Finite Group Databasebeta

← #14813469

Subgroups — #14813469

Order 2816.

844 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622480C211yesmaximal, characteristic, complemented
2C2×#10622611C211yesmaximal, characteristic, complemented
3#13072039C211yesmaximal, characteristic
4#13071560C211yesmaximal, characteristic
5#13070151C211yesmaximal, characteristic, complemented
6#13070095C211yesmaximal, characteristic, complemented
7#13070048C211yesmaximal, characteristic, complemented
8#13069815C211yesmaximal, characteristic, complemented
9#13069248C211yesmaximal, characteristic, complemented
10#13069190C211yesmaximal, characteristic, complemented
11#13069037C211yesmaximal, characteristic, complemented
12#13068926C211yesmaximal, characteristic, complemented
13#13068906C211yesmaximal, characteristic
14#13068812C211yesmaximal, characteristic, complemented
15C11×#1854C211yesmaximal, characteristic, complemented
16C2×C11×#117C2211yescharacteristic
17C2×C4×C22⋊D11C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C2×#66950C2211yescharacteristic
22C2×#66945C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C11×#380C2211yescharacteristic
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31#10622611—24no—
32#10622600C2211yescharacteristic
33#10622600C2211yescharacteristic
34#10622598C2211yescharacteristic
35#10622589C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622587C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622574—21no—
45#10622570—21no—
46#10622566—21no—
47#10622558—21no—
48#10622553—21no—
49#10622541—21no—
50#10622480—24no—
51#10622282—21no—
52#10622262—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11D411yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×#117—22no—
68C11×#117—41no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C42×C11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11D411yescharacteristic
79C4×C22⋊D11—22no—
80C4×C22⋊D11—22no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4D411yescharacteristic
86#66979—22no—
87#66979—41no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93#66977—22no—
94#66977—22no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4D411yescharacteristic
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8—22no—
104C22×C11⋊C8—22no—
105C22×C11⋊C8—22no—
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108#66950—22no—
109#66950—41no—
110#66945—22no—
111#66945—41no—
112C11×#107—41no—
113C11×#106—22no—
114C11×C22⋊C8—22no—
115C11×#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122(C2×D11)⋊C8—22no—
123(C2×D11)⋊C8—22no—
124#66880—22no—
125#66880—41no—
126#66874—22no—
127#66874—22no—
128#66872—22no—
129#66872—22no—
130#66871—22no—
131#66871D414yescomplemented
132#26139—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C23×D11C2×D411yescharacteristic
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
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—41no—
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—
175C11×C4⋊C4—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⋊C4C2×D412yes—
183C11×C22⋊C4—42no—
184C11×C22⋊C4—81no—
185C42×C11—42no—
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—42no—
193(C2×D11)⋊C4—81no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—42no—
200C4⋊Dic11—42no—
201C4⋊Dic11C2×D412yes—
202Dic11⋊C4—22no—
203Dic11⋊C4—42no—
204Dic11⋊C4—42no—
205Dic11⋊C4—81no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—42no—
209C4×Dic11—42no—
210C4×Dic11—42no—
211C2×C11⋊C8—28no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8C2×D412yes—
217C2×C11⋊C8#4112yes—
218C2×#485—111no—
219C2×#427—111no—
220#2415—111no—
221#2354—111no—
222#2095—111no—
223#2084—111no—
224#2076—111no—
225#2035—111no—
226#1927—111no—
227#1918—111no—
228#1892—111no—
229#1873—111no—
