Finite Group Databasebeta

← #30602411

Subgroups — #30602411

Order 15616.

1550 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840733C211yesmaximal, characteristic
2C2×C4×C22⋊#6923C211yesmaximal, characteristic
3C2×#16840632C214yesmaximal, complemented
4C22×#14519735C211yesmaximal, characteristic
5C22×#11758213C2212yes—
6C22×C22⋊#6923—21no—
7C22×C4×#6923C2212yes—
8#16840733—22no—
9#16840733C414yescomplemented
10C2×#14519834—21no—
11C2×C22⋊#92420—21no—
12C4×C22⋊#6923—22no—
13C4×C22⋊#6923C414yescomplemented
14C2×(C2×#6923)⋊C4—21no—
15#16840632—28no—
16C23×C4×D61C2211yescharacteristic
17C2×#14519735—28no—
18C2×#14519735—21no—
19C2×#14519735—21no—
20C2×#14519735C412yescomplemented
21C2×#14519735C2212yes—
22C22×C4⋊Dic61C411yescharacteristic, complemented
23C22×#11758198—21no—
24C22×C4×Dic61—21no—
25C22×C4⋊C4×C61C411yescharacteristic, complemented
26C23×#6923—22no—
27C2×#11758213—24no—
28C2×#11758213—24no—
29C2×#11758213—22no—
30C2×#11758213C2×C414yescomplemented
31C22×#92420—22no—
32C2×C22⋊#6923—24no—
33C2×C22⋊#6923—24no—
34C2×C22⋊#6923—24no—
35C2×C4×#6923—24no—
36C2×C4×#6923—24no—
37C2×C4×#6923—22no—
38C2×C4×#6923C2×C414yescomplemented
39#14519834—24no—
40C22⋊#92420—24no—
41(C2×#6923)⋊C4—24no—
42C24×D61D411yescharacteristic
43C23×Dic61—21no—
44C23×Dic61D411yescharacteristic
45C22×C4×D61—24no—
46C22×C4×D61—24no—
47C22×C4×D61C2×C411yescharacteristic
48C22×C4×D61C2×C412yes—
49C22×C4×D61C2×C412yes—
50C22×C4×D61D411yescharacteristic
51C22×C4×D61D411yescharacteristic
52C22×C4×D61D412yes—
53C22×C4×D61Q812yes—
54C22×C4×D61C2311yescharacteristic
55#14519735—28no—
56#14519735—28no—
57#14519735—24no—
58#14519735—24no—
59#14519735—24no—
60#14519735D418yes—
61C2×C4⋊Dic61—21no—
62C2×C4⋊Dic61—24no—
63C2×C4⋊Dic61C2×C412yes—
64C2×#11758198—28no—
65C2×#11758198—22no—
66C2×#11758198—22no—
67C2×C4×Dic61—28no—
68C2×C4×Dic61—22no—
69C2×C4×Dic61—22no—
70C23×C4×C61—21no—
71C23×C4×C61C2×C411yescharacteristic
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61—24no—
74C2×C4⋊C4×C61C2×C412yes—
75C24×C61C22⋊C411yescharacteristic
76C23×D61—22no—
77C23×D61—22no—
78C23×D61—22no—
79C23×D61—22no—
80C23×D61—41no—
81C23×D61—41no—
82C23×D61C22⋊C411yescharacteristic
83C23×D61C22⋊C412yes—
84C23×D61C4⋊C412yes—
85C23×D61C2×D411yescharacteristic
86C22×#6923—24no—
87C22×#6923—24no—
88C22×#6923—24no—
89C22×#6923—42no—
90C22×#6923—42no—
91C22×#6923—42no—
92C22×#6923—42no—
93C22×C4×C61—22no—
94C22×C4×C61—22no—
95C22×C4×C61—24no—
96C22×C4×C61—22no—
97C22×C4×C61—42no—
98C22×C4×C61—42no—
99C22×C4×C61C4212yes—
100C22×C4×C61C22⋊C411yescharacteristic
101C22×C4×C61C4⋊C412yes—
102C22×C4×C61C22×C411yescharacteristic
103C22×Dic61—22no—
104C22×Dic61—22no—
105C22×Dic61—24no—
106C22×Dic61—22no—
107C22×Dic61—42no—
108C22×Dic61—42no—
109C22×Dic61C22⋊C411yescharacteristic
110C22×Dic61C22⋊C412yes—
111C22×Dic61C4⋊C412yes—
112C22×Dic61C2×D411yescharacteristic
113C2×C4×D61—22no—
114C2×C4×D61—22no—
115C2×C4×D61—22no—
116C2×C4×D61—22no—
117C2×C4×D61—22no—
118C2×C4×D61—22no—
119C2×C4×D61—28no—
120C2×C4×D61—28no—
121C2×C4×D61—28no—
122C2×C4×D61—28no—
123C2×C4×D61C4212yes—
124C2×C4×D61C22⋊C412yes—
125C2×C4×D61C22⋊C412yes—
