Finite Group Databasebeta

← #29835579

Subgroups — #29835579

Order 15616.

554 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456393C211yesmaximal, characteristic, complemented
2#21456384C211yesmaximal, characteristic, complemented
3#21448104C211yesmaximal, characteristic, complemented
4#21448082C211yesmaximal, characteristic, complemented
5#21448059C211yesmaximal, characteristic, complemented
6#21448054C211yesmaximal, characteristic, complemented
7#21447932C211yesmaximal, characteristic, complemented
8#21447930C211yesmaximal, characteristic, complemented
9#21447920C211yesmaximal, characteristic, complemented
10#21447674C211yesmaximal, characteristic, complemented
11#21447670C211yesmaximal, characteristic, complemented
12D16×Dic61C211yesmaximal, characteristic, complemented
13#21447663C211yesmaximal, characteristic, complemented
14M32×Dic61C211yesmaximal, characteristic, complemented
15C61×#2218C211yesmaximal, characteristic, complemented
16#16840307—21no—
17#16840293—21no—
18C2×#14519722C2211yescharacteristic
19C2×#14519721C2211yescharacteristic
20C2×#14519718C2211yescharacteristic
21C2×#14519717C2211yescharacteristic
22#16840166C2211yescharacteristic
23#16840163C2211yescharacteristic
24#16840145C2211yescharacteristic
25#16840137C2211yescharacteristic
26#16840115—21no—
27#16840107—21no—
28#16840003C2211yescharacteristic
29#16839998C2211yescharacteristic
30#16839996—21no—
31#16839989—21no—
32#16839856C2211yescharacteristic
33#16839853—21no—
34D8×Dic61C2211yescharacteristic
35D8×Dic61C2211yescharacteristic
36#16839844C2211yescharacteristic
37#16839842—21no—
38C2×C8×Dic61C2211yescharacteristic
39#16839589C2211yescharacteristic
40#16839588C2211yescharacteristic
41#16839587C2211yescharacteristic
42#16839567C2211yescharacteristic
43#16839565C2211yescharacteristic
44#16839564C2211yescharacteristic
45#16839563C2211yescharacteristic
46#16839563C2211yescharacteristic
47#16839562C2211yescharacteristic
48#16839537C2211yescharacteristic
49#16839537C2211yescharacteristic
50C16×Dic61C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C2×D16×C61C2211yescharacteristic
53C2×M32×C61C2211yescharacteristic
54C61×#466C2211yescharacteristic
55C61×#466C2211yescharacteristic
56C61×#367C2211yescharacteristic
57C61×#357C2211yescharacteristic
58C61×#357C2211yescharacteristic
59C2×#11758224—41no—
60C2×Dic244C2311yescharacteristic
61C2×#11758200—21no—
62C2×D488C2311yescharacteristic
63C2×#11758199—21no—
64C22×#92418D411yescharacteristic
65#14519776—21no—
66#14519773—21no—
67#14519770—41no—
68#14519768—21no—
69#14519764—21no—
70#14519763—41no—
71#14519758—41no—
72#14519756—21no—
73#14519751—21no—
74#14519749—41no—
75#14519742—21no—
76D4×Dic61—21no—
77D4×Dic61—21no—
78D4×Dic61—41no—
79#14519739—21no—
80#14519737—41no—
81#14519733—41no—
82C2×C4×Dic61D411yescharacteristic
83#14519722—22no—
84#14519721—22no—
85#14519718—22no—
86#14519717—22no—
87C2×#11758185C2311yescharacteristic
88C2×#11758185C2311yescharacteristic
89#14519711C2311yescharacteristic
