Finite Group Databasebeta

← #14827060

Subgroups — #14827060

Order 2816.

774 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073207C211yesmaximal, characteristic, complemented
2#13071689C211yesmaximal, characteristic, complemented
3#13070139C211yesmaximal, characteristic, complemented
4#13069925C211yesmaximal, characteristic
5#13069855C211yesmaximal, characteristic, complemented
6#13069695C211yesmaximal, characteristic
7#13069470C211yesmaximal, characteristic, complemented
8#13069257C211yesmaximal, characteristic, complemented
9#13069234C211yesmaximal, characteristic, complemented
10#13069193C211yesmaximal, characteristic, complemented
11#13069173C211yesmaximal, characteristic, complemented
12#13068972C211yesmaximal, characteristic, complemented
13#13068964C211yesmaximal, characteristic
14#13068630C211yesmaximal, characteristic, complemented
15C4×C11×#102C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66989C2211yescharacteristic
18C22×#4323C2211yescharacteristic
19C22×#4314C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25#10622834C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27#10622823—21no—
28C4×C22⋊Dic11—21no—
29C2×#66885C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33#10622601C2211yescharacteristic
34#10622601C2211yescharacteristic
35#10622590C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622586C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42#10622558—21no—
43#10622557—21no—
44#10622553—21no—
45#10622553—21no—
46#10622552C2211yescharacteristic
47C4×Dic11⋊C4C2211yescharacteristic
48#10622542C2211yescharacteristic
49#10622288—21no—
50#10622288—21no—
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C22×D44C2311yescharacteristic
62C22×Dic22C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C4×D4×C11—22no—
66C4×D4×C11—41no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C42×C11—21no—
72C2×C42×C11C2311yescharacteristic
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77#66989—22no—
78#66989—22no—
79C2×#4323—22no—
80C2×#4323—41no—
81C2×#4323—41no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4D411yescharacteristic
93C2×Dic11⋊C4D411yescharacteristic
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11C2311yescharacteristic
97C2×C4×Dic11C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C2×#4314—22no—
101C2×#4314—22no—
102C2×#4314—41no—
103#66940—22no—
104#66940—41no—
105C11×#102—22no—
106C11×#102—22no—
107C4×C8×C11—41no—
108C11×#95—21no—
109#66896—41no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95D411yescharacteristic
117C11⋊#95D411yescharacteristic
118#66885—41no—
119#66881—22no—
120#66880—41no—
121Dic11⋊C8—41no—
122#66874—22no—
123#66874—41no—
124#66873—22no—
125#66871—41no—
126#27072—111nomaximal, Sylow
127C24×C11—21no—
128C23×D11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11#4112yes—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—81no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22#4112yes—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11#4112yes—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4#4112yes—
175C11×C22⋊C4—42no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—81no—
179C22⋊Dic11—24no—
180C22⋊Dic11—24no—
181C22⋊Dic11—42no—
182C22⋊Dic11—81no—
183#4323—44no—
184(C2×D11)⋊C4—42no—
185(C2×D11)⋊C4—42no—
186(C2×D11)⋊C4—81no—
187(C2×D11)⋊C4—81no—
188(C2×D11)⋊C4—81no—
189(C2×D11)⋊C4—81no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194Dic11⋊C4—22no—
195Dic11⋊C4—41no—
196Dic11⋊C4—42no—
197Dic11⋊C4—81no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—42no—
203C4×Dic11—81no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210#4314—44no—
