Finite Group Databasebeta

← #30600605

Subgroups — #30600605

Order 15616.

546 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#436C211yesmaximal, characteristic
2#21462000C211yesmaximal, characteristic, complemented
3#21461687C211yesmaximal, characteristic
4D61⋊#333C211yesmaximal, characteristic, complemented
5#21460698C211yesmaximal, characteristic, complemented
6#21460648C211yesmaximal, characteristic, complemented
7#476×D61C211yesmaximal, characteristic
8C2×D61⋊M16—21no—
9#16840797—21no—
10#16840796—21no—
11#16840795—22no—
12D61⋊(C4⋊C8)C2211yescharacteristic
13D61⋊(C4⋊C8)C2211yescharacteristic
14C2×#14519839—21no—
15D61⋊(C22⋊C8)—21no—
16C4×D61⋊C8C2211yescharacteristic
17#16840708C2211yescharacteristic
18#16840635—21no—
19#16840635—21no—
20#16840635—21no—
21#16840622—22no—
22C4⋊Q8×D61C2211yescharacteristic
23C4×D4×D61C2211yescharacteristic
24#16840053C411yescharacteristic, complemented
25#16840052C411yescharacteristic, complemented
26#16840051—21no—
27#16840050—21no—
28#16840049C411yescharacteristic, complemented
29#106×D61—21no—
30C4⋊C8×D61C2211yescharacteristic
31#102×D61—21no—
32C61×#476C411yescharacteristic, complemented
33C2×#11758213—22no—
34D61⋊M16—42no—
35D61⋊M16—42no—
36C2×#11758217—22no—
37C2×D61⋊C8—21no—
38C2×D61⋊C8—21no—
39C2×D61⋊C8D411yescharacteristic
40C2×D61⋊C8D411yescharacteristic
41C2×C4⋊#6923—21no—
42C2×C4⋊#6923—21no—
43C2×C4⋊#6923—21no—
44#14519844—21no—
45#14519844D412yes—
46C4⋊#92420—21no—
47C4⋊#92420—21no—
48#14519839—42no—
49#14519834—22no—
50C22⋊#92420—22no—
51C4×#92420—21no—
52C4×#92420—21no—
53C2×Q8×D61—21no—
54C2×D4×D61D411yescharacteristic
55C22×C4×D61—21no—
56C2×C8×D61—21no—
57#14519777C2×C411yescharacteristic
58#14519776—21no—
59#14519776—21no—
60#14519775—21no—
61C4×D244C2×C411yescharacteristic
62D4×Dic61D411yescharacteristic
63#14519739D411yescharacteristic
64C4×C22⋊D61—21no—
65#14519737—21no—
66C4⋊C4×D61—21no—
67C4⋊C4×D61—21no—
68C4⋊C4×D61D411yescharacteristic
69C22⋊C4×D61—21no—
70C42×D61C2311yescharacteristic
71#14519709—21no—
72#14519708—21no—
73#14519708—21no—
74C4⋊#92418C2×C411yescharacteristic
75#14519706—21no—
76#14519699—21no—
77#14519698—21no—
78#14519697—21no—
79C4⋊Q8×C61C2×C411yescharacteristic
80C4×D4×C61C2×C411yescharacteristic
81#106×C61—21no—
82C4⋊C8×C61C2×C411yescharacteristic
83#102×C61—21no—
84C23×D61—21no—
85C22×#6923—41no—
86C2×Q8×C61—21no—
87C2×D4×C61C22⋊C411yescharacteristic
88C22×C4×C61—21no—
89C2×C22⋊D61—21no—
90C22×Dic61—21no—
91Q8×D61—81no—
92Q8×D61—81no—
93D4×D61—21no—
94D4×D61—21no—
95D4×D61—21no—
96D4×D61—21no—
97C2×D244C22⋊C411yescharacteristic
98C2×C4×D61—21no—
99C2×C4×D61—21no—
100C2×C4×D61—21no—
101C2×C4×D61—41no—
102C2×C4×D61—41no—
103C2×C4×D61—41no—
104C2×C4×D61—41no—
105C2×C4×D61—41no—
106C2×C4×D61C2×D411yescharacteristic
