Finite Group Databasebeta

← #29834935

Subgroups — #29834935

Order 15616.

654 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456395C211yesmaximal, characteristic, complemented
2C4×D8×D61C211yesmaximal, characteristic, complemented
3#21448001C211yesmaximal, characteristic, complemented
4#21447998C211yesmaximal, characteristic, complemented
5#21447955C211yesmaximal, characteristic, complemented
6#21447954C211yesmaximal, characteristic, complemented
7#21447853C211yesmaximal, characteristic, complemented
8#21447852C211yesmaximal, characteristic, complemented
9#21447732C211yesmaximal, characteristic, complemented
10#21447729C211yesmaximal, characteristic, complemented
11C4×D976C211yesmaximal, characteristic, complemented
12C4×#14519718C211yesmaximal, characteristic, complemented
13C4×#14519718C211yesmaximal, characteristic, complemented
14#21447616C211yesmaximal, characteristic, complemented
15C4×D16×C61C211yesmaximal, characteristic, complemented
16C2×D8×D61C2211yescharacteristic
17#16840309—21no—
18C4×D4×D61—21no—
19C2×D976C2211yescharacteristic
20C2×#14519718C2211yescharacteristic
21C2×#14519718C2211yescharacteristic
22#16840166C2211yescharacteristic, complemented
23#16840137C2211yescharacteristic, complemented
24#16840107—21no—
25#16839999C2211yescharacteristic
26#16839997—21no—
27#16839995C2211yescharacteristic
28C4×D488C2211yescharacteristic
29C4×D488C2211yescharacteristic, complemented
30D8×Dic61C2211yescharacteristic
31#16839844C2211yescharacteristic
32C4×#11758199—21no—
33C4×#11758199—21no—
34#16839842—21no—
35#107×D61C2211yescharacteristic
36#102×D61—21no—
37C4×C8×D61C2211yescharacteristic
38#16839588C2211yescharacteristic, complemented
39#16839587C2211yescharacteristic, complemented
40#16839587C2211yescharacteristic, complemented
41#16839580C2211yescharacteristic, complemented
42#16839580C2211yescharacteristic, complemented
43#16839564C2211yescharacteristic
44#16839564C2211yescharacteristic, complemented
45#16839563C2211yescharacteristic
46#16839563C2211yescharacteristic, complemented
47#16839562C2211yescharacteristic
48#16839562C2211yescharacteristic, complemented
49#16839541C2211yescharacteristic
50#16839541C2211yescharacteristic
51C4×#11758185C2211yescharacteristic, complemented
52C2×D16×C61C2211yescharacteristic
53C4×D8×C61C2211yescharacteristic
54C4×D8×C61C2211yescharacteristic, complemented
55C61×#366C2211yescharacteristic, complemented
56C61×#357C2211yescharacteristic
57C61×#357C2211yescharacteristic, complemented
58C4×C16×C61C2211yescharacteristic, complemented
59C2×#11758222—41no—
60C2×D4×D61—21no—
61C22×C4×D61—41no—
62C2×D488C2311yescharacteristic
63C2×D488C2311yescharacteristic
64C2×#11758199—21no—
65C2×#11758199—21no—
66D8×D61—22no—
67D8×D61—22no—
68C2×C8×D61D411yescharacteristic
69C2×C8×D61C2311yescharacteristic
70#14519776—21no—
71#14519773—21no—
72#14519763—41no—
73#14519752—21no—
74#14519750—41no—
75#14519748—21no—
76C4×D244—21no—
77C4×D244—21no—
78D4×Dic61—21no—
79#14519739—21no—
80C4×C22⋊D61—41no—
81C4×C22⋊D61—41no—
82#14519737—41no—
83C4⋊C4×D61—21no—
84C22⋊C4×D61—41no—
85C42×D61D411yescharacteristic
86D976—22no—
87#14519718—22no—
88#14519718—22no—
89C2×#11758185C2311yescharacteristic
90C2×#11758185C2311yescharacteristic
91#14519711C2311yescharacteristic
92#14519711C2311yescharacteristic
93#14519710—21no—
94#14519710—21no—
95#14519699—21no—
96#14519699—21no—
97#14519698—21no—
98#14519698—21no—
99#14519697—21no—
100#14519697—21no—
101C4×#92418D411yescharacteristic
102C8×Dic61D411yescharacteristic
103C8×Dic61C2311yescharacteristic
104C2×D8×C61C2311yescharacteristic
105C2×D8×C61C2311yescharacteristic
106C4×D4×C61—21no—
107C4×D4×C61—21no—
108D16×C61—22no—
109C2×C16×C61C2311yescharacteristic
110C2×C16×C61C2311yescharacteristic
111#107×C61C2311yescharacteristic
112#107×C61C2311yescharacteristic
113#102×C61—21no—
114#102×C61—21no—
115C4×C8×C61C2311yescharacteristic
116C23×D61—41no—
117C2×D4×C61—21no—
118C2×D4×C61—21no—
119C22×C4×C61—41no—
120C22×C4×C61—41no—
121C2×C22⋊D61—41no—
122C2×C22⋊D61—41no—
