Finite Group Databasebeta

← C41×#1510 #19105290

Subgroups — C41×#1510 #19105290

Order 5248.

326 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C2×#121×C41C211yesmaximal, characteristic
2C41×#407C211yesmaximal, characteristic, complemented
3C41×#381C211yesmaximal, characteristic, complemented
4C41×#327C214yesmaximal, complemented
5C22×D4×C41—21no—
6C22×D4×C41C411yescharacteristic, complemented
7C23×C4×C41C2211yescharacteristic
8C2×M16×C41—21no—
9#121×C41—21no—
10#121×C41—21no—
11#121×C41C412yescomplemented
12#121×C41C2212yes—
13C2×C4⋊C4×C41C411yescharacteristic, complemented
14C2×C22⋊C4×C41—21no—
15C2×C22⋊C4×C41—21no—
16C22⋊C8×C41—21no—
17C22⋊C8×C41C2212yescomplemented
18#95×C41—21no—
19#95×C41C2212yescomplemented
20C24×C41—21no—
21C24×C41D411yescharacteristic
22C2×D4×C41—22no—
23C2×D4×C41—22no—
24C2×D4×C41—21no—
25C2×D4×C41—42no—
26C2×D4×C41—44no—
27C2×D4×C41C2×C412yes—
28C22×C4×C41—21no—
29C22×C4×C41—22no—
30C22×C4×C41—42no—
31C22×C4×C41C2×C411yescharacteristic
32C22×C4×C41C2×C411yescharacteristic
33C22×C4×C41D411yescharacteristic
34C22×C4×C41D411yescharacteristic
35C22×C4×C41D411yescharacteristic
36C22×C4×C41C2311yescharacteristic
37M16×C41—42no—
38C2×C8×C41—22no—
39C4⋊C4×C41—21no—
40C4⋊C4×C41C2×C412yes—
41C22⋊C4×C41—22no—
42C22⋊C4×C41—22no—
43C22⋊C4×C41—42no—
44C23×C41—22no—
45C23×C41—22no—
46C23×C41—22no—
47C23×C41—41no—
48C23×C41—42no—
49C23×C41—42no—
50C23×C41—42no—
51C23×C41C22⋊C411yescharacteristic
52C23×C41C22⋊C411yescharacteristic
53C23×C41C2×D411yescharacteristic
54D4×C41—42no—
55D4×C41—42no—
56D4×C41—44no—
57D4×C41—44no—
58C2×C4×C41—22no—
59C2×C4×C41—22no—
60C2×C4×C41—22no—
61C2×C4×C41—41no—
62C2×C4×C41—41no—
63C2×C4×C41—41no—
64C2×C4×C41—41no—
65C2×C4×C41—42no—
66C2×C4×C41—42no—
67C2×C4×C41—42no—
68C2×C4×C41—42no—
69C2×C4×C41C22⋊C411yescharacteristic
70C2×C4×C41C22⋊C411yescharacteristic
71C2×C4×C41C22×C411yescharacteristic
72C2×C4×C41C2×D411yescharacteristic
73C8×C41—42no—
74C22×C41—21no—
75C22×C41—21no—
76C22×C41—21no—
77C22×C41—21no—
78C22×C41—21no—
79C22×C41—21no—
80C22×C41—21no—
81C22×C41—44no—
82C22×C41—42no—
83C22×C41—42no—
84C22×C41—42no—
85C22×C41—84no—
86C22×C41#9912yes—
87C22×C41C2×C22⋊C411yescharacteristic
88C22×C41AGL(1,ℤ/8)12yes—
89C4×C41—21no—
90C4×C41—21no—
91C4×C41—21no—
92C4×C41—21no—
93C4×C41—42no—
94C4×C41—82no—
95#1510C4111yesmaximal, characteristic, direct product factor, Sylow
96C2×C41—22no—
97C2×C41—22no—
98C2×C41—41no—
99C2×C41—82no—
100C2×C41C2×#9911yescharacteristic
101C2×C41#41811yescharacteristic
102C2×C41#42111yescharacteristic
103C2×#121C2×C4111yescharacteristic
104#407C2×C4111yescharacteristic, complemented
105#381C2×C4111yescharacteristic, complemented
