Finite Group Databasebeta

← #29837644

Subgroups — #29837644

Order 15616.

482 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458238C211yesmaximal, characteristic
2#21458208C211yesmaximal, characteristic, complemented
3#21448093C211yesmaximal, characteristic, complemented
4#21448025C211yesmaximal, characteristic, complemented
5#21448024C211yesmaximal, characteristic, complemented
6#21447998C211yesmaximal, characteristic, complemented
7#21447997C211yesmaximal, characteristic, complemented
8#21447969C211yesmaximal, characteristic, complemented
9#21447964C211yesmaximal, characteristic, complemented
10#21447929C211yesmaximal, characteristic, complemented
11SD32×Dic61C211yesmaximal, characteristic, complemented
12#21447649C211yesmaximal, characteristic, complemented
13#21447607C211yesmaximal, characteristic, complemented
14#21447604C211yesmaximal, characteristic, complemented
15C61×#2220C211yesmaximal, characteristic, complemented
16#16840476—21no—
17#16840470—21no—
18C2×#14519716C2211yescharacteristic
19#16840166C2211yescharacteristic
20#16840166C2211yescharacteristic
21#16840096—21no—
22#16840095—21no—
23#16840085—21no—
24#16840083—21no—
25#16840055—21no—
26#16840050—21no—
27#16840000C2211yescharacteristic
28#16839995C2211yescharacteristic
29Q16×Dic61C2211yescharacteristic
30D8×Dic61C2211yescharacteristic
31C8×C22⋊D61C2211yescharacteristic
32#16839800C2211yescharacteristic
33#16839799C2211yescharacteristic
34C2×#14519711C2211yescharacteristic
35#107×D61C2211yescharacteristic
36#16839590C2211yescharacteristic
37#16839590C2211yescharacteristic
38#16839589C2211yescharacteristic
39#16839588C2211yescharacteristic
40#16839588C2211yescharacteristic
41#16839587C2211yescharacteristic
42#16839587C2211yescharacteristic
43#16839587C2211yescharacteristic
44#16839580C2211yescharacteristic
45#16839566C2211yescharacteristic
46#16839566C2211yescharacteristic
47#16839563C2211yescharacteristic
48#16839563C2211yescharacteristic
49C22⋊#11758185C2211yescharacteristic
50#16839541C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C2×SD32×C61C2211yescharacteristic
53C2×M32×C61C2211yescharacteristic
54C61×#467C2211yescharacteristic
55C61×#466C2211yescharacteristic
56C61×#366C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×#357C2211yescharacteristic
59C2×C8×D61C2311yescharacteristic
60#14519776—21no—
61#14519776—21no—
62#14519767—41no—
63#14519764—41no—
64#14519763—41no—
65#14519757—41no—
66#14519754—41no—
67#14519753—21no—
68#14519749—41no—
69#14519748—21no—
70Q8×Dic61—21no—
71D4×Dic61—21no—
72C4×C22⋊D61D411yescharacteristic
73#14519737—41no—
74#14519736—21no—
75#14519735—21no—
76#14519733—41no—
77C2×C4⋊Dic61—21no—
78C4⋊C4×D61—21no—
79#14519716—22no—
80C2×#11758185C2311yescharacteristic
81C2×#11758185C2311yescharacteristic
82#14519711—21no—
83#14519711C2311yescharacteristic
84#14519711C2311yescharacteristic
85#14519711C2311yescharacteristic
86#14519711C2311yescharacteristic
87#14519710—21no—
88#14519710—21no—
89#14519710—21no—
90#14519709—21no—
91#14519708—21no—
92#14519706D411yescharacteristic
93#14519701—21no—
94#14519701—21no—
95#14519698—21no—
96#14519698—21no—
97C22⋊#92418D411yescharacteristic
98#14519689D411yescharacteristic
99C8×Dic61C2311yescharacteristic
100C2×Q16×C61C2311yescharacteristic
101C2×D8×C61C2311yescharacteristic
102C22×C8×C61C2311yescharacteristic
103C22⋊Q8×C61—21no—
104#121×C61—21no—
105SD32×C61—22no—
106M32×C61—22no—
107C2×C16×C61C2311yescharacteristic
108C2×C16×C61C2311yescharacteristic
109#107×C61C2311yescharacteristic
110#107×C61C2311yescharacteristic
111#103×C61—21no—
112#102×C61—21no—
113C2×Q8×C61—21no—
114C2×D4×C61—21no—
115C2×D4×C61—41no—
116C22×C4×C61C2×D411yescharacteristic
117C2×C22⋊D61—41no—
118C2×C22⋊D61D811yescharacteristic
119C22×Dic61—41no—
120C22×Dic61—41no—
