Finite Group Databasebeta

← #14814530

Subgroups — #14814530

Order 2816.

816 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072061C211yesmaximal, characteristic
2#13071541C211yesmaximal, characteristic
3#13070189C211yesmaximal, characteristic, complemented
4#13070043C211yesmaximal, characteristic, complemented
5#13070038C211yesmaximal, characteristic, complemented
6#13069822C211yesmaximal, characteristic, complemented
7#13069255C211yesmaximal, characteristic, complemented
8#13069190C211yesmaximal, characteristic, complemented
9#13069039C211yesmaximal, characteristic, complemented
10#13068927C211yesmaximal, characteristic, complemented
11#13068923C211yesmaximal, characteristic, complemented
12#13068908C211yesmaximal, characteristic
13#13068804C211yesmaximal, characteristic, complemented
14#13068710C211yesmaximal, characteristic, complemented
15C2×C11×#340C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21C2×#66950C2211yescharacteristic
22C2×#66945C2211yescharacteristic
23#10622826—21no—
24#10622826—21no—
25#10622825—21no—
26#10622825C2211yescharacteristic
27C4×C22⋊Dic11—21no—
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33#10622607—21no—
34#10622603—21no—
35#10622600C2211yescharacteristic
36#10622600C2211yescharacteristic
37#10622598C2211yescharacteristic
38#10622596—21no—
39#10622591—21no—
40#10622590C2211yescharacteristic
41C4⋊C4×Dic11C2211yescharacteristic
42#10622587C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11D411yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C22×C8×C11—22no—
66C22×C8×C11—41no—
67C22×C8×C11—41no—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—41no—
75C2×C11×C4⋊C4—41no—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11D411yescharacteristic
83C4×C22⋊D11—22no—
84C4×C22⋊D11—22no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4D411yescharacteristic
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95#66977—22no—
96#66977—22no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4D411yescharacteristic
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104#66950—22no—
105#66950—41no—
106#66945—22no—
107#66945—41no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C22⋊(C11⋊C8)—22no—
118(C2×D11)⋊C8—41no—
119(C2×D11)⋊C8—41no—
120#66880—41no—
121#66880—41no—
122#66874—22no—
123#66874—41no—
124#66871—22no—
125#66871—41no—
126#26210—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C23×D11C2×D411yescharacteristic
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11—81no—
142C22×C4×C11—81no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11#4112yes—
145C22×C4×C11#4112yes—
146C22×C4×C11C2411yescharacteristic
147C2×C22⋊D11—22no—
148C2×C22⋊D11—22no—
149C2×C22⋊D11—22no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—44no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—42no—
183C11×C4⋊C4—42no—
184C11×C4⋊C4#4112yes—
185C11×C4⋊C4#4112yes—
186C22⋊Dic11—22no—
187C22⋊Dic11—42no—
188C22⋊Dic11—42no—
189(C2×D11)⋊C4—22no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—81no—
193(C2×D11)⋊C4—81no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—42no—
201C4⋊Dic11—81no—
202Dic11⋊C4—22no—
203Dic11⋊C4—42no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—42no—
207C4×Dic11—81no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214#2417—111no—
215#2352—111no—
216#2101—111no—
217#2075—111no—
218#2074—111no—
219#2036—111no—
220#1928—111no—
221#1918—111no—
222#1892—111no—
223#1873—111no—
224#1872—111no—
225#1869—111no—
226#1852—111no—
227#1825—111no—
228C2×#340D1111yescharacteristic, complemented
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11#12312yes—
234C23×C11#13512yes—
235C23×C11#13712yes—
236C23×C11C22×D411yescharacteristic
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
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—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—84no—
263C2×C4×C11—84no—
264C2×C4×C11#12312yes—
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11H(5,𝔽2)11yescharacteristic
270C2×C4×C11H(5,𝔽2)11yescharacteristic
271C22⋊D11—44no—
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—21no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C4×D11—41no—
294C4×D11—41no—
295C4×D11—41no—
296C4×D11—41no—
297Dic22—41no—
298Dic22—41no—
299Dic22—41no—
300Dic22—41no—
301C8×C11—41no—
302C8×C11—41no—
303C11⋊C8—41no—
304C11⋊C8—41no—
305C23×C8C2×D1111yescharacteristic
306C2×C22⋊Q8—111no—
307C2×C22⋊Q8—111no—
308C2×C4×D4—111no—
309C2×#117—111no—
310C22×C4⋊C4C2×D1111yescharacteristic
311C22×C4⋊C4C2×D1111yescharacteristic
312C2×#107—111no—
313C2×#107—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#103—111no—
318C2×C22⋊C8—111no—
319C2×C22⋊C8—111no—
320C2×C22⋊C8—111no—
321#398—221no—
322#396—221no—
323#391—111no—
324#389—111no—
325#388—221no—
326#387—221no—
327#386—221no—
328#386—221no—
329#382—111no—
330#380—111no—
331#380—111no—
332#380—111no—
333#380—221no—
334C4×C4⋊C4—111no—
335C4×C22⋊C4—221no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340C2×D1111yescharacteristic
343#340C2×D1111yescharacteristic
344#340C2×D1111yescharacteristic
345#340C2×D1111yescharacteristic
346#336—111no—
347#336—111no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11#48514yes—
355C22×C11C2×#12311yescharacteristic