90#14519711C2311yescharacteristic
91#14519710—21no—
92#14519708—21no—
93#14519702—21no—
94#14519700—21no—
95#14519699—21no—
96#14519698—21no—
97#14519698—21no—
98#14519697—21no—
99C8×Dic61D411yescharacteristic
100C8×Dic61D411yescharacteristic
101C8×Dic61C2311yescharacteristic
102C8×Dic61C2311yescharacteristic
103C2×D8×C61C2311yescharacteristic
104C2×D8×C61C2311yescharacteristic
105C22×C8×C61C2311yescharacteristic
106#121×C61—21no—
107#121×C61—21no—
108D16×C61—22no—
109M32×C61—22no—
110C2×C16×C61C2311yescharacteristic
111C2×C16×C61C2311yescharacteristic
112#107×C61C2311yescharacteristic
113#107×C61C2311yescharacteristic
114#102×C61—21no—
115#102×C61—21no—
116C2×D4×C61—21no—
117C2×D4×C61—21no—
118C2×D4×C61—41no—
119C2×D4×C61—41no—
120C22×C4×C61C2×D411yescharacteristic
121C2×C22⋊D61—41no—
122C2×C22⋊D61—41no—
123C2×C22⋊D61—41no—
124C22×Dic61—41no—
125C22×Dic61—41no—
126C22×Dic61D811yescharacteristic
127C22×Dic61D811yescharacteristic
128#11758224—84no—
129C2×D244—21no—
130C2×C4×D61—41no—
131C2×Dic122—21no—
132C2×Dic122—41no—
133D8×C61—21no—
134D8×C61—21no—
135D8×C61—21no—
136D8×C61—21no—
137C2×C8×C61—21no—
138C2×C8×C61—21no—
139C2×C8×C61C2×D411yescharacteristic
140C2×C8×C61C2411yescharacteristic
141C4⋊C4×C61—21no—
142C4⋊C4×C61—21no—
143C22⋊C4×C61—41no—
144C22⋊C4×C61—41no—
145C22⋊Dic61—41no—
146C22⋊Dic61—41no—
147C22⋊Dic61—41no—
148C22⋊Dic61—41no—
149C22⋊Dic61—41no—
150#11758200—42no—
151#11758199—42no—
152#11758198—41no—
153#11758198—41no—
154C4⋊Dic61—21no—
155C4⋊Dic61—21no—
156C4⋊Dic61—41no—
157#11758196—41no—
158#11758196—41no—
159#11758196—41no—
160#11758196—41no—
161C4×Dic61—41no—
162C4×Dic61D811yescharacteristic
163C4×Dic61D811yescharacteristic
164C4×Dic61C2×D411yescharacteristic
165C4×Dic61C2×D411yescharacteristic
166C2×#92418—22no—
167C2×#92418C2×D411yescharacteristic
168C2×#92418C2×D411yescharacteristic
169Dic244—21no—
170Dic244—21no—
171D488—21no—
172D488—21no—
173C16×C61—21no—
174C16×C61#4112yescomplemented
175#11758185—21no—
176#11758185#4112yescomplemented
177C23×C61—41no—
178C23×C61—41no—
179C23×C61C2×D811yescharacteristic
180C22×D61—41no—
181D4×C61—41no—
182D4×C61—41no—
183D4×C61—41no—
184D4×C61—41no—
185D4×C61—82no—
186D4×C61—82no—
187C2×C4×C61—21no—
188C2×C4×C61—21no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61C2×D811yescharacteristic
192C2×C4×C61C22×D411yescharacteristic
193C22⋊D61—82no—
194C22⋊D61—82no—
195C22⋊D61—82no—
196C2×Dic61—22no—
197C2×Dic61—41no—
198C2×Dic61—41no—
199C2×Dic61—41no—
200C2×Dic61—41no—
201C2×Dic61—82no—
202C2×Dic61—82no—
203C2×Dic61C2×D811yescharacteristic
204C2×Dic61C2×D811yescharacteristic
205C2×Dic61C2×D811yescharacteristic
206C2×Dic61C2×D811yescharacteristic
207D244—41no—
208D244—41no—
209C4×D61—82no—
210Dic122—41no—
211Dic122—41no—
212Dic122—82no—
213C8×C61—21no—
214C8×C61C2×#4111yescharacteristic
215C8×C61C2×#4111yescharacteristic
216#92418—21no—
217#92418#13512yes—
218#33737—611nomaximal, Sylow
219C22×C61—21no—
220C22×C61—21no—
221C22×C61—21no—
222C22×C61—81no—
223C22×C61—81no—
224C22×C61—81no—
