Finite Group Databasebeta

← #30610485

Subgroups — #30610485

Order 15616.

1138 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462740C211yesmaximal, characteristic, complemented
2#21462626C211yesmaximal, characteristic, complemented
3#21461162C212yesmaximal, complemented
4#21461157C212yesmaximal, complemented
5#21461153C212yesmaximal, complemented
6#21461148C212yesmaximal, complemented
7#21461121C211yesmaximal, characteristic, complemented
8#21461116C211yesmaximal, characteristic, complemented
9#21461112C211yesmaximal, characteristic, complemented
10C2×Q8⋊#92420C211yesmaximal, characteristic, complemented
11#21459028C211yesmaximal, characteristic
12#16840812—21no—
13#16840812—21no—
14#16840796—21no—
15#16840796—21no—
16#16840791—22no—
17#16840791—22no—
18#16840784C2212yes—
19#16840781C2212yes—
20#16840778C2211yescharacteristic
21#16840778C2211yescharacteristic
22#16840766C2212yes—
23C2×C4⋊#92420C2211yescharacteristic
24C4×#11758213C2212yes—
25C2×C4×#92420C2211yescharacteristic
26#16840612C2211yescharacteristic
27#16840612C2211yescharacteristic
28#16840612C2212yes—
29Q8⋊#92420C2212yes—
30Q8⋊#92420C2212yes—
31Q8⋊#92420C2212yes—
32Q8⋊#92420C2212yes—
33#16840610C2211yescharacteristic
34#16840610C2211yescharacteristic
35#16840610C2212yes—
36C2×#14519825C411yescharacteristic
37#16840244—21no—
38#16840244C412yes—
39#16840242—22no—
40#16840242C411yescharacteristic
41#16840242C411yescharacteristic
42#16840238—21no—
43#16840238C412yes—
44C4×#11758226—21no—
45C4×#11758226C2212yes—
46#16840230—22no—
47#16840230C2211yescharacteristic
48#16840230C2211yescharacteristic
49C2×Q8×Dic61C2211yescharacteristic
50C4×Q8×D61—21no—
51C4×Q8×D61C2212yes—
52C61×#519C411yescharacteristic
53C2×#11758213—22no—
54C2×#11758213—22no—
55C22×#92420—21no—
56C22×#92420—21no—
57C4⋊#92420—21no—
58C4⋊#92420—22no—
59C4⋊#92420—21no—
60C4⋊#92420—22no—
61C4⋊#92420C2312yes—
62C4⋊#92420C2311yescharacteristic
63C4⋊#92420C2311yescharacteristic
64#14519834—22no—
65#14519834—22no—
66C22⋊#92420—21no—
67C22⋊#92420—21no—
68#14519832—22no—
69#14519832—22no—
70C4×#92420—21no—
71C4×#92420—21no—
72C4×#92420C2311yescharacteristic
73C4×#92420C2311yescharacteristic
74C4×#92420C2312yes—
75#14519825—24no—
76#14519825—24no—
77C2×#11758226—21no—
78C2×#11758226C2×C412yes—
79C2×#11758222—22no—
80C2×#11758222C2×C411yescharacteristic
81C2×#11758222C2×C411yescharacteristic
82C2×Q8×D61—21no—
83C2×Q8×D61C2×C412yes—
84Q8×Dic61—21no—
85Q8×Dic61—21no—
86Q8×Dic61C2×C412yes—
87Q8×Dic61C2312yes—
88C4×Dic122—21no—
89C4×Dic122—22no—
90C4×Dic122—22no—
91C4×Dic122C2×C412yes—
92#14519742—22no—
93#14519742—22no—
94#14519742C2×C411yescharacteristic
95#14519742D411yescharacteristic
96#14519742D411yescharacteristic
97#14519742C2311yescharacteristic
98C4×D244—21no—
99C4×D244—22no—
100C4×D244—22no—
101C4×D244C2×C412yes—
102#14519739—22no—
