Finite Group Databasebeta

← #29835125

Subgroups — #29835125

Order 15616.

568 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456460C211yesmaximal, characteristic, complemented
2#21454666C211yesmaximal, characteristic, complemented
3#21448025C211yesmaximal, characteristic, complemented
4#21448013C211yesmaximal, characteristic, complemented
5#21447964C211yesmaximal, characteristic, complemented
6#21447955C211yesmaximal, characteristic, complemented
7#21447877C211yesmaximal, characteristic, complemented
8#21447876C211yesmaximal, characteristic, complemented
9#21447746C211yesmaximal, characteristic, complemented
10#21447732C211yesmaximal, characteristic
11#21447696C211yesmaximal, characteristic, complemented
12C4×#14519720C211yesmaximal, characteristic, complemented
13C4×#14519718C211yesmaximal, characteristic, complemented
14#21447627C211yesmaximal, characteristic, complemented
15C61×#2175C211yesmaximal, characteristic, complemented
16C2×D8×D61C2211yescharacteristic
17#16840384—21no—
18#16840234—21no—
19C2×#14519720C2211yescharacteristic
20C2×D976C2211yescharacteristic
21C2×#14519718C2211yescharacteristic
22#16840166C2211yescharacteristic, complemented
23#16840147C2211yescharacteristic, complemented
24#16840123—21no—
25#16840011—21no—
26#16840000C2211yescharacteristic
27#16839999C2211yescharacteristic
28#16839872—21no—
29#16839871—21no—
30#16839860—21no—
31C4×D488C2211yescharacteristic
32C4×D488C2211yescharacteristic, complemented
33D8×Dic61C2211yescharacteristic
34#16839844C2211yescharacteristic
35#16839799C2211yescharacteristic
36#16839765—21no—
37#16839716C2211yescharacteristic
38#16839590C2211yescharacteristic, complemented
39#16839589C2211yescharacteristic, complemented
40#16839587C2211yescharacteristic, complemented
41#16839580C2211yescharacteristic, complemented
42#16839580C2211yescharacteristic, complemented
43#16839566C2211yescharacteristic, complemented
44#16839564C2211yescharacteristic
45#16839564C2211yescharacteristic, complemented
46#16839563C2211yescharacteristic
47#16839562C2211yescharacteristic
48#16839562C2211yescharacteristic, complemented
49#16839541C2211yescharacteristic
50#16839541C2211yescharacteristic
51C4×#11758185C2211yescharacteristic, complemented
52C2×SD32×C61C2211yescharacteristic
53C4×Q16×C61C2211yescharacteristic, complemented
54C4×D8×C61C2211yescharacteristic
55C61×#366C2211yescharacteristic, complemented
56C61×#358C2211yescharacteristic, complemented
57C61×#357C2211yescharacteristic
58C61×#346C2211yescharacteristic, complemented
59C2×D4×D61—21no—
60C2×#11758201—21no—
61C2×D488C2311yescharacteristic
62C2×D488C2311yescharacteristic
63C2×#11758199—21no—
64D8×D61—22no—
65D8×D61—22no—
66C2×#11758189D411yescharacteristic
67C2×C8×D61C2311yescharacteristic
68#14519776—21no—
69#14519771—41no—
70#14519766—21no—
71#14519765—41no—
72#14519762—41no—
73#14519755—41no—
74#14519753—21no—
75#14519752—21no—
76C4×D244—21no—
77C4×D244—21no—
78D4×Dic61—21no—
79#14519739—21no—
80C4×C22⋊D61—41no—
81#14519737—41no—
82#14519735—21no—
83#14519734D411yescharacteristic
84C2×#11758198—41no—
85C22⋊C4×D61—41no—
86#14519720—22no—
87D976—22no—
88#14519718—22no—
89C2×#11758185C2311yescharacteristic
90C2×#11758185C2311yescharacteristic
91#14519711C2311yescharacteristic
92#14519711C2311yescharacteristic
93#14519710—21no—
94#14519708—21no—
95#14519701—21no—
96#14519699—21no—
97#14519699—21no—
98#14519698—21no—
99#14519697—21no—
100#14519697—21no—
101#14519688D411yescharacteristic
102#14519687D411yescharacteristic
103C8×Dic61C2311yescharacteristic
104C2×Q16×C61C2311yescharacteristic
105C2×D8×C61C2311yescharacteristic
106C4×Q8×C61—21no—
107C4×D4×C61—21no—
108SD32×C61—22no—
109C2×C16×C61C2311yescharacteristic
110C2×C16×C61C2311yescharacteristic
111#107×C61C2311yescharacteristic
112#107×C61C2311yescharacteristic
113#103×C61—21no—
114#102×C61—21no—