123C2×C22⋊D61—41no—
124C2×C22⋊D61—41no—
125C22×Dic61—41no—
126D4×D61—24no—
127D4×D61—42no—
128#11758222—84no—
129C2×D244—21no—
130C2×D244—21no—
131C2×D244—41no—
132C2×C4×D61—41no—
133C2×C4×D61—41no—
134C2×C4×D61—41no—
135C2×C4×D61—41no—
136C2×C4×D61—84no—
137C2×C4×D61D811yescharacteristic
138C2×C4×D61D811yescharacteristic
139C2×C4×D61C2×D411yescharacteristic
140C2×Dic122—41no—
141D8×C61—21no—
142D8×C61—21no—
143D8×C61—21no—
144D8×C61#4112yescomplemented
145C2×C8×C61C2×D411yescharacteristic
146C2×C8×C61C2411yescharacteristic
147C4⋊C4×C61—21no—
148C4⋊C4×C61—21no—
149C22⋊C4×C61—41no—
150C22⋊C4×C61—41no—
151C42×C61C2×D411yescharacteristic
152C22⋊Dic61—41no—
153C22⋊Dic61—41no—
154#11758199—24no—
155#11758199—42no—
156#11758198—41no—
157#11758198—41no—
158#11758198—41no—
159#11758198—41no—
160C4⋊Dic61—21no—
161C4⋊Dic61—21no—
162#11758196—41no—
163#11758196—41no—
164C4×Dic61D811yescharacteristic
165C4×Dic61D811yescharacteristic
166C4×Dic61C2×D411yescharacteristic
167C2×#92418C2×D411yescharacteristic
168C2×#92418C2×D411yescharacteristic
169D488—21no—
170D488—21no—
171D488—21no—
172D488#4112yescomplemented
173C8×D61—21no—
174C8×D61—21no—
175C8×D61—41no—
176C16×C61—21no—
177C16×C61—21no—
178#11758185—21no—
179#11758185—21no—
180C23×C61—41no—
181C23×C61—41no—
182C22×D61—44no—
183C22×D61—41no—
184C22×D61—41no—
185C22×D61—82no—
186C22×D61—82no—
187C22×D61C2×D811yescharacteristic
188D4×C61—22no—
189D4×C61—41no—
190D4×C61—41no—
191D4×C61—41no—
192C2×C4×C61—41no—
193C2×C4×C61—41no—
194C2×C4×C61—82no—
195C2×C4×C61—82no—
196C2×C4×C61C2×D811yescharacteristic
197C2×C4×C61C2×D811yescharacteristic
198C2×C4×C61C22×D411yescharacteristic
199C22⋊D61—44no—
200C22⋊D61—82no—
201C22⋊D61—82no—
202C22⋊D61—82no—
203C2×Dic61—41no—
204C2×Dic61—41no—
205C2×Dic61—82no—
206C2×Dic61C2×D811yescharacteristic
207C2×Dic61C2×D811yescharacteristic
208C2×Dic61C2×D811yescharacteristic
209D244—22no—
210D244—41no—
211D244—41no—
212D244—41no—
213D244—82no—
214C4×D61—21no—
215C4×D61—21no—
216C4×D61—41no—
217C4×D61—82no—
218C4×D61—82no—
219C4×D61—82no—
220C4×D61—82no—
221C4×D61D1614yescomplemented
222Dic122—82no—
223C8×C61—21no—
224C8×C61C2×#4111yescharacteristic
225C8×C61C2×#4111yescharacteristic
226#92418—21no—
227#92418—21no—
228#33660—611nomaximal, Sylow
229C22×C61—42no—
230C22×C61—81no—
231C22×C61—81no—
232C22×C61—81no—
233C22×C61—81no—
234C22×C61—81no—
235C22×C61C22×D811yescharacteristic
236C2×D61—21no—
237C2×D61—21no—
238C2×D61—42no—
239C2×D61—88no—
240C2×D61—81no—
241C2×D61—81no—
242C2×D61—81no—
243C2×D61—81no—
244C2×D61—81no—
245C2×D61C2×D1612yes—
246C4×C61—21no—
247C4×C61—81no—
248C4×C61—81no—
249C4×C61C2×D1612yes—
250C4×C61#52511yescharacteristic
251C4×C61#57511yescharacteristic
252Dic61—21no—
253Dic61—21no—
254Dic61—81no—
255Dic61—81no—
256Dic61C2×D1612yes—
257#3169—611no—
258C2×C4×D8—611no—
259#2232—611no—
260#2232—611no—
261#2224—611no—
262#2224—611no—
263#2206—611no—
264#2206—611no—
265#2184—611no—
266#2184—611no—
267C4×D16—611no—
268C4×D16—611no—
269C4×D16—611no—
270C4×D16D6111yescharacteristic, complemented
271#2162—611no—
272C2×C61—82no—
273C2×C61—161no—
274C2×C61#310011yescharacteristic
275C2×C61C22×D1611yescharacteristic
276C2×C61#341411yescharacteristic
277D61—22no—
278D61—82no—
279D61—161no—
280C22×D8—611no—
281#532—1221no—
282C2×C4×D4—1221no—
283C2×D16—611no—
284C2×D16—611no—
285C2×D16—611no—
286C2×D16C2×D6111yescharacteristic
287#500—611no—
288#493—611no—
289#486—1221no—
290#466—611no—
291#466—611no—
292#466—1221no—
293C4×D8—611no—
294C4×D8—611no—
295C4×D8—611no—
296C4×D8—611no—
297C4×D8—1221no—
298C4×D8—1221no—
299C4×D8—1221no—
300C4×D8C2×D6111yescharacteristic
301C4×D8C2×D6111yescharacteristic, complemented
302C2×#107—611no—
303C2×#102—1221no—
304C2×C4×C8—611no—
305#366—611no—
306#366—611no—
307#366—611no—
308#366C2×D6111yescharacteristic, complemented
309C4⋊C16—611no—
310C4⋊C16—611no—
311#357—611no—
312#357—611no—
313#357—611no—
314#357—611no—
315#357—611no—
316#357—611no—
317#357C2×D6111yescharacteristic
318#357C2×D6111yescharacteristic, complemented
319C22⋊C16—611no—
