Finite Group Databasebeta

← #30595215

Subgroups — #30595215

Order 15616.

336 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 50 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#21446642C211yesmaximal, characteristic
3C2×#14519836—22no—
4#16840667—22no—
5#16840667C414yescomplemented
6C2×#14519774C2211yescharacteristic
7C2×#14519697—22no—
8C2×#14519688C411yescharacteristic, complemented
9C61×#382C411yescharacteristic, complemented
10C2×C22⋊#6923—42no—
11#14519836—24no—
12#14519836—42no—
13C22×D244—41no—
14C22×D244D412yes—
15C22×#92418—21no—
16#14519774—41no—
17#14519774C2×C412yes—
18#14519774D411yescharacteristic
19#14519774Q811yescharacteristic
20#14519697—44no—
21#14519688—41no—
22C2×C4⋊C4×C61—21no—
23C2×C42×C61C2×C411yescharacteristic
24#95×C61—41no—
25C23×D61—22no—
26C22×#6923—82no—
27C22×C4×C61—21no—
28C22×C4×C61—41no—
29C22×C4×C61C22⋊C411yescharacteristic
30C2×D244—22no—
31C2×D244—42no—
32C2×D244—42no—
33C2×D244—42no—
34C2×D244—41no—
35C2×D244—41no—
36C2×D244—82no—
37C2×D244—82no—
38C2×D244C22⋊C412yes—
39C2×D244C4⋊C412yes—
40C22⋊#6923—44no—
41C22⋊#6923—82no—
42C4⋊C4×C61—42no—
43C42×C61—21no—
44C42×C61C4211yescharacteristic
45C42×C61C4⋊C411yescharacteristic
46C2×#92418—22no—
47C2×#92418—41no—
48C2×#92418—41no—
49C23×C61#9911yescharacteristic
50C22×D61—22no—
51C22×D61—22no—
52C22×D61—42no—
53C22×D61—42no—
54C22×D61—82no—
55C22×D61—82no—
56C2×#6923—84no—
57C2×#6923—162no—
58C2×#6923—162no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—21no—
62C2×C4×C61—21no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61—81no—
66C2×C4×C61—81no—
67C2×C4×C61—81no—
68C2×C4×C61#9511yescharacteristic
69C2×C4×C61#9911yescharacteristic
70D244—42no—
71D244—42no—
72D244—82no—
73D244—84no—
74D244—82no—
75D244—82no—
76#92418—42no—
77#7504—611nomaximal, Sylow
78C22×C61—21no—
79C22×C61—21no—
80C22×C61#34211yescharacteristic
81C22×C61#35311yescharacteristic
82C22×C61#35411yescharacteristic
83C2×D61—42no—
84C2×D61—42no—
85C2×D61—82no—
86C2×D61—82no—
87C2×D61—82no—
88C2×D61—82no—
89C2×D61—162no—
90#6923—164no—
91C4×C61—21no—
92C4×C61—21no—
93C4×C61—41no—
94C4×C61—41no—
95C4×C61—161no—
96C2×#353—612no—
97#1961—611no—
98C2×C61—21no—
99C2×C61—21no—
100C2×C61#139311yescharacteristic
101C2×C61#141211yescharacteristic
102C2×C61#141211yescharacteristic
103D61—82no—
104D61—82no—
105C2×#127—611no—
106C2×#102—1222no—
107C2×#99—1222no—
108C2×#97—611no—
109#382#692311yescharacteristic, complemented
110#353—614no—
111#353—1222no—
112C61#750411yescharacteristic, complemented, Sylow
113C22×D4—612no—
114C22×D4—2441no—
115C22×C8—1221no—
116#127—612no—
117#127—611no—
118#127—611no—
119#127—2441no—
120C2×C4⋊C4—21no—
121C2×C22⋊C4—2442no—
122C2×C42C2×#692311yescharacteristic
123#102—2444no—
124#99—1224no—
125#99—2442no—
126#97—2441no—
127#95—41no—
128C24—1222no—
129C2×D4—612no—
130C2×D4—612no—
131C2×D4—1222no—
132C2×D4—4882no—
133C2×D4—4882no—
134C2×D4—2442no—
135C2×D4—2441no—
136C2×D4—2441no—
137C2×D4—2442no—
138C2×D4—2442no—
139C22×C4—21no—
140C22×C4—41no—
141C22×C4—4882no—
142C22×C4C22⋊#692311yescharacteristic
143C2×C8—1222no—
144C2×C8—2441no—
145C2×C8—2441no—
146C4⋊C4—42no—
147C22⋊C4—4882no—
148C22⋊C4—2444no—
149C42—21no—
150C42C4×#692311yescharacteristic
151C42C4⋊#692311yescharacteristic
152C23—1222no—
153C23—1222no—
154C23—4882no—
155C23—4882no—
156C23—2442no—
157C23—2442no—
158C23#1451983511yescharacteristic
159D4—4882no—
160D4—4884no—
161D4—4882no—
162D4—4882no—
163D4—2442no—
164D4—2442no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—81no—
172C2×C4—81no—
173C2×C4—81no—
174C2×C4—9762no—
175C2×C4—9762no—
176C2×C4—4884no—
177C2×C4(C2×#6923)⋊C411yescharacteristic
178C2×C4#1451983611yescharacteristic
179C8—2442no—
180C22—21no—
181C22—21no—
182C22—9762no—
183C22—4882no—
184C22—4882no—
185C22—4882no—
186C22—4882no—
187C22—2442no—
188C22—2442no—
189C22#1684064011yescharacteristic
190C22#1684066611yescharacteristic
191C22#1684066811yescharacteristic
192C4—21no—
193C4—21no—
194C4—41no—
195C4—41no—
196C4—161no—
197C4—9764no—
198C2—21no—
199C2—21no—
200C2—4882no—
201C2—4882no—
202C2#2146091411yescharacteristic
203C2#2146095811yescharacteristic
204C2#2146095911yescharacteristic
subgroupG/H
centerC22#16840668
commutatorC42×C61C42
FrattiniC2×C42C2×#6923
FittingC61×#382C4
socleC22×C61#354
prime radical, cosocleC2×#14519774C22
hypercenter#382#6923
hypocenterC61#7504
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
5. #16840667C4semidirect
8. C2×#14519688C4semidirect
9. C61×#382C4semidirect
109. #382#6923semidirect
112. C61#7504semidirect

Maximal subgroups

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

subgroupindex
C2×#168406672
#214466422
#750461