Finite Group Databasebeta

← #29718993

Subgroups — #29718993

Order 15616.

1280 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519698C211yesmaximal, characteristic, complemented
2#21450291C211yesmaximal, characteristic, complemented
3D4×C22⋊Dic61C211yesmaximal, characteristic, complemented
4#21447225C212yesmaximal, complemented
5#21447127C212yesmaximal, complemented
6#21446248C211yesmaximal, characteristic, complemented
7#21446169C212yesmaximal, complemented
8#21445996C211yesmaximal, characteristic, complemented
9#21445906C211yesmaximal, characteristic, complemented
10#21445817C212yesmaximal, complemented
11C2×C61×#447C211yesmaximal, characteristic
12C23×#92418C2211yescharacteristic
13C2×#14519758—21no—
14C2×#14519758—21no—
15C2×D4×Dic61C2212yes—
16C22×C4⋊Dic61C2211yescharacteristic
17C22×C22⋊Dic61—21no—
18C2×#14519706C2212yescomplemented
19C2×#14519698—24no—
20C2×#14519698C2212yes—
21C2×#14519698C2212yes—
22C2×#14519698C2212yescomplemented
23#16839698—22no—
24#16839665C2212yes—
25#16839665C2212yescomplemented
26#16839642—22no—
27#16839631C2212yescomplemented
28#16839622C2211yescharacteristic
29#16839618—21no—
30C4×C22⋊Dic61C2211yescharacteristic
31#16839525C2212yescomplemented
32#16839525C2212yescomplemented
33#16839524C2212yescomplemented
34#16839516C2212yescomplemented
35C23×D4×C61C2211yescharacteristic
36C22×D8×C61C2211yescharacteristic
37C22×D8×C61C2211yescharacteristic
38C2×#121×C61C2211yescharacteristic
39C61×#447—24no—
40C2×#102×C61C2211yescharacteristic
41C2×#102×C61C2211yescharacteristic
42C2×C22⋊C8×C61C2211yescharacteristic
43C23×Dic61—21no—
44C23×Dic61—22no—
45C22×#92418—22no—
46C22×#92418—42no—
47C22×#92418C2312yes—
48#14519758—44no—
49#14519758—44no—
50D4×Dic61—24no—
51D4×Dic61—42no—
52C2×C4⋊Dic61—22no—
53C2×C4⋊Dic61—22no—
54C2×C4⋊Dic61—21no—
55C2×C4⋊Dic61C2312yes—
56C2×C4⋊Dic61C2312yes—
57C2×#11758196—22no—
58C2×#11758196—22no—
59C2×C22⋊Dic61—21no—
60C2×C22⋊Dic61—22no—
61C2×C22⋊Dic61—22no—
62C2×C22⋊Dic61—22no—
63C2×C22⋊Dic61—22no—
64C2×C22⋊Dic61—22no—
65C2×C22⋊Dic61—44no—
66C2×C22⋊Dic61D411yescharacteristic
67C2×C22⋊Dic61D411yescharacteristic
68C2×C4×Dic61C2312yes—
69#14519706—42no—
70#14519698—24no—
71#14519698—24no—
72#14519698—42no—
73#14519684—21no—
74#14519684D412yes—
75C25×C61—21no—
76C22×D4×C61—24no—
77C22×D4×C61—21no—
78C22×D4×C61—21no—
79C22×D4×C61—22no—
80C22×D4×C61—42no—
81C22×D4×C61D414yes—
82C22×D4×C61C2311yescharacteristic
83C22×D4×C61C2311yescharacteristic
84C22×D4×C61C2311yescharacteristic
85C23×C4×C61C2311yescharacteristic
86C2×D8×C61—22no—
87C2×D8×C61—22no—
88C2×D8×C61—24no—
89C2×D8×C61—42no—
90C22×C8×C61C2311yescharacteristic
91C22×C8×C61C2311yescharacteristic
92#121×C61—22no—
93#121×C61—22no—
94C2×C4⋊C4×C61C2311yescharacteristic
95C2×C22⋊C4×C61—21no—
96#102×C61—22no—
97#102×C61—22no—
98C22⋊C8×C61—22no—
99C24×C61—21no—
100C24×C61—21no—
101C24×C61—24no—
102C24×C61—21no—
103C24×C61—44no—
104C24×C61—42no—
105C24×C61—42no—
106C24×C61—82no—
107C24×C61C2×D411yescharacteristic
108C2×D4×C61—28no—
109C2×D4×C61—24no—
110C2×D4×C61—21no—
111C2×D4×C61—21no—
112C2×D4×C61—22no—
113C2×D4×C61—21no—
114C2×D4×C61—21no—
115C2×D4×C61—22no—
116C2×D4×C61—22no—
117C2×D4×C61—22no—