121C2×C4×D61—41no—
122C2×C4×D61C2×D411yescharacteristic
123C2×Dic122—41no—
124C2×Dic122—41no—
125Q16×C61—21no—
126Q16×C61—21no—
127D8×C61—21no—
128D8×C61—21no—
129C2×C8×C61—21no—
130C2×C8×C61—21no—
131C2×C8×C61C2×D411yescharacteristic
132C2×C8×C61C2411yescharacteristic
133C4⋊C4×C61—21no—
134C4⋊C4×C61—21no—
135C4⋊C4×C61—41no—
136C22⋊C4×C61—41no—
137C22⋊C4×C61—41no—
138C22⋊Dic61—41no—
139C22⋊Dic61—41no—
140C22⋊Dic61—41no—
141C22⋊Dic61D811yescharacteristic
142#11758198—41no—
143#11758198—41no—
144#11758198D811yescharacteristic
145C4⋊Dic61—21no—
146C4⋊Dic61—21no—
147C4⋊Dic61—21no—
148C4⋊Dic61—21no—
149C4⋊Dic61—41no—
150C4⋊Dic61—41no—
151#11758196—41no—
152#11758196—41no—
153#11758196—41no—
154#11758196—41no—
155#11758196D811yescharacteristic
156C4×Dic61—41no—
157C4×Dic61—41no—
158C4×Dic61—41no—
159C4×Dic61C2×D411yescharacteristic
160C2×#92418C2×D411yescharacteristic
161C2×#92418C2×D411yescharacteristic
162C8×D61—21no—
163C8×D61—21no—
164C16×C61—21no—
165C16×C61#4112yes—
166#11758185—21no—
167#11758185—21no—
168C23×C61—41no—
169C23×C61C2×D811yescharacteristic
170C22×D61C2×D811yescharacteristic
171Q8×C61—41no—
172Q8×C61—41no—
173D4×C61—41no—
174D4×C61—41no—
175D4×C61—161no—
176C2×C4×C61—21no—
177C2×C4×C61—21no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61C2×D811yescharacteristic
182C2×C4×C61C22×D411yescharacteristic
183C22⋊D61—22no—
184C22⋊D61—161no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—82no—
190C2×Dic61—161no—
191C2×Dic61C2×D811yescharacteristic
192C2×Dic61C2×D811yescharacteristic
193C2×Dic61C2×D811yescharacteristic
194C4×D61—21no—
195C4×D61—21no—
196C4×D61—161no—
197Dic122—161no—
198Dic122—161no—
199C8×C61—21no—
200C8×C61C2×#4111yescharacteristic
201C8×C612−1+411yescharacteristic
202#92418—21no—
203#92418—21no—
204#33924—611nomaximal, Sylow
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—81no—
209C22×C61—81no—
210C22×C61—81no—
211C22×C61C22×D811yescharacteristic
212C2×D61—21no—
213C2×D61—21no—
214C2×D61—21no—
215C4×C61—21no—
216C4×C61—81no—
217C4×C61—81no—
218C4×C61—81no—
219C4×C61#54711yescharacteristic
220C4×C61#57811yescharacteristic
221Dic61—21no—
222Dic61—21no—
223Dic61—81no—
224Dic61—81no—
225Dic61—81no—
226Dic61—81no—
227Dic61#51012yes—
228#3341—611no—
229#3338—611no—
230#2252—611no—
231#2237—611no—
232#2237—611no—
233#2232—611no—
234#2232—611no—
235#2227—611no—
236#2226—611no—
237#2220—611no—
238#2220D6111yescharacteristic, complemented
239C4×SD32—611no—
240#2169—611no—
241#2159—611no—
242#2159—611no—
243C2×C61—41no—
244C2×C61—161no—
245C2×C61#333411yescharacteristic
246C2×C61C2×#51011yescharacteristic
247C2×C61#341511yescharacteristic
248D61—41no—
249#555—1221no—
250#554—1221no—
251C2×SD32C2×D6111yescharacteristic
252C2×M32—611no—
253C2×M32C2×D6111yescharacteristic
254#500—611no—
255#500—611no—
256#484—1221no—
257#484—1221no—
258#482—1221no—
259#482—1221no—
260#477—1221no—
261#476—1221no—
262#467—611no—
263#467C2×D6111yescharacteristic
264#466—611no—
265#466C2×D6111yescharacteristic
266C4×Q16—611no—
267C4×D8—611no—
268C8×D4—611no—
269#427—611no—
270#427—611no—
271C2×#107—611no—
272C2×#107—611no—
273#367—611no—
274#367—611no—
275#367—611no—
276#366—611no—
277#366—611no—
278#366—611no—
279#366—611no—
280#366—611no—
281#366C2×D6111yescharacteristic
282C4⋊C16—611no—
283#358—611no—
284#358—611no—
285#358C2×D6111yescharacteristic
286#357—611no—
287#357—611no—
288#357C2×D6111yescharacteristic
289C22⋊C16—611no—
290C22⋊C16—611no—
291C4×C16—611no—
292C61#3392411yescharacteristic, complemented, Sylow
293C2×Q16C22×D6111yescharacteristic
294C2×D8C22×D6111yescharacteristic
295C22×C8—611no—
296C22×C8C22×D6111yescharacteristic
297C4⋊Q8—1221no—
298C4⋊Q8—1221no—
299#125—2441no—
300#124—2441no—
301#124—2441no—
302C22⋊Q8—21no—
303C22⋊Q8—1221no—
304C22⋊Q8—2441no—
305C22⋊Q8—2441no—
