Finite Group Databasebeta

← #29837603

Subgroups — #29837603

Order 15616.

502 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458247C211yesmaximal, characteristic, complemented
2#21458164C211yesmaximal, characteristic
3#21448093C211yesmaximal, characteristic, complemented
4#21448023C211yesmaximal, characteristic, complemented
5#21448021C211yesmaximal, characteristic, complemented
6#21448012C211yesmaximal, characteristic, complemented
7#21448010C211yesmaximal, characteristic, complemented
8#21447960C211yesmaximal, characteristic, complemented
9#21447955C211yesmaximal, characteristic, complemented
10#21447933C211yesmaximal, characteristic, complemented
11#21447932C211yesmaximal, characteristic, complemented
12#21447670C211yesmaximal, characteristic, complemented
13#21447649C211yesmaximal, characteristic, complemented
14#21447606C211yesmaximal, characteristic, complemented
15C61×#2159C211yesmaximal, characteristic, complemented
16#16840480—21no—
17#16840413—21no—
18C2×#14519722C2211yescharacteristic
19C2×#14519716C2211yescharacteristic
20#16840166C2211yescharacteristic
21#16840166C2211yescharacteristic
22#16840106—21no—
23#16840103—21no—
24#16840077—21no—
25#16840075—21no—
26#16840046—21no—
27#16840041—21no—
28#16840004C2211yescharacteristic
29#16840003C2211yescharacteristic
30#16839999C2211yescharacteristic
31#16839998C2211yescharacteristic
32#16839856C2211yescharacteristic
33#16839844C2211yescharacteristic
34C8×C22⋊D61C2211yescharacteristic
35#16839799C2211yescharacteristic
36#107×D61C2211yescharacteristic
37#16839589C2211yescharacteristic
38#16839588C2211yescharacteristic
39#16839587C2211yescharacteristic
40#16839587C2211yescharacteristic
41#16839587C2211yescharacteristic
42#16839580C2211yescharacteristic
43#16839567C2211yescharacteristic
44#16839565C2211yescharacteristic
45#16839565C2211yescharacteristic
46#16839564C2211yescharacteristic
47#16839562C2211yescharacteristic
48#16839562C2211yescharacteristic
49C22⋊#11758185C2211yescharacteristic
50#16839541C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C2×M32×C61C2211yescharacteristic
53C61×#427C2211yescharacteristic
54C2×#107×C61C2211yescharacteristic
55C61×#367C2211yescharacteristic
56C61×#367C2211yescharacteristic
57C61×#366C2211yescharacteristic
58C61×#366C2211yescharacteristic
59C2×#11758222—41no—
60C2×Dic244C2311yescharacteristic
61C2×D488C2311yescharacteristic
62C2×C8×D61C2311yescharacteristic
63#14519776—21no—
64#14519776—21no—
65#14519771—41no—
66#14519770—41no—
67#14519763—41no—
68#14519762—41no—
69#14519760—41no—
70#14519757—21no—
71#14519756—21no—
72#14519755—41no—
73#14519752—21no—
74#14519751—21no—
75C4×Dic122—41no—
76#14519742—21no—
77#14519739—21no—
78C4×C22⋊D61D411yescharacteristic
79#14519735—21no—
80C4⋊C4×D61—21no—
81#14519722—22no—
82#14519716—22no—
83C2×#11758185C2311yescharacteristic
84C2×#11758185C2311yescharacteristic
85#14519711C2311yescharacteristic
86#14519711C2311yescharacteristic
87#14519710—21no—
88#14519710—21no—
89#14519710—21no—
90#14519708—21no—
91#14519706D411yescharacteristic
92#14519702—21no—
93#14519700—21no—
94#14519700—21no—
95#14519699—21no—
96#14519697—21no—
97#14519697—21no—
98C22⋊#92418D411yescharacteristic
99#14519689D411yescharacteristic
100C8×Dic61C2311yescharacteristic
101C22×C8×C61C2311yescharacteristic
102#117×C61—21no—
103C2×C4⋊C4×C61—21no—
104M32×C61—22no—
105C2×C16×C61C2311yescharacteristic
106C2×C16×C61C2311yescharacteristic
107#107×C61—21no—
108#107×C61C2311yescharacteristic
109#107×C61C2311yescharacteristic
110#107×C61C2311yescharacteristic
111#107×C61C2311yescharacteristic
112#106×C61—21no—
113C22×C4×C61—41no—
114C22×C4×C61C2×D411yescharacteristic
115C2×C22⋊D61—41no—
116C2×C22⋊D61D811yescharacteristic
117#11758222—84no—
118C2×D244—21no—
119C2×D244—41no—
120C2×C4×D61—41no—
121C2×C4×D61—41no—
