Finite Group Databasebeta

← #29834755

Subgroups — #29834755

Order 15616.

524 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456331C211yesmaximal, characteristic, complemented
2C2×#16839878C211yesmaximal, characteristic
3#21447994C214yesmaximal, complemented
4#21447989C214yesmaximal, complemented
5#21447593C211yesmaximal, characteristic, complemented
6C2×#16839582C211yesmaximal, characteristic, complemented
7#21447556C211yesmaximal, characteristic
8#21447554C211yesmaximal, characteristic
9C61×#2155C211yesmaximal, characteristic, complemented
10C2×#14519799C2211yescharacteristic
11C2×#14519785—21no—
12#16840315—21no—
13C2×#14519717C2211yescharacteristic
14#16840166—21no—
15#16840163—21no—
16#16840162C2212yescomplemented
17#16840159C2212yescomplemented
18#16839878—21no—
19#16839878—21no—
20#16839878C2212yes—
21#16839878C2212yes—
22#16839800C2211yescharacteristic
23#16839798—21no—
24C2×#14519703—21no—
25C2×C8×Dic61C2211yescharacteristic
26#16839586C2214yescomplemented
27#16839582C2212yescomplemented
28#16839582C2212yescomplemented
29#16839573C2214yes—
30#16839571C2214yes—
31C2×M32×C61C2211yescharacteristic
32C2×#108×C61C2211yescharacteristic
33C61×#427C2211yescharacteristic
34C61×#365C2214yescomplemented
35C2×#11758222—21no—
36#14519799—21no—
37#14519799—21no—
38#14519799Q812yescomplemented
39#14519799C2312yes—
40C2×Dic244Q811yescharacteristic, complemented
41C2×#11758190—21no—
42C2×D488Q811yescharacteristic, complemented
43#14519785—22no—
44#14519785—22no—
45#14519785—41no—
46#14519785—41no—
47C2×#11758189—41no—
48C22×#92418D411yescharacteristic
49C2×C8×D61—41no—
50#14519776—22no—
51#14519768—22no—
52#14519754—42no—
53C4×Dic122—42no—
54#14519736—21no—
55C2×C4×Dic61D411yescharacteristic
56#14519717—21no—
57#14519717C2312yes—
58C2×#11758185—21no—
59#14519711—21no—
60#14519710—22no—
61#14519709C2312yes—
62#14519708—22no—
63#14519703—22no—
64#14519703—22no—
65C8×Dic61D411yescharacteristic
66C8×Dic61D411yescharacteristic
67C8×Dic61C2311yescharacteristic
68C8×Dic61C2311yescharacteristic
69C2×M16×C61—21no—
70C22×C8×C61C2311yescharacteristic
71#117×C61—21no—
72M32×C61—21no—
73M32×C61C2312yes—
74C2×C16×C61—21no—
75#108×C61—21no—
76#108×C61C2312yes—
77#107×C61—21no—
78#106×C61C2312yes—
79C22×C4×C61C2×D411yescharacteristic
80C2×C22⋊D61—41no—
81C22×Dic61—21no—
82#11758222—22no—
83#11758222—22no—
84#11758222—41no—
85#11758222—41no—
86C2×D244—21no—
87C2×C4×D61—41no—
88C2×Dic122—21no—
89C2×Dic122—42no—
90M16×C61—22no—
91M16×C61—41no—
92C2×C8×C61—41no—
93C2×C8×C61C2×D411yescharacteristic
94C2×C8×C61C2×Q811yescharacteristic
95C2×C8×C61C2×Q811yescharacteristic
96C2×C8×C61#4111yescharacteristic
97C2×C8×C61#4111yescharacteristic
98C2×C8×C61C2411yescharacteristic
99C4⋊C4×C61—22no—
100C22⋊C4×C61—41no—
101C42×C61—41no—
102C22⋊Dic61—41no—
103C4⋊Dic61—22no—
104C4⋊Dic61—42no—
105#11758196—42no—
106#11758196—42no—
107C4×Dic61—21no—
108C4×Dic61—41no—
109C4×Dic61C2×D411yescharacteristic
110C4×Dic61C2×D411yescharacteristic
111C2×#92418SD1611yescharacteristic
112C2×#92418SD1611yescharacteristic
113C2×#92418SD1611yescharacteristic
114C2×#92418SD1611yescharacteristic
