Finite Group Databasebeta

← #14926365

Subgroups — #14926365

Order 2816.

2866 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623014C211yesmaximal, characteristic, complemented
2#13076955C212yesmaximal, complemented
3#13076903C212yesmaximal, complemented
4#13074429C212yesmaximal, complemented
5#13074421C212yesmaximal, complemented
6#13072434C218yesmaximal, complemented
7#13072419C218yesmaximal, complemented
8#13071230C211yesmaximal, characteristic, complemented
9#13071194C212yesmaximal
10C2×#10622823C212yesmaximal, complemented
11C22×C4×D4×C11C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C2×C4×D4×C11—28no—
16C2×C4×D4×C11C2218yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C2×#66977C2212yes—
24C2×#66977C2212yes—
25C2×#66977C2214yescomplemented
26C22×Dic11⋊C4C2214yescomplemented
27#10623014—28no—
28C2×#66931C2214yescomplemented
29C2×#66931C2214yescomplemented
30#10622860C2214yes—
31#10622833C2214yes—
32#10622833C2218yes—
33#10622833C2214yes—
34#10622825C2212yes—
35#10622825C2212yes—
36#10622825C2214yescomplemented
37#10622824C2214yes—
38#10622823C2214yes—
39#10622823C2214yes—
40#10622823C2218yescomplemented
41#10622823C2218yescomplemented
42C2×C11⋊#95C2214yescomplemented
43#10622599C2214yescomplemented
44#10622597C2218yescomplemented
45#10622592C2214yescomplemented
46#10622563C2218yescomplemented
47#10622562C2214yescomplemented
48#10622561C2218yescomplemented
49#10622560C2214yescomplemented
50#10622546C2218yescomplemented
51#10622542C2214yescomplemented
52#10622541C2214yescomplemented
53C25×C11C2311yescharacteristic
54C25×C11C2311yescharacteristic
55C22×D4×C11—24no—
56C22×D4×C11—24no—
57C22×D4×C11Q818yescomplemented
58C22×D4×C11C2314yes—
59C23×C4×C11—24no—
60C23×C4×C11—24no—
61C23×C4×C11—44no—
62C23×C4×C11—44no—
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2314yes—
65C23×C4×C11C2314yes—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×Dic11C2312yes—
71C23×Dic11C2312yes—
72C23×Dic11C2314yes—
73C22×Dic22C2312yes—
74C22×Dic22C2312yes—
75C4×D4×C11—232no—
76C2×C11×C4⋊C4—24no—
77C2×C11×C4⋊C4C2314yes—
78C2×C11×C22⋊C4—24no—
79C2×C11×C22⋊C4D418yes—
80C2×C11×C22⋊C4C2314yes—
81C2×C11×C22⋊C4C2314yes—
82C2×C42×C11—24no—
83C2×C42×C11C2314yes—
84C2×C22⋊Dic11—28no—
85C2×C22⋊Dic11—28no—
86C2×C22⋊Dic11C2314yes—
87C2×C22⋊Dic11C2314yes—
88C2×C22⋊Dic11C2314yes—
89C2×C22⋊Dic11C2314yes—
90C2×C22⋊Dic11C2318yes—
91C2×C22⋊Dic11C2318yes—
92C2×C4⋊Dic11C2312yes—
93C2×C4⋊Dic11C2312yes—
94C2×C4⋊Dic11C2314yes—
95C2×C4⋊Dic11C2314yes—
96#66977—28no—
97#66977—28no—
98#66977—48no—
99C2×Dic11⋊C4—48no—
100C2×Dic11⋊C4C2314yes—
101C2×Dic11⋊C4C2314yes—
102C2×Dic11⋊C4C2318yes—
103C2×Dic11⋊C4C2318yes—
104#66931—216no—
105#66931—216no—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C11⋊#95C2318yes—
109C11⋊#95C2314yes—
110C11⋊#95C2318yes—
111C11⋊#95C2314yes—
112#34985—111nomaximal, Sylow
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—42no—
116C24×C11—42no—
117C24×C11—42no—
118C24×C11—42no—
119C24×C11C2×D414yes—
120C24×C11C2×Q814yes—
121C24×C11C2×Q814yes—
122C24×C11#4114yes—
123C24×C11C2412yes—
124C24×C11C2411yescharacteristic
125C24×C11C2412yes—
126C2×D4×C11—232no—
127C2×D4×C11—28no—
