Finite Group Databasebeta

← C101×#7515 #38789666

Subgroups — C101×#7515 #38789666

Order 25856.

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

normal subgroups only

This group has 210 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×#1619C211yesmaximal, characteristic
2C101×#1408C211yesmaximal, characteristic, complemented
3C101×#1357C211yesmaximal, characteristic, complemented
4D42×C101C411yescharacteristic, complemented
5#493×C101C2211yescharacteristic
6#459×C101—21no—
7#364×C101—21no—
8#353×C101—21no—
9#331×C101C411yescharacteristic, complemented
10D4⋊C8×C101—21no—
11C22×D4×C101—41no—
12C2×D8×C101—41no—
13C2×D8×C101—41no—
14#127×C101C2×C411yescharacteristic
15#127×C101D411yescharacteristic
16#121×C101—41no—
17#120×C101—41no—
18C4×D4×C101—21no—
19M32×C101—41no—
20C4⋊C8×C101—21no—
21#102×C101—41no—
22#99×C101—41no—
23C4×C8×C101D411yescharacteristic
24C24×C101—41no—
25C2×D4×C101—21no—
26C2×D4×C101—21no—
27C2×D4×C101—21no—
28C2×D4×C101—41no—
29C2×D4×C101—41no—
30C2×D4×C101—42no—
31C2×D4×C101—82no—
32C2×D4×C101—82no—
33C22×C4×C101—41no—
34D8×C101—81no—
35D8×C101—81no—
36D8×C101—82no—
37C2×C8×C101—21no—
38C2×C8×C101—41no—
39C4⋊C4×C101—21no—
40C22⋊C4×C101—41no—
41C22⋊C4×C101—41no—
42C22⋊C4×C101—81no—
43C42×C101C22⋊C411yescharacteristic
44C16×C101—81no—
45C23×C101—41no—
46C23×C101—41no—
47C23×C101—41no—
48C23×C101—84no—
49C23×C101—161no—
50D4×C101—22no—
51D4×C101—41no—
52D4×C101—81no—
53D4×C101—81no—
54D4×C101—81no—
55D4×C101—81no—
56D4×C101—81no—
57D4×C101—81no—
58D4×C101—84no—
59C2×C4×C101—21no—
60C2×C4×C101—41no—
61C2×C4×C101—81no—
62C2×C4×C101—81no—
63C2×C4×C101—161no—
64C2×C4×C101#9911yescharacteristic
65C8×C101—21no—
66C8×C101—21no—
67C8×C101—81no—
68C22×C101—42no—
69C22×C101—81no—
70C22×C101—82no—
71C22×C101—81no—
72C22×C101—81no—
73C22×C101—81no—
74C22×C101—161no—
75C22×C101—162no—
76C22×C101—162no—
77C22×C101AΣL(1,𝔽16)11yescharacteristic
78C4×C101—21no—
79C4×C101—21no—
80C4×C101—21no—
81C4×C101—81no—
82C4×C101—321no—
83#7515C10111yesmaximal, characteristic, direct product factor, Sylow
84C2×C101—21no—
85C2×C101—82no—
86C2×C101—161no—
87C2×C101—161no—
88C2×C101#140211yescharacteristic
89#1619C2×C10111yescharacteristic
90#1408C2×C10111yescharacteristic, complemented
91#1357C2×C10111yescharacteristic, complemented
92C101#751511yescharacteristic, direct product factor, Sylow
93D42C4×C10111yescharacteristic, complemented
94#493C22×C10111yescharacteristic
95#459—21no—
96#364—21no—
97#353—21no—
98#331C4×C10111yescharacteristic, complemented
99D4⋊C8—21no—
100C22×D4—41no—
101C2×D8—41no—
102C2×D8—41no—
103#127C2×C4×C10111yescharacteristic
104#127D4×C10111yescharacteristic
105#121—41no—
106#120—41no—
107C4×D4—21no—
108M32—41no—
109C4⋊C8—21no—
110#102—41no—
111#99—41no—
112C4×C8D4×C10111yescharacteristic
113C24—41no—
114C2×D4—21no—
115C2×D4—21no—
116C2×D4—21no—
117C2×D4—41no—
118C2×D4—41no—
119C2×D4—42no—
120C2×D4—82no—
121C2×D4—82no—
122C22×C4—41no—
123D8—81no—
124D8—81no—
125D8—82no—
126C2×C8—21no—
127C2×C8—41no—
128C4⋊C4—21no—
129C22⋊C4—41no—
130C22⋊C4—41no—
131C22⋊C4—81no—
132C42C22⋊C4×C10111yescharacteristic
133C16—81no—
134C23—41no—
135C23—41no—
136C23—41no—
137C23—84no—
138C23—161no—
139D4—22no—
140D4—41no—
141D4—81no—
142D4—81no—
143D4—81no—
144D4—81no—
145D4—81no—
146D4—81no—
147D4—84no—
148C2×C4—21no—
149C2×C4—41no—
150C2×C4—81no—
151C2×C4—81no—
152C2×C4—161no—
153C2×C4#99×C10111yescharacteristic
154C8—21no—
155C8—21no—
156C8—81no—
157C22—42no—
158C22—81no—
159C22—82no—
160C22—81no—
161C22—81no—
162C22—81no—
163C22—161no—
164C22—162no—
165C22—162no—
166C22AΣL(1,𝔽16)×C10111yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—81no—
171C4—321no—
172C2—21no—
173C2—82no—
174C2—161no—
175C2—161no—
176C2C101×#140211yescharacteristic
subgroupG/H
center, socleC2×C101#1402
commutator#127C2×C4×C101
Frattini, cosocle#493C22×C101
prime radicalC101×#1619C2
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
2. C101×#1408C2semidirect
3. C101×#1357C2semidirect
4. D42×C101C4semidirect
9. #331×C101C4semidirect
83. #7515C101direct (N × H)
90. #1408C2×C101semidirect
91. #1357C2×C101semidirect
92. C101#7515direct (N × H)
93. D42C4×C101semidirect
98. #331C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#16192
C101×#14082
C101×#13572
#7515101