107C2×C4×D61C2×D411yescharacteristic
108C2×C4×D61#4111yescharacteristic
109C2×Dic122—21no—
110C2×Dic122—41no—
111#11758217—44no—
112C2×#92420—21no—
113C2×#92420—21no—
114C2×#92420—22no—
115C2×#92420—41no—
116C4⋊#6923—41no—
117C4⋊#6923—41no—
118C4⋊#6923—41no—
119C4⋊#6923—41no—
120C4⋊#6923—81no—
121#11758213—44no—
122D61⋊C8—21no—
123D61⋊C8—21no—
124D61⋊C8—21no—
125D61⋊C8—41no—
126D61⋊C8—41no—
127D61⋊C8—41no—
128D61⋊C8—41no—
129D61⋊C8SD1612yes—
130C2×C8×C61—21no—
131C4⋊C4×C61—21no—
132C4⋊C4×C61—21no—
133C4⋊C4×C61C22⋊C411yescharacteristic
134C22⋊C4×C61—21no—
135C42×C61C22×C411yescharacteristic
136C22⋊Dic61—21no—
137#11758198—21no—
138#11758198—21no—
139C4⋊Dic61—21no—
140C4⋊Dic61—21no—
141C4⋊Dic61C22⋊C411yescharacteristic
142#11758196—21no—
143#11758196—41no—
144#11758196—41no—
145C4×Dic61C2×D411yescharacteristic
146C4×Dic61C2×D411yescharacteristic
147C4×Dic61#4111yescharacteristic
148C2×#92418—21no—
149C8×D61—41no—
150C8×D61—41no—
151C23×C61—21no—
152C22×D61—21no—
153C22×D61—41no—
154C22×D61—41no—
155C22×D61—41no—
156C22×D61—41no—
157C22×D61—41no—
158C22×D61—41no—
159C22×D61#12111yescharacteristic
160C2×#6923—81no—
161C2×#6923—81no—
162C2×#6923—81no—
163Q8×C61—81no—
164D4×C61—21no—
165D4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61C2×C22⋊C411yescharacteristic
171C2×C4×C61C4×D411yescharacteristic
172C2×C4×C61C4×D411yescharacteristic
173C22⋊D61—41no—
174C22⋊D61—41no—
175C2×Dic61—21no—
176C2×Dic61—41no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61#12011yescharacteristic
180C2×Dic61#12111yescharacteristic
181C2×Dic61#12311yescharacteristic
182D244—21no—
183D244—21no—
184C4×D61—21no—
185C4×D61—21no—
186C4×D61—41no—
187C4×D61—41no—
188C4×D61—41no—
189C4×D61—41no—
190C4×D61—41no—
191C4×D61—41no—
192C4×D61—81no—
193C4×D61—81no—
194C4×D61C2×SD1611yescharacteristic
195C4×D61#13511yescharacteristic
196C4×D61AGL(1,ℤ/8)11yescharacteristic
197C4×D61AGL(1,ℤ/8)11yescharacteristic
198C4×D61#13711yescharacteristic
199C4×D61#13711yescharacteristic
200C4×D61#13711yescharacteristic
201C4×D61#13711yescharacteristic
202Dic122—82no—
203Dic122—81no—
204#92420—22no—
205#92420—42no—
206#92420—41no—
207#92420—81no—
208C8×C61—41no—
209#92418—41no—
210#9223—611nomaximal, Sylow
211C22×C61—41no—
212C22×C61—41no—
213C22×C61—41no—
214C22×C61#38611yescharacteristic
215C2×D61—41no—
216C2×D61—41no—
217C2×D61—41no—
218C2×D61—81no—
219C2×D61—81no—
220C2×D61—81no—
221C2×D61—81no—
222C2×D61#46111yescharacteristic
223C2×D61#46311yescharacteristic
224C2×D61#46811yescharacteristic
225C2×D61#47011yescharacteristic
226C2×D61#47111yescharacteristic
227C2×D61#47211yescharacteristic
228#6923—161no—
229C4×C61—21no—
230C4×C61—41no—
231C4×C61—81no—
232C4×C61#41711yescharacteristic
233C4×C61#41911yescharacteristic
234C4×C61C4×SD1611yescharacteristic