103#14519739—22no—
104#14519739C2×C411yescharacteristic
105#14519739D411yescharacteristic
106#14519739D411yescharacteristic
107#14519739C2311yescharacteristic
108#14519737—22no—
109#14519737—21no—
110#14519737—21no—
111#14519737—22no—
112#14519737D412yes—
113#14519737D412yes—
114#14519735—21no—
115#14519735—22no—
116#14519735—22no—
117#14519735C2×C412yes—
118#14519734—22no—
119#14519734—22no—
120#14519734—21no—
121#14519734C2×C412yes—
122C2×C4⋊Dic61—21no—
123C2×C4⋊Dic61C2×C411yescharacteristic
124C4⋊C4×D61—22no—
125C4⋊C4×D61—21no—
126C4⋊C4×D61—22no—
127C4⋊C4×D61C2×C412yes—
128C2×C4×Dic61—21no—
129C2×C4×Dic61C2311yescharacteristic
130C42×D61—22no—
131C42×D61—22no—
132C42×D61—21no—
133C42×D61C2312yes—
134C22×Q8×C61C2×C411yescharacteristic
135C4×Q8×C61—21no—
136C4×Q8×C61—21no—
137C4×Q8×C61C2×C412yes—
138C4×Q8×C61C2×C412yes—
139#117×C61—22no—
140#117×C61C2×C411yescharacteristic
141#117×C61C2×C411yescharacteristic
142C2×Q8×C61—21no—
143C2×Q8×C61—22no—
144C2×Q8×C61M1614yescomplemented
145C2×Q8×C61C22×C412yes—
146C22×C4×C61—21no—
147C22×C4×C61C22×C411yescharacteristic
148C2×C22⋊D61—21no—
149C2×C22⋊D61C22⋊C412yes—
150C22×Dic61—21no—
151C22×Dic61C2×D411yescharacteristic
152C22×Dic61C2×D411yescharacteristic
153#11758226—28no—
154#11758226—24no—
155#11758226—24no—
156Q8×D61—28no—
157Q8×D61—24no—
158Q8×D61—24no—
159#11758222—216no—
160#11758222—22no—
161#11758222—22no—
162#11758222—22no—
163#11758222M1614yescomplemented
164C2×D244—22no—
165C2×D244C22⋊C411yescharacteristic
166C2×D244C22×C411yescharacteristic
167C2×C4×D61—22no—
168C2×C4×D61—21no—
169C2×C4×D61—22no—
170C2×C4×D61—21no—
171C2×C4×D61—22no—
172C2×C4×D61—22no—
173C2×C4×D61—21no—
174C2×C4×D61C22×C412yes—
175C2×C4×D61C2×D412yes—
176C2×C4×D61C2×D412yes—
177C2×Dic122—22no—
178C2×Dic122C22⋊C411yescharacteristic
179C2×Dic122C22×C411yescharacteristic
180C2×#92420—21no—
181C2×#92420—21no—
182C2×#92420—21no—
183C2×#92420—21no—
184C2×#92420—22no—
185C2×#92420—22no—
186C2×#92420—42no—
187C2×#92420—81no—
188#11758213—44no—
189#11758213—82no—
190C4⋊C4×C61—22no—
191C4⋊C4×C61—22no—
192C4⋊C4×C61C22⋊C411yescharacteristic
193C4⋊C4×C61C22⋊C411yescharacteristic
194C4⋊C4×C61C22×C411yescharacteristic
195C4⋊C4×C61C22×C411yescharacteristic
196C22⋊C4×C61—21no—
197C22⋊C4×C61C22⋊C412yes—
198C42×C61—22no—
199C42×C61—22no—
200C42×C61—21no—
201C42×C61C22×C412yes—
202#11758198—22no—
203#11758198—22no—
204#11758198—21no—
205#11758198—21no—
206#11758198C22⋊C412yes—
207#11758198C22⋊C412yes—
208C4⋊Dic61—21no—
209C4⋊Dic61—22no—
210C4⋊Dic61—22no—
211C4⋊Dic61C22×C412yes—
212#11758196—22no—
213#11758196—22no—
214#11758196—21no—
215#11758196—21no—
216#11758196C22⋊C412yes—
217#11758196C22⋊C412yes—
218C4×Dic61—22no—
219C4×Dic61—21no—
220C4×Dic61—22no—
221C4×Dic61—22no—
222C4×Dic61—21no—
223C4×Dic61—22no—
224C4×Dic61C22×C411yescharacteristic
