Finite Group Databasebeta

← #30602428

Subgroups — #30602428

Order 15616.

1374 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519856C211yesmaximal, characteristic
2C2×#16840733C211yesmaximal, characteristic
3C2×#16840645C214yesmaximal, complemented
4#407×D61C211yesmaximal, characteristic
5C22×#11758213C2212yes—
6C2×#14519856—28no—
7C2×#14519856—21no—
8C2×#14519856—21no—
9C2×#14519856C412yes—
10C2×#14519856C2212yes—
11C22×C4⋊#6923—21no—
12C22×C22⋊#6923C412yes—
13C22×C4×#6923—21no—
14#16840733—21no—
15#16840733—21no—
16#16840733—21no—
17#16840733—21no—
18C2×#14519834C412yescomplemented
19C2×C22⋊#92420C412yescomplemented
20#16840645—28no—
21C23×C4×D61C2211yescharacteristic
22C2×M16×D61C2212yes—
23#16839726C411yescharacteristic, complemented
24#16839725C412yescomplemented
25#16839724—21no—
26#16839724—21no—
27C22⋊C8×D61—21no—
28C22⋊C8×D61—21no—
29C61×#407C411yescharacteristic, complemented
30C23×#6923—22no—
31C2×#11758213—22no—
32C2×#11758213—22no—
33C2×#11758213—24no—
34C2×#11758213—24no—
35C22×#92420C2×C414yescomplemented
36#14519856—28no—
37#14519856—28no—
38#14519856—24no—
39#14519856—28no—
40#14519856D418yes—
41C2×C4⋊#6923—28no—
42C2×C4⋊#6923—22no—
43C2×C4⋊#6923—22no—
44C2×C22⋊#6923—22no—
45C2×C22⋊#6923—28no—
46C2×C22⋊#6923C2×C414yes—
47C2×C4×#6923—28no—
48C2×C4×#6923—22no—
49C2×C4×#6923—22no—
50#14519834—22no—
51#14519834—22no—
52C22⋊#92420—22no—
53C22⋊#92420—22no—
54C24×D61C2×C411yescharacteristic
55C23×Dic61C2×C411yescharacteristic
56C22×C4×D61—24no—
57C22×C4×D61—24no—
58C22×C4×D61C2×C411yescharacteristic
59C22×C4×D61C2×C411yescharacteristic
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C22×C4×D61D411yescharacteristic
67C22×C4×D61Q811yescharacteristic
68C22×C4×D61Q811yescharacteristic
69C22×C4×D61C2311yescharacteristic
70C2×#11758194C2×C412yescomplemented
71C2×#11758189—22no—
72M16×D61—24no—
73M16×D61—24no—
74C2×C8×D61—22no—
75C22⋊#92418—21no—
76C22⋊#92418—21no—
77#14519689—22no—
78#14519689—22no—
79C23×C4×C61C2×C411yescharacteristic
80C2×M16×C61C2×C412yescomplemented
81C22⋊C8×C61—21no—
82C22⋊C8×C61—21no—
83C24×C61C4211yescharacteristic
84C23×D61—22no—
85C23×D61—22no—
86C23×D61—42no—
87C23×D61—42no—
88C23×D61C4211yescharacteristic
89C23×D61C22⋊C411yescharacteristic
90C23×D61C22⋊C411yescharacteristic
91C23×D61C4⋊C411yescharacteristic
92C23×D61C4⋊C411yescharacteristic
93C23×D61C22×C411yescharacteristic
94C22×#6923—28no—
95C22×#6923—24no—
96C22×#6923—44no—
97C22×#6923—44no—
98C22×C4×C61—24no—
99C22×C4×C61C4211yescharacteristic
100C22×C4×C61C22⋊C411yescharacteristic
101C22×C4×C61C22⋊C411yescharacteristic
102C22×C4×C61C4⋊C411yescharacteristic