235C4×C61#44011yescharacteristic
236Dic61—21no—
237Dic61—41no—
238Dic61—81no—
239Dic61#45011yescharacteristic
240Dic61#45211yescharacteristic
241Dic61#46811yescharacteristic
242Dic61#47011yescharacteristic
243C2×#476—611no—
244C2×#436—611no—
245#1990—611no—
246#1802—611no—
247C2×#333—611no—
248#1296—611no—
249#1277—611no—
250C2×C61—81no—
251C2×C61#187711yescharacteristic
252C2×C61#189411yescharacteristic
253C2×C61#190711yescharacteristic
254D61—81no—
255D61#169111yescharacteristic
256D61#169511yescharacteristic
257D61#169711yescharacteristic
258D61#170311yescharacteristic
259C22×M16—1221no—
260C2×C4⋊Q8—611no—
261C2×C4×D4—611no—
262#476—611no—
263#476—611no—
264#476—611no—
265#476—1221no—
266#476—1221no—
267#476#692311yescharacteristic, complemented
268#436—1222no—
269#436—1221no—
270#436—1221no—
271C2×#106—1221no—
272C2×C4⋊C8—611no—
273C2×C4⋊C8—611no—
274C2×C4⋊C8—611no—
275C2×#102—1221no—
276C2×#102—1221no—
277C2×C22⋊C8—1221no—
278C2×C4×C8—611no—
279#384—611no—
280#340—1221no—
281#340—1221no—
282#340—1221no—
283#333—1222no—
284C61#922311yescharacteristic, complemented, Sylow
285C22×Q8—1221no—
286C22×D4—611no—
287C23×C4—1221no—
288C2×M16—1222no—
289C2×M16—1222no—
290C2×M16—2442no—
291C2×M16—2442no—
292C22×C8—611no—
293C22×C8—611no—
294C22×C8—1221no—
295C22×C8—1221no—
296C22×C8—1221no—
297C4⋊Q8—611no—
298C4⋊Q8—1221no—
299C4⋊Q8—1221no—
300C4⋊Q8—1221no—
301C4⋊Q8C2×#692311yescharacteristic
302C4×D4—611no—
303C4×D4—611no—
304C4×D4—611no—
305C4×D4—1221no—
306C4×D4—1221no—
307C4×D4C2×#692311yescharacteristic
308C2×C4⋊C4—611no—
309C2×C4⋊C4—1221no—
310C2×C4⋊C4—1221no—
311C2×C4⋊C4—1221no—
312C2×C4⋊C4—1221no—
313C2×C4⋊C4—1221no—
314C2×C22⋊C4—1221no—
315C2×C42—611no—
316#106—21no—
317#106—1221no—
318#106—1221no—
319#106—1221no—
320C4⋊C8—612no—
321C4⋊C8—611no—
322C4⋊C8—1221no—
323C4⋊C8—1221no—
324C4⋊C8—1221no—
325C4⋊C8—1221no—
326C4⋊C8C2×#692311yescharacteristic
327#102—21no—
328#102—1221no—
329#102—1221no—
330#102—1221no—
331#102—2442no—
332C22⋊C8—1222no—
333C22⋊C8—1222no—
334C4×C8—1221no—
335C4×C8—1221no—
336C24—1221no—
337C2×Q8—21no—
338C2×Q8—1221no—
339C2×Q8—4881no—
340C2×Q8—4881no—
341C2×Q8—2441no—
342C2×D4—611no—
343C2×D4—1221no—
344C2×D4—1221no—
345C2×D4—1221no—
346C2×D4—1221no—
347C2×D4—1221no—
348C2×D4C22⋊#692311yescharacteristic
349C22×C4—21no—
350C22×C4—611no—
351C22×C4—611no—
352C22×C4—611no—
353C22×C4—1221no—
354C22×C4—1221no—
355C22×C4—1221no—
356C22×C4—1221no—
357C22×C4—2441no—
358C22×C4—2441no—
359C22×C4—2441no—
360C22×C4—2441no—
361C22×C4—2441no—
362C22×C4—2441no—
363M16—2444no—
364M16—2444no—
365C2×C8—21no—
366C2×C8—612no—
367C2×C8—1221no—
368C2×C8—1221no—
369C2×C8—1221no—
370C2×C8—1222no—
371C2×C8—1221no—
372C2×C8—1221no—
373C2×C8—1221no—
374C2×C8—2441no—
375C2×C8—2441no—
376C2×C8—2441no—
