Finite Group Databasebeta

← #14814623

Subgroups — #14814623

Order 2816.

840 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072048C211yesmaximal, characteristic
2#13071516C211yesmaximal, characteristic
3#13070178C211yesmaximal, characteristic, complemented
4#13070043C211yesmaximal, characteristic, complemented
5#13069811C211yesmaximal, characteristic, complemented
6#13069254C211yesmaximal, characteristic, complemented
7#13069195C211yesmaximal, characteristic, complemented
8#13069046C211yesmaximal, characteristic, complemented
9#13068920C211yesmaximal, characteristic, complemented
10#13068920C211yesmaximal, characteristic, complemented
11#13068912C211yesmaximal, characteristic
12#13068816C211yesmaximal, characteristic, complemented
13#13068701C211yesmaximal, characteristic, complemented
14#13068334C211yesmaximal, characteristic, complemented
15C11×#2072C211yesmaximal, characteristic, complemented
16C2×#66999C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C22×#4313C2211yescharacteristic
19C2×#66946—21no—
20C2×#66945C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C11×#391C2211yescharacteristic
27C11×#384C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34#10622602—21no—
35#10622602—21no—
36#10622600C2211yescharacteristic
37#10622600C2211yescharacteristic
38#10622600C2211yescharacteristic
39#10622586—21no—
40C2×#66871C2211yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622288—21no—
44#10622285—21no—
45#10622282—21no—
46#10622260—21no—
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49C11×#336C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D44D411yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11—21no—
63C22×C4×D11C2311yescharacteristic
64C22×C4×D11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73#66999—22no—
74#66999—22no—
75#66999—22no—
76#66999—41no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4D411yescharacteristic
84C2×(C2×D11)⋊C4D411yescharacteristic
85C2×C4⋊Dic11D411yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C2×#4313—22no—
100C2×#4313—41no—
101C2×#4313—41no—
102#66946—44no—
103#66945—22no—
104#66945—41no—
105C4⋊C4×D11—22no—
106C4⋊C4×D11—22no—
107C4⋊C4×D11—41no—
108C4⋊C4×D11—41no—
109C4×D44—22no—
110C4×D44—22no—
111C11×#103—41no—
112C11×#103—41no—
113C11×#95—21no—
114C11×#95—21no—
115#66899—22no—
116#66899—41no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122(C2×D11)⋊C8—22no—
123(C2×D11)⋊C8—41no—
124(C2×D11)⋊C8—41no—
125#66881—22no—
126#66871—41no—
127#26216—111nomaximal, Sylow
128C23×D11C2×D411yescharacteristic
129C23×D11C2×D411yescharacteristic
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C2×D44—22no—
150C2×D44—22no—
151C2×D44—22no—
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—42no—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11—42no—
166C2×C4×D11—81no—
167C2×C4×D11—81no—
168C2×C4×D11#4112yes—
169C2×C4×D11#4112yes—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
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—81no—
184C42×C11—21no—
185C42×C11—21no—
186(C2×D11)⋊C4—22no—
187(C2×D11)⋊C4—22no—
188(C2×D11)⋊C4—42no—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194C4⋊Dic11—22no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11#4112yes—
202C4⋊Dic11#4112yes—
203Dic11⋊C4—42no—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208C4×Dic11—42no—
209C4×Dic11—42no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216#4313—44no—
217#2415—111no—
218D4×C4⋊C4—111no—
219#2100—111no—
220#2075—111no—
221#2072D1111yescharacteristic, complemented
222#2035—111no—
223#1928—111no—
224#1919—111no—
225#1894—111no—
226#1872—111no—
227#1872—111no—
228#1870—111no—
229#1854—111no—
230#1823—111no—
231#1736—111no—
232C23×C11C22×D411yescharacteristic
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11#12312yes—
