Finite Group Databasebeta

← #29607232

Subgroups — #29607232

Order 15616.

1542 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic122C211yesmaximal, characteristic
2C2×#16839629C211yesmaximal, characteristic
3C2×#16839626C211yesmaximal, characteristic
4#21444089C212yesmaximal
5#21444085C212yesmaximal
6#21444071C212yesmaximal
7#21444070C212yesmaximal
8#21444046C211yesmaximal, characteristic
9#21444043C211yesmaximal, characteristic
10#21444043C211yesmaximal, characteristic
11C61×#1434C211yesmaximal, characteristic
12C23×Dic122C2211yescharacteristic
13C2×C4×Dic122—24no—
14C2×C4×Dic122—24no—
15C2×C4×Dic122C418yescomplemented
16C22×C4⋊Dic61C2211yescharacteristic
17C22×#11758196C2211yescharacteristic
18C22×#11758196C2211yescharacteristic
19C22×#11758196C2212yes—
20C22×C4×Dic61C2211yescharacteristic
21C22×C4×Dic61C2211yescharacteristic
22#16839629—24no—
23#16839626—24no—
24C2×#14519684C2211yescharacteristic
25C2×#14519684C2212yes—
26C2×#14519684C2211yescharacteristic
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2212yes—
30C2×#14519684C2212yes—
31C2×#14519684C2212yes—
32C2×#14519684C2212yes—
33C2×#14519684C2212yes—
34C2×#14519684C2212yes—
35C22×C42×C61C2211yescharacteristic
36C2×#95×C61C2211yescharacteristic
37C2×#95×C61C2211yescharacteristic
38C2×#95×C61C2212yes—
39C2×#95×C61C2212yes—
40C22×Dic122—24no—
41C22×Dic122—22no—
42C22×Dic122—22no—
43C22×Dic122—24no—
44C22×Dic122C2×C414yes—
45C23×Dic61C2312yes—
46C23×Dic61C2312yes—
47C23×Dic61C2311yescharacteristic
48C23×Dic61C2311yescharacteristic
49C23×Dic61C2311yescharacteristic
50C23×Dic61C2311yescharacteristic
51C4×Dic122—232no—
52C2×C4⋊Dic61—22no—
53C2×C4⋊Dic61—22no—
54C2×C4⋊Dic61C2×C414yes—
55C2×#11758196—22no—
56C2×#11758196—22no—
57C2×#11758196—22no—
58C2×#11758196—22no—
59C2×#11758196—24no—
60C2×#11758196—42no—
61C2×#11758196—42no—
62C2×#11758196C2×C414yes—
63C2×#11758196C2×C414yes—
64C2×C4×Dic61—22no—
65C2×C4×Dic61—22no—
66C2×C4×Dic61C2×C414yes—
67C2×C4×Dic61C2×C414yes—
68C2×C4×Dic61D414yes—
69C2×C4×Dic61D414yes—
70#14519684—22no—
71#14519684—22no—
72#14519684—24no—
73#14519684—24no—
74#14519684—24no—
75#14519684—24no—
76#14519684—24no—
77#14519684—24no—
78#14519684—42no—
79#14519684—42no—
80#14519684—42no—
81C23×C4×C61C2312yes—
82C23×C4×C61C2312yes—
83C23×C4×C61C2311yescharacteristic
84C23×C4×C61C2311yescharacteristic
85C23×C4×C61C2311yescharacteristic
86C2×C42×C61—22no—
87C2×C42×C61—22no—
88C2×C42×C61C2×C414yes—
89#95×C61—22no—
90#95×C61—22no—
91#95×C61—24no—
92#95×C61—42no—
93C24×C61C2411yescharacteristic
94C22×C4×C61—21no—
95C22×C4×C61—21no—
96C22×C4×C61—22no—
97C22×C4×C61—22no—
98C22×C4×C61—22no—
99C22×C4×C61—21no—
100C22×C4×C61—21no—
101C22×C4×C61—21no—
102C22×C4×C61—21no—
103C22×C4×C61—21no—
104C22×C4×C61—21no—
105C22×C4×C61—22no—
106C22×C4×C61—22no—
107C22×C4×C61—22no—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—22no—
111C22×C4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61—22no—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61C22×C412yes—
120C22×C4×C61C22×C412yes—
121C22×C4×C61C22×C412yes—
122C22×C4×C61C2×D412yes—
123C22×C4×C61C2×D412yes—
124C22×C4×C61#4114yes—