225C22×C61—81no—
226C22×C61—81no—
227C22×C61—81no—
228C22×C61C22×D811yescharacteristic
229C2×D61—81no—
230C2×D61—81no—
231C2×D61—81no—
232C4×C61—21no—
233C4×C61—81no—
234C4×C61—81no—
235C4×C61#53211yescharacteristic
236C4×C61C2×#13511yescharacteristic
237Dic61—21no—
238Dic61—21no—
239Dic61—21no—
240Dic61—81no—
241Dic61—81no—
242Dic61—81no—
243Dic61#50912yes—
244#3169—611no—
245#3168—611no—
246#2255—611no—
247#2250—611no—
248#2244—611no—
249#2243—611no—
250#2220—611no—
251#2220—611no—
252#2218—611no—
253#2218D6111yescharacteristic, complemented
254C4×SD32—611no—
255C4×SD32—611no—
256C4×D16—611no—
257C4×D16—611no—
258C4×M32—611no—
259C2×C61—41no—
260C2×C61—161no—
261C2×C61—161no—
262C2×C61#316911yescharacteristic
263C2×C61C2×#50911yescharacteristic
264C2×C61#341411yescharacteristic
265D61—161no—
266#532—1221no—
267#529—1221no—
268C2×SD32—611no—
269C2×SD32—611no—
270C2×D16—611no—
271C2×D16C2×D6111yescharacteristic
272C2×M32—611no—
273C2×M32C2×D6111yescharacteristic
274#500—611no—
275#499—611no—
276#495—611no—
277#493—611no—
278#488—1221no—
279#486—1221no—
280#467—611no—
281#466—611no—
282#466—1221no—
283#466C2×D6111yescharacteristic
284#466C2×D6111yescharacteristic
285#465—1221no—
286C4×Q16—611no—
287C4×SD16—1221no—
288C4×D8—611no—
289C4×D8—611no—
290C4×D8—611no—
291C4×D8—1221no—
292C2×C4×C8—611no—
293#367—611no—
294#367C2×D6111yescharacteristic
295#366—611no—
296#366—611no—
297#358—611no—
298#358—611no—
299#357—611no—
300#357—611no—
301#357—611no—
302#357—611no—
303#357C2×D6111yescharacteristic
304#357C2×D6111yescharacteristic
305#346—611no—
306#346—611no—
307C4×C16—611no—
308C4×C16—611no—
309C61#3373711yescharacteristic, complemented, Sylow
310C2×#41—2441no—
311C2×Q16—611no—
312C2×SD16—1221no—
313C2×D8—611no—
314C2×D8—1221no—
315C2×D8C22×D6111yescharacteristic
316C2×D8C22×D6111yescharacteristic
317C22×C8—611no—
318C22×C8C22×D6111yescharacteristic
319C4⋊Q8—1221no—
320#127—1221no—
321#126—2441no—
322#125—1221no—
323#124—1221no—
324#124—2441no—
325#123—2441no—
326C22⋊Q8—1221no—
327#121—21no—
328#121—21no—
329#121—1221no—
330#121—2441no—
331C4×Q8—1221no—
332C4×D4—1221no—
333C4×D4—1221no—
334C4×D4—1221no—
335C4×D4—2441no—
336C4×D4—2441no—
337#117—2441no—
338C2×C42—611no—
339SD32—1222no—
340SD32—1222no—
341D16—22no—
342D16—1222no—
343M32—22no—
344M32—1222no—
345C2×C16—611no—
346C2×C16—611no—
347C2×C16C22×D6111yescharacteristic
348C2×C16C22×D6111yescharacteristic
349#107—611no—
350#107—611no—
351#107—1221no—
352#107C22×D6111yescharacteristic
353#107C22×D6111yescharacteristic
354#106—1221no—
355#103—1221no—
356#103—1221no—
357#102—21no—
358#102—21no—
359#102—1221no—
360#102—1221no—
361#102—1221no—
362#102—1221no—
363C4×C8—611no—
364C4×C8—611no—
365C4×C8—611no—
366C4×C8—611no—
367#41—4884no—
368C2×Q8—1221no—
369C2×Q8—2441no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—1221no—
375C2×D4—2441no—
376C2×D4—2441no—
377C2×D4—2441no—
378C22×C4—611no—
379C22×C4—611no—
380C22×C4—2441no—
381C22×C4—2441no—
382C22×C4—2441no—
383C22×C4D4×D6111yescharacteristic
