Finite Group Databasebeta

← #14683036

Subgroups — #14683036

Order 2816.

1918 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622833C211yesmaximal, characteristic
2C2×#10622833C211yesmaximal, characteristic
3#13066875C212yesmaximal, complemented
4#13066859C212yesmaximal, complemented
5#13066859C212yesmaximal, complemented
6#13066849C212yesmaximal, complemented
7#13066838C212yesmaximal, complemented
8#13066838C212yesmaximal, complemented
9C2×C11×#390C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C24×Dic11C2211yescharacteristic
12C24×Dic11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2212yes—
15C22×C11×C22⋊C4C2212yes—
16C22×C42×C11C2211yescharacteristic
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2211yescharacteristic
21C22×Dic11⋊C4C2212yes—
22C11×#390—24no—
23#10622833—24no—
24#10622833C418yescomplemented
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C25×C11C2311yescharacteristic
35C25×C11C2311yescharacteristic
36C22×D4×C11—41no—
37C22×D4×C11—41no—
38C22×D4×C11—41no—
39C22×D4×C11—41no—
40C22×D4×C11C2×C414yes—
41C22×D4×C11D414yes—
42C22×D4×C11Q814yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×Dic11—22no—
47C23×Dic11—24no—
48C23×Dic11—41no—
49C23×Dic11—41no—
50C23×Dic11—41no—
51C23×Dic11—41no—
52C23×Dic11—42no—
53C23×Dic11—42no—
54C23×Dic11—42no—
55C23×Dic11C2×C414yescomplemented
56C23×Dic11C2312yes—
57C23×Dic11C2312yes—
58C23×Dic11C2312yes—
59C23×Dic11C2312yes—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—41no—
62C2×C11×C4⋊C4—41no—
63C2×C11×C22⋊C4—24no—
64C2×C11×C22⋊C4—24no—
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4—24no—
67C2×C11×C22⋊C4—42no—
68C2×C11×C22⋊C4—42no—
69C2×C42×C11—22no—
70C2×C42×C11—41no—
71C2×C42×C11—41no—
72C2×C22⋊Dic11—24no—
73C2×C22⋊Dic11—22no—
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—42no—
76C2×C22⋊Dic11—42no—
77C2×C22⋊Dic11—41no—
78C2×C22⋊Dic11—41no—
79C2×C22⋊Dic11—42no—
80C2×C22⋊Dic11—41no—
81C2×C22⋊Dic11—41no—
82C2×C22⋊Dic11C2×C418yes—
83C2×C22⋊Dic11C2×C414yescomplemented
84C2×Dic11⋊C4—24no—
85C2×Dic11⋊C4—42no—
86C2×Dic11⋊C4—42no—
87C11⋊#95—24no—
88C11⋊#95—24no—
89C11⋊#95—42no—
90C11⋊#95—42no—
91C11⋊#95—42no—
92C11⋊#95—42no—
93C11⋊#95—42no—
94C11⋊#95—42no—
95C11⋊#95C2×C418yescomplemented
96#14513—111nomaximal, Sylow
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—22no—
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—21no—
105C24×C11—21no—
106C24×C11—21no—
107C24×C11—21no—
108C24×C11—22no—
109C24×C11—21no—
110C24×C11—21no—
111C24×C11—21no—
112C24×C11—21no—
113C24×C11C22×C412yes—
114C24×C11C22×C412yes—
115C24×C11C2×D412yes—
116C24×C11C2×D412yes—
117C24×C11C2×Q812yes—
118C24×C11C2×Q812yes—
119C24×C11C2411yescharacteristic
120C2×D4×C11—44no—
121C2×D4×C11—44no—
122C2×D4×C11—44no—
123C2×D4×C11—44no—
124C2×D4×C11—44no—
125C2×D4×C11—44no—
126C2×D4×C11C4⋊C4116yescomplemented
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
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×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11C22×C412yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×Q812yes—
147C22×C4×C11#4114yes—
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×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—44no—
174C22×Dic11—48no—
175C22×Dic11—48no—
176C22×Dic11—44no—
177C22×Dic11—44no—