125C22×Dic61—21no—
126C22×Dic61—21no—
127C22×Dic61—22no—
128C22×Dic61—22no—
129C22×Dic61—22no—
130C22×Dic61—21no—
131C22×Dic61—21no—
132C22×Dic61—21no—
133C22×Dic61—21no—
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61—21no—
138C22×Dic61—21no—
139C22×Dic61—21no—
140C22×Dic61—22no—
141C22×Dic61—22no—
142C22×Dic61—22no—
143C22×Dic61—22no—
144C22×Dic61—22no—
145C22×Dic61—22no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61—22no—
150C22×Dic61—22no—
151C22×Dic61—22no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61C22×C412yes—
155C22×Dic61C22×C412yes—
156C22×Dic61C22×C412yes—
157C22×Dic61C22×C412yes—
158C22×Dic61C2×D412yes—
159C22×Dic61C2×D412yes—
160C22×Dic61C2×D412yes—
161C22×Dic61C2×D412yes—
162C22×Dic61#4114yes—
163C2×Dic122—216no—
164C2×Dic122—216no—
165C2×Dic122—28no—
166C2×Dic122—28no—
167C2×Dic122—28no—
168C42×C61—28no—
169C4⋊Dic61—28no—
170#11758196—28no—
171#11758196—28no—
172#11758196—48no—
173C4×Dic61—28no—
174C4×Dic61C22⋊C4116yes—
175C23×C61C23×C411yescharacteristic
176C23×C61C22×D411yescharacteristic
177C23×C61C22×D411yescharacteristic
178C23×C61C2×#4112yes—
179C23×C61C2×#4112yes—
180C23×C61H(5,𝔽2)11yescharacteristic
181C23×C61H(5,𝔽2)11yescharacteristic
182C23×C612−1+412yes—
183C23×C612−1+412yes—
184C23×C612−1+411yescharacteristic
185C23×C612−1+411yescharacteristic
186C2×C4×C61—22no—
187C2×C4×C61—22no—
188C2×C4×C61—22no—
189C2×C4×C61—22no—
190C2×C4×C61—24no—
191C2×C4×C61—24no—
192C2×C4×C61—24no—
193C2×C4×C61—24no—
194C2×C4×C61—22no—
195C2×C4×C61—22no—
196C2×C4×C61—22no—
197C2×C4×C61—41no—
198C2×C4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61—41no—
201C2×C4×C61—42no—
202C2×C4×C61—42no—
203C2×C4×C61—42no—
204C2×C4×C61—42no—
205C2×C4×C61—42no—
206C2×C4×C61—42no—
207C2×C4×C61—42no—
208C2×C4×C61—42no—
209C2×C4×C61—42no—
210C2×C4×C61—42no—
211C2×C4×C61—42no—
212C2×C4×C61—42no—
213C2×C4×C61—42no—
214C2×C4×C61—42no—
215C2×C4×C61C2×C22⋊C414yes—
216C2×C4×C61#11714yes—
217C2×Dic61—22no—
218C2×Dic61—22no—
219C2×Dic61—22no—
220C2×Dic61—22no—
221C2×Dic61—22no—
222C2×Dic61—22no—
223C2×Dic61—24no—
224C2×Dic61—24no—
225C2×Dic61—24no—
226C2×Dic61—24no—
227C2×Dic61—22no—
228C2×Dic61—22no—
229C2×Dic61—22no—
230C2×Dic61—22no—
231C2×Dic61—22no—
232C2×Dic61—22no—
233C2×Dic61—22no—
234C2×Dic61—41no—
235C2×Dic61—41no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61—42no—
239C2×Dic61—42no—
240C2×Dic61—42no—
241C2×Dic61—42no—
242C2×Dic61—42no—
243C2×Dic61—42no—
244C2×Dic61—42no—
245C2×Dic61—42no—
246C2×Dic61—42no—
247C2×Dic61—42no—
248C2×Dic61—42no—
249C2×Dic61—42no—
250C2×Dic61—42no—
251C2×Dic61—42no—
252C2×Dic61C2×C22⋊C414yes—
253C2×Dic61C2×C22⋊C414yes—
254C2×Dic61#11714yes—
255Dic122—232no—
256#14346—611nomaximal, Sylow
257C22×C61C22×C22⋊C411yescharacteristic
258C22×C61C2×#11711yescharacteristic
259C22×C61C2×#11711yescharacteristic
260C22×C61#51911yescharacteristic
261C22×C61#51911yescharacteristic
262C22×C61#52011yescharacteristic
263C22×C61#52011yescharacteristic
264C22×C61#52512yes—
265C22×C61#52512yes—
266C22×C61#53511yescharacteristic
267C22×C61#53612yes—
268C22×C61#53612yes—
269C22×C61#53611yescharacteristic
