Finite Group Databasebeta

← #14764822

Subgroups — #14764822

Order 2816.

1176 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622724C211yesmaximal, characteristic, complemented
2C4×#67006C211yesmaximal, characteristic
3#13069412C212yesmaximal, complemented
4#13069232C212yesmaximal, complemented
5#13069226C212yesmaximal, complemented
6#13068910C212yesmaximal, complemented
7#13068908C211yesmaximal, characteristic, complemented
8#13068794C211yesmaximal, characteristic, complemented
9#13068526C211yesmaximal, characteristic, complemented
10#13068392C211yesmaximal, characteristic, complemented
11C22×C11×C22⋊C8C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C2×#67006C411yescharacteristic
16C2×C4×C22⋊D11C2211yescharacteristic
17C2×C4×C22⋊D11C2212yes—
18C22×#4313C2211yescharacteristic, complemented
19C2×C11×C22⋊C8—24no—
20C2×C11×C22⋊C8C2212yes—
21C2×C11×C22⋊C8C2212yes—
22#10622860C411yescharacteristic
23#10622826C412yes—
24#10622826C411yescharacteristic
25#10622823C412yes—
26#10622823C411yescharacteristic
27C4×C22⋊Dic11C2211yescharacteristic
28C4×C22⋊Dic11C2212yes—
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2212yes—
32C2×C22⋊(C11⋊C8)C2212yes—
33#10622724—24no—
34C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
35C2×(C2×D11)⋊C8C2212yescomplemented
36C2×#66879C2211yescharacteristic, complemented
37C2×#66879C2212yescomplemented
38C2×Dic11⋊C8C2211yescharacteristic, complemented
39C2×Dic11⋊C8C2212yescomplemented
40#10622188C2212yescomplemented
41#10622188C2212yescomplemented
42#10622188C2212yescomplemented
43C25×C11C2×C411yescharacteristic
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—42no—
47C23×C4×C11—42no—
48C23×C4×C11C2×C411yescharacteristic
49C23×C4×C11C2×C412yes—
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C22×C22⋊D11C2×C411yescharacteristic
53C22×C22⋊D11C2×C412yes—
54C22×C4×D11C2311yescharacteristic
55C22×C8×C11—22no—
56C22×C8×C11—42no—
57C22×C8×C11—42no—
58C22×C8×C11D414yescomplemented
59C22×C8×C11C2312yes—
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62#67006—24no—
63C2×C22⋊Dic11C2×C411yescharacteristic
64C2×C22⋊Dic11C2×C412yes—
65C2×C22⋊Dic11C2×C411yescharacteristic
66C2×C22⋊Dic11C2×C411yescharacteristic
67C2×C22⋊Dic11C2×C412yes—
68C2×C22⋊Dic11C2×C412yes—
69C4×C22⋊D11—22no—
70C4×C22⋊D11—22no—
71C4×C22⋊D11—42no—
72C4×C22⋊D11—42no—
73C2×(C2×D11)⋊C4C2×C411yescharacteristic
74C2×(C2×D11)⋊C4C2×C412yes—
75C2×Dic11⋊C4C2×C411yescharacteristic
76C2×Dic11⋊C4C2×C412yes—
77C2×C4×Dic11C2311yescharacteristic
78C2×C4×Dic11C2312yes—
79C22×C11⋊C8C2312yes—
80C22×C11⋊C8C2311yescharacteristic
81C22×C11⋊C8C2311yescharacteristic
82C2×#4313—22no—
83C2×#4313—42no—
84C11×C22⋊C8—24no—
85C11×C22⋊C8—24no—
86C11⋊#95C2×C412yes—
87C11⋊#95C2×C412yes—
88C11⋊#95C2×C412yes—
89C22⋊(C11⋊C8)—22no—
90C22⋊(C11⋊C8)—22no—
91C22⋊(C11⋊C8)—42no—
92C22⋊(C11⋊C8)—42no—
93(C2×D11)⋊C8—22no—
94(C2×D11)⋊C8—42no—
95#66879—22no—
96#66879—42no—
97Dic11⋊C8—22no—
98Dic11⋊C8—42no—
99#22034—111nomaximal, Sylow
100C24×C11—22no—
101C24×C11—22no—
102C24×C11—42no—
103C24×C11—42no—
104C24×C11M1614yescomplemented
