Finite Group Databasebeta

← #20251447

Subgroups — #20251447

Order 6016.

430 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13094018C211yesmaximal, characteristic
2#15689061C212yesmaximal, complemented
3#15689058C212yesmaximal
4#15689054C212yesmaximal, complemented
5#15689049C212yesmaximal
6#15689042C212yesmaximal, complemented
7#15689034C212yesmaximal
8#15688991C211yesmaximal, characteristic, complemented
9C2×C4⋊Q8×C47C211yesmaximal, characteristic, complemented
10#13094018—24no—
11C2×Dic47⋊C4C2211yescharacteristic
12C2×Dic47⋊C4C2211yescharacteristic
13C2×Dic47⋊C4C2211yescharacteristic
14C2×Dic47⋊C4C2214yes—
15C2×(C2×D47)⋊C4C2211yescharacteristic
16C2×(C2×D47)⋊C4C2211yescharacteristic
17C2×(C2×D47)⋊C4C2211yescharacteristic
18C2×(C2×D47)⋊C4C2214yes—
19C47⋊#95C2212yes—
20C47⋊#95C2212yes—
21C47⋊#95C2212yes—
22C47⋊#95C2214yes—
23C47⋊#95C2214yes—
24C22×Q8×C47C2212yes—
25C4⋊Q8×C47—24no—
26C2×C4⋊C4×C47C2212yes—
27C2×C4⋊C4×C47C2212yes—
28C2×C42×C47C2211yescharacteristic
29C23×D47C2311yescharacteristic
30C2×Q8×C47—24no—
31C2×Q8×C47—44no—
32C22×C4×C47C2314yes—
33C22×C4×C47C2311yescharacteristic
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2311yescharacteristic
36C22×Dic47C2314yes—
37C22×Dic47C2311yescharacteristic
38C22×Dic47C2311yescharacteristic
39C22×Dic47C2311yescharacteristic
40C4⋊C4×C47—24no—
41C4⋊C4×C47—24no—
42C42×C47D414yes—
43(C2×D47)⋊C4—22no—
44(C2×D47)⋊C4—22no—
45(C2×D47)⋊C4—22no—
46(C2×D47)⋊C4—44no—
47Dic47⋊C4—22no—
48Dic47⋊C4—22no—
49Dic47⋊C4—22no—
50Dic47⋊C4—44no—
51C23×C47C2411yescharacteristic
52C22×D47—21no—
53C22×D47—22no—
54C22×D47—22no—
55C22×D47—22no—
56Q8×C47—48no—
57C2×C4×C47—22no—
58C2×C4×C47—22no—
59C2×C4×C47—22no—
60C2×C4×C47—24no—
61C2×C4×C47—24no—
62C2×C4×C47—24no—
63C2×C4×C47C2×D412yes—
64C2×C4×C47C2×D412yes—
65C2×C4×C47C2×D412yes—
66C2×Dic47—21no—
67C2×Dic47—21no—
68C2×Dic47—21no—
69C2×Dic47—22no—
70C2×Dic47—24no—
71C2×Dic47—22no—
72C2×Dic47—22no—
73C2×Dic47—24no—
74C2×Dic47—24no—
75C22×C47C22×D411yescharacteristic
76C22×C47H(5,𝔽2)12yes—
77C22×C472−1+412yes—
78C22×C472−1+412yes—
79C2×D47—41no—
80C2×D47—41no—
81C2×D47—41no—
82C2×D47—44no—
83C4×C47—22no—
84C4×C47—22no—
85C4×C47—22no—
86C4×C47—44no—
87Dic47—41no—
88Dic47—41no—
89Dic47—41no—
90Dic47—44no—
91#2821—471nomaximal, Sylow
92C2×C47#53511yescharacteristic
93C2×C47#53611yescharacteristic
94C2×C47#53611yescharacteristic
95C2×C47#56314yes—
96D47—81no—
97C2×C4⋊Q8D4711yescharacteristic, complemented
98C2×#126—471no—
99#400—472no—
100#399—472no—
101#398—472no—
102#397—472no—
103#395—472no—
104#393—472no—
105#383—471no—
106C47#282111yescharacteristic, complemented, Sylow
107C22×Q8C2×D4712yes—
108C4⋊Q8—24no—
109#126—944no—
110C2×C4⋊C4—471no—
111C2×C4⋊C4—471no—
112C2×C4⋊C4—471no—
113C2×C4⋊C4—474no—
114C2×C4⋊C4C2×D4712yes—
115C2×C4⋊C4C2×D4712yes—
116C2×C22⋊C4—471no—
117C2×C22⋊C4—471no—
118C2×C22⋊C4—471no—
119C2×C22⋊C4—474no—
120C2×C42C2×D4711yescharacteristic
121#95—472no—
122#95—472no—
123#95—472no—
124#95—474no—
125#95—474no—
126C24—471no—
127C2×Q8—24no—
128C2×Q8—44no—
129C22×C4—474no—
130C22×C4—471no—
131C22×C4—471no—
132C22×C4—471no—
133C22×C4C22×D4714yes—
134C22×C4C22×D4711yescharacteristic
135C22×C4C22×D4711yescharacteristic
136C22×C4C22×D4711yescharacteristic
137C4⋊C4—24no—
138C4⋊C4—24no—
139C4⋊C4—942no—
140C4⋊C4—942no—
141C4⋊C4—942no—
142C4⋊C4—1884no—
143C22⋊C4—942no—
144C22⋊C4—942no—
145C22⋊C4—942no—
146C22⋊C4—1884no—
147C42C22⋊D4714yes—
148C23—941no—
149C23—942no—
150C23—942no—
151C23—942no—
152C23C23×D4711yescharacteristic
153Q8—48no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—941no—
161C2×C4—941no—
162C2×C4—941no—
163C2×C4—944no—
164C2×C4—942no—
165C2×C4—944no—
166C2×C4—944no—
167C2×C4—942no—
168C2×C4—942no—
169C2×C4C2×C22⋊D4712yes—
170C2×C4C2×C22⋊D4712yes—
171C2×C4C2×C22⋊D4712yes—
172C22—1884no—
173C22—1881no—
174C22—1881no—
175C22—1881no—
176C22C22×C22⋊D4711yescharacteristic
177C22#1309406912yes—
178C22#1309407212yes—
179C22#1309407212yes—
180C4—22no—
181C4—22no—
182C4—22no—
183C4—44no—
184C4—1884no—
185C4—1881no—
186C4—1881no—
187C4—1881no—
188C2—3761no—
189C2#1568969011yescharacteristic
190C2#1568969711yescharacteristic
191C2#1568969711yescharacteristic
192C2#1568987214yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×C4⋊Q8×C47C2
hypercenterC2×C4⋊Q8D47
hypocenterC47#2821
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #15689061C2semidirect
4. #15689054C2semidirect
6. #15689042C2semidirect
8. #15688991C2semidirect
9. C2×C4⋊Q8×C47C2semidirect
97. C2×C4⋊Q8D47semidirect
106. C47#2821semidirect