Finite Group Databasebeta

← #17993589

Subgroups — #17993589

Order 4736.

228 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 53 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#14558159C211yesmaximal, characteristic
2#14557864C212yesmaximal, complemented
3#14557458C211yesmaximal, characteristic
4#14557271C212yesmaximal, complemented
5C37×#323C211yesmaximal, characteristic
6#11924515—21no—
7#11924515C2212yes—
8#11924513—22no—
9#11924513—22no—
10C2×C4⋊Dic37C2211yescharacteristic
11C2×C22⋊Dic37—21no—
12C2×C22⋊Dic37—21no—
13#11924468—22no—
14#11924461—22no—
15#11924443—21no—
16#11924443C2211yescharacteristic
17C2×C22⋊C4×C37C2211yescharacteristic
18C22⋊C8×C37C2212yes—
19C24×C37D411yescharacteristic
20C22×C4×C37D411yescharacteristic
21C22×C4×C37C2311yescharacteristic
22C22×Dic37—21no—
23C22×Dic37—21no—
24C22×Dic37—21no—
25C22×Dic37—21no—
26C2×Dic74—21no—
27C2×Dic74D412yes—
28C2×C8×C37—22no—
29C22⋊C4×C37—22no—
30C22⋊Dic37—22no—
31C22⋊Dic37—22no—
32C22⋊Dic37—42no—
33C4⋊Dic37—21no—
34C4⋊Dic37—22no—
35C4⋊Dic37D412yes—
36#10596936—22no—
37#10596936—22no—
38C23×C37—21no—
39C23×C37—21no—
40C23×C37—41no—
41C23×C37—41no—
42C23×C37SD1612yes—
43C23×C37C2×D411yescharacteristic
44C2×C4×C37—21no—
45C2×C4×C37—41no—
46C2×C4×C37—41no—
47C2×C4×C37C2×D412yes—
48C2×Dic37—22no—
49C2×Dic37—22no—
50C2×Dic37—41no—
51C2×Dic37—41no—
52C2×Dic37—41no—
53C2×Dic37—41no—
54C2×Dic37—41no—
55C2×Dic37—41no—
56C2×Dic37—81no—
57C2×Dic37—81no—
58Dic74—42no—
59Dic74—81no—
60C8×C37—42no—
61C22×C37—21no—
62C22×C37—21no—
63C22×C37—22no—
64C22×C37—42no—
65C22×C37—41no—
66C22×C37—41no—
67C22×C37—81no—
68C22×C37#12011yescharacteristic
69C22×C37C2×SD1611yescharacteristic
70C22×C37#13711yescharacteristic
71C4×C37—22no—
72C4×C37—41no—
73Dic37—42no—
74Dic37—42no—
75Dic37—81no—
76Dic37—81no—
77#1608—371nomaximal, Sylow
78C2×C37—21no—
79C2×C37—21no—
80C2×C37—42no—
81C2×C37#44811yescharacteristic
82C2×C37#45511yescharacteristic
83C2×C37#45811yescharacteristic
84#543—371no—
85#483—372no—
86#397—371no—
87#328—372no—
88#323D3711yescharacteristic
89C37#160811yescharacteristic, complemented, Sylow
90C22⋊Q8—372no—
91C22⋊Q8—742no—
92C22⋊Q8—742no—
93C22⋊Q8—741no—
94C2×C4⋊C4—371no—
95C2×C22⋊C4—741no—
96C2×C22⋊C4—741no—
97C2×C22⋊C4C2×D3711yescharacteristic
98#106—742no—
99#103—742no—
100C22⋊C8C2×D3712yes—
101#95—371no—
102#95—741no—
103C24D14811yescharacteristic
104C2×Q8—372no—
105C2×Q8—741no—
106C22×C4—741no—
107C22×C4—741no—
108C22×C4—741no—
109C22×C4—741no—
110C22×C4D14811yescharacteristic
111C22×C4C22×D3711yescharacteristic
112C2×C8—22no—
113C4⋊C4—372no—
114C4⋊C4—742no—
115C4⋊C4—741no—
116C4⋊C4—742no—
117C4⋊C4—742no—
118C22⋊C4—22no—
119C22⋊C4—742no—
120C22⋊C4—742no—
121C22⋊C4—1482no—
122C23—21no—
123C23—21no—
124C23—41no—
125C23—41no—
126C23#1059693012yes—
127C23C2×D14811yescharacteristic
128Q8—2961no—
129Q8—1482no—
130C2×C4—21no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—2961no—
134C2×C4—2961no—
135C2×C4—742no—
136C2×C4—742no—
137C2×C4—1481no—
138C2×C4—1481no—
139C2×C4—1481no—
140C2×C4—1481no—
141C2×C4—1481no—
142C2×C4—1481no—
143C2×C4D4×D3712yes—
144C8—42no—
145C22—21no—
146C22—21no—
147C22—22no—
148C22—42no—
149C22—41no—
150C22—41no—
151C22—81no—
152C22#1192450611yescharacteristic
153C22C2×#1059693011yescharacteristic
154C22#1192456911yescharacteristic
155C4—22no—
156C4—41no—
157C4—2961no—
158C4—2961no—
159C4—1482no—
160C4—1482no—
161C2—21no—
162C2—21no—
163C2—42no—
164C2#1455767411yescharacteristic
165C2#1455771311yescharacteristic
166C2#1455772411yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#323C2
socleC22×C37#120
prime radicalC24×C37D4
hypercenter#323D37
hypocenterC37#1608
LCSG ▷ C22×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #14557864C2semidirect
4. #14557271C2semidirect
89. C37#1608semidirect

Maximal subgroups

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

subgroupindex
#145581592
#145578642
#145574582
#145572712
C37×#3232
#160837