225C4×Dic61C2×D411yescharacteristic
226C4×Dic61C2×D411yescharacteristic
227C4×Dic61C2×D412yes—
228C4×Dic61C2×D412yes—
229C4×Dic61C2411yescharacteristic
230C23×C61C2×C22⋊C411yescharacteristic
231C22×D61—21no—
232C22×D61C2×C22⋊C412yes—
233Q8×C61—22no—
234Q8×C61—24no—
235Q8×C61C2×M1614yes—
236C2×C4×C61—22no—
237C2×C4×C61—24no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61C2×C22⋊C412yes—
241C2×C4×C61C2×C22⋊C412yes—
242C2×C4×C61C2×C22⋊C411yescharacteristic
243C2×C4×C61C2×M1612yes—
244C2×C4×C61C2×M1612yes—
245C2×C4×C61C23×C411yescharacteristic
246C22⋊D61—24no—
247C22⋊D61—24no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—22no—
252C2×Dic61—41no—
253C2×Dic61—81no—
254C2×Dic61C2×C22⋊C411yescharacteristic
255C2×Dic61C2×C22⋊C411yescharacteristic
256C2×Dic61C2×C22⋊C412yes—
257C2×Dic61C22×D411yescharacteristic
258C2×Dic61C22×D411yescharacteristic
259D244—28no—
260D244—21no—
261D244—22no—
262D244C2×M1612yes—
263C4×D61—28no—
264C4×D61—28no—
265C4×D61—22no—
266C4×D61—22no—
267C4×D61—24no—
268C4×D61—22no—
269C4×D61—22no—
270C4×D61—42no—
271C4×D61—41no—
272C4×D61—41no—
273C4×D61—81no—
274C4×D61—82no—
275C4×D61—82no—
276Dic122—28no—
277Dic122—21no—
278Dic122—22no—
279Dic122C2×M1612yes—
280#92420—22no—
281#92420—42no—
282#92420—41no—
283#92420—41no—
284#92420—42no—
285#92420—41no—
286#17454—611nomaximal, Sylow
287C22×C61—21no—
288C22×C61—21no—
289C22×C61#40712yes—
290C22×C61C22×C22⋊C411yescharacteristic
291C2×D61—22no—
292C2×D61—22no—
293C2×D61—22no—
294C2×D61—22no—
295C2×D61—41no—
296C2×D61—41no—
297C4×C61—24no—
298C4×C61—22no—
299C4×C61—22no—
300C4×C61—41no—
301C4×C61—41no—
302C4×C61#40712yes—
303C4×C61C22×M1611yescharacteristic
304C4×C61C22×M1611yescharacteristic
305Dic61—22no—
306Dic61—22no—
307Dic61—21no—
308Dic61—21no—
309Dic61—21no—
310Dic61—42no—
311Dic61#57711yescharacteristic
312Dic61#57811yescharacteristic
313C4×2−1+4—611no—
314#2989—611no—
315#2965—611no—
316#1491—612no—
317#1489—612no—
318#1488—612no—
319#1487—612no—
320#1479—611no—
321#1477—611no—
322#1476—611no—
323C2×Q8⋊C8—611no—
324C2×C61—22no—
325C2×C61C2×#40711yescharacteristic
326C2×C61#289811yescharacteristic
327C2×C61#290111yescharacteristic
328D61—42no—
329D61—42no—
330C2×2−1+4—611no—
331#520—611no—
332#520—612no—
333#520—611no—
334#520—1222no—
335#520—1221no—
336#519—612no—
337#519—1221no—
338#519#692311yescharacteristic
339C4×#41—611no—
340C4×#41—612no—
341C4×#41—611no—
342C4×#41—1222no—
343C4×#41—1221no—
344C2×C4×Q8—611no—
345C2×C4×Q8—612no—
346C2×C4×Q8—1221no—
347#446—1221no—
348#446—1221no—
349#436—1221no—
350#436—1221no—
351#435—1222no—
352#435—1222no—
353#432—612no—
354#431—611no—
355#431—612no—
356#431—611no—
357#423—612no—
358C2×C4⋊C8—611no—
359C4×M16—612no—
360C2×C4×C8—611no—
361Q8⋊C8—612no—
362Q8⋊C8—612no—
363Q8⋊C8—612no—
364Q8⋊C8—612no—
365Q8⋊C8—611no—
366Q8⋊C8—611no—
367Q8⋊C8—612no—
