Finite Group Databasebeta

← #30608391

Subgroups — #30608391

Order 15616.

388 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840667C212yesmaximal
2#21460959C212yesmaximal, complemented
3#21460958C212yesmaximal, complemented
4#21456195C211yesmaximal, characteristic
5C2×#14519836—22no—
6#16840667—22no—
7#16840667C2214yes—
8C2×#14519774C2211yescharacteristic
9#16840128C411yescharacteristic, complemented
10#16840128C411yescharacteristic, complemented
11#16840128C2211yescharacteristic
12#16840128C2211yescharacteristic
13#16840110—22no—
14#16839766—22no—
15C4×#11758194C411yescharacteristic, complemented
16C61×#533C411yescharacteristic, complemented
17C2×C22⋊#6923—42no—
18#14519836—24no—
19#14519836—42no—
20C22×D244—41no—
21C22×D244D412yes—
22C2×#11758194—21no—
23#14519774—41no—
24#14519774C2×C411yescharacteristic
25#14519774D412yes—
26#14519774C2311yescharacteristic
27#14519697—22no—
28#14519697—22no—
29#14519697—22no—
30#14519697—22no—
31#14519688C2×C411yescharacteristic, complemented
32#14519688C2×C411yescharacteristic, complemented
33C4×#92418—21no—
34C4⋊Q8×C61—21no—
35#125×C61C2×C411yescharacteristic, complemented
36#125×C61C2×C411yescharacteristic, complemented
37C22⋊Q8×C61—41no—
38C4×Q8×C61—41no—
39#117×C61—21no—
40C2×C42×C61C2×C411yescharacteristic
41C23×D61—22no—
42C22×#6923—82no—
43C2×Q8×C61—41no—
44C22×C4×C61—21no—
45C22×C4×C61C22⋊C411yescharacteristic
46C2×D244—22no—
47C2×D244—42no—
48C2×D244—42no—
49C2×D244—41no—
50C2×D244—42no—
51C2×D244—41no—
52C2×D244—84no—
53C2×D244C22⋊C412yes—
54C2×D244C2×D412yes—
55C22⋊#6923—44no—
56C22⋊#6923—82no—
57C4⋊C4×C61—21no—
58C4⋊C4×C61—21no—
59C4⋊C4×C61—41no—
60C4⋊C4×C61—41no—
61C4⋊C4×C61—41no—
62C22⋊C4×C61—41no—
63C42×C61—21no—
64C42×C61—41no—
65C42×C61C22⋊C411yescharacteristic
66C42×C61C22×C411yescharacteristic
67#11758194—42no—
68C2×#92418—21no—
69C2×#92418—21no—
70C23×C61#9911yescharacteristic
71C22×D61—22no—
72C22×D61—22no—
73C22×D61—42no—
74C22×D61—42no—
75C22×D61—84no—
76C2×#6923—84no—
77C2×#6923—164no—
78Q8×C61—82no—
79C2×C4×C61—22no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—42no—
83C2×C4×C61—41no—
84C2×C4×C61—41no—
85C2×C4×C61#9911yescharacteristic
86C2×C4×C61C2×C22⋊C411yescharacteristic
87D244—42no—
88D244—42no—
89D244—82no—
90D244—84no—
91D244—82no—
92D244—82no—
93#92418—41no—
94#92418—41no—
95#13595—611nomaximal, Sylow
96C22×C61—41no—
97C22×C61#35412yes—
98C22×C61C2×#9911yescharacteristic
99C2×D61—42no—
100C2×D61—42no—
101C2×D61—84no—
102C2×D61—82no—
103C2×D61—82no—
104C2×D61—162no—
105#6923—164no—
106C4×C61—22no—
107C4×C61—21no—
108C4×C61—21no—
109C4×C61—41no—
110C4×C61—81no—
111C4×C61—81no—
112#3138—611no—
113C2×#353—612no—
114#1412—612no—
115#1412—612no—
116C2×C61—21no—
117C2×C61—22no—
118C2×C61C2×#35411yescharacteristic
119D61—82no—
120D61—82no—
121#533#692311yescharacteristic, complemented
122C2×#127—611no—
123#490—611no—
124#490—611no—
125#490—611no—
126#490—611no—
127#486—1222no—
128#418—1222no—
129C2×#99—1222no—
130C4×M16—611no—
131#353—614no—
132#353—1222no—
133C61#1359511yescharacteristic, complemented, Sylow
134C22×D4—612no—
135C22×D4—2441no—
136C2×M16—1221no—
137C4⋊Q8—21no—
138#127—612no—
139#127—611no—
140#127—611no—
141#127—2441no—
142#125C2×#692311yescharacteristic, complemented
143#125C2×#692311yescharacteristic, complemented
144C22⋊Q8—41no—
145C4×Q8—41no—
146#117—21no—
147C2×C22⋊C4—2442no—
148C2×C42C2×#692311yescharacteristic
149#102—1222no—
150#102—1222no—
151#102—1222no—
152#102—1222no—
153#99—1224no—
154#99—2442no—
155#97—611no—
156#97—611no—
157C4×C8—1221no—
158C24—1222no—
159C2×Q8—41no—
160C2×D4—612no—
161C2×D4—612no—
162C2×D4—1222no—
163C2×D4—4884no—
164C2×D4—2442no—
165C2×D4—2441no—
166C2×D4—2441no—
167C2×D4—2442no—
168C2×D4—2442no—
169C22×C4—21no—
170C22×C4—4882no—
171C22×C4C22⋊#692311yescharacteristic
172M16—2442no—
173C2×C8—1221no—
174C2×C8—1221no—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C4⋊C4—41no—
180C22⋊C4—41no—
181C22⋊C4—4882no—
182C22⋊C4—2444no—
183C42—21no—
184C42—41no—
185C42C22⋊#692311yescharacteristic
186C42C22×#692311yescharacteristic
187C23—1222no—
188C23—1222no—
189C23—4884no—
190C23—2442no—
191C23—2442no—
192C23#1451983511yescharacteristic
193Q8—82no—
194D4—4884no—
195D4—4882no—
196D4—4882no—
197D4—4882no—
198D4—2442no—
199D4—2442no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—42no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—9764no—
207C2×C4—4884no—
208C2×C4#1451983511yescharacteristic
209C2×C4C2×C22⋊#692311yescharacteristic
210C8—2441no—
211C8—2441no—
212C22—41no—
213C22—9762no—
214C22—4882no—
215C22—4882no—
216C22—4884no—
217C22—2442no—
218C22—2442no—
219C22#1684066812yes—
220C22C2×#1451983511yescharacteristic
221C4—22no—
222C4—21no—
223C4—21no—
224C4—41no—
225C4—81no—
226C4—81no—
227C4—9764no—
228C2—21no—
229C2—22no—
230C2—4882no—
231C2—4882no—
232C2C2×#1684066811yescharacteristic
subgroupG/H
centerC2C2×#16840668
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#533C4
socleC2×C61C2×#354
prime radicalC2×#14519774C22
cosocle#14519774C23
hypercenter#533#6923
hypocenterC61#13595
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #21460959C2semidirect
3. #21460958C2semidirect
9. #16840128C4semidirect
10. #16840128C4semidirect
15. C4×#11758194C4semidirect
16. C61×#533C4semidirect
31. #14519688C2×C4semidirect
32. #14519688C2×C4semidirect
35. #125×C61C2×C4semidirect
36. #125×C61C2×C4semidirect
121. #533#6923semidirect
133. C61#13595semidirect
142. #125C2×#6923semidirect
143. #125C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168406672
#214609592
#214609582
#214561952
#1359561