Finite Group Databasebeta

← #14680787

Subgroups — #14680787

Order 2816.

1590 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622605C211yesmaximal, characteristic
2C2×#10622585C212yesmaximal, complemented
3C2×#10622553C211yesmaximal, characteristic
4C2×#10622603C212yesmaximal
5#13066884C211yesmaximal, characteristic, complemented
6#13066882C212yesmaximal, complemented
7#13066879C211yesmaximal, characteristic, complemented
8#13066860C212yesmaximal
9#13066858C211yesmaximal, characteristic
10C4×C11⋊#95C211yesmaximal, characteristic, complemented
11C2×C11×#389C211yesmaximal, characteristic, complemented
12C22×C11×C4⋊C4C2212yes—
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×(C2×D11)⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×Dic11⋊C4C2211yescharacteristic
22C22×Dic11⋊C4C2212yes—
23C22×Dic11⋊C4C2212yes—
24C22×C4×Dic11C2212yes—
25C11×#389—24no—
26C2×C11×#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36#10622605C418yescomplemented
37#10622603—28no—
38#10622585—28no—
39#10622553—24no—
40C24×D11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2312yes—
50C23×Dic11C2312yes—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—24no—
54C2×C11×C4⋊C4—24no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—24no—
57C2×C11×C4⋊C4—42no—
58C2×C11×C4⋊C4C2×C414yes—
59C2×C42×C11—42no—
60C2×C42×C11D414yes—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—24no—
64C2×(C2×D11)⋊C4—24no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—24no—
68C2×(C2×D11)⋊C4—24no—
69C2×(C2×D11)⋊C4—42no—
70C2×(C2×D11)⋊C4—42no—
71C2×(C2×D11)⋊C4—42no—
72C2×(C2×D11)⋊C4C2×C418yes—
73C2×(C2×D11)⋊C4C2×C414yes—
74C2×Dic11⋊C4—24no—
75C2×Dic11⋊C4—24no—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—24no—
78C2×Dic11⋊C4—24no—
79C2×Dic11⋊C4—42no—
80C2×Dic11⋊C4—42no—
81C2×Dic11⋊C4C2×C418yes—
82C2×C4×Dic11—42no—
83C2×C4×Dic11—42no—
84C2×C4×Dic11D418yes—
85C11×#95—24no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89C11⋊#95—24no—
90C11⋊#95—24no—
91C11⋊#95—24no—
92C11⋊#95—24no—
93C11⋊#95—24no—
94C11⋊#95C2×C414yes—
95#14322—111nomaximal, Sylow
96C24×C11C2411yescharacteristic
97C23×D11—22no—
98C23×D11—21no—
99C23×D11—21no—
100C23×D11—22no—
101C23×D11—22no—
102C23×D11—21no—
103C23×D11—21no—
104C23×D11—21no—
105C23×D11—22no—
106C23×D11—21no—
107C23×D11C22×C412yes—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11C22×C414yes—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D414yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11#4112yes—
137C22×Dic11—22no—
138C22×Dic11—21no—
139C22×Dic11—22no—
140C22×Dic11—21no—
141C22×Dic11—22no—
142C22×Dic11—21no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—21no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—21no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—21no—
158C22×Dic11—22no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11C22×C412yes—
162C22×Dic11C22×C414yes—
163C22×Dic11C2×D414yes—
164C22×Dic11C2×D414yes—
165C22×Dic11#4114yes—
166C11×C4⋊C4—28no—
167C11×C4⋊C4—44no—
168C11×C4⋊C4—48no—
169C42×C11—44no—
170(C2×D11)⋊C4—216no—
171(C2×D11)⋊C4—28no—
172(C2×D11)⋊C4—44no—
173(C2×D11)⋊C4—48no—
174(C2×D11)⋊C4—44no—
175Dic11⋊C4—216no—
176Dic11⋊C4—48no—
177Dic11⋊C4—44no—
178C4×Dic11—48no—
179C2×#399—111no—
180C2×#389—112no—
181C2×#389D1111yescharacteristic, complemented
182C2×#388—111no—
183C2×#388—112no—
184#1445—112no—
185#1445—111no—
186#1444—111no—
187#1439—112no—
188#1439—111no—
189C4×#95—111no—
190C23×C11C23×C411yescharacteristic
191C23×C11C22×D412yes—
192C23×C11C22×D411yescharacteristic
193C23×C11C2×#4111yescharacteristic
194C23×C11C2×#4112yes—
195C23×C11H(5,𝔽2)12yes—
196C23×C11H(5,𝔽2)11yescharacteristic
197C23×C112−1+411yescharacteristic
198C23×C112−1+412yes—
199C23×C112−1+411yescharacteristic
200C23×C112−1+411yescharacteristic