128C2×D4×C11—28no—
129C2×D4×C11C2×Q8116yes—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—24no—
134C22×C4×C11—22no—
135C22×C4×C11—28no—
136C22×C4×C11—28no—
137C22×C4×C11—28no—
138C22×C4×C11—28no—
139C22×C4×C11—42no—
140C22×C4×C11—44no—
141C22×C4×C11—44no—
142C22×C4×C11—42no—
143C22×C4×C11—42no—
144C22×C4×C11—416no—
145C22×C4×C11—416no—
146C22×C4×C11C2×D414yes—
147C22×C4×C11C2×D414yes—
148C22×C4×C11C2×Q814yes—
149C22×C4×C11C2412yes—
150C22×C4×C11C2412yes—
151C22×C4×C11C2412yes—
152C22×C4×C11C2412yes—
153C22×C4×C11C2412yes—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—28no—
157C22×Dic11—44no—
158C22×Dic11—44no—
159C22×Dic11—44no—
160C22×Dic11—44no—
161C22×Dic11C2418yes—
162C22×Dic11C2414yes—
163C22×Dic11C2414yes—
164C2×Dic22—24no—
165C2×Dic22—24no—
166C2×Dic22—44no—
167C2×Dic22—44no—
168C11×C4⋊C4—28no—
169C11×C22⋊C4—28no—
170C11×C22⋊C4C2×D4116yes—
171C42×C11—28no—
172C22⋊Dic11—28no—
173C22⋊Dic11—28no—
174C22⋊Dic11—28no—
175C22⋊Dic11—28no—
176C22⋊Dic11—48no—
177C22⋊Dic11—48no—
178C4⋊Dic11—24no—
179C4⋊Dic11—24no—
180C4⋊Dic11—44no—
181C4⋊Dic11—44no—
182Dic11⋊C4—28no—
183Dic11⋊C4—28no—
184Dic11⋊C4—216no—
185Dic11⋊C4—48no—
186C2×#543—111no—
187C22×C4×D4D1111yescharacteristic
188#2855—112no—
189#2848—112no—
190#2627—112no—
191#2626—112no—
192#2450—118no—
193#2449—118no—
194#2315—111no—
195#2308—112no—
196C2×#385—112no—
197C23×C11—24no—
198C23×C11—22no—
199C23×C11—24no—
200C23×C11—22no—
201C23×C11—28no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—44no—
207C23×C11—44no—
208C23×C11—48no—
209C23×C11—48no—
210C23×C11—48no—
211C23×C11—44no—
212C23×C11—48no—
213C23×C11—44no—
214C23×C11C22⋊Q8116yescomplemented
215C23×C11C22×D412yes—
216C23×C11C22×D414yes—
217C23×C11C22×Q814yes—
218C23×C11C22×Q812yes—
219C23×C11C22×Q814yes—
220C23×C11C2×#4112yes—
221C23×C11C2×#4114yes—
222C23×C11C2511yescharacteristic
223D4×C11—232no—
224C2×C4×C11—28no—
225C2×C4×C11—28no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—44no—
235C2×C4×C11—44no—
236C2×C4×C11—416no—
237C2×C4×C11—416no—
238C2×C4×C11—44no—
239C2×C4×C11C22×D414yes—
240C2×C4×C11C22×D414yes—
241C2×C4×C11C22×Q814yes—
242C2×C4×C11H(5,𝔽2)14yes—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—28no—
246C2×Dic11—28no—
247C2×Dic11—28no—
248C2×Dic11—28no—
249C2×Dic11—28no—
250C2×Dic11—416no—
251C2×Dic11—84no—
252C2×Dic11—84no—
253Dic22—84no—
254Dic22—84no—
255C23×D4C2×D1111yescharacteristic
256C24×C4C2×D1111yescharacteristic
257C24×C4C2×D1111yescharacteristic
258#543—228no—
259C2×C22⋊Q8—112no—
260C2×C22⋊Q8—112no—
261C2×C22⋊Q8—114no—
262C2×C22⋊Q8—114no—
263C2×C22⋊Q8—114no—
264C2×C4×D4—28no—
265C2×C4×D4C2×D1118yes—
266C22×C4⋊C4—114no—
267C22×C4⋊C4C2×D1111yescharacteristic
268C22×C22⋊C4—112no—
269C22×C22⋊C4—112no—
270C22×C22⋊C4C2×D1111yescharacteristic
271C22×C22⋊C4C2×D1111yescharacteristic
272C22×C42C2×D1111yescharacteristic
273#400—114no—
274#399—114no—
275#398—118no—
276#396—118no—
277#395—114no—
278#393—114no—
279#391—114no—
280#389—114no—
281#387—118no—
282#386—114no—
283#386—118no—
284#386—114no—
285#385—114no—
286#385—118no—
287#385—114no—
288#385—118no—
289#385—118no—
290#381—114no—
291#380—112no—
292#380—112no—