320C22⋊C16—611no—
321C4×C16—611no—
322C4×C16C2×D6111yescharacteristic, complemented
323C61#3366011yescharacteristic, complemented, Sylow
324C2×#41—2441no—
325C22×D4—1221no—
326C23×C4—2441no—
327C2×D8—611no—
328C2×D8—611no—
329C2×D8—1221no—
330C2×D8—1221no—
331C2×D8—1222no—
332C2×D8—1222no—
333C2×D8C22×D6111yescharacteristic
334C2×D8C22×D6111yescharacteristic
335C22×C8—611no—
336C22×C8—611no—
337C4⋊Q8—1221no—
338#127—1221no—
339#124—2441no—
340#121—1221no—
341#121—1221no—
342#121—2441no—
343C4×D4—21no—
344C4×D4—21no—
345C4×D4—1221no—
346C4×D4—1221no—
347C4×D4—1221no—
348C4×D4—1221no—
349C4×D4—2441no—
350C4×D4—2441no—
351C4×D4—2441no—
352C2×C4⋊C4—1221no—
353C2×C22⋊C4—2441no—
354C2×C42—611no—
355D16—22no—
356D16—1222no—
357D16—1222no—
358D16—1222no—
359C2×C16—611no—
360C2×C16—611no—
361C2×C16C22×D6111yescharacteristic
362C2×C16C22×D6111yescharacteristic
363#107—611no—
364#107—611no—
365#107—1221no—
366#107—1221no—
367#107C22×D6111yescharacteristic
368#107C22×D6111yescharacteristic
369#102—21no—
370#102—21no—
371#102—1221no—
372#102—1221no—
373#102—1221no—
374#102—1221no—
375#102—1221no—
376#102—1221no—
377C4×C8—611no—
378C4×C8—611no—
379C4×C8—611no—
380C4×C8C22×D6111yescharacteristic
381C24—2441no—
382#41—4884no—
383C2×Q8—2441no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—1224no—
387C2×D4—1221no—
388C2×D4—1221no—
389C2×D4—2441no—
390C2×D4—2441no—
391C2×D4—2441no—
392C2×D4—2441no—
393C2×D4—2442no—
394C2×D4—2441no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—611no—
398C22×C4—611no—
399C22×C4—611no—
400C22×C4—4884no—
401C22×C4—2441no—
402C22×C4—2441no—
403C22×C4—2441no—
404C22×C4—2441no—
405C22×C4—2441no—
406D8—21no—
407D8—21no—
408D8—21no—
409D8—612no—
410D8—1224no—
411D8—1221no—
412D8—1221no—
413D8—1221no—
414D8—2442no—
415D8#1175822212yescomplemented
416C2×C8—611no—
417C2×C8—611no—
418C2×C8—1221no—
419C2×C8—1221no—
420C2×C8—2441no—
421C2×C8D4×D6111yescharacteristic
422C2×C8C23×D6111yescharacteristic
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—1221no—
426C4⋊C4—1221no—
427C4⋊C4—2441no—
428C4⋊C4—2441no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—2441no—
432C22⋊C4—2441no—
433C22⋊C4—2441no—
434C22⋊C4—2441no—
435C22⋊C4—2441no—
436C22⋊C4—2441no—
437C42—611no—
438C42—611no—
439C42—611no—
440C42D4×D6111yescharacteristic
441C16—21no—
442C16—21no—
443C16—1221no—
444C16—1221no—
445C23—41no—
446C23—41no—
447C23—611no—
448C23—4882no—
449C23—4882no—
450C23—2444no—
451C23—2441no—
452C23—2441no—
453Q8—4882no—
454D4—22no—
455D4—41no—
456D4—41no—
457D4—41no—
458D4—1222no—
459D4—4882no—
460D4—4882no—
461D4—4882no—
462D4—4882no—
463D4—2444no—
464D4—2441no—
465D4—2441no—
466D4—2441no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—82no—
470C2×C4—82no—
471C2×C4—611no—
472C2×C4—614no—
473C2×C4—611no—
474C2×C4—611no—
475C2×C4—1221no—
476C2×C4—1221no—
477C2×C4—4882no—
478C2×C4—4882no—
479C2×C4—4882no—
480C2×C4—4882no—
481C2×C4—4882no—
482C2×C4—2441no—
483C2×C4—2441no—
484C2×C4—2441no—
485C2×C4D8×D6111yescharacteristic
486C2×C4D8×D6111yescharacteristic
487C2×C4C2×D4×D6111yescharacteristic
488C8—21no—
489C8—1221no—
490C8—1221no—
491C8#41×D6111yescharacteristic
492C8C2×#1175822211yescharacteristic
493C22—42no—
494C22—81no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—81no—
499C22—612no—
500C22—1221no—
501C22—1221no—
502C22—4888no—
503C22—4881no—
504C22—4881no—
505C22—4881no—
506C22—4881no—
507C22—4881no—
508C22—2442no—
509C22C2×D8×D6111yescharacteristic
510C4—21no—
511C4—81no—
512C4—81no—
513C4—612no—
514C4—1221no—
515C4—1221no—
516C4—4881no—
517C4—4881no—
518C4D16×D6112yes—
519C4#1684027111yescharacteristic
520C4#1684055911yescharacteristic
521C2—82no—
522C2—161no—
523C2—1222no—
524C2—9761no—
525C2—4882no—
526C2#2145581711yescharacteristic
527C2C2×D16×D6111yescharacteristic
528C2#2145895211yescharacteristic
subgroupG/H
centerC2×C4D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC4×D16×C61C2
socleC22×C61C22×D8
hypercenterC4×D16D61
hypocenterC61#33660
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×D16

