Finite Group Databasebeta

← #14788158

Subgroups — #14788158

Order 2816.

1114 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623001C211yesmaximal, characteristic
2C2×#10622464C211yesmaximal, characteristic, complemented
3C2×#10622462C211yesmaximal, characteristic, complemented
4C4×#66977C211yesmaximal, characteristic
5#13069813C212yesmaximal
6#13069626C212yesmaximal
7#13069567C211yesmaximal, characteristic, complemented
8#13069538C211yesmaximal, characteristic, complemented
9#13068956C212yesmaximal, complemented
10#13068887C212yesmaximal, complemented
11C11×#1797C211yesmaximal, characteristic
12C22×C42×C11C2211yescharacteristic
13C2×#66979—21no—
14C2×#66977—21no—
15C2×#66977C2211yescharacteristic
16C2×#66977C2212yes—
17C22×Dic44C2212yes—
18#10623001—24no—
19#10623001—24no—
20C2×#66923—21no—
21C2×#66922C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C2×C4×Dic22—21no—
24C2×C4×Dic22C2211yescharacteristic
25C2×C4×Dic22C2212yes—
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×C22⋊C8C2212yes—
29#10622825C2211yescharacteristic
30#10622823—21no—
31C4×C22⋊Dic11—21no—
32C2×#66881C2212yes—
33C2×#66880C2212yes—
34C2×#66880C2212yes—
35C2×#66880C2212yes—
36C2×#66880C2212yes—
37C4×C4⋊Dic11C2211yescharacteristic
38#10622546—21no—
39C4×Dic11⋊C4—21no—
40#10622542C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622464—24no—
43#10622462—24no—
44C11×#336C2212yes—
45#10622189C2212yes—
46#10622189C2212yes—
47C23×C4×C11D411yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C22×Dic22—21no—
51C22×Dic22C2312yes—
52C22×Dic22C2311yescharacteristic
53C22×C8×C11C2312yes—
54C22×C8×C11C2312yes—
55C2×C42×C11—22no—
56C2×C42×C11—22no—
57C2×C42×C11D411yescharacteristic
58C2×C42×C11D411yescharacteristic
59C2×C42×C11C2311yescharacteristic
60C2×C42×C11C2311yescharacteristic
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—21no—
63C2×C22⋊Dic11—21no—
64#66979—28no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2312yes—
71C2×C4⋊Dic11C2311yescharacteristic
72#66977—28no—
73#66977—24no—
74#66977—22no—
75#66977—24no—
76#66977—22no—
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—22no—
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11—21no—
84C2×C4×Dic11—21no—
85C2×Dic44—24no—
86C2×Dic44—24no—
87C2×Dic44—42no—
88#66923—28no—
89#66922—22no—
90#66922—22no—
91#66922D414yes—
92#66922D414yes—
93C4×Dic22—28no—
94C4×Dic22—24no—
95C4×Dic22—24no—
96C4×Dic22—22no—
97C4×Dic22—22no—
98C11×C4⋊C8—22no—
99C11×C4⋊C8—22no—
100C11×C22⋊C8—42no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106#66881—24no—
107#66880—24no—
108#66880—24no—
109#66880—24no—
110#66880—42no—
111#24157—111nomaximal, Sylow
112C24×C11C2×D411yescharacteristic
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2411yescharacteristic
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C2×Dic22—24no—
138C2×Dic22—21no—
139C2×Dic22—21no—
140C2×Dic22—22no—
141C2×Dic22—22no—
142C2×Dic22—22no—
143C2×Dic22—21no—
144C2×Dic22—22no—
145C2×Dic22—21no—
146C2×Dic22—22no—
147C2×Dic22—21no—
148C2×Dic22—42no—
149C2×Dic22—42no—
150C2×Dic22C2×D414yes—
151C2×Dic22#4112yes—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C42×C11—22no—
159C42×C11—22no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11C2×D412yes—
163C42×C11C2×D412yes—
164C22⋊Dic11—28no—
165C22⋊Dic11—24no—
166C22⋊Dic11—42no—
167C4⋊Dic11—24no—
168C4⋊Dic11—24no—
169C4⋊Dic11—24no—
170C4⋊Dic11—22no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11C2×D414yes—
177C4⋊Dic11#4112yes—
178Dic11⋊C4—28no—
179Dic11⋊C4—28no—
180Dic11⋊C4—24no—
181Dic11⋊C4—42no—
182Dic11⋊C4—42no—
183C4×Dic11—28no—
184C4×Dic11—42no—
185C4×Dic11—42no—
186Dic44—48no—
187C2×#533—111no—
188C2×#475—111no—
189C2×#462—111no—
