Finite Group Databasebeta

← #29838073

Subgroups — #29838073

Order 15616.

510 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458828C211yesmaximal, characteristic
2#21458823C211yesmaximal, characteristic, complemented
3#21448087C211yesmaximal, characteristic, complemented
4#21448073C211yesmaximal, characteristic
5#21447883C211yesmaximal, characteristic, complemented
6#21447878C211yesmaximal, characteristic, complemented
7#21447867C211yesmaximal, characteristic, complemented
8#21447862C211yesmaximal, characteristic, complemented
9#21447861C211yesmaximal, characteristic, complemented
10#21447857C211yesmaximal, characteristic
11#21447725C211yesmaximal, characteristic, complemented
12#21447685C211yesmaximal, characteristic, complemented
13#21447684C211yesmaximal, characteristic, complemented
14Q32×Dic61C211yesmaximal, characteristic, complemented
15C61×#2251C211yesmaximal, characteristic, complemented
16#16840494—21no—
17#16840487—21no—
18C2×#14519723C2211yescharacteristic
19C2×#14519722C2211yescharacteristic
20C2×#14519721C2211yescharacteristic
21C2×#14519720C2211yescharacteristic
22C2×#14519720C2211yescharacteristic
23#16840147C2211yescharacteristic
24#16840140C2211yescharacteristic
25#16840140C2211yescharacteristic
26#16840137C2211yescharacteristic
27#16839979—21no—
28#16839974—21no—
29#16839970—21no—
30#16839970—21no—
31#16839969—21no—
32#16839960—21no—
33C8×Dic122C2211yescharacteristic
34C4×Dic244C2211yescharacteristic
35Q16×Dic61C2211yescharacteristic
36Q16×Dic61C2211yescharacteristic
37Q16×Dic61C2211yescharacteristic
38C4×D488C2211yescharacteristic
39D8×Dic61C2211yescharacteristic
40#16839588C2211yescharacteristic
41C4⋊#11758185C2211yescharacteristic
42#16839580C2211yescharacteristic
43#16839580C2211yescharacteristic
44#16839567C2211yescharacteristic
45#16839566C2211yescharacteristic
46#16839566C2211yescharacteristic
47#16839566C2211yescharacteristic
48#16839564C2211yescharacteristic
49#16839563C2211yescharacteristic
50#16839537C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C2×Q32×C61C2211yescharacteristic
53C2×Q32×C61C2211yescharacteristic
54C2×SD32×C61C2211yescharacteristic
55C2×SD32×C61C2211yescharacteristic
56C61×#495C2211yescharacteristic
57C61×#494C2211yescharacteristic
58C61×#346C2211yescharacteristic
59C2×Dic244C2311yescharacteristic
60C2×#11758202—21no—
61C2×#11758202—21no—
62C2×#11758201—21no—
63C2×D488C2311yescharacteristic
64C2×#11758199—21no—
65#14519775—21no—
66#14519775—21no—
67#14519773—21no—
68#14519768—41no—
69#14519767—41no—
70#14519767—41no—
71#14519766—21no—
72#14519763—41no—
73#14519761—41no—
74#14519759—41no—
75Q8×Dic61—21no—
76Q8×Dic61—21no—
77Q8×Dic61—21no—
78C4×Dic122—21no—
79C4×Dic122D411yescharacteristic
80#14519742—41no—
81C4×D244—21no—
82D4×Dic61—21no—
83#14519737—41no—
84#14519723—41no—
85#14519722—22no—
86#14519721—41no—
87#14519720—41no—
88#14519720—41no—
89C2×#11758185C2311yescharacteristic
90C2×#11758185C2311yescharacteristic
