Finite Group Databasebeta

← #20253210

Subgroups — #20253210

Order 6016.

384 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13094016C211yesmaximal, characteristic, complemented
2#15689430C214yesmaximal, complemented
3#15689423C214yesmaximal, complemented
4#15689166C212yesmaximal, complemented
5#15689147C211yesmaximal, characteristic, complemented
6#15689124C212yesmaximal
7C4×#41×C47C211yesmaximal, characteristic
8C2×#10625329C2212yes—
9#13094016—21no—
10#13094016—21no—
11#13094016C2214yes—
12C2×C4⋊Dic47C2212yes—
13C2×Dic47⋊C4—22no—
14#13093957C2214yes—
15#13093955C2214yes—
16C4⋊(C47⋊C8)C2214yes—
17#13093948C2214yes—
18#13093945C2214yes—
19C2×#41×C47C2211yescharacteristic
20C4×Q8×C47C2212yes—
21C4×D4×C47—22no—
22C4×D4×C47C2212yes—
23#117×C47—21no—
24#117×C47C2211yescharacteristic
25C2×C42×C47—21no—
26C2×C42×C47C2211yescharacteristic
27#41×C47—22no—
28#41×C47Q814yes—
29C2×Q8×C47C2311yescharacteristic
30C2×D4×C47—21no—
31C2×D4×C47C2311yescharacteristic
32C22×C4×C47—21no—
33C22×C4×C47—22no—
34C22×C4×C47D412yes—
35C22×C4×C47C2311yescharacteristic
36C22×Dic47—22no—
37C4⋊C4×C47—22no—
38C4⋊C4×C47C2312yes—
39C22⋊C4×C47—21no—
40C22⋊C4×C47—22no—
41C42×C47—21no—
42C42×C47—22no—
43C42×C47D411yescharacteristic
44C42×C47D411yescharacteristic
45C42×C47C2312yes—
46C4⋊Dic47—22no—
47C4⋊Dic47C2314yes—
48Dic47⋊C4—24no—
49Dic47⋊C4—24no—
50#10625329—24no—
51C2×C47⋊C8C2314yes—
52C23×C47—21no—
53C23×C47C2×D411yescharacteristic
54Q8×C47—21no—
55Q8×C47C2×Q812yes—
56D4×C47—24no—
57D4×C47—21no—
58D4×C47C2×Q812yes—
59C2×C4×C47—21no—
60C2×C4×C47—24no—
61C2×C4×C47—22no—
62C2×C4×C47—42no—
63C2×C4×C47—44no—
64C2×C4×C47C2×D412yes—
65C2×C4×C47C2×D412yes—
66C2×C4×C47C2×D411yescharacteristic
67C2×C4×C47C2×Q812yes—
68C2×C4×C47#4112yes—
69C2×C4×C47C2411yescharacteristic
70C2×Dic47—24no—
71C2×Dic47—44no—
72C47⋊C8—24no—
73C22×C47—22no—
74C22×C47—22no—
75C22×C47—42no—
76C22×C47C22⋊Q812yes—
77C22×C47C22×D411yescharacteristic
78C4×C47—22no—
79C4×C47—22no—
80C4×C47—22no—
81C4×C47—42no—
82C4×C47C22⋊Q812yes—
83C4×C47C22×Q811yescharacteristic
84C4×C47C2×#4111yescharacteristic
85Dic47—44no—
86#3080—471nomaximal, Sylow
87C2×C47—22no—
88C2×C47—42no—
89C2×C47C2×C22⋊Q811yescharacteristic
90C2×C47#57512yes—
91C2×#125—471no—
92C4×#41D4711yescharacteristic
93#479—474no—
94#478—474no—
95#428—472no—
96#423—471no—
97#417—472no—
98C47#308011yescharacteristic, complemented, Sylow
99C2×#41C2×D4711yescharacteristic
100C2×M16—472no—
101#125—474no—
102#125—941no—
103#125—941no—
104C4×Q8C2×D4712yes—
105C4×D4—22no—
106C4×D4C2×D4712yes—
107#117—21no—
108#117C2×D4711yescharacteristic
109C2×C4⋊C4—472no—
110C2×C4⋊C4—942no—
111C2×C42—21no—
112C2×C42C2×D4711yescharacteristic
113#107—474no—
114#106—474no—
115C4⋊C8—474no—
116#103—474no—
117#102—474no—
118#41—22no—
119#41Dic9414yes—
120C2×Q8C22×D4711yescharacteristic
121C2×D4—21no—
122C2×D4C22×D4711yescharacteristic
123C22×C4—21no—
124C22×C4—22no—
125C22×C4—942no—
126C22×C4C22⋊D4712yes—
127C22×C4C22×D4711yescharacteristic
128M16—944no—
129C2×C8—474no—
130C4⋊C4—22no—
131C4⋊C4—474no—
132C4⋊C4—944no—
133C4⋊C4—944no—
134C4⋊C4—942no—
135C4⋊C4C22×D4712yes—
136C22⋊C4—21no—
137C22⋊C4—22no—
138C42—21no—
139C42—22no—
140C42C22⋊D4711yescharacteristic
141C42C22⋊D4711yescharacteristic
142C42C22×D4712yes—
143C23—21no—
144C23C2×C22⋊D4711yescharacteristic
145Q8—21no—
146Q8C2×Dic9412yes—
147D4—24no—
148D4—21no—
149D4C2×Dic9412yes—
150C2×C4—21no—
151C2×C4—24no—
152C2×C4—22no—
153C2×C4—42no—
154C2×C4—44no—
155C2×C4—944no—
156C2×C4—1884no—
157C2×C4C2×Dic9412yes—
158C2×C4#1062535012yes—
159C2×C4C2×C22⋊D4712yes—
160C2×C4C2×C22⋊D4712yes—
161C2×C4C2×C22⋊D4711yescharacteristic
162C2×C4C23×D4711yescharacteristic
163C8—944no—
164C22—22no—
165C22—22no—
166C22—42no—
167C22#1309400312yes—
168C22C22×C22⋊D4711yescharacteristic
169C4—22no—
170C4—22no—
171C4—22no—
172C4—42no—
173C4—1884no—
174C4#1309400312yes—
175C4C22×Dic9411yescharacteristic
176C4C2×#1062535011yescharacteristic
177C2—22no—
178C2—42no—
179C2C2×#1309400311yescharacteristic
180C2#1568992112yes—
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC4×#41×C47C2
socleC22×C47C22×D4
hypercenterC4×#41D47
hypocenterC47#3080
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#13094016C2semidirect
2. #15689430C2semidirect
3. #15689423C2semidirect
4. #15689166C2semidirect
5. #15689147C2semidirect
98. C47#3080semidirect