Finite Group Databasebeta

← #14788840

Subgroups — #14788840

Order 2816.

1430 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2C2×#10622644C211yesmaximal, characteristic, complemented
3C2×#10622799C212yesmaximal
4C4×#66999C211yesmaximal, characteristic
5#13069860C212yesmaximal, complemented
6#13069714C212yesmaximal, complemented
7#13069540C211yesmaximal, characteristic, complemented
8#13069538C211yesmaximal, characteristic, complemented
9#13068593C211yesmaximal, characteristic
10#13068549C212yesmaximal
11C2×C11×#462C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2212yes—
13C22×C11×Q16C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C2×#66999C2211yescharacteristic
17C2×#66997C2212yes—
18C22×#4326C2212yes—
19D11×C4⋊Q8—24no—
20D11×C4⋊Q8—24no—
21C2×C4⋊C4×D11—21no—
22C2×C4⋊C4×D11—21no—
23C2×#66941—21no—
24C2×#66941—21no—
25C2×C42×D11C2211yescharacteristic
26C2×#66922C2211yescharacteristic
27C11×#462—24no—
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#103C2212yes—
30#10622843C2211yescharacteristic
31C2×#66899C2212yes—
32C2×#66899C2212yes—
33#10622799—28no—
34C2×(C2×D11)⋊C8C2212yes—
35C2×#66880C2212yes—
36C2×#66880C2212yes—
37#10622644—24no—
38#10622602—21no—
39#10622600C2211yescharacteristic
40#10622591—21no—
41#10622586C2211yescharacteristic
42C2×#66874C2212yes—
43C4×(C2×D11)⋊C4—21no—
44C4×C4⋊Dic11C2211yescharacteristic
45C4×Dic11⋊C4—21no—
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47#10622188C2212yes—
48C22×Q8×C11C2311yescharacteristic
49C22×Q8×C11C2312yes—
50C2×Q8×D11—24no—
51C2×Q8×D11—24no—
52C2×Q8×D11—24no—
53C2×Q8×D11—24no—
54C2×Q8×D11—42no—
55C2×Q8×D11—42no—
56C22×C4×D11—22no—
57C22×C4×D11D411yescharacteristic
58C22×C4×D11D411yescharacteristic
59C22×C4×D11C2311yescharacteristic
60C22×Dic22—22no—
61C22×Dic22C2312yes—
62C2×C11×Q16—24no—
63C2×C11×Q16—24no—
64C2×C11×Q16—42no—
65C22×C8×C11C2312yes—
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8D414yes—
68C4×Q8×C11—22no—
69C4×Q8×C11—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76#66999—22no—
77#66999D414yes—
78#66997—24no—
79#66997—24no—
80C2×#4326—24no—
81C2×#4326—24no—
82C2×#4326—42no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11D411yescharacteristic
95C2×C4×Dic11D411yescharacteristic
96C2×C4×Dic11C2311yescharacteristic
97C22×C11⋊C8C2312yes—
98C4⋊C4×D11—28no—
99C4⋊C4×D11—28no—
100#66941—28no—
101#66941—28no—
102C42×D11—22no—
103C42×D11—22no—
104#66922—22no—
105#66922D414yes—
106C11×C4⋊C8—22no—
107C11×#103—24no—
108#66899—24no—
109#66899—42no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115(C2×D11)⋊C8—24no—
116#66880—24no—
117#66880—42no—
118#66874—24no—
119C4⋊(C11⋊C8)—22no—
120#24212—111nomaximal, Sylow
121C23×D11C2×D411yescharacteristic
122C2×Q8×C11—22no—
123C2×Q8×C11—21no—
124C2×Q8×C11—22no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—22no—
132C2×Q8×C11C2×D412yes—
133C2×Q8×C11C2×D414yes—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—21no—
141C22×Dic11—22no—
142C22×Dic11—21no—
143C22×Dic11C2×D411yescharacteristic
144C22×Dic11C2×D411yescharacteristic