106#327C2×C4114yescomplemented
107C41#151011yescharacteristic, direct product factor, Sylow
108C22×D4—21no—
109C22×D4C4×C4111yescharacteristic, complemented
110C23×C4C22×C4111yescharacteristic
111C2×M16—21no—
112#121—21no—
113#121—21no—
114#121C4×C4112yescomplemented
115#121C22×C4112yes—
116C2×C4⋊C4C4×C4111yescharacteristic, complemented
117C2×C22⋊C4—21no—
118C2×C22⋊C4—21no—
119C22⋊C8—21no—
120C22⋊C8C22×C4112yescomplemented
121#95—21no—
122#95C22×C4112yescomplemented
123C24—21no—
124C24D4×C4111yescharacteristic
125C2×D4—22no—
126C2×D4—22no—
127C2×D4—21no—
128C2×D4—42no—
129C2×D4—44no—
130C2×D4C2×C4×C4112yes—
131C22×C4—21no—
132C22×C4—22no—
133C22×C4—42no—
134C22×C4C2×C4×C4111yescharacteristic
135C22×C4C2×C4×C4111yescharacteristic
136C22×C4D4×C4111yescharacteristic
137C22×C4D4×C4111yescharacteristic
138C22×C4D4×C4111yescharacteristic
139C22×C4C23×C4111yescharacteristic
140M16—42no—
141C2×C8—22no—
142C4⋊C4—21no—
143C4⋊C4C2×C4×C4112yes—
144C22⋊C4—22no—
145C22⋊C4—22no—
146C22⋊C4—42no—
147C23—22no—
148C23—22no—
149C23—22no—
150C23—41no—
151C23—42no—
152C23—42no—
153C23—42no—
154C23C22⋊C4×C4111yescharacteristic
155C23C22⋊C4×C4111yescharacteristic
156C23C2×D4×C4111yescharacteristic
157D4—42no—
158D4—42no—
159D4—44no—
160D4—44no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4C22⋊C4×C4111yescharacteristic
173C2×C4C22⋊C4×C4111yescharacteristic
174C2×C4C22×C4×C4111yescharacteristic
175C2×C4C2×D4×C4111yescharacteristic
176C8—42no—
177C22—21no—
178C22—21no—
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—44no—
185C22—42no—
186C22—42no—
187C22—42no—
188C22—84no—
189C22#99×C4112yes—
190C22C2×C22⋊C4×C4111yescharacteristic
191C22AGL(1,ℤ/8)×C4112yes—
192C4—21no—
193C4—21no—
194C4—21no—
195C4—21no—
196C4—42no—
197C4—82no—
198C2—22no—
199C2—22no—
200C2—41no—
201C2—82no—
202C2C2×#99×C4111yescharacteristic
203C2C41×#41811yescharacteristic
204C2C41×#42111yescharacteristic
subgroupG/H
center, socleC22×C41C2×C22⋊C4
commutatorC2×C4C22×C4×C41
Frattini, cosocleC22×C4C23×C41
prime radicalC2×#121×C41C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#407C2semidirect
3. C41×#381C2semidirect
4. C41×#327C2semidirect
6. C22×D4×C41C4semidirect
11. #121×C41C4semidirect
13. C2×C4⋊C4×C41C4semidirect
17. C22⋊C8×C41C22semidirect
19. #95×C41C22semidirect
95. #1510C41direct (N × H)
104. #407C2×C41semidirect
105. #381C2×C41semidirect
106. #327C2×C41semidirect
107. C41#1510direct (N × H)
109. C22×D4C4×C41semidirect
114. #121C4×C41semidirect
116. C2×C4⋊C4C4×C41semidirect
120. C22⋊C8C22×C41semidirect
122. #95C22×C41semidirect

Maximal subgroups

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

subgroupindex
C2×#121×C412
C41×#4072
C41×#3812
C41×#3272
#151041