Finite Group Databasebeta

← #14680816

Subgroups — #14680816

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×#10622604C211yesmaximal, characteristic
2C2×#10622552C211yesmaximal, characteristic
3#13066872C211yesmaximal, characteristic, complemented
4#13066869C211yesmaximal, characteristic, complemented
5#13066864C212yesmaximal, complemented
6#13066858C212yesmaximal, complemented
7#13066856C211yesmaximal, characteristic
8#13066852C212yesmaximal, complemented
9#13066852C212yesmaximal, complemented
10C4×C11⋊#95C211yesmaximal, characteristic, complemented
11C2×C11×#387C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4×Dic11C2212yes—
24C11×#387—24no—
25C2×C11×#95C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36#10622604C418yescomplemented
37#10622552—24no—
38C24×D11C2312yes—
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2312yes—
48C23×Dic11C2312yes—
49C22×D44—22no—
50C22×D44—22no—
51C22×D44—42no—
52C22×D44—42no—
53C22×D44C2×C414yes—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—42no—
58C2×C11×C4⋊C4C2×C414yes—
59C2×C42×C11—42no—
60C2×C42×C11D414yes—
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—42no—
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)⋊C4—42no—
77C2×(C2×D11)⋊C4C2×C418yes—
78C2×(C2×D11)⋊C4C2×C418yes—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—42no—
81C2×C4×Dic11—24no—
82C2×C4×Dic11—42no—
83C2×C4×Dic11—42no—
84C11×#95—22no—
85C11×#95—22no—
86C11×#95—22no—
87C11×#95—22no—
88C11⋊#95—22no—
89C11⋊#95—24no—
90C11⋊#95—42no—
91C11⋊#95—42no—
92C11⋊#95—42no—
93C11⋊#95—42no—
94C11⋊#95C2×C414yes—
95#14325—111nomaximal, Sylow
96C24×C11C2411yescharacteristic
97C23×D11—22no—
98C23×D11—22no—
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—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11C22×C412yes—
142C22×C4×C11C22×C412yes—
143C22×C4×C11C22×C412yes—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11#4112yes—
148C22×C4×C11#4114yes—
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×Dic11C22×C414yes—
169C22×Dic11#4114yes—
170C2×D44—28no—
171C2×D44—48no—
172C2×D44—44no—
173C2×D44—44no—
174C2×D44—48no—
175C11×C4⋊C4—28no—
176C11×C4⋊C4—44no—
177C42×C11—44no—
178(C2×D11)⋊C4—48no—
179(C2×D11)⋊C4—48no—
180(C2×D11)⋊C4—48no—
181(C2×D11)⋊C4—48no—
182(C2×D11)⋊C4—48no—
183(C2×D11)⋊C4—48no—
184C4⋊Dic11—44no—
185C4×Dic11—48no—
186C2×#394—111no—
187C2×#390—111no—
188C2×#387D1111yescharacteristic, complemented
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×C11C23×C411yescharacteristic
198C23×C11C22×D411yescharacteristic
199C23×C11C2×#4111yescharacteristic
200C23×C11C2×#4112yes—
201C23×C11C2×#4112yes—
202C23×C11H(5,𝔽2)12yes—
203C23×C11H(5,𝔽2)12yes—
204C23×C11H(5,𝔽2)11yescharacteristic
205C23×C11H(5,𝔽2)11yescharacteristic
206C23×C11H(5,𝔽2)11yescharacteristic
207C23×C112−1+411yescharacteristic
208C22×D11—24no—
209C22×D11—24no—
210C22×D11—24no—
211C22×D11—24no—
212C22×D11—24no—
213C22×D11—24no—
214C22×D11—24no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—42no—
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—
243C2×C4×C11—24no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—24no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—41no—
266C2×C4×C11—42no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—42no—
278C2×C4×C11C4×D414yes—
279C2×C4×C11#12414yes—
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×Dic11—42no—
298C2×Dic11—42no—
299C2×Dic11—42no—
300C2×Dic11—42no—
301D44—416no—
302C23×D4—111no—
