Finite Group Databasebeta

← #17995116

Subgroups — #17995116

Order 4736.

312 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 85 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#14558300C211yesmaximal, characteristic
2#14558104C211yesmaximal, characteristic
3#14557541C212yesmaximal, complemented
4#14557289C212yesmaximal, complemented
5C37×#410C211yesmaximal, characteristic
6C22×Dic74C2211yescharacteristic
7#11924543—24no—
8C2×#10596934—22no—
9C2×#10596934C2212yes—
10#11924534C412yescomplemented
11#11924523C412yescomplemented
12#11924517—22no—
13#11924515—22no—
14#11924495C2211yescharacteristic
15#11924459—24no—
16C2×#41×C37C2211yescharacteristic
17#117×C37C2212yes—
18#99×C37—22no—
19#41×C37—22no—
20#41×C37—22no—
21C2×Q8×C37C2×C411yescharacteristic
22C2×D4×C37C2×C411yescharacteristic
23C2×D4×C37D412yes—
24C22×C4×C37D412yes—
25C22×C4×C37C2311yescharacteristic
26C22×Dic37—21no—
27C2×Dic74—22no—
28C2×Dic74—22no—
29C2×Dic74—21no—
30C2×Dic74C2×C412yes—
31C4⋊C4×C37—22no—
32C22⋊C4×C37—22no—
33C42×C37—22no—
34C22⋊Dic37—24no—
35C22⋊Dic37—21no—
36C4⋊Dic37—21no—
37#10596936—24no—
38C4×Dic37C2×C412yes—
39#10596934—24no—
40#10596934—22no—
41#10596934—22no—
42C2×#64436—24no—
43C2×#64436D414yes—
44C23×C37C22⋊C412yes—
45C23×C37C2×D411yescharacteristic
46Q8×C37—22no—
47D4×C37—24no—
48D4×C37—22no—
49C2×C4×C37—22no—
50C2×C4×C37—22no—
51C2×C4×C37—42no—
52C2×C4×C37C22⋊C412yes—
53C2×C4×C37C22×C411yescharacteristic
54C2×C4×C37C2×D411yescharacteristic
55C2×C4×C37C2×D412yes—
56C2×C4×C37#4112yes—
57C2×Dic37—22no—
58C2×Dic37—22no—
59C2×Dic37—42no—
60Dic74—24no—
61Dic74—41no—
62Dic74—41no—
63#64436—24no—
64C22×C37—22no—
65C22×C37—41no—
66C22×C37—42no—
67C22×C37C2×C22⋊C411yescharacteristic
68C22×C37#12112yes—
69C4×C37—22no—
70C4×C37—82no—
71C4×C37C4×D412yes—
72C4×C37#12011yescharacteristic
73C4×C37#12311yescharacteristic
74Dic37—42no—
75Dic37—42no—
76#1909—371nomaximal, Sylow
77C2×C37—21no—
78C2×C37—22no—
79C2×C37—42no—
80C2×C37#38611yescharacteristic
81#568—371no—
82#536—371no—
83#419—372no—
84#410D3711yescharacteristic
85H(3,ℤ/4)—372no—
86C37#190911yescharacteristic, complemented, Sylow
87C2×#41C2×D3711yescharacteristic
88C22×Q8—371no—
89#131—744no—
90C2×M16—372no—
91C2×M16—742no—
92C4⋊Q8—372no—
93#124—372no—
94#123—742no—
95C22⋊Q8—742no—
96#117—371no—
97#117C2×D3712yes—
98#103—744no—
99#99—22no—
100#41—22no—
101#41—22no—
102C2×Q8—372no—
103C2×Q8—741no—
104C2×Q8—742no—
105C2×Q8—742no—
106C2×Q8C4×D3711yescharacteristic
107C2×D4C4×D3711yescharacteristic
108C2×D4C22⋊D3712yes—
109C22×C4—741no—
110C22×C4D14812yes—
111C22×C4C22×D3711yescharacteristic
112M16—744no—
113M16—742no—
114M16—742no—
115C2×C8—374no—
116C2×C8—744no—
117C4⋊C4—22no—
118C4⋊C4—744no—
119C4⋊C4—741no—
120C22⋊C4—22no—
121C22⋊C4—744no—
122C22⋊C4—741no—
123C42—22no—
124C42—372no—
125C23#1059693812yes—
126C23C2×C22⋊D3711yescharacteristic
127Q8—22no—
128Q8—744no—
129Q8—1481no—
130Q8—1481no—
131D4—24no—
132D4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—42no—
136C2×C4—742no—
137C2×C4—742no—
138C2×C4—1482no—
139C2×C4#1059693812yes—
140C2×C4C2×C4×D3711yescharacteristic
141C2×C4C2×D14811yescharacteristic
142C2×C4D4×D3712yes—
143C2×C4#1059696412yes—
144C8—744no—
145C22—22no—
146C22—41no—
147C22—42no—
148C22C2×#1059693811yescharacteristic
149C22#1192450812yes—
150C4—22no—
151C4—82no—
152C4—1482no—
153C4—1482no—
154C4#1192449612yes—
155C4#1192450611yescharacteristic
156C4#1192452011yescharacteristic
157C2—22no—
158C2—21no—
159C2—42no—
160C2#1455741011yescharacteristic
subgroupG/H
centerC2#14557410
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#410C2
socleC2×C37#386
prime radicalC2×#41×C37C22
cosocleC22×C4×C37C23
hypercenter#410D37
hypocenterC37#1909
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #14557541C2semidirect
4. #14557289C2semidirect
10. #11924534C4semidirect
11. #11924523C4semidirect
86. C37#1909semidirect

Maximal subgroups

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

subgroupindex
#145583002
#145581042
#145575412
#145572892
C37×#4102
#190937