Finite Group Databasebeta

← #17993601

Subgroups — #17993601

Order 4736.

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

normal subgroups only

This group has 254 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#14558114C211yesmaximal, characteristic
2#14557847C212yesmaximal, complemented
3#14557463C211yesmaximal, characteristic, complemented
4#14557268C212yesmaximal, complemented
5C37×#324C211yesmaximal, characteristic, complemented
6C2×#10596962—21no—
7#11924516—22no—
8#11924511—22no—
9#11924510—21no—
10#11924510C2212yes—
11C2×C4⋊Dic37C2211yescharacteristic
12C2×#10596936—21no—
13#11924470—22no—
14#11924458—22no—
15#11924443—21no—
16#11924443C2211yescharacteristic
17C2×C4⋊C4×C37C2211yescharacteristic
18C22⋊C8×C37C2212yes—
19C22×C4×C37D411yescharacteristic
20C22×C4×C37D411yescharacteristic
21C22×C4×C37C2311yescharacteristic
22C2×C22⋊D37—22no—
23C22×Dic37—21no—
24C22×Dic37—21no—
25#10596962—42no—
26#10596962—42no—
27C2×D148—21no—
28C2×D148—21no—
29C2×D148D412yes—
30C2×C4×D37—22no—
31C2×Dic74—21no—
32C2×C8×C37—22no—
33C4⋊C4×C37—22no—
34#10596938—22no—
35#10596938—22no—
36C4⋊Dic37—21no—
37C4⋊Dic37—22no—
38C4⋊Dic37D412yes—
39#10596936—42no—
40C23×C37C2×D411yescharacteristic
41C22×D37—22no—
42C2×C4×C37—21no—
43C2×C4×C37—21no—
44C2×C4×C37—21no—
45C2×C4×C37—41no—
46C2×C4×C37—41no—
47C2×C4×C37D812yes—
48C2×C4×C37C2×D412yes—
49C22⋊D37—42no—
50C22⋊D37—42no—
51C2×Dic37—22no—
52C2×Dic37—22no—
53C2×Dic37—41no—
54C2×Dic37—41no—
55C2×Dic37—41no—
56C2×Dic37—41no—
57C2×Dic37—41no—
58D148—42no—
59D148—42no—
60D148—81no—
61C4×D37—44no—
62Dic74—42no—
63C8×C37—42no—
64C22×C37—21no—
65C22×C37—21no—
66C22×C37#12011yescharacteristic
67C22×C37C2×D811yescharacteristic
68C22×C37AGL(1,ℤ/8)11yescharacteristic
69C2×D37—42no—
70C2×D37—42no—
71C2×D37—42no—
72C4×C37—22no—
73C4×C37—22no—
74C4×C37—41no—
75Dic37—42no—
76Dic37—42no—
77Dic37—81no—
78#1610—371nomaximal, Sylow
79C2×C37—21no—
80C2×C37—21no—
81C2×C37#44711yescharacteristic
82C2×C37#45611yescharacteristic
83C2×C37#45811yescharacteristic
84D37—82no—
85#537—371no—
86#480—372no—
87#398—371no—
88#327—372no—
89#324D3711yescharacteristic, complemented
90C37#161011yescharacteristic, complemented, Sylow
91C2×#41—741no—
92C22⋊Q8—742no—
93#121—372no—
94#121—742no—
95#121—741no—
96C2×C4⋊C4—371no—
97C2×C4⋊C4—741no—
98C2×C4⋊C4C2×D3711yescharacteristic
99#107—742no—
100#102—742no—
101C22⋊C8C2×D3712yes—
102#95—371no—
103#95—741no—
104#41—1482no—
105#41—1482no—
106C2×Q8—741no—
107C2×D4—372no—
108C2×D4—741no—
109C2×D4—741no—
110C2×D4—742no—
111C22×C4—742no—
112C22×C4—741no—
113C22×C4—741no—
114C22×C4D14811yescharacteristic
115C22×C4D14811yescharacteristic
116C22×C4C22×D3711yescharacteristic
117C2×C8—22no—
118C4⋊C4—22no—
119C4⋊C4—372no—
120C4⋊C4—741no—
121C4⋊C4—742no—
122C4⋊C4—1482no—
123C22⋊C4—742no—
124C22⋊C4—742no—
125C23—742no—
126C23C2×D14811yescharacteristic
127Q8—1482no—
128D4—2961no—
129D4—1482no—
130D4—1482no—
131D4—1482no—
132D4—1482no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—742no—
139C2×C4—742no—
140C2×C4—1484no—
141C2×C4—1481no—
142C2×C4—1481no—
143C2×C4—1481no—
144C2×C4—1481no—
145C2×C4—1481no—
146C2×C4D29612yes—
147C2×C4D4×D3712yes—
148C8—42no—
149C22—21no—
150C22—21no—
151C22—1482no—
152C22—1482no—
153C22—1482no—
154C22#1192450611yescharacteristic
155C22C2×D29611yescharacteristic
156C22#1192456411yescharacteristic
157C4—22no—
158C4—22no—
159C4—41no—
160C4—2961no—
161C4—1482no—
162C4—1482no—
163C2—21no—
164C2—21no—
165C2—2962no—
166C2#1455766911yescharacteristic
167C2#1455771811yescharacteristic
168C2#1455772411yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#324C2
socleC22×C37#120
prime radical#14558114C2
hypercenter#324D37
hypocenterC37#1610
LCSG ▷ C22×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #14557847C2semidirect
3. #14557463C2semidirect
4. #14557268C2semidirect
5. C37×#324C2semidirect
89. #324D37semidirect
90. C37#1610semidirect

Maximal subgroups

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

subgroupindex
#145581142
#145578472
#145574632
#145572682
C37×#3242
#161037