Finite Group Databasebeta

← #20244525

Subgroups — #20244525

Order 6016.

326 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 91 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×#13094024C211yesmaximal, characteristic, complemented
2C2×#13093946C212yesmaximal
3#15689025C211yesmaximal, characteristic
4#15688886C212yesmaximal, complemented
5C47×#336C211yesmaximal, characteristic, complemented
6C22×Dic94—21no—
7C22×D188C2211yescharacteristic
8#13094024—24no—
9C2×C4⋊Dic47—21no—
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2212yes—
12C2×(C2×D47)⋊C4—21no—
13C2×(C2×D47)⋊C4—21no—
14#13093946—24no—
15C22×C8×C47C2212yes—
16C2×C42×C47C2211yescharacteristic
17C23×D47—21no—
18C22×C4×C47D411yescharacteristic
19C22×C4×C47D411yescharacteristic
20C22×C4×C47C2311yescharacteristic
21C22×Dic47—22no—
22C22×Dic47—21no—
23C2×D188—22no—
24C2×D188—22no—
25C2×D188—21no—
26C2×D188Q812yescomplemented
27C2×Dic94—24no—
28C2×Dic94—42no—
29C2×Dic94—42no—
30C2×C8×C47—22no—
31C2×C8×C47—22no—
32C2×C8×C47—22no—
33C42×C47—22no—
34(C2×D47)⋊C4—42no—
35(C2×D47)⋊C4—42no—
36C4⋊Dic47—24no—
37C4⋊Dic47—22no—
38C4⋊Dic47—22no—
39C4⋊Dic47D414yes—
40C23×C47C2×D411yescharacteristic
41C22×D47—22no—
42C22×D47—41no—
43C22×D47—41no—
44C22×D47—41no—
45C22×D47—41no—
46C22×D47—41no—
47C22×D47—41no—
48C2×C4×C47—21no—
49C2×C4×C47—21no—
50C2×C4×C47—21no—
51C2×C4×C47—21no—
52C2×C4×C47D812yes—
53C2×C4×C47SD1612yes—
54C2×C4×C47C2×D412yes—
55C2×C4×C47C2×Q811yescharacteristic
56C2×C4×C47#4112yes—
57C2×C4×C47#4111yescharacteristic
58C2×Dic47—24no—
59C2×Dic47—42no—
60C2×Dic47—42no—
61C2×Dic47—41no—
62C2×Dic47—41no—
63C2×Dic47—41no—
64D188—24no—
65D188—42no—
66Dic94—48no—
67C8×C47—42no—
68C22×C47#12011yescharacteristic
69C22×C47C22⋊Q811yescharacteristic
70C22×C47#12411yescharacteristic
71C22×C47C2×D811yescharacteristic
72C22×C47C2×SD1611yescharacteristic
73C22×C47AGL(1,ℤ/8)11yescharacteristic
74C22×C47#13711yescharacteristic
75C2×D47—42no—
76C2×D47—42no—
77C2×D47—42no—
78C2×D47—81no—
79C2×D47—81no—
80C2×D47—81no—
81C2×D47—81no—
82C4×C47—22no—
83C4×C47—22no—
84C4×C47C22⋊Q812yes—
85C4×C47#12412yes—
86Dic47—44no—
87Dic47—81no—
88#2023—471nomaximal, Sylow
89C2×C47#39311yescharacteristic
90C2×C47#44711yescharacteristic
91C2×C47#44811yescharacteristic
92C2×C47#47411yescharacteristic
93C2×C47#47611yescharacteristic
94C2×C47#48611yescharacteristic
95C2×C47#48911yescharacteristic
96D47—82no—
97C2×C4⋊Q8—471no—
98C2×#102—472no—
99#390—471no—
100#340—472no—
101#336D4711yescharacteristic, complemented
102C47#202311yescharacteristic, complemented, Sylow
103C22×Q8—941no—
104C22×D4—471no—
105C22×C8C2×D4712yes—
106C4⋊Q8—944no—
107C2×C4⋊C4—472no—
108C2×C4⋊C4—471no—
109C2×C4⋊C4—941no—
110C2×C22⋊C4—941no—
111C2×C22⋊C4—941no—
112C2×C42C2×D4711yescharacteristic
113#102—944no—
114C24—941no—
115C2×Q8—944no—
116C2×Q8—1882no—
117C2×Q8—1882no—
118C2×D4—472no—
119C2×D4—942no—
120C2×D4—942no—
121C2×D4—941no—
122C22×C4—942no—
123C22×C4—941no—
124C22×C4D18811yescharacteristic
125C22×C4D18811yescharacteristic
126C22×C4C22×D4711yescharacteristic
127C2×C8—22no—
128C2×C8—22no—
129C2×C8—22no—
130C4⋊C4—474no—
131C4⋊C4—944no—
132C4⋊C4—942no—
133C4⋊C4—942no—
134C22⋊C4—1882no—
135C22⋊C4—1882no—
136C42—22no—
137C23—942no—
138C23—1881no—
139C23—1881no—
140C23—1881no—
141C23—1881no—
142C23—1881no—
143C23—1881no—
144C23C2×D18811yescharacteristic
145Q8—1888no—
146D4—944no—
147D4—1882no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—944no—
153C2×C4—1881no—
154C2×C4—1881no—
155C2×C4—1881no—
156C2×C4—1882no—
157C2×C4—1882no—
158C2×C4#1062532512yes—
159C2×C4D37612yes—
160C2×C4#1062535012yes—
161C2×C4D4×D4712yes—
162C2×C4#1062535211yescharacteristic
163C2×C4Q8×D4711yescharacteristic
164C8—42no—
165C22—3761no—
166C22—3761no—
167C22—3761no—
168C22—3761no—
169C22—1882no—
170C22—1882no—
171C22—1882no—
172C22#1309399411yescharacteristic
173C22#1309400411yescharacteristic
174C22#1309401211yescharacteristic
175C22C2×D37611yescharacteristic
176C22C2×#1062532511yescharacteristic
177C22#1309405211yescharacteristic
178C22#1309405711yescharacteristic
179C4—22no—
180C4—22no—
181C4—3761no—
182C4—1884no—
183C4#1309400212yes—
184C4#1309401012yes—
185C2—3762no—
186C2#1568903611yescharacteristic
187C2#1568925911yescharacteristic
188C2#1568926411yescharacteristic
189C2#1568940411yescharacteristic
190C2#1568941411yescharacteristic
191C2#1568947011yescharacteristic
192C2#1568948311yescharacteristic
subgroupG/H
centerC23C2×D188
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#336C2
socleC23×C47C2×D4
hypercenter#336D47
hypocenterC47#2023
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
1. C2×#13094024C2semidirect
4. #15688886C2semidirect
5. C47×#336C2semidirect
26. C2×D188Q8semidirect
101. #336D47semidirect
102. C47#2023semidirect