384Q16—1221no—
385Q16—1221no—
386SD16—2442no—
387D8—21no—
388D8—21no—
389D8—21no—
390D8—21no—
391D8—1221no—
392D8—1221no—
393D8—2442no—
394C2×C8—21no—
395C2×C8—21no—
396C2×C8—611no—
397C2×C8—611no—
398C2×C8—1222no—
399C2×C8D4×D6111yescharacteristic
400C2×C8C23×D6111yescharacteristic
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—1221no—
404C4⋊C4—1221no—
405C4⋊C4—2441no—
406C4⋊C4—2441no—
407C4⋊C4—2441no—
408C4⋊C4—2441no—
409C4⋊C4—2441no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—2441no—
413C22⋊C4—2441no—
414C22⋊C4—2441no—
415C22⋊C4—2441no—
416C22⋊C4—2441no—
417C22⋊C4—2441no—
418C22⋊C4—2441no—
419C42—611no—
420C42—611no—
421C42—611no—
422C42—611no—
423C42—2441no—
424C16—21no—
425C16—612no—
426C16—1221no—
427C16#1175822412yescomplemented
428C23—41no—
429C23—41no—
430C23—2441no—
431C23D8×D6111yescharacteristic
432Q8—4882no—
433Q8—2441no—
434Q8—2441no—
435D4—41no—
436D4—41no—
437D4—41no—
438D4—41no—
439D4—82no—
440D4—82no—
441D4—4882no—
442D4—4882no—
443D4—4882no—
444D4—2441no—
445D4—2441no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—611no—
451C2×C4—611no—
452C2×C4—611no—
453C2×C4—611no—
454C2×C4—1222no—
455C2×C4—4882no—
456C2×C4—4882no—
457C2×C4—4882no—
458C2×C4—2441no—
459C2×C4—2441no—
460C2×C4—2441no—
461C2×C4—2441no—
462C2×C4D8×D6111yescharacteristic
463C2×C4C2×D4×D6111yescharacteristic
464C8—21no—
465C8—612no—
466C8—1221no—
467C8#41×D6111yescharacteristic
468C8C2×#1175822411yescharacteristic
469C22—21no—
470C22—21no—
471C22—21no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—4881no—
479C22—4881no—
480C22—4881no—
481C22C2×D8×D6111yescharacteristic
482C4—21no—
483C4—81no—
484C4—81no—
485C4—612no—
486C4—1221no—
487C4—1221no—
488C4—1221no—
489C4—4881no—
490C4—4881no—
491C4—4881no—
492C4#1684030711yescharacteristic
493C4#135×D6111yescharacteristic
494C2—41no—
495C2—161no—
496C2—161no—
497C2—9761no—
498C2#2145639311yescharacteristic
499C2#509×D6111yescharacteristic
500C2#2145895111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2218C2
socleC22×C61C22×D8
hypercenter#2218D61
hypocenterC61#33737
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2218

Complements

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

NH ≅ G/Ntype
1. #21456393C2semidirect
2. #21456384C2semidirect
3. #21448104C2semidirect
4. #21448082C2semidirect
5. #21448059C2semidirect
6. #21448054C2semidirect
7. #21447932C2semidirect
8. #21447930C2semidirect
9. #21447920C2semidirect
10. #21447674C2semidirect
11. #21447670C2semidirect
12. D16×Dic61C2semidirect
13. #21447663C2semidirect
14. M32×Dic61C2semidirect
15. C61×#2218C2semidirect
174. C16×C61#41semidirect
176. #11758185#41semidirect
253. #2218D61semidirect
309. C61#33737semidirect
427. C16#11758224semidirect

Maximal subgroups

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

subgroupindex
#214563932
#214563842
#214481042
#214480822
#214480592
#214480542
#214479322
#214479302
#214479202
#214476742
#214476702
D16×Dic612
#214476632
M32×Dic612
C61×#22182
#3373761