201C22×D11—22no—
202C22×D11—24no—
203C22×D11—22no—
204C22×D11—24no—
205C22×D11—22no—
206C22×D11—41no—
207C22×D11—42no—
208C22×D11—41no—
209C22×D11—41no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—42no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—41no—
221C22×D11—42no—
222C22×D11—41no—
223C22×D11—42no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11C4×D414yes—
252C2×C4×C11#12714yes—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—22no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—41no—
265C2×Dic11—42no—
266C2×Dic11—41no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—42no—
274C2×Dic11—41no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—42no—
281C2×Dic11C4×D418yes—
282C22×C4⋊C4—112no—
283C22×C4⋊C4—111no—
284C22×C4⋊C4—112no—
285C22×C4⋊C4C2×D1112yes—
286C22×C4⋊C4C2×D1111yescharacteristic
287C22×C4⋊C4C2×D1111yescharacteristic
288C22×C22⋊C4—112no—
289C22×C22⋊C4—111no—
290C22×C22⋊C4—111no—
291C22×C22⋊C4—112no—
292C22×C22⋊C4—111no—
293C22×C42—112no—
294C22×C42C2×D1111yescharacteristic
295#399—118no—
296#389—24no—
297#389—228no—
298#388—228no—
299#388—224no—
300C2×#95—111no—
301C2×#95—112no—
302C2×#95—111no—
303C2×#95—112no—
304C2×#95—112no—
305C2×#95—112no—
306C2×#95—111no—
307C2×#95—112no—
308C2×#95—111no—
309C2×#95C2×D1112yes—
310C22×C11C2×C4×D411yescharacteristic
311C22×C11C2×C4×D412yes—
312C22×C11#51911yescharacteristic
313C22×C11#52012yes—
314C22×C11#52011yescharacteristic
315C22×C11C2×#12711yescharacteristic
316C22×C11#53212yes—
317C22×C11#53211yescharacteristic
318C22×C11#53411yescharacteristic
319C22×C11#53412yes—
320C22×C11#53612yes—
321C22×C11#53612yes—
322C22×C11#53611yescharacteristic
323C22×C11#53611yescharacteristic
324C22×C11#53711yescharacteristic
325C22×C11#53712yes—
326C22×C11#53912yes—
327C22×C11#53912yes—
328C22×C11#53912yes—
329C22×C11#54111yescharacteristic
330C22×C11#54112yes—
331C22×C11#54211yescharacteristic
332C22×C11#54212yes—
333C2×D11—42no—
334C2×D11—44no—
335C2×D11—42no—
336C2×D11—42no—
337C2×D11—44no—
338C2×D11—81no—
339C2×D11—81no—
340C2×D11—81no—
341C2×D11—82no—
342C2×D11—81no—
343C2×D11—82no—
344C4×C11—24no—
345C4×C11—24no—
346C4×C11—44no—
347C4×C11—42no—
348C4×C11—82no—
349Dic11—28no—
350Dic11—42no—
351Dic11—44no—
352Dic11—81no—
353Dic11—81no—
354C25—111no—
355C23×C4—112no—
356C23×C4—111no—
357C23×C4—112no—
358C23×C4—111no—
359C23×C4—111no—
360C23×C4C22×D1112yes—
361C23×C4C22×D1112yes—
362C23×C4C22×D1111yescharacteristic
363C23×C4C22×D1111yescharacteristic
364C23×C4C22×D1111yescharacteristic
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—118no—
373C2×C4⋊C4—224no—
374C2×C4⋊C4—224no—
375C2×C4⋊C4—224no—
376C2×C4⋊C4—224no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—442no—
379C2×C4⋊C4—442no—
380C2×C4⋊C4C4×D1114yes—
381C2×C22⋊C4—118no—
382C2×C22⋊C4—114no—
383C2×C22⋊C4—224no—
384C2×C22⋊C4—224no—
385C2×C22⋊C4—222no—
386C2×C22⋊C4—222no—
387C2×C22⋊C4—224no—
388C2×C22⋊C4—224no—
389C2×C22⋊C4—222no—
390C2×C22⋊C4—222no—
391C2×C22⋊C4—442no—
392C2×C22⋊C4—442no—
393C2×C22⋊C4—442no—
394C2×C42—42no—
395C2×C42—118no—
396C2×C42—442no—
397C2×C42—442no—
398C2×C42C22⋊D1114yes—
399#95—24no—
400#95—114no—
401#95—224no—
402#95—224no—
403#95—224no—
404#95—224no—
405#95—224no—
406#95—222no—
407#95—222no—
408#95—222no—
409C2×C11C4×#12711yescharacteristic
410C2×C11#232212yes—
411C2×C11#232211yescharacteristic
412C2×C11#232311yescharacteristic
413C2×C11#232312yes—
414C2×C11#265611yescharacteristic
415C2×C11#265811yescharacteristic
416C2×C11#266311yescharacteristic
417C2×C11#266312yes—
418C2×C11#266411yescharacteristic
419C2×C11#266412yes—
420D11—82no—
421C24—112no—
422C24—221no—
423C24—222no—
424C24—222no—
425C24—222no—
426C24—221no—
427C24—221no—
428C24—222no—
429C24—221no—
430C24—221no—
431C24—221no—