105C24×C11C22×C412yes—
106C24×C11C22×C411yescharacteristic
107C23×D11C22×C411yescharacteristic
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—24no—
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—42no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11—44no—
122C22×C4×C11—44no—
123C22×C4×C11—48no—
124C22×C4×C11C22×C412yes—
125C22×C4×C11C22×C411yescharacteristic
126C22×C4×C11C2×D412yes—
127C22×C4×C11#4112yes—
128C22×C4×C11C2411yescharacteristic
129C2×C22⋊D11—22no—
130C2×C22⋊D11—24no—
131C2×C22⋊D11—22no—
132C2×C22⋊D11—22no—
133C2×C22⋊D11—42no—
134C2×C22⋊D11—42no—
135C22×Dic11C22×C411yescharacteristic
136C22×Dic11C22×C412yes—
137C22×Dic11C22×C411yescharacteristic
138C22×Dic11C22×C412yes—
139C22×Dic11C22×C411yescharacteristic
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×C4×D11—22no—
143C2×C4×D11—22no—
144C2×C8×C11—22no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—44no—
150C2×C8×C11—44no—
151C2×C8×C11C2×D412yes—
152C2×C8×C11C2×D412yes—
153C22⋊Dic11—22no—
154C22⋊Dic11—24no—
155C22⋊Dic11—22no—
156C22⋊Dic11—22no—
157C22⋊Dic11—42no—
158C22⋊Dic11—42no—
159(C2×D11)⋊C4—22no—
160(C2×D11)⋊C4—42no—
161Dic11⋊C4—22no—
162Dic11⋊C4—42no—
163C4×Dic11—21no—
164C4×Dic11—21no—
165C4×Dic11—22no—
166C4×Dic11—22no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174#4313—44no—
175C2×#435—111no—
176C22×C22⋊C8D1111yescharacteristic, complemented
177C4×#120—111no—
178#1955—112no—
179#1924—112no—
180#1924—112no—
181#1870—112no—
182#1869—111no—
183#1850—111no—
184#1779—111no—
185#1752—111no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—28no—
195C23×C11—48no—
196C23×C11—44no—
197C23×C11—44no—
198C23×C11—48no—
199C23×C11C4×D412yes—
200C23×C11C2×M1614yes—
201C23×C11C2×M1612yes—
202C23×C11#13112yes—
203C23×C11C23×C411yescharacteristic
204C22×D11—21no—
205C22×D11—22no—
206C22×D11—21no—
207C22×D11—21no—
208C22×D11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—24no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—48no—
217C2×C4×C11—44no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11C4×D412yes—
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C2×C4×C11H(5,𝔽2)12yes—
226C2×C4×C11H(5,𝔽2)12yes—
227C22⋊D11—48no—
228C22⋊D11—44no—
229C2×Dic11—21no—
230C2×Dic11—21no—
231C2×Dic11—21no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—21no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—21no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C4×D11—41no—
243C4×D11—41no—
244C4×D11—42no—
245C8×C11—22no—
246C8×C11—22no—
247C8×C11—42no—
248C11⋊C8—41no—
249C11⋊C8—41no—
250C11⋊C8—42no—
251C24×C4C2×D1111yescharacteristic
252C22×M16—111no—
253C23×C8C2×D1111yescharacteristic
254C23×C8C2×D1111yescharacteristic
255C2×#120—111no—
256C2×C4×D4—111no—
257C2×C4×D4—112no—
258#435—224no—
259C2×C4⋊C8—111no—
260C2×C4⋊C8—112no—
261C2×C22⋊C8—24no—
262C2×C22⋊C8—111no—
263C2×C22⋊C8—111no—
264C2×C22⋊C8—111no—
265C2×C22⋊C8—112no—
266C2×C22⋊C8—112no—
267C2×C22⋊C8—112no—
268C2×C22⋊C8C2×D1112yes—
269C2×C22⋊C8C2×D1112yes—
270C2×#97—111no—
271C2×#97—112no—
272#386—111no—