246C22×D11AGL(1,ℤ/8)12yes—
247Q8×C11—41no—
248Q8×C11—41no—
249Q8×C11—41no—
250Q8×C11—41no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
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—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11#13712yes—
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11H(5,𝔽2)11yescharacteristic
274C2×C4×C11H(5,𝔽2)11yescharacteristic
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—21no—
281C2×Dic11—21no—
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#12312yes—
293D44—28no—
294C4×D11—22no—
295C4×D11—22no—
296C4×D11—22no—
297C4×D11—22no—
298C4×D11—41no—
299C4×D11—41no—
300C4×D11—41no—
301C4×D11—41no—
302C4×D11—84no—
303C4×D11—84no—
304C8×C11—41no—
305C8×C11—41no—
306C11⋊C8—41no—
307C11⋊C8—41no—
308C22×M16—111no—
309C2×C22⋊Q8—111no—
310C2×C22⋊Q8—111no—
311C2×C4×D4—111no—
312C2×C4×D4—221no—
313C2×#117—111no—
314C22×C4⋊C4—111no—
315C22×C4⋊C4—111no—
316C2×#107—111no—
317C2×#106—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×#103C2×D1111yescharacteristic
321C2×#103C2×D1111yescharacteristic
322C2×C22⋊C8—111no—
323C2×C22⋊C8—111no—
324C2×C22⋊C8—111no—
325#397—221no—
326#394—221no—
327#391C2×D1111yescharacteristic
328#389—111no—
329#389—221no—
330#389—221no—
331#388—221no—
332#385—221no—
333#385—221no—
334#384C2×D1111yescharacteristic
335#380—111no—
336#380—111no—
337#380—111no—
338C4×C4⋊C4—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340C2×D1111yescharacteristic
348#340C2×D1111yescharacteristic
349#336—111no—
350#336C2×D1111yescharacteristic
351C22×C11C2×#12311yescharacteristic
352C22×C11#54611yescharacteristic
353C22×C11#54611yescharacteristic
354C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
355C22×C11C2×#13711yescharacteristic
356C22×C11#57711yescharacteristic
357C22×C11#57811yescharacteristic
358C2×D11—22no—
359C2×D11—22no—
360C2×D11—22no—
361C2×D11—22no—
362C2×D11—22no—
363C2×D11—22no—
364C2×D11—41no—
365C2×D11—41no—
366C2×D11—41no—
367C2×D11—41no—
368C2×D11—41no—
369C2×D11—41no—
370C2×D11—41no—
371C2×D11—41no—
372C4×C11—22no—
373C4×C11—41no—
374C4×C11—81no—
375C4×C11—81no—
376C4×C11—81no—
377C4×C11—81no—
378C4×C11#52911yescharacteristic
379C4×C11#53811yescharacteristic
380C4×C11#55311yescharacteristic
381C4×C11#55311yescharacteristic
382Dic11—22no—
383Dic11—42no—
384Dic11—41no—
385Dic11—42no—
386Dic11—81no—
387Dic11—81no—
388C22×Q8C22×D1111yescharacteristic
389C22×D4—111no—
390C23×C4—111no—
391C23×C4—111no—
392C23×C4—221no—
393C23×C4—221no—
394C2×M16—222no—
395C2×M16—441no—
396C2×M16—441no—
397C22×C8—111no—
398C22×C8—111no—
399C22×C8C22×D1111yescharacteristic
400C22×C8C22×D1111yescharacteristic
401C22⋊Q8—222no—
402C22⋊Q8—222no—
403C22⋊Q8—222no—
404C22⋊Q8—441no—
405C4×D4—222no—
406C4×D4—222no—
407C4×D4—444no—
408#117—222no—
409#117—441no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—222no—
418C2×C4⋊C4—222no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—441no—
425C2×C4⋊C4—441no—
426C2×C4⋊C4C22×D1111yescharacteristic
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C22⋊C4—111no—
430C2×C22⋊C4—111no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C42—221no—
438C2×C42—221no—
439C2×C42C22×D1111yescharacteristic
440#107—441no—
441#106—222no—
442#103—41no—
443#103—41no—
444#103—222no—
445#103—441no—
446C22⋊C8—222no—
447C22⋊C8—441no—
448C22⋊C8—441no—
449#95—21no—
450#95—21no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
456C2×C11#244411yescharacteristic
457C2×C11#309211yescharacteristic
458C2×C11#309711yescharacteristic
459C2×C11#330811yescharacteristic
460C2×C11#331011yescharacteristic
461C2×C11#332811yescharacteristic
462C2×C11#333111yescharacteristic
463D11—42no—
464D11—42no—
465C24—111no—
466C24—111no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×D4—222no—
