Finite Group Databasebeta

← #29834834

Subgroups — #29834834

Order 15616.

632 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#466×D61C211yesmaximal, characteristic
2C2×#16839799C211yesmaximal, characteristic, complemented
3#21448013C212yesmaximal, complemented
4#21448009C212yesmaximal, complemented
5#21448005C211yesmaximal, characteristic, complemented
6#21448002C211yesmaximal, characteristic, complemented
7#21447999C211yesmaximal, characteristic, complemented
8#21447604C212yesmaximal, complemented
9#21447533C212yesmaximal, complemented
10#21447428C211yesmaximal, characteristic, complemented
11C61×#2232C211yesmaximal, characteristic, complemented
12C2×D8×D61C2211yescharacteristic
13C22×C8×D61C2211yescharacteristic
14#121×D61—21no—
15C2×#14519735—21no—
16C2×#14519716C2212yes—
17#16839999C2211yescharacteristic
18#16839998C2211yescharacteristic
19#16839997—21no—
20#16839996—21no—
21#16839995C2211yescharacteristic
22#16839799—21no—
23#16839799—21no—
24#16839799C2212yes—
25#16839799C2212yescomplemented
26C2×#14519711C2211yescharacteristic, complemented
27#107×D61C2211yescharacteristic
28C2×#14519708—21no—
29#102×D61—21no—
30#16839590C2212yescomplemented
31#16839589C2212yescomplemented
32#16839587C2212yescomplemented
33#16839564C2212yescomplemented
34#16839563C2212yescomplemented
35#16839562C2212yescomplemented
36C22⋊#11758185C2211yescharacteristic, complemented
37#16839541C2212yescomplemented
38C61×#466C2211yescharacteristic
39C2×#107×C61C2211yescharacteristic, complemented
40C61×#366C2212yescomplemented
41C61×#357C2212yescomplemented
42C61×C22⋊C16C2211yescharacteristic, complemented
43C2×D4×D61—21no—
44C2×D4×D61—41no—
45C22×C4×D61D411yescharacteristic
46C2×D488C2311yescharacteristic
47C2×#11758199—21no—
48D8×D61—24no—
49C22×#92418D411yescharacteristic
50C2×C8×D61—24no—
51C2×C8×D61D411yescharacteristic
52C2×C8×D61D411yescharacteristic
53C2×C8×D61C2311yescharacteristic
54C2×C8×D61C2311yescharacteristic
55#14519752—21no—
56#14519751—21no—
57#14519750—41no—
58#14519749—41no—
59#14519748—21no—
60#14519735—22no—
61#14519735—22no—
62#14519735—41no—
63#14519735—41no—
64C2×C4⋊Dic61—21no—
65C4⋊C4×D61—21no—
66C2×#11758198—41no—
67C22⋊C4×D61—41no—
68C2×C4×Dic61—41no—
69#14519716—24no—
70C2×#11758185C2312yes—
71#14519711—21no—
72#14519711C2311yescharacteristic
73#14519711C2312yes—
74#14519710—21no—
75#14519708—22no—
76#14519708—22no—
77#14519699—21no—
78#14519698—21no—
79#14519697—21no—
80C2×D8×C61C2311yescharacteristic
81C22×C8×C61C2311yescharacteristic
82#121×C61—21no—
83C2×C4⋊C4×C61—21no—
84C2×C16×C61C2312yes—
85#107×C61—21no—
86#107×C61C2311yescharacteristic
87#107×C61C2312yes—
88#102×C61—21no—
89C23×D61—41no—
90C23×D61D811yescharacteristic
91C2×D4×C61—21no—
92C2×D4×C61—41no—
93C22×C4×C61—41no—
94C22×C4×C61C2×D411yescharacteristic
95C2×C22⋊D61—41no—
96C2×C22⋊D61—41no—
97C2×C22⋊D61—41no—
98C22×Dic61—41no—
99C22×Dic61D811yescharacteristic
100D4×D61—42no—
101D4×D61—42no—
102D4×D61—84no—
103C2×D244—21no—
104C2×D244—41no—
105C2×C4×D61—22no—
106C2×C4×D61—22no—
107C2×C4×D61—41no—
108C2×C4×D61D811yescharacteristic
109C2×C4×D61D811yescharacteristic
110C2×C4×D61C2×D411yescharacteristic
111C2×C4×D61C2×D411yescharacteristic
112D8×C61—22no—
113C2×C8×C61—22no—
114C2×C8×C61C2×D411yescharacteristic
115C2×C8×C61C2411yescharacteristic
116C4⋊C4×C61—21no—
117C4⋊C4×C61—22no—
118C4⋊C4×C61—41no—
119C22⋊C4×C61—41no—
120C22⋊Dic61—41no—
121#11758199—42no—
122#11758198—42no—
123#11758198—42no—
124#11758198—41no—
125#11758198—41no—
126C4⋊Dic61—21no—
127C4⋊Dic61—22no—
128C4⋊Dic61—41no—
129#11758196—41no—
130C4×Dic61—42no—
131C4×Dic61—42no—
132C2×#92418—22no—
133C2×#92418C2×D411yescharacteristic
134C2×#92418C2×D411yescharacteristic
135D488—22no—
136C8×D61—22no—
137C8×D61—22no—
138C8×D61—22no—
139C8×D61#4114yes—
140C16×C61—22no—
141#11758185—22no—
142C23×C61—41no—
143C23×C61C2×D811yescharacteristic
144C22×D61—22no—
145C22×D61—22no—
146C22×D61—41no—
147C22×D61—41no—
148C22×D61—82no—
149C22×D61—82no—
150C22×D61—82no—
151C22×D61C2×D811yescharacteristic
152C22×D61C2×D811yescharacteristic
153D4×C61—41no—
154D4×C61—41no—
155D4×C61—82no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—42no—
159C2×C4×C61—41no—
160C2×C4×C61—82no—
161C2×C4×C61C2×D811yescharacteristic
162C2×C4×C61C22×D411yescharacteristic
163C22⋊D61—82no—
164C22⋊D61—82no—
165C22⋊D61—82no—
166C2×Dic61—22no—
167C2×Dic61—42no—
168C2×Dic61—41no—
169C2×Dic61—82no—
170C2×Dic61C2×D811yescharacteristic
171C2×Dic61C2×D811yescharacteristic
172D244—41no—
173D244—41no—
174D244—82no—
175C4×D61—22no—
176C4×D61—21no—
177C4×D61—21no—
178C4×D61—22no—
179C4×D61—82no—
180C4×D61#12312yes—
181C4×D61#13712yes—
182C8×C61—21no—
183C8×C61C2×#4112yes—
184#92418—21no—
185#92418#12312yes—
186#33648—611nomaximal, Sylow
187C22×C61—21no—
188C22×C61—21no—
189C22×C61—81no—
190C22×C61—81no—
