Finite Group Databasebeta

← #29834838

Subgroups — #29834838

Order 15616.

632 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#466×D61C211yesmaximal, characteristic
2#427×D61C211yesmaximal, characteristic, complemented
3#21448011C211yesmaximal, characteristic, complemented
4#21448010C211yesmaximal, characteristic, complemented
5#21448007C211yesmaximal, characteristic, complemented
6#21448006C211yesmaximal, characteristic, complemented
7#21448003C211yesmaximal, characteristic, complemented
8#21448001C211yesmaximal, characteristic, complemented
9#21447998C211yesmaximal, characteristic, complemented
10#21447606C211yesmaximal, characteristic, complemented
11#21447604C211yesmaximal, characteristic, complemented
12#21447533C211yesmaximal, characteristic, complemented
13#21447533C211yesmaximal, characteristic, complemented
14#21447428C211yesmaximal, characteristic, complemented
15C61×#2234C211yesmaximal, characteristic, complemented
16C2×D8×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18#121×D61—21no—
19#117×D61—21no—
20C2×#14519716C2211yescharacteristic
21C2×#14519716C2211yescharacteristic
22#16839999C2211yescharacteristic
23#16839998C2211yescharacteristic
24#16839997—21no—
25#16839996—21no—
26#16839995C2211yescharacteristic
27#16839800C2211yescharacteristic, complemented
28#16839799C2211yescharacteristic
29#16839799C2211yescharacteristic
30#16839798—21no—
31#16839797—21no—
32#107×D61C2211yescharacteristic
33#107×D61C2211yescharacteristic, complemented
34#107×D61C2211yescharacteristic, complemented
35#106×D61—21no—
36#102×D61—21no—
37#16839590C2211yescharacteristic, complemented
38#16839589C2211yescharacteristic, complemented
39#16839589C2211yescharacteristic, complemented
40#16839588C2211yescharacteristic, complemented
41#16839587C2211yescharacteristic, complemented
42#16839587C2211yescharacteristic, complemented
43#16839564C2211yescharacteristic, complemented
44#16839564C2211yescharacteristic, complemented
45#16839563C2211yescharacteristic, complemented
46#16839563C2211yescharacteristic, complemented
47#16839562C2211yescharacteristic, complemented
48#16839562C2211yescharacteristic, complemented
49C22⋊#11758185C2211yescharacteristic, complemented
50#16839541C2211yescharacteristic, complemented
51#16839541C2211yescharacteristic, complemented
52C61×#466C2211yescharacteristic
53C61×#427C2211yescharacteristic, complemented
54C61×#367C2211yescharacteristic, complemented
55C61×#366C2211yescharacteristic, complemented
56C61×#357C2211yescharacteristic, complemented
57C61×#357C2211yescharacteristic, complemented
58C61×C22⋊C16C2211yescharacteristic, complemented
59C2×D4×D61—21no—
60C2×D4×D61—41no—
61C22×C4×D61D411yescharacteristic
62C2×D488C2311yescharacteristic
63C2×#11758199—21no—
64D8×D61—22no—
65D8×D61—22no—
66C22×#92418D411yescharacteristic
67C2×C8×D61—22no—
68C2×C8×D61—22no—
69C2×C8×D61D411yescharacteristic
70C2×C8×D61D411yescharacteristic
71C2×C8×D61C2311yescharacteristic
72C2×C8×D61C2311yescharacteristic
73#14519752—21no—
74#14519751—21no—
75#14519750—41no—
76#14519749—41no—
77#14519748—21no—
78#14519736—21no—
79#14519735—21no—
80#14519735—21no—
81#14519734—41no—
82#14519733—41no—
83C4⋊C4×D61—21no—
84C4⋊C4×D61—21no—
85C4⋊C4×D61—21no—
86C22⋊C4×D61—41no—
87C22⋊C4×D61—41no—
88C42×D61—41no—
89#14519716—22no—
90#14519716—22no—
91C2×#11758185C2311yescharacteristic
92C2×#11758185C2311yescharacteristic
93#14519711C2311yescharacteristic
94#14519711C2311yescharacteristic
95#14519711C2311yescharacteristic
96#14519710—21no—
97#14519710—21no—
98#14519710—21no—
99#14519709—21no—
100#14519708—21no—
101#14519708—21no—
102#14519699—21no—
103#14519698—21no—
104#14519697—21no—
105C2×D8×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107#121×C61—21no—
108#117×C61—21no—
109C2×C16×C61C2311yescharacteristic
110C2×C16×C61C2311yescharacteristic
111#107×C61C2311yescharacteristic
112#107×C61C2311yescharacteristic
113#107×C61C2311yescharacteristic
114#106×C61—21no—
115#102×C61—21no—
116C23×D61—41no—
117C23×D61D811yescharacteristic
118C2×D4×C61—21no—
119C2×D4×C61—41no—