115C2×#92418C2×D411yescharacteristic
116C2×#92418C2×D411yescharacteristic
117Dic244—21no—
118Dic244C2×Q812yes—
119D488—21no—
120D488C2×Q812yes—
121#11758190—22no—
122#11758190—22no—
123#11758189—42no—
124#11758189—42no—
125C8×D61—42no—
126C8×D61—42no—
127C16×C61—22no—
128#11758185—22no—
129C23×C61AGL(1,ℤ/8)11yescharacteristic
130C22×D61—41no—
131C2×C4×C61—42no—
132C2×C4×C61C22⋊Q811yescharacteristic
133C2×C4×C61C22⋊Q811yescharacteristic
134C2×C4×C61C2×SD1611yescharacteristic
135C2×C4×C61C2×SD1611yescharacteristic
136C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C61C22×D411yescharacteristic
138C22⋊D61—42no—
139C22⋊D61—42no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—42no—
143C2×Dic61—41no—
144C2×Dic61—42no—
145D244—22no—
146D244—41no—
147C4×D61—42no—
148C4×D61—42no—
149Dic122—22no—
150Dic122—41no—
151Dic122—84no—
152C8×C61—42no—
153C8×C61C22⋊Q811yescharacteristic
154C8×C61C22⋊Q811yescharacteristic
155C8×C61C22×Q811yescharacteristic
156C8×C61C2×#4111yescharacteristic
157#92418C2×SD1611yescharacteristic
158#92418C2×SD1611yescharacteristic
159#92418C2×SD1611yescharacteristic
160#92418C2×SD1611yescharacteristic
161#33637—611nomaximal, Sylow
162C22×C61—41no—
163C22×C61#47611yescharacteristic
164C22×C61#47611yescharacteristic
165C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
166C2×D61—42no—
167C2×D61—82no—
168C4×C61—82no—
169C4×C61#47611yescharacteristic
170C4×C61#47611yescharacteristic
171C4×C61C2×C22⋊Q811yescharacteristic
172C4×C61C22×SD1611yescharacteristic
173Dic61—22no—
174Dic61—41no—
175Dic61—42no—
176Dic61—82no—
177#3160—611no—
178C2×#443—611no—
179#2231—614no—
180#2230—614no—
181#2155—611no—
182#2155D6111yescharacteristic, complemented
183C2×#364—611no—
184#2145—611no—
185#2145—611no—
186C2×C61—21no—
187C2×C61—21no—
188C2×C61—21no—
189C2×C61C2×#47611yescharacteristic
190D61—82no—
191C2×#135—611no—
192C2×#131—1221no—
193#533—1221no—
194C2×M32—611no—
195C2×M32C2×D6111yescharacteristic
196#500—1221no—
197#499—612no—
198#499—1221no—
199#498—612no—
200#443—612no—
201#443—612no—
202#443—1221no—
203#443—1221no—
204C2×#108C2×D6111yescharacteristic
205#427—611no—
206#427—1221no—
207#427C2×D6111yescharacteristic
208C2×#104—1221no—
209C2×C4×C8—611no—
210#365—614no—
211#365C2×D6114yescomplemented
212#364—612no—
213#364—612no—
214#360—614no—
215#360—614no—
216C61#3363711yescharacteristic, complemented, Sylow
217C2×#41—1221no—
218#135—612no—
219#135—612no—
220#135—1221no—
221#135—1221no—
222C2×Q16—611no—
223C2×SD16—1221no—
224C2×D8—611no—
225#131—1222no—
226#131—1222no—
227#131—2441no—
228#131—2441no—
229C2×M16—21no—
230C2×M16—2441no—
231C22×C8—611no—
232C22×C8—2441no—
233C22×C8C22×D6111yescharacteristic
234C4⋊Q8—1222no—
235#125—1222no—
236C22⋊Q8—2442no—
237C4×Q8—2442no—
238#117—21no—
239#117—1221no—
240C2×C42—611no—
241M32—21no—
242M32—612no—
243M32—1221no—
244M32C22×D6112yes—
245C2×C16—21no—
246C2×C16—1221no—
247#108—21no—
248#108C22×D6112yes—
249#107—21no—
250#107—1222no—
251#107—1221no—
252#106—612no—
253#106—1222no—
254#106C22×D6112yes—
255#104—1222no—
256#104—1222no—
257C4×C8—611no—
258C4×C8—611no—
259C4×C8—611no—