211#2513—111no—
212#2367—111no—
213#2092—111no—
214#2054—111no—
215#2042—111no—
216#2012—111no—
217#1968—111no—
218#1928—111no—
219#1925—111no—
220#1919—111no—
221#1916—111no—
222#1880—111no—
223#1879—111no—
224#1805—111no—
225C4×#102D1111yescharacteristic, complemented
226C23×C11—22no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11C22×D411yescharacteristic
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241D4×C11—22no—
242D4×C11—22no—
243D4×C11—41no—
244D4×C11—41no—
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—41no—
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×C11#13512yes—
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—22no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288D44—41no—
289D44—41no—
290D44—41no—
291D44—41no—
292Dic22—22no—
293Dic22—22no—
294Dic22—41no—
295Dic22—41no—
296C8×C11—22no—
297C8×C11—41no—
298C11⋊C8—41no—
299C11⋊C8—41no—
300C22×SD16—111no—
301C22×D8—111no—
302C2×#124—111no—
303C2×C4×Q8—111no—
304C2×C4×D4C2×D1111yescharacteristic
305C2×#107—111no—
306C2×#106—111no—
307C2×C4⋊C8—111no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#103—111no—
311C2×#102—111no—
312C2×#102—111no—
313C2×#102—111no—
314C2×#102C2×D1111yescharacteristic
315C2×#102C2×D1111yescharacteristic
316C2×C4×C8C2×D1111yescharacteristic
317#397—221no—
318#397—221no—
319#391—111no—
320#390—111no—
321#390—111no—
322#390—111no—
323#390—111no—
324#389—111no—
325#388—221no—
326#388—221no—
327#388—221no—
328#388—221no—
329#385—221no—
330#382—111no—
331C4×C4⋊C4—111no—
332C4×C4⋊C4—111no—
333C4×C4⋊C4C2×D1111yescharacteristic
334C4×C22⋊C4—221no—
335#340—111no—
336#340—111no—
337#340C2×D1111yescharacteristic
338#340C2×D1111yescharacteristic
339#336—111no—
340#336—111no—
341#336—111no—
342#336—111no—
343C22×C11—42no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11#52511yescharacteristic
351C22×C11#54611yescharacteristic
352C22×C11#55011yescharacteristic
353C22×C11C2×#13511yescharacteristic
354C22×C11#57511yescharacteristic
355C22×C11#57611yescharacteristic
356C22×C11#57711yescharacteristic
357C2×D11—81no—
358C2×D11—81no—
359C2×D11—81no—
360C2×D11—81no—
361C2×D11—81no—
362C2×D11—81no—
363C2×D11—81no—
364C4×C11—22no—
365C4×C11—42no—
366C4×C11—41no—
367C4×C11—81no—
368C4×C11—81no—
369C4×C11#52911yescharacteristic
370C4×C11#53811yescharacteristic
371C4×C11#55111yescharacteristic
372C4×C11#55311yescharacteristic
373Dic11—41no—
374Dic11—41no—
375Dic11—42no—
376Dic11—41no—
377Dic11—41no—
378Dic11—81no—
379Dic11—81no—
380C22×Q8—111no—
381C22×D4—111no—
382C22×D4C22×D1111yescharacteristic
383C23×C4—21no—
384C2×SD16—222no—
385C2×SD16—222no—
386C2×SD16—441no—
387C2×D8—222no—
388C2×D8—441no—
389C2×D8—441no—
390C22×C8—111no—
391C22×C8—111no—
392C22×C8C22×D1111yescharacteristic
393C22×C8C22×D1111yescharacteristic
394#124—222no—
395#124—222no—
396C4×Q8—222no—
397C4×Q8—441no—
398C4×D4—22no—
399C4×D4—41no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C22⋊C4—21no—
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×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C42—21no—
421C2×C42—111no—
422C2×C42—111no—
423C2×C42—221no—
424C2×C42—221no—
425C2×C42C22×D1111yescharacteristic
426#107—441no—
427#106—222no—
428C4⋊C8—441no—
429#103—222no—
430#103—441no—
431#103—441no—
432#102—22no—
433#102—22no—
434#102—222no—
435#102—441no—
436#102—441no—
437C4×C8—41no—
438#95—21no—
439#95—111no—
440#95—111no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447C2×C11—82no—
448C2×C11#246711yescharacteristic
449C2×C11#310211yescharacteristic
450C2×C11#311911yescharacteristic
451C2×C11#329711yescharacteristic
452C2×C11#332111yescharacteristic