118C2×D4×C61—22no—
119C2×D4×C61—44no—
120C2×D4×C61—48no—
121C2×D4×C61—44no—
122C2×D4×C61—42no—
123C2×D4×C61—42no—
124C2×D4×C61—42no—
125C2×D4×C61C2×D412yes—
126C2×D4×C61C2×D412yes—
127C2×D4×C61#4114yes—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—21no—
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D412yes—
133C22×C4×C61#4112yes—
134C22×C4×C61C2411yescharacteristic
135C22×Dic61—22no—
136C22×Dic61—22no—
137C22×Dic61—44no—
138C22×Dic61—42no—
139C22×Dic61—42no—
140C22×Dic61—42no—
141C22×Dic61—44no—
142C22×Dic61—82no—
143C22×Dic61C2×D412yes—
144C22×Dic61C2×D412yes—
145D8×C61—44no—
146D8×C61—44no—
147C2×C8×C61—21no—
148C2×C8×C61—21no—
149C2×C8×C61—22no—
150C2×C8×C61—22no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C22⋊C4×C61—42no—
154C22⋊Dic61—22no—
155C22⋊Dic61—44no—
156C22⋊Dic61—44no—
157C22⋊Dic61—42no—
158C22⋊Dic61—44no—
159C22⋊Dic61—44no—
160C22⋊Dic61—82no—
161C22⋊Dic61D814yescomplemented
162C4⋊Dic61—22no—
163C4⋊Dic61—22no—
164C4⋊Dic61—22no—
165C4⋊Dic61—22no—
166C4⋊Dic61—42no—
167#11758196—44no—
168#11758196—44no—
169C4×Dic61—22no—
170C4×Dic61—22no—
171C2×#92418—22no—
172C2×#92418—22no—
173C2×#92418—22no—
174C2×#92418—44no—
175C23×C61—22no—
176C23×C61—22no—
177C23×C61—22no—
178C23×C61—24no—
179C23×C61—22no—
180C23×C61—48no—
181C23×C61—41no—
182C23×C61—41no—
183C23×C61—42no—
184C23×C61—42no—
185C23×C61—41no—
186C23×C61—41no—
187C23×C61—42no—
188C23×C61—48no—
189C23×C61—41no—
190C23×C61—42no—
191C23×C61—41no—
192C23×C61—41no—
193C23×C61—42no—
194C23×C61—84no—
195C23×C61—88no—
196C23×C61—88no—
197C23×C61#12112yes—
198C23×C61C2×D812yes—
199C23×C61AGL(1,ℤ/8)12yes—
200C23×C61C22×D411yescharacteristic
201D4×C61—22no—
202D4×C61—22no—
203D4×C61—22no—
204D4×C61—24no—
205D4×C61—48no—
206D4×C61—41no—
207D4×C61—41no—
208D4×C61—42no—
209D4×C61—42no—
210D4×C61—84no—
211D4×C61#12314yescomplemented
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—22no—
215C2×C4×C61—24no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61#12112yes—
220C2×C4×C61C22×D411yescharacteristic
221C2×C4×C61C2×#4112yes—
222C2×C4×C61C2×#4111yescharacteristic
223C2×C4×C61H(5,𝔽2)12yes—
224C2×Dic61—22no—
225C2×Dic61—22no—
226C2×Dic61—22no—
227C2×Dic61—22no—
228C2×Dic61—22no—
229C2×Dic61—42no—
230C2×Dic61—42no—
231C2×Dic61—42no—
232C2×Dic61—42no—
233C2×Dic61—42no—
234C2×Dic61—42no—
235C2×Dic61—88no—
236C2×Dic61—84no—
237C2×Dic61C2×D814yes—
238C8×C61—41no—
239C8×C61—41no—
240#92418—42no—
241#24526—611nomaximal, Sylow
242C22×C61—22no—
243C22×C61—24no—
244C22×C61—22no—
245C22×C61—24no—
246C22×C61—24no—
247C22×C61—42no—
248C22×C61—44no—
249C22×C61—42no—
250C22×C61—44no—
251C22×C61—42no—
252C22×C61—42no—
253C22×C61—42no—
254C22×C61—816no—
255C22×C61—82no—
256C22×C61—82no—
257C22×C61—81no—
258C22×C61—81no—
259C22×C61—82no—
260C22×C61—81no—
261C22×C61—82no—
262C22×C61#45914yes—
263C22×C61C2×#12111yescharacteristic
264C22×C61#54612yes—
265C22×C61C22×D811yescharacteristic
266C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
267C22×C61#57712yes—
268C4×C61—22no—
269C4×C61—81no—
270C4×C61C2×#12311yescharacteristic
271C4×C61#53411yescharacteristic
272C4×C61#55112yes—
273Dic61—24no—
274Dic61—42no—
275Dic61—82no—
276Dic61—82no—
