Finite Group Databasebeta

← #18010076

Subgroups — #18010076

Order 4736.

248 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 56 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#14558555C212yesmaximal, complemented
2#14558389C212yesmaximal, complemented
3#14558388C212yesmaximal, complemented
4#124×D37C211yesmaximal, characteristic
5C4⋊#64438—22no—
6#11924593—22no—
7#11924591C2214yescomplemented
8C2×Q8×D37C411yescharacteristic
9C2×D4×D37C411yescharacteristic
10#11924525C2211yescharacteristic
11#11924524C411yescharacteristic
12#11924523C2211yescharacteristic
13#11924522—22no—
14C22⋊C4×D37—22no—
15C42×D37C2211yescharacteristic
16#124×C37C411yescharacteristic
17C23×D37—21no—
18C2×Q8×C37C2×C411yescharacteristic
19C2×D4×C37C2×C411yescharacteristic
20C2×C22⋊D37—21no—
21Q8×D37—42no—
22D4×D37—42no—
23C2×D148C2×C411yescharacteristic
24C2×C4×D37—21no—
25C2×C4×D37C2×C411yescharacteristic
26C2×C4×D37D412yes—
27C2×Dic74—21no—
28C2×Dic74C2×C411yescharacteristic
29C2×#64438—24no—
30C22⋊C4×C37—22no—
31C42×C37C2×C411yescharacteristic
32C22⋊Dic37—22no—
33#10596938—22no—
34#10596938—22no—
35C4×Dic37D412yes—
36C4×Dic37C2311yescharacteristic
37C23×C37—21no—
38C22×D37—21no—
39C22×D37—44no—
40C22×D37—42no—
41C22×D37C22⋊C411yescharacteristic
42Q8×C37—41no—
43D4×C37—41no—
44C2×C4×C37—21no—
45C2×C4×C37C22⋊C412yes—
46C2×C4×C37C22×C411yescharacteristic
47C22⋊D37—42no—
48C2×Dic37—21no—
49C2×Dic37C22⋊C411yescharacteristic
50C2×Dic37C2×D412yes—
51D148—41no—
52C4×D37—22no—
53C4×D37—42no—
54C4×D37—42no—
55Dic74—42no—
56Dic74—41no—
57#64438—44no—
58C22×C37—41no—
59C22×C37—42no—
60C22×C37C2×C22⋊C411yescharacteristic
61C2×D37—22no—
62C2×D37—41no—
63C2×D37—42no—
64C2×D37—84no—
65C2×D37#10012yes—
66C4×C37—21no—
67C4×C37—22no—
68C4×C37—41no—
69Dic37—21no—
70Dic37—22no—
71Dic37—41no—
72#1533—371nomaximal, Sylow
73C2×C37—81no—
74C2×C37C2×#10011yescharacteristic
75C2×C37#42112yes—
76D37—22no—
77D37—81no—
78C2×#124—371no—
79#432—372no—
80#329—372no—
81#329—372no—
82C37#153311yescharacteristic, complemented, Sylow
83C22×Q8—371no—
84C22×D4—371no—
85#124—371no—
86#124—371no—
87#124—371no—
88#124—742no—
89#124#386611yescharacteristic
90C2×C22⋊C4—742no—
91C2×C42—371no—
92C4⋊C8—742no—
93C22⋊C8—742no—
94#97—374no—
95C24—741no—
96C2×Q8—371no—
97C2×Q8—741no—
98C2×Q8—1482no—
99C2×Q8C2×#386611yescharacteristic
100C2×D4—371no—
101C2×D4—741no—
102C2×D4—1482no—
103C2×D4C2×#386611yescharacteristic
104C22×C4—371no—
105C22×C4—372no—
106C22×C4—741no—
107C2×C8—744no—
108C22⋊C4—22no—
109C22⋊C4—742no—
110C22⋊C4—742no—
111C22⋊C4—742no—
112C42—372no—
113C42—371no—
114C42C2×#386611yescharacteristic
115C23—21no—
116C23—371no—
117C23—741no—
118C23—1482no—
119C23—1484no—
120Q8—41no—
121Q8—1481no—
122Q8—1482no—
123D4—41no—
124D4—1481no—
125D4—1482no—
126C2×C4—21no—
127C2×C4—372no—
128C2×C4—371no—
129C2×C4—742no—
130C2×C4—741no—
131C2×C4—1482no—
132C2×C4—1482no—
133C2×C4C22⋊#386612yes—
134C2×C4C22×#386611yescharacteristic
135C8—1484no—
136C22—41no—
137C22—42no—
138C22—372no—
139C22—2964no—
140C22—742no—
141C22—1481no—
142C22—1482no—
143C22C2×C22⋊#386611yescharacteristic
144C4—21no—
145C4—22no—
146C4—41no—
147C4—741no—
148C4—742no—
149C4—1481no—
150C2—81no—
151C2—2961no—
152C2—742no—
153C2D37⋊#10011yescharacteristic
154C2#1455853012yes—
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#124×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC2×D4×D37C4
cosocleC4×Dic37C23
hypercenter#124#3866
hypocenterC37#1533
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #14558555C2semidirect
2. #14558389C2semidirect
3. #14558388C2semidirect
7. #11924591C22semidirect
82. C37#1533semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145585552
#145583892
#145583882
#124×D372
#153337