Finite Group Databasebeta

← #29835122

Subgroups — #29835122

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#21456459C211yesmaximal, characteristic, complemented
2#21454671C211yesmaximal, characteristic, complemented
3#21448024C211yesmaximal, characteristic, complemented
4#21448011C211yesmaximal, characteristic, complemented
5#21447964C211yesmaximal, characteristic, complemented
6#21447954C211yesmaximal, characteristic, complemented
7#21447876C211yesmaximal, characteristic, complemented
8#21447876C211yesmaximal, characteristic, complemented
9#21447731C211yesmaximal, characteristic
10#21447692C211yesmaximal, characteristic, complemented
11#21447684C211yesmaximal, characteristic, complemented
12SD32×Dic61C211yesmaximal, characteristic, complemented
13#21447663C211yesmaximal, characteristic, complemented
14#21447623C211yesmaximal, characteristic, complemented
15C61×#2187C211yesmaximal, characteristic, complemented
16#16840385—21no—
17#16840237—21no—
18C2×#14519718C2211yescharacteristic
19C2×#14519718C2211yescharacteristic
20#16840166C2211yescharacteristic, complemented
21#16840147C2211yescharacteristic, complemented
22#16840123—21no—
23#16840010—21no—
24#16839998C2211yescharacteristic
25#16839874—21no—
26#16839874—21no—
27#16839865—21no—
28Q16×Dic61C2211yescharacteristic, complemented
29D8×Dic61C2211yescharacteristic
30D8×Dic61C2211yescharacteristic
31D8×Dic61C2211yescharacteristic
32D8×Dic61C2211yescharacteristic
33#16839844C2211yescharacteristic, complemented
34#16839800C2211yescharacteristic
35#16839767—21no—
36#16839717C2211yescharacteristic
37#16839590C2211yescharacteristic, complemented
38#16839589C2211yescharacteristic, complemented
39#16839588C2211yescharacteristic, complemented
40#16839587C2211yescharacteristic, complemented
41#16839580C2211yescharacteristic, complemented
42#16839580C2211yescharacteristic, complemented
43#16839566C2211yescharacteristic, complemented
44#16839566C2211yescharacteristic, complemented
45#16839564C2211yescharacteristic, complemented
46#16839564C2211yescharacteristic, complemented
47#16839563C2211yescharacteristic
48#16839563C2211yescharacteristic
49C22⋊#11758185C2211yescharacteristic
50#16839537C2211yescharacteristic, complemented
51C16×Dic61C2211yescharacteristic, complemented
52C22×D8×C61C2211yescharacteristic
53C2×SD32×C61C2211yescharacteristic
54C2×SD32×C61C2211yescharacteristic
55C61×#467C2211yescharacteristic
56C61×#357C2211yescharacteristic
57C61×#357C2211yescharacteristic
58C61×C22⋊C16C2211yescharacteristic
59C2×#11758201—21no—
60C2×D488C2311yescharacteristic
61C2×#11758194D411yescharacteristic
62#14519776—21no—
63#14519772—41no—
64#14519766—21no—
65#14519763—41no—
66#14519759—41no—
67#14519757—41no—
68#14519751—21no—
69Q8×Dic61—21no—
70D4×Dic61—21no—
71D4×Dic61—21no—
72D4×Dic61—21no—
73D4×Dic61—21no—
74D4×Dic61—41no—
75D4×Dic61—41no—
76#14519739—21no—
77#14519736—21no—
78#14519736D411yescharacteristic
79C2×C22⋊Dic61—41no—
80C2×C22⋊Dic61—41no—
81#14519718—22no—
82#14519718—22no—
83C2×#11758185C2311yescharacteristic
84C2×#11758185C2311yescharacteristic
85#14519711C2311yescharacteristic
86#14519711C2311yescharacteristic
87#14519711C2311yescharacteristic
88#14519710—21no—
89#14519709—21no—
90#14519701—21no—
91#14519699—21no—
92#14519698—21no—
93#14519698—21no—
94#14519698—21no—
95#14519698—21no—
96#14519697—21no—
97#14519687D411yescharacteristic
98#14519687D411yescharacteristic
99C8×Dic61C2311yescharacteristic
100C8×Dic61C2311yescharacteristic
101C22×D4×C61—21no—
102C2×Q16×C61C2311yescharacteristic
103C2×D8×C61—22no—
104C2×D8×C61—22no—
105C2×D8×C61—21no—