356C22×C11#54611yescharacteristic
357C22×C11#54611yescharacteristic
358C22×C11C2×#13511yescharacteristic
359C22×C11C2×#13711yescharacteristic
360C22×C11#57611yescharacteristic
361C22×C11#57811yescharacteristic
362C2×D11—41no—
363C2×D11—41no—
364C2×D11—41no—
365C2×D11—41no—
366C2×D11—41no—
367C2×D11—41no—
368C2×D11—41no—
369C4×C11—22no—
370C4×C11—42no—
371C4×C11—42no—
372C4×C11—81no—
373C4×C11—81no—
374C4×C11#52911yescharacteristic
375C4×C11#53811yescharacteristic
376C4×C11#55311yescharacteristic
377C4×C11#55311yescharacteristic
378Dic11—41no—
379Dic11—41no—
380Dic11—41no—
381Dic11—81no—
382Dic11—81no—
383Dic11—81no—
384Dic11—81no—
385C22×Q8—111no—
386C22×D4—111no—
387C23×C4—21no—
388C23×C4—21no—
389C23×C4—111no—
390C23×C4C22×D1111yescharacteristic
391C22×C8—22no—
392C22×C8—41no—
393C22×C8—41no—
394C22×C8—111no—
395C22×C8—111no—
396C22×C8C22×D1111yescharacteristic
397C22×C8C22×D1111yescharacteristic
398C22⋊Q8—222no—
399C22⋊Q8—222no—
400C22⋊Q8—222no—
401C22⋊Q8—441no—
402C4×D4—222no—
403C4×D4—222no—
404#117—222no—
405#117—441no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—41no—
411C2×C4⋊C4—41no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C22⋊C4—111no—
424C2×C22⋊C4—111no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C42—111no—
432C2×C42—221no—
433C2×C42—221no—
434#107—222no—
435#107—441no—
436#103—222no—
437#103—441no—
438#103—441no—
439#103—441no—
440C22⋊C8—222no—
441C22⋊C8—441no—
442C22⋊C8—441no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95—221no—
452C2×C11—24no—
453C2×C11#244411yescharacteristic
454C2×C11C2×#48511yescharacteristic
455C2×C11#309811yescharacteristic
456C2×C11#329711yescharacteristic
457C2×C11#330011yescharacteristic
458C2×C11#331211yescharacteristic
459C2×C11#331411yescharacteristic
460D11—81no—
461C24—111no—
462C24D4×D1111yescharacteristic
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×D4—222no—
470C2×D4—222no—
471C2×D4—222no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—81no—
485C22×C4—81no—
486C22×C4—111no—
487C22×C4—111no—
488C22×C4—111no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4#433912yes—
500C22×C4D4×D1111yescharacteristic
501C22×C4#434312yes—
502C22×C4C23×D1111yescharacteristic
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—44no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—42no—
523C4⋊C4—42no—
524C4⋊C4—222no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—442no—
532C4⋊C4—442no—
533C4⋊C4—881no—
534C4⋊C4#433912yes—
535C4⋊C4#433912yes—
536C22⋊C4—222no—
537C22⋊C4—222no—
538C22⋊C4—442no—
539C22⋊C4—442no—
540C22⋊C4—442no—
541C22⋊C4—442no—
542C22⋊C4—881no—
543C22⋊C4—881no—
544C42—221no—
545C42—221no—
546C42—442no—
547C42—881no—
548C11#2621011yescharacteristic, complemented, Sylow
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—221no—
554C23—221no—
555C23—221no—
556C23—221no—
557C23—221no—
558C23—221no—
559C23—221no—
560C23#6694712yes—
561C23#6696812yes—
562C23#6696912yes—
563C23C2×D4×D1111yescharacteristic
564Q8—441no—
565Q8—441no—
566Q8—441no—
567Q8—441no—
568D4—444no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—84no—
588C2×C4—84no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4#6694712yes—
615C2×C4C2×#433911yescharacteristic
616C2×C4C2×#433911yescharacteristic
617C2×C4C2×#433911yescharacteristic
618C2×C4#6703711yescharacteristic
619C2×C4#6703711yescharacteristic
620C2×C4C2×#434311yescharacteristic
621C8—41no—
622C8—41no—
623C8—441no—
624C8—441no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—441no—
632C22—441no—
633C22—441no—
634C22—441no—
635C22—441no—
636C22—441no—
637C22—441no—
638C22#1062248014yes—
639C22#1062302111yescharacteristic
640C22#1062302111yescharacteristic
641C22C2×#6694711yescharacteristic
642C22#1062328811yescharacteristic
643C22C2×#6696811yescharacteristic
644C22C2×#6696911yescharacteristic
645C22#1062329711yescharacteristic
646C4—22no—
647C4—42no—
648C4—42no—
649C4—81no—
650C4—81no—
651C4—441no—
652C4—441no—
653C4—441no—
654C4—881no—
655C4—881no—
656C4—881no—
657C4—881no—
658C4#1062301011yescharacteristic
659C4#1062302511yescharacteristic
660C4#1062304511yescharacteristic
661C4#1062304511yescharacteristic
662C2—24no—
663C2—881no—
664C2#1307236611yescharacteristic
665C2C2×#1062248011yescharacteristic
666C2#1307859911yescharacteristic
667C2#1308046211yescharacteristic
668C2#1308049911yescharacteristic
669C2#1308066311yescharacteristic
670C2#1308069311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#340C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
hypercenterC2×#340D11
hypocenterC11#26210
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
3. #13070189C2semidirect
4. #13070043C2semidirect
5. #13070038C2semidirect
6. #13069822C2semidirect
7. #13069255C2semidirect
8. #13069190C2semidirect
9. #13069039C2semidirect
10. #13068927C2semidirect
11. #13068923C2semidirect
13. #13068804C2semidirect
14. #13068710C2semidirect
15. C2×C11×#340C2semidirect
228. C2×#340D11semidirect
548. C11#26210semidirect

Maximal subgroups

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

subgroupindex
#130720612
#130715412
#130701892
#130700432
#130700382
#130698222
#130692552
#130691902
#130690392
#130689272
#130689232
#130689082
#130688042
#130687102
C2×C11×#3402
#2621011