Finite Group Databasebeta

← #14788159

Subgroups — #14788159

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×#10623259C211yesmaximal, characteristic
2C2×#10622644C211yesmaximal, characteristic, complemented
3C4×#66999C211yesmaximal, characteristic
4#13069814C212yesmaximal
5#13069625C212yesmaximal
6#13069569C211yesmaximal, characteristic, complemented
7#13069538C211yesmaximal, characteristic, complemented
8#13068954C212yesmaximal, complemented
9#13068881C212yesmaximal, complemented
10#13068593C211yesmaximal, characteristic
11C2×C11×#475C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×#66999—21no—
15C2×#66999C2211yescharacteristic
16C2×Q8×Dic11—21no—
17C22×#4326C2212yes—
18#10623259—24no—
19#10623259—24no—
20C2×#66950C2212yes—
21C2×#66945—21no—
22C2×#66943—21no—
23C2×#66940C2212yes—
24C2×C42×D11C2211yescharacteristic
25C2×#66922C2211yescharacteristic
26C11×#475—24no—
27C2×C11×#106C2212yes—
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#103C2212yes—
30#10622843C2211yescharacteristic
31C2×(C2×D11)⋊C8C2212yes—
32C2×#66880C2212yes—
33C2×#66880C2212yes—
34#10622644—24no—
35#10622602—21no—
36#10622600C2211yescharacteristic
37#10622591—21no—
38#10622586C2211yescharacteristic
39C2×#66874C2212yes—
40C4×(C2×D11)⋊C4—21no—
41C4×C4⋊Dic11C2211yescharacteristic
42C4×Dic11⋊C4—21no—
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44#10622188C2212yes—
45#10622167C2212yes—
46#10622167C2212yes—
47C22×Q8×C11—21no—
48C22×Q8×C11C2311yescharacteristic
49C22×C4×D11D411yescharacteristic
50C22×C4×D11D411yescharacteristic
51C22×C4×D11C2311yescharacteristic
52C22×Dic22C2312yes—
53C22×C8×C11C2312yes—
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8D414yes—
56C4×Q8×C11—22no—
57C4×Q8×C11—22no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C4⋊C4C2312yes—
62C2×C42×C11—21no—
63C2×C42×C11C2311yescharacteristic
64#66999—28no—
65#66999—22no—
66#66999—22no—
67Q8×Dic11—28no—
68C2×#4326—24no—
69C2×#4326—24no—
70C2×#4326—42no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×Dic11⋊C4—22no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11—21no—
84C2×C4×Dic11D411yescharacteristic
85C2×C4×Dic11D411yescharacteristic
86C2×C4×Dic11C2311yescharacteristic
87C22×C11⋊C8C2312yes—
88#66950—24no—
89#66950—24no—
90#66945—28no—
91#66943—28no—
92#66940—24no—
93#66940—24no—
94C42×D11—22no—
95C42×D11—22no—
96#66922—22no—
97#66922D414yes—
98C11×#106—24no—
99C11×C4⋊C8—22no—
100C11×#103—24no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106(C2×D11)⋊C8—42no—
107#66880—24no—
108#66880—42no—
109#66874—24no—
110C4⋊(C11⋊C8)—22no—
111#24157—111nomaximal, Sylow
112C23×D11C2×D411yescharacteristic
113C2×Q8×C11—24no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—42no—
120C2×Q8×C11—42no—
121C2×Q8×C11#4112yes—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C22×Dic11—21no—
129C22×Dic11—22no—
130C22×Dic11—21no—
131C22×Dic11C2×D411yescharacteristic
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×C4×D11—21no—
143C2×C4×D11—21no—
144C2×C4×D11—21no—
145C2×C4×D11—21no—
146C2×Dic22—22no—
147C2×Dic22—22no—
148C2×Dic22—22no—
149C2×Dic22—22no—
150C2×Dic22—22no—
151C2×Dic22C2×D414yes—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4C2×D414yes—
161C42×C11—42no—
162C42×C11C2×D412yes—
163C42×C11C2×D412yes—
164#4326—48no—
165(C2×D11)⋊C4—28no—
166(C2×D11)⋊C4—24no—
167(C2×D11)⋊C4—42no—
168C4⋊Dic11—28no—
169C4⋊Dic11—24no—
170C4⋊Dic11—24no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11#4112yes—
175Dic11⋊C4—28no—
176Dic11⋊C4—24no—
177Dic11⋊C4—42no—
178C4×Dic11—28no—
179C4×Dic11—22no—
180C4×Dic11—22no—
181C4×Dic11—21no—
