Finite Group Databasebeta

← #30608393

Subgroups — #30608393

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#21460960C214yesmaximal, complemented
3#21456194C211yesmaximal, characteristic
4C2×#14519836—22no—
5#16840667—22no—
6#16840667C2214yes—
7#16840319C411yescharacteristic, complemented
8C2×#14519774C2211yescharacteristic
9#16840127C412yescomplemented
10#16840127C2212yes—
11#16840109—22no—
12#16839768—22no—
13C4×M16×C61C411yescharacteristic, complemented
14C2×C22⋊#6923—42no—
15#14519836—24no—
16#14519836—42no—
17C22×D244—41no—
18C22×D244D412yes—
19#14519777—21no—
20#14519774—41no—
21#14519774C2×C411yescharacteristic
22#14519774D412yes—
23#14519774C2311yescharacteristic
24#14519769C2×C412yescomplemented
25#14519756—41no—
26C4×Dic122—41no—
27#14519736—21no—
28#14519699—24no—
29#14519699—24no—
30C2×M16×C61—21no—
31C2×C42×C61C2×C411yescharacteristic
32#97×C61C2×C412yescomplemented
33C4×C8×C61—21no—
34C23×D61—22no—
35C22×#6923—82no—
36C22×C4×C61—21no—
37C22×C4×C61C22⋊C411yescharacteristic
38C2×D244—22no—
39C2×D244—42no—
40C2×D244—42no—
41C2×D244—41no—
42C2×D244—42no—
43C2×D244—41no—
44C2×D244—84no—
45C2×D244C22⋊C412yes—
46C2×D244C2×D412yes—
47C2×Dic122—41no—
48C22⋊#6923—44no—
49C22⋊#6923—82no—
50M16×C61—42no—
51C2×C8×C61—22no—
52C42×C61—21no—
53C42×C61C22⋊C411yescharacteristic
54C42×C61C22×C411yescharacteristic
55C22⋊Dic61—41no—
56C4⋊Dic61—22no—
57C4⋊Dic61—41no—
58#11758196—42no—
59C4×Dic61—41no—
60C23×C61#9911yescharacteristic
61C22×D61—22no—
62C22×D61—22no—
63C22×D61—42no—
64C22×D61—42no—
65C22×D61—84no—
66C2×#6923—84no—
67C2×#6923—164no—
68C2×C4×C61—22no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—42no—
72C2×C4×C61#9911yescharacteristic
73C2×C4×C61C2×C22⋊C411yescharacteristic
74C2×Dic61—42no—
75D244—42no—
76D244—42no—
77D244—82no—
78D244—84no—
79D244—82no—
80D244—82no—
81Dic122—82no—
82C8×C61—42no—
83#13595—611nomaximal, Sylow
84C22×C61—41no—
85C22×C61#35412yes—
86C22×C61C2×#9911yescharacteristic
87C2×D61—42no—
88C2×D61—42no—
89C2×D61—84no—
90C2×D61—82no—
91C2×D61—82no—
92C2×D61—162no—
93#6923—164no—
94C4×C61—22no—
95C4×C61—21no—
96C4×C61—21no—
97C4×C61—41no—
98Dic61—82no—
99#3138—611no—
100C2×#353—612no—
101#1412—614no—
102C2×C61—21no—
103C2×C61—22no—
104C2×C61C2×#35411yescharacteristic
105D61—82no—
106D61—82no—
107#533—611no—
108C2×#127—611no—
109#490—612no—
110#490—612no—
111#486—1222no—
112#418—1222no—
113C2×#99—1222no—
114C4×M16#692311yescharacteristic, complemented
115#353—614no—
116#353—1222no—
117C61#1359511yescharacteristic, complemented, Sylow
118C22×D4—612no—
119C22×D4—2441no—
120C2×M16—21no—
121C4⋊Q8—1221no—
122#127—612no—
123#127—611no—
124#127—611no—
125#127—2441no—
126#125—612no—
127C22⋊Q8—2441no—
128C4×Q8—2441no—
129#117—1221no—
130C2×C22⋊C4—2442no—
131C2×C42C2×#692311yescharacteristic
132#102—1224no—
133#102—1224no—
134#99—1224no—
135#99—2442no—
136#97C2×#692312yescomplemented
137C4×C8—21no—
138C24—1222no—
139C2×Q8—2441no—
140C2×D4—612no—
141C2×D4—612no—
142C2×D4—1222no—
143C2×D4—4884no—
144C2×D4—2442no—
145C2×D4—2441no—
146C2×D4—2441no—
147C2×D4—2442no—
148C2×D4—2442no—
149C22×C4—21no—
150C22×C4—4882no—
151C22×C4C22⋊#692311yescharacteristic
152M16—42no—
153C2×C8—22no—
154C4⋊C4—1222no—
155C4⋊C4—2442no—
156C4⋊C4—2441no—
157C22⋊C4—4882no—
158C22⋊C4—2444no—
159C22⋊C4—2441no—
160C42—21no—
161C42—2441no—
162C42C22⋊#692311yescharacteristic
163C42C22×#692311yescharacteristic
164C23—1222no—
165C23—1222no—
166C23—4884no—
167C23—2442no—
168C23—2442no—
169C23#1451983611yescharacteristic
170Q8—4882no—
171D4—4884no—
172D4—4882no—
173D4—4882no—
174D4—4882no—
175D4—2442no—
176D4—2442no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—42no—
181C2×C4—9764no—
182C2×C4—4884no—
183C2×C4—2442no—
184C2×C4#1451983611yescharacteristic
185C2×C4C2×C22⋊#692311yescharacteristic
186C8—42no—
187C22—41no—
188C22—9762no—
189C22—4882no—
190C22—4882no—
191C22—4884no—
192C22—2442no—
193C22—2442no—
194C22#1684066912yes—
195C22C2×#1451983611yescharacteristic
196C4—22no—
197C4—21no—
198C4—21no—
199C4—41no—
200C4—9764no—
201C4—4882no—
202C2—21no—
203C2—22no—
204C2—4882no—
205C2—4882no—
206C2C2×#1684066911yescharacteristic
subgroupG/H
centerC2C2×#16840669
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC4×M16×C61C4
socleC2×C61C2×#354
prime radicalC2×#14519774C22
cosocle#14519774C23
hypercenterC4×M16#6923
hypocenterC61#13595
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. #21460960C2semidirect
7. #16840319C4semidirect
9. #16840127C4semidirect
13. C4×M16×C61C4semidirect
24. #14519769C2×C4semidirect
32. #97×C61C2×C4semidirect
114. C4×M16#6923semidirect
117. C61#13595semidirect
136. #97C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168406672
#214609602
#214561942
#1359561