293#380—114no—
294#379—114no—
295C2×#95—114no—
296C22×C11—24no—
297C22×C11—28no—
298C22×C11—22no—
299C22×C11—24no—
300C22×C11—22no—
301C22×C11—24no—
302C22×C11—24no—
303C22×C11—28no—
304C22×C11—24no—
305C22×C11—28no—
306C22×C11—416no—
307C22×C11—416no—
308C22×C11—44no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11C2×C22⋊Q814yes—
312C22×C11C2×C22⋊Q818yes—
313C22×C11C23×D411yescharacteristic
314C22×C11C23×Q811yescharacteristic
315C22×C11C22×#4111yescharacteristic
316C22×C11C2×H(5,𝔽2)12yes—
317C22×C11#58512yes—
318C4×C11—24no—
319C4×C11—24no—
320C4×C11—24no—
321C4×C11—24no—
322C4×C11—42no—
323Dic11—48no—
324Dic11—44no—
325Dic11—44no—
326C25C22×D1111yescharacteristic
327C25C22×D1111yescharacteristic
328C22×Q8—112no—
329C22×Q8—112no—
330C22×D4—24no—
331C22×D4—24no—
332C22×D4Dic2218yescomplemented
333C22×D4C22×D1114yes—
334C23×C4—24no—
335C23×C4—24no—
336C23×C4—44no—
337C23×C4—44no—
338C23×C4—112no—
339C23×C4—114no—
340C23×C4—112no—
341C23×C4C22×D1111yescharacteristic
342C23×C4C22×D1114yes—
343C23×C4C22×D1114yes—
344C23×C4C22×D1111yescharacteristic
345C23×C4C22×D1111yescharacteristic
346C23×C4C22×D1111yescharacteristic
347C23×C4C22×D1111yescharacteristic
348C22⋊Q8—228no—
349C22⋊Q8—228no—
350C22⋊Q8—2216no—
351C22⋊Q8—2216no—
352C22⋊Q8—448no—
353C4×D4—232no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—118no—
356C2×C4⋊C4—112no—
357C2×C4⋊C4—114no—
358C2×C4⋊C4—114no—
359C2×C4⋊C4—112no—
360C2×C4⋊C4—118no—
361C2×C4⋊C4—114no—
362C2×C4⋊C4—114no—
363C2×C4⋊C4—448no—
364C2×C4⋊C4C22×D1114yes—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—114no—
367C2×C22⋊C4—114no—
368C2×C22⋊C4—114no—
369C2×C22⋊C4—114no—
370C2×C22⋊C4—118no—
371C2×C22⋊C4—118no—
372C2×C22⋊C4—228no—
373C2×C22⋊C4—228no—
374C2×C22⋊C4C22⋊D1118yes—
375C2×C22⋊C4C22×D1114yes—
376C2×C22⋊C4C22×D1114yes—
377C2×C42—24no—
378C2×C42C22×D1114yes—
379#95—118no—
380#95—118no—
381#95—114no—
382#95—114no—
383#95—118no—
384#95—118no—
385C2×C11—24no—
386C2×C11—28no—
387C2×C11—44no—
388C2×C11C22×C22⋊Q811yescharacteristic
389C2×C11#345912yes—
390C2×C11#348411yescharacteristic
391C2×C11#348511yescharacteristic
392C2×C11#350112yes—
393C24—22no—
394C24—22no—
395C24—42no—
396C24—42no—
397C24—42no—
398C24—42no—
399C24C2×Dic2214yes—
400C24C2×Dic2214yes—
401C24#433914yes—
402C24C2×C22⋊D1114yes—
403C24C23×D1112yes—
404C24C23×D1111yescharacteristic
405C24C23×D1112yes—
406C2×Q8—224no—
407C2×Q8—224no—
408C2×Q8—444no—
409C2×Q8—444no—
410C2×D4—232no—
411C2×D4—28no—
412C2×D4—28no—
413C2×D4C2×Dic22116yes—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—28no—
420C22×C4—28no—
421C22×C4—28no—
422C22×C4—28no—
423C22×C4—42no—
424C22×C4—44no—
425C22×C4—44no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—416no—
429C22×C4—416no—
430C22×C4—118no—
431C22×C4—114no—
432C22×C4—114no—
433C22×C4—228no—
434C22×C4—224no—
435C22×C4—224no—
436C22×C4—444no—
437C22×C4—444no—
438C22×C4—444no—
439C22×C4—444no—
440C22×C4C2×Dic2214yes—
441C22×C4C2×C22⋊D1114yes—
442C22×C4C2×C22⋊D1114yes—
443C22×C4C23×D1112yes—
444C22×C4C23×D1112yes—
445C22×C4C23×D1112yes—
446C22×C4C23×D1112yes—
447C22×C4C23×D1112yes—
448C4⋊C4—28no—
449C4⋊C4—2216no—
450C4⋊C4—228no—
451C4⋊C4—228no—
