Finite Group Databasebeta

← #14756902

Subgroups — #14756902

Order 2816.

938 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622369C211yesmaximal, characteristic
2#13071255C211yesmaximal, characteristic, complemented
3#13070977C211yesmaximal, characteristic, complemented
4#13069237C211yesmaximal, characteristic, complemented
5#13069235C211yesmaximal, characteristic, complemented
6#13069211C211yesmaximal, characteristic, complemented
7#13069205C211yesmaximal, characteristic, complemented
8#13068964C211yesmaximal, characteristic
9#13068962C211yesmaximal, characteristic
10#13068865C211yesmaximal, characteristic, complemented
11#107×Dic11C211yesmaximal, characteristic, complemented
12#13068443C211yesmaximal, characteristic, complemented
13#13068440C211yesmaximal, characteristic, complemented
14#13068366C211yesmaximal, characteristic, complemented
15C11×#1862C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C22×#4323C2211yescharacteristic
20C2×#66946C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26C4×C22⋊Dic11—21no—
27C2×C11⋊#95—21no—
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33#10622603—21no—
34#10622601C2211yescharacteristic
35#10622600—21no—
36#10622598C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C22⋊C4×Dic11—21no—
43C22⋊C4×Dic11—21no—
44#10622552C2211yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46#10622545C2211yescharacteristic
47#10622369C418yescomplemented
48#10622283—21no—
49#10622277—21no—
50C11×#340C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×Dic11—21no—
63C23×Dic11—21no—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C42×C11C2311yescharacteristic
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78D4×Dic11—22no—
79D4×Dic11—22no—
80D4×Dic11—22no—
81D4×Dic11C2×C414yes—
82C2×#4323—22no—
83C2×#4323—22no—
84C2×#4323C2×C414yes—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2311yescharacteristic
99C2×C4×Dic11C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102#66946—22no—
103#66946C2×C414yescomplemented
104C11×#107—22no—
105C11×#102—22no—
106C11×#102C2×C414yes—
107C11×#95—21no—
108#66896—22no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95D411yescharacteristic
115C11⋊#95D411yescharacteristic
116C11⋊#95D411yescharacteristic
117C11⋊#95D411yescharacteristic
118#66885—22no—
119#66885C2×C414yescomplemented
120#66882—22no—
121#66879—22no—
122C8×Dic11C2×C414yescomplemented
123#66873—22no—
124#66871C2×C414yescomplemented
125#21129—111nomaximal, Sylow
126C24×C11—21no—
127C23×D11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11C22×C412yes—
132C2×D4×C11#4112yes—
133C2×D4×C11#4112yes—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—24no—
137C22×C4×C11—21no—
138C22×C4×C11—81no—
139C22×C4×C11—81no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—81no—
149C22×Dic11—81no—
150C22×Dic11—81no—
151C22×Dic11—81no—
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44C22×C412yes—
162C2×C4×D11—24no—
163C2×C4×D11—81no—
164C2×C4×D11—81no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11C22×C412yes—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—81no—
176C11×C4⋊C4C22×C412yes—
177C11×C4⋊C4#4112yes—
178C11×C22⋊C4—24no—
179C42×C11—21no—
180C42×C11—21no—
181C22⋊Dic11—24no—
182C22⋊Dic11—24no—
183#4323—28no—
184(C2×D11)⋊C4—24no—
185(C2×D11)⋊C4—81no—
186(C2×D11)⋊C4—81no—
187(C2×D11)⋊C4—81no—
188(C2×D11)⋊C4—81no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—81no—
194C4⋊Dic11C22×C412yes—
195C4⋊Dic11#4112yes—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—81no—
199C4×Dic11—81no—
200C4×Dic11—81no—
201C4×Dic11—81no—
202C4×Dic11C22×C412yes—
203C4×Dic11#4112yes—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8C22×C412yes—
210C2×C4×D8—111no—
211#2319—111no—
212#2275—111no—
213#1925—111no—
214#1925—111no—
215#1921—111no—
216#1921—111no—
217#1879—111no—
218#1879—111no—
219#1862—111no—