260C4×C8—611no—
261#41—1222no—
262#41—1222no—
263#41—2441no—
264#41—2441no—
265C2×Q8—1221no—
266C2×Q8—2442no—
267C2×D4—1221no—
268C2×D4—2441no—
269C22×C4—1221no—
270C22×C4—2441no—
271C22×C4D4×D6111yescharacteristic
272Q16—612no—
273Q16—1221no—
274SD16—1222no—
275SD16—1222no—
276D8—612no—
277D8—1221no—
278M16—22no—
279M16—41no—
280M16—2442no—
281M16—2442no—
282C2×C8—41no—
283C2×C8—611no—
284C2×C8—611no—
285C2×C8—611no—
286C2×C8—611no—
287C2×C8—611no—
288C2×C8—611no—
289C2×C8—2442no—
290C2×C8—2442no—
291C2×C8#1175822211yescharacteristic
292C2×C8#1175822211yescharacteristic
293C2×C8D4×D6111yescharacteristic
294C2×C8Q8×D6111yescharacteristic
295C2×C8Q8×D6111yescharacteristic
296C2×C8C23×D6111yescharacteristic
297C4⋊C4—22no—
298C4⋊C4—1222no—
299C4⋊C4—2442no—
300C4⋊C4—2442no—
301C4⋊C4—2442no—
302C22⋊C4—41no—
303C22⋊C4—2441no—
304C42—41no—
305C42—611no—
306C42—611no—
307C42—1221no—
308C42—2441no—
309C16—22no—
310C16—1222no—
311C23—2441no—
312C23#1451980411yescharacteristic
313Q8—1222no—
314Q8—4884no—
315Q8—2441no—
316D4—1222no—
317D4—2442no—
318D4—2442no—
319D4—2441no—
320C2×C4—42no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—2442no—
324C2×C4—2442no—
325C2×C4—2441no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4#1451975511yescharacteristic
329C2×C4#1451975511yescharacteristic
330C2×C4SD16×D6111yescharacteristic
331C2×C4SD16×D6111yescharacteristic
332C2×C4#1451980411yescharacteristic
333C2×C4C2×D4×D6111yescharacteristic
334C8—42no—
335C8—611no—
336C8—611no—
337C8—611no—
338C8—611no—
339C8#1451975511yescharacteristic
340C8#1451975511yescharacteristic
341C8C2×Q8×D6111yescharacteristic
342C8C2×#1175822211yescharacteristic
343C22—41no—
344C22—4882no—
345C22—2442no—
346C22#1684005111yescharacteristic
347C22#1684005111yescharacteristic
348C22C2×#1451980411yescharacteristic
349C4—82no—
350C4—1222no—
351C4—4882no—
352C4—2441no—
353C4—2442no—
354C4#1684005111yescharacteristic
355C4#1684005111yescharacteristic
356C4C2×#1451975511yescharacteristic
357C4C2×SD16×D6111yescharacteristic
358C2—21no—
359C2—21no—
360C2—21no—
361C2—4882no—
362C2C2×#1684005111yescharacteristic
subgroupG/H
centerC4#16840051
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2155C2
socleC2×C61C2×#476
prime radicalC2×#14519799C22
hypercenter#2155D61
hypocenterC61#33637
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #2155

Complements

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

NH ≅ G/Ntype
1. #21456331C2semidirect
3. #21447994C2semidirect
4. #21447989C2semidirect
5. #21447593C2semidirect
6. C2×#16839582C2semidirect
9. C61×#2155C2semidirect
16. #16840162C22semidirect
17. #16840159C22semidirect
26. #16839586C22semidirect
27. #16839582C22semidirect
28. #16839582C22semidirect
34. C61×#365C22semidirect
38. #14519799Q8semidirect
40. C2×Dic244Q8semidirect
42. C2×D488Q8semidirect
182. #2155D61semidirect
211. #365C2×D61semidirect
216. C61#33637semidirect

Maximal subgroups

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

subgroupindex
#214563312
C2×#168398782
#214479942
#214479892
#214475932
C2×#168395822
#214475562
#214475542
C61×#21552
#3363761