122C2×C4×D61C2×D411yescharacteristic
123C2×Dic122—21no—
124C2×Dic122—41no—
125C2×Dic122—41no—
126C2×C8×C61—21no—
127C2×C8×C61—21no—
128C2×C8×C61C2×D411yescharacteristic
129C2×C8×C61C2411yescharacteristic
130C4⋊C4×C61—21no—
131C4⋊C4×C61—21no—
132C4⋊C4×C61—21no—
133C4⋊C4×C61—21no—
134C4⋊C4×C61—41no—
135C22⋊C4×C61—41no—
136C42×C61—41no—
137C22⋊Dic61—41no—
138C22⋊Dic61D811yescharacteristic
139#11758198—41no—
140#11758198—41no—
141#11758198—41no—
142#11758198—41no—
143#11758198—41no—
144#11758198D811yescharacteristic
145C4⋊Dic61—21no—
146C4⋊Dic61—21no—
147C4⋊Dic61—41no—
148#11758196—41no—
149#11758196—41no—
150#11758196—41no—
151#11758196—41no—
152#11758196—41no—
153#11758196D811yescharacteristic
154C4×Dic61—41no—
155C4×Dic61—41no—
156C4×Dic61C2×D411yescharacteristic
157C2×#92418C2×D411yescharacteristic
158C2×#92418C2×D411yescharacteristic
159Dic244—21no—
160Dic244—21no—
161D488—21no—
162D488—21no—
163C8×D61—21no—
164C8×D61—21no—
165C16×C61—21no—
166C16×C61#4112yescomplemented
167#11758185—21no—
168#11758185—21no—
169C23×C61C2×D811yescharacteristic
170C22×D61—41no—
171C22×D61C2×D811yescharacteristic
172C2×C4×C61—21no—
173C2×C4×C61—21no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—82no—
179C2×C4×C61C2×D811yescharacteristic
180C2×C4×C61C22×D411yescharacteristic
181C22⋊D61—22no—
182C22⋊D61—82no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61C2×D811yescharacteristic
187C2×Dic61C2×D811yescharacteristic
188C2×Dic61C2×D811yescharacteristic
189D244—41no—
190D244—41no—
191D244—82no—
192C4×D61—21no—
193C4×D61—21no—
194C4×D61—82no—
195C4×D61—82no—
196Dic122—41no—
197Dic122—41no—
198Dic122—82no—
199Dic122—82no—
200C8×C61—21no—
201C8×C61C2×#4111yescharacteristic
202C8×C612−1+411yescharacteristic
203#92418—21no—
204#92418—21no—
205#33920—611nomaximal, Sylow
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—21no—
209C22×C61C22×D811yescharacteristic
210C2×D61—21no—
211C2×D61—21no—
212C2×D61—21no—
213C2×D61—81no—
214C2×D61—81no—
215C2×D61—81no—
216C4×C61—21no—
217C4×C61—81no—
218C4×C61—81no—
219C4×C61—81no—
220C4×C61—81no—
221C4×C61#54711yescharacteristic
222C4×C61#57811yescharacteristic
223Dic61—21no—
224Dic61—21no—
225Dic61—81no—
226Dic61—81no—
227Dic61—81no—
228Dic61#50912yes—
229#3342—611no—
230#3334—611no—
231#2252—611no—
232#2236—611no—
233#2236—611no—
234#2234—611no—
235#2234—611no—
236#2225—611no—
237#2224—611no—
238#2220—611no—
239#2220—611no—
240C4×SD32—611no—
241#2169—611no—
242#2159—611no—
243#2159D6111yescharacteristic, complemented
244C2×C61—41no—
245C2×C61#333411yescharacteristic
246C2×C61C2×#50911yescharacteristic
247C2×C61#341711yescharacteristic
248D61—41no—
249D61—161no—
250#556—1221no—
251#547—1221no—
252C2×SD32—611no—
253C2×M32—611no—
254C2×M32C2×D6111yescharacteristic
255#500—611no—
256#500—611no—
257#485—1221no—
258#485—1221no—
259#480—1221no—
260#480—1221no—
261#475—1221no—
262#474—1221no—
263#467—611no—
264#467—611no—
265#466—611no—
266#466—611no—
267C4×Q16—611no—
268C4×D8—611no—
269C8×D4—611no—
270#427—611no—
271#427C2×D6111yescharacteristic
272C2×#107—611no—
273C2×#107C2×D6111yescharacteristic
274#367—611no—
275#367C2×D6111yescharacteristic
276#367C2×D6111yescharacteristic
277#366—611no—
278#366—611no—
279#366—611no—
280#366—611no—
281#366C2×D6111yescharacteristic
282#366C2×D6111yescharacteristic
283C4⋊C16—611no—
284#358—611no—
285#358—611no—
286#358—611no—
287#357—611no—
288#357—611no—
289#357—611no—
290C22⋊C16—611no—
291C22⋊C16—611no—
292C4×C16—611no—
293C61#3392011yescharacteristic, complemented, Sylow
294C2×#41—2441no—
295C2×Q16—611no—
296C2×D8—611no—
297C22×C8—611no—
298C22×C8C22×D6111yescharacteristic
299C4⋊Q8—1221no—
300C4⋊Q8—1221no—
301#126—2441no—
302#126—2441no—
303#124—2441no—
304#123—2441no—
305#123—2441no—
306C22⋊Q8—1221no—
307C22⋊Q8—1221no—
308C22⋊Q8—2441no—
309#121—1221no—
310#121—1221no—
311C4×Q8—1221no—