270C22×C61#53711yescharacteristic
271C22×C61#53711yescharacteristic
272C22×C61#54112yes—
273C22×C61#54112yes—
274C22×C61#54112yes—
275C22×C61#54112yes—
276C22×C61#54212yes—
277C22×C61#54212yes—
278C22×C61#54212yes—
279C22×C61#54212yes—
280C4×C61—24no—
281C4×C61—24no—
282C4×C61—42no—
283C4×C61—82no—
284C4×C61—82no—
285Dic61—24no—
286Dic61—24no—
287Dic61—24no—
288Dic61—42no—
289Dic61—82no—
290Dic61—82no—
291C22×C4×Q8—611no—
292C2×#383—611no—
293C2×#382—611no—
294#1446—612no—
295#1445—612no—
296#1441—612no—
297#1441—612no—
298#1434—611no—
299#1434—611no—
300#1434—611no—
301#1434D6111yescharacteristic
302C2×C61#228011yescharacteristic
303C2×C61#231011yescharacteristic
304C2×C61#231111yescharacteristic
305C2×C61#232011yescharacteristic
306C2×C61#232011yescharacteristic
307C2×C61#232011yescharacteristic
308C2×C61#232011yescharacteristic
309C2×C61#263212yes—
310C2×C61#263412yes—
311C2×C61#263712yes—
312C2×C61#263712yes—
313C23×Q8—611no—
314C2×C4×Q8—618no—
315C2×C4×Q8—1224no—
316C2×C4×Q8—1224no—
317C22×C4⋊C4—611no—
318C22×C4⋊C4—611no—
319C22×C4⋊C4—611no—
320C22×C4⋊C4—612no—
321C22×C42—611no—
322C22×C42—611no—
323C22×C42C2×D6111yescharacteristic
324#383—1224no—
325#382—1224no—
326C2×#95—611no—
327C2×#95—611no—
328C2×#95—612no—
329C2×#95—612no—
330C2×#95—612no—
331C2×#95—612no—
332C2×#95—612no—
333C2×#95—612no—
334C2×#95—612no—
335C2×#95—612no—
336C2×#95—612no—
337C2×#95C2×D6111yescharacteristic
338C2×#95C2×D6111yescharacteristic
339C2×#95C2×D6112yes—
340C2×#95C2×D6112yes—
341C61#1434611yescharacteristic, complemented, Sylow
342C22×Q8—614no—
343C22×Q8—1222no—
344C22×Q8—1222no—
345C22×Q8—1224no—
346C22×Q8—1224no—
347C23×C4—611no—
348C23×C4—611no—
349C23×C4—611no—
350C23×C4—611no—
351C23×C4—612no—
352C23×C4—612no—
353C23×C4C22×D6112yes—
354C23×C4C22×D6112yes—
355C23×C4C22×D6111yescharacteristic
356C23×C4C22×D6111yescharacteristic
357C23×C4C22×D6111yescharacteristic
358C4×Q8—12232no—
359C2×C4⋊C4—614no—
360C2×C4⋊C4—614no—
361C2×C4⋊C4—614no—
362C2×C4⋊C4—1222no—
363C2×C4⋊C4—1222no—
364C2×C4⋊C4—1222no—
365C2×C4⋊C4—1222no—
366C2×C4⋊C4—1222no—
367C2×C4⋊C4—1222no—
368C2×C4⋊C4—1224no—
369C2×C4⋊C4—2442no—
370C2×C4⋊C4—2442no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—614no—
374C2×C42—614no—
375C2×C42—614no—
376C2×C42—614no—
377C2×C42—1222no—
378C2×C42—1222no—
379C2×C42C4×D6114yes—
380#95—24no—
381#95—22no—
382#95—22no—
383#95—42no—
384#95—1224no—
385#95—1224no—
386#95—1224no—
387#95—1224no—
388#95—1224no—
389#95—1224no—
390#95—1222no—
391#95—1222no—
392#95—2442no—
393#95—2442no—
394#95—2442no—
395C24C23×D6111yescharacteristic
396C2×Q8—1228no—
397C2×Q8—1228no—
398C2×Q8—12216no—
399C2×Q8—12216no—
400C2×Q8—1228no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—612no—
427C22×C4—612no—
428C22×C4—612no—
429C22×C4—612no—
430C22×C4—612no—
431C22×C4—612no—
432C22×C4—612no—
433C22×C4—614no—
434C22×C4—612no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4—1222no—
438C22×C4—1222no—
439C22×C4—1222no—
440C22×C4—1221no—
441C22×C4—1221no—
442C22×C4—1221no—
443C22×C4—1221no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4—1221no—
447C22×C4—1221no—
448C22×C4—1221no—
449C22×C4—1221no—
