Finite Group Databasebeta

← AΣL(1,𝔽16)×Dic61 #29595147

Subgroups — AΣL(1,𝔽16)×Dic61 #29595147

Order 15616.

844 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#120×Dic61C211yesmaximal, characteristic
2C2×#16839549C211yesmaximal, characteristic
3#100×Dic61C211yesmaximal, characteristic, complemented
4#99×Dic61C211yesmaximal, characteristic, complemented
5#21443938C211yesmaximal, characteristic, complemented
6#21443936C211yesmaximal, characteristic, complemented
7C2×C61×AΣL(1,𝔽16)C211yesmaximal, characteristic
8C24×Dic61C411yescharacteristic, complemented
9C2×D4×Dic61—21no—
10C2×D4×Dic61C2211yescharacteristic
11C2×#14519694C2211yescharacteristic
12C2×#14519692C2211yescharacteristic
13M16×Dic61—21no—
14#16839642—21no—
15#16839642C2211yescharacteristic
16#16839637—21no—
17#16839637C411yescharacteristic, complemented
18#16839618C411yescharacteristic, complemented
19C22⋊C4×Dic61—21no—
20C22⋊C4×Dic61—21no—
21C22⋊C4×Dic61C411yescharacteristic, complemented
22#16839549C414yescomplemented
23#16839530—21no—
24#16839528—21no—
25C2×#120×C61C2211yescharacteristic
26C2×#100×C61C2211yescharacteristic
27C2×#99×C61C2211yescharacteristic
28C61×AΣL(1,𝔽16)C414yescomplemented
29C23×Dic61—21no—
30C23×Dic61—21no—
31C23×Dic61—44no—
32C23×Dic61—41no—
33C23×Dic61—41no—
34C23×Dic61C2×C411yescharacteristic
35C23×Dic61C2×C411yescharacteristic
36C23×Dic61D411yescharacteristic
37C2×#11758194—21no—
38D4×Dic61—41no—
39D4×Dic61—41no—
40D4×Dic61—44no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61D411yescharacteristic
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61C2×C411yescharacteristic
48C2×C22⋊Dic61C2×C411yescharacteristic
49C2×C22⋊Dic61D411yescharacteristic
50C2×C4×Dic61—21no—
51C2×C4×Dic61—41no—
52C2×C4×Dic61D411yescharacteristic
53#14519694—21no—
54#14519694C2×C412yescomplemented
55#14519692—21no—
56#14519692C2×C412yescomplemented
57#14519687—41no—
58C8×Dic61—41no—
59#14519684—21no—
60#14519684—21no—
61#14519684—21no—
62#14519684—41no—
63C25×C61C2×C411yescharacteristic
64C22×D4×C61—21no—
65C22×D4×C61C2311yescharacteristic
66C2×M16×C61—21no—
67#120×C61—21no—
68#120×C61—21no—
69#120×C61C2×C412yes—
70#120×C61C2×C412yes—
71C2×C22⋊C4×C61—21no—
72C2×C22⋊C4×C61—21no—
73C2×C22⋊C4×C61C2×C411yescharacteristic
74#100×C61—21no—
75#100×C61C2×C412yescomplemented
76#99×C61—21no—
77#99×C61C2×C412yescomplemented
78C24×C61—21no—
79C24×C61—21no—
80C24×C61—42no—
81C24×C61—41no—
82C24×C61—42no—
83C24×C61—41no—
84C24×C61C4212yescomplemented
85C24×C61C22×C411yescharacteristic
86C24×C61C2×D411yescharacteristic
87C2×D4×C61—22no—
88C2×D4×C61—22no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—42no—
92C2×D4×C61—42no—
93C2×D4×C61C22×C411yescharacteristic
94C2×D4×C61C22×C411yescharacteristic
95C2×D4×C61#4111yescharacteristic
96C2×D4×C61#4111yescharacteristic
97C22×C4×C61—21no—
98C22×C4×C61—41no—
99C22×C4×C61C2×D411yescharacteristic
100C22×Dic61—24no—
101C22×Dic61—21no—
102C22×Dic61—21no—
103C22×Dic61—21no—
104C22×Dic61—21no—
105C22×Dic61—21no—
106C22×Dic61—21no—
107C22×Dic61—42no—
108C22×Dic61—42no—
109C22×Dic61—42no—
110C22×Dic61—42no—
111C22×Dic61—42no—
112C22×Dic61—42no—
113C22×Dic61—42no—
114C22×Dic61—44no—
115C22×Dic61—44no—
116C22×Dic61—44no—
117C22×Dic61—41no—
118C22×Dic61—41no—
119C22×Dic61—41no—
120C22×Dic61—44no—
121C22×Dic61—41no—
122C22×Dic61C22⋊C411yescharacteristic
123C22×Dic61C22⋊C411yescharacteristic
124C22×Dic61C22⋊C411yescharacteristic
125C22×Dic61C22⋊C411yescharacteristic
126M16×C61—22no—
127M16×C61—41no—
128C2×C8×C61—41no—
129C22⋊C4×C61—21no—
130C22⋊C4×C61—22no—
131C22⋊C4×C61—22no—
132C22⋊C4×C61—22no—
133C22⋊C4×C61—41no—
134C22⋊C4×C61C4212yescomplemented
135C22⋊Dic61—22no—
136C22⋊Dic61—41no—
137C22⋊Dic61—41no—
138C22⋊Dic61—42no—
139C22⋊Dic61—42no—
140C22⋊Dic61—41no—
141C22⋊Dic61—42no—
142C22⋊Dic61—41no—
143C4⋊Dic61—41no—
144C4⋊Dic61—42no—
145C4×Dic61—21no—
146C4×Dic61—21no—
147C4×Dic61—42no—
148C4×Dic61—82no—
149#11758194—22no—