106C2×D8×C61C2311yescharacteristic
107C2×D8×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C22⋊Q8×C61—21no—
110SD32×C61—22no—
111SD32×C61—22no—
112C2×C16×C61C2311yescharacteristic
113C2×C16×C61C2311yescharacteristic
114#107×C61C2311yescharacteristic
115#103×C61—21no—
116C24×C61—41no—
117C2×Q8×C61—21no—
118C2×D4×C61—24no—
119C2×D4×C61—21no—
120C2×D4×C61—21no—
121C2×D4×C61—42no—
122C2×D4×C61—41no—
123C22×C4×C61C2×D411yescharacteristic
124C2×C22⋊D61—41no—
125C22×Dic61—41no—
126C22×Dic61—41no—
127C22×Dic61—41no—
128C22×Dic61—41no—
129C2×D244—21no—
130C2×C4×D61—41no—
131C2×Dic122—41no—
132Q16×C61—21no—
133Q16×C61—21no—
134D8×C61—24no—
135D8×C61—21no—
136D8×C61—21no—
137D8×C61#4112yes—
138D8×C61#4112yes—
139C2×C8×C61—21no—
140C2×C8×C61—21no—
141C2×C8×C61C2×D411yescharacteristic
142C2×C8×C61C2411yescharacteristic
143C4⋊C4×C61—21no—
144C4⋊C4×C61—41no—
145C22⋊C4×C61—41no—
146C22⋊Dic61—41no—
147C22⋊Dic61—41no—
148C22⋊Dic61—41no—
149C22⋊Dic61—41no—
150C22⋊Dic61—41no—
151C22⋊Dic61D811yescharacteristic
152C22⋊Dic61D811yescharacteristic
153#11758201—42no—
154#11758198—41no—
155#11758198—41no—
156#11758198—41no—
157#11758198—41no—
158C4⋊Dic61—21no—
159C4⋊Dic61—21no—
160C4⋊Dic61—21no—
161C4⋊Dic61—41no—
162C4⋊Dic61D811yescharacteristic
163C4⋊Dic61D811yescharacteristic
164#11758196—41no—
165C4×Dic61—41no—
166C4×Dic61—41no—
167C4×Dic61C2×D411yescharacteristic
168C4×Dic61C2×D411yescharacteristic
169#11758194—41no—
170C2×#92418C2×D411yescharacteristic
171C2×#92418C2×D411yescharacteristic
172D488—21no—
173D488—21no—
174C16×C61—21no—
175C16×C61—21no—
176#11758185—21no—
177#11758185—21no—
178C23×C61—44no—
179C23×C61—41no—
180C23×C61—41no—
181C23×C61—161no—
182C23×C61—161no—
183C23×C61C2×D811yescharacteristic
184C22×D61—41no—
185Q8×C61—41no—
186Q8×C61—41no—
187D4×C61—22no—
188D4×C61—22no—
189D4×C61—44no—
190D4×C61—41no—
191D4×C61—41no—
192C2×C4×C61—21no—
193C2×C4×C61—21no—
194C2×C4×C61—41no—
195C2×C4×C61—41no—
196C2×C4×C61C2×D811yescharacteristic
197C2×C4×C61C22×D411yescharacteristic
198C22⋊D61—161no—
199C2×Dic61—41no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61—161no—
203C2×Dic61—161no—
204C2×Dic61—161no—
205C2×Dic61—161no—
206C2×Dic61C2×D811yescharacteristic
207C2×Dic61C2×D811yescharacteristic
208C2×Dic61C2×D811yescharacteristic
209C2×Dic61C2×D811yescharacteristic
210D244—41no—
211D244—41no—
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—21no—
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—42no—
224C22×C61—42no—
225C22×C61—81no—
226C22×C61—81no—
227C22×C61—81no—
228C22×C61—81no—
229C22×C61—164no—
230C22×C61C22×D811yescharacteristic
231C2×D61—81no—
232C2×D61—81no—
233C2×D61—81no—
234C4×C61—21no—
235C4×C61—81no—
236C4×C61—81no—
237C4×C61#52511yescharacteristic
238C4×C61#57511yescharacteristic
239Dic61—21no—
240Dic61—21no—
241Dic61—21no—
242Dic61—21no—
243Dic61—81no—
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#2187D6111yescharacteristic, complemented
255#2184—611no—
256#2177—611no—
257#2175—611no—
258C4×SD32—611no—
259C4×D16—611no—
260#2164—611no—
261C2×C61—41no—
262C2×C61—82no—
263C2×C61—82no—
264C2×C61#310011yescharacteristic
265C2×C61#341511yescharacteristic
266C2×C61#341611yescharacteristic
267D61—161no—
268C22×D8C2×D6111yescharacteristic
269#542—1221no—
270#518—1221no—
271C2×SD32C2×D6111yescharacteristic
272C2×SD32C2×D6111yescharacteristic
273C2×D16—611no—
274C2×D16—611no—
275#500—611no—
276#495—611no—
277#489—1221no—
278#468—1221no—
279#467C2×D6111yescharacteristic
280#466—611no—
281#442—1221no—
282#442—1221no—
283#440—1221no—
284C4×Q16—611no—
285C4×D8—611no—
286C4×D8—611no—
287C4×D8—611no—
