Finite Group Databasebeta

← C47×#2198 #20239808

Subgroups — C47×#2198 #20239808

Order 6016.

246 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 56 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
1C47×#559C211yesmaximal, characteristic, complemented
2C47×#458C212yesmaximal, complemented
3C47×#453C211yesmaximal, characteristic
4C47×#353C211yesmaximal, characteristic, complemented
5C47×#352C212yesmaximal, complemented
6H(5,𝔽2)×C47C2211yescharacteristic
7AGL(1,ℤ/8)×C47—21no—
8#127×C47C2211yescharacteristic
9#124×C47—22no—
10#123×C47—21no—
11#123×C47—22no—
12#123×C47C2212yes—
13C4×Q8×C47—21no—
14C4×D4×C47—22no—
15#104×C47—21no—
16#100×C47C2211yescharacteristic
17#99×C47—22no—
18#99×C47C2212yes—
19#41×C47—21no—
20#41×C47—41no—
21C2×Q8×C47—21no—
22C2×D4×C47—22no—
23C2×D4×C47—22no—
24C2×D4×C47—41no—
25C2×D4×C47D411yescharacteristic
26C2×D4×C47C2311yescharacteristic
27C22×C4×C47—21no—
28C22×C4×C47D412yes—
29SD16×C47—41no—
30D8×C47—41no—
31M16×C47—21no—
32C4⋊C4×C47—21no—
33C4⋊C4×C47—22no—
34C4⋊C4×C47—42no—
35C22⋊C4×C47—22no—
36C22⋊C4×C47—21no—
37C22⋊C4×C47—22no—
38C22⋊C4×C47—22no—
39C22⋊C4×C47—42no—
40C22⋊C4×C47D412yes—
41C42×C47—22no—
42C42×C47D411yescharacteristic
43C23×C47—22no—
44C23×C47—21no—
45C23×C47C2×D412yes—
46Q8×C47—21no—
47Q8×C47—42no—
48D4×C47—21no—
49D4×C47—41no—
50D4×C47—41no—
51D4×C47—44no—
52D4×C47—42no—
53D4×C47—41no—
54C2×C4×C47—21no—
55C2×C4×C47—22no—
56C2×C4×C47—22no—
57C2×C4×C47—22no—
58C2×C4×C47—41no—
59C2×C4×C47—42no—
60C2×C4×C47—42no—
61C2×C4×C47—81no—
62C2×C4×C47C2×D411yescharacteristic
63C8×C47—41no—
64C22×C47—22no—
65C22×C47—42no—
66C22×C47—42no—
67C22×C47—41no—
68C22×C47—41no—
69C22×C47—82no—
70C22×C47#12011yescharacteristic
71C4×C47—22no—
72C4×C47—21no—
73C4×C47—42no—
74C4×C47—41no—
75C4×C47—42no—
76C4×C47—82no—
77#2198C4711yesmaximal, characteristic, direct product factor, Sylow
78C2×C47—21no—
79C2×C47—42no—
80C2×C47—81no—
81C2×C47—81no—
82C2×C47B(4,𝔽2)11yescharacteristic
83#559C2×C4711yescharacteristic, complemented
84#458C2×C4712yescomplemented
85#453C2×C4711yescharacteristic
86#353C2×C4711yescharacteristic, complemented
87#352C2×C4712yescomplemented
88C47#219811yescharacteristic, direct product factor, Sylow
89H(5,𝔽2)C22×C4711yescharacteristic
90AGL(1,ℤ/8)—21no—
91#127C22×C4711yescharacteristic
92#124—22no—
93#123—21no—
94#123—22no—
95#123C22×C4712yes—
96C4×Q8—21no—
97C4×D4—22no—
98#104—21no—
99#100C22×C4711yescharacteristic
100#99—22no—
101#99C22×C4712yes—
102#41—21no—
103#41—41no—
104C2×Q8—21no—
105C2×D4—22no—
106C2×D4—22no—
107C2×D4—41no—
108C2×D4D4×C4711yescharacteristic
109C2×D4C23×C4711yescharacteristic
110C22×C4—21no—
111C22×C4D4×C4712yes—
112SD16—41no—
113D8—41no—
114M16—21no—
115C4⋊C4—21no—
116C4⋊C4—22no—
117C4⋊C4—42no—
118C22⋊C4—22no—
119C22⋊C4—21no—
120C22⋊C4—22no—
121C22⋊C4—22no—
122C22⋊C4—42no—
123C22⋊C4D4×C4712yes—
124C42—22no—
125C42D4×C4711yescharacteristic
126C23—22no—
127C23—21no—
128C23C2×D4×C4712yes—
129Q8—21no—
130Q8—42no—
131D4—21no—
132D4—41no—
133D4—41no—
134D4—44no—
135D4—42no—
136D4—41no—
137C2×C4—21no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—22no—
141C2×C4—41no—
142C2×C4—42no—
143C2×C4—42no—
144C2×C4—81no—
145C2×C4C2×D4×C4711yescharacteristic
146C8—41no—
147C22—22no—
148C22—42no—
149C22—42no—
150C22—41no—
151C22—41no—
152C22—82no—
153C22#120×C4711yescharacteristic
154C4—22no—
155C4—21no—
156C4—42no—
157C4—41no—
158C4—42no—
159C4—82no—
160C2—21no—
161C2—42no—
162C2—81no—
163C2—81no—
164C2C47×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C47B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C23×C47
prime radicalC47×#453C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C47 ◁ C22×C47 ◁ C2×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#559C2semidirect
2. C47×#458C2semidirect
4. C47×#353C2semidirect
5. C47×#352C2semidirect
77. #2198C47direct (N × H)
83. #559C2×C47semidirect
84. #458C2×C47semidirect
86. #353C2×C47semidirect
87. #352C2×C47semidirect
88. C47#2198direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#5592
C47×#4582
C47×#4532
C47×#3532
C47×#3522
#219847