312C4×Q8—2441no—
313C4×D4—611no—
314C4×D4—1221no—
315#117—21no—
316#117—1221no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—1221no—
319SD32—1222no—
320M32—22no—
321M32—1222no—
322C2×C16—611no—
323C2×C16—611no—
324C2×C16C22×D6111yescharacteristic
325C2×C16C22×D6111yescharacteristic
326#107—21no—
327#107—611no—
328#107—611no—
329#107—1221no—
330#107—1221no—
331#107—1221no—
332#107C22×D6111yescharacteristic
333#107C22×D6111yescharacteristic
334#107C22×D6111yescharacteristic
335#107C22×D6111yescharacteristic
336#106—21no—
337#106—1221no—
338C4⋊C8—611no—
339#103—1221no—
340#103—1221no—
341#103—1221no—
342#102—1221no—
343#102—1221no—
344#102—1221no—
345C22⋊C8—611no—
346C22⋊C8—611no—
347C4×C8—611no—
348#41—4884no—
349C2×Q8—1221no—
350C2×Q8—2441no—
351C2×Q8—2441no—
352C2×D4—611no—
353C2×D4—1221no—
354C2×D4—2441no—
355C2×D4—2441no—
356C22×C4—41no—
357C22×C4—611no—
358C22×C4—2441no—
359C22×C4—2441no—
360C22×C4D4×D6111yescharacteristic
361Q16—1221no—
362Q16—1221no—
363D8—1221no—
364D8—1221no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8—611no—
368C2×C8—611no—
369C2×C8—1221no—
370C2×C8—1221no—
371C2×C8D4×D6111yescharacteristic
372C2×C8C23×D6111yescharacteristic
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—41no—
378C4⋊C4—611no—
379C4⋊C4—1221no—
380C4⋊C4—1221no—
381C4⋊C4—2441no—
382C4⋊C4—2441no—
383C4⋊C4—2441no—
384C4⋊C4—2441no—
385C4⋊C4—2441no—
386C4⋊C4—2441no—
387C22⋊C4—41no—
388C22⋊C4—611no—
389C22⋊C4—611no—
390C22⋊C4—2441no—
391C22⋊C4—2441no—
392C22⋊C4—2441no—
393C22⋊C4—2441no—
394C22⋊C4—2441no—
395C22⋊C4—2441no—
396C42—41no—
397C42—611no—
398C42—2441no—
399C42—2441no—
400C16—21no—
401C16—1221no—
402C16—1221no—
403C16#1175822212yescomplemented
404C23—611no—
405C23—2441no—
406C23D8×D6111yescharacteristic
407Q8—4882no—
408Q8—4882no—
409Q8—2441no—
410Q8—2441no—
411D4—1222no—
412D4—4882no—
413D4—4882no—
414D4—2441no—
415D4—2441no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—82no—
423C2×C4—611no—
424C2×C4—611no—
425C2×C4—611no—
426C2×C4—1221no—
427C2×C4—1221no—
428C2×C4—4882no—
429C2×C4—4882no—
430C2×C4—2441no—
431C2×C4—2441no—
432C2×C4—2441no—
433C2×C4D8×D6111yescharacteristic
434C2×C4C2×D4×D6111yescharacteristic
435C8—21no—
436C8—1221no—
437C8—1221no—
438C8C2×#1175822211yescharacteristic
439C8#1451982511yescharacteristic
440C22—21no—
441C22—21no—
442C22—21no—
443C22—1221no—
444C22—1221no—
445C22—1221no—
446C22—4881no—
447C22—4881no—
448C22—4881no—
449C22C2×D8×D6111yescharacteristic
450C4—21no—
451C4—81no—
452C4—81no—
453C4—81no—
454C4—81no—
455C4—612no—
456C4—1221no—
457C4—1221no—
458C4—4881no—
459C4—4881no—
460C4—4881no—
461C4#1684041311yescharacteristic
462C4#1684057511yescharacteristic
463C2—41no—
464C2—9761no—
465C2—2441no—
466C2#2145816411yescharacteristic
467C2#509×D6111yescharacteristic
468C2#2145897111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2159C2
socleC22×C61C22×D8
prime radical#21458164C2
hypercenter#2159D61
hypocenterC61#33920
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2159

Complements

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

NH ≅ G/Ntype
1. #21458247C2semidirect
3. #21448093C2semidirect
4. #21448023C2semidirect
5. #21448021C2semidirect
6. #21448012C2semidirect
7. #21448010C2semidirect
8. #21447960C2semidirect
9. #21447955C2semidirect
10. #21447933C2semidirect
11. #21447932C2semidirect
12. #21447670C2semidirect
13. #21447649C2semidirect
14. #21447606C2semidirect
15. C61×#2159C2semidirect
166. C16×C61#41semidirect
243. #2159D61semidirect
293. C61#33920semidirect
403. C16#11758222semidirect

Maximal subgroups

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

subgroupindex
#214582472
#214581642
#214480932
#214480232
#214480212
#214480122
#214480102
#214479602
#214479552
#214479332
#214479322
#214476702
#214476492
#214476062
C61×#21592
#3392061