Finite Group Databasebeta

← #30616078

Subgroups — #30616078

Order 15616.

890 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462303C211yesmaximal, characteristic, complemented
2#21462258C211yesmaximal, characteristic
3#21461898C212yesmaximal, complemented
4#21461881C212yesmaximal, complemented
5#21461812C212yesmaximal
6#21461784C212yesmaximal
7C4×#14519845C211yesmaximal, characteristic, complemented
8#21461591C211yesmaximal, characteristic, complemented
9#21461589C211yesmaximal, characteristic
10#21461537C211yesmaximal, characteristic, complemented
11C4×SD16×D61C211yesmaximal, characteristic
12C2×D4×#6923C2212yes—
13C2×#14519845C2212yes—
14C2×#14519840C2212yes—
15C2×#14519839C2212yes—
16#16840721C2211yescharacteristic
17(C2×#6923)⋊Q8C2212yes—
18#16840713C2212yes—
19#16840711—22no—
20#16840707—21no—
21#16840706—21no—
22C4⋊C4×#6923C2212yes—
23C4×C4⋊#6923C2211yescharacteristic
24C4×C4⋊#6923C2211yescharacteristic
25C22⋊C4×#6923—22no—
26C4×C22⋊#6923—21no—
27#16840698C2211yescharacteristic
28C2×(C2×#6923)⋊C4—21no—
29#16840636C2212yes—
30#16840635C2212yes—
31#16840635C2212yes—
32(C2×#6923)⋊C8C2212yes—
33(C2×#6923)⋊C8C2212yes—
34C2×SD16×D61C2211yescharacteristic
35C4×Q8×D61C2211yescharacteristic
36C4×D4×D61C2211yescharacteristic
37#16839853C411yescharacteristic, complemented
38C4×#11758190C411yescharacteristic, complemented
39SD16×Dic61C411yescharacteristic, complemented
40C4×#11758201C411yescharacteristic, complemented
41#16839849C411yescharacteristic, complemented
42C4×#11758200C411yescharacteristic, complemented
43#16839847C411yescharacteristic, complemented
44#106×D61C2211yescharacteristic
45#103×D61C2211yescharacteristic
46#102×D61C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48C4×SD16×C61C411yescharacteristic, complemented
49C23×#6923—22no—
50C2×D61⋊C8C2312yes—
51D4×#6923—24no—
52D4×#6923—24no—
53C2×C4⋊#6923—22no—
54C2×C4⋊#6923C2312yes—
55C2×C4⋊#6923C2312yes—
56C2×C22⋊#6923—22no—
57C2×C4×#6923—22no—
58C2×C4×#6923—21no—
59C2×C4×#6923—21no—
60C2×C4×#6923C2312yes—
61#14519845—24no—
62#14519840—24no—
63#14519839—24no—
64#14519832—21no—
65#14519832—21no—
66(C2×#6923)⋊C4—22no—
67(C2×#6923)⋊C4—22no—
68(C2×#6923)⋊C4—22no—
69(C2×#6923)⋊C4—22no—
70(C2×#6923)⋊C4—21no—
71(C2×#6923)⋊C4—21no—
72(C2×#6923)⋊C4D411yescharacteristic
73(C2×#6923)⋊C4D411yescharacteristic
74(C2×#6923)⋊C4D412yes—
75C2×Q8×D61C2311yescharacteristic
76C2×D4×D61C2311yescharacteristic
77C22×C4×D61—21no—
78C2×#11758190C2×C411yescharacteristic
79C2×#11758200C2×C411yescharacteristic
80C2×#11758201C2×C411yescharacteristic
81SD16×D61—24no—
82C2×C8×D61C2311yescharacteristic
83C2×C8×D61C2311yescharacteristic
84Q8×Dic61C2×C411yescharacteristic, complemented
85C4×Dic122—21no—
86C4×Dic122C2×C411yescharacteristic, complemented
87#14519742—21no—
88#14519742C2×C411yescharacteristic, complemented
89C4×D244C2×C411yescharacteristic
90D4×Dic61C2×C411yescharacteristic
