Finite Group Databasebeta

← #14680818

Subgroups — #14680818

Order 2816.

1650 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622834C211yesmaximal, characteristic
2C2×#10622594C211yesmaximal, characteristic, complemented
3#13066873C211yesmaximal, characteristic, complemented
4#13066869C211yesmaximal, characteristic, complemented
5#13066865C212yesmaximal, complemented
6#13066861C212yesmaximal, complemented
7#13066857C211yesmaximal, characteristic
8#13066853C212yesmaximal, complemented
9#13066853C212yesmaximal, complemented
10#95×Dic11C211yesmaximal, characteristic, complemented
11C2×C11×#394C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2212yes—
15C22×C11×C22⋊C4C2212yes—
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2212yes—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4×Dic11C2212yes—
23C22×C4×Dic11C2211yescharacteristic
24C11×#394C418yescomplemented
25C2×C11×#95C2211yescharacteristic
26#10622834—24no—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37#10622594—24no—
38C25×C11C2312yes—
39C22×D4×C11—22no—
40C22×D4×C11—22no—
41C22×D4×C11—42no—
42C22×D4×C11—42no—
43C22×D4×C11C2×C414yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2312yes—
50C23×Dic11C2311yescharacteristic
51C23×Dic11C2311yescharacteristic
52C23×Dic11C2312yes—
53C23×Dic11C2311yescharacteristic
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4C2×C414yes—
57C2×C11×C22⋊C4—42no—
58C2×C11×C22⋊C4—42no—
59C2×C11×C22⋊C4—42no—
60C2×C11×C22⋊C4—42no—
61C2×C11×C22⋊C4C2×C418yes—
62C2×C11×C22⋊C4C2×C418yes—
63C2×C22⋊Dic11—24no—
64C2×C22⋊Dic11—24no—
65C2×C22⋊Dic11—24no—
66C2×C22⋊Dic11—24no—
67C2×C22⋊Dic11—24no—
68C2×C22⋊Dic11—24no—
69C2×C22⋊Dic11—42no—
70C2×C22⋊Dic11—42no—
71C2×C22⋊Dic11—42no—
72C2×C22⋊Dic11—42no—
73C2×C22⋊Dic11—42no—
74C2×C22⋊Dic11—42no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—42no—
78C2×C4⋊Dic11—42no—
79C2×C4×Dic11—24no—
80C2×C4×Dic11—42no—
81C2×C4×Dic11—42no—
82C2×C4×Dic11—42no—
83C2×C4×Dic11D414yes—
84C11×#95C2×C414yes—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89C11⋊#95—22no—
90C11⋊#95—24no—
91C11⋊#95—42no—
92C11⋊#95—42no—
93C11⋊#95—42no—
94C11⋊#95—42no—
95#14325—111nomaximal, Sylow
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—22no—
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—22no—
105C24×C11—22no—
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11C22×C414yes—
111C24×C11C2411yescharacteristic
112C2×D4×C11—28no—
113C2×D4×C11—48no—
114C2×D4×C11—44no—
115C2×D4×C11—44no—
116C2×D4×C11—48no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
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—21no—
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—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11C22×C414yes—
136C22×C4×C11C22×C412yes—
137C22×C4×C11C22×C412yes—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11#4112yes—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—22no—
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—21no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11C2×D412yes—
172C22×Dic11C2×D412yes—
173C22×Dic11#4114yes—
174C22×Dic11#4114yes—
175C11×C4⋊C4—28no—
176C11×C22⋊C4—48no—
177C11×C22⋊C4—48no—
178C22⋊Dic11—48no—
179C22⋊Dic11—48no—
180C22⋊Dic11—48no—
181C22⋊Dic11—48no—
182C4⋊Dic11—44no—
183C4⋊Dic11—44no—
184C4×Dic11—44no—
185C4×Dic11—48no—
186C2×#394D1111yescharacteristic
187C2×#390—111no—
188C2×#387—111no—
189#1442—111no—
190#1441—111no—
191#1440—112no—
192#1439—112no—
193#1438—111no—
194#1437—112no—
195#1437—112no—
196C4×#95—111no—
197C23×C11—24no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11—42no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11—42no—
232C23×C11C23×C411yescharacteristic
233C23×C11C22×D411yescharacteristic
234C23×C11C2×#4111yescharacteristic
235C23×C11C2×#4112yes—
236C23×C11C2×#4112yes—
237C23×C11H(5,𝔽2)12yes—
238C23×C11H(5,𝔽2)12yes—
239C23×C11H(5,𝔽2)11yescharacteristic
240C23×C11H(5,𝔽2)11yescharacteristic
241C23×C11H(5,𝔽2)11yescharacteristic
242C23×C112−1+411yescharacteristic
243D4×C11—416no—