126C2×C4×D61C4⋊C412yes—
127C2×C4×D61C4⋊C412yes—
128C2×C4×D61C4⋊C412yes—
129C2×C4×D61C22×C411yescharacteristic
130C2×C4×D61C22×C411yescharacteristic
131C2×C4×D61C2×D414yes—
132C2×C4×D61C2×D411yescharacteristic
133C2×C4×D61C2×Q811yescharacteristic
134C2×C4×D61#4114yes—
135C22⋊#6923—216no—
136C2×#92420—24no—
137C2×#92420—42no—
138C2×#92420—42no—
139C4×#6923—28no—
140C4×#6923—44no—
141#11758213—28no—
142#11758213—44no—
143C4⋊C4×C61—24no—
144C4⋊C4×C61—22no—
145C4⋊C4×C61C22⋊C414yescomplemented
146#11758198—28no—
147#11758198—28no—
148C4⋊Dic61—24no—
149C4⋊Dic61—22no—
150C4⋊Dic61C22⋊C414yescomplemented
151C4×Dic61—28no—
152C4×Dic61—28no—
153C23×C61—21no—
154C23×C61—21no—
155C23×C61—21no—
156C23×C61—21no—
157C23×C61#9512yes—
158C23×C61#10412yes—
159C23×C61#10412yes—
160C23×C61C2×C22⋊C411yescharacteristic
161C22×D61—21no—
162C22×D61—21no—
163C22×D61—21no—
164C22×D61—21no—
165C22×D61—24no—
166C22×D61—24no—
167C22×D61—21no—
168C22×D61—21no—
169C22×D61—21no—
170C22×D61—21no—
171C22×D61—21no—
172C22×D61—21no—
173C22×D61—24no—
174C22×D61—24no—
175C22×D61—42no—
176C22×D61—42no—
177C22×D61—44no—
178C22×D61—44no—
179C22×D61—44no—
180C22×D61—44no—
181C22×D61#9512yes—
182C22×D61C2×C22⋊C411yescharacteristic
183C22×D61C2×C4⋊C411yescharacteristic
184C22×D61#12012yes—
185C22×D61#12312yes—
186C2×#6923—28no—
187C2×#6923—44no—
188C2×#6923—44no—
189C2×#6923—44no—
190C2×#6923—44no—
191C2×#6923—44no—
192C2×#6923—44no—
193C2×C4×C61—21no—
194C2×C4×C61—21no—
195C2×C4×C61—24no—
196C2×C4×C61—24no—
197C2×C4×C61—24no—
198C2×C4×C61—48no—
199C2×C4×C61—42no—
200C2×C4×C61—42no—
201C2×C4×C61#9512yes—
202C2×C4×C61C2×C4211yescharacteristic
203C2×C4×C61C2×C22⋊C412yes—
204C2×C4×C61C2×C4⋊C411yescharacteristic
205C2×C4×C61#11712yes—
206C2×Dic61—21no—
207C2×Dic61—21no—
208C2×Dic61—24no—
209C2×Dic61—24no—
210C2×Dic61—24no—
211C2×Dic61—48no—
212C2×Dic61—42no—
213C2×Dic61—42no—
214C2×Dic61#9512yes—
215C2×Dic61C2×C22⋊C411yescharacteristic
216C2×Dic61C2×C4⋊C411yescharacteristic
217C2×Dic61#12012yes—
218C2×Dic61#12312yes—
219C4×D61—24no—
220C4×D61—24no—
221C4×D61—24no—
222C4×D61—24no—
223C4×D61—24no—
224C4×D61—24no—
225C4×D61C4×D414yes—
226C4×D61C4×D414yes—
227C4×D61#12114yes—
228C4×D61C22⋊Q814yes—
229#92420—44no—
230#10733—611nomaximal, Sylow
231C22×C61—22no—
232C22×C61—22no—
233C22×C61—22no—
234C22×C61—22no—
235C22×C61—22no—
236C22×C61—22no—
237C22×C61#33914yescomplemented
238C22×C61C2×#9511yescharacteristic
239C22×C61#37911yescharacteristic
240C22×C61#38111yescharacteristic
241C22×C61C2×#10411yescharacteristic
242C22×C61C2×#10411yescharacteristic
243C22×C61#42111yescharacteristic
244C22×C61#42111yescharacteristic
245C2×D61—22no—
246C2×D61—22no—
247C2×D61—21no—
248C2×D61—21no—
249C2×D61—21no—
250C2×D61—21no—
251C2×D61—22no—
252C2×D61—22no—
253C2×D61—22no—
254C2×D61—22no—
255C2×D61—22no—
256C2×D61—48no—
257C2×D61—48no—
258C2×D61—41no—
259C2×D61—41no—
260C2×D61—41no—
261C2×D61—41no—
262C2×D61#38512yes—
263C2×D61#38612yes—
264#6923—48no—
265C4×C61—22no—
266C4×C61—44no—
267C4×C61C4×C22⋊C412yes—
268C4×C61#38012yes—
269Dic61—22no—
270Dic61—44no—
271Dic61#38512yes—
272Dic61#38612yes—
273C22×#117—611no—
274C2×#407—611no—
275C2×C4×C22⋊C4—611no—