103C22×C4×C61C4⋊C411yescharacteristic
104C22×C4×C61C22×C411yescharacteristic
105C22×Dic61—24no—
106C22×Dic61C4211yescharacteristic
107C22×Dic61C22⋊C411yescharacteristic
108C22×Dic61C22⋊C411yescharacteristic
109C22×Dic61C4⋊C411yescharacteristic
110C22×Dic61C4⋊C411yescharacteristic
111C22×Dic61C22×C411yescharacteristic
112C2×C4×D61—22no—
113C2×C4×D61—22no—
114C2×C4×D61—24no—
115C2×C4×D61—24no—
116C2×C4×D61—22no—
117C2×C4×D61—22no—
118C2×C4×D61—22no—
119C2×C4×D61—22no—
120C2×C4×D61—24no—
121C2×C4×D61—24no—
122C2×C4×D61—24no—
123C2×C4×D61—24no—
124C2×C4×D61—22no—
125C2×C4×D61—22no—
126C2×C4×D61—22no—
127C2×C4×D61—22no—
128C2×C4×D61C22⋊C411yescharacteristic
129C2×C4×D61C22⋊C411yescharacteristic
130C2×C4×D61C22⋊C411yescharacteristic
131C2×C4×D61C22⋊C411yescharacteristic
132C2×C4×D61C22⋊C411yescharacteristic
133C2×C4×D61C22⋊C411yescharacteristic
134C2×C4×D61C4⋊C411yescharacteristic
135C2×C4×D61C4⋊C411yescharacteristic
136C2×C4×D61C4⋊C411yescharacteristic
137C2×C4×D61C4⋊C411yescharacteristic
138C2×C4×D61C4⋊C411yescharacteristic
139C2×C4×D61C4⋊C411yescharacteristic
140C2×C4×D61C2×D414yes—
141C2×C4×D61C2×D411yescharacteristic
142C2×C4×D61C2×D411yescharacteristic
143C2×C4×D61C2×D411yescharacteristic
144C2×C4×D61C2×Q811yescharacteristic
145C2×C4×D61#4114yes—
146C22⋊#6923—28no—
147C22⋊#6923—24no—
148C22⋊#6923C22⋊C418yes—
149C2×#92420—24no—
150C2×#92420—28no—
151C4⋊#6923—28no—
152C4⋊#6923—28no—
153C4×#6923—28no—
154C4×#6923—28no—
155#11758213—42no—
156#11758213—44no—
157#11758213—42no—
158M16×C61—24no—
159C2×C8×C61—22no—
160#11758194—24no—
161C2×#92418—22no—
162#11758189—42no—
163#11758189—42no—
164C8×D61—44no—
165C23×C61—22no—
166C23×C61—22no—
167C23×C61—41no—
168C23×C61#9511yescharacteristic
169C23×C61#9511yescharacteristic
170C23×C61C2×C4211yescharacteristic
171C22×D61—22no—
172C22×D61—22no—
173C22×D61—21no—
174C22×D61—21no—
175C22×D61—22no—
176C22×D61—22no—
177C22×D61—22no—
178C22×D61—22no—
179C22×D61—21no—
180C22×D61—22no—
181C22×D61—22no—
182C22×D61—21no—
183C22×D61—41no—
184C22×D61—41no—
185C22×D61—41no—
186C22×D61—41no—
187C22×D61—41no—
188C22×D61—41no—
189C22×D61—41no—
190C22×D61—48no—
191C22×D61—48no—
192C22×D61#9511yescharacteristic
193C22×D61#9511yescharacteristic
194C22×D61C2×C22⋊C411yescharacteristic
195C22×D61C2×C22⋊C412yes—
196C22×D61C2×C4⋊C411yescharacteristic
197C22×D61#11712yes—
198C2×#6923—28no—
199C2×#6923—416no—
200C2×#6923—44no—
201C2×#6923—44no—
202C2×C4×C61—22no—
203C2×C4×C61—22no—
204C2×C4×C61—22no—
205C2×C4×C61—22no—
206C2×C4×C61—22no—
207C2×C4×C61#9511yescharacteristic
208C2×C4×C61#9511yescharacteristic
209C2×C4×C61C2×C22⋊C411yescharacteristic
210C2×C4×C61C2×C4⋊C411yescharacteristic