230#1869—111no—
231#1854—111no—
232#1854D1111yescharacteristic, complemented
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11#12312yes—
240C23×C11C22×D411yescharacteristic
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
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—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11#12312yes—
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11H(5,𝔽2)11yescharacteristic
272C2×C4×C112−1+411yescharacteristic
273C22⋊D11—44no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—22no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
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—
293C2×Dic11—41no—
294C2×Dic11#13512yes—
295C4×D11—41no—
296C4×D11—41no—
297C4×D11—41no—
298C4×D11—41no—
299Dic22—41no—
300Dic22—41no—
301Dic22—41no—
302Dic22—41no—
303C8×C11—41no—
304C8×C11—41no—
305C11⋊C8—22no—
306C11⋊C8—22no—
307C23×C8—111no—
308C2×C22⋊Q8—111no—
309C2×C22⋊Q8—111no—
310C2×C4×D4—111no—
311C2×#117—111no—
312C2×#117—111no—
313C2×#117C2×D1111yescharacteristic
314#485—224no—
315#427—224no—
316C2×#107—111no—
317C2×#107—111no—
318C2×#107C2×D1111yescharacteristic
319C2×#106—111no—
320C2×#106—111no—
321C2×#106C2×D1111yescharacteristic
322C2×#103—111no—
323C2×#103—111no—
324C2×#103—111no—
325C2×#103—111no—
326C2×C22⋊C8—111no—
327C2×C22⋊C8—111no—
328C2×C22⋊C8C2×D1111yescharacteristic
329#397—221no—
330#394—221no—
331#391—111no—
332#390—221no—
333#389—111no—
334#389—221no—
335#388—221no—
336#388—221no—
337#388—221no—
338#384—111no—
339#380—111no—
340#380—111no—
341#380C2×D1111yescharacteristic
342C4×C4⋊C4—111no—
343C4×C4⋊C4—221no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340C2×D1111yescharacteristic
349#340C2×D1111yescharacteristic
350#336—111no—
351#336—111no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11C2×#12311yescharacteristic
360C22×C11D4211yescharacteristic
361C22×C11#54711yescharacteristic
362C22×C11C2×#13511yescharacteristic
363C22×C11#57511yescharacteristic
364C22×C11#57711yescharacteristic
365C22×C11#57811yescharacteristic
366C2×D11—41no—
367C2×D11—41no—
368C2×D11—41no—
369C2×D11—41no—
370C2×D11—41no—
371C2×D11—41no—
372C2×D11—41no—
373C4×C11—22no—
374C4×C11—42no—
375C4×C11—81no—
376C4×C11—81no—
377C4×C11—81no—
378C4×C11#52511yescharacteristic
379C4×C11#53911yescharacteristic
380C4×C11#54811yescharacteristic
381C4×C11#55311yescharacteristic
382Dic11—22no—
383Dic11—41no—
384Dic11—41no—
385Dic11—42no—
386Dic11—81no—
387Dic11—81no—
388Dic11—81no—
389C22×Q8—111no—
390C22×D4—111no—
391C23×C4—111no—
392C23×C4C22×D1111yescharacteristic
393C22×C8—111no—
394C22×C8—111no—
395C22×C8—222no—
396C22×C8—222no—
397C22×C8—222no—
398C22×C8C22×D1111yescharacteristic
399C22×C8C22×D1111yescharacteristic
400C22⋊Q8—222no—
401C22⋊Q8—222no—
402C22⋊Q8—222no—
403C22⋊Q8—441no—
404C4×D4—222no—
405C4×D4—222no—
406#117—22no—
407#117—41no—
408#117—222no—
409#117—222no—
410#117—441no—
411#117—441no—
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⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C4⋊C4C22×D1111yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—111no—
428C2×C22⋊C4—111no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C42—21no—
436C2×C42—111no—
437C2×C42—221no—
438C2×C42—221no—
439C2×C42—221no—
440#107—41no—
441#107—114no—
442#107—222no—
443#106—22no—
444#106—222no—
445#106—222no—
446#103—222no—
447#103—222no—
448#103—222no—
449#103—441no—
450C22⋊C8—22no—
451C22⋊C8—222no—
452C22⋊C8—222no—
453#95—21no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460C2×C11—42no—
461C2×C11#244311yescharacteristic
462C2×C11#309111yescharacteristic
463C2×C11#309711yescharacteristic
464C2×C11#327111yescharacteristic
465C2×C11#328311yescharacteristic
466C2×C11#334011yescharacteristic
467C2×C11#334911yescharacteristic
