Finite Group Databasebeta

← #29567609

Subgroups — #29567609

Order 15616.

210 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 37 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#21447335C211yesmaximal, characteristic
2#21443755C211yesmaximal, characteristic
3C61×#1297C211yesmaximal, characteristic
4#16839811C411yescharacteristic, complemented
5#16839810—21no—
6#16839726—21no—
7#16839544—21no—
8#16839520C411yescharacteristic, complemented
9C61×#407C2211yescharacteristic
10C4×C22⋊C4×C61—21no—
11C2×#11758194—21no—
12C2×#11758194—21no—
13#14519717—41no—
14#14519713—41no—
15#14519712—42no—
16C22⋊#92418—42no—
17C23×C4×C61D411yescharacteristic
18C2×M16×C61C2×C411yescharacteristic
19C2×M16×C61D411yescharacteristic
20C2×C22⋊C4×C61—41no—
21C2×C42×C61—41no—
22C22⋊C8×C61—41no—
23#95×C61—22no—
24C24×C61SD1611yescharacteristic
25C22×C4×C61—21no—
26C22×C4×C61—21no—
27C22×C4×C61—41no—
28C22×C4×C61—41no—
29C22×C4×C61—42no—
30C22×C4×C61C22⋊C411yescharacteristic
31C22×C4×C61Q1611yescharacteristic
32M16×C61—41no—
33M16×C61—41no—
34C2×C8×C61—21no—
35C2×C8×C61—21no—
36C22⋊C4×C61—44no—
37C42×C61—81no—
38C42×C61—81no—
39#11758194—41no—
40#11758194—41no—
41#11758194—41no—
42#11758194—41no—
43C2×#92418—22no—
44C2×#92418—41no—
45#11758185—81no—
46C23×C61—21no—
47C23×C61—42no—
48C23×C61—41no—
49C23×C61#10311yescharacteristic
50C2×C4×C61—21no—
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—41no—
54C2×C4×C61—41no—
55C2×C4×C61—41no—
56C2×C4×C61—44no—
57C2×C4×C61—81no—
58C2×C4×C61—82no—
59C2×C4×C61—82no—
60C2×C4×C61#9911yescharacteristic
61C2×C4×C61#10411yescharacteristic
62C8×C61—41no—
63C8×C61—41no—
64#92418—42no—
65#92418—81no—
66#7432—611nomaximal, Sylow
67C22×C61—22no—
68C22×C61—21no—
69C22×C61—41no—
70C22×C61—41no—
71C22×C61—42no—
72C22×C61—41no—
73C22×C61—81no—
74C22×C61#32811yescharacteristic
75C4×C61—21no—
76C4×C61—41no—
77C4×C61—84no—
78C4×C61#35211yescharacteristic
79C4×C61#35311yescharacteristic
80#2091—611no—
81#1320—611no—
82#1297D6111yescharacteristic
83C2×C61—21no—
84C2×C61—42no—
85C2×C61—41no—
86C2×C61#135211yescharacteristic
87#430—611no—
88#430—1221no—
89#407—1221no—
90#407C2×D6111yescharacteristic
91C4×C22⋊C4—21no—
92#349—1221no—
93#338—611no—
94C61#743211yescharacteristic, complemented, Sylow
95C23×C4C22⋊D6111yescharacteristic
96C2×M16—1221no—
97C2×M16—1221no—
98C2×M16C4×D6111yescharacteristic
99C2×M16D24411yescharacteristic
100C2×C22⋊C4—41no—
101C2×C42—41no—
102M32—2441no—
103#108—2441no—
104#108—2442no—
105C22⋊C8—41no—
106C22⋊C8—2442no—
107#95—22no—
108C24#1175820011yescharacteristic
109C22×C4—21no—
110C22×C4—21no—
111C22×C4—41no—
112C22×C4—41no—
113C22×C4—42no—
114C22×C4#1175819811yescharacteristic
115C22×C4#1175820211yescharacteristic
116M16—41no—
117M16—41no—
118M16—2441no—
119M16—2441no—
120M16—2441no—
121M16—2441no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—1222no—
125C2×C8—2441no—
126C22⋊C4—44no—
127C42—81no—
128C42—81no—
129C16—4881no—
130C23—21no—
131C23—42no—
132C23—41no—
133C23#1451970011yescharacteristic
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—44no—
141C2×C4—81no—
142C2×C4—82no—
143C2×C4—82no—
144C2×C4#1451969111yescharacteristic
145C2×C4#1451970511yescharacteristic
146C8—41no—
147C8—41no—
148C8—4881no—
149C8—2442no—
150C22—22no—
151C22—21no—
152C22—41no—
153C22—41no—
154C22—42no—
155C22—41no—
156C22—81no—
157C22#1683949811yescharacteristic
158C4—21no—
159C4—41no—
160C4—84no—
161C4#1683955111yescharacteristic
162C4#1683955411yescharacteristic
163C2—21no—
164C2—42no—
165C2—41no—
166C2#2144384211yescharacteristic
subgroupG/H
centerC4#16839554
commutatorC2×M16×C61C2×C4
Frattini#407C2×D61
FittingC61×#1297C2
socleC2×C61#1352
prime radicalC24×C61SD16
cosocleC61×#407C22
hypercenter#1297D61
hypocenterC61#7432
LCSG ▷ C2×M16×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #407 ◁ #1297

Complements

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

NH ≅ G/Ntype
4. #16839811C4semidirect
8. #16839520C4semidirect
94. C61#7432semidirect

Maximal subgroups

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

subgroupindex
#214473352
#214437552
C61×#12972
#743261