Finite Group Databasebeta

← #20254835

Subgroups — #20254835

Order 6016.

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

normal subgroups only

This group has 346 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, complemented
2#15689728C211yesmaximal, characteristic
3#15689431C212yesmaximal, complemented
4#15689424C212yesmaximal, complemented
5#15689369C212yesmaximal, complemented
6#15689352C212yesmaximal, complemented
7#15689329C212yesmaximal, complemented
8#15689324C212yesmaximal, complemented
9C47×#424C211yesmaximal, characteristic, complemented
10C2×#10625325C2212yes—
11C2×#10625325C2212yes—
12#13094024C2211yescharacteristic
13#13094021C2211yescharacteristic
14#13094017—22no—
15#13094016C2211yescharacteristic
16#13094016C2211yescharacteristic
17#13094014—22no—
18#13094009—22no—
19#13094003C2212yes—
20#13093998C2212yes—
21#13093997—22no—
22C4×Dic94C2212yes—
23C4×D188C2212yes—
24#13093958C2212yes—
25#13093956C2212yes—
26#13093949C2212yes—
27#13093949C2212yes—
28#13093946C2212yes—
29#13093946C2212yes—
30C2×M16×C47C2211yescharacteristic
31C22×C8×C47C2211yescharacteristic
32#117×C47C2211yescharacteristic
33C4⋊C8×C47C2212yes—
34C4⋊C8×C47C2212yes—
35C22×C4×C47C2311yescharacteristic
36C2×C22⋊D47—22no—
37C2×D188—22no—
38C2×D188C2312yes—
39C2×C4×D47—22no—
40C2×Dic94C2312yes—
41M16×C47—41no—
42C2×C8×C47—41no—
43C2×C8×C47C2312yes—
44C2×C8×C47C2312yes—
45C4⋊C4×C47D412yes—
46C22⋊C4×C47D412yes—
47C42×C47C2311yescharacteristic
48C42×C47C2311yescharacteristic
49C22⋊Dic47—22no—
50(C2×D47)⋊C4—22no—
51(C2×D47)⋊C4—22no—
52C4⋊Dic47—22no—
53C4⋊Dic47C2312yes—
54C4⋊Dic47C2312yes—
55Dic47⋊C4—22no—
56Dic47⋊C4—22no—
57Dic47⋊C4—22no—
58Dic47⋊C4—22no—
59C4×Dic47—22no—
60#10625325—42no—
61#10625325—42no—
62C23×C47C2×D411yescharacteristic
63C22×D47—22no—
64C2×C4×C47—21no—
65C2×C4×C47—21no—
66C2×C4×C47C2×D412yes—
67C2×C4×C47C2×D411yescharacteristic
68C2×C4×C47C2×D412yes—
69C2×C4×C47C2411yescharacteristic
70C22⋊D47—82no—
71C2×Dic47—22no—
72C2×Dic47—22no—
73C2×Dic47—22no—
74D188—22no—
75D188—22no—
76D188—82no—
77C4×D47—82no—
78Dic94—22no—
79Dic94—22no—
80C8×C47—22no—
81C8×C47—22no—
82C22×C47—21no—
83C22×C47—22no—
84C22×C47C22×D411yescharacteristic
85C2×D47—42no—
86C2×D47—42no—
87C2×D47—42no—
88C4×C47—21no—
89C4×C47—22no—
90C4×C47—22no—
91C4×C47H(5,𝔽2)11yescharacteristic
92C4×C472−1+411yescharacteristic
93Dic47—42no—
94Dic47—42no—
95Dic47—42no—
96#3260—471nomaximal, Sylow
97C2×C47—41no—
98C2×C47#53711yescharacteristic
99C2×C47#57712yes—
100D47—82no—
101#541—471no—
102#540—471no—
103#479—472no—
104#478—472no—
105#468—472no—
106#465—472no—
107#461—472no—
108#460—472no—
109#424D4711yescharacteristic, complemented
110C47#326011yescharacteristic, complemented, Sylow
111C2×SD16—472no—
112C2×SD16—472no—
113C2×M16C2×D4711yescharacteristic
114C22×C8C2×D4711yescharacteristic
115C4⋊Q8—471no—
116#127—471no—
117#126—942no—
118#125—471no—
119#125—471no—
120#125—942no—
121#123—942no—
122C22⋊Q8—472no—
123#121—472no—
124#121—942no—
125C4×Q8—472no—
126C4×D4—472no—
127#117C2×D4711yescharacteristic
128#107—472no—
129#106—472no—
130C4⋊C8C2×D4712yes—
131C4⋊C8C2×D4712yes—
132#103—472no—
133#103—472no—
134#102—472no—
135#102—472no—
136C2×Q8—472no—
137C2×D4—472no—
138C2×D4—942no—
139C2×D4—942no—
140C22×C4—942no—
141C22×C4C22×D4711yescharacteristic
142SD16—1882no—
143SD16—1882no—
144M16—41no—
145C2×C8—41no—
146C2×C8C22×D4712yes—
147C2×C8C22×D4712yes—
148C4⋊C4—472no—
149C4⋊C4—472no—
150C4⋊C4—942no—
151C4⋊C4—942no—
152C4⋊C4—942no—
153C4⋊C4—942no—
154C4⋊C4—942no—
155C4⋊C4D18812yes—
156C22⋊C4—942no—
157C22⋊C4—942no—
158C22⋊C4—942no—
159C22⋊C4D18812yes—
160C42—942no—
161C42C22×D4711yescharacteristic
162C42C22×D4711yescharacteristic
163C23—942no—
164C23C2×D18811yescharacteristic
165Q8—942no—
166Q8—942no—
167D4—942no—
168D4—942no—
169D4—3762no—
170D4—3762no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—942no—
174C2×C4—942no—
175C2×C4—942no—
176C2×C4—3762no—
177C2×C4C2×D18812yes—
178C2×C4C2×D18812yes—
179C2×C4C2×D18811yescharacteristic
180C2×C4C23×D4711yescharacteristic
181C8—22no—
182C8—22no—
183C22—22no—
184C22—21no—
185C22—1882no—
186C22—1882no—
187C22—1882no—
188C22C22×D18811yescharacteristic
189C4—22no—
190C4—22no—
191C4—21no—
192C4—1882no—
193C4—1882no—
194C4—1882no—
195C4#1309406911yescharacteristic
196C4#1309407211yescharacteristic
197C2—41no—
198C2—3762no—
199C2#1568970411yescharacteristic
200C2#1568993512yes—
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#424C2
socleC22×C47C22×D4
hypercenter#424D47
hypocenterC47#3260
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #15689735C2semidirect
3. #15689431C2semidirect
4. #15689424C2semidirect
5. #15689369C2semidirect
6. #15689352C2semidirect
7. #15689329C2semidirect
8. #15689324C2semidirect
9. C47×#424C2semidirect
109. #424D47semidirect
110. C47#3260semidirect