178C22×Dic11—48no—
179C22×Dic11—44no—
180C22×Dic11—48no—
181C22×Dic11—44no—
182C22×Dic11—44no—
183C22×Dic11C22×C414yes—
184C22×Dic11C22×C414yes—
185C22×Dic11#4114yes—
186C11×C4⋊C4—44no—
187C11×C22⋊C4—48no—
188C11×C22⋊C4—48no—
189C42×C11—44no—
190C22⋊Dic11—48no—
191C22⋊Dic11—44no—
192C22⋊Dic11—48no—
193C22⋊Dic11—44no—
194Dic11⋊C4—48no—
195C2×#390D1111yescharacteristic
196C2×#386—111no—
197C2×#386—111no—
198#1442—112no—
199#1439—112no—
200#1439—112no—
201#1436—112no—
202C22⋊#95—112no—
203C22⋊#95—112no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—22no—
207C23×C11—24no—
208C23×C11—22no—
209C23×C11—24no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—24no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11—24no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—42no—
244C23×C11—41no—
245C23×C11—42no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11C2×C4⋊C414yes—
249C23×C11C2×C4⋊C414yes—
250C23×C11C23×C411yescharacteristic
251C23×C11C22×D411yescharacteristic
252C23×C11C22×Q811yescharacteristic
253C23×C11C2×#4112yes—
254C23×C11C2×#4112yes—
255C23×C11H(5,𝔽2)11yescharacteristic
256C23×C11H(5,𝔽2)11yescharacteristic
257C23×C11H(5,𝔽2)11yescharacteristic
258C23×C11H(5,𝔽2)11yescharacteristic
259C23×C11H(5,𝔽2)12yes—
260C23×C11H(5,𝔽2)12yes—
261D4×C11—416no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—24no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
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×C11—42no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11C2×C4⋊C414yes—
283C2×Dic11—24no—
284C2×Dic11—24no—
285C2×Dic11—24no—
286C2×Dic11—24no—
287C2×Dic11—24no—
288C2×Dic11—24no—
289C2×Dic11—24no—
290C2×Dic11—24no—
291C2×Dic11—24no—
292C2×Dic11—416no—
293C2×Dic11—416no—
294C2×Dic11—42no—
295C2×Dic11—42no—
296C2×Dic11—42no—
297C2×Dic11—42no—
298C2×Dic11—42no—
299C2×Dic11—42no—
300C2×Dic11—42no—
301C2×Dic11—42no—
302C2×Dic11—42no—
303C2×Dic11—42no—
304C2×Dic11—42no—
305C2×Dic11—42no—
306C2×Dic11—42no—
307C2×Dic11—42no—
308C2×Dic11—42no—
309C2×Dic11—42no—
310C2×Dic11—42no—
311C2×Dic11—42no—
312C2×Dic11—42no—
313C23×D4C2×D1111yescharacteristic
314C24×C4—111no—
315C24×C4—111no—
316C22×C4⋊C4—112no—
317C22×C4⋊C4C2×D1111yescharacteristic
318C22×C22⋊C4—112no—
319C22×C22⋊C4—111no—
320C22×C22⋊C4—112no—
321C22×C22⋊C4—111no—
322C22×C22⋊C4C2×D1112yes—
323C22×C22⋊C4C2×D1112yes—
324C22×C42C2×D1111yescharacteristic
325#390—24no—
326#386—118no—
327#386—224no—
328C2×#95—112no—
329C2×#95—112no—
330C2×#95—112no—
331C2×#95—112no—
332C2×#95—112no—
333C2×#95—112no—
334C2×#95—112no—
335C2×#95—112no—
336C2×#95—112no—
337C22×C11—24no—
338C22×C11—24no—
339C22×C11—28no—
340C22×C11—28no—
341C22×C11—44no—
342C22×C11—44no—
343C22×C11—42no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11—44no—
350C22×C11—44no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—44no—
356C22×C11—44no—
357C22×C11—42no—
358C22×C11—42no—
359C22×C11C22×C4⋊C411yescharacteristic
360C22×C11C4×#4112yes—
361C22×C11#51811yescharacteristic
362C22×C11#51811yescharacteristic
363C22×C11#51812yes—
364C22×C11#53411yescharacteristic
365C22×C11#53411yescharacteristic
366C22×C11#53812yes—
367C22×C11#53812yes—
368C22×C11#54012yes—
369C22×C11#54012yes—
370C22×C11#54311yescharacteristic
371C22×C11#54311yescharacteristic
372C22×C11#54612yes—
373C22×C11#54612yes—