182C4×Dic11—21no—
183C4×Dic11—42no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×#533—111no—
188C2×#475D1111yescharacteristic, complemented
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#1797—111no—
198C23×C11C22×D411yescharacteristic
199C22×D11—21no—
200C22×D11—21no—
201C22×D11—21no—
202C22×D11—21no—
203C22×D11—21no—
204C22×D11—21no—
205C22×D11#13712yes—
206Q8×C11—22no—
207Q8×C11—22no—
208Q8×C11—41no—
209Q8×C11—41no—
210Q8×C11—48no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11#12012yes—
223C2×C4×C11#12012yes—
224C2×C4×C11#13512yes—
225C2×C4×C11#13712yes—
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C2×C4×C11H(5,𝔽2)11yescharacteristic
231C2×C4×C112−1+411yescharacteristic
232C2×Dic11—21no—
233C2×Dic11—21no—
234C2×Dic11—21no—
235C2×Dic11—21no—
236C2×Dic11—24no—
237C2×Dic11—21no—
238C2×Dic11—22no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11#13712yes—
250C4×D11—28no—
251C4×D11—41no—
252C4×D11—41no—
253C4×D11—41no—
254C4×D11—41no—
255C4×D11—44no—
256Dic22—24no—
257Dic22—24no—
258Dic22—42no—
259Dic22—42no—
260C8×C11—42no—
261C11⋊C8—42no—
262C22×Q16—112no—
263#533—224no—
264#533—224no—
265C2×C4⋊Q8—111no—
266C2×C4⋊Q8C2×D1111yescharacteristic
267C2×#125—221no—
268C2×C22⋊Q8—111no—
269C2×C22⋊Q8—112no—
270C2×C22⋊Q8—221no—
271C2×C4×Q8—112no—
272C2×C4×Q8—221no—
273C2×C4×Q8C2×D1111yescharacteristic
274C2×#117—221no—
275C22×C42—111no—
276#475—24no—
277#462—224no—
278C2×#106C2×D1112yes—
279C2×C4⋊C8—111no—
280C2×C4⋊C8C2×D1111yescharacteristic
281C2×#103—112no—
282C2×#103—112no—
283C2×#103—112no—
284C2×#103C2×D1112yes—
285C2×C22⋊C8—112no—
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#336—112no—
297C22×C11C2×#12011yescharacteristic
298C22×C11#52511yescharacteristic
299C22×C11#53711yescharacteristic
300C22×C11C2×#13511yescharacteristic
301C22×C11C2×#13711yescharacteristic
302C22×C11C2×#13711yescharacteristic
303C22×C11C2×#13711yescharacteristic
304C2×D11—22no—
305C2×D11—22no—
306C2×D11—22no—
307C2×D11—41no—
308C2×D11—41no—
309C2×D11—41no—
310C2×D11—41no—
311C4×C11—22no—
312C4×C11—42no—
313C4×C11—44no—
314C4×C11—81no—
315C4×C11#45214yes—
316C4×C11#54611yescharacteristic
317C4×C11#54711yescharacteristic
318C4×C11#54811yescharacteristic
319C4×C11#55011yescharacteristic
320Dic11—22no—
321Dic11—42no—
322Dic11—44no—
323Dic11—41no—
324Dic11—41no—
325Dic11—81no—
326C22×Q8—21no—
327C22×Q8—112no—
328C22×Q8C22×D1111yescharacteristic
329C23×C4—111no—
330C23×C4—111no—
331C23×C4—111no—
332C2×Q16—224no—
333C2×Q16—224no—
334C2×Q16—442no—
335C22×C8—112no—
336C22×C8C22×D1112yes—
337C4⋊Q8—22no—
338C4⋊Q8—114no—
339C4⋊Q8—222no—
340C4⋊Q8C22⋊D1114yes—
341#125—228no—
342C22⋊Q8—224no—
343C22⋊Q8—222no—
344C22⋊Q8—228no—
345C22⋊Q8—222no—
346C22⋊Q8—224no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×Q8—224no—
350C4×Q8—228no—
351C4×Q8—224no—
352#117—228no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4—221no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4C22×D1111yescharacteristic
364C2×C4⋊C4C22×D1112yes—
365C2×C22⋊C4—222no—
366C2×C22⋊C4—221no—
367C2×C22⋊C4—221no—
368C2×C42—21no—
369C2×C42—111no—
370C2×C42—111no—
371C2×C42—111no—
372C2×C42—222no—
373C2×C42—222no—
374C2×C42—222no—
375C2×C42—221no—
376C2×C42C22×D1111yescharacteristic
377#106—24no—
378C4⋊C8—22no—
379C4⋊C8—222no—
380#103—24no—
381#103—224no—
382#103—224no—
383#103—442no—
384C22⋊C8—442no—
385#95—221no—
386#95—221no—
387#95—221no—
388#95—221no—
389#95—221no—
390C2×C11#240711yescharacteristic
391C2×C11C2×#45211yescharacteristic
392C2×C11#300411yescharacteristic
393C2×C11#310711yescharacteristic
394C2×C11#311311yescharacteristic