303C22×C4⋊C4—111no—
304C22×C4⋊C4C2×D1111yescharacteristic
305C22×C4⋊C4C2×D1111yescharacteristic
306C22×C22⋊C4—112no—
307C22×C22⋊C4—112no—
308C22×C22⋊C4—112no—
309C22×C22⋊C4—112no—
310C22×C22⋊C4—112no—
311C22×C22⋊C4—112no—
312C22×C42—112no—
313C22×C42C2×D1111yescharacteristic
314#394—118no—
315#390—224no—
316#387—24no—
317C2×#95—111no—
318C2×#95—111no—
319C2×#95—112no—
320C2×#95—112no—
321C2×#95—112no—
322C2×#95—112no—
323C2×#95—112no—
324C2×#95C2×D1111yescharacteristic
325C2×#95C2×D1111yescharacteristic
326C2×#95C2×D1111yescharacteristic
327C2×#95C2×D1111yescharacteristic
328C22×C11C2×C4×D411yescharacteristic
329C22×C11C4×#4112yes—
330C22×C11#51811yescharacteristic
331C22×C11#51812yes—
332C22×C11#52011yescharacteristic
333C22×C11C2×#12411yescharacteristic
334C22×C11#52912yes—
335C22×C11#53211yescharacteristic
336C22×C11#53411yescharacteristic
337C22×C11#53511yescharacteristic
338C22×C11#53511yescharacteristic
339C22×C11#53711yescharacteristic
340C22×C11#53812yes—
341C22×C11#53812yes—
342C22×C11#53812yes—
343C22×C11#53812yes—
344C22×C11#53912yes—
345C22×C11#54011yescharacteristic
346C22×C11#54012yes—
347C22×C11#54012yes—
348C22×C11#54012yes—
349C22×C11#54212yes—
350C22×C11#54211yescharacteristic
351C2×D11—44no—
352C2×D11—44no—
353C2×D11—44no—
354C2×D11—44no—
355C2×D11—44no—
356C2×D11—44no—
357C2×D11—44no—
358C2×D11—82no—
359C2×D11—82no—
360C2×D11—82no—
361C2×D11—82no—
362C2×D11—82no—
363C2×D11—82no—
364C2×D11—82no—
365C2×D11—82no—
366C4×C11—24no—
367C4×C11—24no—
368C4×C11—42no—
369C4×C11—42no—
370C4×C11—42no—
371C4×C11—81no—
372C4×C11—81no—
373Dic11—44no—
374Dic11—44no—
375Dic11—82no—
376C25—112no—
377C22×D4—114no—
378C22×D4—222no—
379C22×D4—222no—
380C22×D4—442no—
381C22×D4—442no—
382C23×C4—112no—
383C23×C4—112no—
384C23×C4—112no—
385C23×C4C22×D1111yescharacteristic
386C23×C4C22×D1111yescharacteristic
387C23×C4C22×D1111yescharacteristic
388C23×C4C22×D1111yescharacteristic
389C23×C4C22×D1111yescharacteristic
390C23×C4C22×D1111yescharacteristic
391C23×C4C22×D1111yescharacteristic
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—42no—
396C2×C4⋊C4—222no—
397C2×C4⋊C4—442no—
398C2×C4⋊C4C4×D1114yes—
399C2×C22⋊C4—118no—
400C2×C22⋊C4—118no—
401C2×C22⋊C4—224no—
402C2×C22⋊C4—224no—
403C2×C22⋊C4—224no—
404C2×C22⋊C4—224no—
405C2×C22⋊C4—224no—
406C2×C22⋊C4—224no—
407C2×C22⋊C4—442no—
408C2×C22⋊C4—442no—
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⋊C4—442no—
416C2×C22⋊C4—442no—
417C2×C42—42no—
418C2×C42—224no—
419C2×C42—442no—
420C2×C42—442no—
421C2×C42C22⋊D1114yes—
422#95—22no—
423#95—22no—
424#95—22no—
425#95—22no—
426#95—114no—
427#95—224no—
428#95—222no—
429#95—442no—
430#95—442no—
431#95—442no—
432#95—442no—
433C2×C11C4×#12411yescharacteristic
434C2×C11#232111yescharacteristic
435C2×C11#232411yescharacteristic
436C2×C11#233312yes—
437C2×C11#233512yes—
438C2×C11#263911yescharacteristic
439C2×C11#264111yescharacteristic
440C2×C11#264812yes—
441C2×C11#265112yes—
442C2×C11#266111yescharacteristic
443C2×C11#266211yescharacteristic
444D11—84no—
445C24—114no—
446C24—222no—
447C24—222no—
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—228no—
462C2×D4—448no—
463C2×D4—444no—
464C2×D4—448no—
465C2×D4—444no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
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—222no—
515C22×C4—222no—
516C22×C4C2×C4×D1112yes—
517C22×C4C2×C4×D1112yes—
518C22×C4C2×C4×D1112yes—
519C22×C4#433912yes—
520C22×C4#434314yes—
521C22×C4C2×C22⋊D1112yes—