244C2×C4×C11—24no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—24no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—24no—
251C2×C4×C11—22no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—22no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11C4×D414yes—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—24no—
277C2×Dic11—24no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—42no—
289C2×Dic11—42no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—42no—
294C2×Dic11—42no—
295C2×Dic11—42no—
296C2×Dic11—42no—
297C2×Dic11—42no—
298C2×Dic11—42no—
299C2×Dic11—42no—
300C2×Dic11—42no—
301C2×Dic11#12414yes—
302C23×D4C2×D1111yescharacteristic
303C22×C4⋊C4—111no—
304C22×C4⋊C4—111no—
305C22×C4⋊C4C2×D1111yescharacteristic
306C22×C22⋊C4—112no—
307C22×C22⋊C4—112no—
308C22×C22⋊C4—112no—
309C22×C22⋊C4—112no—
310C22×C22⋊C4C2×D1112yes—
311C22×C22⋊C4C2×D1112yes—
312C22×C42—111no—
313C22×C42—112no—
314#394Dic1118yescomplemented
315#390—224no—
316#387—224no—
317C2×#95—111no—
318C2×#95—112no—
319C2×#95—111no—
320C2×#95—111no—
321C2×#95—111no—
322C2×#95—111no—
323C2×#95—112no—
324C2×#95—112no—
325C2×#95—112no—
326C2×#95—112no—
327C2×#95C2×D1111yescharacteristic
328C22×C11—44no—
329C22×C11—44no—
330C22×C11—44no—
331C22×C11—44no—
332C22×C11—44no—
333C22×C11—44no—
334C22×C11—44no—
335C22×C11—82no—
336C22×C11—82no—
337C22×C11—82no—
338C22×C11—82no—
339C22×C11—82no—
340C22×C11—82no—
341C22×C11—82no—
342C22×C11—82no—
343C22×C11C2×C4×D411yescharacteristic
344C22×C11C4×#4112yes—
345C22×C11#51812yes—
346C22×C11#51811yescharacteristic
347C22×C11#52011yescharacteristic
348C22×C11C2×#12411yescharacteristic
349C22×C11#52912yes—
350C22×C11#53211yescharacteristic
351C22×C11#53411yescharacteristic
352C22×C11#53511yescharacteristic
353C22×C11#53511yescharacteristic
354C22×C11#53711yescharacteristic
355C22×C11#53812yes—
356C22×C11#53812yes—
357C22×C11#53812yes—
358C22×C11#53812yes—
359C22×C11#53912yes—
360C22×C11#54012yes—
361C22×C11#54012yes—
362C22×C11#54011yescharacteristic
363C22×C11#54012yes—
364C22×C11#54211yescharacteristic
365C22×C11#54212yes—
366C4×C11—24no—
367C4×C11—42no—
368C4×C11—42no—
369C4×C11—44no—
370Dic11—24no—
371Dic11—44no—
372Dic11—42no—
373Dic11—82no—
374Dic11—81no—
375Dic11—81no—
376C25C22×D1112yes—
377C22×D4—22no—
378C22×D4—22no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4C2×Dic1114yes—
382C23×C4—111no—
383C23×C4—111no—
384C23×C4—112no—
385C23×C4—111no—
386C23×C4—112no—
387C23×C4—111no—
388C23×C4C22×D1111yescharacteristic
389C23×C4C22×D1111yescharacteristic
390C23×C4C22×D1112yes—
391C23×C4C22×D1111yescharacteristic
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—222no—
395C2×C4⋊C4—222no—
396C2×C4⋊C4—442no—
397C2×C4⋊C4—442no—
398C2×C4⋊C4C2×Dic1114yes—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—224no—
404C2×C22⋊C4—224no—
405C2×C22⋊C4—224no—
406C2×C22⋊C4—224no—
407C2×C22⋊C4—224no—
408C2×C22⋊C4—224no—
409C2×C22⋊C4—442no—
410C2×C22⋊C4—442no—
411C2×C22⋊C4—442no—
412C2×C22⋊C4—442no—
413C2×C22⋊C4—442no—
414C2×C22⋊C4—442no—
415C2×C22⋊C4C2×Dic1118yes—
416C2×C22⋊C4C2×Dic1118yes—
417C2×C42—114no—
418C2×C42—224no—
419C2×C42—442no—
420C2×C42—442no—
421C2×C42—442no—
422#95—224no—
423#95—222no—
424#95—222no—
425#95—222no—
426#95—222no—
427#95—222no—
428#95—442no—
429#95—442no—
430#95—442no—
431#95—442no—
432#95C2×Dic1114yes—
433C2×C11—84no—
434C2×C11C4×#12411yescharacteristic
435C2×C11#232111yescharacteristic
436C2×C11#232411yescharacteristic
437C2×C11#233312yes—
438C2×C11#233512yes—
439C2×C11#263911yescharacteristic
440C2×C11#264111yescharacteristic
441C2×C11#264812yes—
442C2×C11#265112yes—
443C2×C11#266111yescharacteristic
444C2×C11#266211yescharacteristic
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24C22×Dic1114yes—
460C24C23×D1111yescharacteristic
461C2×D4—28no—
462C2×D4—48no—
463C2×D4—44no—
464C2×D4—44no—
465C2×D4—48no—
466C22×C4—22no—
467C22×C4—22no—
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—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—112no—
485C22×C4—114no—
486C22×C4—112no—
487C22×C4—114no—