91#14519739C2×C411yescharacteristic
92C4×C22⋊D61—21no—
93#14519737—21no—
94C4⋊C4×D61—21no—
95C4⋊C4×D61C2311yescharacteristic
96C4⋊C4×D61C2311yescharacteristic
97C22⋊C4×D61—21no—
98C42×D61—21no—
99C42×D61C2311yescharacteristic
100#14519709C2×C411yescharacteristic, complemented
101#14519708C2×C411yescharacteristic, complemented
102#14519708C2×C411yescharacteristic, complemented
103#14519702C2×C411yescharacteristic, complemented
104#14519701C2×C411yescharacteristic, complemented
105#14519700C2×C411yescharacteristic, complemented
106#14519699C2×C411yescharacteristic
107#14519698C2×C411yescharacteristic
108#14519697C2×C411yescharacteristic
109C4×#92418C2×C411yescharacteristic, complemented
110C8×Dic61C2×C411yescharacteristic, complemented
111C8×Dic61C2×C411yescharacteristic, complemented
112C2×SD16×C61C2×C411yescharacteristic
113C4×Q8×C61C2×C411yescharacteristic, complemented
114C4×D4×C61C2×C411yescharacteristic
115#106×C61C2×C411yescharacteristic, complemented
116#103×C61C2×C411yescharacteristic, complemented
117#102×C61C2×C411yescharacteristic
118C4×C8×C61C2×C411yescharacteristic, complemented
119C23×D61—21no—
120C22×#6923—22no—
121C22×#6923—28no—
122C22×#6923—22no—
123C22×#6923—82no—
124C22×#6923—82no—
125C22×#6923C2×D412yes—
126C22×#6923C2×D412yes—
127C2×Q8×C61C22×C411yescharacteristic
128C2×D4×C61C22×C411yescharacteristic
129C22×C4×C61—21no—
130C2×C22⋊D61—21no—
131C22×Dic61—21no—
132Q8×D61—22no—
133Q8×D61—22no—
134D4×D61—22no—
135D4×D61#4114yes—
136C2×D244C22×C411yescharacteristic
137C2×C4×D61—21no—
138C2×C4×D61—21no—
139C2×C4×D61—21no—
140C2×C4×D61—21no—
141C2×C4×D61—21no—
142C2×C4×D61—82no—
143C2×C4×D61C2×D411yescharacteristic
144C2×C4×D61C2×D411yescharacteristic
145C2×C4×D61C2411yescharacteristic
146C2×Dic122—21no—
147C2×Dic122C22×C411yescharacteristic
148C22⋊#6923—28no—
149C2×#92420—22no—
150C4⋊#6923—22no—
151C4⋊#6923—22no—
152C4⋊#6923—22no—
153C4⋊#6923—82no—
154C4⋊#6923#4114yes—
155C4×#6923—22no—
156C4×#6923—22no—
157C4×#6923—81no—
158C4×#6923—81no—
159C4×#6923—82no—
160D61⋊C8—22no—
161D61⋊C8—22no—
162SD16×C61—22no—
163C2×C8×C61C22×C411yescharacteristic
164C2×C8×C61C22×C411yescharacteristic
165C4⋊C4×C61—21no—
166C4⋊C4×C61C22×C411yescharacteristic
167C4⋊C4×C61C22×C411yescharacteristic
168C22⋊C4×C61—21no—
169C42×C61—21no—
170C42×C61C22×C411yescharacteristic
171C22⋊Dic61—21no—
172#11758201—22no—
173#11758200—22no—
174#11758198—21no—
175#11758198—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61C22×C411yescharacteristic
178C4⋊Dic61C22×C411yescharacteristic
179#11758196—21no—
180#11758196—21no—
181#11758196—21no—
182#11758196—21no—
183C4×Dic61—21no—
184C4×Dic61—21no—
185C4×Dic61—21no—
186C4×Dic61C22×C411yescharacteristic
187C4×Dic61#4111yescharacteristic
188C4×Dic61#4111yescharacteristic
189C2×#92418C22×C411yescharacteristic
190C2×#92418C22×C411yescharacteristic
191#11758190—22no—
192C8×D61—22no—
193C8×D61—22no—