368D4⋊C8—611no—
369D4⋊C8—611no—
370D4⋊C8—612no—
371C61#1745411yescharacteristic, complemented, Sylow
3722−1+4—1224no—
3732−1+4—1224no—
374C2×#41—611no—
375C2×#41—612no—
376C2×#41—611no—
377C2×#41—1222no—
378C2×#41—1221no—
379C22×Q8—612no—
380C22×Q8—1221no—
381C22×Q8C2×#692311yescharacteristic
382C2×M16—1222no—
383C2×M16—1222no—
384C22×C8—1221no—
385C22×C8—1221no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8—611no—
389C4×Q8—611no—
390C4×Q8—612no—
391C4×Q8—612no—
392C4×Q8—611no—
393C4×Q8—611no—
394C4×Q8—612no—
395C4×Q8—1222no—
396C4×Q8—1222no—
397C4×Q8—1221no—
398C4×Q8—1222no—
399C4×Q8—1221no—
400C4×Q8—1221no—
401C4×Q8—1222no—
402C4×Q8C2×#692312yes—
403C4×Q8C2×#692312yes—
404C4×D4—611no—
405C4×D4—611no—
406C4×D4—612no—
407C4×D4—612no—
408C4×D4—611no—
409C4×D4—611no—
410C4×D4—612no—
411C4×D4—1222no—
412C4×D4—1222no—
413C4×D4—1221no—
414C4×D4—1221no—
415C4×D4—1221no—
416C4×D4—1222no—
417C4×D4—1222no—
418C4×D4—1222no—
419C4×D4—1222no—
420#117—22no—
421#117—612no—
422#117—612no—
423#117—1221no—
424#117—1222no—
425#117—1222no—
426#117—1222no—
427#117—1222no—
428#117—1221no—
429#117C2×#692311yescharacteristic
430#117C2×#692311yescharacteristic
431C2×C4⋊C4—611no—
432C2×C4⋊C4—612no—
433C2×C4⋊C4—1222no—
434C2×C4⋊C4—1222no—
435C2×C4⋊C4—1221no—
436C2×C4⋊C4—1221no—
437C2×C42—611no—
438C2×C42—612no—
439C2×C42—1222no—
440C2×C42—1221no—
441C2×C42—1222no—
442C2×C42—1221no—
443C4⋊C8—612no—
444C4⋊C8—611no—
445C4⋊C8—611no—
446C4⋊C8—1221no—
447C4⋊C8—1222no—
448C4⋊C8—1222no—
449C4⋊C8—1221no—
450C22⋊C8—1221no—
451C22⋊C8—1221no—
452C22⋊C8—1222no—
453C22⋊C8—1222no—
454#97—1222no—
455#97—1222no—
456C4×C8—611no—
457C4×C8—611no—
458C4×C8—612no—
459C4×C8—1221no—
460C4×C8—1221no—
461#41—614no—
462#41—12216no—
463#41—1224no—
464#41—1228no—
465#41—1224no—
466#41—1222no—
467#41—1222no—
468#41—1222no—
469C2×Q8—21no—
470C2×Q8—22no—
471C2×Q8—611no—
472C2×Q8—611no—
473C2×Q8—1222no—
474C2×Q8—1224no—
475C2×Q8—1228no—
476C2×Q8—1224no—
477C2×Q8#1175821314yescomplemented
478C2×Q8C22×#692312yes—
479C2×D4—612no—
480C2×D4—611no—
481C2×D4—611no—
482C2×D4—1222no—
483C2×D4—1221no—
484C22×C4—21no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—612no—
488C22×C4—612no—
489C22×C4—612no—
490C22×C4—1222no—
491C22×C4—1221no—
492C22×C4—1221no—
493C22×C4—1222no—
494C22×C4—1222no—
495C22×C4—1221no—
496C22×C4—1221no—
497C22×C4—1222no—
498C22×C4C22×#692311yescharacteristic
499M16—4882no—
500M16—2444no—
501C2×C8—1221no—
502C2×C8—1221no—
503C2×C8—1222no—
504C2×C8—1221no—
505C2×C8—1221no—
506C2×C8—1222no—
507C2×C8—4881no—
508C2×C8—2442no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—612no—
512C4⋊C4—612no—
513C4⋊C4—612no—
514C4⋊C4—1222no—
515C4⋊C4—1221no—
516C4⋊C4—1222no—
517C4⋊C4—1222no—
518C4⋊C4—1221no—
519C4⋊C4—1221no—
520C4⋊C4—1222no—
521C4⋊C4C22⋊#692311yescharacteristic
522C4⋊C4C22⋊#692311yescharacteristic