488C22×C4—222no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4—222no—
496C22×C4—221no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—222no—
504C22×C4—221no—
505C22×C4—222no—
506C22×C4—222no—
507C22×C4—222no—
508C22×C4—222no—
509C22×C4—221no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—222no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4D4×D1112yes—
519C22×C4#434112yes—
520C22×C4C22×Dic1114yes—
521C22×C4C22×Dic1112yes—
522C22×C4C22×Dic1112yes—
523C22×C4C22×Dic1112yes—
524C4⋊C4—28no—
525C4⋊C4—444no—
526C4⋊C4—444no—
527C22⋊C4—48no—
528C22⋊C4—48no—
529C22⋊C4—448no—
530C22⋊C4—448no—
531C22⋊C4—448no—
532C22⋊C4—448no—
533C42—444no—
534C42—448no—
535C11#1432511yescharacteristic, complemented, Sylow
536C23—24no—
537C23—24no—
538C23—24no—
539C23—24no—
540C23—24no—
541C23—24no—
542C23—24no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23—42no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—42no—
562C23—42no—
563C23—42no—
564C23—42no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23C2×D4×D1111yescharacteristic
572C23C2×#434111yescharacteristic
573C23#6703712yes—
574C23#6703712yes—
575C23#6703711yescharacteristic
576C23#6703711yescharacteristic
577C23#41×D1112yes—
578C23#41×D1112yes—
579C23#6704211yescharacteristic
580C23#6704311yescharacteristic
581C23C23×Dic1111yescharacteristic
582D4—416no—
583C2×C4—24no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—24no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—22no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—41no—
606C2×C4—114no—
607C2×C4—222no—
608C2×C4—222no—
609C2×C4—224no—
610C2×C4—224no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—224no—
614C2×C4—224no—
615C2×C4—222no—
616C2×C4—224no—
617C2×C4—442no—
618C2×C4—442no—
619C2×C4—442no—
620C2×C4—442no—
621C2×C4—442no—
622C2×C4—442no—
623C2×C4—441no—
624C2×C4—442no—
625C2×C4—441no—
626C2×C4—442no—
627C2×C4—441no—
628C2×C4—441no—
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—441no—
638C2×C4—441no—
639C2×C4—442no—
640C2×C4D4×Dic1114yes—
641C22—44no—
642C22—44no—
643C22—44no—
644C22—44no—
645C22—44no—
646C22—44no—
647C22—44no—
648C22—82no—
649C22—82no—
650C22—82no—
651C22—82no—
652C22—82no—
653C22—82no—
654C22—82no—
655C22—82no—
656C22#1062312011yescharacteristic
657C22#1062312311yescharacteristic
658C22#1062312412yes—
659C22#1062313411yescharacteristic
660C22#1062313811yescharacteristic
661C22#1062313911yescharacteristic
662C22#1062314412yes—
663C22#1062314412yes—
664C22#1062314612yes—
665C22#1062314612yes—
666C22#1062315011yescharacteristic
667C22#1062318812yes—
668C22#1062319112yes—
669C22#1062319312yes—
670C22#1062319412yes—
671C22#1062319911yescharacteristic
672C22D11×#12411yescharacteristic
673C22#1062321112yes—
674C22C2×D4×Dic1111yescharacteristic
675C22#1062332911yescharacteristic
676C22#1062332912yes—
677C22#41×Dic1112yes—
678C22#1062335811yescharacteristic
679C4—24no—
680C4—44no—
681C4—42no—
682C4—42no—
683C4—224no—
684C4—442no—
685C4—444no—
686C4—881no—
687C4—881no—
688C4—882no—
689C2—84no—
690C2#124×Dic1111yescharacteristic
691C2#1307127711yescharacteristic
692C2#1307131111yescharacteristic
693C2#1307138312yes—
694C2#1307141012yes—
695C2#1307454711yescharacteristic
696C2#1307455811yescharacteristic
697C2#1307460112yes—
698C2#1307464612yes—
699C2#1307475111yescharacteristic
700C2#1307476111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#394C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#394D11
hypocenterC11#14325
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C2×#10622594C2semidirect
3. #13066873C2semidirect
4. #13066869C2semidirect
5. #13066865C2semidirect
6. #13066861C2semidirect
8. #13066853C2semidirect
9. #13066853C2semidirect
10. #95×Dic11C2semidirect
24. C11×#394C4semidirect
314. #394Dic11semidirect
535. C11#14325semidirect

Maximal subgroups

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

subgroupindex
C2×#106228342
C2×#106225942
#130668732
#130668692
#130668652
#130668612
#130668572
#130668532
#95×Dic112
C2×C11×#3942
#1432511