194C23×C61—21no—
195C22×D61—21no—
196C22×D61—24no—
197C22×D61—42no—
198C22×D61—41no—
199C22×D61—41no—
200C22×D61C22×D411yescharacteristic
201C2×#6923—22no—
202C2×#6923—22no—
203C2×#6923—24no—
204C2×#6923—22no—
205C2×#6923—22no—
206C2×#6923—22no—
207C2×#6923—22no—
208C2×#6923—42no—
209C2×#6923—42no—
210C2×#6923—42no—
211C2×#6923—42no—
212C2×#6923—42no—
213C2×#6923—88no—
214Q8×C61—21no—
215Q8×C61—21no—
216D4×C61—21no—
217D4×C61#11712yes—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—81no—
222C2×C4×C61C4×D411yescharacteristic
223C2×C4×C61C4×D411yescharacteristic
224C2×C4×C61C23×C411yescharacteristic
225C22⋊D61—24no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—81no—
230C2×Dic61C4×D411yescharacteristic
231C2×Dic61C4×D411yescharacteristic
232C2×Dic61C2×#4111yescharacteristic
233D244—21no—
234D244#11712yes—
235C4×D61—21no—
236C4×D61—21no—
237C4×D61—22no—
238C4×D61—42no—
239C4×D61—42no—
240C4×D61—41no—
241C4×D61—41no—
242C4×D61—81no—
243C4×D61—81no—
244C4×D61C2×#4112yes—
245C4×D61C2×#4112yes—
246Dic122—21no—
247Dic122—21no—
248Dic122—42no—
249#92420—42no—
250C8×C61—21no—
251C8×C61—21no—
252#92418—21no—
253#92418—21no—
254#21133—611nomaximal, Sylow
255C22×C61—22no—
256C22×C61—41no—
257C22×C61—41no—
258C22×C61C2×C4×D411yescharacteristic
259C2×D61—22no—
260C2×D61—41no—
261C2×D61—41no—
262C2×D61—44no—
263C2×D61—44no—
264C2×D61#52512yes—
265C2×D61#57711yescharacteristic
266C2×D61#57712yes—
267C2×D61#57711yescharacteristic
268#6923—42no—
269#6923—44no—
270#6923—42no—
271#6923—82no—
272C4×C61—21no—
273C4×C61—21no—
274C4×C61—41no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61C2×#11711yescharacteristic
278C4×C61C4×#4111yescharacteristic
279Dic61—21no—
280Dic61—21no—
281Dic61—41no—
282Dic61—41no—
283Dic61—41no—
284Dic61#52912yes—
285C2×C4×SD16—611no—
286#2320—611no—
287#2275—611no—
288#1927—612no—
289#1919—612no—
290#1877—612no—
291#1864—612no—
292C4×#106—611no—
293#1763—611no—
294#1762—611no—
295#1746—611no—
296C2×C61—42no—
297C2×C61#229011yescharacteristic
298C2×C61#294911yescharacteristic
299C2×C61#295211yescharacteristic
300D61—42no—
301D61#312312yes—
302D61#312512yes—
303C22×SD16—611no—
304C2×C4×Q8—611no—
305C2×C4×D4—611no—
306C2×C4×D4—612no—
307C4×SD16—611no—
308C4×SD16—611no—
309C4×SD16—611no—
310C4×SD16—611no—
311C4×SD16—611no—
312C4×SD16—611no—
313C4×SD16—611no—
314C4×SD16#692311yescharacteristic, complemented
315C2×#106—611no—
316C2×#106—612no—
317C2×#103—611no—
318C2×#103—612no—
319C2×#102—611no—
320C2×#102—612no—
321C2×#97—611no—
322C2×C4×C8—611no—
323#391—612no—
324#389—612no—
325#387—1222no—
326#383—1221no—
327#382—1221no—
328C4×C4⋊C4—611no—
329C4×C4⋊C4—612no—
330C4×C4⋊C4—611no—
331C4×C22⋊C4—1221no—
332C4×C22⋊C4—1222no—
333#376—611no—
334C2×#95—1221no—
335#340—612no—
336#340—612no—
337#340—612no—
338#336—612no—
339#336—612no—
340C61#2113311yescharacteristic, complemented, Sylow
341C22×Q8—611no—
342C22×D4—611no—
