Finite Group Databasebeta

← #17993930

Subgroups — #17993930

Order 4736.

184 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 49 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#14557943C211yesmaximal, characteristic, complemented
2#14557903C211yesmaximal, characteristic, complemented
3#14557892C211yesmaximal, characteristic
4#14557275C211yesmaximal, characteristic, complemented
5#14557275C211yesmaximal, characteristic, complemented
6#14557273C211yesmaximal, characteristic
7C37×#563C211yesmaximal, characteristic
8#11924536C2211yescharacteristic
9#11924469—21no—
10#11924467—21no—
11#11924460—21no—
12#11924459—21no—
13#11924459—21no—
14#11924457—21no—
15#11924447C2211yescharacteristic
16#11924447C2211yescharacteristic
17#11924447C2211yescharacteristic
18C4⋊Q8×C37—21no—
19#126×C37—21no—
20#126×C37—21no—
21#125×C37C2211yescharacteristic
22#125×C37C2211yescharacteristic
23#124×C37C2211yescharacteristic
24#123×C37—21no—
25C22⋊Q8×C37—21no—
26C22⋊Q8×C37—21no—
27C2×Q8×C37—21no—
28C2×Q8×C37D411yescharacteristic
29C2×D4×C37D411yescharacteristic
30C22×C4×C37—21no—
31C2×Dic74—21no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37—21no—
34C4⋊C4×C37—21no—
35C4⋊C4×C37—21no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37—21no—
38C4⋊C4×C37D411yescharacteristic
39C4⋊C4×C37D411yescharacteristic
40C4⋊C4×C37D411yescharacteristic
41C4⋊C4×C37D411yescharacteristic
42C22⋊C4×C37—21no—
43C22⋊C4×C37—21no—
44C22⋊C4×C37—21no—
45C22⋊C4×C37—21no—
46C22⋊C4×C37—21no—
47C42×C37—21no—
48C42×C37C2311yescharacteristic
49C4⋊Dic37—21no—
50C4⋊Dic37—21no—
51C2×#64436—21no—
52C2×#64436—21no—
53C2×#64436—21no—
54C23×C37—21no—
55Q8×C37—41no—
56Q8×C37—81no—
57D4×C37—41no—
58C2×C4×C37—21no—
59C2×C4×C37—21no—
60C2×C4×C37—21no—
61C2×C4×C37—21no—
62C2×C4×C37—21no—
63C2×C4×C37—81no—
64C2×C4×C37C2×D411yescharacteristic
65C2×C4×C37C2×D411yescharacteristic
66C2×C4×C37C2×D411yescharacteristic
67C2×Dic37—41no—
68Dic74—42no—
69#64436—22no—
70#64436—41no—
71#64436—41no—
72C22×C37—41no—
73C22×C37—41no—
74C22×C37—41no—
75C22×C37#12011yescharacteristic
76C4×C37—21no—
77C4×C37—21no—
78C4×C37—21no—
79C4×C37—41no—
80C4×C37—41no—
81C4×C37—41no—
82C4×C37—41no—
83C4×C37—41no—
84Dic37—81no—
85#1664—371nomaximal, Sylow
86C2×C37—81no—
87C2×C37#45411yescharacteristic
88C2×C37#45511yescharacteristic
89C2×C37#45611yescharacteristic
90#563D3711yescharacteristic
91#501—371no—
92#491—371no—
93#489—371no—
94#330—371no—
95#330—371no—
96#329—371no—
97C37#166411yescharacteristic, complemented, Sylow
98C4⋊Q8—21no—
99C4⋊Q8—371no—
100#126—21no—
101#126—21no—
102#125C2×D3711yescharacteristic
103#125C2×D3711yescharacteristic
104#124C2×D3711yescharacteristic
105#123—21no—
106C22⋊Q8—21no—
107C22⋊Q8—21no—
108#107—741no—
109#106—741no—
110#103—741no—
111#103—741no—
112#103—741no—
113#102—741no—
114#97—371no—
115#97—371no—
116#97—371no—
117C2×Q8—21no—
118C2×Q8—741no—
119C2×Q8C22⋊D3711yescharacteristic
120C2×D4C22⋊D3711yescharacteristic
121C22×C4—21no—
122C2×C8—741no—
123C2×C8—741no—
124C2×C8—741no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—741no—
132C4⋊C4—741no—
133C4⋊C4C22⋊D3711yescharacteristic
134C4⋊C4C22⋊D3711yescharacteristic
135C4⋊C4C22⋊D3711yescharacteristic
136C4⋊C4C22⋊D3711yescharacteristic
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C22⋊C4—21no—
141C22⋊C4—21no—
142C42—21no—
143C42C22×D3711yescharacteristic
144C23—21no—
145Q8—41no—
146Q8—81no—
147Q8—1482no—
148D4—41no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—81no—
155C2×C4—1481no—
156C2×C4C2×C22⋊D3711yescharacteristic
157C2×C4C2×C22⋊D3711yescharacteristic
158C2×C4C2×C22⋊D3711yescharacteristic
159C8—742no—
160C8—1481no—
161C8—1481no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#1192450511yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—41no—
172C4—41no—
173C4—41no—
174C4—2961no—
175C2—81no—
176C2#1455770611yescharacteristic
177C2#1455771111yescharacteristic
178C2#1455771611yescharacteristic
subgroupG/H
centerC22#11924505
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#563C2
socleC22×C37#120
prime radicalC2×D4×C37D4
hypercenter#563D37
hypocenterC37#1664
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
1. #14557943C2semidirect
2. #14557903C2semidirect
4. #14557275C2semidirect
5. #14557275C2semidirect
97. C37#1664semidirect

Maximal subgroups

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

subgroupindex
#145579432
#145579032
#145578922
#145572752
#145572732
C37×#5632
#166437