115C4×C8×C61C2311yescharacteristic
116C23×D61—41no—
117C2×Q8×C61—21no—
118C2×D4×C61—21no—
119C22×C4×C61—41no—
120C2×C22⋊D61—41no—
121C22×Dic61—41no—
122D4×D61—24no—
123D4×D61—42no—
124C2×D244—21no—
125C2×D244—21no—
126C2×D244—41no—
127C2×C4×D61—41no—
128C2×C4×D61—41no—
129C2×C4×D61—41no—
130C2×C4×D61C2×D411yescharacteristic
131C2×Dic122—41no—
132Q16×C61—21no—
133Q16×C61—21no—
134D8×C61—21no—
135D8×C61#4112yes—
136C2×C8×C61C2×D411yescharacteristic
137C2×C8×C61C2411yescharacteristic
138C4⋊C4×C61—21no—
139C4⋊C4×C61—21no—
140C4⋊C4×C61—41no—
141C22⋊C4×C61—41no—
142C42×C61—41no—
143C42×C61C2×D411yescharacteristic
144C22⋊Dic61—41no—
145#11758201—42no—
146#11758199—24no—
147#11758198—41no—
148#11758198—41no—
149#11758198—41no—
150#11758198—41no—
151#11758198—41no—
152#11758198—41no—
153#11758198—41no—
154#11758198—41no—
155#11758198D811yescharacteristic
156#11758198D811yescharacteristic
157C4⋊Dic61—21no—
158C4⋊Dic61—21no—
159#11758196—41no—
160#11758196—41no—
161#11758196D811yescharacteristic
162#11758196D811yescharacteristic
163C4×Dic61—41no—
164C4×Dic61C2×D411yescharacteristic
165C2×#92418C2×D411yescharacteristic
166C2×#92418C2×D411yescharacteristic
167D488—21no—
168D488—21no—
169D488—21no—
170D488#4112yes—
171#11758189—41no—
172C8×D61—21no—
173C8×D61—21no—
174C16×C61—21no—
175C16×C61—21no—
176#11758185—21no—
177#11758185—21no—
178C23×C61—41no—
179C22×D61—44no—
180C22×D61—41no—
181C22×D61—41no—
182C22×D61—161no—
183C22×D61—161no—
184C22×D61C2×D811yescharacteristic
185Q8×C61—41no—
186Q8×C61—41no—
187D4×C61—22no—
188D4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61—161no—
193C2×C4×C61C2×D811yescharacteristic
194C2×C4×C61C2×D811yescharacteristic
195C2×C4×C61C22×D411yescharacteristic
196C22⋊D61—44no—
197C2×Dic61—41no—
198C2×Dic61—41no—
199C2×Dic61—161no—
200C2×Dic61C2×D811yescharacteristic
201C2×Dic61C2×D811yescharacteristic
202C2×Dic61C2×D811yescharacteristic
203D244—22no—
204D244—41no—
205D244—41no—
206D244—41no—
207D244—161no—
208C4×D61—21no—
209C4×D61—21no—
210C4×D61—161no—
211C4×D61—161no—
212C4×D61—161no—
213Dic122—161no—
214C8×C61—21no—
215C8×C61C2×#4111yescharacteristic
216C8×C61C2×#4111yescharacteristic
217#92418—21no—
218#92418—21no—
219#33678—611nomaximal, Sylow
220C22×C61—42no—
221C22×C61—81no—
222C22×C61—81no—
223C22×C61C22×D811yescharacteristic
224C2×D61—21no—
225C2×D61—21no—
226C2×D61—21no—
227C2×D61—42no—
228C2×D61—81no—
229C2×D61—81no—
230C2×D61—81no—
231C2×D61—81no—
232C2×D61—81no—
233C2×D61—164no—
234C4×C61—21no—
235C4×C61—21no—
236C4×C61—81no—
237C4×C61—81no—
238C4×C61—81no—
239C4×C61#52511yescharacteristic
240C4×C61#57511yescharacteristic
241Dic61—21no—
242Dic61—21no—
243Dic61—21no—
244Dic61—81no—
245Dic61—81no—
246#3175—611no—
247#2948—611no—
248#2237—611no—
249#2234—611no—
250#2226—611no—
251#2224—611no—
252#2210—611no—
253#2210—611no—
254#2187—611no—
255#2184—611no—
256#2177—611no—
257#2175D6111yescharacteristic, complemented
258C4×SD32—611no—
259C4×D16—611no—
260#2164—611no—
261C2×C61—82no—
262C2×C61#310011yescharacteristic
263C2×C61#341511yescharacteristic
264C2×C61#341611yescharacteristic
265D61—41no—
266D61—82no—
267D61—161no—
268C22×D8—611no—
269#542—1221no—
270#518—1221no—
271C2×SD32—611no—
272C2×SD32C2×D6111yescharacteristic
273C2×D16—611no—
274C2×D16—611no—
275#500—611no—
276#495—611no—
277#489—1221no—
278#468—1221no—
279#467—611no—
280#466—611no—
281#442—1221no—
282#442—1221no—
283#440—1221no—
284C4×Q16C2×D6111yescharacteristic, complemented
285C4×D8—611no—
286C4×D8—611no—
287C4×D8—611no—
288C4×D8—611no—
289C4×D8C2×D6111yescharacteristic
290#427—611no—
291#418—1221no—
292#405—611no—
293#367—611no—
294#367—611no—
295#366—611no—
296#366C2×D6111yescharacteristic, complemented
297C4⋊C16—611no—
298C4⋊C16—611no—
299#358—611no—
300#358C2×D6111yescharacteristic, complemented
301#357—611no—
302#357—611no—
303#357—611no—
