Finite Group Databasebeta

← C101×#7516 #38789667

Subgroups — C101×#7516 #38789667

Order 25856.

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

normal subgroups only

This group has 162 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×#1620C211yesmaximal, characteristic
2C101×#1408C211yesmaximal, characteristic
3C101×#1357C211yesmaximal, characteristic
4#559×C101C411yescharacteristic, complemented
5#493×C101C2211yescharacteristic
6#460×C101—21no—
7#364×C101—21no—
8#353×C101—21no—
9#331×C101C411yescharacteristic, complemented
10Q8⋊C8×C101—21no—
11C2×SD16×C101—41no—
12C2×D8×C101—41no—
13#127×C101C2×C411yescharacteristic
14#127×C101D411yescharacteristic
15#124×C101—41no—
16#123×C101—41no—
17C4×Q8×C101—21no—
18C4×D4×C101—41no—
19M32×C101—41no—
20C4⋊C8×C101—21no—
21#102×C101—41no—
22#99×C101—41no—
23C4×C8×C101D411yescharacteristic
24C2×Q8×C101—21no—
25C2×D4×C101—21no—
26C2×D4×C101—21no—
27C2×D4×C101—41no—
28C2×D4×C101—41no—
29C22×C4×C101—41no—
30SD16×C101—82no—
31D8×C101—81no—
32D8×C101—81no—
33C2×C8×C101—21no—
34C2×C8×C101—41no—
35C4⋊C4×C101—21no—
36C4⋊C4×C101—41no—
37C22⋊C4×C101—42no—
38C22⋊C4×C101—41no—
39C22⋊C4×C101—81no—
40C42×C101—41no—
41C42×C101C22⋊C411yescharacteristic
42C16×C101—81no—
43C23×C101—41no—
44C23×C101—41no—
45Q8×C101—41no—
46Q8×C101—41no—
47D4×C101—81no—
48D4×C101—81no—
49D4×C101—81no—
50D4×C101—81no—
51D4×C101—81no—
52D4×C101—81no—
53C2×C4×C101—21no—
54C2×C4×C101—41no—
55C2×C4×C101—41no—
56C2×C4×C101—161no—
57C2×C4×C101—161no—
58C2×C4×C101#9911yescharacteristic
59C8×C101—21no—
60C8×C101—21no—
61C8×C101—81no—
62C22×C101—82no—
63C22×C101—81no—
64C22×C101—81no—
65C22×C101—161no—
66C22×C101AΣL(1,𝔽16)11yescharacteristic
67C4×C101—21no—
68C4×C101—21no—
69C4×C101—21no—
70C4×C101—81no—
71C4×C101—81no—
72C4×C101—321no—
73#7516C10111yesmaximal, characteristic, direct product factor, Sylow
74C2×C101—21no—
75C2×C101—161no—
76C2×C101—161no—
77C2×C101#140211yescharacteristic
78#1620C2×C10111yescharacteristic
79#1408C2×C10111yescharacteristic
80#1357C2×C10111yescharacteristic
81C101#751611yescharacteristic, direct product factor, Sylow
82#559C4×C10111yescharacteristic, complemented
83#493C22×C10111yescharacteristic
84#460—21no—
85#364—21no—
86#353—21no—
87#331C4×C10111yescharacteristic, complemented
88Q8⋊C8—21no—
89C2×SD16—41no—
90C2×D8—41no—
91#127C2×C4×C10111yescharacteristic
92#127D4×C10111yescharacteristic
93#124—41no—
94#123—41no—
95C4×Q8—21no—
96C4×D4—41no—
97M32—41no—
98C4⋊C8—21no—
99#102—41no—
100#99—41no—
101C4×C8D4×C10111yescharacteristic
102C2×Q8—21no—
103C2×D4—21no—
104C2×D4—21no—
105C2×D4—41no—
106C2×D4—41no—
107C22×C4—41no—
108SD16—82no—
109D8—81no—
110D8—81no—
111C2×C8—21no—
112C2×C8—41no—
113C4⋊C4—21no—
114C4⋊C4—41no—
115C22⋊C4—42no—
116C22⋊C4—41no—
117C22⋊C4—81no—
118C42—41no—
119C42C22⋊C4×C10111yescharacteristic
120C16—81no—
121C23—41no—
122C23—41no—
123Q8—41no—
124Q8—41no—
125D4—81no—
126D4—81no—
127D4—81no—
128D4—81no—
129D4—81no—
130D4—81no—
131C2×C4—21no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—161no—
135C2×C4—161no—
136C2×C4#99×C10111yescharacteristic
137C8—21no—
138C8—21no—
139C8—81no—
140C22—82no—
141C22—81no—
142C22—81no—
143C22—161no—
144C22AΣL(1,𝔽16)×C10111yescharacteristic
145C4—21no—
146C4—21no—
147C4—21no—
148C4—81no—
149C4—81no—
150C4—321no—
151C2—21no—
152C2—161no—
153C2—161no—
154C2C101×#140211yescharacteristic
subgroupG/H
center, socleC2×C101#1402
commutator#127C2×C4×C101
Frattini, cosocle#493C22×C101
prime radical#493×C101C22
LCSG ▷ #127 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C101 ◁ C22×C101 ◁ C2×C4×C101 ◁ C42×C101 ◁ #493×C101 ◁ G

Complements

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

NH ≅ G/Ntype
4. #559×C101C4semidirect
9. #331×C101C4semidirect
73. #7516C101direct (N × H)
81. C101#7516direct (N × H)
82. #559C4×C101semidirect
87. #331C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#16202
C101×#14082
C101×#13572
#7516101