191C22×C61—81no—
192C22×C61#50912yes—
193C22×C61C22×D811yescharacteristic
194C2×D61—21no—
195C2×D61—21no—
196C2×D61—21no—
197C2×D61—21no—
198C2×D61—21no—
199C2×D61—44no—
200C2×D61—81no—
201C2×D61—81no—
202C2×D61—81no—
203C2×D61—164no—
204C2×D61#48012yes—
205C4×C61—21no—
206C4×C61—81no—
207C4×C61—82no—
208C4×C61C2×#12311yescharacteristic
209C4×C61C2×#13711yescharacteristic
210Dic61—21no—
211Dic61—81no—
212Dic61—82no—
213Dic61#48012yes—
214C2×#466—611no—
215C2×#427—611no—
216#2234—612no—
217#2234—612no—
218#2233—611no—
219#2233—611no—
220#2232—611no—
221#2232D6111yescharacteristic, complemented
222#2159—612no—
223#2140—612no—
224#2112—611no—
225C2×C61—22no—
226C2×C61—161no—
227C2×C61C2×#48011yescharacteristic
228C2×C61C2×#50911yescharacteristic
229C2×C61#341411yescharacteristic
230D61—22no—
231D61—41no—
232D61—161no—
233C22×D8—611no—
234C23×C8—611no—
235C2×#121—1221no—
236C2×#117—1221no—
237C2×M32—612no—
238#466—611no—
239#466—611no—
240#466—611no—
241#466—1221no—
242#466—1221no—
243#466C2×D6111yescharacteristic
244#427—612no—
245#427—612no—
246#427—1221no—
247#427—1221no—
248C2×#107—611no—
249C2×#107—611no—
250C2×#107C2×D6111yescharacteristic, complemented
251C2×#106—1221no—
252C2×#102—1221no—
253#367—612no—
254#367—612no—
255#366—612no—
256#366C2×D6112yescomplemented
257#357—612no—
258#357—612no—
259#357—612no—
260#357C2×D6112yescomplemented
261C22⋊C16—611no—
262C22⋊C16—612no—
263C22⋊C16C2×D6111yescharacteristic, complemented
264C61#3364811yescharacteristic, complemented, Sylow
265C22×D4—1221no—
266C22×D4—2441no—
267C23×C4—611no—
268C2×D8—611no—
269C2×D8—1224no—
270C2×D8—1221no—
271C2×D8C22×D6111yescharacteristic
272C22×C8—611no—
273C22×C8—611no—
274C22×C8—611no—
275C22×C8—611no—
276C22×C8—611no—
277C22×C8—1224no—
278C22×C8C22×D6111yescharacteristic
279#121—21no—
280#121—1221no—
281#121—1221no—
282#121—1221no—
283#121—2441no—
284#121—2441no—
285#117—1222no—
286#117—1222no—
287#117—2441no—
288#117—2441no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—1221no—
291C2×C4⋊C4—1221no—
292C2×C22⋊C4—2441no—
293C2×C22⋊C4—2441no—
294C2×C42—2441no—
295M32—1224no—
296C2×C16—612no—
297C2×C16C22×D6112yes—
298#107—21no—
299#107—612no—
300#107—611no—
301#107—1221no—
302#107—1221no—
303#107C22×D6112yes—
304#107C22×D6111yescharacteristic
305#106—1222no—
306#106—1222no—
307#102—21no—
308#102—1221no—
309#102—1221no—
310#102—1221no—
311C24—611no—
312C24—2441no—
313C2×D4—21no—
314C2×D4—41no—
315C2×D4—1221no—
316C2×D4—4884no—
317C2×D4—2441no—
318C2×D4—2442no—
319C2×D4—2442no—
320C2×D4—2441no—
321C2×D4—2441no—
322C2×D4—2441no—
323C22×C4—41no—
324C22×C4—611no—
325C22×C4—611no—
326C22×C4—611no—
327C22×C4—611no—
328C22×C4—611no—
329C22×C4—1222no—
330C22×C4—1222no—
331C22×C4—2441no—
332C22×C4—2441no—
333C22×C4D4×D6111yescharacteristic
334D8—22no—
335D8—1222no—
336D8—2442no—
337C2×C8—22no—
338C2×C8—611no—
339C2×C8—614no—
340C2×C8—611no—
341C2×C8—1222no—
342C2×C8—1222no—
343C2×C8—1222no—
344C2×C8—1222no—
345C2×C8D4×D6111yescharacteristic
346C2×C8C23×D6111yescharacteristic
347C4⋊C4—21no—
348C4⋊C4—22no—
349C4⋊C4—41no—
350C4⋊C4—1221no—
351C4⋊C4—1222no—
352C4⋊C4—2441no—
353C4⋊C4—2441no—
354C22⋊C4—41no—
355C22⋊C4—2441no—
356C22⋊C4—2442no—
357C22⋊C4—2442no—
358C22⋊C4—2441no—
359C22⋊C4—2441no—
360C42—2442no—
361C42—2442no—
362C16—22no—
363C16—1222no—
364C23—41no—
365C23—611no—
366C23—611no—
367C23—1222no—
368C23—1222no—
369C23—4882no—
370C23—4882no—
371C23—4882no—
372C23—2441no—
373C23—2441no—
374C23D8×D6111yescharacteristic
375D4—41no—
376D4—41no—
377D4—82no—
378D4—4882no—
379D4—4882no—
380D4—4882no—
381D4—4882no—
382D4—2441no—
383D4—2441no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—82no—
389C2×C4—611no—
390C2×C4—612no—
391C2×C4—612no—
392C2×C4—611no—
393C2×C4—1222no—
394C2×C4—1222no—
395C2×C4—1222no—
396C2×C4—1221no—
397C2×C4—1221no—
398C2×C4—4882no—
399C2×C4—4882no—
400C2×C4—2442no—
401C2×C4—2441no—
402C2×C4D8×D6111yescharacteristic
403C2×C4C2×D4×D6111yescharacteristic
404C8—21no—
405C8—612no—
406C8—1221no—
407C8#41×D6112yes—
408C22—21no—
409C22—21no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22—612no—
414C22—1221no—
415C22—1221no—
416C22—1221no—
417C22—1221no—
418C22—1221no—
419C22—9764no—
420C22—4881no—
421C22—4881no—
422C22—4881no—
423C22—2444no—
424C22#1684019612yes—
425C22C2×D8×D6111yescharacteristic
426C4—21no—
427C4—82no—
428C4—81no—
429C4—612no—
430C4—1221no—
431C4—4882no—
432C4—4881no—
433C4#123×D6111yescharacteristic
434C4#137×D6111yescharacteristic
435C2—22no—
436C2—161no—
437C2—1222no—
438C2—9761no—
439C2—2441no—
440C2#480×D6111yescharacteristic
441C2C2×#1684019611yescharacteristic
442C2#2145895411yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2232C2
socleC22×C61C22×D8
prime radical#466×D61C2
hypercenter#2232D61
hypocenterC61#33648
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2232