288C4×D8—611no—
289C4×D8—611no—
290#427—611no—
291#418—1221no—
292#405—611no—
293#367—611no—
294#367—611no—
295#366—611no—
296#366—611no—
297C4⋊C16—611no—
298C4⋊C16—611no—
299#358—611no—
300#358—611no—
301#357—611no—
302#357—611no—
303#357—611no—
304#357—611no—
305#357C2×D6111yescharacteristic
306#357C2×D6111yescharacteristic
307C22⋊C16—611no—
308C22⋊C16C2×D6111yescharacteristic
309#346—611no—
310C4×C16—611no—
311C61#3367811yescharacteristic, complemented, Sylow
312C22×D4—21no—
313C2×Q16C22×D6111yescharacteristic
314C2×SD16—1221no—
315C2×D8—22no—
316C2×D8—22no—
317C2×D8—21no—
318C2×D8—611no—
319C2×D8C22×D6111yescharacteristic
320C2×D8C22×D6111yescharacteristic
321C2×M16—611no—
322C22×C8C22×D6111yescharacteristic
323C4⋊Q8—1221no—
324#126—2441no—
325#124—1221no—
326#124—2441no—
327#123—2441no—
328C22⋊Q8—21no—
329C22⋊Q8—2441no—
330#121—1221no—
331C4×Q8—1221no—
332C4×D4—1221no—
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—22no—
345D16—1222no—
346D16—1222no—
347C2×C16—611no—
348C2×C16—611no—
349C2×C16C22×D6111yescharacteristic
350C2×C16C22×D6111yescharacteristic
351#107—611no—
352#107—611no—
353#107—611no—
354#107—1221no—
355#107C22×D6111yescharacteristic
356#106—1221no—
357#103—21no—
358#103—1221no—
359#102—1221no—
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×C8—611no—
369C24—41no—
370C2×Q8—21no—
371C2×Q8—2441no—
372C2×D4—24no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—42no—
376C2×D4—41no—
377C2×D4—1221no—
378C2×D4—2441no—
379C22×C4—2441no—
380C22×C4—2441no—
381C22×C4—2441no—
382C22×C4—2441no—
383C22×C4—2441no—
384C22×C4D4×D6111yescharacteristic
385Q16—21no—
386Q16—21no—
387SD16—2442no—
388D8—24no—
389D8—21no—
390D8—21no—
391D8—1221no—
392D8—1221no—
393D8#1175822412yes—
394D8#1175822412yes—
395M16—2441no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—611no—
399C2×C8—611no—
400C2×C8D4×D6111yescharacteristic
401C2×C8C23×D6111yescharacteristic
402C4⋊C4—21no—
403C4⋊C4—41no—
404C4⋊C4—611no—
405C4⋊C4—611no—
406C4⋊C4—1221no—
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—611no—
424C42—611no—
425C42—2441no—
426C42—2441no—
427C16—21no—
428C16—21no—
429C16—1221no—
430C16—1221no—
431C23—44no—
432C23—41no—
433C23—41no—
434C23—161no—
435C23—161no—
436C23—2441no—
437C23D8×D6111yescharacteristic
438Q8—41no—
439Q8—41no—
440Q8—9761no—
441D4—22no—
442D4—22no—
443D4—44no—
444D4—41no—
445D4—41no—
446D4—9761no—
447D4—2441no—
448D4—2441no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—611no—
454C2×C4—611no—
455C2×C4—611no—
456C2×C4—611no—
457C2×C4—9761no—
458C2×C4—9761no—
459C2×C4—9761no—
460C2×C4—9761no—
461C2×C4—9761no—
462C2×C4—2441no—
463C2×C4—2441no—
464C2×C4—2441no—
465C2×C4D8×D6111yescharacteristic
466C2×C4C2×D4×D6111yescharacteristic
467C8—21no—
468C8—1221no—
469C8—1221no—
470C8C2×#1175822411yescharacteristic
471C8C2×#1175822411yescharacteristic
472C22—21no—
473C22—21no—
474C22—21no—
475C22—42no—
476C22—42no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22—164no—
482C22—4881no—
483C22—4881no—
484C22—4881no—
485C22C2×D8×D6111yescharacteristic
486C4—21no—
487C4—81no—
488C4—81no—
489C4—1221no—
490C4—1221no—
491C4—1221no—
492C4—1221no—
493C4—4881no—
494C4—4881no—
495C4—4881no—
496C4#1684026811yescharacteristic
497C4#1684055811yescharacteristic
498C2—41no—
499C2—82no—
500C2—82no—
501C2—9761no—
502C2#2145581411yescharacteristic
503C2#2145895911yescharacteristic
504C2#2145896111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2187C2
socleC22×C61C22×D8
prime radical#21447731C2
hypercenter#2187D61
hypocenterC61#33678
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2187

