Finite Group Databasebeta

← #30594117

Subgroups — #30594117

Order 15616.

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

normal subgroups only

This group has 294 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
1#21460863C212yesmaximal, complemented
2#21446624C211yesmaximal, characteristic
3C2×#14519851—22no—
4C2×#14519774C411yescharacteristic
5C2×#14519697—22no—
6C2×C4×#92418C2211yescharacteristic
7C61×#384C411yescharacteristic
8#14519851—24no—
9#14519851—42no—
10C2×#11758187—42no—
11C22×D244—21no—
12C22×D244—41no—
13C22×#92418D412yes—
14#14519774—21no—
15#14519774—41no—
16#14519774C812yes—
17#14519697—42no—
18#14519697—42no—
19C4×#92418—41no—
20C2×C4⋊C4×C61—21no—
21C2×C4⋊C4×C61—41no—
22C2×C42×C61C2×C411yescharacteristic
23C23×D61—41no—
24C22×C4×C61—21no—
25C22×C4×C61—41no—
26C22×C4×C61C22⋊C411yescharacteristic
27C2×D244—22no—
28C2×D244—42no—
29C2×D244—42no—
30C2×D244—42no—
31C2×D244—42no—
32C2×D244—41no—
33C2×D244—82no—
34C2×D244—82no—
35C4⋊C4×C61—42no—
36C4⋊C4×C61—82no—
37C42×C61—21no—
38C42×C61C2×C811yescharacteristic
39C42×C61M1611yescharacteristic
40C2×#92418—22no—
41C2×#92418—22no—
42C2×#92418D812yes—
43C2×#92418SD1612yes—
44#11758187—44no—
45C23×C61#10011yescharacteristic
46C22×D61—42no—
47C22×D61—82no—
48C22×D61—82no—
49C22×D61—81no—
50C22×D61—81no—
51C2×C4×C61—22no—
52C2×C4×C61—22no—
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61—82no—
56C2×C4×C61—81no—
57C2×C4×C61C22⋊C811yescharacteristic
58C2×C4×C61#9911yescharacteristic
59C2×C4×C61#10212yes—
60C2×C4×C61#10412yes—
61D244—44no—
62D244—84no—
63D244—84no—
64D244—82no—
65#92418—22no—
66#92418—22no—
67#7107—611nomaximal, Sylow
68C22×C61—21no—
69C22×C61—21no—
70C22×C61#32311yescharacteristic
71C22×C61#32911yescharacteristic
72C22×C61#33111yescharacteristic
73C2×D61—84no—
74C2×D61—82no—
75C2×D61—162no—
76C2×D61—161no—
77C2×D61—161no—
78C4×C61—22no—
79C4×C61—22no—
80C4×C61—161no—
81C4×C61D4⋊C812yes—
82C4×C61#32712yes—
83#1957—611no—
84#1376—612no—
85C2×C61—21no—
86C2×C61—21no—
87C2×C61#127011yescharacteristic
88C2×C61#135711yescharacteristic
89C2×C61#135911yescharacteristic
90D61—162no—
91C2×#127—611no—
92C2×M32—1222no—
93C2×#102—1222no—
94C2×C4×C8—611no—
95#384#692311yescharacteristic
96C61#710711yescharacteristic, complemented, Sylow
97C22×D4—1221no—
98C22×D4—2441no—
99C22×C8—612no—
100#127—612no—
101#127—1221no—
102#127—2441no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—41no—
105C2×C42C2×#692311yescharacteristic
106M32—1224no—
107M32—2442no—
108C2×C16—2442no—
109#102—2442no—
110#102—2442no—
111C4×C8—2441no—
112C24—2441no—
113C2×D4—1222no—
114C2×D4—4882no—
115C2×D4—4882no—
116C2×D4—2442no—
117C2×D4—2442no—
118C2×D4—2441no—
119C2×D4—2442no—
120C2×D4—2442no—
121C22×C4—21no—
122C22×C4—41no—
123C22×C4C22⋊#692311yescharacteristic
124C2×C8—612no—
125C2×C8—612no—
126C2×C8—1222no—
127C2×C8—1222no—
128C4⋊C4—42no—
129C4⋊C4—82no—
130C42—21no—
131C42D61⋊C811yescharacteristic
132C42#1175821311yescharacteristic
133C16—2444no—
134C23—4882no—
135C23—4882no—
136C23—4881no—
137C23—4881no—
138C23—2442no—
139C23#1451983711yescharacteristic
140D4—4884no—
141D4—4884no—
142D4—4882no—
143D4—2444no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—82no—
149C2×C4—81no—
150C2×C4#1451983411yescharacteristic
151C2×C4#1451983611yescharacteristic
152C2×C4#1451983912yes—
153C2×C4#1451984212yes—
154C8—1222no—
155C8—1222no—
156C22—21no—
157C22—21no—
158C22—9762no—
159C22—9761no—
160C22—9761no—
161C22—4884no—
162C22—4882no—
163C22#1684060611yescharacteristic
164C22#1684061811yescharacteristic
165C22#1684062011yescharacteristic
166C4—22no—
167C4—22no—
168C4—161no—
169C4#1684061012yes—
170C4#1684061412yes—
171C2—21no—
172C2—21no—
173C2—9762no—
174C2#2146063611yescharacteristic
175C2#2146082711yescharacteristic
176C2#2146083011yescharacteristic
subgroupG/H
centerC22#16840620
commutatorC42×C61C2×C8
FrattiniC2×C42C2×#6923
FittingC61×#384C4
socleC22×C61#331
prime radicalC2×#14519774C4
cosocleC2×C4×#92418C22
hypercenter#384#6923
hypocenterC61#7107
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
1. #21460863C2semidirect
96. C61#7107semidirect

Maximal subgroups

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

subgroupindex
#214608632
#214466242
#710761