343C23×C4—1221no—
344C23×C4—1222no—
345C2×SD16—611no—
346C2×SD16—611no—
347C2×SD16—611no—
348C2×SD16—1224no—
349C2×SD16C2×#692311yescharacteristic
350C22×C8—611no—
351C22×C8—611no—
352C22×C8—612no—
353C4×Q8—611no—
354C4×Q8—611no—
355C4×Q8—611no—
356C4×Q8—1221no—
357C4×Q8—1221no—
358C4×Q8C2×#692311yescharacteristic, complemented
359C4×D4—611no—
360C4×D4—611no—
361C4×D4—611no—
362C4×D4—1221no—
363C4×D4—1221no—
364C4×D4—1224no—
365C4×D4—1224no—
366C4×D4C2×#692311yescharacteristic
367C2×C4⋊C4—612no—
368C2×C4⋊C4—611no—
369C2×C4⋊C4—611no—
370C2×C4⋊C4—612no—
371C2×C4⋊C4—1221no—
372C2×C4⋊C4—1222no—
373C2×C22⋊C4—1221no—
374C2×C22⋊C4—1222no—
375C2×C42—611no—
376C2×C42—612no—
377C2×C42—1221no—
378C2×C42—1221no—
379C2×C42—1222no—
380C2×C42—1221no—
381#106—611no—
382#106—611no—
383#106—611no—
384#106—1224no—
385#106C2×#692311yescharacteristic, complemented
386#103—611no—
387#103—611no—
388#103—611no—
389#103—1224no—
390#103C2×#692311yescharacteristic, complemented
391#102—611no—
392#102—611no—
393#102—611no—
394#102—1224no—
395#102C2×#692311yescharacteristic
396#97—1221no—
397#97—1221no—
398C4×C8—611no—
399C4×C8—611no—
400C4×C8—611no—
401C4×C8C2×#692311yescharacteristic, complemented
402#95—611no—
403#95—611no—
404#95—612no—
405#95—1221no—
406#95—1222no—
407#95—1221no—
408#95—1222no—
409#95—1222no—
410#95—1222no—
411C24—1221no—
412C2×Q8—611no—
413C2×Q8—1221no—
414C2×Q8—1222no—
415C2×Q8—1222no—
416C2×Q8C22×#692311yescharacteristic
417C2×D4—614no—
418C2×D4—611no—
419C2×D4—1222no—
420C2×D4—1221no—
421C2×D4C22×#692311yescharacteristic
422C22×C4—21no—
423C22×C4—611no—
424C22×C4—611no—
425C22×C4—611no—
426C22×C4—612no—
427C22×C4—612no—
428C22×C4—1221no—
429C22×C4—1221no—
430C22×C4—1221no—
431C22×C4—1221no—
432C22×C4—1221no—
433C22×C4—1228no—
434C22×C4—1222no—
435C22×C4—1221no—
436C22×C4—1222no—
437C22×C4—4882no—
438C22×C4—4882no—
439C22×C4—4882no—
440SD16—22no—
441SD16—1222no—
442SD16—1222no—
443SD16—1222no—
444C2×C8—611no—
445C2×C8—611no—
446C2×C8—1222no—
447C2×C8—1222no—
448C2×C8—1222no—
449C2×C8—1222no—
450C2×C8—1222no—
451C2×C8C22×#692311yescharacteristic
452C2×C8C22×#692311yescharacteristic
453C4⋊C4—21no—
454C4⋊C4—614no—
455C4⋊C4—611no—
456C4⋊C4—611no—
457C4⋊C4—1221no—
458C4⋊C4—1221no—
459C4⋊C4—1221no—
460C4⋊C4—1221no—
461C4⋊C4—1222no—
462C4⋊C4—1222no—
463C4⋊C4—1222no—
464C4⋊C4—1221no—
465C4⋊C4—4882no—
466C4⋊C4C22×#692311yescharacteristic
467C4⋊C4C22×#692311yescharacteristic
468C22⋊C4—21no—
469C22⋊C4—1221no—
470C22⋊C4—1221no—
471C22⋊C4—1228no—
472C22⋊C4—1221no—
473C42—21no—
474C42—611no—
475C42—611no—
476C42—611no—
477C42—1221no—
478C42—1221no—
479C42—1222no—
480C42—1222no—
481C42—1221no—
482C42—4881no—
483C42—4881no—
484C42—4882no—
485C42C22×#692311yescharacteristic
486C23—21no—
487C23—611no—
488C23—1224no—
489C23—1221no—
490C23—2442no—
491C23—2441no—
492C23—2441no—
493Q8—21no—
494Q8—21no—
495Q8—1221no—
496Q8—1221no—
497Q8—2442no—