150#11758194—41no—
151C2×#92418—41no—
152C23×C61—22no—
153C23×C61—22no—
154C23×C61—22no—
155C23×C61—21no—
156C23×C61—21no—
157C23×C61—21no—
158C23×C61—21no—
159C23×C61—41no—
160C23×C61—41no—
161C23×C61—44no—
162C23×C61—42no—
163C23×C61—41no—
164C23×C61—44no—
165C23×C61—42no—
166C23×C61—41no—
167C23×C61—41no—
168C23×C61—41no—
169C23×C61—42no—
170C23×C61—48no—
171C23×C61—42no—
172C23×C61—41no—
173C23×C61—41no—
174C23×C61—42no—
175C23×C61—42no—
176C23×C61C2×C4211yescharacteristic
177C23×C61C2×C22⋊C411yescharacteristic
178C23×C61#11711yescharacteristic
179C23×C61C4×D411yescharacteristic
180C23×C61C4×D411yescharacteristic
181D4×C61—41no—
182D4×C61—41no—
183D4×C61—41no—
184D4×C61—41no—
185D4×C61—44no—
186D4×C61—44no—
187C2×C4×C61—21no—
188C2×C4×C61—21no—
189C2×C4×C61—22no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61—42no—
193C2×C4×C61—81no—
194C2×C4×C61—81no—
195C2×C4×C61C4×D411yescharacteristic
196C2×C4×C61C4×D411yescharacteristic
197C2×Dic61—22no—
198C2×Dic61—22no—
199C2×Dic61—21no—
200C2×Dic61—21no—
201C2×Dic61—21no—
202C2×Dic61—44no—
203C2×Dic61—42no—
204C2×Dic61—41no—
205C2×Dic61—48no—
206C2×Dic61—42no—
207C2×Dic61—41no—
208C2×Dic61—42no—
209C2×Dic61—44no—
210C2×Dic61—42no—
211C2×Dic61—41no—
212C2×Dic61—41no—
213C2×Dic61—41no—
214C2×Dic61—42no—
215C2×Dic61—41no—
216C2×Dic61—42no—
217C2×Dic61—41no—
218C2×Dic61—41no—
219C2×Dic61—81no—
220C2×Dic61—81no—
221C2×Dic61—81no—
222C2×Dic61#9911yescharacteristic
223C2×Dic61#9911yescharacteristic
224C8×C61—42no—
225#92418—42no—
226C4×AΣL(1,𝔽16)—611nomaximal, Sylow
227C22×C61—21no—
228C22×C61—21no—
229C22×C61—24no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—41no—
235C22×C61—41no—
236C22×C61—41no—
237C22×C61—41no—
238C22×C61—42no—
239C22×C61—42no—
240C22×C61—42no—
241C22×C61—42no—
242C22×C61—44no—
243C22×C61—44no—
244C22×C61—44no—
245C22×C61—44no—
246C22×C61—42no—
247C22×C61—41no—
248C22×C61—41no—
249C22×C61—41no—
250C22×C61—42no—
251C22×C61—41no—
252C22×C61—42no—
253C22×C61—81no—
254C22×C61C4×C22⋊C411yescharacteristic
255C22×C61C2×#9911yescharacteristic
256C22×C61#41011yescharacteristic
257C4×C61—21no—
258C4×C61—21no—
259C4×C61—42no—
260C4×C61—82no—
261Dic61—21no—
262Dic61—42no—
263Dic61—41no—
264Dic61—41no—
265Dic61—41no—
266Dic61—81no—
267Dic61—82no—
268Dic61AΣL(1,𝔽16)12yesdirect product factor
269C4×#120—611no—
270C2×AΣL(1,𝔽16)—611no—
271C2×AΣL(1,𝔽16)D6111yescharacteristic
272C4×#100—611no—
273C4×#99—611no—
274#1390—611no—
275#1390—611no—
276C2×C61—21no—
277C2×C61—21no—
278C2×C61—41no—
279C2×C61—41no—
280C2×C61—44no—
281C2×C61—41no—
282C2×C61—41no—
283C2×C61C4×#9911yescharacteristic
284C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
285C2×C61#212011yescharacteristic
286C24×C4—611no—
287C2×#120C2×D6111yescharacteristic
288C2×C4×D4—611no—
289C2×C4×D4—1221no—
290C2×#100—611no—
291C2×#100C2×D6111yescharacteristic
292C2×#99—611no—
293C2×#99C2×D6111yescharacteristic
294C4×M16—1221no—
295#386—611no—
296#386—1221no—
297#385—611no—
298#385—1221no—
299#379—611no—
300C4×C22⋊C4—611no—
301C4×C22⋊C4—1221no—
302C4×C22⋊C4—1221no—
303AΣL(1,𝔽16)—614no—
304AΣL(1,𝔽16)Dic6114yesdirect product factor
305#343—1221no—
306#342—1221no—
307C61C4×AΣL(1,𝔽16)11yescharacteristic, complemented, Sylow
308C25C4×D6111yescharacteristic
309C22×D4—21no—
310C22×D4C22×D6111yescharacteristic
311C23×C4—611no—
312C23×C4—611no—
313C23×C4—611no—
314C23×C4—1221no—
315C23×C4—1221no—
316C23×C4—2441no—
317C23×C4—2441no—
318C23×C4—2444no—
319C2×M16—21no—
320C2×M16—1221no—
321#120—21no—
322#120—21no—
323#120C4×D6112yes—
324#120C2×Dic6112yes—
325C4×D4—2441no—
326C4×D4—2441no—
327C4×D4—2444no—
328C2×C4⋊C4—611no—
329C2×C4⋊C4—1221no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—611no—
333C2×C22⋊C4—611no—
334C2×C22⋊C4—611no—
335C2×C22⋊C4—1221no—
336C2×C22⋊C4—1221no—
337C2×C22⋊C4—1221no—
338C2×C22⋊C4—1221no—
339C2×C22⋊C4C4×D6111yescharacteristic
340C2×C42—611no—
341C2×C42—1221no—
342C2×C42—2441no—
343#100—21no—
344#100—612no—