304#357—611no—
305#357—611no—
306#357C2×D6111yescharacteristic
307C22⋊C16—611no—
308C22⋊C16—611no—
309#346C2×D6111yescharacteristic, complemented
310C4×C16—611no—
311C61#3367811yescharacteristic, complemented, Sylow
312C22×D4—1221no—
313C2×Q16C22×D6111yescharacteristic
314C2×SD16—1221no—
315C2×D8—611no—
316C2×D8—611no—
317C2×D8—1221no—
318C2×D8—1222no—
319C2×D8—1222no—
320C2×D8C22×D6111yescharacteristic
321C2×M16—611no—
322C22×C8—611no—
323C4⋊Q8—1221no—
324#126—2441no—
325#124—1221no—
326#124—2441no—
327#123—2441no—
328C22⋊Q8—1221no—
329C22⋊Q8—2441no—
330#121—1221no—
331C4×Q8—21no—
332C4×D4—21no—
333C4×D4—1221no—
334C4×D4—1221no—
335C4×D4—1221no—
336C4×D4—1221no—
337C4×D4—2441no—
338C4×D4—2441no—
339#117—611no—
340#117—1221no—
341C2×C22⋊C4—2441no—
342C2×C22⋊C4—2441no—
343SD32—22no—
344SD32—1222no—
345D16—1222no—
346D16—1222no—
347C2×C16—611no—
348C2×C16—611no—
349C2×C16C22×D6111yescharacteristic
350C2×C16C22×D6111yescharacteristic
351#107—611no—
352#107—611no—
353#107—1221no—
354#107C22×D6111yescharacteristic
355#107C22×D6111yescharacteristic
356#106—1221no—
357#103—21no—
358#103—1221no—
359#102—21no—
360#102—1221no—
361#102—1221no—
362#102—1221no—
363#102—1221no—
364#102—1221no—
365#97—611no—
366#97—611no—
367C4×C8—611no—
368C4×C8C22×D6111yescharacteristic
369C24—2441no—
370C2×Q8—21no—
371C2×Q8—2441no—
372C2×D4—21no—
373C2×D4—1224no—
374C2×D4—1221no—
375C2×D4—1221no—
376C2×D4—2441no—
377C2×D4—2441no—
378C2×D4—2442no—
379C22×C4—41no—
380C22×C4—611no—
381C22×C4—2441no—
382C22×C4—2441no—
383C22×C4—2441no—
384C22×C4—2441no—
385Q16—21no—
386Q16—21no—
387SD16—2442no—
388D8—21no—
389D8—612no—
390D8—1224no—
391D8—1221no—
392D8—1221no—
393D8—1221no—
394D8#1175822212yes—
395M16—2441no—
396C2×C8—611no—
397C2×C8—611no—
398C2×C8—1221no—
399C2×C8—1221no—
400C2×C8D4×D6111yescharacteristic
401C2×C8C23×D6111yescharacteristic
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—41no—
405C4⋊C4—611no—
406C4⋊C4—611no—
407C4⋊C4—1221no—
408C4⋊C4—1221no—
409C4⋊C4—2441no—
410C4⋊C4—2441no—
411C22⋊C4—41no—
412C22⋊C4—611no—
413C22⋊C4—611no—
414C22⋊C4—2441no—
415C22⋊C4—2441no—
416C22⋊C4—2441no—
417C22⋊C4—2441no—
418C22⋊C4—2441no—
419C22⋊C4—2441no—
420C22⋊C4—2441no—
421C22⋊C4—2441no—
422C22⋊C4—2441no—
423C42—41no—
424C42—611no—
425C42—2441no—
426C42D4×D6111yescharacteristic
427C16—21no—
428C16—21no—
429C16—1221no—
430C16—1221no—
431C23—41no—
432C23—611no—
433C23—9761no—
434C23—9761no—
435C23—2444no—
436C23—2441no—
437C23—2441no—
438Q8—41no—
439Q8—41no—
440Q8—9761no—
441D4—22no—
442D4—41no—
443D4—1222no—
444D4—9761no—
445D4—2444no—
446D4—2441no—
447D4—2441no—
448D4—2441no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—161no—
453C2×C4—611no—
454C2×C4—611no—
455C2×C4—611no—
456C2×C4—1221no—
457C2×C4—1221no—
458C2×C4—9761no—
459C2×C4—9761no—
460C2×C4—9761no—
461C2×C4—9761no—
462C2×C4—2441no—
463C2×C4—2441no—
464C2×C4D8×D6111yescharacteristic
465C2×C4D8×D6111yescharacteristic
466C2×C4C2×D4×D6111yescharacteristic
467C8—21no—
468C8—1221no—
469C8—1221no—
470C8#41×D6111yescharacteristic
471C8C2×#1175822211yescharacteristic
472C22—42no—
473C22—81no—
474C22—81no—
475C22—1221no—
476C22—1221no—
477C22—1221no—
478C22—9764no—
479C22—4881no—
480C22—4881no—
481C22—4881no—
482C22—4881no—
483C22—4881no—
484C22—2442no—
485C22C2×D8×D6111yescharacteristic
486C4—21no—
487C4—21no—
488C4—81no—
489C4—81no—
490C4—81no—
491C4—1221no—
492C4—1221no—
493C4—1221no—
494C4—4881no—
495C4—4881no—
496C4#1684027111yescharacteristic
497C4#1684055911yescharacteristic
498C2—82no—
499C2—9761no—
500C2—4882no—
501C2—2441no—
502C2#2145581711yescharacteristic
503C2#2145895911yescharacteristic
504C2#2145896411yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2175C2
socleC22×C61C22×D8
prime radical#21447732C2
hypercenter#2175D61
hypocenterC61#33678
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2175