190C4×C22⋊Q8—111no—
191#2035—112no—
192#2001—112no—
193#1988—111no—
194#1981—111no—
195#1878—112no—
196#1865—112no—
197#1797D1111yescharacteristic
198C23×C11—21no—
199C23×C11—21no—
200C23×C11—21no—
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—21no—
204C23×C11#13712yes—
205C23×C11C22×D411yescharacteristic
206C2×C4×C11—28no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—44no—
222C2×C4×C11#12012yes—
223C2×C4×C11#12012yes—
224C2×C4×C11#13512yes—
225C2×C4×C11#13712yes—
226C2×C4×C11#13712yes—
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11H(5,𝔽2)11yescharacteristic
232C2×C4×C112−1+411yescharacteristic
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—41no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—42no—
243C2×Dic11—41no—
244C2×Dic11—42no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251Dic22—22no—
252Dic22—24no—
253Dic22—24no—
254Dic22—22no—
255Dic22—41no—
256Dic22—42no—
257Dic22—41no—
258Dic22—42no—
259Dic22—48no—
260C8×C11—42no—
261C8×C11—42no—
262C22×Q16—112no—
263#533—224no—
264#533—224no—
265C2×C4⋊Q8—111no—
266C2×C4⋊Q8—111no—
267C2×#125—221no—
268C2×C22⋊Q8—112no—
269C2×C22⋊Q8—111no—
270C2×C22⋊Q8—221no—
271C2×C4×Q8—111no—
272C2×C4×Q8—112no—
273C2×C4×Q8—221no—
274C2×#117—221no—
275C22×C42C2×D1111yescharacteristic
276#475—224no—
277#462—224no—
278C2×#106—112no—
279C2×C4⋊C8C2×D1111yescharacteristic
280C2×C4⋊C8C2×D1111yescharacteristic
281C2×#103—112no—
282C2×#103—112no—
283C2×#103—112no—
284C2×#103—112no—
285C2×C22⋊C8C2×D1112yes—
286#391—111no—
287#389—111no—
288#387—221no—
289#385—221no—
290#380—111no—
291C4×C4⋊C4—111no—
292C4×C4⋊C4—221no—
293C4×C22⋊C4—221no—
294#340—112no—
295#340—112no—
296#336C2×D1112yes—
297C22×C11—22no—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—41no—
301C22×C11—41no—
302C22×C11—41no—
303C22×C11—41no—
304C22×C11C2×#12011yescharacteristic
305C22×C11#52511yescharacteristic
306C22×C11#53711yescharacteristic
307C22×C11C2×#13511yescharacteristic
308C22×C11C2×#13711yescharacteristic
309C22×C11C2×#13711yescharacteristic
310C22×C11C2×#13711yescharacteristic
311C4×C11—22no—
312C4×C11—22no—
313C4×C11—41no—
314C4×C11—41no—
315C4×C11#45214yes—
316C4×C11#54611yescharacteristic
317C4×C11#54711yescharacteristic
318C4×C11#54811yescharacteristic
319C4×C11#55011yescharacteristic
320Dic11—42no—
321Dic11—42no—
322Dic11—44no—
323Dic11—44no—
324Dic11—81no—
325Dic11—81no—
326C22×Q8—112no—
327C22×Q8—111no—
328C22×Q8—221no—
329C23×C4D4411yescharacteristic
330C23×C4D4411yescharacteristic
331C23×C4C22×D1111yescharacteristic
332C2×Q16—224no—
333C2×Q16—224no—
334C2×Q16—442no—
335C22×C8C22×D1112yes—
336C22×C8C22×D1112yes—
337C4⋊Q8—114no—
338C4⋊Q8—114no—
339C4⋊Q8—222no—
340C4⋊Q8—222no—
341#125—228no—
342C22⋊Q8—224no—
343C22⋊Q8—222no—
344C22⋊Q8—224no—
345C22⋊Q8—222no—
346C22⋊Q8—228no—
347C4×Q8—224no—
348C4×Q8—224no—
349C4×Q8—228no—
350C4×Q8—222no—
351C4×Q8—222no—
352#117—228no—
353C2×C4⋊C4—112no—
354C2×C4⋊C4—111no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—221no—
358C2×C4⋊C4—221no—
359C2×C4⋊C4—222no—
360C2×C4⋊C4—222no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C22⋊C4—222no—
366C2×C22⋊C4—221no—
367C2×C22⋊C4—221no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—222no—
371C2×C42—221no—
372C2×C42—221no—
373C2×C42D4411yescharacteristic
374C2×C42D4411yescharacteristic
375C2×C42C22×D1111yescharacteristic
376C2×C42C22×D1111yescharacteristic
377#106—224no—
378C4⋊C8—22no—
379C4⋊C8—22no—
380#103—224no—
381#103—224no—
382#103—224no—
383#103—442no—
384C22⋊C8—42no—
385#95—221no—
386#95—221no—
387#95—221no—
388#95—221no—
389#95—221no—
390C2×C11—42no—
391C2×C11#240711yescharacteristic
392C2×C11C2×#45211yescharacteristic
393C2×C11#300411yescharacteristic
