Finite Group Databasebeta

← #14676180

Subgroups — #14676180

Order 2816.

1710 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66940C211yesmaximal, characteristic
2C2×#10622263C211yesmaximal, characteristic
3C2×C4×Dic11⋊C4C211yesmaximal, characteristic
4#13066886C212yesmaximal
5#13066882C212yesmaximal
6#13066851C211yesmaximal, characteristic
7#13066849C211yesmaximal, characteristic
8#13066848C211yesmaximal, characteristic
9Dic11⋊#95C212yesmaximal
10Dic11⋊#95C212yesmaximal
11C11×#1436C211yesmaximal, characteristic
12C23×Dic22C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×Dic11⋊C4C2212yes—
16C22×Dic11⋊C4C2211yescharacteristic
17C22×Dic11⋊C4C2211yescharacteristic
18C22×Dic11⋊C4C2212yes—
19C22×C4×Dic11C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C2×#66940—24no—
24C2×#66940—24no—
25C2×#66940C418yescomplemented
26C2×C11×#95C2212yes—
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C4×Dic11⋊C4—24no—
39#10622263—24no—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×Dic11C2312yes—
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C22×Dic22—24no—
52C22×Dic22—22no—
53C22×Dic22—22no—
54C22×Dic22—24no—
55C22×Dic22C2×C414yes—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4C2×C414yes—
59C2×C42×C11—22no—
60C2×C42×C11—42no—
61C2×Dic11⋊C4—22no—
62C2×Dic11⋊C4—22no—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—24no—
66C2×Dic11⋊C4—24no—
67C2×Dic11⋊C4—24no—
68C2×Dic11⋊C4—24no—
69C2×Dic11⋊C4—24no—
70C2×Dic11⋊C4C2×C414yes—
71C2×Dic11⋊C4C2×C414yes—
72C2×Dic11⋊C4Q818yescomplemented
73C2×C4×Dic11—22no—
74C2×C4×Dic11—22no—
75C2×C4×Dic11—22no—
76C2×C4×Dic11—22no—
77C2×C4×Dic11—22no—
78C2×C4×Dic11—42no—
79C2×C4×Dic11C2×C414yes—
80C2×C4×Dic11C2×C414yes—
81C2×C4×Dic11C2×C414yes—
82C2×C4×Dic11D414yes—
83C2×C4×Dic11D414yes—
84#66940—232no—
85C11×#95—22no—
86C11×#95—24no—
87C11×#95—42no—
88C11⋊#95—22no—
89C11⋊#95—24no—
90C11⋊#95—24no—
91C11⋊#95—24no—
92C11⋊#95—24no—
93C11⋊#95—24no—
94C11⋊#95—42no—
95C11⋊#95—42no—
96C11⋊#95—42no—
97#13925—111nomaximal, Sylow
98C24×C11C2411yescharacteristic
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
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—22no—
120C22×C4×C11—22no—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C22×C412yes—
123C22×C4×C11C22×C412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×Q814yes—
127C22×C4×C11#4114yes—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—22no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11C22×C412yes—
151C22×Dic11C22×C412yes—
152C22×Dic11C22×C412yes—
153C22×Dic11C22×C412yes—
154C22×Dic11C2×D412yes—
155C22×Dic11C2×D412yes—
156C22×Dic11C2×D412yes—
157C22×Dic11C2×D412yes—
158C22×Dic11C2×Q814yes—
159C22×Dic11C2×Q814yes—
160C22×Dic11#4114yes—
161C22×Dic11#4114yes—
162C2×Dic22—216no—
163C2×Dic22—216no—
164C2×Dic22—28no—
165C2×Dic22—28no—
166C2×Dic22—28no—
167C11×C4⋊C4—28no—
168C42×C11—44no—
169Dic11⋊C4—28no—
170Dic11⋊C4—216no—
171Dic11⋊C4—28no—
172Dic11⋊C4—48no—
173C4×Dic11—28no—
174C4×Dic11—28no—
175C4×Dic11—44no—
176C4×Dic11C22⋊C4116yes—
177C22×C4×Q8—111no—
178C2×#382—111no—
179C2×C4×C4⋊C4—111no—
180#1446—112no—
181#1445—112no—
182#1436—111no—
183#1436—111no—
184#1436—111no—