276C2×#339—614no—
277C2×C61—24no—
278C2×C61C22⋊#9511yescharacteristic
279C2×C61C2×#33911yescharacteristic
280C2×C61#173311yescharacteristic
281C2×C61#178911yescharacteristic
282C2×C61#178911yescharacteristic
283C2×C61#182611yescharacteristic
284C2×C61#182611yescharacteristic
285D61—22no—
286D61—22no—
287D61—42no—
288C24×C4—611no—
289C22×M16—612no—
290C2×#117—612no—
291C2×#117—612no—
292C2×#117—1228no—
293C2×#117—1221no—
294C2×#117—1221no—
295C22×C4⋊C4—611no—
296C22×C4⋊C4#692311yescharacteristic, complemented
297C22×C22⋊C4—1221no—
298C22×C22⋊C4—1221no—
299C22×C42—612no—
300C22×C42—1221no—
301#407—614no—
302#407—1222no—
303C2×C22⋊C8—1221no—
304C2×C22⋊C8—1221no—
305C4×C22⋊C4—614no—
306C4×C22⋊C4—1222no—
307C2×#95—1221no—
308#339—1228no—
309C61#1073311yescharacteristic, complemented, Sylow
310C25—611no—
311C23×C4—21no—
312C23×C4—611no—
313C23×C4—611no—
314C23×C4—612no—
315C23×C4—612no—
316C23×C4—612no—
317C23×C4—612no—
318C23×C4—611no—
319C23×C4—611no—
320C23×C4—611no—
321C23×C4—1224no—
322C23×C4—1224no—
323C23×C4—1222no—
324C23×C4—1221no—
325C23×C4C2×#692311yescharacteristic
326C2×M16—614no—
327C2×M16—1222no—
328C2×M16—1224no—
329C2×M16—1224no—
330C22×C8—1222no—
331#117—618no—
332#117—1224no—
333#117—1224no—
334#117—1228no—
335#117—1228no—
336#117—1224no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—612no—
340C2×C4⋊C4—1224no—
341C2×C4⋊C4—1221no—
342C2×C4⋊C4C2×#692312yes—
343C2×C22⋊C4—1222no—
344C2×C22⋊C4—1222no—
345C2×C22⋊C4—1228no—
346C2×C22⋊C4—1224no—
347C2×C22⋊C4—1224no—
348C2×C22⋊C4—1224no—
349C2×C42—614no—
350C2×C42—1222no—
351C2×C42—1222no—
352C2×C42—1228no—
353C2×C42—1224no—
354C2×C42—1224no—
355C2×C42—1222no—
356C22⋊C8—1224no—
357C22⋊C8—1224no—
358#95—1224no—
359C24—611no—
360C24—611no—
361C24—612no—
362C24—612no—
363C24—1222no—
364C24—1222no—
365C24—1222no—
366C24—1222no—
367C24—2441no—
368C24—2441no—
369C24C22⋊#692311yescharacteristic
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—24no—
373C22×C4—22no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—611no—
377C22×C4—611no—
378C22×C4—611no—
379C22×C4—614no—
380C22×C4—611no—
381C22×C4—611no—
382C22×C4—614no—
383C22×C4—612no—
384C22×C4—612no—
385C22×C4—611no—
386C22×C4—612no—
387C22×C4—612no—
388C22×C4—612no—
389C22×C4—612no—
390C22×C4—612no—
391C22×C4—612no—
392C22×C4—1222no—
393C22×C4—1222no—
394C22×C4—1228no—
395C22×C4—1228no—
396C22×C4—1228no—
397C22×C4—1228no—
398C22×C4—1222no—
399C22×C4—1222no—
400C22×C4—1222no—
401C22×C4—1222no—
402C22×C4—1222no—
403C22×C4—1222no—
404C22×C4—1224no—
405C22×C4—1224no—
406C22×C4—1224no—
407C22×C4—1224no—
408C22×C4—1222no—
409C22×C4—2442no—
410C22×C4—2442no—
411C22×C4—2442no—
412C22×C4—2442no—
413C22×C4—2442no—
414C22×C4—2442no—
415C22×C4C4×#692312yes—
416C22×C4C4⋊#692312yes—
417C22×C4C22⋊#692311yescharacteristic
418C22×C4C22×#692311yescharacteristic
419M16—1228no—
420M16—2444no—
421C2×C8—1224no—
422C2×C8—2442no—
423C2×C8—2442no—
424C4⋊C4—24no—
425C4⋊C4—22no—
426C4⋊C4—614no—
427C4⋊C4—1224no—
428C4⋊C4—1222no—
429C4⋊C4C22⋊#692314yescomplemented
430C22⋊C4—1228no—
431C22⋊C4—1228no—
432C22⋊C4—12216no—
433C42—1228no—
434C42—1228no—
435C42—1228no—