145C22×Dic11C2×D411yescharacteristic
146Q8×D11—48no—
147Q8×D11—48no—
148Q8×D11—48no—
149Q8×D11—48no—
150C2×C4×D11—22no—
151C2×C4×D11—28no—
152C2×C4×D11—22no—
153C2×C4×D11—22no—
154C2×C4×D11—22no—
155C2×C4×D11—22no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—44no—
161C2×C4×D11—44no—
162C2×C4×D11Q1614yescomplemented
163C2×C4×D11C2×D412yes—
164C2×C4×D11#4112yes—
165C2×Dic22—28no—
166C2×Dic22—22no—
167C2×Dic22—22no—
168C2×Dic22—22no—
169C2×Dic22—22no—
170C2×Dic22—22no—
171C2×Dic22—44no—
172C2×Dic22—44no—
173C2×Dic22C2×D414yes—
174C11×Q16—48no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C11×C4⋊C4—24no—
179C11×C4⋊C4—24no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—42no—
183C42×C11—42no—
184C42×C11C2×D412yes—
185C42×C11C2×D412yes—
186#4326—48no—
187(C2×D11)⋊C4—24no—
188(C2×D11)⋊C4—42no—
189C4⋊Dic11—24no—
190C4⋊Dic11—24no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11C2×D412yes—
195Dic11⋊C4—28no—
196Dic11⋊C4—28no—
197Dic11⋊C4—24no—
198Dic11⋊C4—42no—
199C4×Dic11—22no—
200C4×Dic11—22no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—42no—
204C2×C11⋊C8—22no—
205C2×C11⋊C8—22no—
206C2×C11⋊C8—22no—
207C22×C4⋊Q8—111no—
208C2×#462—111no—
209C2×#462D1111yescharacteristic, complemented
210C2×#451—112no—
211C4×C22⋊Q8—111no—
212#2043—112no—
213#2016—112no—
214#1981—111no—
215#1981—111no—
216#1797—111no—
217#1787—112no—
218C23×C11C22×D411yescharacteristic
219C22×D11—21no—
220C22×D11—21no—
221C22×D11—21no—
222C22×D11—21no—
223C22×D11#12112yes—
224C22×D11C2×Q1612yes—
225C22×D11#13712yes—
226Q8×C11—22no—
227Q8×C11—22no—
228Q8×C11—24no—
229Q8×C11—24no—
230Q8×C11—42no—
231Q8×C11—42no—
232Q8×C11—41no—
233Q8×C11—41no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—41no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11#12012yes—
246C2×C4×C11#12012yes—
247C2×C4×C11C2×Q1612yes—
248C2×C4×C11#13712yes—
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11H(5,𝔽2)11yescharacteristic
254C2×C4×C11H(5,𝔽2)11yescharacteristic
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—24no—
262C2×Dic11—22no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11#12112yes—
271C2×Dic11C2×Q1612yes—
272C2×Dic11#13712yes—
273C4×D11—28no—
274C4×D11—22no—
275C4×D11—22no—
276C4×D11—22no—
277C4×D11—22no—
278C4×D11—28no—
279C4×D11—416no—
280Dic22—24no—
281Dic22—24no—
282Dic22—416no—
283Dic22—42no—
284Dic22—42no—
285C8×C11—42no—
286C11⋊C8—42no—
287C23×Q8—112no—
288C22×Q16—112no—
289C22×Q16C2×D1112yes—
290C2×C4⋊Q8—112no—
291C2×C4⋊Q8—111no—
292C2×C4⋊Q8—221no—
293C2×C4⋊Q8—221no—
294C2×C4⋊Q8—224no—
295C2×C4⋊Q8—224no—
296C2×C4⋊Q8C2×D1111yescharacteristic
297C2×C22⋊Q8—111no—
298C2×C4×Q8C2×D1111yescharacteristic
299C22×C4⋊C4—221no—
300C22×C4⋊C4—221no—
301C22×C42—111no—
302#462—24no—
303#462—224no—
304#451—228no—
305C2×C4⋊C8—111no—
306C2×C4⋊C8C2×D1111yescharacteristic
307C2×#103—112no—
308C2×#103—112no—
309C2×#103—112no—
310C2×#103—112no—
311C2×#103—112no—
312C2×#103C2×D1112yes—
313C2×C22⋊C8—112no—
314#391—111no—
315#389—111no—
316#387—221no—
317#385—221no—
318#380—111no—
