Finite Group Databasebeta

← #29837588

Subgroups — #29837588

Order 15616.

476 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458223C211yesmaximal, characteristic
2#21458189C211yesmaximal, characteristic, complemented
3#21448098C211yesmaximal, characteristic, complemented
4#21448025C211yesmaximal, characteristic, complemented
5#21448015C211yesmaximal, characteristic, complemented
6#21448009C211yesmaximal, characteristic, complemented
7#21448003C211yesmaximal, characteristic, complemented
8#21447983C211yesmaximal, characteristic, complemented
9#21447976C211yesmaximal, characteristic, complemented
10#21447929C211yesmaximal, characteristic, complemented
11#21447929C211yesmaximal, characteristic, complemented
12#21447652C211yesmaximal, characteristic, complemented
13#21447606C211yesmaximal, characteristic, complemented
14#21447606C211yesmaximal, characteristic, complemented
15C4×SD32×C61C211yesmaximal, characteristic, complemented
16#16840462—21no—
17#16840453—21no—
18C2×#14519716C2211yescharacteristic
19C2×#14519716C2211yescharacteristic
20#16840164C2211yescharacteristic
21#16840164C2211yescharacteristic
22#16840101—21no—
23#16840091—21no—
24#16840085—21no—
25#16840079—21no—
26#16840069—21no—
27#16840062—21no—
28#16840000C2211yescharacteristic
29#16840000C2211yescharacteristic
30#16839995C2211yescharacteristic
31#16839995C2211yescharacteristic
32C8×D244C2211yescharacteristic
33#16839799C2211yescharacteristic
34#16839799C2211yescharacteristic
35#107×D61C2211yescharacteristic
36#107×D61C2211yescharacteristic
37#16839590C2211yescharacteristic
38#16839590C2211yescharacteristic
39#16839589C2211yescharacteristic
40#16839589C2211yescharacteristic
41#16839588C2211yescharacteristic
42#16839588C2211yescharacteristic
43#16839587C2211yescharacteristic
44#16839587C2211yescharacteristic
45C4⋊#11758185C2211yescharacteristic
46#16839566C2211yescharacteristic
47#16839566C2211yescharacteristic
48#16839563C2211yescharacteristic
49#16839563C2211yescharacteristic
50#16839541C2211yescharacteristic
51#16839541C2211yescharacteristic
52C2×SD32×C61C2211yescharacteristic
53C4×Q16×C61C2211yescharacteristic
54C4×D8×C61C2211yescharacteristic
55C61×#367C2211yescharacteristic
56C61×#358C2211yescharacteristic
57C61×#357C2211yescharacteristic
58C4×C16×C61C2211yescharacteristic
59C2×C8×D61C2311yescharacteristic
60C2×C8×D61C2311yescharacteristic
61#14519771—41no—
62#14519770—41no—
63#14519769—21no—
64#14519769—21no—
65#14519767—41no—
66#14519762—41no—
67#14519760—41no—
68#14519753—21no—
69#14519753—21no—
70#14519750—41no—
71#14519748—21no—
72#14519748—21no—
73C4×D244D411yescharacteristic
74C4×C22⋊D61—41no—
75#14519735—21no—
76#14519735—21no—
77#14519734—41no—
78C4⋊C4×D61—21no—
79C4⋊C4×D61—21no—
80#14519716—22no—
81#14519716—22no—
82C2×#11758185C2311yescharacteristic
83C2×#11758185C2311yescharacteristic
84#14519711C2311yescharacteristic
85#14519711C2311yescharacteristic
86#14519711C2311yescharacteristic
87#14519711C2311yescharacteristic
88#14519710—21no—
89#14519710—21no—
90#14519709—21no—
91#14519709—21no—
92#14519708—21no—
93#14519708—21no—
94C4⋊#92418D411yescharacteristic
95#14519701—21no—
96#14519701—21no—
97#14519698—21no—
98#14519698—21no—
99#14519689D411yescharacteristic
100#14519689D411yescharacteristic
101C2×Q16×C61C2311yescharacteristic
102C2×D8×C61C2311yescharacteristic
103C4×Q8×C61—21no—
104C4×D4×C61—21no—
105SD32×C61—22no—
106C2×C16×C61C2311yescharacteristic
107C2×C16×C61C2311yescharacteristic
108#107×C61C2311yescharacteristic
109#107×C61C2311yescharacteristic
110#103×C61—21no—
111#102×C61—21no—
112C4×C8×C61C2311yescharacteristic
113C2×Q8×C61—21no—
114C2×D4×C61—21no—
115C22×C4×C61—41no—
116C2×C22⋊D61—41no—
117C2×C22⋊D61—41no—
118C2×D244D811yescharacteristic