211C2×C4×C61C4×D414yes—
212C2×Dic61—22no—
213C2×Dic61—22no—
214C2×Dic61—22no—
215C2×Dic61—22no—
216C2×Dic61—22no—
217C2×Dic61#9511yescharacteristic
218C2×Dic61#9511yescharacteristic
219C2×Dic61C2×C22⋊C411yescharacteristic
220C2×Dic61C2×C4⋊C411yescharacteristic
221C2×Dic61C4×D414yes—
222C4×D61—21no—
223C4×D61—21no—
224C4×D61—22no—
225C4×D61—22no—
226C4×D61—21no—
227C4×D61—21no—
228C4×D61—22no—
229C4×D61—22no—
230C4×D61—22no—
231C4×D61—22no—
232C4×D61—22no—
233C4×D61—22no—
234C4×D61—22no—
235C4×D61—22no—
236C4×D61#12012yes—
237C4×D61#12012yes—
238C4×D61#12114yes—
239C4×D61C22⋊Q814yes—
240C4×D61#12312yes—
241C4×D61#12312yes—
242#92420—44no—
243C8×C61—42no—
244#92418—42no—
245#10738—611nomaximal, Sylow
246C22×C61—21no—
247C22×C61—21no—
248C22×C61—21no—
249C22×C61—21no—
250C22×C61—21no—
251C22×C61—21no—
252C22×C61—21no—
253C22×C61—44no—
254C22×C61#34412yescomplemented
255C22×C61C2×#9511yescharacteristic
256C22×C61C4×C22⋊C412yes—
257C2×D61—24no—
258C2×D61—24no—
259C2×D61—21no—
260C2×D61—21no—
261C2×D61—21no—
262C2×D61—21no—
263C2×D61—21no—
264C2×D61—21no—
265C2×D61—21no—
266C2×D61—21no—
267C2×D61—21no—
268C2×D61—42no—
269C2×D61—42no—
270C2×D61—44no—
271C2×D61—44no—
272C2×D61—44no—
273C2×D61—42no—
274C2×D61—42no—
275C2×D61#34412yescomplemented
276C2×D61#37911yescharacteristic
277C2×D61#38012yes—
278C2×D61#38111yescharacteristic
279#6923—48no—
280C4×C61—21no—
281C4×C61—21no—
282C4×C61#38512yes—
283C4×C61#38612yes—
284Dic61—21no—
285Dic61—21no—
286Dic61#38512yes—
287Dic61#38612yes—
288C22×#117—611no—
289C2×#407—611no—
290C2×#407—611no—
291C2×#344—614no—
292C2×C61—22no—
293C2×C61—22no—
294C2×C61—41no—
295C2×C61C22⋊#9511yescharacteristic
296C2×C61C2×#34411yescharacteristic
297C2×C61C2×#34411yescharacteristic
298D61—21no—
299D61—22no—
300D61—21no—
301D61—22no—
302D61—41no—
303C24×C4—611no—
304C22×M16—612no—
305C22×M16—612no—
306C2×#117—612no—
307C2×#117—612no—
308C2×#117—1228no—
309C2×#117—1221no—
310C2×#117—1221no—
311C22×C4⋊C4—1221no—
312C22×C22⋊C4—612no—
313C22×C42—1221no—
314#407—611no—
315#407—612no—
316#407—1221no—
317#407—1221no—
318#407—1221no—
319#407—1221no—
320#407—1221no—
321#407—1221no—
322#407#692311yescharacteristic, complemented
323C2×C22⋊C8—612no—
324C2×C22⋊C8—612no—
325C2×C22⋊C8—1221no—
326C2×C22⋊C8—1221no—
327#344—1228no—
328C61#1073811yescharacteristic, complemented, Sylow
329C25—611no—
330C23×C4—611no—
331C23×C4—611no—
332C23×C4—611no—
333C23×C4—611no—
334C23×C4—611no—
335C23×C4—611no—
336C23×C4—611no—
337C23×C4—611no—
338C23×C4—611no—
339C23×C4—611no—
340C23×C4—611no—
341C23×C4—611no—
342C23×C4—611no—
343C23×C4—1224no—
344C23×C4—1224no—
345C23×C4—1222no—