277C2×#447D6111yescharacteristic
278C22×#102—611no—
279#2501—611no—
280D4×C22⋊C4—611no—
281#2071—612no—
282#2054—612no—
283#1893—611no—
284#1879—612no—
285#1850—611no—
286#1823—611no—
287#1802—612no—
288C2×C61—24no—
289C2×C61—44no—
290C2×C61—82no—
291C2×C61—161no—
292C2×C61#241211yescharacteristic
293C2×C61C2×#45911yescharacteristic
294C2×C61#304211yescharacteristic
295C2×C61#329412yes—
296C2×C61#330612yes—
297C23×D4C2×D6111yescharacteristic
298C22×D8C2×D6111yescharacteristic
299C22×D8C2×D6111yescharacteristic
300C23×C8—611no—
301C2×#123—1221no—
302C2×#123—1221no—
303C2×#121C2×D6111yescharacteristic
304C2×C4×D4—612no—
305C22×C4⋊C4—611no—
306C22×C22⋊C4—1221no—
307#447—24no—
308C2×C4⋊C8—612no—
309C2×#102—612no—
310C2×#102—612no—
311C2×#102—612no—
312C2×#102—1224no—
313C2×#102C2×D6111yescharacteristic
314C2×#102C2×D6111yescharacteristic
315C2×C22⋊C8C2×D6111yescharacteristic
316#399—1222no—
317#390—612no—
318#390—612no—
319#386—1222no—
320#384—612no—
321#380—611no—
322#379—1221no—
323C4×C22⋊C4—611no—
324#340—612no—
325#340—612no—
326#340—612no—
327#336—612no—
328C61#2452611yescharacteristic, complemented, Sylow
329C25—21no—
330C22×D4—24no—
331C22×D4—21no—
332C22×D4—21no—
333C22×D4—22no—
334C22×D4—42no—
335C22×D4C22⋊D6114yes—
336C22×D4C22×D6111yescharacteristic
337C22×D4C22×D6111yescharacteristic
338C22×D4C22×D6111yescharacteristic
339C23×C4—1222no—
340C23×C4—1221no—
341C23×C4C22×D6111yescharacteristic
342C2×D8—24no—
343C2×D8—22no—
344C2×D8—22no—
345C2×D8—42no—
346C22×C8—612no—
347C22×C8—1222no—
348C22×C8—2442no—
349C22×C8C22×D6111yescharacteristic
350C22×C8C22×D6111yescharacteristic
351#123—2444no—
352#123—2444no—
353#121—22no—
354#121—22no—
355C4×D4—1224no—
356C4×D4—2442no—
357C2×C4⋊C4—612no—
358C2×C4⋊C4—612no—
359C2×C4⋊C4—1222no—
360C2×C4⋊C4—1222no—
361C2×C4⋊C4—1222no—
362C2×C4⋊C4—1222no—
363C2×C4⋊C4—1221no—
364C2×C4⋊C4C22×D6111yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—611no—
367C2×C22⋊C4—611no—
368C2×C22⋊C4—1222no—
369C2×C22⋊C4—1222no—
370C2×C22⋊C4—1222no—
371C2×C22⋊C4—1222no—
372C2×C22⋊C4—1222no—
373C2×C22⋊C4—1221no—
374C2×C22⋊C4—2444no—
375C2×C42—612no—
376C4⋊C8—2442no—
377#102—22no—
378#102—22no—
379#102—1224no—
380#102—1224no—
381#102—2442no—
382C22⋊C8—22no—
383#95—612no—
384#95—1221no—
385C24—21no—
386C24—21no—
387C24—24no—
388C24—21no—
389C24—44no—
390C24—42no—
391C24—42no—
392C24—82no—
393C24D4×D6111yescharacteristic
394C2×D4—28no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—22no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—24no—
405C2×D4—44no—
406C2×D4—48no—
407C2×D4—44no—
408C2×D4—42no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4#1175822414yes—
412C2×D4C2×C22⋊D6112yes—
413C2×D4C2×C22⋊D6112yes—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—612no—
418C22×C4—612no—
419C22×C4—1222no—
420C22×C4—1222no—
421C22×C4—4882no—
422C22×C4—2444no—
423C22×C4—2444no—
424C22×C4—2442no—
425C22×C4—2442no—
426C22×C4—2442no—
427C22×C4D4×D6111yescharacteristic
428C22×C4#1175822412yes—
429C22×C4C2×C22⋊D6112yes—
430C22×C4C23×D6111yescharacteristic
431D8—44no—
432D8—44no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—1222no—
438C2×C8—1222no—
439C2×C8—1222no—