119C2×C4×D61—41no—
120C2×C4×D61—41no—
121C2×C4×D61C2×D411yescharacteristic
122C2×C4×D61C2×D411yescharacteristic
123Q16×C61—21no—
124Q16×C61—21no—
125D8×C61—21no—
126D8×C61—21no—
127C2×C8×C61C2×D411yescharacteristic
128C2×C8×C61C2411yescharacteristic
129C4⋊C4×C61—21no—
130C4⋊C4×C61—21no—
131C4⋊C4×C61—41no—
132C22⋊C4×C61—41no—
133C42×C61—41no—
134C42×C61C2×D411yescharacteristic
135C22⋊Dic61—41no—
136C22⋊Dic61—41no—
137#11758198—41no—
138#11758198—41no—
139#11758198—41no—
140#11758198—41no—
141#11758198D811yescharacteristic
142#11758198D811yescharacteristic
143C4⋊Dic61—21no—
144C4⋊Dic61—21no—
145C4⋊Dic61—21no—
146C4⋊Dic61—21no—
147C4⋊Dic61D811yescharacteristic
148#11758196—41no—
149#11758196—41no—
150#11758196—41no—
151#11758196—41no—
152#11758196—41no—
153#11758196—41no—
154#11758196—41no—
155#11758196—41no—
156C4×Dic61—41no—
157C4×Dic61—41no—
158C2×#92418C2×D411yescharacteristic
159C2×#92418C2×D411yescharacteristic
160C8×D61—21no—
161C8×D61—21no—
162C8×D61—21no—
163C8×D61—21no—
164C16×C61—21no—
165C16×C61#4112yes—
166#11758185—21no—
167#11758185—21no—
168C23×C61—41no—
169C22×D61C2×D811yescharacteristic
170C22×D61C2×D811yescharacteristic
171Q8×C61—41no—
172Q8×C61—41no—
173D4×C61—41no—
174D4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—161no—
179C2×C4×C61C2×D811yescharacteristic
180C2×C4×C61C2×D811yescharacteristic
181C2×C4×C61C22×D411yescharacteristic
182C22⋊D61—82no—
183C22⋊D61—161no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61C2×D811yescharacteristic
189C2×Dic61C2×D811yescharacteristic
190D244—41no—
191C4×D61—21no—
192C4×D61—21no—
193C4×D61—21no—
194C4×D61—21no—
195C4×D61—82no—
196C4×D61—161no—
197C8×C61—21no—
198C8×C61C2×#4111yescharacteristic
199C8×C612−1+411yescharacteristic
200#92418—21no—
201#92418—21no—
202#33918—611nomaximal, Sylow
203C22×C61—81no—
204C22×C61—81no—
205C22×C61—81no—
206C22×C61C22×D811yescharacteristic
207C2×D61—21no—
208C2×D61—21no—
209C2×D61—21no—
210C2×D61—21no—
211C2×D61—21no—
212C2×D61—21no—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—81no—
216C4×C61—81no—
217C4×C61—81no—
218C4×C61#54711yescharacteristic
219C4×C61#57811yescharacteristic
220Dic61—21no—
221Dic61—21no—
222Dic61—81no—
223Dic61—81no—
224Dic61—81no—
225Dic61—81no—
226#3339—611no—
227#3336—611no—
228#2253—611no—
229#2237—611no—
230#2235—611no—
231#2234—611no—
232#2233—611no—
233#2229—611no—
234#2228—611no—
235#2220—611no—
236#2220—611no—
237C4×SD32D6111yescharacteristic, complemented
238#2169—611no—
239#2159—611no—
240#2159—611no—
241C2×C61—161no—
242C2×C61#333411yescharacteristic
243C2×C61#341411yescharacteristic
244C2×C61#341611yescharacteristic
245D61—41no—
246D61—41no—
247#553—1221no—
248#552—1221no—
249C2×SD32C2×D6111yescharacteristic
250C2×M32—611no—
251C2×M32—611no—
252#499—611no—
253#499—611no—
254#485—1221no—
255#483—1221no—
256#482—1221no—
257#481—1221no—
258#479—1221no—
259#478—1221no—
260#467—611no—
261#467—611no—
262#466—611no—
263#466—611no—
264C4×Q16C2×D6111yescharacteristic
265C4×D8C2×D6111yescharacteristic
266C8×D4—611no—
267#427—611no—
268#427—611no—
269C2×#107—611no—
270C2×#107—611no—
271#367—611no—
272#367—611no—
273#367—611no—
274#367—611no—
275#367C2×D6111yescharacteristic
276#366—611no—
277#366—611no—
278#366—611no—
279#366—611no—
280C4⋊C16—611no—
281#358—611no—
282#358—611no—
283#358C2×D6111yescharacteristic
284#357—611no—
285#357—611no—
286#357C2×D6111yescharacteristic
287C22⋊C16—611no—
288C22⋊C16—611no—
289C4×C16C2×D6111yescharacteristic
290C61#3391811yescharacteristic, complemented, Sylow
291C2×Q16C22×D6111yescharacteristic
292C2×D8C22×D6111yescharacteristic
293C22×C8—611no—
294C22×C8—611no—
295#126—2441no—
296#126—2441no—
297#125—1221no—
298#125—1221no—
299#125—2441no—
300#123—2441no—
301#123—2441no—
302C22⋊Q8—1221no—