319C4×C4⋊C4—111no—
320C4×C4⋊C4—221no—
321C4×C22⋊C4—221no—
322#336—112no—
323C22×C11C2×#12011yescharacteristic
324C22×C11C2×#12111yescharacteristic
325C22×C11#53511yescharacteristic
326C22×C11C22×Q1611yescharacteristic
327C22×C11C2×#13711yescharacteristic
328C22×C11C2×#13711yescharacteristic
329C22×C11C2×#13711yescharacteristic
330C2×D11—22no—
331C2×D11—22no—
332C2×D11—22no—
333C2×D11—22no—
334C2×D11—22no—
335C2×D11—22no—
336C2×D11#46214yescomplemented
337C4×C11—22no—
338C4×C11—42no—
339C4×C11—44no—
340C4×C11—81no—
341C4×C11#45114yescomplemented
342C4×C11D4211yescharacteristic
343C4×C11D4211yescharacteristic
344C4×C11#54611yescharacteristic
345C4×C11#54611yescharacteristic
346Dic11—22no—
347Dic11—22no—
348Dic11—22no—
349Dic11—44no—
350Dic11—42no—
351Dic11—81no—
352C22×Q8—112no—
353C22×Q8—222no—
354C22×Q8—224no—
355C22×Q8—224no—
356C22×Q8—224no—
357C22×Q8—224no—
358C22×Q8—442no—
359C22×Q8—442no—
360C22×Q8C22×D1111yescharacteristic
361C22×Q8C22×D1112yes—
362C23×C4—111no—
363C23×C4—111no—
364C23×C4—111no—
365C23×C4—222no—
366C2×Q16—24no—
367C2×Q16—24no—
368C2×Q16—42no—
369C2×Q16—224no—
370C2×Q16—224no—
371C2×Q16—442no—
372C22×C8—112no—
373C22×C8C22×D1112yes—
374C4⋊Q8—22no—
375C4⋊Q8—114no—
376C4⋊Q8—228no—
377C4⋊Q8—228no—
378C4⋊Q8—224no—
379C4⋊Q8—224no—
380C4⋊Q8—222no—
381C4⋊Q8C22⋊D1114yes—
382C22⋊Q8—114no—
383C22⋊Q8—222no—
384C4×Q8—22no—
385C4×Q8—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—228no—
392C2×C4⋊C4—228no—
393C2×C4⋊C4—222no—
394C2×C4⋊C4—222no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C42—21no—
403C2×C42—111no—
404C2×C42—111no—
405C2×C42—111no—
406C2×C42—222no—
407C2×C42—222no—
408C2×C42—221no—
409C2×C42C22×D1111yescharacteristic
410C4⋊C8—22no—
411C4⋊C8—222no—
412#103—24no—
413#103—224no—
414#103—224no—
415#103—224no—
416#103—442no—
417#103—442no—
418C22⋊C8—224no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424C2×C11#240811yescharacteristic
425C2×C11C2×#45111yescharacteristic
426C2×C11#300411yescharacteristic
427C2×C11C2×#46211yescharacteristic
428C2×C11#303911yescharacteristic
429C2×C11#320911yescharacteristic
430C2×C11#321811yescharacteristic
431D11—24no—
432C24—111no—
433C2×Q8—22no—
434C2×Q8—21no—
435C2×Q8—22no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—114no—
444C2×Q8—228no—
445C2×Q8—222no—
446C2×Q8—222no—
447C2×Q8—222no—
448C2×Q8—222no—
449C2×Q8—222no—
450C2×Q8—444no—
451C2×Q8—444no—
452C2×Q8—448no—
453C2×Q8—448no—
454C2×Q8—448no—
455C2×Q8—448no—
456C2×Q8D4×D1112yes—
457C2×Q8C2×C22⋊D1114yes—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—111no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—114no—
465C22×C4—112no—
466C22×C4—112no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—228no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—222no—
479C22×C4—221no—
480C22×C4—444no—
481C22×C4—444no—
482C22×C4D4×D1111yescharacteristic
483C22×C4D4×D1111yescharacteristic
484C22×C4C23×D1111yescharacteristic
485Q16—48no—
486Q16—448no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—222no—
491C2×C8—222no—
492C2×C8—222no—