374C22×C11#55111yescharacteristic
375C22×C11#55312yes—
376C22×C11#55412yes—
377C22×C11#55412yes—
378C22×C11#55911yescharacteristic
379C22×C11#56011yescharacteristic
380C22×C11#56012yes—
381C22×C11H(3,𝔽4)11yescharacteristic
382C4×C11—24no—
383C4×C11—44no—
384C4×C11—82no—
385Dic11—44no—
386Dic11—44no—
387Dic11—44no—
388Dic11—82no—
389C25C22×D1111yescharacteristic
390C25C22×D1111yescharacteristic
391C22×D4—41no—
392C22×D4—41no—
393C22×D4—41no—
394C22×D4—41no—
395C22×D4Dic2214yes—
396C22×D4C4×D1114yes—
397C22×D4C22⋊D1114yes—
398C23×C4—112no—
399C23×C4—112no—
400C23×C4—112no—
401C23×C4—114no—
402C23×C4—112no—
403C23×C4—224no—
404C23×C4—222no—
405C23×C4—441no—
406C23×C4—441no—
407C23×C4—441no—
408C23×C4—441no—
409C23×C4—442no—
410C23×C4—442no—
411C23×C4—442no—
412C23×C4C22×D1112yes—
413C23×C4C22×D1112yes—
414C23×C4C22×D1111yescharacteristic
415C2×C4⋊C4—22no—
416C2×C4⋊C4—41no—
417C2×C4⋊C4—41no—
418C2×C4⋊C4—224no—
419C2×C4⋊C4—442no—
420C2×C4⋊C4—442no—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—24no—
423C2×C22⋊C4—24no—
424C2×C22⋊C4—24no—
425C2×C22⋊C4—42no—
426C2×C22⋊C4—42no—
427C2×C22⋊C4—118no—
428C2×C22⋊C4—114no—
429C2×C22⋊C4—224no—
430C2×C22⋊C4—224no—
431C2×C22⋊C4—222no—
432C2×C22⋊C4—441no—
433C2×C22⋊C4—442no—
434C2×C22⋊C4—441no—
435C2×C22⋊C4—442no—
436C2×C22⋊C4—442no—
437C2×C22⋊C4—441no—
438C2×C22⋊C4—441no—
439C2×C42—22no—
440C2×C42—41no—
441C2×C42—41no—
442#95—118no—
443#95—224no—
444#95—224no—
445#95—442no—
446#95—442no—
447#95—442no—
448#95—442no—
449#95—442no—
450#95—442no—
451C2×C11—44no—
452C2×C11—44no—
453C2×C11#231511yescharacteristic
454C2×C11#233312yes—
455C2×C11#234912yes—
456C2×C11#237411yescharacteristic
457C2×C11#237511yescharacteristic
458C2×C11#268411yescharacteristic
459C2×C11#268812yes—
460C2×C11#270911yescharacteristic
461C2×C11#274811yescharacteristic
462C2×C11#278012yes—
463C2×C11#280411yescharacteristic
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—21no—
474C24—21no—
475C24—21no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24C2×Dic2212yes—
481C24C2×Dic2212yes—
482C24C2×C4×D1112yes—
483C24C2×C4×D1112yes—
484C24C2×C22⋊D1112yes—
485C24C2×C22⋊D1112yes—
486C24C23×D1111yescharacteristic
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4Dic11⋊C4116yescomplemented
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—114no—
512C22×C4—114no—
513C22×C4—114no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—222no—
517C22×C4—222no—
518C22×C4—222no—
519C22×C4—222no—
520C22×C4—222no—
521C22×C4—222no—
522C22×C4—222no—
523C22×C4—222no—
524C22×C4—222no—
525C22×C4—222no—
526C22×C4—222no—
527C22×C4—222no—
528C22×C4—222no—
529C22×C4—222no—
530C22×C4—222no—
531C22×C4—222no—
532C22×C4—222no—
533C22×C4—222no—
534C22×C4—222no—
535C22×C4—222no—
536C22×C4—222no—
537C22×C4—222no—
538C22×C4—222no—
539C22×C4—444no—
540C22×C4—448no—
541C22×C4—444no—
542C22×C4—448no—
543C22×C4—448no—
544C22×C4—444no—
545C22×C4—444no—
546C22×C4—448no—
547C22×C4—444no—
548C22×C4—444no—
549C22×C4C2×Dic2212yes—
550C22×C4C2×C4×D1112yes—
551C22×C4#434114yes—
552C22×C4C2×C22⋊D1112yes—
553C4⋊C4—44no—
554C4⋊C4—448no—
555C22⋊C4—48no—
556C22⋊C4—48no—
557C22⋊C4—444no—
558C22⋊C4—448no—
559C22⋊C4—448no—
560C22⋊C4—444no—
561C42—44no—
562C11#1451311yescharacteristic, complemented, Sylow
563C23—22no—
564C23—22no—
565C23—22no—
566C23—22no—