120C22×C4×C61C2×D411yescharacteristic
121C2×C22⋊D61—41no—
122C2×C22⋊D61—41no—
123C2×C22⋊D61—41no—
124C22×Dic61D811yescharacteristic
125D4×D61—42no—
126D4×D61—42no—
127D4×D61—84no—
128C2×D244—21no—
129C2×D244—41no—
130C2×C4×D61—22no—
131C2×C4×D61—22no—
132C2×C4×D61—41no—
133C2×C4×D61—41no—
134C2×C4×D61—41no—
135C2×C4×D61D811yescharacteristic
136C2×C4×D61D811yescharacteristic
137C2×C4×D61C2×D411yescharacteristic
138C2×C4×D61C2×D411yescharacteristic
139D8×C61—21no—
140D8×C61—21no—
141C2×C8×C61—21no—
142C2×C8×C61—21no—
143C2×C8×C61C2×D411yescharacteristic
144C2×C8×C61C2411yescharacteristic
145C4⋊C4×C61—21no—
146C4⋊C4×C61—21no—
147C4⋊C4×C61—21no—
148C22⋊C4×C61—41no—
149C22⋊C4×C61—41no—
150C42×C61—41no—
151C22⋊Dic61—41no—
152C22⋊Dic61—41no—
153#11758199—42no—
154#11758198—41no—
155#11758198—41no—
156#11758198—41no—
157#11758198—41no—
158C4⋊Dic61—21no—
159C4⋊Dic61—21no—
160C4⋊Dic61—21no—
161#11758196—41no—
162#11758196—41no—
163#11758196—41no—
164C4×Dic61—41no—
165C4×Dic61—41no—
166C4×Dic61—41no—
167C2×#92418—22no—
168C2×#92418C2×D411yescharacteristic
169C2×#92418C2×D411yescharacteristic
170D488—21no—
171D488—21no—
172C8×D61—22no—
173C8×D61—21no—
174C8×D61—21no—
175C8×D61—22no—
176C8×D61#4112yes—
177C8×D61#4112yes—
178C16×C61—21no—
179C16×C61—21no—
180#11758185—21no—
181#11758185—21no—
182C23×C61—41no—
183C23×C61C2×D811yescharacteristic
184C22×D61—22no—
185C22×D61—22no—
186C22×D61—41no—
187C22×D61—41no—
188C22×D61—82no—
189C22×D61—82no—
190C22×D61—82no—
191C22×D61C2×D811yescharacteristic
192C22×D61C2×D811yescharacteristic
193D4×C61—41no—
194D4×C61—41no—
195D4×C61—82no—
196C2×C4×C61—21no—
197C2×C4×C61—21no—
198C2×C4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61—41no—
201C2×C4×C61C2×D811yescharacteristic
202C2×C4×C61C22×D411yescharacteristic
203C22⋊D61—82no—
204C22⋊D61—82no—
205C22⋊D61—82no—
206C2×Dic61—22no—
207C2×Dic61—41no—
208C2×Dic61—41no—
209C2×Dic61—41no—
210C2×Dic61C2×D811yescharacteristic
211C2×Dic61C2×D811yescharacteristic
212D244—41no—
213D244—41no—
214D244—82no—
215C4×D61—22no—
216C4×D61—21no—
217C4×D61—21no—
218C4×D61—22no—
219C4×D61—82no—
220C4×D61—82no—
221C4×D61—82no—
222C4×D61#12312yes—
223C4×D61#13712yes—
224C8×C61—21no—
225C8×C61C2×#4111yescharacteristic
226C8×C61C2×#4111yescharacteristic
227#92418—21no—
228#92418#12312yes—
229#33648—611nomaximal, Sylow
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—81no—
234C22×C61—81no—
235C22×C61—81no—
236C22×C61C22×D811yescharacteristic
237C2×D61—21no—
238C2×D61—21no—
239C2×D61—21no—
240C2×D61—21no—
241C2×D61—44no—
242C2×D61—81no—
243C2×D61—81no—
244C2×D61—81no—
245C2×D61—164no—
246C2×D61#48012yes—
247C2×D61#50912yes—
248C4×C61—21no—
249C4×C61—81no—
250C4×C61—81no—
251C4×C61—81no—
252C4×C61C2×#12311yescharacteristic
253C4×C61C2×#13711yescharacteristic
254Dic61—21no—
255Dic61—81no—
256Dic61—81no—
257Dic61—81no—
258Dic61#48012yes—
259C2×#466—611no—
260C2×#427—611no—
261#2234—611no—
262#2234—611no—
263#2234—611no—
264#2234D6111yescharacteristic, complemented
265#2233—611no—
266#2233—611no—
267#2232—611no—
268#2232—611no—
269#2159—611no—
270#2159—611no—
271#2140—611no—
272#2140—611no—
273#2112—611no—
274C2×C61—41no—
275C2×C61—161no—
276C2×C61C2×#48011yescharacteristic
277C2×C61C2×#50911yescharacteristic
278C2×C61#341411yescharacteristic
279D61—22no—
280D61—22no—
281D61—161no—
282C22×D8—611no—
283C23×C8—611no—
284C2×#121—1221no—
285C2×#117—1221no—
286C2×M32—611no—
287C2×M32—611no—
288#466—611no—
289#466—611no—
290#466—611no—
291#466—1221no—
292#466—1221no—
293#466C2×D6111yescharacteristic
294#427—611no—
295#427—611no—
296#427—611no—
297#427—1221no—
298#427—1221no—
299#427C2×D6111yescharacteristic, complemented
300C2×#107—611no—
301C2×#107—611no—
302C2×#107—611no—
303C2×#106—1221no—
304C2×#102—1221no—
305#367—611no—
306#367—611no—
307#367—611no—
308#367C2×D6111yescharacteristic, complemented
309#366—611no—
310#366—611no—
311#366—611no—
312#366C2×D6111yescharacteristic, complemented
313#357—611no—
314#357—611no—
315#357—611no—
316#357—611no—
317#357—611no—
318#357—611no—
319#357C2×D6111yescharacteristic, complemented