377C2×C8—2441no—
378C2×C8—2441no—
379C2×C8—2441no—
380C2×C8—2441no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—611no—
384C4⋊C4—1221no—
385C4⋊C4—1221no—
386C4⋊C4—1221no—
387C4⋊C4—4881no—
388C4⋊C4—2441no—
389C4⋊C4—2441no—
390C4⋊C4—2441no—
391C4⋊C4—2441no—
392C4⋊C4—2441no—
393C4⋊C4—2441no—
394C4⋊C4C22⋊#692311yescharacteristic
395C22⋊C4—21no—
396C22⋊C4—1221no—
397C22⋊C4—1221no—
398C22⋊C4—1221no—
399C42—611no—
400C42—611no—
401C42—611no—
402C42C22×#692311yescharacteristic
403C23—21no—
404C23—611no—
405C23—1221no—
406C23—2441no—
407C23—2441no—
408C23—2441no—
409C23—2441no—
410C23—2441no—
411C23—2441no—
412Q8—81no—
413Q8—4881no—
414Q8—4882no—
415D4—21no—
416D4—21no—
417D4—1221no—
418D4—1221no—
419D4—2441no—
420D4—2441no—
421C2×C4—21no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—611no—
426C2×C4—611no—
427C2×C4—611no—
428C2×C4—611no—
429C2×C4—611no—
430C2×C4—611no—
431C2×C4—611no—
432C2×C4—611no—
433C2×C4—611no—
434C2×C4—611no—
435C2×C4—611no—
436C2×C4—1221no—
437C2×C4—1221no—
438C2×C4—1221no—
439C2×C4—4881no—
440C2×C4—4881no—
441C2×C4—4881no—
442C2×C4—4881no—
443C2×C4—4881no—
444C2×C4—2441no—
445C2×C4—2441no—
446C2×C4—2441no—
447C2×C4—2441no—
448C2×C4—2441no—
449C2×C4—2441no—
450C2×C4—2441no—
451C2×C4—2441no—
452C2×C4—2441no—
453C2×C4C2×C22⋊#692311yescharacteristic
454C2×C4D4×#692311yescharacteristic
455C2×C4D4×#692311yescharacteristic
456C8—41no—
457C8—1222no—
458C8—4881no—
459C8—2441no—
460C8—2442no—
461C8—2441no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—611no—
466C22—611no—
467C22—611no—
468C22—611no—
469C22—611no—
470C22—611no—
471C22—4881no—
472C22—4881no—
473C22—4881no—
474C22—4881no—
475C22—2441no—
476C22—2441no—
477C22—2441no—
478C22#1684071011yescharacteristic
479C4—21no—
480C4—41no—
481C4—81no—
482C4—611no—
483C4—611no—
484C4—611no—
485C4—611no—
486C4—1221no—
487C4—9761no—
488C4—4881no—
489C4—2441no—
490C4#1684075311yescharacteristic
491C4#1684075511yescharacteristic
492C4SD16×#692311yescharacteristic
493C4#1684080111yescharacteristic
494C2—81no—
495C2—611no—
496C2—611no—
497C2—611no—
498C2—611no—
499C2—4881no—
500C2#2146181211yescharacteristic
501C2#2146183411yescharacteristic
502C2#2146185811yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#476C4
socleC22×C61#386
prime radicalC2×D4×D61D4
cosocleC42×D61C23
hypercenter#476#6923
hypocenterC61#9223
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #21462000C2semidirect
4. D61⋊#333C2semidirect
5. #21460698C2semidirect
6. #21460648C2semidirect
24. #16840053C4semidirect
25. #16840052C4semidirect
28. #16840049C4semidirect
32. C61×#476C4semidirect
267. #476#6923semidirect
284. C61#9223semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4362
#214620002
#214616872
D61⋊#3332
#214606982
#214606482
#476×D612
#922361