Finite Group Databasebeta

← #29836402

Subgroups — #29836402

Order 15616.

500 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#21456469C211yesmaximal, characteristic, complemented
2#21447983C211yesmaximal, characteristic, complemented
3#21447976C211yesmaximal, characteristic, complemented
4#21447963C211yesmaximal, characteristic, complemented
5#21447953C211yesmaximal, characteristic, complemented
6#21447934C211yesmaximal, characteristic, complemented
7#21447920C211yesmaximal, characteristic, complemented
8#21447917C211yesmaximal, characteristic, complemented
9#21447903C211yesmaximal, characteristic, complemented
10#21447871C211yesmaximal, characteristic, complemented
11#21447871C211yesmaximal, characteristic, complemented
12#21447859C211yesmaximal, characteristic, complemented
13#21447854C211yesmaximal, characteristic, complemented
14#21447578C211yesmaximal, characteristic, complemented
15C61×#3175C211yesmaximal, characteristic, complemented
16#16840367—21no—
17C2×#14519720C2211yescharacteristic
18C2×#14519720C2211yescharacteristic
19C2×#14519718C2211yescharacteristic
20C2×#14519718C2211yescharacteristic
21C2×#14519717C2211yescharacteristic
22C22×#11758185C2211yescharacteristic
23#16840164C2211yescharacteristic
24#16840139C2211yescharacteristic
25#16840127—21no—
26#16840015—21no—
27#16839998C2211yescharacteristic
28#16839998C2211yescharacteristic
29#16839875—21no—
30C4×D488C2211yescharacteristic
31C4×D488C2211yescharacteristic
32#16839589C2211yescharacteristic
33#16839589C2211yescharacteristic
34#16839587C2211yescharacteristic
35#16839587C2211yescharacteristic
36C4⋊#11758185C2211yescharacteristic
37C4⋊#11758185C2211yescharacteristic
38C4⋊#11758185C2211yescharacteristic
39C4⋊#11758185C2211yescharacteristic
40#16839566C2211yescharacteristic
41#16839566C2211yescharacteristic
42#16839563C2211yescharacteristic
43#16839563C2211yescharacteristic
44#16839562C2211yescharacteristic
45#16839562C2211yescharacteristic
46#16839562C2211yescharacteristic
47#16839562C2211yescharacteristic
48C61×#542—21no—
49C61×#500C2211yescharacteristic
50C61×#495C2211yescharacteristic
51C61×#489—21no—
52C61×#468—21no—
53C61×#467C2211yescharacteristic
54C61×#466C2211yescharacteristic
55C61×#440—21no—
56C4×Q16×C61C2211yescharacteristic
57C4×D8×C61C2211yescharacteristic
58C61×#405C2211yescharacteristic
59C2×D488—21no—
60C2×D488C2311yescharacteristic
61C2×D488C2311yescharacteristic
62#14519774—21no—
63#14519769—21no—
64#14519762—41no—
65#14519762—41no—
66#14519751—21no—
67#14519751—21no—
68#14519750—41no—
69#14519750—41no—
70C4×D244—21no—
71C4×D244—21no—
72#14519720—41no—
73#14519720—41no—
74#14519718—41no—
75#14519718—41no—
76#14519717—41no—
77C2×#11758185—41no—
78C2×#11758185C2311yescharacteristic
79C2×#11758185C2311yescharacteristic
80C2×#11758185C2311yescharacteristic
81C2×#11758185C2311yescharacteristic
82#14519711C2311yescharacteristic
83#14519711C2311yescharacteristic
84#14519709—21no—
85#14519699—21no—
86#14519699—21no—
87#14519699—21no—
88#14519699—21no—
