Finite Group Databasebeta

← #20254838

Subgroups — #20254838

Order 6016.

322 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 117 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
1#15689735C211yesmaximal, characteristic
2#15689430C212yesmaximal, complemented
3#15689427C212yesmaximal, complemented
4#15689379C212yesmaximal
5#15689362C212yesmaximal
6#15689333C212yesmaximal, complemented
7#15689330C212yesmaximal, complemented
8#15689150C211yesmaximal, characteristic
9C47×#541C211yesmaximal, characteristic
10C2×#10625337C2212yes—
11C2×#10625337C2212yes—
12C2×#10625329C2211yescharacteristic
13C22×C47⋊C8C2211yescharacteristic
14#13094024C2211yescharacteristic
15#13094017—22no—
16#13094016C2211yescharacteristic
17#13094014—22no—
18#13094003C2212yes—
19C4×Dic94C2212yes—
20#13093957C2212yes—
21#13093955C2212yes—
22C4⋊(C47⋊C8)C2212yes—
23C4⋊(C47⋊C8)C2212yes—
24#13093948C2212yes—
25#13093948C2212yes—
26#13093947C2212yes—
27#13093947C2212yes—
28C4⋊Q8×C47C2211yescharacteristic
29#126×C47—22no—
30#125×C47—22no—
31#125×C47C2211yescharacteristic
32C22⋊Q8×C47C2212yes—
33C4×Q8×C47C2212yes—
34#117×C47C2211yescharacteristic
35C2×Q8×C47C2312yes—
36C22×C4×C47C2311yescharacteristic
37C2×Dic94C2312yes—
38C4⋊C4×C47—22no—
39C4⋊C4×C47—22no—
40C4⋊C4×C47—22no—
41C4⋊C4×C47—22no—
42C4⋊C4×C47D412yes—
43C4⋊C4×C47C2312yes—
44C22⋊C4×C47—22no—
45C22⋊C4×C47D412yes—
46C42×C47—22no—
47C42×C47C2311yescharacteristic
48C42×C47C2311yescharacteristic
49C22⋊Dic47—22no—
50#10625337—42no—
51#10625337—42no—
52C4⋊Dic47—22no—
53C4⋊Dic47C2312yes—
54Dic47⋊C4—22no—
55Dic47⋊C4—22no—
56Dic47⋊C4—22no—
57C4×Dic47—22no—
58#10625329—41no—
59C2×C47⋊C8—41no—
60C2×C47⋊C8C2312yes—
61C2×C47⋊C8C2312yes—
62C23×C47C2×D411yescharacteristic
63Q8×C47—22no—
64Q8×C47—22no—
65C2×C4×C47—21no—
66C2×C4×C47—21no—
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47C2×D412yes—
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D412yes—
72C2×C4×C47C2411yescharacteristic
73C2×Dic47—22no—
74C2×Dic47—22no—
75Dic94—22no—
76Dic94—22no—
77C47⋊C8—22no—
78C47⋊C8—22no—
79C22×C47—21no—
80C22×C47—22no—
81C22×C47C22×D411yescharacteristic
82C4×C47—21no—
83C4×C47—22no—
84C4×C47—22no—
85C4×C47—42no—
86C4×C47—42no—
87C4×C47H(5,𝔽2)11yescharacteristic
88C4×C472−1+411yescharacteristic
89Dic47—42no—
90Dic47—42no—
91#3261—471nomaximal, Sylow
92C2×C47—41no—
93C2×C47#53711yescharacteristic
94C2×C47#57812yes—
95#541—471no—
96#541D4711yescharacteristic
97#479—472no—
98#479—472no—
99#470—472no—
100#467—472no—
101#462—472no—
102#462—472no—
103#424—471no—
104C47#326111yescharacteristic, complemented, Sylow
105C2×Q16—472no—
106C2×Q16—472no—
107C2×M16—471no—
108C22×C8—471no—
109C4⋊Q8—471no—
110C4⋊Q8C2×D4711yescharacteristic
111#126—22no—
112#126—942no—
113#125—22no—
114#125—471no—
115#125—942no—
116#125C2×D4711yescharacteristic
117C22⋊Q8—472no—
118C22⋊Q8C2×D4712yes—
119C4×Q8—472no—
120C4×Q8C2×D4712yes—
121#117C2×D4711yescharacteristic
122#107—472no—
123#106—472no—
124C4⋊C8—472no—
125C4⋊C8—472no—
126#103—472no—
127#103—472no—
128#103—472no—
129#103—472no—
130C2×Q8—472no—
131C2×Q8C22×D4712yes—
132C22×C4C22×D4711yescharacteristic
133Q16—1882no—
134Q16—1882no—
135M16—1881no—
136C2×C8—472no—
137C2×C8—472no—
138C2×C8—1881no—
139C4⋊C4—22no—
140C4⋊C4—22no—
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—472no—
144C4⋊C4—942no—
145C4⋊C4—942no—
146C4⋊C4—942no—
147C4⋊C4—942no—
148C4⋊C4C22⋊D4712yes—
149C4⋊C4C22×D4712yes—
150C22⋊C4—22no—
151C22⋊C4—942no—
152C22⋊C4C22⋊D4712yes—
153C42—22no—
154C42—942no—
155C42C22×D4711yescharacteristic
156C42C22×D4711yescharacteristic
157C23C2×C22⋊D4711yescharacteristic
158Q8—22no—
159Q8—22no—
160Q8—942no—
161Q8—942no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—942no—
167C2×C4—942no—
168C2×C4C2×C22⋊D4712yes—
169C2×C4C2×C22⋊D4712yes—
170C2×C4C2×C22⋊D4711yescharacteristic
171C2×C4C23×D4711yescharacteristic
172C8—942no—
173C8—942no—
174C22—22no—
175C22—21no—
176C22C22×C22⋊D4711yescharacteristic
177C4—22no—
178C4—22no—
179C4—21no—
180C4—42no—
181C4—42no—
182C4—1882no—
183C4—1882no—
184C4#1309407011yescharacteristic
185C4#1309407111yescharacteristic
186C2—41no—
187C2#1568970111yescharacteristic
188C2#1568993812yes—
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#541C2
socleC22×C47C22×D4
hypercenter#541D47
hypocenterC47#3261
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #15689430C2semidirect
3. #15689427C2semidirect
6. #15689333C2semidirect
7. #15689330C2semidirect
104. C47#3261semidirect