468D11—81no—
469C24—111no—
470C24D4×D1111yescharacteristic
471C2×Q8—221no—
472C2×Q8—221no—
473C2×Q8—221no—
474C2×Q8—221no—
475C2×Q8—221no—
476C2×Q8—221no—
477C2×D4—222no—
478C2×D4—222no—
479C2×D4—441no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—111no—
489C22×C4—111no—
490C22×C4—111no—
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—221no—
500C22×C4—221no—
501C22×C4#433912yes—
502C22×C4D4×D1111yescharacteristic
503C22×C4#434312yes—
504C22×C4C23×D1111yescharacteristic
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—112no—
512C2×C8—112no—
513C2×C8—228no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—112no—
526C4⋊C4—222no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—442no—
533C4⋊C4—442no—
534C4⋊C4—442no—
535C4⋊C4—442no—
536C4⋊C4—881no—
537C4⋊C4D4×D1112yes—
538C22⋊C4—42no—
539C22⋊C4—81no—
540C22⋊C4—222no—
541C22⋊C4—222no—
542C22⋊C4—442no—
543C22⋊C4—442no—
544C22⋊C4—442no—
545C22⋊C4—442no—
546C22⋊C4—442no—
547C22⋊C4—881no—
548C42—42no—
549C42—221no—
550C42—221no—
551C42—442no—
552C42—442no—
553C42—442no—
554C11#2613911yescharacteristic, complemented, Sylow
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—221no—
562C23—221no—
563C23—221no—
564C23—221no—
565C23—221no—
566C23—221no—
567C23—221no—
568C23#6694712yes—
569C23C2×D4×D1111yescharacteristic
570Q8—441no—
571Q8—441no—
572Q8—441no—
573Q8—441no—
574D4—444no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
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—41no—
593C2×C4—112no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—222no—
601C2×C4—221no—
602C2×C4—221no—
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—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4#6694712yes—
619C2×C4C2×#433911yescharacteristic
620C2×C4C2×D4×D1111yescharacteristic
621C2×C4#6703711yescharacteristic
622C2×C4C2×#434311yescharacteristic
623C2×C4#41×D1111yescharacteristic
624C2×C4#6704311yescharacteristic
625C8—41no—
626C8—41no—
627C8—222no—
628C8—222no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—441no—
637C22—441no—
638C22—441no—
639C22—441no—
640C22—441no—
641C22—441no—
642C22—441no—
643C22C2×#6694711yescharacteristic
644C22#1062312111yescharacteristic
645C22#1062318611yescharacteristic
646C22D11×#13511yescharacteristic
647C22#1062329911yescharacteristic
648C22#1062330611yescharacteristic
649C22#1062331011yescharacteristic
650C4—22no—
651C4—42no—
652C4—81no—
653C4—81no—
654C4—81no—
655C4—222no—
656C4—442no—
657C4—441no—
658C4—441no—
659C4—881no—
660C4—881no—
661C4—881no—
662C4#1062307111yescharacteristic
663C4#1062308311yescharacteristic
664C4#1062315811yescharacteristic
665C4#1062317611yescharacteristic
666C2—42no—
667C2—881no—
668C2#1307235511yescharacteristic
669C2#1307853311yescharacteristic
670C2#1307858711yescharacteristic
671C2#1308019411yescharacteristic
672C2#1308033111yescharacteristic
673C2#1308102711yescharacteristic
674C2#1308115011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1854C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
hypercenter#1854D11
hypocenterC11#26139
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
1. C2×#10622480C2semidirect
2. C2×#10622611C2semidirect
5. #13070151C2semidirect
6. #13070095C2semidirect
7. #13070048C2semidirect
8. #13069815C2semidirect
9. #13069248C2semidirect
10. #13069190C2semidirect
11. #13069037C2semidirect
12. #13068926C2semidirect
14. #13068812C2semidirect
15. C11×#1854C2semidirect
131. #66871D4semidirect
232. #1854D11semidirect
554. C11#26139semidirect

Maximal subgroups

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

subgroupindex
C2×#106224802
C2×#106226112
#130720392
#130715602
#130701512
#130700952
#130700482
#130698152
#130692482
#130691902
#130690372
#130689262
#130689062
#130688122
C11×#18542
#2613911