185#1436D1111yescharacteristic
186C4⋊#95—112no—
187C4⋊#95—112no—
188C23×C11C23×C411yescharacteristic
189C23×C11C22×D411yescharacteristic
190C23×C11C22×D411yescharacteristic
191C23×C11C22×Q812yes—
192C23×C11C2×#4112yes—
193C23×C11C2×#4112yes—
194C23×C11C2×#4112yes—
195C23×C11H(5,𝔽2)12yes—
196C23×C112−1+412yes—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—24no—
205C2×C4×C11—22no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11C2×C22⋊C414yes—
225C2×C4×C11#11714yes—
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—24no—
234C2×Dic11—22no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11C2×C22⋊C414yes—
254C2×Dic11C2×C22⋊C414yes—
255C2×Dic11#11714yes—
256C2×Dic11C4×Q818yes—
257C2×Dic11C22⋊Q818yes—
258C2×Dic11#12414yes—
259C2×Dic11C4⋊Q814yes—
260Dic22—232no—
261C23×Q8—111no—
262C2×C4×Q8—118no—
263C2×C4×Q8—224no—
264C2×C4×Q8—224no—
265C22×C4⋊C4—111no—
266C22×C4⋊C4—111no—
267C22×C4⋊C4—112no—
268C22×C4⋊C4—112no—
269C22×C4⋊C4C2×D1111yescharacteristic
270C22×C42—111no—
271C22×C42—111no—
272C22×C42—111no—
273C22×C42—111no—
274C22×C42C2×D1111yescharacteristic
275#382—224no—
276C4×C4⋊C4—224no—
277C2×#95—112no—
278C2×#95—112no—
279C2×#95—112no—
280C2×#95—111no—
281C2×#95—112no—
282C2×#95—112no—
283C2×#95—112no—
284C2×#95—112no—
285C2×#95—112no—
286C2×#95C2×D1112yes—
287C2×#95C2×D1111yescharacteristic
288C2×#95C2×D1112yes—
289C22×C11C22×C22⋊C411yescharacteristic
290C22×C11C2×#11711yescharacteristic
291C22×C11C2×#11711yescharacteristic
292C22×C11C2×C4×Q812yes—
293C22×C11#52012yes—
294C22×C11C2×C22⋊Q812yes—
295C22×C11#52512yes—
296C22×C11#52512yes—
297C22×C11C2×#12411yescharacteristic
298C22×C11C2×C4⋊Q811yescharacteristic
299C22×C11#53511yescharacteristic
300C22×C11#53611yescharacteristic
301C22×C11#53712yes—
302C22×C11#55412yes—
303C22×C11#55412yes—
304C22×C11#55612yes—
305C22×C11#55612yes—
306C22×C11#55712yes—
307C22×C11#55712yes—
308C22×C11#55912yes—
309C22×C11#55912yes—
310C4×C11—24no—
311C4×C11—24no—
312C4×C11—42no—
313C4×C11—44no—
314C4×C11—82no—
315Dic11—24no—
316Dic11—24no—
317Dic11—42no—
318Dic11—44no—
319Dic11—82no—
320Dic11#39118yes—
321C22×Q8—114no—
322C22×Q8—222no—
323C22×Q8—222no—
324C22×Q8—224no—
325C22×Q8—224no—
326C23×C4—111no—
327C23×C4—111no—
328C23×C4—111no—
329C23×C4—111no—
330C23×C4—112no—
331C23×C4—112no—
332C23×C4C22×D1112yes—
333C23×C4C22×D1111yescharacteristic
334C23×C4C22×D1112yes—
335C23×C4C22×D1111yescharacteristic
336C23×C4C22×D1111yescharacteristic
337C4×Q8—2232no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—114no—
341C2×C4⋊C4—114no—
342C2×C4⋊C4—118no—
343C2×C4⋊C4—222no—
344C2×C4⋊C4—222no—
345C2×C4⋊C4—224no—
346C2×C4⋊C4—224no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—224no—
350C2×C4⋊C4—224no—
351C2×C4⋊C4—224no—
352C2×C4⋊C4C4×D1114yes—
353C2×C42—22no—
354C2×C42—42no—
355C2×C42—114no—
356C2×C42—114no—
357C2×C42—114no—
358C2×C42—114no—
359C2×C42—114no—
360C2×C42—222no—
361C2×C42—222no—
362C2×C42—222no—
363C2×C42—222no—
364C2×C42—222no—
365C2×C42—442no—
366#95—24no—
367#95—22no—
368#95—42no—
369#95—224no—
370#95—224no—
371#95—224no—
372#95—224no—
373#95—224no—
374#95—222no—
375#95—442no—
376#95—442no—
377#95—442no—
378C2×C11#228011yescharacteristic
379C2×C11C2×#39111yescharacteristic
