Finite Group Databasebeta

← #29567849

Subgroups — #29567849

Order 15616.

142 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 25 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#21444957C211yesmaximal, characteristic
2#21443858C211yesmaximal, characteristic
3C61×#1411C211yesmaximal, characteristic
4#16840492C411yescharacteristic
5#16840054—21no—
6#16839583—21no—
7#16839511C411yescharacteristic
8#16839494—21no—
9C61×#494C2211yescharacteristic
10C61×#356—21no—
11#14519776—41no—
12#14519775—41no—
13C4×Dic122—21no—
14#14519742—41no—
15#14519717—41no—
16#14519710—41no—
17C4⋊#92418—21no—
18#14519700—41no—
19C2×Q16×C61—41no—
20C4⋊Q8×C61C2×C411yescharacteristic
21C4⋊Q8×C61D411yescharacteristic
22#101×C61—41no—
23C4×C8×C61D411yescharacteristic
24C2×Q8×C61—21no—
25C2×Q8×C61—21no—
26C2×Dic122—21no—
27C2×Dic122—41no—
28Q16×C61—81no—
29Q16×C61—81no—
30M16×C61—81no—
31C2×C8×C61—21no—
32C4⋊C4×C61—41no—
33C4⋊C4×C61—41no—
34C42×C61C22⋊C411yescharacteristic
35C4⋊Dic61—21no—
36#11758196—42no—
37#11758196—41no—
38C4×Dic61—41no—
39C4×Dic61—41no—
40C2×#92418—41no—
41#11758185—81no—
42Q8×C61—81no—
43Q8×C61—81no—
44C2×C4×C61—21no—
45C2×C4×C61—41no—
46C2×C4×C61—41no—
47C2×C4×C61#9911yescharacteristic
48C2×Dic61—41no—
49C2×Dic61—41no—
50Dic122—22no—
51Dic122—41no—
52Dic122—161no—
53C8×C61—21no—
54C8×C61—21no—
55C8×C61—161no—
56#92418—81no—
57#7522—611nomaximal, Sylow
58C22×C61AΣL(1,𝔽16)11yescharacteristic
59C4×C61—21no—
60C4×C61—21no—
61C4×C61—21no—
62C4×C61—81no—
63C4×C61—81no—
64Dic61—42no—
65Dic61—81no—
66#1633—611no—
67#1411D6111yescharacteristic
68#1358—611no—
69C2×C61—21no—
70C2×C61#140211yescharacteristic
71Q82—611no—
72#494C2×D6111yescharacteristic
73#477—1221no—
74#364—1221no—
75#356—21no—
76#333—611no—
77Q8⋊C8—1221no—
78C61#752211yescharacteristic, complemented, Sylow
79C2×Q16—41no—
80C4⋊Q8—2441no—
81C4⋊Q8—2441no—
82C4⋊Q8C4×D6111yescharacteristic
83C4⋊Q8C22⋊D6111yescharacteristic
84C4×Q8—1221no—
85C4×Q8—2441no—
86M32—2441no—
87#107—2441no—
88C4⋊C8—1221no—
89#103—2441no—
90#101—41no—
91C4×C8D24411yescharacteristic
92C2×Q8—21no—
93C2×Q8—21no—
94C2×Q8—1221no—
95C2×Q8—2441no—
96Q16—81no—
97Q16—81no—
98M16—81no—
99C2×C8—21no—
100C2×C8—2441no—
101C4⋊C4—41no—
102C4⋊C4—41no—
103C4⋊C4—1221no—
104C4⋊C4—2442no—
105C4⋊C4—2441no—
106C42—2441no—
107C42—2441no—
108C42#1175819811yescharacteristic
109C16—4881no—
110Q8—81no—
111Q8—81no—
112Q8—1222no—
113Q8—9761no—
114Q8—2441no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—2441no—
119C2×C4—2441no—
120C2×C4#1451969111yescharacteristic
121C8—21no—
122C8—21no—
123C8—161no—
124C8—4881no—
125C22#1683954811yescharacteristic
126C4—21no—
127C4—21no—
128C4—21no—
129C4—81no—
130C4—81no—
131C4—4881no—
132C4—2442no—
133C2—21no—
134C2#2144396311yescharacteristic
subgroupG/H
centerC2#21443963
commutatorC4⋊Q8×C61C2×C4
Frattini#494C2×D61
FittingC61×#1411C2
socleC2×C61#1402
prime radicalC22×C61AΣL(1,𝔽16)
cosocleC61×#494C22
hypercenter#1411D61
hypocenterC61#7522
LCSG ▷ C4⋊Q8×C61 ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #494 ◁ #1411

Complements

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

NH ≅ G/Ntype
78. C61#7522semidirect

Maximal subgroups

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

subgroupindex
#214449572
#214438582
C61×#14112
#752261