Finite Group Databasebeta

← C113×#7533 #43275553

Subgroups — C113×#7533 #43275553

Order 28928.

156 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 30 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
1C113×#1715C211yesmaximal, characteristic
2C113×#1408C211yesmaximal, characteristic
3C113×#1408C211yesmaximal, characteristic
4#498×C113C411yescharacteristic, complemented
5#493×C113C2211yescharacteristic
6#492×C113—21no—
7#486×C113—21no—
8#353×C113—21no—
9#353×C113—21no—
10#322×C113C411yescharacteristic, complemented
11C2×SD16×C113—42no—
12C2×D8×C113—41no—
13C4⋊Q8×C113—21no—
14#127×C113D411yescharacteristic
15#127×C113D411yescharacteristic
16#106×C113—41no—
17#102×C113—42no—
18#99×C113—41no—
19#99×C113—41no—
20C4×C8×C113—21no—
21C4×C8×C113C2×C411yescharacteristic
22C2×Q8×C113—41no—
23C2×D4×C113—21no—
24C2×D4×C113—21no—
25C2×D4×C113—41no—
26C2×D4×C113—41no—
27SD16×C113—84no—
28D8×C113—82no—
29C2×C8×C113—21no—
30C2×C8×C113—22no—
31C4⋊C4×C113—41no—
32C4⋊C4×C113—41no—
33C22⋊C4×C113—81no—
34C22⋊C4×C113—81no—
35C42×C113C22⋊C411yescharacteristic
36C23×C113—41no—
37C23×C113—41no—
38Q8×C113—82no—
39D4×C113—81no—
40D4×C113—81no—
41D4×C113—82no—
42D4×C113—82no—
43C2×C4×C113—21no—
44C2×C4×C113—81no—
45C2×C4×C113—161no—
46C2×C4×C113—161no—
47C2×C4×C113#9911yescharacteristic
48C8×C113—22no—
49C8×C113—42no—
50C22×C113—81no—
51C22×C113—81no—
52C22×C113—161no—
53C22×C113—161no—
54C22×C113#35311yescharacteristic
55C4×C113—22no—
56C4×C113—21no—
57C4×C113—161no—
58C4×C113—321no—
59C4×C113—321no—
60#7533C11311yesmaximal, characteristic, direct product factor, Sylow
61C2×C113—21no—
62C2×C113—161no—
63C2×C113—161no—
64C2×C113#140911yescharacteristic
65#1715C2×C11311yescharacteristic
66#1408C2×C11311yescharacteristic
67#1408C2×C11311yescharacteristic
68C113#753311yescharacteristic, direct product factor, Sylow
69#498C4×C11311yescharacteristic, complemented
70#493C22×C11311yescharacteristic
71#492—21no—
72#486—21no—
73#353—21no—
74#353—21no—
75#322C4×C11311yescharacteristic, complemented
76C2×SD16—42no—
77C2×D8—41no—
78C4⋊Q8—21no—
79#127D4×C11311yescharacteristic
80#127D4×C11311yescharacteristic
81#106—41no—
82#102—42no—
83#99—41no—
84#99—41no—
85C4×C8—21no—
86C4×C8C2×C4×C11311yescharacteristic
87C2×Q8—41no—
88C2×D4—21no—
89C2×D4—21no—
90C2×D4—41no—
91C2×D4—41no—
92SD16—84no—
93D8—82no—
94C2×C8—21no—
95C2×C8—22no—
96C4⋊C4—41no—
97C4⋊C4—41no—
98C22⋊C4—81no—
99C22⋊C4—81no—
100C42C22⋊C4×C11311yescharacteristic
101C23—41no—
102C23—41no—
103Q8—82no—
104D4—81no—
105D4—81no—
106D4—82no—
107D4—82no—
108C2×C4—21no—
109C2×C4—81no—
110C2×C4—161no—
111C2×C4—161no—
112C2×C4#99×C11311yescharacteristic
113C8—22no—
114C8—42no—
115C22—81no—
116C22—81no—
117C22—161no—
118C22—161no—
119C22#353×C11311yescharacteristic
120C4—22no—
121C4—21no—
122C4—161no—
123C4—321no—
124C4—321no—
125C2—21no—
126C2—161no—
127C2—161no—
128C2C113×#140911yescharacteristic
subgroupG/H
center, socleC2×C113#1409
commutatorC4×C8C2×C4×C113
Frattini, cosocle#493C22×C113
prime radical#493×C113C22
LCSG ▷ C4×C8 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C113 ◁ C22×C113 ◁ C2×C4×C113 ◁ C42×C113 ◁ #493×C113 ◁ G

Complements

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

NH ≅ G/Ntype
4. #498×C113C4semidirect
10. #322×C113C4semidirect
60. #7533C113direct (N × H)
68. C113#7533direct (N × H)
69. #498C4×C113semidirect
75. #322C4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#17152
C113×#14082
#7533113