523C4⋊C4C22×#692311yescharacteristic
524C4⋊C4C22×#692311yescharacteristic
525C22⋊C4—21no—
526C22⋊C4—612no—
527C22⋊C4—612no—
528C22⋊C4—1221no—
529C22⋊C4—1221no—
530C22⋊C4—1222no—
531C22⋊C4—1222no—
532C22⋊C4C22⋊#692312yes—
533C42—22no—
534C42—22no—
535C42—21no—
536C42—611no—
537C42—611no—
538C42—612no—
539C42—612no—
540C42—611no—
541C42—611no—
542C42—1222no—
543C42—1221no—
544C42—1222no—
545C42—1222no—
546C42—1221no—
547C42—1222no—
548C42C22×#692312yes—
549C23—612no—
550C23—1221no—
551C23C2×C22⋊#692311yescharacteristic
552Q8—24no—
553Q8—22no—
554Q8—612no—
555Q8—1228no—
556Q8—1222no—
557Q8—1221no—
558Q8C2×#1175821314yes—
559D4—612no—
560D4—1228no—
561D4—1224no—
562D4—1224no—
563D4—1222no—
564D4—1221no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—611no—
570C2×C4—611no—
571C2×C4—611no—
572C2×C4—612no—
573C2×C4—611no—
574C2×C4—1222no—
575C2×C4—1222no—
576C2×C4—1228no—
577C2×C4—1228no—
578C2×C4—1221no—
579C2×C4—1221no—
580C2×C4—1221no—
581C2×C4—1224no—
582C2×C4—1222no—
583C2×C4—1222no—
584C2×C4—1222no—
585C2×C4—4882no—
586C2×C4—4881no—
587C2×C4—4882no—
588C2×C4—4881no—
589C2×C4—2442no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4C2×C22⋊#692312yes—
594C2×C4C2×C22⋊#692312yes—
595C2×C4C2×C22⋊#692311yescharacteristic
596C2×C4D61⋊M1612yes—
597C2×C4C2×#1175821312yes—
598C2×C4C23×#692311yescharacteristic
599C8—1222no—
600C8—2441no—
601C8—2442no—
602C8—2441no—
603C8—2441no—
604C8—2442no—
605C22—21no—
606C22—21no—
607C22—1222no—
608C22—1222no—
609C22—1222no—
610C22—1222no—
611C22—2441no—
612C22—2441no—
613C22#1684073312yes—
614C22C22×C22⋊#692311yescharacteristic
615C4—24no—
616C4—22no—
617C4—22no—
618C4—41no—
619C4—41no—
620C4—611no—
621C4—611no—
622C4—1222no—
623C4—1222no—
624C4—1221no—
625C4—1221no—
626C4—1221no—
627C4—2442no—
628C4#1684073312yes—
629C4C2×D61⋊M1611yescharacteristic
630C4C22×#1175821311yescharacteristic
631C2—22no—
632C2—2442no—
633C2—2442no—
634C2C2×#1684073311yescharacteristic
635C2#2146244111yescharacteristic
636C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#519C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519825C4
cosocleC4×Dic61C24
hypercenter#519#6923
hypocenterC61#17454
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
1. #21462740C2semidirect
2. #21462626C2semidirect
3. #21461162C2semidirect
4. #21461157C2semidirect
5. #21461153C2semidirect
6. #21461148C2semidirect
7. #21461121C2semidirect
8. #21461116C2semidirect
9. #21461112C2semidirect
10. C2×Q8⋊#92420C2semidirect
144. C2×Q8×C61M16semidirect
163. #11758222M16semidirect
371. C61#17454semidirect
477. C2×Q8#11758213semidirect

Maximal subgroups

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

subgroupindex
#214627402
#214626262
#214611622
#214611572
#214611532
#214611482
#214611212
#214611162
#214611122
C2×Q8⋊#924202
#214590282
#1745461