346C23×C4C2×#692311yescharacteristic
347C2×M16—612no—
348C2×M16—1222no—
349C2×M16—1224no—
350C2×M16—1224no—
351C2×M16—1222no—
352C2×M16—1222no—
353C2×M16—1224no—
354C2×M16—1224no—
355C2×M16C2×#692312yescomplemented
356C22×C8—614no—
357C22×C8—1222no—
358#117—618no—
359#117—1228no—
360#117—1224no—
361#117—1228no—
362#117—1228no—
363C2×C4⋊C4—1222no—
364C2×C4⋊C4—1222no—
365C2×C4⋊C4—1228no—
366C2×C22⋊C4—614no—
367C2×C22⋊C4—1228no—
368C2×C22⋊C4—1222no—
369C2×C42—1222no—
370C2×C42—1222no—
371C2×C42—1228no—
372C22⋊C8—21no—
373C22⋊C8—21no—
374C22⋊C8—1222no—
375C22⋊C8—1222no—
376C22⋊C8—1222no—
377C22⋊C8—1222no—
378C22⋊C8—1222no—
379C22⋊C8—1222no—
380C22⋊C8—1221no—
381C22⋊C8—1221no—
382C24—611no—
383C24—611no—
384C24—611no—
385C24—611no—
386C24—611no—
387C24—611no—
388C24—1222no—
389C24—1222no—
390C24—2442no—
391C24—2442no—
392C24C4×#692311yescharacteristic
393C22×C4—24no—
394C22×C4—611no—
395C22×C4—611no—
396C22×C4—611no—
397C22×C4—611no—
398C22×C4—611no—
399C22×C4—614no—
400C22×C4—614no—
401C22×C4—611no—
402C22×C4—611no—
403C22×C4—611no—
404C22×C4—611no—
405C22×C4—611no—
406C22×C4—611no—
407C22×C4—611no—
408C22×C4—611no—
409C22×C4—611no—
410C22×C4—611no—
411C22×C4—611no—
412C22×C4—611no—
413C22×C4—611no—
414C22×C4—611no—
415C22×C4—611no—
416C22×C4—611no—
417C22×C4—611no—
418C22×C4—1222no—
419C22×C4—1222no—
420C22×C4—1222no—
421C22×C4—1222no—
422C22×C4—1224no—
423C22×C4—1224no—
424C22×C4—1224no—
425C22×C4—1222no—
426C22×C4—1222no—
427C22×C4—1224no—
428C22×C4—1224no—
429C22×C4—1222no—
430C22×C4—1222no—
431C22×C4—1222no—
432C22×C4—1222no—
433C22×C4—1224no—
434C22×C4—1224no—
435C22×C4—1224no—
436C22×C4—1228no—
437C22×C4—2444no—
438C22×C4—2444no—
439C22×C4C4×#692311yescharacteristic
440C22×C4C4⋊#692311yescharacteristic
441C22×C4C4⋊#692311yescharacteristic
442C22×C4C22⋊#692311yescharacteristic
443C22×C4C22⋊#692311yescharacteristic
444C22×C4C22×#692311yescharacteristic
445M16—24no—
446M16—1224no—
447M16—2442no—
448M16—2442no—
449M16—2442no—
450M16—2442no—
451M16—2444no—
452C2×C8—22no—
453C2×C8—1224no—
454C2×C8—1228no—
455C2×C8—1222no—
456C2×C8—2444no—
457C4⋊C4—1228no—
458C4⋊C4—1228no—
459C22⋊C4—618no—
460C22⋊C4—1224no—
461C22⋊C4—1228no—
462C42—1228no—
463C42—1228no—
464C23—22no—
465C23—22no—
466C23—41no—
467C23—611no—
468C23—611no—
469C23—611no—
470C23—612no—
471C23—612no—
472C23—611no—
473C23—1221no—
474C23—1221no—
475C23—1222no—
476C23—1221no—
477C23—1222no—
478C23—1222no—
479C23—1221no—
480C23—1222no—
481C23—1222no—
482C23—1222no—
483C23—1222no—
484C23—1222no—
485C23—2441no—
486C23—2441no—
487C23—2441no—
488C23—2441no—
489C23—2441no—
490C23—2441no—
491C23—2441no—
492C23—2448no—
493C23—2448no—