440C2×C8—2444no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—1222no—
444C4⋊C4—1222no—
445C4⋊C4—1222no—
446C4⋊C4—1222no—
447C4⋊C4—2444no—
448C4⋊C4—2444no—
449C4⋊C4—2442no—
450C22⋊C4—42no—
451C22⋊C4—614no—
452C22⋊C4—1222no—
453C22⋊C4—4882no—
454C22⋊C4—2444no—
455C22⋊C4—2444no—
456C22⋊C4—2444no—
457C22⋊C4—2444no—
458C22⋊C4—2442no—
459C42—1222no—
460C42—1222no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23—24no—
465C23—22no—
466C23—48no—
467C23—41no—
468C23—41no—
469C23—42no—
470C23—48no—
471C23—41no—
472C23—41no—
473C23—42no—
474C23—42no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—42no—
479C23—42no—
480C23—84no—
481C23—88no—
482C23—88no—
483C23#1451974912yes—
484C23D8×D6112yes—
485C23#1451980112yes—
486C23C2×D4×D6111yescharacteristic
487D4—22no—
488D4—22no—
489D4—22no—
490D4—24no—
491D4—48no—
492D4—41no—
493D4—41no—
494D4—42no—
495D4—42no—
496D4—84no—
497D4#1451975814yescomplemented
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—614no—
506C2×C4—1222no—
507C2×C4—1222no—
508C2×C4—1222no—
509C2×C4—1222no—
510C2×C4—1222no—
511C2×C4—4888no—
512C2×C4—4884no—
513C2×C4—2442no—
514C2×C4—2442no—
515C2×C4—2442no—
516C2×C4—2442no—
517C2×C4—2442no—
518C2×C4—2442no—
519C2×C4#1451974912yes—
520C2×C4C22×C22⋊D6111yescharacteristic
521C2×C4C2×#1175822412yes—
522C2×C4C2×#1175822411yescharacteristic
523C2×C4#1451982212yes—
524C8—41no—
525C8—41no—
526C8—2442no—
527C22—22no—
528C22—24no—
529C22—24no—
530C22—22no—
531C22—24no—
532C22—44no—
533C22—42no—
534C22—44no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—816no—
540C22—82no—
541C22—82no—
542C22—81no—
543C22—82no—
544C22—81no—
545C22—82no—
546C22—81no—
547C22#1683995514yes—
548C22C2×#1451974911yescharacteristic
549C22#1684039912yes—
550C22C2×D8×D6111yescharacteristic
551C22C2×#1451980111yescharacteristic
552C22#1684057212yes—
553C4—22no—
554C4—81no—
555C4—1224no—
556C4—4882no—
557C4—4882no—
558C4—2442no—
559C4C2×#1451975811yescharacteristic
560C4#1684032111yescharacteristic
561C4#1684044312yes—
562C2—24no—
563C2—44no—
564C2—82no—
565C2—161no—
566C2#2144921611yescharacteristic
567C2C2×#1683995511yescharacteristic
568C2#2145533311yescharacteristic
569C2#2145762512yes—
570C2#2145778412yes—
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#447C2
socleC23×C61C22×D4
hypercenterC2×#447D61
hypocenterC61#24526
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C22×#14519698C2semidirect
2. #21450291C2semidirect
3. D4×C22⋊Dic61C2semidirect
4. #21447225C2semidirect
5. #21447127C2semidirect
6. #21446248C2semidirect
7. #21446169C2semidirect
8. #21445996C2semidirect
9. #21445906C2semidirect
10. #21445817C2semidirect
18. C2×#14519706C22semidirect
22. C2×#14519698C22semidirect
25. #16839665C22semidirect
27. #16839631C22semidirect
31. #16839525C22semidirect
32. #16839525C22semidirect
33. #16839524C22semidirect
34. #16839516C22semidirect
161. C22⋊Dic61D8semidirect
211. D4×C61#123semidirect
328. C61#24526semidirect
497. D4#14519758semidirect

Maximal subgroups

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

subgroupindex
C22×#145196982
#214502912
D4×C22⋊Dic612
#214472252
#214471272
#214462482
#214461692
#214459962
#214459062
#214458172
C2×C61×#4472
#2452661