Complements

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

NH ≅ G/Ntype
2. C2×#16839799C2semidirect
3. #21448013C2semidirect
4. #21448009C2semidirect
5. #21448005C2semidirect
6. #21448002C2semidirect
7. #21447999C2semidirect
8. #21447604C2semidirect
9. #21447533C2semidirect
10. #21447428C2semidirect
11. C61×#2232C2semidirect
25. #16839799C22semidirect
26. C2×#14519711C22semidirect
30. #16839590C22semidirect
31. #16839589C22semidirect
32. #16839587C22semidirect
33. #16839564C22semidirect
34. #16839563C22semidirect
35. #16839562C22semidirect
36. C22⋊#11758185C22semidirect
37. #16839541C22semidirect
39. C2×#107×C61C22semidirect
40. C61×#366C22semidirect
41. C61×#357C22semidirect
42. C61×C22⋊C16C22semidirect
221. #2232D61semidirect
250. C2×#107C2×D61semidirect
256. #366C2×D61semidirect
260. #357C2×D61semidirect
263. C22⋊C16C2×D61semidirect
264. C61#33648semidirect

Maximal subgroups

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

subgroupindex
#466×D612
C2×#168397992
#214480132
#214480092
#214480052
#214480022
#214479992
#214476042
#214475332
#214474282
C61×#22322
#3364861