493C4⋊C4—24no—
494C4⋊C4—24no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—42no—
498C4⋊C4—112no—
499C4⋊C4—224no—
500C4⋊C4—228no—
501C4⋊C4—228no—
502C4⋊C4—224no—
503C4⋊C4—224no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—442no—
508C22⋊C4—224no—
509C22⋊C4—442no—
510C42—42no—
511C42—222no—
512C42—222no—
513C42—221no—
514C42—221no—
515C42—442no—
516C42D4×D1112yes—
517C42C2×C22⋊D1112yes—
518C11#2421211yescharacteristic, complemented, Sylow
519C23—112no—
520C23—112no—
521C23—112no—
522C23—221no—
523C23—221no—
524C23—221no—
525C23—221no—
526C23C2×D4×D1111yescharacteristic
527Q8—22no—
528Q8—24no—
529Q8—24no—
530Q8—22no—
531Q8—41no—
532Q8—42no—
533Q8—41no—
534Q8—42no—
535Q8—224no—
536Q8—224no—
537Q8—4416no—
538Q8—442no—
539Q8—442no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—112no—
552C2×C4—112no—
553C2×C4—112no—
554C2×C4—228no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—228no—
562C2×C4—222no—
563C2×C4—222no—
564C2×C4—222no—
565C2×C4—222no—
566C2×C4—224no—
567C2×C4—222no—
568C2×C4—4416no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—442no—
572C2×C4—442no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4Q16×D1112yes—
577C2×C4#6697112yes—
578C2×C4#6699012yes—
579C2×C4#6699012yes—
580C2×C4C2×D4×D1111yescharacteristic
581C2×C4C2×D4×D1111yescharacteristic
582C2×C4#6703711yescharacteristic
583C2×C4#41×D1111yescharacteristic
584C2×C4#6704211yescharacteristic
585C2×C4C22×C22⋊D1111yescharacteristic
586C8—42no—
587C8—442no—
588C22—114no—
589C22—222no—
590C22—222no—
591C22—222no—
592C22—222no—
593C22—222no—
594C22—222no—
595C22D11×#12111yescharacteristic
596C22#1062313811yescharacteristic
597C22C2×Q16×D1111yescharacteristic
598C22C2×#6697111yescharacteristic
599C22D11×#13711yescharacteristic
600C22D11×#13711yescharacteristic
601C22C2×#6699011yescharacteristic
602C4—22no—
603C4—44no—
604C4—42no—
605C4—81no—
606C4—222no—
607C4—222no—
608C4—222no—
609C4—442no—
610C4—444no—
611C4—881no—
612C4#1062279914yescomplemented
613C4#1062314011yescharacteristic
614C4#1062314311yescharacteristic
615C4D4×C22⋊D1111yescharacteristic
616C4#1062336011yescharacteristic
617C2—224no—
618C2#1307196811yescharacteristic
619C2C2×#1062279911yescharacteristic
620C2#1307784811yescharacteristic
621C2D11×#46211yescharacteristic
622C2#1307810011yescharacteristic
623C2#1307956311yescharacteristic
624C2#1307964711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#462C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×#462D11
hypocenterC11#24212
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
2. C2×#10622644C2semidirect
5. #13069860C2semidirect
6. #13069714C2semidirect
7. #13069540C2semidirect
8. #13069538C2semidirect
11. C2×C11×#462C2semidirect
162. C2×C4×D11Q16semidirect
209. C2×#462D11semidirect
336. C2×D11#462semidirect
341. C4×C11#451semidirect
518. C11#24212semidirect
612. C4#10622799semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
C2×#106226442
C2×#106227992
C4×#669992
#130698602
#130697142
#130695402
#130695382
#130685932
#130685492
C2×C11×#4622
#2421211