Finite Group Databasebeta

← #29567409

Subgroups — #29567409

Order 15616.

184 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 39 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#21446795C211yesmaximal, characteristic
2#21443770C211yesmaximal, characteristic
3C61×#1327C211yesmaximal, characteristic
4#16840319C411yescharacteristic
5C42×Dic61C411yescharacteristic
6#16839544—21no—
7#16839523—21no—
8#16839523—21no—
9C61×#423C2211yescharacteristic
10C61×#349—21no—
11#14519777—21no—
12#14519769C812yes—
13#14519756—41no—
14C4×Dic122—41no—
15#14519736—21no—
16C2×C4×Dic61—21no—
17C2×C4×Dic61—41no—
18#14519717—41no—
19C2×M16×C61D411yescharacteristic
20C2×M16×C61D411yescharacteristic
21C2×C42×C61C2×C411yescharacteristic
22M32×C61—41no—
23C4⋊C8×C61—41no—
24C22×C4×C61—21no—
25C22×C4×C61C22⋊C411yescharacteristic
26C22×Dic61—41no—
27C2×Dic122—41no—
28M16×C61—41no—
29M16×C61—41no—
30C2×C8×C61—21no—
31C2×C8×C61—21no—
32C42×C61—21no—
33C42×C61C2×C811yescharacteristic
34C42×C61M1611yescharacteristic
35C22⋊Dic61—41no—
36C4⋊Dic61—22no—
37C4⋊Dic61—41no—
38#11758196—42no—
39C4×Dic61—22no—
40C4×Dic61—41no—
41C4×Dic61—44no—
42C4×Dic61—41no—
43C16×C61—81no—
44#11758185—81no—
45C23×C61#10011yescharacteristic
46C2×C4×C61—21no—
47C2×C4×C61—21no—
48C2×C4×C61—21no—
49C2×C4×C61—21no—
50C2×C4×C61—42no—
51C2×C4×C61C22⋊C811yescharacteristic
52C2×C4×C61#9911yescharacteristic
53C2×Dic61—42no—
54C2×Dic61—44no—
55C2×Dic61—42no—
56Dic122—82no—
57C8×C61—41no—
58C8×C61—41no—
59#7361—611nomaximal, Sylow
60C22×C61—21no—
61C22×C61—41no—
62C22×C61#32311yescharacteristic
63C4×C61—22no—
64C4×C61—21no—
65C4×C61—41no—
66C4×C61#35411yescharacteristic
67C4×C61#35611yescharacteristic
68Dic61—44no—
69Dic61—82no—
70#1994—611no—
71#1327—611no—
72#1327D6111yescharacteristic
73C2×C61—21no—
74C2×C61—41no—
75C2×C61#131911yescharacteristic
76#533—611no—
77#423C2×D6111yescharacteristic
78C43—611no—
79#349—21no—
80#349—1221no—
81#339—1221no—
82#339—1221no—
83C61#736111yescharacteristic, complemented, Sylow
84C2×M16D24411yescharacteristic
85C2×M16C22⋊D6111yescharacteristic
86C4⋊Q8—1221no—
87#125—612no—
88C22⋊Q8—2441no—
89C4×Q8—2441no—
90#117—1221no—
91C2×C42—1221no—
92C2×C42—2441no—
93C2×C42C4×D6111yescharacteristic
94M32—41no—
95M32—2441no—
96C4⋊C8—41no—
97C2×Q8—2441no—
98C22×C4—21no—
99C22×C4—2441no—
100C22×C4#1175819811yescharacteristic
101M16—41no—
102M16—41no—
103C2×C8—21no—
104C2×C8—21no—
105C4⋊C4—1222no—
106C4⋊C4—2442no—
107C4⋊C4—2441no—
108C22⋊C4—2441no—
109C42—21no—
110C42—1222no—
111C42—2441no—
112C42—2444no—
113C42—2441no—
114C42C8×D6111yescharacteristic
115C42#1175818911yescharacteristic
116C16—81no—
117C16—4881no—
118C23#1451969311yescharacteristic
119Q8—4882no—
120C2×C4—21no—
121C2×C4—21no—
122C2×C4—21no—
123C2×C4—21no—
124C2×C4—42no—
125C2×C4—2442no—
126C2×C4—2442no—
127C2×C4—2444no—
128C2×C4#1451968911yescharacteristic
129C2×C4#1451969111yescharacteristic
130C8—41no—
131C8—41no—
132C22—21no—
133C22—41no—
134C22#1683948511yescharacteristic
135C4—22no—
136C4—21no—
137C4—41no—
138C4—4882no—
139C4—2444no—
140C4#1683955611yescharacteristic
141C4#1683956011yescharacteristic
142C2—21no—
143C2—41no—
144C2#2144375211yescharacteristic
subgroupG/H
centerC4#16839556
commutatorC42×C61C2×C8
Frattini#423C2×D61
FittingC61×#1327C2
socleC2×C61#1319
prime radicalC23×C61#100
cosocleC61×#423C22
hypercenter#1327D61
hypocenterC61#7361
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #423 ◁ #1327

Complements

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

NH ≅ G/Ntype
83. C61#7361semidirect

Maximal subgroups

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

subgroupindex
#214467952
#214437702
C61×#13272
#736161