303C22⋊Q8—1221no—
304#121—1221no—
305#121—1221no—
306#121—2441no—
307C4×Q8—21no—
308C4×D4—21no—
309C4×D4—611no—
310C4×D4—2441no—
311#117—1221no—
312#117—1221no—
313#117—2441no—
314C2×C4⋊C4—1221no—
315C2×C4⋊C4—1221no—
316SD32—22no—
317M32—1222no—
318M32—1222no—
319C2×C16—611no—
320C2×C16—611no—
321C2×C16C22×D6111yescharacteristic
322C2×C16C22×D6111yescharacteristic
323#107—611no—
324#107—611no—
325#107—611no—
326#107—611no—
327#107—1221no—
328#107—1221no—
329#107C22×D6111yescharacteristic
330#107C22×D6111yescharacteristic
331#106—1221no—
332#106—1221no—
333#106—1221no—
334#106—1221no—
335C4⋊C8—611no—
336#103—21no—
337#103—1221no—
338#103—1221no—
339#102—21no—
340#102—1221no—
341#102—1221no—
342C22⋊C8—611no—
343C22⋊C8—611no—
344C4×C8C22×D6111yescharacteristic
345C2×Q8—21no—
346C2×D4—21no—
347C2×D4—611no—
348C2×D4—2441no—
349C2×D4—2441no—
350C22×C4—41no—
351C22×C4—611no—
352C22×C4—611no—
353C22×C4—2441no—
354C22×C4—2441no—
355Q16—21no—
356Q16—21no—
357D8—21no—
358D8—21no—
359C2×C8—611no—
360C2×C8—611no—
361C2×C8—1221no—
362C2×C8—1221no—
363C2×C8—1221no—
364C2×C8—1221no—
365C2×C8D4×D6111yescharacteristic
366C2×C8C23×D6111yescharacteristic
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—41no—
370C4⋊C4—611no—
371C4⋊C4—1221no—
372C4⋊C4—1221no—
373C4⋊C4—1221no—
374C4⋊C4—1221no—
375C4⋊C4—2441no—
376C4⋊C4—2441no—
377C4⋊C4—2441no—
378C4⋊C4—2441no—
379C4⋊C4—2441no—
380C4⋊C4—2441no—
381C4⋊C4—2441no—
382C4⋊C4—2441no—
383C22⋊C4—41no—
384C22⋊C4—611no—
385C22⋊C4—611no—
386C22⋊C4—2441no—
387C22⋊C4—2441no—
388C22⋊C4—2441no—
389C22⋊C4—2441no—
390C22⋊C4—2441no—
391C22⋊C4—2441no—
392C42—41no—
393C42—2441no—
394C42—2441no—
395C42D4×D6111yescharacteristic
396C16—21no—
397C16—1221no—
398C16—1221no—
399C16#1175822212yes—
400C23—41no—
401C23—611no—
402C23—611no—
403Q8—41no—
404Q8—41no—
405D4—41no—
406D4—41no—
407D4—9761no—
408D4—4882no—
409D4—2441no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—161no—
414C2×C4—611no—
415C2×C4—611no—
416C2×C4—1221no—
417C2×C4—1221no—
418C2×C4—1221no—
419C2×C4—1221no—
420C2×C4—9761no—
421C2×C4—4882no—
422C2×C4—2441no—
423C2×C4—2441no—
424C2×C4—2441no—
425C2×C4—2441no—
426C2×C4D8×D6111yescharacteristic
427C2×C4D8×D6111yescharacteristic
428C2×C4C2×D4×D6111yescharacteristic
429C8—21no—
430C8—1221no—
431C8—1221no—
432C8C2×#1175822211yescharacteristic
433C8#1451982411yescharacteristic
434C22—81no—
435C22—81no—
436C22—81no—
437C22—1221no—
438C22—1221no—
439C22—1221no—
440C22—1221no—
441C22—1221no—
442C22—1221no—
443C22C2×D8×D6111yescharacteristic
444C4—21no—
445C4—21no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—1221no—
450C4—1221no—
451C4—4881no—
452C4—4881no—
453C4—4881no—
454C4—4881no—
455C4#1684041711yescharacteristic
456C4#1684057611yescharacteristic
457C2—161no—
458C2—2441no—
459C2—2441no—
460C2#2145816811yescharacteristic
461C2#2145895211yescharacteristic
462C2#2145896111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC4×SD32×C61C2
socleC22×C61C22×D8
prime radical#21458223C2
hypercenterC4×SD32D61
hypocenterC61#33918
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
2. #21458189C2semidirect
3. #21448098C2semidirect
4. #21448025C2semidirect
5. #21448015C2semidirect
6. #21448009C2semidirect
7. #21448003C2semidirect
8. #21447983C2semidirect
9. #21447976C2semidirect
10. #21447929C2semidirect
11. #21447929C2semidirect
12. #21447652C2semidirect
13. #21447606C2semidirect
14. #21447606C2semidirect
15. C4×SD32×C61C2semidirect
237. C4×SD32D61semidirect
290. C61#33918semidirect

Maximal subgroups

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

subgroupindex
#214582232
#214581892
#214480982
#214480252
#214480152
#214480092
#214480032
#214479832
#214479762
#214479292
#214476522
#214476062
C4×SD32×C612
#3391861