89C2×Q16×C61C2311yescharacteristic
90C2×SD16×C61—21no—
91C2×D8×C61C2311yescharacteristic
92C2×M16×C61D411yescharacteristic
93C22×C8×C61C2311yescharacteristic
94C4⋊Q8×C61—21no—
95#126×C61—41no—
96#124×C61—21no—
97#124×C61—41no—
98#123×C61—41no—
99C22⋊Q8×C61—21no—
100C22⋊Q8×C61—41no—
101#121×C61—21no—
102C4×Q8×C61—21no—
103C4×D4×C61—21no—
104#117×C61D411yescharacteristic
105#107×C61—21no—
106#107×C61C2311yescharacteristic
107#107×C61C2311yescharacteristic
108#103×C61—21no—
109#103×C61—21no—
110#102×C61—21no—
111#102×C61—21no—
112#97×C61D411yescharacteristic
113#97×C61D411yescharacteristic
114C4×C8×C61C2311yescharacteristic
115C4×C8×C61C2311yescharacteristic
116C2×Q8×C61—21no—
117C2×Q8×C61—41no—
118C2×D4×C61—21no—
119C2×D4×C61—41no—
120C22×C4×C61—41no—
121C22×C4×C61C2×D411yescharacteristic
122C2×C22⋊D61—41no—
123C2×C22⋊D61—41no—
124C2×D244—21no—
125C2×D244—21no—
126C2×D244—41no—
127C2×D244—41no—
128C2×C4×D61—41no—
129C2×C4×D61—41no—
130Q16×C61—21no—
131Q16×C61—21no—
132SD16×C61—42no—
133D8×C61—21no—
134D8×C61—21no—
135M16×C61—41no—
136C2×C8×C61—21no—
137C2×C8×C61—21no—
138C2×C8×C61C2×D411yescharacteristic
139C2×C8×C61C2×D411yescharacteristic
140C2×C8×C61C2×D411yescharacteristic
141C2×C8×C61C2411yescharacteristic
142C4⋊C4×C61—21no—
143C4⋊C4×C61—21no—
144C4⋊C4×C61—41no—
145C4⋊C4×C61—41no—
146C4⋊C4×C61—41no—
147C4⋊C4×C61D811yescharacteristic
148C4⋊C4×C61D811yescharacteristic
149C22⋊C4×C61—41no—
150C22⋊C4×C61—41no—
151C22⋊C4×C61—41no—
152C22⋊C4×C61—41no—
153C22⋊C4×C61—41no—
154C22⋊C4×C61D811yescharacteristic
155C22⋊C4×C61D811yescharacteristic
156C42×C61—41no—
157C42×C61C2×D411yescharacteristic
158C42×C61C2×D411yescharacteristic
159#11758198—41no—
160#11758198—41no—
161#11758198—41no—
162#11758198—41no—
163C4⋊Dic61—21no—
164C4⋊Dic61—21no—
165#11758196—41no—
166#11758196—41no—
167D488—21no—
168D488—21no—
169D488—21no—
170D488—21no—
171D488—42no—
172#11758185—21no—
173#11758185—21no—
174#11758185—21no—
175#11758185—21no—
176C23×C61—41no—
177C23×C61C2×D811yescharacteristic
178C22×D61—41no—
179C22×D61—41no—
180Q8×C61—41no—
181Q8×C61—41no—
182Q8×C61—161no—
183D4×C61—41no—
184D4×C61—41no—
185D4×C61—161no—
186C2×C4×C61—21no—
187C2×C4×C61—21no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—161no—
192C2×C4×C61C2×D811yescharacteristic
193C2×C4×C61C2×D811yescharacteristic
194C2×C4×C61C2×D811yescharacteristic
195C2×C4×C61C2×D811yescharacteristic
196C2×C4×C61C2×D811yescharacteristic
197C2×C4×C61C22×D411yescharacteristic
198C22⋊D61—161no—
199C22⋊D61—161no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202D244—41no—
203D244—41no—
204D244—41no—
205D244—41no—
206D244—161no—
207D244—161no—
208C4×D61—161no—
209C4×D61—161no—
210C8×C61—21no—
211C8×C61—21no—
212C8×C61—21no—
213C8×C61H(5,𝔽2)11yescharacteristic
214C8×C612−1+411yescharacteristic
215#33823—611nomaximal, Sylow
216C22×C61—21no—
217C22×C61—21no—
218C22×C61—21no—
219C22×C61—81no—
220C22×C61—81no—
221C22×C61—81no—
222C22×C61C22×D811yescharacteristic
223C2×D61—81no—
224C2×D61—81no—
225C2×D61—81no—
226C2×D61—81no—