220#1862D1111yescharacteristic, complemented
221C4×#107—111no—
222#1762—111no—
223#1762—111no—
224#1746—111no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11C22×D411yescharacteristic
233C22×D11—22no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240D4×C11—22no—
241D4×C11—22no—
242D4×C11—22no—
243D4×C11#11714yes—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—84no—
260C2×C4×C11C23×C411yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—22no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—22no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—84no—
286C2×Dic11—84no—
287C2×Dic11C4×D412yes—
288C2×Dic11C4×D412yes—
289D44—22no—
290D44—22no—
291D44—41no—
292D44—41no—
293C4×D11—84no—
294C8×C11—22no—
295C8×C11—41no—
296C11⋊C8—22no—
297C11⋊C8—41no—
298C22×D8—111no—
299C2×C4×D4—111no—
300C2×C4×D4—111no—
301C2×C4×D4—111no—
302C2×C4×D4C2×D1111yescharacteristic
303C4×D8—118no—
304C2×#107—111no—
305C2×#107—111no—
306C2×#107C2×D1111yescharacteristic
307C2×#102—111no—
308C2×#102—111no—
309C2×#102—111no—
310C2×#102—111no—
311C2×#102C2×D1111yescharacteristic
312C2×#102C2×D1111yescharacteristic
313C2×#97—111no—
314C2×C4×C8—111no—
315#390—111no—
316#390—111no—
317#389—111no—
318#389C2×D1111yescharacteristic
319#388—221no—
320#388—221no—
321#381—221no—
322#380—221no—
323C4×C4⋊C4—111no—
324C4×C4⋊C4—111no—
325C4×C4⋊C4—111no—
326C4×C4⋊C4—111no—
327C4×C22⋊C4—221no—
328C4×C22⋊C4—221no—
329C4×C22⋊C4—221no—
330#376—111no—
331C2×#95—221no—
332#340—111no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340C2×D1111yescharacteristic
338#336—111no—
339#336—111no—
340#336—111no—
341#336C2×D1111yescharacteristic
342C22×C11—24no—
343C22×C11—42no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11C2×C4×D411yescharacteristic
350C22×C11#52511yescharacteristic
351C22×C11#52511yescharacteristic
352C22×C11#57611yescharacteristic
353C22×C11#57611yescharacteristic
354C22×C11#57611yescharacteristic
355C22×C11#57811yescharacteristic
356C2×D11—42no—
357C2×D11—42no—
358C2×D11—42no—
359C2×D11—81no—
360C2×D11—81no—
361C2×D11—81no—
362C2×D11—81no—
363C4×C11—41no—
364C4×C11—42no—
365C4×C11—41no—
366C4×C11—42no—
367C4×C11—81no—
368C4×C11C2×#11711yescharacteristic
369C4×C11C4×#4111yescharacteristic
370C4×C11#52911yescharacteristic
371C4×C11#52911yescharacteristic
372Dic11—22no—
373Dic11—22no—
374Dic11—41no—
375Dic11—42no—
376Dic11—41no—
377Dic11—42no—
378Dic11—81no—
379C22×D4—111no—
380C22×D4C22×D1111yescharacteristic
381C23×C4—21no—
382C23×C4—221no—
383C23×C4—221no—
384C23×C4—221no—
385C2×D8—114no—
386C2×D8—222no—
387C2×D8—222no—
388C22×C8—111no—
389C22×C8—111no—
390C22×C8C22×D1111yescharacteristic
391C22×C8C22×D1111yescharacteristic
392C4×D4—22no—
393C4×D4—22no—
394C4×D4—114no—
395C4×D4—114no—
396C4×D4—222no—
397C4×D4—222no—
398C4×D4—222no—
399C4×D4—222no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C42—111no—
417C2×C42—111no—
418C2×C42—221no—
419C2×C42—221no—
420C2×C42—221no—
421C2×C42—221no—
422C2×C42C22×D1111yescharacteristic
423#107—22no—
424#107—114no—
425#107—222no—
426#102—22no—
427#102—114no—
428#102—222no—
429#102—222no—
430#102—222no—
431#102C4×D1114yes—
432#97—222no—
433C4×C8—114no—
434#95—21no—
435#95—111no—
436#95—111no—
437#95—111no—
438#95—111no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444C2×C11—44no—
445C2×C11#229011yescharacteristic
446C2×C11#294811yescharacteristic
447C2×C11#295111yescharacteristic
448C2×C11#312211yescharacteristic
449C2×C11#312211yescharacteristic
450C2×C11#312411yescharacteristic
451C2×C11#312411yescharacteristic
452D11—82no—
453C24—21no—
454C24—221no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—112no—
459C2×D4—221no—
460C2×D4—221no—
461C2×D4—221no—
462C2×D4—221no—
463C2×D4—221no—
464C2×D4C2×C4×D1112yes—
465C2×D4#434112yes—
466C2×D4#434312yes—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—24no—
470C22×C4—21no—
471C22×C4—81no—