432C24C23×D1111yescharacteristic
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—114no—
456C22×C4—114no—
457C22×C4—114no—
458C22×C4—112no—
459C22×C4—114no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—221no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—221no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4C2×C4×D1114yes—
485C22×C4C2×C4×D1112yes—
486C22×C4#433912yes—
487C22×C4D4×D1114yes—
488C22×C4C2×C22⋊D1112yes—
489C22×C4C2×C22⋊D1112yes—
490C22×C4C2×C22⋊D1112yes—
491C4⋊C4—28no—
492C4⋊C4—44no—
493C4⋊C4—48no—
494C4⋊C4—2216no—
495C4⋊C4—448no—
496C4⋊C4—444no—
497C22⋊C4—2216no—
498C22⋊C4—228no—
499C22⋊C4—444no—
500C22⋊C4—448no—
501C22⋊C4—444no—
502C42—44no—
503C42—448no—
504C11#1432211yescharacteristic, complemented, Sylow
505C23—224no—
506C23—222no—
507C23—224no—
508C23—222no—
509C23—222no—
510C23—442no—
511C23—442no—
512C23—442no—
513C23—441no—
514C23—442no—
515C23—441no—
516C23—441no—
517C23—441no—
518C23—441no—
519C23—441no—
520C23—441no—
521C23—441no—
522C23—442no—
523C23—442no—
524C23—442no—
525C23—442no—
526C23—442no—
527C23—442no—
528C23C22×C4×D1111yescharacteristic
529C23C2×#433911yescharacteristic
530C23C2×D4×D1112yes—
531C23#6703712yes—
532C23#6704012yes—
533C23#6704011yescharacteristic
534C23#6704011yescharacteristic
535C23#41×D1112yes—
536C23#6704211yescharacteristic
537C23#6704311yescharacteristic
538C23C22×C22⋊D1111yescharacteristic
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—118no—
567C2×C4—224no—
568C2×C4—224no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—222no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—442no—
579C2×C4—441no—
580C2×C4—442no—
581C2×C4—441no—
582C2×C4—442no—
583C2×C4—442no—
584C2×C4—442no—
585C2×C4—442no—
586C2×C4—442no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—442no—
594C2×C4—442no—
595C2×C4C4×C22⋊D1114yes—
596C2×C4#6699314yes—
597C22—442no—
598C22—444no—
599C22—442no—
600C22—442no—
601C22—444no—
602C22—881no—
603C22—881no—
604C22—881no—
605C22—882no—
606C22—881no—
607C22—882no—
608C22#1062303512yes—
609C22#1062304612yes—
610C22C4×D4×D1112yes—
611C22#1062307912yes—
612C22#1062310311yescharacteristic
613C22#1062310511yescharacteristic
614C22#1062311311yescharacteristic
615C22#1062311411yescharacteristic
616C22#1062312812yes—
617C22#1062313612yes—
618C22#1062316912yes—
619C22#1062317112yes—
620C22#1062322312yes—
621C22#1062322712yes—
622C22#1062325512yes—
623C22#1062325512yes—
624C22C2×C4×C22⋊D1111yescharacteristic
625C22C2×#6699311yescharacteristic
626C22#1062333511yescharacteristic
627C22#1062334711yescharacteristic
628C22#1062334711yescharacteristic
629C22#1062336311yescharacteristic
630C22#1062336411yescharacteristic
631C4—24no—
632C4—24no—
633C4—44no—
634C4—42no—
635C4—82no—
636C4—228no—
637C4—442no—
638C4—444no—
639C4—881no—
640C4—881no—
641C2—882no—
642C2C4×#6699311yescharacteristic
643C2#1307128012yes—
644C2#1307128511yescharacteristic
645C2#1307129211yescharacteristic
646C2#1307129312yes—
647C2#1307472011yescharacteristic
648C2#1307472811yescharacteristic
649C2#1307476711yescharacteristic
650C2#1307477012yes—
651C2#1307477711yescharacteristic
652C2#1307477912yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#389C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#389D11
hypocenterC11#14322
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×#10622585C2semidirect
5. #13066884C2semidirect
6. #13066882C2semidirect
7. #13066879C2semidirect
10. C4×C11⋊#95C2semidirect
11. C2×C11×#389C2semidirect
36. #10622605C4semidirect
181. C2×#389D11semidirect
504. C11#14322semidirect

Maximal subgroups

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

subgroupindex
C2×#106226052
C2×#106225852
C2×#106225532
C2×#106226032
#130668842
#130668822
#130668792
#130668602
#130668582
C4×C11⋊#952
C2×C11×#3892
#1432211