Complements

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

NH ≅ G/Ntype
1. #21456395C2semidirect
2. C4×D8×D61C2semidirect
3. #21448001C2semidirect
4. #21447998C2semidirect
5. #21447955C2semidirect
6. #21447954C2semidirect
7. #21447853C2semidirect
8. #21447852C2semidirect
9. #21447732C2semidirect
10. #21447729C2semidirect
11. C4×D976C2semidirect
12. C4×#14519718C2semidirect
13. C4×#14519718C2semidirect
14. #21447616C2semidirect
15. C4×D16×C61C2semidirect
22. #16840166C22semidirect
23. #16840137C22semidirect
29. C4×D488C22semidirect
38. #16839588C22semidirect
39. #16839587C22semidirect
40. #16839587C22semidirect
41. #16839580C22semidirect
42. #16839580C22semidirect
44. #16839564C22semidirect
46. #16839563C22semidirect
48. #16839562C22semidirect
51. C4×#11758185C22semidirect
54. C4×D8×C61C22semidirect
55. C61×#366C22semidirect
57. C61×#357C22semidirect
58. C4×C16×C61C22semidirect
144. D8×C61#41semidirect
172. D488#41semidirect
221. C4×D61D16semidirect
270. C4×D16D61semidirect
301. C4×D8C2×D61semidirect
308. #366C2×D61semidirect
318. #357C2×D61semidirect
322. C4×C16C2×D61semidirect
323. C61#33660semidirect
415. D8#11758222semidirect

Maximal subgroups

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

subgroupindex
#214563952
C4×D8×D612
#214480012
#214479982
#214479552
#214479542
#214478532
#214478522
#214477322
#214477292
C4×D9762
C4×#145197182
#214476162
C4×D16×C612
#3366061