345#100—1221no—
346#100C2×Dic6112yescomplemented
347#99—21no—
348#99—612no—
349#99—1221no—
350#99C2×Dic6112yescomplemented
351#97—2441no—
352C4×C8—2441no—
353#95—1221no—
354#95—1221no—
355#95—1221no—
356#95—2441no—
357C24—21no—
358C24—21no—
359C24—42no—
360C24—41no—
361C24—42no—
362C24—41no—
363C24C4×Dic6112yescomplemented
364C24C2×C4×D6111yescharacteristic
365C24D4×D6111yescharacteristic
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—42no—
371C2×D4—42no—
372C2×D4C2×C4×D6111yescharacteristic
373C2×D4#1175822411yescharacteristic
374C2×D4#1175822411yescharacteristic
375C2×D4C22×Dic6111yescharacteristic
376C22×C4—21no—
377C22×C4—41no—
378C22×C4—611no—
379C22×C4—611no—
380C22×C4—611no—
381C22×C4—611no—
382C22×C4—1221no—
383C22×C4—1221no—
384C22×C4—1221no—
385C22×C4—1221no—
386C22×C4—1224no—
387C22×C4—1221no—
388C22×C4—1221no—
389C22×C4—2441no—
390C22×C4—2441no—
391C22×C4—2442no—
392C22×C4—2442no—
393C22×C4—2442no—
394C22×C4—2442no—
395C22×C4—2442no—
396C22×C4—2442no—
397C22×C4—2441no—
398C22×C4—2442no—
399C22×C4—2444no—
400C22×C4—2444no—
401C22×C4—2444no—
402C22×C4—2441no—
403C22×C4—2444no—
404C22×C4D4×D6111yescharacteristic
405M16—22no—
406M16—41no—
407M16—1222no—
408M16—2441no—
409C2×C8—41no—
410C2×C8—2441no—
411C4⋊C4—2441no—
412C4⋊C4—2442no—
413C22⋊C4—21no—
414C22⋊C4—22no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—41no—
418C22⋊C4—1222no—
419C22⋊C4—2441no—
420C22⋊C4—2441no—
421C22⋊C4—2442no—
422C22⋊C4—2442no—
423C22⋊C4—2441no—
424C22⋊C4—2442no—
425C22⋊C4—2441no—
426C22⋊C4C4×Dic6112yescomplemented
427C42—1221no—
428C42—1221no—
429C42—4882no—
430C42—2442no—
431C23—22no—
432C23—22no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—22no—
437C23—21no—
438C23—41no—
439C23—44no—
440C23—42no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23—44no—
445C23—42no—
446C23—41no—
447C23—41no—
448C23—42no—
449C23—42no—
450C23—42no—
451C23—48no—
452C23—42no—
453C23—41no—
454C23—41no—
455C23C2×C4×Dic6111yescharacteristic
456C23C22⋊C4×D6111yescharacteristic
457C23#1451973311yescharacteristic
458C23#1451973711yescharacteristic
459C23D4×Dic6111yescharacteristic
460D4—41no—
461D4—41no—
462D4—41no—
463D4—41no—
464D4—44no—
465D4—44no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—81no—
473C2×C4—81no—
474C2×C4—611no—
475C2×C4—611no—
476C2×C4—1222no—
477C2×C4—1222no—
478C2×C4—1221no—
479C2×C4—1221no—
480C2×C4—1221no—
481C2×C4—4881no—
482C2×C4—4881no—
483C2×C4—4881no—
484C2×C4—2442no—
485C2×C4—2442no—
486C2×C4—2444no—
487C2×C4—2442no—
488C2×C4—2444no—
489C2×C4—2441no—
490C2×C4—2442no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4—2441no—
494C2×C4—2448no—
495C2×C4—2442no—
496C2×C4—2441no—
497C2×C4—2441no—
498C2×C4—2441no—
499C2×C4—2441no—
500C2×C4—2442no—
501C2×C4#1451973711yescharacteristic
502C2×C4D4×Dic6111yescharacteristic
503C8—42no—
504C8—2442no—
505C22—21no—
506C22—21no—
507C22—24no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—41no—
513C22—41no—
514C22—41no—
515C22—41no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—44no—
521C22—44no—
522C22—44no—
523C22—44no—
524C22—41no—
525C22—42no—
526C22—41no—
527C22—41no—
528C22—42no—
529C22—41no—
530C22—42no—
531C22—81no—
532C22C22⋊C4×Dic6111yescharacteristic
533C22#99×D6111yescharacteristic
534C22#1683973411yescharacteristic
535C4—21no—
536C4—21no—
537C4—42no—
538C4—82no—
539C4—612no—
540C4—1221no—
541C4—4881no—
542C4—4882no—
543C4—2441no—
544C4—2442no—
545C4—2441no—
546C4—2441no—
547C2—21no—
548C2—21no—
549C2—41no—
550C2—41no—
551C2—44no—
552C2—41no—
553C2—41no—
554C2#99×Dic6111yescharacteristic
555C2AΣL(1,𝔽16)×D6111yescharacteristic
556C2#2144745711yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC23×C61C2×C42
FrattiniC22×D4C22×D61
FittingC2×C61×AΣL(1,𝔽16)C2
socleC22×C61C2×#99
prime radicalC2×#120×C61C22
cosocleC22×D4×C61C23
hypercenterC2×AΣL(1,𝔽16)D61
hypocenterC61C4×AΣL(1,𝔽16)
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×AΣL(1,𝔽16)