320#357C2×D6111yescharacteristic, complemented
321C22⋊C16—611no—
322C22⋊C16—611no—
323C22⋊C16—611no—
324C22⋊C16C2×D6111yescharacteristic, complemented
325C61#3364811yescharacteristic, complemented, Sylow
326C22×D4—1221no—
327C22×D4—2441no—
328C23×C4—611no—
329C2×D8—611no—
330C2×D8—1222no—
331C2×D8—1222no—
332C2×D8—1221no—
333C2×D8C22×D6111yescharacteristic
334C22×C8—611no—
335C22×C8—611no—
336C22×C8—611no—
337C22×C8—611no—
338C22×C8—611no—
339C22×C8—1222no—
340C22×C8—1222no—
341C22×C8C22×D6111yescharacteristic
342#121—21no—
343#121—1221no—
344#121—1221no—
345#121—1221no—
346#121—2441no—
347#121—2441no—
348#117—21no—
349#117—1221no—
350#117—1221no—
351#117—1221no—
352#117—2441no—
353#117—2441no—
354C2×C4⋊C4—1221no—
355C2×C4⋊C4—1221no—
356C2×C4⋊C4—1221no—
357C2×C22⋊C4—2441no—
358C2×C22⋊C4—2441no—
359C2×C42—2441no—
360M32—1222no—
361M32—1222no—
362C2×C16—611no—
363C2×C16—611no—
364C2×C16C22×D6111yescharacteristic
365C2×C16C22×D6111yescharacteristic
366#107—611no—
367#107—611no—
368#107—611no—
369#107—1221no—
370#107—1221no—
371#107—1221no—
372#107C22×D6111yescharacteristic
373#107C22×D6111yescharacteristic
374#107C22×D6111yescharacteristic
375#106—21no—
376#106—1221no—
377#106—1221no—
378#106—1221no—
379#102—21no—
380#102—1221no—
381#102—1221no—
382#102—1221no—
383C24—611no—
384C24—2441no—
385C2×D4—21no—
386C2×D4—41no—
387C2×D4—1221no—
388C2×D4—4884no—
389C2×D4—2441no—
390C2×D4—2442no—
391C2×D4—2442no—
392C2×D4—2441no—
393C2×D4—2441no—
394C2×D4—2441no—
395C22×C4—611no—
396C22×C4—611no—
397C22×C4—611no—
398C22×C4—611no—
399C22×C4—611no—
400C22×C4—1222no—
401C22×C4—1222no—
402C22×C4—2441no—
403C22×C4—2441no—
404C22×C4—2441no—
405C22×C4D4×D6111yescharacteristic
406D8—21no—
407D8—21no—
408D8—1221no—
409D8—1221no—
410D8—2442no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—611no—
414C2×C8—612no—
415C2×C8—612no—
416C2×C8—611no—
417C2×C8—1222no—
418C2×C8—1222no—
419C2×C8—1222no—
420C2×C8—1221no—
421C2×C8—1221no—
422C2×C8D4×D6111yescharacteristic
423C2×C8C23×D6111yescharacteristic
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—1221no—
428C4⋊C4—1221no—
429C4⋊C4—1221no—
430C4⋊C4—2441no—
431C4⋊C4—2441no—
432C4⋊C4—2441no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—2441no—
436C22⋊C4—2441no—
437C22⋊C4—2441no—
438C22⋊C4—2441no—
439C22⋊C4—2441no—
440C22⋊C4—2441no—
441C42—41no—
442C42—2441no—
443C42—2441no—
444C42—2441no—
445C16—21no—
446C16—21no—
447C16—1221no—
448C16—1221no—
449C23—41no—
450C23—611no—
451C23—611no—
452C23—1222no—
453C23—1222no—
454C23—4882no—
455C23—4882no—
456C23—4882no—
457C23—2441no—
458C23—2441no—
459C23D8×D6111yescharacteristic
460D4—41no—
461D4—41no—
462D4—82no—
463D4—4882no—
464D4—4882no—
465D4—4882no—
466D4—4882no—
467D4—2441no—
468D4—2441no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—611no—
475C2×C4—612no—
476C2×C4—612no—
477C2×C4—611no—
478C2×C4—1222no—
479C2×C4—1222no—
480C2×C4—1222no—
481C2×C4—1221no—
482C2×C4—1221no—
483C2×C4—4882no—
484C2×C4—4882no—
485C2×C4—4882no—
486C2×C4—2441no—
487C2×C4—2441no—
488C2×C4—2441no—
489C2×C4D8×D6111yescharacteristic
490C2×C4C2×D4×D6111yescharacteristic
491C8—21no—
492C8—612no—
493C8—1221no—
494C8#41×D6111yescharacteristic
495C8#41×D6111yescharacteristic
496C22—21no—
497C22—21no—
498C22—21no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—612no—
503C22—612no—
504C22—1221no—
505C22—1221no—
506C22—1221no—
507C22—1221no—
508C22—9764no—
509C22—4881no—
510C22—4881no—
511C22—4881no—
512C22—2444no—
513C22C2×D8×D6111yescharacteristic
514C4—21no—
515C4—81no—
516C4—81no—
517C4—81no—
518C4—612no—
519C4—1221no—
520C4—4881no—
521C4—4881no—
522C4—4881no—
523C4#123×D6111yescharacteristic
524C4#137×D6111yescharacteristic
525C2—41no—
526C2—161no—
527C2—1222no—
528C2—1222no—
529C2—9761no—
530C2#480×D6111yescharacteristic
531C2#509×D6111yescharacteristic
532C2#2145895211yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2234C2
socleC22×C61C22×D8
prime radical#466×D61C2
hypercenter#2234D61
hypocenterC61#33648
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2234