Complements

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

NH ≅ G/Ntype
1. #21456459C2semidirect
2. #21454671C2semidirect
3. #21448024C2semidirect
4. #21448011C2semidirect
5. #21447964C2semidirect
6. #21447954C2semidirect
7. #21447876C2semidirect
8. #21447876C2semidirect
10. #21447692C2semidirect
11. #21447684C2semidirect
12. SD32×Dic61C2semidirect
13. #21447663C2semidirect
14. #21447623C2semidirect
15. C61×#2187C2semidirect
20. #16840166C22semidirect
21. #16840147C22semidirect
28. Q16×Dic61C22semidirect
33. #16839844C22semidirect
37. #16839590C22semidirect
38. #16839589C22semidirect
39. #16839588C22semidirect
40. #16839587C22semidirect
41. #16839580C22semidirect
42. #16839580C22semidirect
43. #16839566C22semidirect
44. #16839566C22semidirect
45. #16839564C22semidirect
46. #16839564C22semidirect
50. #16839537C22semidirect
51. C16×Dic61C22semidirect
254. #2187D61semidirect
311. C61#33678semidirect

Maximal subgroups

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

subgroupindex
#214564592
#214546712
#214480242
#214480112
#214479642
#214479542
#214478762
#214477312
#214476922
#214476842
SD32×Dic612
#214476632
#214476232
C61×#21872
#3367861