494C23(C2×#6923)⋊C411yescharacteristic
495C23(C2×#6923)⋊C411yescharacteristic
496C23C2×C4×#692311yescharacteristic
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—611no—
503C2×C4—611no—
504C2×C4—614no—
505C2×C4—612no—
506C2×C4—614no—
507C2×C4—612no—
508C2×C4—612no—
509C2×C4—614no—
510C2×C4—612no—
511C2×C4—611no—
512C2×C4—611no—
513C2×C4—1222no—
514C2×C4—1222no—
515C2×C4—1222no—
516C2×C4—1222no—
517C2×C4—1221no—
518C2×C4—1221no—
519C2×C4—1222no—
520C2×C4—1222no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—1222no—
524C2×C4—1222no—
525C2×C4—1222no—
526C2×C4—1222no—
527C2×C4—1222no—
528C2×C4—1222no—
529C2×C4—1222no—
530C2×C4—1222no—
531C2×C4—1222no—
532C2×C4—1228no—
533C2×C4—24416no—
534C2×C4—2444no—
535C2×C4—2444no—
536C2×C4(C2×#6923)⋊C411yescharacteristic
537C2×C4(C2×#6923)⋊C411yescharacteristic
538C2×C4C2×C22⋊#692311yescharacteristic
539C2×C4C2×C4⋊#692311yescharacteristic
540C2×C4D4×#692314yes—
541C8—42no—
542C8—2444no—
543C8—2442no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—21no—
551C22—44no—
552C22—611no—
553C22—612no—
554C22—611no—
555C22—612no—
556C22—1224no—
557C22—1224no—
558C22—1221no—
559C22—1221no—
560C22—1221no—
561C22—1221no—
562C22—1221no—
563C22—1221no—
564C22—1221no—
565C22—1221no—
566C22—1221no—
567C22—2442no—
568C22—2442no—
569C22—2444no—
570C22—2444no—
571C22—2444no—
572C22—2442no—
573C22—2442no—
574C22#1684064512yescomplemented
575C22C2×(C2×#6923)⋊C411yescharacteristic
576C22C22⋊C4×#692312yes—
577C4—21no—
578C4—21no—
579C4—612no—
580C4—612no—
581C4—1221no—
582C4—1221no—
583C4—2448no—
584C4#1684070912yes—
585C4#1684071012yes—
586C2—22no—
587C2—22no—
588C2—41no—
589C2—1221no—
590C2—1221no—
591C2—1222no—
592C2—1222no—
593C2—2441no—
594C2#2146099211yescharacteristic
595C2C2×#1684064511yescharacteristic
596C2#2146153111yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC23×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#407C4
socleC22×C61C2×#95
prime radicalC24×D61C2×C4
cosocleC22×C4×D61C23
hypercenter#407#6923
hypocenterC61#10738
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. C2×#16840645C2semidirect
18. C2×#14519834C4semidirect
19. C2×C22⋊#92420C4semidirect
23. #16839726C4semidirect
24. #16839725C4semidirect
29. C61×#407C4semidirect
35. C22×#92420C2×C4semidirect
70. C2×#11758194C2×C4semidirect
80. C2×M16×C61C2×C4semidirect
254. C22×C61#344semidirect
275. C2×D61#344semidirect
322. #407#6923semidirect
328. C61#10738semidirect
355. C2×M16C2×#6923semidirect
574. C22#16840645semidirect

Maximal subgroups

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

subgroupindex
C22×#145198562
C2×#168407332
C2×#168406452
#407×D612
#1073861