Complements

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

NH ≅ G/Ntype
2. #427×D61C2semidirect
3. #21448011C2semidirect
4. #21448010C2semidirect
5. #21448007C2semidirect
6. #21448006C2semidirect
7. #21448003C2semidirect
8. #21448001C2semidirect
9. #21447998C2semidirect
10. #21447606C2semidirect
11. #21447604C2semidirect
12. #21447533C2semidirect
13. #21447533C2semidirect
14. #21447428C2semidirect
15. C61×#2234C2semidirect
27. #16839800C22semidirect
33. #107×D61C22semidirect
34. #107×D61C22semidirect
37. #16839590C22semidirect
38. #16839589C22semidirect
39. #16839589C22semidirect
40. #16839588C22semidirect
41. #16839587C22semidirect
42. #16839587C22semidirect
43. #16839564C22semidirect
44. #16839564C22semidirect
45. #16839563C22semidirect
46. #16839563C22semidirect
47. #16839562C22semidirect
48. #16839562C22semidirect
49. C22⋊#11758185C22semidirect
50. #16839541C22semidirect
51. #16839541C22semidirect
53. C61×#427C22semidirect
54. C61×#367C22semidirect
55. C61×#366C22semidirect
56. C61×#357C22semidirect
57. C61×#357C22semidirect
58. C61×C22⋊C16C22semidirect
264. #2234D61semidirect
299. #427C2×D61semidirect
308. #367C2×D61semidirect
312. #366C2×D61semidirect
319. #357C2×D61semidirect
320. #357C2×D61semidirect
324. C22⋊C16C2×D61semidirect
325. C61#33648semidirect

Maximal subgroups

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

subgroupindex
#466×D612
#427×D612
#214480112
#214480102
#214480072
#214480062
#214480032
#214480012
#214479982
#214476062
#214476042
#214475332
#214474282
C61×#22342
#3364861