472C22×C4—81no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—224no—
478C22×C4—224no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—224no—
482C22×C4—221no—
483C22×C4—881no—
484C22×C4—881no—
485C22×C4—881no—
486C22×C4—881no—
487C22×C4—881no—
488C22×C4—881no—
489C22×C4D4×D1111yescharacteristic
490C22×C4D4×D1111yescharacteristic
491C22×C4C23×D1111yescharacteristic
492D8—228no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—112no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8C2×C4×D1112yes—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—81no—
510C4⋊C4—112no—
511C4⋊C4—112no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—881no—
517C4⋊C4C2×C4×D1112yes—
518C4⋊C4#434112yes—
519C22⋊C4—24no—
520C22⋊C4—224no—
521C22⋊C4—224no—
522C22⋊C4—224no—
523C22⋊C4—881no—
524C22⋊C4—881no—
525C22⋊C4—881no—
526C22⋊C4—881no—
527C42—21no—
528C42—21no—
529C42—112no—
530C42—112no—
531C42—221no—
532C42—221no—
533C42—881no—
534C42—881no—
535C42—881no—
536C42—881no—
537C11#2112911yescharacteristic, complemented, Sylow
538C23—22no—
539C23—22no—
540C23—22no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—222no—
546C23—441no—
547C23—441no—
548C23—441no—
549C23—441no—
550C23—441no—
551C23—441no—
552C23C2×D4×D1111yescharacteristic
553D4—22no—
554D4—22no—
555D4—22no—
556D4—222no—
557D4—222no—
558D4—441no—
559D4—441no—
560D4#6694514yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—84no—
577C2×C4—112no—
578C2×C4—112no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—222no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—222no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—884no—
599C2×C4—884no—
600C2×C4—884no—
601C2×C4C22×C4×D1111yescharacteristic
602C2×C4C2×#434111yescharacteristic
603C2×C4C2×#434111yescharacteristic
604C2×C4C2×#434311yescharacteristic
605C2×C4#41×D1111yescharacteristic
606C2×C4#41×D1111yescharacteristic
607C8—22no—
608C8—41no—
609C8—222no—
610C8—441no—
611C22—24no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—442no—
619C22—442no—
620C22—442no—
621C22—881no—
622C22—881no—
623C22—881no—
624C22—881no—
625C22C4×D4×D1111yescharacteristic
626C22#1062311711yescharacteristic
627C22#1062315811yescharacteristic
628C22#1062328811yescharacteristic
629C22#1062330011yescharacteristic
630C22#1062330511yescharacteristic
631C22#1062331011yescharacteristic
632C4—41no—
633C4—42no—
634C4—41no—
635C4—42no—
636C4—81no—
637C4—222no—
638C4—222no—
639C4—441no—
640C4—442no—
641C4—441no—
642C4—442no—
643C4—881no—
644C4C2×#6694511yescharacteristic
645C4C4×#434111yescharacteristic
646C4#1062315511yescharacteristic
647C4#1062318011yescharacteristic
648C2—44no—
649C2—882no—
650C2#1307105211yescharacteristic
651C2#1307746311yescharacteristic
652C2#1307748811yescharacteristic
653C2#1307885311yescharacteristic
654C2#1307886111yescharacteristic
655C2#1307887911yescharacteristic
656C2#1307888311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1862C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
cosocleC22×C4×C11C24
hypercenter#1862D11
hypocenterC11#21129
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
2. #13071255C2semidirect
3. #13070977C2semidirect
4. #13069237C2semidirect
5. #13069235C2semidirect
6. #13069211C2semidirect
7. #13069205C2semidirect
10. #13068865C2semidirect
11. #107×Dic11C2semidirect
12. #13068443C2semidirect
13. #13068440C2semidirect
14. #13068366C2semidirect
15. C11×#1862C2semidirect
47. #10622369C4semidirect
103. #66946C2×C4semidirect
119. #66885C2×C4semidirect
122. C8×Dic11C2×C4semidirect
124. #66871C2×C4semidirect
220. #1862D11semidirect
537. C11#21129semidirect

Maximal subgroups

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

subgroupindex
C2×#106223692
#130712552
#130709772
#130692372
#130692352
#130692112
#130692052
#130689642
#130689622
#130688652
#107×Dic112
#130684432
#130684402
#130683662
C11×#18622
#2112911