498D4—21no—
499D4—612no—
500D4—1224no—
501D4—1221no—
502D4#1451985612yes—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—81no—
507C2×C4—611no—
508C2×C4—612no—
509C2×C4—612no—
510C2×C4—611no—
511C2×C4—611no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4—1222no—
515C2×C4—1222no—
516C2×C4—1222no—
517C2×C4—1222no—
518C2×C4—1224no—
519C2×C4—1222no—
520C2×C4—1222no—
521C2×C4—1222no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—4881no—
526C2×C4—4881no—
527C2×C4—4881no—
528C2×C4—4888no—
529C2×C4—2442no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4—2442no—
533C2×C4—2442no—
534C2×C4—2442no—
535C2×C4—2442no—
536C2×C4—2442no—
537C2×C4—2442no—
538C2×C4D4×#692311yescharacteristic
539C2×C4D4×#692311yescharacteristic
540C2×C4C23×#692311yescharacteristic
541C8—21no—
542C8—21no—
543C8—1221no—
544C8—1221no—
545C8—2442no—
546C22—22no—
547C22—41no—
548C22—41no—
549C22—612no—
550C22—612no—
551C22—611no—
552C22—611no—
553C22—1222no—
554C22—2444no—
555C22—2444no—
556C22—2441no—
557C22—2441no—
558C22C2×D4×#692311yescharacteristic
559C4—21no—
560C4—21no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—612no—
565C4—1221no—
566C4—1221no—
567C4—4882no—
568C4—2442no—
569C4—2442no—
570C4—2444no—
571C4—2441no—
572C4—2441no—
573C4—2441no—
574C4C2×#1451985611yescharacteristic
575C4#41×#692311yescharacteristic
576C2—42no—
577C2—612no—
578C2—612no—
579C2—2442no—
580C2#2146227311yescharacteristic
581C2#2146257911yescharacteristic
582C2#2146258211yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC4×SD16×C61C4
socleC22×C61C2×C4×D4
prime radicalC2×D4×D61C23
cosocleC2×C4×D61C24
hypercenterC4×SD16#6923
hypocenterC61#21133
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #21462303C2semidirect
3. #21461898C2semidirect
4. #21461881C2semidirect
7. C4×#14519845C2semidirect
8. #21461591C2semidirect
10. #21461537C2semidirect
37. #16839853C4semidirect
38. C4×#11758190C4semidirect
39. SD16×Dic61C4semidirect
40. C4×#11758201C4semidirect
41. #16839849C4semidirect
42. C4×#11758200C4semidirect
43. #16839847C4semidirect
48. C4×SD16×C61C4semidirect
84. Q8×Dic61C2×C4semidirect
86. C4×Dic122C2×C4semidirect
88. #14519742C2×C4semidirect
100. #14519709C2×C4semidirect
101. #14519708C2×C4semidirect
102. #14519708C2×C4semidirect
103. #14519702C2×C4semidirect
104. #14519701C2×C4semidirect
105. #14519700C2×C4semidirect
109. C4×#92418C2×C4semidirect
110. C8×Dic61C2×C4semidirect
111. C8×Dic61C2×C4semidirect
113. C4×Q8×C61C2×C4semidirect
115. #106×C61C2×C4semidirect
116. #103×C61C2×C4semidirect
118. C4×C8×C61C2×C4semidirect
314. C4×SD16#6923semidirect
340. C61#21133semidirect
358. C4×Q8C2×#6923semidirect
385. #106C2×#6923semidirect
390. #103C2×#6923semidirect
401. C4×C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623032
#214622582
#214618982
#214618812
#214618122
#214617842
C4×#145198452
#214615912
#214615892
#214615372
C4×SD16×D612
#2113361