395C2×C11#324811yescharacteristic
396C2×C11#325511yescharacteristic
397D11—42no—
398C24—111no—
399C2×Q8—24no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—42no—
406C2×Q8—42no—
407C2×Q8—114no—
408C2×Q8—222no—
409C2×Q8—222no—
410C2×Q8—222no—
411C2×Q8—222no—
412C2×Q8—222no—
413C2×Q8#434312yes—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—111no—
418C22×C4—111no—
419C22×C4—111no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—221no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4D4×D1111yescharacteristic
436C22×C4D4×D1111yescharacteristic
437C22×C4C23×D1111yescharacteristic
438Q16—448no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—222no—
445C4⋊C4—24no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—42no—
450C4⋊C4—112no—
451C4⋊C4—228no—
452C4⋊C4—228no—
453C4⋊C4—224no—
454C4⋊C4—224no—
455C4⋊C4—224no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—442no—
460C4⋊C4C2×C22⋊D1114yes—
461C22⋊C4—228no—
462C22⋊C4—224no—
463C22⋊C4—442no—
464C42—42no—
465C42—228no—
466C42—222no—
467C42—222no—
468C42—221no—
469C42—221no—
470C42—442no—
471C42D4×D1112yes—
472C42C2×C22⋊D1112yes—
473C11#2415711yescharacteristic, complemented, Sylow
474C23—112no—
475C23—221no—
476C23—221no—
477C23—221no—
478C23—221no—
479C23—221no—
480C23—221no—
481C23C2×D4×D1111yescharacteristic
482Q8—22no—
483Q8—22no—
484Q8—48no—
485Q8—41no—
486Q8—41no—
487Q8—224no—
488Q8—224no—
489Q8—442no—
490Q8—442no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—112no—
503C2×C4—228no—
504C2×C4—221no—
505C2×C4—221no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—224no—
511C2×C4—222no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—441no—
515C2×C4—441no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4—444no—
519C2×C4—441no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4#6696812yes—
527C2×C4#6696912yes—
528C2×C4#6699012yes—
529C2×C4#6699012yes—
530C2×C4C2×D4×D1111yescharacteristic
531C2×C4C2×#434311yescharacteristic
532C2×C4#6704011yescharacteristic
533C2×C4#41×D1111yescharacteristic
534C2×C4#6704211yescharacteristic
535C2×C4C22×C22⋊D1111yescharacteristic
536C8—42no—
537C8—442no—
538C22—222no—
539C22—222no—
540C22—222no—
541C22—441no—
542C22—441no—
543C22—441no—
544C22—441no—
545C22#1062315811yescharacteristic
546C22#1062316011yescharacteristic
547C22C2×#6696811yescharacteristic
548C22C2×#6696911yescharacteristic
549C22D11×#13711yescharacteristic
550C22D11×#13711yescharacteristic
551C22C2×#6699011yescharacteristic
552C4—22no—
553C4—44no—
554C4—42no—
555C4—81no—
556C4—222no—
557C4—441no—
558C4—441no—
559C4—444no—
560C4—442no—
561C4—881no—
562C4#1062278614yes—
563C4#1062316111yescharacteristic
564C4#1062316211yescharacteristic
565C4#1062334811yescharacteristic
566C4#1062336511yescharacteristic
567C2—442no—
568C2#1307196311yescharacteristic
569C2C2×#1062278611yescharacteristic
570C2#1307784811yescharacteristic
571C2#1307869011yescharacteristic
572C2#1307874811yescharacteristic
573C2#1307995611yescharacteristic
574C2#1308000911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#475C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×#475D11
hypocenterC11#24157
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
2. C2×#10622644C2semidirect
6. #13069569C2semidirect
7. #13069538C2semidirect
8. #13068954C2semidirect
9. #13068881C2semidirect
11. C2×C11×#475C2semidirect
188. C2×#475D11semidirect
473. C11#24157semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106226442
C4×#669992
#130698142
#130696252
#130695692
#130695382
#130689542
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