380C2×C11#231111yescharacteristic
381C2×C11#235512yes—
382C2×C11#235512yes—
383C2×C11#258012yes—
384C2×C11#258112yes—
385C2×C11#258412yes—
386C2×C11#259212yes—
387C24C23×D1111yescharacteristic
388C2×Q8—228no—
389C2×Q8—228no—
390C2×Q8—2216no—
391C2×Q8—2216no—
392C2×Q8—228no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—112no—
416C22×C4—112no—
417C22×C4—112no—
418C22×C4—114no—
419C22×C4—114no—
420C22×C4—112no—
421C22×C4—112no—
422C22×C4—112no—
423C22×C4—112no—
424C22×C4—114no—
425C22×C4—112no—
426C22×C4—114no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4C2×C4×D1112yes—
450C22×C4C2×C4×D1112yes—
451C22×C4C2×C4×D1112yes—
452C22×C4#433914yes—
453C22×C4D4×D1112yes—
454C22×C4D4×D1112yes—
455C22×C4Q8×D1114yes—
456C4⋊C4—28no—
457C4⋊C4—228no—
458C4⋊C4—2216no—
459C4⋊C4—228no—
460C4⋊C4—448no—
461C42—44no—
462C42—1116no—
463C42—228no—
464C42—228no—
465C42—444no—
466C11#1392511yescharacteristic, complemented, Sylow
467C23C22×C4×D1111yescharacteristic
468C23C2×#433912yes—
469C23C2×D4×D1111yescharacteristic
470C23C2×D4×D1111yescharacteristic
471C23#6703712yes—
472C23C2×Q8×D1112yes—
473C23#41×D1112yes—
474C23#41×D1112yes—
475C23#6704312yes—
476Q8—2232no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—114no—
505C2×C4—114no—
506C2×C4—118no—
507C2×C4—118no—
508C2×C4—114no—
509C2×C4—114no—
510C2×C4—114no—
511C2×C4—222no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—224no—
516C2×C4—224no—
517C2×C4—224no—
518C2×C4—224no—
519C2×C4—222no—
520C2×C4—224no—
521C2×C4—224no—
522C2×C4—224no—
523C2×C4—224no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—441no—
528C2×C4—442no—
529C2×C4—441no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4—442no—
533C2×C4—442no—
534C2×C4—442no—
535C2×C4—442no—
536C2×C4—442no—
537C2×C4—442no—
538C2×C4#6692514yes—
539C2×C4C22⋊C4×D1114yes—
540C22C2×#6692511yescharacteristic
541C22C2×C22⋊C4×D1111yescharacteristic
542C22#1062304212yes—
543C22D11×#11711yescharacteristic
544C22#1062306412yes—
545C22#1062307712yes—
546C22#1062307812yes—
547C22#1062307812yes—
548C22#1062309012yes—
549C22#1062309812yes—
550C22C4×Q8×D1112yes—
551C22#1062312311yescharacteristic
552C22#1062312812yes—
553C22D11×C22⋊Q812yes—
554C22#1062316712yes—
555C22#1062317911yescharacteristic
556C22#1062319512yes—
557C22D11×#12411yescharacteristic
558C22#1062321612yes—
559C22#1062323312yes—
560C22D11×C4⋊Q811yescharacteristic
561C4—24no—
562C4—24no—
563C4—44no—
564C4—42no—
565C4—82no—
566C4—118no—
567C4—224no—
568C4—224no—
569C4—444no—
570C4—442no—
571C4—882no—
572C2#1307099711yescharacteristic
573C2D11×#39111yescharacteristic
574C2#1307120311yescharacteristic
575C2#1307156912yes—
576C2#1307157012yes—
577C2#1307397312yes—
578C2#1307398112yes—
579C2#1307400212yes—
580C2#1307410212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1436D11
hypocenterC11#13925
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
25. C2×#66940C4semidirect
72. C2×Dic11⋊C4Q8semidirect
466. C11#13925semidirect

Maximal subgroups

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

subgroupindex
C22×#669402
C2×#106222632
C2×C4×Dic11⋊C42
#130668862
#130668822
#130668512
#130668492
#130668482
Dic11⋊#952
C11×#14362
#1392511