306#121—21no—
307#121—1221no—
308#121—2441no—
309C4×Q8—1221no—
310C4×D4—611no—
311C4×D4—1221no—
312C4×D4—2441no—
313#117—1221no—
314#117—1221no—
315#117—2441no—
316C2×C4⋊C4—1221no—
317C2×C4⋊C4—1221no—
318SD32—22no—
319M32—22no—
320M32—1222no—
321C2×C16—611no—
322C2×C16—611no—
323C2×C16C22×D6111yescharacteristic
324C2×C16C22×D6111yescharacteristic
325#107—611no—
326#107—611no—
327#107—611no—
328#107—611no—
329#107—1221no—
330#107—1221no—
331#107—1221no—
332#107—1221no—
333#107C22×D6111yescharacteristic
334#107C22×D6111yescharacteristic
335#106—1221no—
336#106—1221no—
337C4⋊C8—611no—
338#103—21no—
339#103—1221no—
340#103—1221no—
341#102—21no—
342#102—1221no—
343#102—1221no—
344C22⋊C8—611no—
345C22⋊C8—611no—
346C4×C8—611no—
347C2×Q8—21no—
348C2×Q8—2441no—
349C2×Q8—2441no—
350C2×D4—21no—
351C2×D4—41no—
352C2×D4—611no—
353C2×D4—2441no—
354C22×C4—611no—
355C22×C4—2441no—
356C22×C4—2441no—
357C22×C4—2441no—
358C22×C4D4×D6111yescharacteristic
359Q16—21no—
360Q16—21no—
361D8—21no—
362D8—21no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—611no—
366C2×C8—611no—
367C2×C8—1221no—
368C2×C8—1221no—
369C2×C8D4×D6111yescharacteristic
370C2×C8C23×D6111yescharacteristic
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—41no—
374C4⋊C4—611no—
375C4⋊C4—1221no—
376C4⋊C4—1221no—
377C4⋊C4—1221no—
378C4⋊C4—1221no—
379C4⋊C4—2441no—
380C4⋊C4—2441no—
381C4⋊C4—2441no—
382C4⋊C4—2441no—
383C4⋊C4—2441no—
384C4⋊C4—2441no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—611no—
388C22⋊C4—611no—
389C22⋊C4—2441no—
390C22⋊C4—2441no—
391C22⋊C4—2441no—
392C22⋊C4—2441no—
393C22⋊C4—2441no—
394C42—611no—
395C42—2441no—
396C42—2441no—
397C42—2441no—
398C16—21no—
399C16—1221no—
400C16—1221no—
401C16#1175822412yes—
402C23—41no—
403C23—611no—
404C23D8×D6111yescharacteristic
405Q8—41no—
406Q8—41no—
407Q8—9761no—
408Q8—9761no—
409D4—41no—
410D4—41no—
411D4—161no—
412D4—1222no—
413D4—9761no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—611no—
420C2×C4—611no—
421C2×C4—611no—
422C2×C4—1221no—
423C2×C4—1221no—
424C2×C4—9761no—
425C2×C4—9761no—
426C2×C4—4882no—
427C2×C4—2441no—
428C2×C4—2441no—
429C2×C4—2441no—
430C2×C4—2441no—
431C2×C4D8×D6111yescharacteristic
432C2×C4C2×D4×D6111yescharacteristic
433C8—21no—
434C8—1221no—
435C8—1221no—
436C8C2×#1175822411yescharacteristic
437C8#1451982411yescharacteristic
438C22—21no—
439C22—21no—
440C22—21no—
441C22—81no—
442C22—81no—
443C22—81no—
444C22—1221no—
445C22—1221no—
446C22—1221no—
447C22C2×D8×D6111yescharacteristic
448C4—21no—
449C4—81no—
450C4—81no—
451C4—81no—
452C4—612no—
453C4—1221no—
454C4—1221no—
455C4—4881no—
456C4—4881no—
457C4—4881no—
458C4—4881no—
459C4#1684041211yescharacteristic
460C4#1684057611yescharacteristic
461C2—41no—
462C2—161no—
463C2—2441no—
464C2#2145816311yescharacteristic
465C2#510×D6111yescharacteristic
466C2#2145895911yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2220C2
socleC22×C61C22×D8
prime radical#21458238C2
hypercenter#2220D61
hypocenterC61#33924
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2220

Complements

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

NH ≅ G/Ntype
2. #21458208C2semidirect
3. #21448093C2semidirect
4. #21448025C2semidirect
5. #21448024C2semidirect
6. #21447998C2semidirect
7. #21447997C2semidirect
8. #21447969C2semidirect
9. #21447964C2semidirect
10. #21447929C2semidirect
11. SD32×Dic61C2semidirect
12. #21447649C2semidirect
13. #21447607C2semidirect
14. #21447604C2semidirect
15. C61×#2220C2semidirect
238. #2220D61semidirect
292. C61#33924semidirect

Maximal subgroups

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

subgroupindex
#214582382
#214582082
#214480932
#214480252
#214480242
#214479982
#214479972
#214479692
#214479642
#214479292
SD32×Dic612
#214476492
#214476072
#214476042
C61×#22202
#3392461