442no—
420C2×C22⋊C4—442no—
421C2×C22⋊C4—442no—
422C2×C42—114no—
423C2×C42—441no—
424C2×C42—441no—
425#95—24no—
426#95—24no—
427#95—41no—
428#95—224no—
429#95—224no—
430#95—224no—
431#95—224no—
432#95—441no—
433C2×C11#231511yescharacteristic
434C2×C11#232512yes—
435C2×C11D4×C4⋊C412yes—
436C2×C11#236611yescharacteristic
437C2×C11#237911yescharacteristic
438C2×C11#267911yescharacteristic
439C2×C11#268212yes—
440C2×C11#268311yescharacteristic
441C2×C11#272411yescharacteristic
442C2×C11#273212yes—
443C2×C11#280411yescharacteristic
444D11—48no—
445C24—114no—
446C24—114no—
447C24—114no—
448C24—222no—
449C24—222no—
450C24—222no—
451C24—222no—
452C24—222no—
453C24—222no—
454C24—222no—
455C24—222no—
456C24—222no—
457C24—222no—
458C24—222no—
459C24—222no—
460C24C23×D1111yescharacteristic
461C2×D4—1116no—
462C2×D4—444no—
463C2×D4—444no—
464C2×D4—444no—
465C2×D4—444no—
466C2×D4—444no—
467C2×D4—444no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—114no—
494C22×C4—114no—
495C22×C4—114no—
496C22×C4—114no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—222no—
506C22×C4—222no—
507C22×C4—222no—
508C22×C4—222no—
509C22×C4—222no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—222no—
513C22×C4—222no—
514C22×C4—448no—
515C22×C4—448no—
516C22×C4—448no—
517C22×C4—448no—
518C22×C4—448no—
519C22×C4—448no—
520C22×C4—448no—
521C22×C4C2×C4×D1112yes—
522C22×C4C2×C4×D1112yes—
523C22×C4C2×C4×D1112yes—
524C22×C4D4×D1114yes—
525C22×C4D4×D1112yes—
526C22×C4Q8×D1112yes—
527C4⋊C4—44no—
528C4⋊C4—44no—
529C4⋊C4—448no—
530C4⋊C4—444no—
531C4⋊C4—448no—
532C22⋊C4—2216no—
533C22⋊C4—2216no—
534C22⋊C4—448no—
535C22⋊C4—448no—
536C22⋊C4—448no—
537C42—444no—
538C11#1444011yescharacteristic, complemented, Sylow
539C23—118no—
540C23—224no—
541C23—224no—
542C23—224no—
543C23—224no—
544C23—224no—
545C23—224no—
546C23—224no—
547C23—224no—
548C23—224no—
549C23—224no—
550C23—224no—
551C23—224no—
552C23—224no—
553C23—224no—
554C23—224no—
555C23—224no—
556C23—224no—
557C23—224no—
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—
574C23C22×C4×D1111yescharacteristic
575C23C2×D4×D1112yes—
576C23C2×D4×D1111yescharacteristic
577C23#6703711yescharacteristic
578C23#6703711yescharacteristic
579C23C2×Q8×D1111yescharacteristic
580C23#6704012yes—
581C23#41×D1112yes—
582C23#6704211yescharacteristic
583C23#6704212yes—
584C23#6704211yescharacteristic
585D4—4416no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—118no—
617C2×C4—224no—
618C2×C4—224no—
619C2×C4—224no—
620C2×C4—224no—
621C2×C4—224no—
622C2×C4—224no—
623C2×C4—224no—
624C2×C4—224no—
625C2×C4—224no—
626C2×C4—4432no—
627C2×C4—442no—
628C2×C4—442no—
629C2×C4—442no—
630C2×C4—442no—
631C2×C4—442no—
632C2×C4—442no—
633C2×C4—442no—
634C2×C4—442no—
635C2×C4—442no—
636C2×C4—442no—
637C2×C4—442no—
638C2×C4C4⋊C4×D1114yes—
639C22—228no—
640C22—228no—
641C22—228no—
642C22—444no—
643C22—444no—
644C22—444no—
645C22—444no—
646C22—444no—
647C22—444no—
648C22—444no—
649C22—444no—
650C22—444no—
651C22—444no—
652C22—444no—
653C22—444no—
654C22#1062301711yescharacteristic
655C22C2×C4⋊C4×D1111yescharacteristic
656C22#1062305211yescharacteristic
657C22C4×D4×D1112yes—
658C22#1062310512yes—
659C22#1062312111yescharacteristic
660C22#1062313012yes—
661C22#1062313611yescharacteristic
662C22#1062313611yescharacteristic
663C22#1062314012yes—
664C22#1062316012yes—
665C22#1062316212yes—
666C22#1062316511yescharacteristic
667C22#1062316511yescharacteristic
668C22#1062317812yes—
669C22#1062318412yes—
670C22#1062319511yescharacteristic
671C22#1062321411yescharacteristic
672C22#1062322112yes—
673C22#1062322312yes—
674C22#1062323512yes—
675C22#1062325812yes—
676C22#1062326611yescharacteristic
677C4—24no—
678C4—44no—
679C4—42no—
680C4—42no—
681C4—82no—
682C4—228no—
683C4—444no—
684C4—882no—
685C2—448no—
686C2#1307122911yescharacteristic
687C2#1307131512yes—
688C2#1307151712yes—
689C2#1307167911yescharacteristic
690C2#1307178811yescharacteristic
691C2#1307494911yescharacteristic
692C2#1307497612yes—
693C2#1307499011yescharacteristic
694C2#1307554311yescharacteristic
695C2#1307563712yes—
696C2#1307656111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1441C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1441D11
hypocenterC11#14440
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
3. C2×#10622281C2semidirect
4. C2×#10622602C2semidirect
5. #13066869C2semidirect
6. #13066860C2semidirect
7. #13066860C2semidirect
8. Dic11⋊#95C2semidirect
9. C11×#1441C2semidirect
32. #10622601C4semidirect
62. C2×C11×C4⋊C4C2×C4semidirect
76. C2×(C2×D11)⋊C4C2×C4semidirect
77. C2×(C2×D11)⋊C4C2×C4semidirect
85. C2×Dic11⋊C4D4semidirect
88. C2×C4×Dic11C2×C4semidirect
172. C2×D44C4⋊C4semidirect
196. #1441D11semidirect
406. C2×C4⋊C4C4×D11semidirect
538. C11#14440semidirect

Maximal subgroups

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

subgroupindex
C2×#106226012
C2×#106222782
C2×#106222812
C2×#106226022
#130668692
#130668602
Dic11⋊#952
C11×#14412
#1444011