91#14519711C2311yescharacteristic
92#14519711C2311yescharacteristic
93C4⋊#92418D411yescharacteristic
94#14519706D411yescharacteristic
95#14519706D411yescharacteristic
96#14519702—21no—
97#14519701—21no—
98#14519701—21no—
99#14519701—21no—
100#14519699—21no—
101#14519698—21no—
102C8×Dic61C2311yescharacteristic
103C8×Dic61C2311yescharacteristic
104C2×Q16×C61—21no—
105C2×Q16×C61C2311yescharacteristic
106C2×Q16×C61C2311yescharacteristic
107C2×Q16×C61C2311yescharacteristic
108C2×SD16×C61—21no—
109C2×D8×C61C2311yescharacteristic
110C4⋊Q8×C61—21no—
111#124×C61—21no—
112Q32×C61—22no—
113Q32×C61—41no—
114SD32×C61—22no—
115SD32×C61—41no—
116C2×C16×C61C2311yescharacteristic
117C2×C16×C61C2311yescharacteristic
118C4×C8×C61C2311yescharacteristic
119C2×Q8×C61—21no—
120C2×Q8×C61—21no—
121C2×Q8×C61—21no—
122C2×D4×C61—21no—
123C2×C22⋊D61—41no—
124C2×C22⋊D61—41no—
125C22×Dic61—41no—
126C2×D244—21no—
127C2×C4×D61—41no—
128C2×Dic122—21no—
129C2×Dic122D811yescharacteristic
130Q16×C61—21no—
131Q16×C61—21no—
132Q16×C61—21no—
133Q16×C61—21no—
134Q16×C61—21no—
135Q16×C61—21no—
136Q16×C61—81no—
137SD16×C61—81no—
138D8×C61—21no—
139D8×C61—21no—
140C2×C8×C61C2×D411yescharacteristic
141C2×C8×C61C2411yescharacteristic
142C4⋊C4×C61—41no—
143C4⋊C4×C61—41no—
144C22⋊C4×C61—41no—
145C22⋊C4×C61—41no—
146C42×C61C2×D411yescharacteristic
147C22⋊Dic61—41no—
148#11758202—81no—
149#11758202—81no—
150#11758201—81no—
151#11758199—81no—
152#11758198—41no—
153#11758198—41no—
154#11758198—41no—
155C4⋊Dic61—21no—
156C4⋊Dic61—21no—
157C4⋊Dic61—41no—
158C4⋊Dic61—41no—
159C4⋊Dic61—41no—
160C4⋊Dic61D811yescharacteristic
161#11758196—41no—
162#11758196—41no—
163#11758196—41no—
164#11758196—41no—
165#11758196—41no—
166#11758196D811yescharacteristic
167#11758196D811yescharacteristic
168C4×Dic61—41no—
169C4×Dic61—41no—
170C4×Dic61—41no—
171C4×Dic61—41no—
172C4×Dic61C2×D411yescharacteristic
173C4×Dic61C2×D411yescharacteristic
174C2×#92418C2×D411yescharacteristic
175C2×#92418C2×D411yescharacteristic
176Dic244—21no—
177Dic244—21no—
178D488—21no—
179D488—21no—
180C16×C61—21no—
181C16×C61#4112yes—
182#11758185—21no—
183#11758185—21no—
184C23×C61—41no—
185C22×D61—41no—
186Q8×C61—41no—
187Q8×C61—41no—
188Q8×C61—41no—
189Q8×C61—41no—
190Q8×C61—41no—
191Q8×C61—41no—
192D4×C61—41no—
193D4×C61—41no—
194C2×C4×C61—41no—
195C2×C4×C61—41no—
196C2×C4×C61—41no—
197C2×C4×C61C2×D811yescharacteristic
198C2×C4×C61C2×D811yescharacteristic
199C2×C4×C61C22×D411yescharacteristic
200C22⋊D61—82no—
201C22⋊D61—161no—
202C2×Dic61—41no—
203C2×Dic61—41no—
204C2×Dic61—41no—
205C2×Dic61—161no—
206C2×Dic61C2×D811yescharacteristic
207C2×Dic61C2×D811yescharacteristic
208C2×Dic61C2×D811yescharacteristic
209C2×Dic61C2×D811yescharacteristic
210D244—41no—
211D244—41no—
212C4×D61—161no—
213Dic122—22no—
214Dic122—41no—
215Dic122—41no—
216C8×C61—21no—
217C8×C61C2×#4111yescharacteristic
218C8×C61H(5,𝔽2)11yescharacteristic
219#92418—21no—
220#92418—21no—