227C2×D61—81no—
228C2×D61—81no—
229C4×C61—21no—
230C4×C61—21no—
231C4×C61—21no—
232C4×C61—21no—
233C4×C61—21no—
234C4×C61—81no—
235C4×C61—81no—
236C4×C61—81no—
237C4×C61#53711yescharacteristic
238C4×C61#57511yescharacteristic
239Dic61—81no—
240Dic61—81no—
241#3176—611no—
242#3175D6111yescharacteristic, complemented
243#2229—611no—
244#2228—611no—
245#2226—611no—
246#2224—611no—
247#2220—611no—
248#2218—611no—
249#2217—611no—
250#2215—611no—
251#2210—611no—
252#2210—611no—
253#2207—611no—
254#2206—611no—
255#2151—611no—
256C2×C61—41no—
257C2×C61—161no—
258C2×C61#324511yescharacteristic
259C2×C61#341511yescharacteristic
260C2×C61#341611yescharacteristic
261D61—161no—
262D61—161no—
263#542—21no—
264#540—1221no—
265C2×SD32—611no—
266C2×SD32—611no—
267C2×D16—611no—
268C2×D16—611no—
269C2×M32—611no—
270C22×C16—611no—
271#500C2×D6111yescharacteristic
272#499—611no—
273#495C2×D6111yescharacteristic
274#493—611no—
275#490—1221no—
276#489—21no—
277#469—1221no—
278#468—21no—
279#467C2×D6111yescharacteristic
280#466—611no—
281#466—611no—
282#466C2×D6111yescharacteristic
283#442—1221no—
284#440—21no—
285C4×Q16C2×D6111yescharacteristic
286C4×D8—611no—
287C4×D8—611no—
288C4×D8C2×D6111yescharacteristic
289#405C2×D6111yescharacteristic
290#367—611no—
291#367—611no—
292#366—611no—
293#366—611no—
294C4⋊C16—611no—
295C4⋊C16—611no—
296C4⋊C16—611no—
297C4⋊C16—611no—
298#358—611no—
299#358—611no—
300#357—611no—
301#357—611no—
302#357—611no—
303#357—611no—
304#357—611no—
305#357—611no—
306C61#3382311yescharacteristic, complemented, Sylow
307C2×Q16C22×D6111yescharacteristic
308C2×SD16—21no—
309C2×D8—611no—
310C2×D8—611no—
311C2×D8—1221no—
312C2×D8C22×D6111yescharacteristic
313C2×M16C22⋊D6111yescharacteristic
314C22×C8C22×D6111yescharacteristic
315C4⋊Q8—21no—
316#127—1221no—
317#126—41no—
318#125—1221no—
319#124—21no—
320#124—41no—
321#123—41no—
322#123—2441no—
323#123—2441no—
324C22⋊Q8—21no—
325C22⋊Q8—41no—
326#121—21no—
327#121—1221no—
328#121—1221no—
329#121—2441no—
330#121—2441no—
331C4×Q8—21no—
332C4×D4—21no—
333C4×D4—1221no—
334C4×D4—1221no—
335#117C22⋊D6111yescharacteristic
336SD32—2441no—
337SD32—2441no—
338D16—2441no—
339D16—2441no—
340M32—2441no—
341C2×C16—611no—
342C2×C16—611no—
343C2×C16—611no—
344C2×C16—611no—
345C2×C16—2441no—
346#107—21no—
347#107—611no—
348#107—611no—
349#107C22×D6111yescharacteristic
350#107C22×D6111yescharacteristic
351#106—1221no—
352#103—21no—
353#103—21no—
354#102—21no—
355#102—21no—
356#102—1221no—
357#102—1221no—
358#102—1221no—
359#102—1221no—
360#97C22⋊D6111yescharacteristic
361#97C22⋊D6111yescharacteristic
362C4×C8C22×D6111yescharacteristic
363C4×C8C22×D6111yescharacteristic
364C2×Q8—21no—
365C2×Q8—41no—
366C2×D4—21no—
367C2×D4—41no—
368C2×D4—1221no—
369C2×D4—1221no—
370C2×D4—2441no—
371C2×D4—2441no—
372C2×D4—2441no—
373C2×D4—2441no—
374C22×C4—41no—
375C22×C4—2441no—
376C22×C4—2441no—
377C22×C4C2×C22⋊D6111yescharacteristic
378Q16—21no—
379Q16—21no—
380SD16—42no—
381D8—21no—
382D8—21no—
383D8—1221no—
384D8—1221no—
