Finite Group Databasebeta

← C101×#7412 #38789563

Subgroups — C101×#7412 #38789563

Order 25856.

208 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 46 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×#2073C211yesmaximal, characteristic
2C101×#1393C211yesmaximal, characteristic
3C101×#1318C211yesmaximal, characteristic
4C2×#102×C101—21no—
5C2×#99×C101—21no—
6#390×C101C2211yescharacteristic
7#382×C101C411yescharacteristic, complemented
8#340×C101—21no—
9#336×C101C411yescharacteristic, complemented
10#324×C101—21no—
11C22×D4×C101D411yescharacteristic
12C22×C8×C101—21no—
13C2×C4⋊C4×C101—21no—
14C2×C4⋊C4×C101D411yescharacteristic
15C2×C22⋊C4×C101—41no—
16C2×C22⋊C4×C101—41no—
17C2×C42×C101C2×C411yescharacteristic
18#102×C101—41no—
19#102×C101—41no—
20#99×C101—22no—
21#99×C101—41no—
22C22⋊C8×C101—41no—
23#95×C101—41no—
24C24×C101—21no—
25C2×D4×C101—21no—
26C2×D4×C101—41no—
27C2×D4×C101—41no—
28C2×D4×C101D811yescharacteristic
29C2×D4×C101SD1611yescharacteristic
30C22×C4×C101—21no—
31C22×C4×C101—21no—
32C22×C4×C101—41no—
33C22×C4×C101—81no—
34C22×C4×C101C22⋊C411yescharacteristic
35C2×C8×C101—41no—
36C2×C8×C101—41no—
37C2×C8×C101—41no—
38C2×C8×C101—81no—
39C4⋊C4×C101—41no—
40C4⋊C4×C101—41no—
41C4⋊C4×C101—41no—
42C22⋊C4×C101—42no—
43C22⋊C4×C101—82no—
44C22⋊C4×C101—81no—
45C42×C101—41no—
46C23×C101—21no—
47C23×C101—21no—
48C23×C101—41no—
49C23×C101—41no—
50C23×C101—81no—
51C23×C101—81no—
52C23×C101#9911yescharacteristic
53D4×C101—41no—
54D4×C101—41no—
55D4×C101—81no—
56C2×C4×C101—21no—
57C2×C4×C101—21no—
58C2×C4×C101—41no—
59C2×C4×C101—41no—
60C2×C4×C101—41no—
61C2×C4×C101—41no—
62C2×C4×C101—81no—
63C2×C4×C101—81no—
64C2×C4×C101—81no—
65C2×C4×C101—82no—
66C2×C4×C101—81no—
67C2×C4×C101—161no—
68C2×C4×C101—161no—
69C2×C4×C101#10211yescharacteristic
70C2×C4×C101#10411yescharacteristic
71C8×C101—81no—
72C8×C101—161no—
73C22×C101—21no—
74C22×C101—21no—
75C22×C101—41no—
76C22×C101—41no—
77C22×C101—81no—
78C22×C101—81no—
79C22×C101—81no—
80C22×C101—81no—
81C22×C101—161no—
82C22×C101#32711yescharacteristic
83C22×C101#35211yescharacteristic
84C22×C101#35411yescharacteristic
85C4×C101—21no—
86C4×C101—21no—
87C4×C101—81no—
88C4×C101—81no—
89C4×C101—161no—
90C4×C101—162no—
91#7412C10111yesmaximal, characteristic, direct product factor, Sylow
92C2×C101—21no—
93C2×C101—21no—
94C2×C101—81no—
95C2×C101—81no—
96C2×C101#134411yescharacteristic
97C2×C101#141211yescharacteristic
98C2×C101#141411yescharacteristic
99#2073C2×C10111yescharacteristic
100#1393C2×C10111yescharacteristic
101#1318C2×C10111yescharacteristic
102C101#741211yescharacteristic, direct product factor, Sylow
103C2×#102—21no—
104C2×#99—21no—
105#390C22×C10111yescharacteristic
106#382C4×C10111yescharacteristic, complemented
107#340—21no—
108#336C4×C10111yescharacteristic, complemented
109#324—21no—
110C22×D4D4×C10111yescharacteristic
111C22×C8—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4D4×C10111yescharacteristic
114C2×C22⋊C4—41no—
115C2×C22⋊C4—41no—
116C2×C42C2×C4×C10111yescharacteristic
117#102—41no—
118#102—41no—
119#99—22no—
120#99—41no—
121C22⋊C8—41no—
122#95—41no—
123C24—21no—
124C2×D4—21no—
125C2×D4—41no—
126C2×D4—41no—
127C2×D4D8×C10111yescharacteristic
128C2×D4SD16×C10111yescharacteristic
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—41no—
132C22×C4—81no—
133C22×C4C22⋊C4×C10111yescharacteristic
134C2×C8—41no—
135C2×C8—41no—
136C2×C8—41no—
137C2×C8—81no—
138C4⋊C4—41no—
139C4⋊C4—41no—
140C4⋊C4—41no—
141C22⋊C4—42no—
142C22⋊C4—82no—
143C22⋊C4—81no—
144C42—41no—
145C23—21no—
146C23—21no—
147C23—41no—
148C23—41no—
149C23—81no—
150C23—81no—
151C23#99×C10111yescharacteristic
152D4—41no—
153D4—41no—
154D4—81no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—81no—
162C2×C4—81no—
163C2×C4—81no—
164C2×C4—82no—
165C2×C4—81no—
166C2×C4—161no—
167C2×C4—161no—
168C2×C4#102×C10111yescharacteristic
169C2×C4#104×C10111yescharacteristic
170C8—81no—
171C8—161no—
172C22—21no—
173C22—21no—
174C22—41no—
175C22—41no—
176C22—81no—
177C22—81no—
178C22—81no—
179C22—81no—
180C22—161no—
181C22#327×C10111yescharacteristic
182C22#352×C10111yescharacteristic
183C22#354×C10111yescharacteristic
184C4—21no—
185C4—21no—
186C4—81no—
187C4—81no—
188C4—161no—
189C4—162no—
190C2—21no—
191C2—21no—
192C2—81no—
193C2—81no—
194C2C101×#134411yescharacteristic
195C2C101×#141211yescharacteristic
196C2C101×#141411yescharacteristic
subgroupG/H
center, socleC22×C101#354
commutatorC2×C42C2×C4×C101
Frattini, cosocle#390C22×C101
prime radicalC22×D4×C101D4
LCSG ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C23×C101 ◁ C22×C4×C101 ◁ #390×C101 ◁ G

Complements

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

NH ≅ G/Ntype
7. #382×C101C4semidirect
9. #336×C101C4semidirect
91. #7412C101direct (N × H)
102. C101#7412direct (N × H)
106. #382C4×C101semidirect
108. #336C4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#20732
C101×#13932
C101×#13182
#7412101