452C4⋊C4—224no—
453C4⋊C4—224no—
454C4⋊C4—448no—
455C4⋊C4—444no—
456C4⋊C4—444no—
457C22⋊C4—28no—
458C22⋊C4—228no—
459C22⋊C4—228no—
460C22⋊C4—228no—
461C22⋊C4—228no—
462C22⋊C4—448no—
463C22⋊C4—448no—
464C22⋊C4C2×C22⋊D11116yes—
465C42—28no—
466C11#3498511yescharacteristic, complemented, Sylow
467C23—22no—
468C23—24no—
469C23—22no—
470C23—24no—
471C23—28no—
472C23—22no—
473C23—24no—
474C23—24no—
475C23—22no—
476C23—44no—
477C23—48no—
478C23—48no—
479C23—48no—
480C23—44no—
481C23—44no—
482C23—44no—
483C23—48no—
484C23#66977116yescomplemented
485C23C22×Dic2214yes—
486C23C22×Dic2212yes—
487C23C22×Dic2214yes—
488C23C2×#433912yes—
489C23C2×#433914yes—
490C23C22×C22⋊D1112yes—
491C23C22×C22⋊D1114yes—
492C23C24×D1111yescharacteristic
493Q8—884no—
494Q8—884no—
495D4—232no—
496C2×C4—28no—
497C2×C4—28no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—22no—
506C2×C4—44no—
507C2×C4—44no—
508C2×C4—416no—
509C2×C4—416no—
510C2×C4—44no—
511C2×C4—228no—
512C2×C4—228no—
513C2×C4—228no—
514C2×C4—228no—
515C2×C4—228no—
516C2×C4—224no—
517C2×C4—224no—
518C2×C4—4416no—
519C2×C4—884no—
520C2×C4—884no—
521C2×C4C22×Dic2214yes—
522C2×C4#6703714yes—
523C2×C4C22×C22⋊D1114yes—
524C2×C4C22×C22⋊D1114yes—
525C22—24no—
526C22—28no—
527C22—22no—
528C22—24no—
529C22—22no—
530C22—24no—
531C22—28no—
532C22—24no—
533C22—28no—
534C22—24no—
535C22—416no—
536C22—416no—
537C22—42no—
538C22—42no—
539C22—44no—
540C22C2×#6697714yes—
541C22C2×#6697718yes—
542C22C23×Dic2211yescharacteristic
543C22C22×#433911yescharacteristic
544C22C2×#6703712yes—
545C22#1062345312yes—
546C22C23×C22⋊D1111yescharacteristic
547C4—24no—
548C4—24no—
549C4—24no—
550C4—24no—
551C4—42no—
552C4—444no—
553C4—444no—
554C4—448no—
555C2—24no—
556C2—28no—
557C2—44no—
558C2C22×#6697711yescharacteristic
559C2#1308202512yes—
560C2#1308225111yescharacteristic
561C2#1308226011yescharacteristic
562C2#1308241912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC22×C4×D4×C11C2
prime radicalC23×D4×C11C22
hypercenterC22×C4×D4D11
hypocenterC11#34985
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10623014C2semidirect
2. #13076955C2semidirect
3. #13076903C2semidirect
4. #13074429C2semidirect
5. #13074421C2semidirect
6. #13072434C2semidirect
7. #13072419C2semidirect
8. #13071230C2semidirect
10. C2×#10622823C2semidirect
25. C2×#66977C22semidirect
26. C22×Dic11⋊C4C22semidirect
28. C2×#66931C22semidirect
29. C2×#66931C22semidirect
36. #10622825C22semidirect
40. #10622823C22semidirect
41. #10622823C22semidirect
42. C2×C11⋊#95C22semidirect
43. #10622599C22semidirect
44. #10622597C22semidirect
45. #10622592C22semidirect
46. #10622563C22semidirect
47. #10622562C22semidirect
48. #10622561C22semidirect
49. #10622560C22semidirect
50. #10622546C22semidirect
51. #10622542C22semidirect
52. #10622541C22semidirect
57. C22×D4×C11Q8semidirect
214. C23×C11C22⋊Q8semidirect
332. C22×D4Dic22semidirect
466. C11#34985semidirect
484. C23#66977semidirect

Maximal subgroups

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

subgroupindex
C2×#106230142
#130769552
#130769032
#130744292
#130744212
#130724342
#130724192
#130712302
#130711942
C2×#106228232
C22×C4×D4×C112
#3498511