385D8—1221no—
386D8—1221no—
387D8—2442no—
388M16—41no—
389C2×C8—21no—
390C2×C8—21no—
391C2×C8C2×C22⋊D6111yescharacteristic
392C2×C8C2×C22⋊D6111yescharacteristic
393C2×C8C2×C22⋊D6111yescharacteristic
394C2×C8C23×D6111yescharacteristic
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C4⋊C4—1221no—
401C4⋊C4—1221no—
402C4⋊C4—2441no—
403C4⋊C4—2441no—
404C4⋊C4#1175819911yescharacteristic
405C4⋊C4#1175819911yescharacteristic
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—2441no—
412C22⋊C4—2441no—
413C22⋊C4—2441no—
414C22⋊C4—2441no—
415C22⋊C4#1175819911yescharacteristic
416C22⋊C4#1175819911yescharacteristic
417C42—41no—
418C42C2×C22⋊D6111yescharacteristic
419C42C2×C22⋊D6111yescharacteristic
420C16—1221no—
421C16—1221no—
422C16—1221no—
423C16—1221no—
424C23—41no—
425C23—2441no—
426C23—2441no—
427C23C2×#1175819911yescharacteristic
428Q8—41no—
429Q8—41no—
430Q8—161no—
431D4—41no—
432D4—41no—
433D4—161no—
434D4—9761no—
435D4—9761no—
436D4—9761no—
437D4—9761no—
438D4—2441no—
439D4—2441no—
440D4—2441no—
441D4—2441no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—161no—
448C2×C4—9761no—
449C2×C4—9761no—
450C2×C4—2441no—
451C2×C4—2441no—
452C2×C4C2×#1175819911yescharacteristic
453C2×C4C2×#1175819911yescharacteristic
454C2×C4C2×#1175819911yescharacteristic
455C2×C4C2×#1175819911yescharacteristic
456C2×C4C2×#1175819911yescharacteristic
457C2×C4C22×C22⋊D6111yescharacteristic
458C8—21no—
459C8—21no—
460C8—21no—
461C8#1451982311yescharacteristic
462C8#1451982411yescharacteristic
463C22—21no—
464C22—21no—
465C22—21no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—4881no—
470C22—4881no—
471C22—4881no—
472C22—4881no—
473C22—4881no—
474C22—4881no—
475C22C22×#1175819911yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—81no—
482C4—81no—
483C4—81no—
484C4—4881no—
485C4—4881no—
486C4#1684034011yescharacteristic
487C4#1684056011yescharacteristic
488C2—41no—
489C2—161no—
490C2—9761no—
491C2—9761no—
492C2#2145712611yescharacteristic
493C2#2145895811yescharacteristic
494C2#2145896311yescharacteristic
subgroupG/H
centerC22C22×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#3175C2
socleC22×C61C22×D8
hypercenter#3175D61
hypocenterC61#33823
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3175

Complements

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

NH ≅ G/Ntype
1. #21456469C2semidirect
2. #21447983C2semidirect
3. #21447976C2semidirect
4. #21447963C2semidirect
5. #21447953C2semidirect
6. #21447934C2semidirect
7. #21447920C2semidirect
8. #21447917C2semidirect
9. #21447903C2semidirect
10. #21447871C2semidirect
11. #21447871C2semidirect
12. #21447859C2semidirect
13. #21447854C2semidirect
14. #21447578C2semidirect
15. C61×#3175C2semidirect
242. #3175D61semidirect
306. C61#33823semidirect

Maximal subgroups

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

subgroupindex
#214564692
#214479832
#214479762
#214479632
#214479532
#214479342
#214479202
#214479172
#214479032
#214478712
#214478592
#214478542
#214475782
C61×#31752
#3382361