Complements

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

NH ≅ G/Ntype
3. #100×Dic61C2semidirect
4. #99×Dic61C2semidirect
5. #21443938C2semidirect
6. #21443936C2semidirect
8. C24×Dic61C4semidirect
17. #16839637C4semidirect
18. #16839618C4semidirect
21. C22⋊C4×Dic61C4semidirect
22. #16839549C4semidirect
28. C61×AΣL(1,𝔽16)C4semidirect
54. #14519694C2×C4semidirect
56. #14519692C2×C4semidirect
75. #100×C61C2×C4semidirect
77. #99×C61C2×C4semidirect
84. C24×C61C42semidirect
134. C22⋊C4×C61C42semidirect
268. Dic61AΣL(1,𝔽16)direct (N × H)
304. AΣL(1,𝔽16)Dic61direct (N × H)
307. C61C4×AΣL(1,𝔽16)semidirect
346. #100C2×Dic61semidirect
350. #99C2×Dic61semidirect
363. C24C4×Dic61semidirect
426. C22⋊C4C4×Dic61semidirect

Maximal subgroups

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

subgroupindex
#120×Dic612
C2×#168395492
#100×Dic612
#99×Dic612
#214439382
#214439362
C2×C61×AΣL(1,𝔽16)2
C4×AΣL(1,𝔽16)61