522C22×C4C2×C22⋊D1112yes—
523C22×C4C2×C22⋊D1112yes—
524C4⋊C4—28no—
525C4⋊C4—44no—
526C4⋊C4—444no—
527C22⋊C4—448no—
528C22⋊C4—448no—
529C22⋊C4—448no—
530C22⋊C4—448no—
531C22⋊C4—448no—
532C22⋊C4—448no—
533C42—44no—
534C42—448no—
535C11#1432511yescharacteristic, complemented, Sylow
536C23—224no—
537C23—224no—
538C23—224no—
539C23—224no—
540C23—224no—
541C23—224no—
542C23—224no—
543C23—442no—
544C23—442no—
545C23—442no—
546C23—442no—
547C23—442no—
548C23—442no—
549C23—442no—
550C23—442no—
551C23—442no—
552C23—442no—
553C23—442no—
554C23—442no—
555C23—442no—
556C23—442no—
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—
571C23C22×C4×D1111yescharacteristic
572C23C2×#433911yescharacteristic
573C23#6703712yes—
574C23C2×#434312yes—
575C23#41×D1112yes—
576C23#6704211yescharacteristic
577C23#6704212yes—
578C23#6704211yescharacteristic
579C23#6704211yescharacteristic
580C23#6704311yescharacteristic
581C23C22×C22⋊D1111yescharacteristic
582D4—4416no—
583C2×C4—24no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—24no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—24no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—42no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—224no—
619C2×C4—224no—
620C2×C4—224no—
621C2×C4—224no—
622C2×C4—224no—
623C2×C4—224no—
624C2×C4—442no—
625C2×C4—442no—
626C2×C4—442no—
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×C4—442no—
639C2×C4C4×C22⋊D1114yes—
640C2×C4#6700014yes—
641C22—444no—
642C22—444no—
643C22—444no—
644C22—444no—
645C22—444no—
646C22—444no—
647C22—444no—
648C22—882no—
649C22—882no—
650C22—882no—
651C22—882no—
652C22—882no—
653C22—882no—
654C22—882no—
655C22—882no—
656C22#1062305211yescharacteristic
657C22#1062305411yescharacteristic
658C22#1062306511yescharacteristic
659C22#1062306611yescharacteristic
660C22#1062307612yes—
661C22#1062309112yes—
662C22C4×#434312yes—
663C22#1062311112yes—
664C22#1062317512yes—
665C22#1062317612yes—
666C22#1062318812yes—
667C22#1062319412yes—
668C22#1062322912yes—
669C22#1062322912yes—
670C22#1062323512yes—
671C22#1062324112yes—
672C22C2×C4×C22⋊D1111yescharacteristic
673C22#1062333511yescharacteristic
674C22C2×#6700011yescharacteristic
675C22#1062336111yescharacteristic
676C22#1062336111yescharacteristic
677C22#1062336311yescharacteristic
678C22#1062336411yescharacteristic
679C4—24no—
680C4—24no—
681C4—42no—
682C4—42no—
683C4—42no—
684C4—81no—
685C4—81no—
686C4—444no—
687C4—444no—
688C4—882no—
689C2—884no—
690C2C4×#6700011yescharacteristic
691C2#1307127011yescharacteristic
692C2#1307130911yescharacteristic
693C2#1307138012yes—
694C2#1307140512yes—
695C2#1307455011yescharacteristic
696C2#1307456211yescharacteristic
697C2#1307461012yes—
698C2#1307465512yes—
699C2#1307474411yescharacteristic
700C2#1307475611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#387C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#387D11
hypocenterC11#14325
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
3. #13066872C2semidirect
4. #13066869C2semidirect
5. #13066864C2semidirect
6. #13066858C2semidirect
8. #13066852C2semidirect
9. #13066852C2semidirect
10. C4×C11⋊#95C2semidirect
11. C2×C11×#387C2semidirect
36. #10622604C4semidirect
188. C2×#387D11semidirect
535. C11#14325semidirect

Maximal subgroups

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

subgroupindex
C2×#106226042
C2×#106225522
#130668722
#130668692
#130668642
#130668582
#130668562
#130668522
C4×C11⋊#952
C2×C11×#3872
#1432511