Finite Group Databasebeta

← #18010899

Subgroups — #18010899

Order 4736.

230 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 52 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#14558520C212yesmaximal
2#14558444C212yesmaximal, complemented
3#14558443C212yesmaximal, complemented
4#14558103C211yesmaximal, characteristic
5C2×#10596957—22no—
6#11924597C2214yes—
7#11924596—22no—
8C2×#10596964C2211yescharacteristic
9C2×Q8×D37C411yescharacteristic
10#11924536C2211yescharacteristic
11#11924534C2211yescharacteristic
12#11924523C411yescharacteristic
13#11924518—22no—
14#11924513—22no—
15#11924493C411yescharacteristic
16#124×C37C411yescharacteristic
17C2×Q8×C37C2×C411yescharacteristic
18C2×D4×C37C2×C411yescharacteristic
19C2×C22⋊D37D412yes—
20C22×Dic37D412yes—
21Q8×D37—42no—
22#10596964—42no—
23C2×C4×D37—21no—
24C2×C4×D37C2×C411yescharacteristic
25C2×Dic74—21no—
26C2×Dic74C2×C411yescharacteristic
27C2×Dic74C2311yescharacteristic
28#10596957—24no—
29#10596957—42no—
30C2×#64438—42no—
31C22⋊C4×C37—22no—
32C42×C37C2×C411yescharacteristic
33C22⋊Dic37—22no—
34#10596938—21no—
35C4⋊Dic37—22no—
36#10596936—21no—
37#10596936—22no—
38C4×Dic37C2×C411yescharacteristic
39C23×C37C22⋊C412yes—
40C22×D37C22⋊C411yescharacteristic
41Q8×C37—41no—
42D4×C37—41no—
43C2×C4×C37—21no—
44C2×C4×C37—21no—
45C2×C4×C37C22×C411yescharacteristic
46C22⋊D37—42no—
47C2×Dic37—22no—
48C2×Dic37—22no—
49C2×Dic37—21no—
50C2×Dic37—21no—
51C2×Dic37C22⋊C411yescharacteristic
52C2×Dic37C2×D412yes—
53C4×D37—22no—
54C4×D37—42no—
55Dic74—41no—
56Dic74—42no—
57Dic74—41no—
58#64438—44no—
59C22×C37—22no—
60C22×C37—42no—
61C22×C37C2×C22⋊C411yescharacteristic
62C2×D37—21no—
63C2×D37—41no—
64C4×C37—21no—
65C4×C37—41no—
66C4×C37—41no—
67Dic37—22no—
68Dic37—41no—
69Dic37—41no—
70Dic37#9912yes—
71#2135—371nomaximal, Sylow
72C2×C37—21no—
73C2×C37—42no—
74C2×C37C2×#9911yescharacteristic
75D37—41no—
76#536—371no—
77#413—372no—
78#356—372no—
79#356—372no—
80C37#213511yescharacteristic, complemented, Sylow
81C2×#41—371no—
82C22×Q8—371no—
83C2×M16—742no—
84C4⋊Q8—371no—
85C4⋊Q8—371no—
86#124—371no—
87#124#386611yescharacteristic
88#123—742no—
89C22⋊Q8—742no—
90#117—371no—
91#101—374no—
92#100—742no—
93#41—1482no—
94C2×Q8—371no—
95C2×Q8—371no—
96C2×Q8—741no—
97C2×Q8—1482no—
98C2×Q8C2×#386611yescharacteristic
99C2×D4—372no—
100C2×D4C2×#386611yescharacteristic
101C22×C4—372no—
102C22×C4—371no—
103C22×C4—741no—
104M16—744no—
105M16—1482no—
106C2×C8—1482no—
107C4⋊C4—741no—
108C4⋊C4—742no—
109C4⋊C4—742no—
110C22⋊C4—22no—
111C22⋊C4—741no—
112C22⋊C4—742no—
113C42—371no—
114C42C2×#386611yescharacteristic
115C23—371no—
116C23C22⋊#386612yes—
117Q8—41no—
118Q8—1481no—
119Q8—1481no—
120Q8—1482no—
121D4—41no—
122D4—1482no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—371no—
126C2×C4—372no—
127C2×C4—742no—
128C2×C4—742no—
129C2×C4—742no—
130C2×C4—741no—
131C2×C4—741no—
132C2×C4—1482no—
133C2×C4C22×#386611yescharacteristic
134C8—1484no—
135C22—22no—
136C22—42no—
137C22—741no—
138C22—1481no—
139C22C2×C22⋊#386611yescharacteristic
140C4—21no—
141C4—41no—
142C4—41no—
143C4—372no—
144C4—742no—
145C4—1481no—
146C4—1481no—
147C2—21no—
148C2—42no—
149C2—1481no—
150C2D37⋊#9911yescharacteristic
subgroupG/H
centerC2D37⋊#99
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#124×C37C4
socleC2×C37C2×#99
prime radicalC2×#10596964C22
cosocleC2×Dic74C23
hypercenter#124#3866
hypocenterC37#2135
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #14558444C2semidirect
3. #14558443C2semidirect
80. C37#2135semidirect

Maximal subgroups

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

subgroupindex
#145585202
#145584442
#145584432
#145581032
#213537