221#33967—611nomaximal, Sylow
222C22×C61—81no—
223C22×C61—81no—
224C22×C61—81no—
225C22×C61C22×D811yescharacteristic
226C2×D61—81no—
227C2×D61—81no—
228C2×D61—81no—
229C4×C61—21no—
230C4×C61—21no—
231C4×C61—81no—
232C4×C61—81no—
233C4×C61—81no—
234C4×C61#55011yescharacteristic
235C4×C61#57611yescharacteristic
236Dic61—21no—
237Dic61—21no—
238Dic61—21no—
239Dic61—81no—
240Dic61—81no—
241Dic61—81no—
242Dic61#51012yes—
243#3396—611no—
244#3395—611no—
245#2251—611no—
246#2251D6111yescharacteristic, complemented
247#2248—611no—
248#2211—611no—
249#2211—611no—
250#2209—611no—
251#2208—611no—
252#2208—611no—
253#2207—611no—
254#2183—611no—
255#2175—611no—
256#2175—611no—
257C4×Q32—611no—
258C2×C61—161no—
259C2×C61#339111yescharacteristic
260C2×C61C2×#51011yescharacteristic
261C2×C61#341611yescharacteristic
262D61—161no—
263#559—1221no—
264#557—1221no—
265C2×Q32—611no—
266C2×Q32C2×D6111yescharacteristic
267C2×Q32C2×D6111yescharacteristic
268C2×SD32—611no—
269C2×SD32—611no—
270C2×SD32—611no—
271C2×SD32—611no—
272C2×SD32C2×D6111yescharacteristic
273C2×SD32C2×D6111yescharacteristic
274#495—611no—
275#495C2×D6111yescharacteristic
276#494—611no—
277#494—611no—
278#494C2×D6111yescharacteristic
279#493—611no—
280#463—1221no—
281#463—1221no—
282#462—1221no—
283#462—1221no—
284#462—1221no—
285#460—1221no—
286C8×Q8—611no—
287C4×Q16—611no—
288C4×Q16—611no—
289C4×Q16—611no—
290C4×Q16—611no—
291C4×D8—611no—
292C4×D8—611no—
293#366—611no—
294C4⋊C16—611no—
295C4⋊C16—611no—
296C4⋊C16—611no—
297#358—611no—
298#358—611no—
299#358—611no—
300#358—611no—
301#357—611no—
302#357—611no—
303#346—611no—
304#346C2×D6111yescharacteristic
305C4×C16—611no—
306C61#3396711yescharacteristic, complemented, Sylow
307C2×Q16—21no—
308C2×Q16—611no—
309C2×Q16—1221no—
310C2×Q16—1221no—
311C2×Q16C22×D6111yescharacteristic
312C2×Q16C22×D6111yescharacteristic
313C2×Q16C22×D6111yescharacteristic
314C2×SD16—21no—
315C2×SD16—1221no—
316C2×D8—611no—
317C2×D8—1221no—
318C2×D8C22×D6111yescharacteristic
319C4⋊Q8—21no—
320C4⋊Q8—1221no—
321C4⋊Q8—1221no—
322#127—1221no—
323#125—2441no—
324#125—2441no—
325#125—2441no—
326#124—21no—
327#124—1221no—
328#124—2441no—
329#123—2441no—
330#123—2441no—
331C4×Q8—611no—
332C4×Q8—1221no—
333C4×Q8—1221no—
334C4×Q8—1221no—
335C4×Q8—1221no—
336C4×Q8—2441no—
337C4×D4—1221no—
338C4×D4—1221no—
339C4×D4—2441no—
340Q32—22no—
341Q32—41no—
342Q32—2441no—
343SD32—22no—
344SD32—41no—
345SD32—1222no—
346SD32—2441no—
347SD32—2441no—
348SD32—2441no—
349C2×C16—611no—
350C2×C16—611no—
351C2×C16C22×D6111yescharacteristic
352C2×C16C22×D6111yescharacteristic
353#107—611no—
354#107—611no—
355C4⋊C8—611no—
356C4⋊C8—611no—
357C4⋊C8—611no—
358#103—1221no—
359#103—1221no—
360#103—1221no—
361#103—1221no—
362#102—1221no—
363#102—1221no—
364C4×C8—611no—
365C4×C8—611no—
366C4×C8C22×D6111yescharacteristic
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—611no—
371C2×Q8—1221no—
372C2×D4—21no—
373C2×D4—1221no—
374C2×D4—2441no—