567C23—22no—
568C23—22no—
569C23—22no—
570C23—22no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—24no—
577C23—24no—
578C23—24no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—41no—
588C23—41no—
589C23—42no—
590C23—42no—
591C23—41no—
592C23—41no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23C2×Dic11⋊C414yes—
608C23C2×Dic11⋊C414yes—
609C23C22×Dic2211yescharacteristic
610C23C22×C4×D1111yescharacteristic
611C23C2×#434112yes—
612C23#6703711yescharacteristic
613C23#6703711yescharacteristic
614C23#6703712yes—
615C23#6703711yescharacteristic
616C23#6703711yescharacteristic
617C23#41×D1112yes—
618C23#6704212yes—
619C23C22×C22⋊D1111yescharacteristic
620D4—416no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—224no—
642C2×C4—224no—
643C2×C4—224no—
644C2×C4—224no—
645C2×C4—224no—
646C2×C4—224no—
647C2×C4—224no—
648C2×C4—224no—
649C2×C4—224no—
650C2×C4—4416no—
651C2×C4—4416no—
652C2×C4—442no—
653C2×C4—442no—
654C2×C4—442no—
655C2×C4—442no—
656C2×C4—442no—
657C2×C4—442no—
658C2×C4—442no—
659C2×C4—442no—
660C2×C4—442no—
661C2×C4—442no—
662C2×C4—442no—
663C2×C4—442no—
664C2×C4—442no—
665C2×C4—442no—
666C2×C4—442no—
667C2×C4—442no—
668C2×C4—442no—
669C2×C4—442no—
670C2×C4—442no—
671C2×C4C2×Dic11⋊C414yes—
672C22—24no—
673C22—24no—
674C22—28no—
675C22—28no—
676C22—44no—
677C22—44no—
678C22—44no—
679C22—44no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—44no—
685C22—44no—
686C22—42no—
687C22—42no—
688C22—42no—
689C22—42no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22#1062301411yescharacteristic
695C22#1062301411yescharacteristic
696C22#1062301711yescharacteristic
697C22#1062301711yescharacteristic
698C22C4×#434112yes—
699C22#1062307012yes—
700C22#1062307412yes—
701C22#1062307612yes—
702C22#1062313212yes—
703C22#1062314612yes—
704C22#1062314812yes—
705C22#1062315112yes—
706C22#1062320912yes—
707C22#1062321011yescharacteristic
708C22#1062321411yescharacteristic
709C22#1062324411yescharacteristic
710C22#1062325012yes—
711C22#1062325111yescharacteristic
712C22C22×Dic11⋊C411yescharacteristic
713C22#1062333511yescharacteristic
714C22#1062333511yescharacteristic
715C22#1062333712yes—
716C22#1062336012yes—
717C4—24no—
718C4—44no—
719C4—82no—
720C4—444no—
721C4—444no—
722C4—444no—
723C4—882no—
724C2—44no—
725C2—44no—
726C2#1307122811yescharacteristic
727C2#1307137512yes—
728C2#1307152112yes—
729C2#1307175111yescharacteristic
730C2#1307175311yescharacteristic
731C2#1307499211yescharacteristic
732C2#1307504612yes—
733C2#1307534311yescharacteristic
734C2#1307582911yescharacteristic
735C2#1307626512yes—
736C2#1307656211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#390C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#390D11
hypocenterC11#14513
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
3. #13066875C2semidirect
4. #13066859C2semidirect
5. #13066859C2semidirect
6. #13066849C2semidirect
7. #13066838C2semidirect
8. #13066838C2semidirect
24. #10622833C4semidirect
55. C23×Dic11C2×C4semidirect
83. C2×C22⋊Dic11C2×C4semidirect
95. C11⋊#95C2×C4semidirect
126. C2×D4×C11C4⋊C4semidirect
493. C2×D4Dic11⋊C4semidirect
562. C11#14513semidirect

Maximal subgroups

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

subgroupindex
C2×#106228332
#130668752
#130668592
#130668492
#130668382
C2×C11×#3902
#1451311