273#386—112no—
274#385—111no—
275#385—112no—
276#379—111no—
277C4×C22⋊C4—111no—
278C4×C22⋊C4—112no—
279#336—112no—
280#336—112no—
281#336—112no—
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—24no—
285C22×C11—24no—
286C22×C11—24no—
287C22×C11—24no—
288C22×C11—24no—
289C22×C11—416no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11#43514yes—
295C22×C11C2×C4×D411yescharacteristic
296C22×C11#51812yes—
297C22×C11C22×M1611yescharacteristic
298C22×C11C2×#13111yescharacteristic
299C22×C11#56812yes—
300C2×D11—41no—
301C2×D11—41no—
302C2×D11—41no—
303C2×D11—42no—
304C2×D11—42no—
305C4×C11—22no—
306C4×C11—42no—
307C4×C11#53411yescharacteristic
308C4×C11#53511yescharacteristic
309C4×C11#53812yes—
310Dic11—41no—
311Dic11—41no—
312Dic11—41no—
313Dic11—42no—
314Dic11—42no—
315C25C4×D1111yescharacteristic
316C22×D4—111no—
317C22×D4—112no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—42no—
321C23×C4—42no—
322C23×C4—111no—
323C23×C4C4×D1111yescharacteristic
324C23×C4C4×D1112yes—
325C23×C4C22×D1112yes—
326C23×C4C22×D1111yescharacteristic
327C2×M16—222no—
328C2×M16—442no—
329C22×C8—22no—
330C22×C8—42no—
331C22×C8—42no—
332C22×C8—111no—
333C22×C8—112no—
334C22×C8—111no—
335C22×C8C22⋊D1114yescomplemented
336C22×C8C22×D1112yes—
337C22×C8C22×D1111yescharacteristic
338C22×C8C22×D1111yescharacteristic
339#120—224no—
340C4×D4—222no—
341C4×D4—222no—
342C4×D4—442no—
343C4×D4—442no—
344C2×C4⋊C4—111no—
345C2×C4⋊C4—112no—
346C2×C22⋊C4—111no—
347C2×C22⋊C4—112no—
348C2×C22⋊C4—111no—
349C2×C22⋊C4—111no—
350C2×C22⋊C4—111no—
351C2×C22⋊C4—112no—
352C2×C22⋊C4—112no—
353C2×C22⋊C4—112no—
354C2×C42—111no—
355C2×C42—112no—
356C4⋊C8—222no—
357C4⋊C8—442no—
358C22⋊C8—24no—
359C22⋊C8—24no—
360C22⋊C8—222no—
361C22⋊C8—222no—
362C22⋊C8—222no—
363C22⋊C8—442no—
364C22⋊C8—442no—
365C22⋊C8—442no—
366#97—222no—
367#97—442no—
368#95—112no—
369#95—112no—
370#95—112no—
371C2×C11—24no—
372C2×C11—44no—
373C2×C11#232111yescharacteristic
374C2×C11C2×#43511yescharacteristic
375C2×C11#293011yescharacteristic
376C2×C11#297312yes—
377C2×C11#297612yes—
378D11—81no—
379C24—22no—
380C24—22no—
381C24—42no—
382C24—42no—
383C24—111no—
384C24#431314yescomplemented
385C24C2×C4×D1112yes—
386C24C2×C4×D1111yescharacteristic
387C2×D4—224no—
388C2×D4—222no—
389C2×D4—222no—
390C2×D4—222no—
391C2×D4—442no—
392C2×D4—442no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—48no—
407C22×C4—44no—
408C22×C4—44no—
409C22×C4—112no—
410C22×C4—111no—
411C22×C4—111no—
412C22×C4—112no—
413C22×C4—111no—
414C22×C4—221no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—221no—
418C22×C4C2×C4×D1112yes—
419C22×C4C2×C4×D1111yescharacteristic
420C22×C4#433912yes—
421C22×C4C2×C22⋊D1112yes—
422C22×C4C23×D1111yescharacteristic
423M16—444no—
424C2×C8—22no—
425C2×C8—22no—
426C2×C8—22no—
427C2×C8—22no—
428C2×C8—22no—
429C2×C8—44no—
430C2×C8—44no—
431C2×C8—222no—
432C2×C8—222no—
433C2×C8—222no—
434C2×C8—222no—
435C2×C8—222no—
436C2×C8—221no—
437C2×C8—221no—
438C2×C8C2×C22⋊D1112yes—
439C2×C8C2×C22⋊D1112yes—
440C4⋊C4—222no—
441C4⋊C4—442no—
442C22⋊C4—224no—
443C22⋊C4—222no—