375C2×D4—2441no—
376C22×C4—2441no—
377C22×C4—2441no—
378Q16—21no—
379Q16—21no—
380Q16—21no—
381Q16—21no—
382Q16—21no—
383Q16—21no—
384Q16—81no—
385Q16—1221no—
386Q16—1221no—
387Q16—4881no—
388Q16—4881no—
389SD16—81no—
390SD16—4881no—
391D8—21no—
392D8—21no—
393D8—1221no—
394D8—1221no—
395D8—4881no—
396C2×C8—611no—
397C2×C8—611no—
398C2×C8D4×D6111yescharacteristic
399C2×C8C23×D6111yescharacteristic
400C4⋊C4—41no—
401C4⋊C4—41no—
402C4⋊C4—611no—
403C4⋊C4—611no—
404C4⋊C4—611no—
405C4⋊C4—1221no—
406C4⋊C4—1221no—
407C4⋊C4—2441no—
408C4⋊C4—2441no—
409C4⋊C4—2441no—
410C4⋊C4—2441no—
411C4⋊C4—2441no—
412C4⋊C4—2441no—
413C4⋊C4—2441no—
414C4⋊C4—2441no—
415C22⋊C4—41no—
416C22⋊C4—41no—
417C22⋊C4—2441no—
418C22⋊C4—2441no—
419C22⋊C4—2441no—
420C22⋊C4—2441no—
421C42—611no—
422C42—611no—
423C42—2441no—
424C42—2441no—
425C42—2441no—
426C42—2441no—
427C42D4×D6111yescharacteristic
428C16—21no—
429C16—1221no—
430C16—1221no—
431C16#1175822412yes—
432C23—41no—
433C23—2441no—
434Q8—41no—
435Q8—41no—
436Q8—41no—
437Q8—41no—
438Q8—41no—
439Q8—41no—
440Q8—1222no—
441Q8—2441no—
442Q8—2441no—
443D4—41no—
444D4—41no—
445D4—9761no—
446D4—4882no—
447D4—2441no—
448D4—2441no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—611no—
453C2×C4—611no—
454C2×C4—611no—
455C2×C4—611no—
456C2×C4—9761no—
457C2×C4—9761no—
458C2×C4—2441no—
459C2×C4—2441no—
460C2×C4—2441no—
461C2×C4D8×D6111yescharacteristic
462C2×C4D8×D6111yescharacteristic
463C2×C4C2×D4×D6111yescharacteristic
464C8—21no—
465C8—1221no—
466C8—1221no—
467C8C2×#1175822411yescharacteristic
468C8#1451982211yescharacteristic
469C22—81no—
470C22—81no—
471C22—81no—
472C22—4881no—
473C22—4881no—
474C22—4881no—
475C22C2×D8×D6111yescharacteristic
476C4—21no—
477C4—21no—
478C4—81no—
479C4—81no—
480C4—81no—
481C4—612no—
482C4—1221no—
483C4—1221no—
484C4—1221no—
485C4—4881no—
486C4—4881no—
487C4—4881no—
488C4#1684043211yescharacteristic
489C4#1684056311yescharacteristic
490C2—161no—
491C2—9761no—
492C2#2145879211yescharacteristic
493C2#510×D6111yescharacteristic
494C2#2145896411yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2251C2
socleC22×C61C22×D8
prime radical#16840137C22
hypercenter#2251D61
hypocenterC61#33967
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2251

Complements

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

NH ≅ G/Ntype
2. #21458823C2semidirect
3. #21448087C2semidirect
5. #21447883C2semidirect
6. #21447878C2semidirect
7. #21447867C2semidirect
8. #21447862C2semidirect
9. #21447861C2semidirect
11. #21447725C2semidirect
12. #21447685C2semidirect
13. #21447684C2semidirect
14. Q32×Dic61C2semidirect
15. C61×#2251C2semidirect
246. #2251D61semidirect
306. C61#33967semidirect

Maximal subgroups

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

subgroupindex
#214588282
#214588232
#214480872
#214480732
#214478832
#214478782
#214478672
#214478622
#214478612
#214478572
#214477252
#214476852
#214476842
Q32×Dic612
C61×#22512
#3396761