Finite Group Databasebeta

← C101×#7535 #38789686

Subgroups — C101×#7535 #38789686

Order 25856.

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

normal subgroups only

This group has 150 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
1C101×#1705C211yesmaximal, characteristic
2C101×#1410C211yesmaximal, characteristic
3C101×#1409C211yesmaximal, characteristic
4#498×C101—21no—
5#498×C101C411yescharacteristic, complemented
6#492×C101—21no—
7#492×C101C2211yescharacteristic
8#356×C101—21no—
9#353×C101—21no—
10C82×C101C411yescharacteristic, complemented
11C2×SD16×C101—41no—
12C2×SD16×C101—42no—
13C4⋊Q8×C101—21no—
14C4⋊Q8×C101D411yescharacteristic
15#127×C101D411yescharacteristic
16#106×C101—42no—
17#106×C101—41no—
18#101×C101—41no—
19#99×C101—41no—
20C4×C8×C101—21no—
21C4×C8×C101C2×C411yescharacteristic
22C2×Q8×C101—21no—
23C2×Q8×C101—41no—
24C2×D4×C101—21no—
25C2×D4×C101—41no—
26SD16×C101—82no—
27SD16×C101—84no—
28M16×C101—81no—
29C2×C8×C101—22no—
30C2×C8×C101—21no—
31C4⋊C4×C101—41no—
32C4⋊C4×C101—41no—
33C4⋊C4×C101—41no—
34C22⋊C4×C101—81no—
35C42×C101C22⋊C411yescharacteristic
36C23×C101—41no—
37Q8×C101—81no—
38Q8×C101—82no—
39D4×C101—81no—
40D4×C101—82no—
41C2×C4×C101—21no—
42C2×C4×C101—41no—
43C2×C4×C101—81no—
44C2×C4×C101—161no—
45C2×C4×C101#9911yescharacteristic
46C8×C101—24no—
47C8×C101—22no—
48C8×C101—161no—
49C22×C101—81no—
50C22×C101—161no—
51C22×C101#35311yescharacteristic
52C4×C101—22no—
53C4×C101—21no—
54C4×C101—81no—
55C4×C101—161no—
56C4×C101—321no—
57#7535C10111yesmaximal, characteristic, direct product factor, Sylow
58C2×C101—21no—
59C2×C101—161no—
60C2×C101#140911yescharacteristic
61#1705C2×C10111yescharacteristic
62#1410C2×C10111yescharacteristic
63#1409C2×C10111yescharacteristic
64C101#753511yescharacteristic, direct product factor, Sylow
65#498—21no—
66#498C4×C10111yescharacteristic, complemented
67#492—21no—
68#492C22×C10111yescharacteristic
69#356—21no—
70#353—21no—
71C82C4×C10111yescharacteristic, complemented
72C2×SD16—41no—
73C2×SD16—42no—
74C4⋊Q8—21no—
75C4⋊Q8D4×C10111yescharacteristic
76#127D4×C10111yescharacteristic
77#106—42no—
78#106—41no—
79#101—41no—
80#99—41no—
81C4×C8—21no—
82C4×C8C2×C4×C10111yescharacteristic
83C2×Q8—21no—
84C2×Q8—41no—
85C2×D4—21no—
86C2×D4—41no—
87SD16—82no—
88SD16—84no—
89M16—81no—
90C2×C8—22no—
91C2×C8—21no—
92C4⋊C4—41no—
93C4⋊C4—41no—
94C4⋊C4—41no—
95C22⋊C4—81no—
96C42C22⋊C4×C10111yescharacteristic
97C23—41no—
98Q8—81no—
99Q8—82no—
100D4—81no—
101D4—82no—
102C2×C4—21no—
103C2×C4—41no—
104C2×C4—81no—
105C2×C4—161no—
106C2×C4#99×C10111yescharacteristic
107C8—24no—
108C8—22no—
109C8—161no—
110C22—81no—
111C22—161no—
112C22#353×C10111yescharacteristic
113C4—22no—
114C4—21no—
115C4—81no—
116C4—161no—
117C4—321no—
118C2—21no—
119C2—161no—
120C2C101×#140911yescharacteristic
subgroupG/H
center, socleC2×C101#1409
commutatorC4×C8C2×C4×C101
Frattini, cosocle#492C22×C101
prime radical#127×C101D4
LCSG ▷ C4×C8 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C101 ◁ C22×C101 ◁ C2×C4×C101 ◁ C42×C101 ◁ #492×C101 ◁ G

Complements

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

NH ≅ G/Ntype
5. #498×C101C4semidirect
10. C82×C101C4semidirect
57. #7535C101direct (N × H)
64. C101#7535direct (N × H)
66. #498C4×C101semidirect
71. C82C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#17052
C101×#14102
C101×#14092
#7535101