444C22⋊C4—222no—
445C22⋊C4—222no—
446C22⋊C4—222no—
447C22⋊C4—442no—
448C22⋊C4—442no—
449C22⋊C4—442no—
450C42—221no—
451C42—222no—
452C42—222no—
453C42—221no—
454C11#2203411yescharacteristic, complemented, Sylow
455C23—22no—
456C23—22no—
457C23—28no—
458C23—22no—
459C23—22no—
460C23—22no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23—48no—
465C23—44no—
466C23—44no—
467C23—48no—
468C23—221no—
469C23—221no—
470C23—222no—
471C23—222no—
472C23—221no—
473C23C2×#431314yes—
474C23C2×#431312yes—
475C23#6695412yes—
476C23C4×C22⋊D1112yes—
477C23C22×C4×D1111yescharacteristic
478D4—448no—
479D4—444no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—48no—
488C2×C4—44no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—221no—
494C2×C4—222no—
495C2×C4—222no—
496C2×C4—221no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—221no—
504C2×C4—221no—
505C2×C4—221no—
506C2×C4—442no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4C4×C22⋊D1112yes—
510C2×C4C2×#433911yescharacteristic
511C2×C4#6703712yes—
512C2×C4#6703712yes—
513C2×C4C22×C22⋊D1111yescharacteristic
514C8—22no—
515C8—22no—
516C8—42no—
517C8—442no—
518C8—441no—
519C8—441no—
520C22—22no—
521C22—24no—
522C22—24no—
523C22—22no—
524C22—24no—
525C22—24no—
526C22—24no—
527C22—416no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—441no—
533C22—441no—
534C22—442no—
535C22—442no—
536C22—441no—
537C22#1062272414yes—
538C22#1062301712yes—
539C22C22×#431311yescharacteristic
540C22C2×#6695411yescharacteristic
541C22#1062327612yes—
542C22C2×C4×C22⋊D1111yescharacteristic
543C4—22no—
544C4—42no—
545C4—441no—
546C4—441no—
547C4—442no—
548C4—442no—
549C4—441no—
550C4#1062302512yes—
551C4#1062333511yescharacteristic
552C4#1062333611yescharacteristic
553C2—24no—
554C2—44no—
555C2—881no—
556C2#1307127411yescharacteristic
557C2C2×#1062272411yescharacteristic
558C2#1307731911yescharacteristic
559C2#1307764212yes—
560C2#1307766112yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC22×C11×C22⋊C8C2
prime radicalC2×#67006C4
cosocleC22×C4×C11C24
hypercenterC22×C22⋊C8D11
hypocenterC11#22034
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#10622724C2semidirect
3. #13069412C2semidirect
4. #13069232C2semidirect
5. #13069226C2semidirect
6. #13068910C2semidirect
7. #13068908C2semidirect
8. #13068794C2semidirect
9. #13068526C2semidirect
10. #13068392C2semidirect
11. C22×C11×C22⋊C8C2semidirect
18. C22×#4313C22semidirect
34. C2×(C2×D11)⋊C8C22semidirect
35. C2×(C2×D11)⋊C8C22semidirect
36. C2×#66879C22semidirect
37. C2×#66879C22semidirect
38. C2×Dic11⋊C8C22semidirect
39. C2×Dic11⋊C8C22semidirect
40. #10622188C22semidirect
41. #10622188C22semidirect
42. #10622188C22semidirect
58. C22×C8×C11D4semidirect
104. C24×C11M16semidirect
176. C22×C22⋊C8D11semidirect
335. C22×C8C22⋊D11semidirect
384. C24#4313semidirect
454. C11#22034semidirect

Maximal subgroups

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

subgroupindex
C2×#106227242
C4×#670062
#130694122
#130692322
#130692262
#130689102
#130689082
#130687942
#130685262
#130683922
C22×C11×C22⋊C82
#2203411