394C2×C11#310711yescharacteristic
395C2×C11#311311yescharacteristic
396C2×C11#324811yescharacteristic
397C2×C11#325511yescharacteristic
398C24C2×D4411yescharacteristic
399C2×Q8—114no—
400C2×Q8—112no—
401C2×Q8—224no—
402C2×Q8—222no—
403C2×Q8—221no—
404C2×Q8—221no—
405C2×Q8—221no—
406C2×Q8—222no—
407C2×Q8—221no—
408C2×Q8—222no—
409C2×Q8—221no—
410C2×Q8—222no—
411C2×Q8—222no—
412C2×Q8—442no—
413C2×Q8—442no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4C2×D4411yescharacteristic
433C22×C4C2×D4411yescharacteristic
434C22×C4C2×D4411yescharacteristic
435C22×C4C2×D4411yescharacteristic
436C22×C4C2×D4411yescharacteristic
437C22×C4C23×D1111yescharacteristic
438Q16—448no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C4⋊C4—114no—
446C4⋊C4—112no—
447C4⋊C4—228no—
448C4⋊C4—228no—
449C4⋊C4—224no—
450C4⋊C4—224no—
451C4⋊C4—224no—
452C4⋊C4—224no—
453C4⋊C4—222no—
454C4⋊C4—221no—
455C4⋊C4—221no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—442no—
460C4⋊C4—442no—
461C22⋊C4—228no—
462C22⋊C4—224no—
463C22⋊C4—442no—
464C42—22no—
465C42—22no—
466C42—21no—
467C42—21no—
468C42—228no—
469C42—442no—
470C42—442no—
471C42D4×D1112yes—
472C42D4×D1112yes—
473C11#2415711yescharacteristic, complemented, Sylow
474C23—21no—
475C23—21no—
476C23—21no—
477C23—21no—
478C23—21no—
479C23—21no—
480C23#6696212yes—
481C23C22×D4411yescharacteristic
482Q8—222no—
483Q8—224no—
484Q8—224no—
485Q8—222no—
486Q8—448no—
487Q8—442no—
488Q8—441no—
489Q8—441no—
490Q8—442no—
491C2×C4—28no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—44no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—224no—
508C2×C4—224no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—441no—
512C2×C4—442no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4—442no—
516C2×C4—441no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4—441no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4#6693512yes—
526C2×C4#6693512yes—
527C2×C4#6695712yes—
528C2×C4#6696212yes—
529C2×C4#6696212yes—
530C2×C4C2×D4×D1111yescharacteristic
531C2×C4C2×D4×D1111yescharacteristic
532C2×C4#6703711yescharacteristic
533C2×C4#6704011yescharacteristic
534C2×C4#41×D1111yescharacteristic
535C2×C4#41×D1111yescharacteristic
536C8—42no—
537C8—42no—
538C22—22no—
539C22—22no—
540C22—22no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22C2×#6693511yescharacteristic
546C22#1062304111yescharacteristic
547C22#1062305511yescharacteristic
548C22C2×#6695711yescharacteristic
549C22C2×#6696211yescharacteristic
550C22C2×#6696211yescharacteristic
551C22C2×#6696211yescharacteristic
552C4—22no—
553C4—22no—
554C4—41no—
555C4—41no—
556C4—444no—
557C4—444no—
558C4—442no—
559C4—442no—
560C4—881no—
561C4—881no—
562C4#1062234614yes—
563C4#1062313011yescharacteristic
564C4#1062314311yescharacteristic
565C4#1062316211yescharacteristic
566C4#1062316411yescharacteristic
567C2—42no—
568C2#1307196211yescharacteristic
569C2C2×#1062234611yescharacteristic
570C2#1307785311yescharacteristic
571C2#1307868811yescharacteristic
572C2#1307874711yescharacteristic
573C2#1307995411yescharacteristic
574C2#1308001011yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1797C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1797D11
hypocenterC11#24157
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. C2×#10622464C2semidirect
3. C2×#10622462C2semidirect
7. #13069567C2semidirect
8. #13069538C2semidirect
9. #13068956C2semidirect
10. #13068887C2semidirect
473. C11#24157semidirect

Maximal subgroups

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

subgroupindex
C2×#106230012
C2×#106224642
C2×#106224622
C4×#669772
#130698132
#130696262
#130695672
#130695382
#130689562
#130688872
C11×#17972
#2415711