474C2×D4—222no—
475C2×D4—222no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—111no—
481C22×C4—112no—
482C22×C4—112no—
483C22×C4—111no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
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—442no—
499C22×C4—442no—
500C22×C4—442no—
501C22×C4—442no—
502C22×C4—881no—
503C22×C4—881no—
504C22×C4D4×D1111yescharacteristic
505C22×C4D4×D1111yescharacteristic
506C22×C4C23×D1111yescharacteristic
507M16—444no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—42no—
527C4⋊C4—81no—
528C4⋊C4—112no—
529C4⋊C4—112no—
530C4⋊C4—222no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—442no—
538C4⋊C4—442no—
539C4⋊C4—442no—
540C4⋊C4—442no—
541C4⋊C4—442no—
542C22⋊C4—222no—
543C22⋊C4—222no—
544C22⋊C4—442no—
545C22⋊C4—442no—
546C22⋊C4—442no—
547C22⋊C4—442no—
548C22⋊C4—442no—
549C22⋊C4—442no—
550C42—21no—
551C42—21no—
552C42—442no—
553C42—442no—
554C11#2621611yescharacteristic, complemented, Sylow
555C23—112no—
556C23—112no—
557C23—221no—
558C23—221no—
559C23—221no—
560C23—221no—
561C23—221no—
562C23—221no—
563C23—221no—
564C23—221no—
565C23—221no—
566C23—221no—
567C23—221no—
568C23—221no—
569C23C2×D4×D1111yescharacteristic
570Q8—41no—
571Q8—41no—
572Q8—41no—
573Q8—41no—
574D4—228no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—112no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—222no—
596C2×C4—222no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—222no—
603C2×C4—221no—
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—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—884no—
619C2×C4—884no—
620C2×C4#6697112yes—
621C2×C4#6703711yescharacteristic
622C2×C4#41×D1111yescharacteristic
623C2×C4#41×D1111yescharacteristic
624C2×C4#41×D1111yescharacteristic
625C2×C4#41×D1111yescharacteristic
626C2×C4#6704211yescharacteristic
627C8—41no—
628C8—41no—
629C8—441no—
630C8—441no—
631C22—222no—
632C22—222no—
633C22—222no—
634C22—222no—
635C22—222no—
636C22—222no—
637C22—441no—
638C22—441no—
639C22—441no—
640C22—441no—
641C22—441no—
642C22—441no—
643C22—441no—
644C22—441no—
645C22#1062314311yescharacteristic
646C22D11×#12311yescharacteristic
647C22#1062320711yescharacteristic
648C22#1062329311yescharacteristic
649C22C2×#6697111yescharacteristic
650C22D11×AGL(1,ℤ/8)11yescharacteristic
651C22#1062331011yescharacteristic
652C4—22no—
653C4—41no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4—81no—
658C4—222no—
659C4—442no—
660C4—442no—
661C4—441no—
662C4—881no—
663C4—881no—
664C4#1062318811yescharacteristic
665C4#1062319211yescharacteristic
666C4#1062323711yescharacteristic
667C4#1062324011yescharacteristic
668C2—442no—
669C2—442no—
670C2#1307236911yescharacteristic
671C2#1307854311yescharacteristic
672C2#1307857811yescharacteristic
673C2#1308060611yescharacteristic
674C2#1308064411yescharacteristic
675C2#1308090211yescharacteristic
676C2#1308093111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2072C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenter#2072D11
hypocenterC11#26216
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2072

Complements

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

NH ≅ G/Ntype
3. #13070178C2semidirect
4. #13070043C2semidirect
5. #13069811C2semidirect
6. #13069254C2semidirect
7. #13069195C2semidirect
8. #13069046C2semidirect
9. #13068920C2semidirect
10. #13068920C2semidirect
12. #13068816C2semidirect
13. #13068701C2semidirect
14. #13068334C2semidirect
15. C11×#2072C2semidirect
221. #2072D11semidirect
554. C11#26216semidirect

Maximal subgroups

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

subgroupindex
#130720482
#130715162
#130701782
#130700432
#130698112
#130692542
#130691952
#130690462
#130689202
#130689122
#130688162
#130687012
#130683342
C11×#20722
#2621611