453C2×C11#339411yescharacteristic
454C2×C11#340311yescharacteristic
455D11—161no—
456C24—21no—
457C24—221no—
458C2×Q8—112no—
459C2×Q8—221no—
460C2×Q8—221no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—221no—
475C2×D4#433912yes—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—81no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4D4×D1111yescharacteristic
490C22×C4D4×D1111yescharacteristic
491C22×C4C23×D1111yescharacteristic
492SD16—444no—
493D8—444no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8#433912yes—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—222no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—441no—
517C4⋊C4—442no—
518C4⋊C4—881no—
519C4⋊C4#433912yes—
520C22⋊C4—42no—
521C22⋊C4—224no—
522C22⋊C4—224no—
523C22⋊C4—442no—
524C22⋊C4—442no—
525C22⋊C4—442no—
526C22⋊C4—881no—
527C22⋊C4—881no—
528C22⋊C4—881no—
529C22⋊C4—881no—
530C22⋊C4—881no—
531C42—21no—
532C42—21no—
533C42—81no—
534C42—221no—
535C42—221no—
536C42—221no—
537C42—221no—
538C42—442no—
539C42—881no—
540C11#2707211yescharacteristic, complemented, Sylow
541C23—22no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—441no—
549C23—441no—
550C23—441no—
551C23—441no—
552C23—441no—
553C23—441no—
554C23—441no—
555C23C2×D4×D1111yescharacteristic
556Q8—222no—
557Q8—222no—
558Q8—441no—
559Q8—441no—
560D4—22no—
561D4—22no—
562D4—41no—
563D4—41no—
564D4—441no—
565D4—441no—
566D4—441no—
567D4—441no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—84no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—222no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4#6696912yes—
605C2×C4C2×#433911yescharacteristic
606C2×C4C2×#433911yescharacteristic
607C2×C4C2×#433911yescharacteristic
608C2×C4#6703711yescharacteristic
609C2×C4#41×D1111yescharacteristic
610C2×C4#6704211yescharacteristic
611C8—22no—
612C8—41no—
613C8—441no—
614C8—441no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—81no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22—881no—
623C22—881no—
624C22—881no—
625C22—881no—
626C22—881no—
627C22—881no—
628C22—881no—
629C22#1062302111yescharacteristic
630C22#1062307811yescharacteristic
631C22#1062308411yescharacteristic
632C22#1062328811yescharacteristic
633C22C2×#6696911yescharacteristic
634C22#1062329911yescharacteristic
635C22#1062330111yescharacteristic
636C4—22no—
637C4—42no—
638C4—41no—
639C4—81no—
640C4—81no—
641C4—442no—
642C4—441no—
643C4—441no—
644C4—441no—
645C4—441no—
646C4—881no—
647C4—881no—
648C4#1062301011yescharacteristic
649C4#1062306111yescharacteristic
650C4#1062308711yescharacteristic
651C4#1062309111yescharacteristic
652C2—82no—
653C2—1761no—
654C2#1307266711yescharacteristic
655C2#1307863811yescharacteristic
656C2#1307881111yescharacteristic
657C2#1308046211yescharacteristic
658C2#1308079811yescharacteristic
659C2#1308161011yescharacteristic
660C2#1308170211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterC4×#102D11
hypocenterC11#27072
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
1. #13073207C2semidirect
2. #13071689C2semidirect
3. #13070139C2semidirect
5. #13069855C2semidirect
7. #13069470C2semidirect
8. #13069257C2semidirect
9. #13069234C2semidirect
10. #13069193C2semidirect
11. #13069173C2semidirect
12. #13068972C2semidirect
14. #13068630C2semidirect
15. C4×C11×#102C2semidirect
225. C4×#102D11semidirect
540. C11#27072semidirect

Maximal subgroups

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

subgroupindex
#130732072
#130716892
#130701392
#130699252
#130698552
#130696952
#130694702
#130692572
#130692342
#130691932
#130691732
#130689722
#130689642
#130686302
C4×C11×#1022
#2707211