450C22×C4—1222no—
451C22×C4—1222no—
452C22×C4—1222no—
453C22×C4—1222no—
454C22×C4—1222no—
455C22×C4—1222no—
456C22×C4—1222no—
457C22×C4—1222no—
458C22×C4—1222no—
459C22×C4—1222no—
460C22×C4—1222no—
461C22×C4—1222no—
462C22×C4—1222no—
463C22×C4—1222no—
464C22×C4C2×C4×D6112yes—
465C22×C4C2×C4×D6112yes—
466C22×C4C2×C4×D6112yes—
467C22×C4#1175822214yes—
468C22×C4D4×D6112yes—
469C22×C4D4×D6112yes—
470C4⋊C4—1228no—
471C4⋊C4—1228no—
472C4⋊C4—1228no—
473C4⋊C4—2448no—
474C42—28no—
475C42—6116no—
476C42—1228no—
477C23C22×C4×D6111yescharacteristic
478C23C2×D4×D6111yescharacteristic
479C23C2×D4×D6111yescharacteristic
480C23#41×D6112yes—
481C23C2×#1175822212yes—
482C23#1451982211yescharacteristic
483C23#1451982311yescharacteristic
484C23#1451982412yes—
485C23#1451982412yes—
486C23#1451982411yescharacteristic
487C23#1451982511yescharacteristic
488Q8—12232no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—614no—
519C2×C4—614no—
520C2×C4—614no—
521C2×C4—1222no—
522C2×C4—1222no—
523C2×C4—1222no—
524C2×C4—1222no—
525C2×C4—1222no—
526C2×C4—1222no—
527C2×C4—1224no—
528C2×C4—1224no—
529C2×C4—1224no—
530C2×C4—1224no—
531C2×C4—1222no—
532C2×C4—1222no—
533C2×C4—1222no—
534C2×C4—1222no—
535C2×C4—1222no—
536C2×C4—1222no—
537C2×C4—1222no—
538C2×C4—2442no—
539C2×C4—2442no—
540C2×C4—2442no—
541C2×C4—2442no—
542C2×C4—2442no—
543C2×C4—2442no—
544C2×C4—2442no—
545C2×C4—2442no—
546C2×C4—2442no—
547C2×C4—2442no—
548C2×C4—2442no—
549C2×C4—2442no—
550C2×C4—2442no—
551C2×C4—2442no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4C22⋊C4×D6114yes—
557C2×C4#1451973414yes—
558C22C2×C22⋊C4×D6111yescharacteristic
559C22#117×D6111yescharacteristic
560C22C2×#1451973411yescharacteristic
561C22#1684023911yescharacteristic
562C22#1684023911yescharacteristic
563C22#1684024211yescharacteristic
564C22#1684024311yescharacteristic
565C22#1684027112yes—
566C22#1684027112yes—
567C22#1684032811yescharacteristic
568C22#1684033412yes—
569C22#1684033412yes—
570C22#1684033511yescharacteristic
571C22#1684034111yescharacteristic
572C22#1684034211yescharacteristic
573C22#1684036912yes—
574C22#1684037012yes—
575C22#1684037112yes—
576C22#1684037412yes—
577C22#1684037612yes—
578C22#1684037712yes—
579C22#1684037812yes—
580C22#1684038312yes—
581C4—24no—
582C4—24no—
583C4—42no—
584C4—82no—
585C4—82no—
586C4—1224no—
587C4—1224no—
588C4—1224no—
589C4—4882no—
590C4—4882no—
591C4—2442no—
592C2#2144820011yescharacteristic
593C2#2144840411yescharacteristic
594C2#2144840811yescharacteristic
595C2#2144846511yescharacteristic
596C2#2144846711yescharacteristic
597C2#2144846911yescharacteristic
598C2#2144847111yescharacteristic
599C2#2145168312yes—
600C2#2145169912yes—
601C2#2145173112yes—
602C2#2145173312yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1434C2
socle, prime radical, cosocleC24×C61C24
hypercenter#1434D61
hypocenterC61#14346
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
15. C2×C4×Dic122C4semidirect
341. C61#14346semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic1222
C2×#168396292
C2×#168396262
#214440892
#214440852
#214440712
#214440702
#214440462
#214440432
C61×#14342
#1434661