436C42—2444no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—612no—
442C23—611no—
443C23—611no—
444C23—612no—
445C23—612no—
446C23—1224no—
447C23—1224no—
448C23—1221no—
449C23—1221no—
450C23—1221no—
451C23—1221no—
452C23—1221no—
453C23—1221no—
454C23—1221no—
455C23—1221no—
456C23—1221no—
457C23—1224no—
458C23—1224no—
459C23—1221no—
460C23—2442no—
461C23—2442no—
462C23—2444no—
463C23—2444no—
464C23—2444no—
465C23—2444no—
466C23(C2×#6923)⋊C412yes—
467C23#1451984112yes—
468C23#1451984212yes—
469C23C2×C22⋊#692311yescharacteristic
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—48no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—612no—
479C2×C4—611no—
480C2×C4—611no—
481C2×C4—612no—
482C2×C4—614no—
483C2×C4—614no—
484C2×C4—614no—
485C2×C4—614no—
486C2×C4—612no—
487C2×C4—1224no—
488C2×C4—1224no—
489C2×C4—1224no—
490C2×C4—1224no—
491C2×C4—1224no—
492C2×C4—1224no—
493C2×C4—1221no—
494C2×C4—1221no—
495C2×C4—1224no—
496C2×C4—1224no—
497C2×C4—1228no—
498C2×C4—1224no—
499C2×C4—2448no—
500C2×C4—2444no—
501C2×C4—2444no—
502C2×C4—2444no—
503C2×C4—2444no—
504C2×C4—2444no—
505C2×C4—2444no—
506C2×C4—2442no—
507C2×C4—2442no—
508C2×C4(C2×#6923)⋊C412yes—
509C2×C4C2×C4×#692311yescharacteristic
510C2×C4C2×C22⋊#692312yes—
511C2×C4C2×C4⋊#692311yescharacteristic
512C2×C4#1451985612yes—
513C8—2444no—
514C22—22no—
515C22—22no—
516C22—22no—
517C22—22no—
518C22—22no—
519C22—22no—
520C22—612no—
521C22—612no—
522C22—1222no—
523C22—1222no—
524C22—1222no—
525C22—1222no—
526C22—1221no—
527C22—1221no—
528C22—1221no—
529C22—1221no—
530C22—1222no—
531C22—1222no—
532C22—1222no—
533C22—2448no—
534C22—2448no—
535C22—2441no—
536C22—2441no—
537C22—2441no—
538C22—2441no—
539C22#1684063214yescomplemented
540C22C2×(C2×#6923)⋊C411yescharacteristic
541C22#1684070311yescharacteristic
542C22#1684070511yescharacteristic
543C22C2×#1451984111yescharacteristic
544C22C2×#1451984211yescharacteristic
545C22#1684076011yescharacteristic
546C22#1684076111yescharacteristic
547C4—22no—
548C4—44no—
549C4—612no—
550C4—612no—
551C4—1222no—
552C4—2448no—
553C4—2444no—
554C4C4×C22⋊#692312yes—
555C4#1684070412yes—
556C2—24no—
557C2—1222no—
558C2—1222no—
559C2—2442no—
560C2#2146099311yescharacteristic
561C2C2×#1684063211yescharacteristic
562C2#2146149811yescharacteristic
563C2#2146166011yescharacteristic
564C2#2146166211yescharacteristic
565C2#2146172511yescharacteristic
566C2#2146172611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×D61D4
cosocleC22×C4×D61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#10733
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#16840632C2semidirect
9. #16840733C4semidirect
13. C4×C22⋊#6923C4semidirect
20. C2×#14519735C4semidirect
22. C22×C4⋊Dic61C4semidirect
25. C22×C4⋊C4×C61C4semidirect
30. C2×#11758213C2×C4semidirect
38. C2×C4×#6923C2×C4semidirect
145. C4⋊C4×C61C22⋊C4semidirect
150. C4⋊Dic61C22⋊C4semidirect
237. C22×C61#339semidirect
296. C22×C4⋊C4#6923semidirect
309. C61#10733semidirect
429. C4⋊C4C22⋊#6923semidirect
539. C22#16840632semidirect

Maximal subgroups

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

subgroupindex
C2×#168407332
C2×C4×C22⋊#69232
C2×#168406322
C22×#145197352
#1073361