Complements

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

NH ≅ G/Ntype
1. #21456460C2semidirect
2. #21454666C2semidirect
3. #21448025C2semidirect
4. #21448013C2semidirect
5. #21447964C2semidirect
6. #21447955C2semidirect
7. #21447877C2semidirect
8. #21447876C2semidirect
9. #21447746C2semidirect
11. #21447696C2semidirect
12. C4×#14519720C2semidirect
13. C4×#14519718C2semidirect
14. #21447627C2semidirect
15. C61×#2175C2semidirect
22. #16840166C22semidirect
23. #16840147C22semidirect
32. C4×D488C22semidirect
38. #16839590C22semidirect
39. #16839589C22semidirect
40. #16839587C22semidirect
41. #16839580C22semidirect
42. #16839580C22semidirect
43. #16839566C22semidirect
45. #16839564C22semidirect
48. #16839562C22semidirect
51. C4×#11758185C22semidirect
53. C4×Q16×C61C22semidirect
55. C61×#366C22semidirect
56. C61×#358C22semidirect
58. C61×#346C22semidirect
257. #2175D61semidirect
284. C4×Q16C2×D61semidirect
296. #366C2×D61semidirect
300. #358C2×D61semidirect
309. #346C2×D61semidirect
311. C61#33678semidirect

Maximal subgroups

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

subgroupindex
#214564602
#214546662
#214480252
#214480132
#214479642
#214479552
#214478772
#214478762
#214477462
#214477322
#214476962
C4×#145197202
C4×#145197182
#214476272
C61×#21752
#3367861