Finite Group Databasebeta

← #17993782

Subgroups — #17993782

Order 4736.

212 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 57 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#14557879C211yesmaximal, characteristic
2#14557818C211yesmaximal, characteristic, complemented
3#14557743C211yesmaximal, characteristic, complemented
4#14557277C211yesmaximal, characteristic
5Q8⋊#64436C211yesmaximal, characteristic, complemented
6Q8⋊#64436C211yesmaximal, characteristic, complemented
7C37×#559C211yesmaximal, characteristic
8C2×#10596942—21no—
9#11924536C2211yescharacteristic
10#11924467—21no—
11C4⋊#64436C2211yescharacteristic
12C4⋊#64436C2211yescharacteristic
13#11924460—21no—
14#11924459—21no—
15#11924457—22no—
16C4×#64436C2211yescharacteristic
17#127×C37C2211yescharacteristic
18#124×C37—21no—
19#124×C37—21no—
20#123×C37—22no—
21C4×Q8×C37C2211yescharacteristic
22C4×Q8×C37C2211yescharacteristic
23C4×D4×C37—21no—
24C4×D4×C37—21no—
25C2×Q8×C37D411yescharacteristic
26C2×Q8×C37D411yescharacteristic
27C2×D4×C37—21no—
28C2×D4×C37—21no—
29C2×D4×C37D412yes—
30C22×C4×C37—22no—
31C2×Dic74—21no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37—21no—
34C4⋊C4×C37D411yescharacteristic
35C4⋊C4×C37D411yescharacteristic
36C22⋊C4×C37—22no—
37C22⋊C4×C37—22no—
38C22⋊C4×C37—22no—
39C42×C37—21no—
40C42×C37—21no—
41C42×C37C2311yescharacteristic
42#10596942—42no—
43C4⋊Dic37—21no—
44C4⋊Dic37—21no—
45C2×#64436—21no—
46C2×#64436—21no—
47C2×#64436—21no—
48C23×C37—22no—
49Q8×C37—21no—
50Q8×C37—21no—
51Q8×C37—21no—
52Q8×C37—21no—
53D4×C37—42no—
54D4×C37—41no—
55D4×C37—41no—
56D4×C37—41no—
57D4×C37—41no—
58C2×C4×C37—21no—
59C2×C4×C37—21no—
60C2×C4×C37—21no—
61C2×C4×C37—21no—
62C2×C4×C37—82no—
63C2×C4×C37C2×D411yescharacteristic
64C2×C4×C37C2×D411yescharacteristic
65C2×C4×C37C2×D411yescharacteristic
66C2×Dic37—41no—
67Dic74—41no—
68Dic74—41no—
69#64436—41no—
70#64436—41no—
71#64436—41no—
72C22×C37—42no—
73C22×C37—42no—
74C22×C37—42no—
75C22×C37#12011yescharacteristic
76C4×C37—21no—
77C4×C37—41no—
78C4×C37—41no—
79C4×C37—41no—
80C4×C37—41no—
81C4×C37#13511yescharacteristic
82C4×C37#13511yescharacteristic
83C4×C37AGL(1,ℤ/8)11yescharacteristic
84C4×C37#13711yescharacteristic
85Dic37—81no—
86#1640—371nomaximal, Sylow
87C2×C37—82no—
88C2×C37#44911yescharacteristic
89C2×C37#45211yescharacteristic
90C2×C37#45511yescharacteristic
91#559D3711yescharacteristic
92#486—371no—
93#475—371no—
94#462—371no—
95#331—371no—
96Q8⋊C8—371no—
97Q8⋊C8—371no—
98C37#164011yescharacteristic, complemented, Sylow
99C2×Q16—741no—
100C4⋊Q8—371no—
101#127C2×D3711yescharacteristic
102#124—21no—
103#124—21no—
104#123—22no—
105C4×Q8C2×D3711yescharacteristic
106C4×Q8C2×D3711yescharacteristic
107C4×D4—21no—
108C4×D4—21no—
109#106—741no—
110C4⋊C8—371no—
111C4⋊C8—371no—
112#103—741no—
113#103—741no—
114#102—742no—
115C4×C8—371no—
116C2×Q8—741no—
117C2×Q8C22⋊D3711yescharacteristic
118C2×Q8C22⋊D3711yescharacteristic
119C2×D4—21no—
120C2×D4—21no—
121C2×D4C22⋊D3712yes—
122C22×C4—22no—
123Q16—1482no—
124C2×C8—741no—
125C2×C8—741no—
126C2×C8—741no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—741no—
130C4⋊C4—741no—
131C4⋊C4C22⋊D3711yescharacteristic
132C4⋊C4C22⋊D3711yescharacteristic
133C22⋊C4—22no—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C42—21no—
137C42—21no—
138C42C22×D3711yescharacteristic
139C23—22no—
140Q8—21no—
141Q8—21no—
142Q8—21no—
143Q8—21no—
144Q8—1481no—
145Q8—1481no—
146D4—42no—
147D4—41no—
148D4—41no—
149D4—41no—
150D4—41no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—82no—
156C2×C4—1481no—
157C2×C4C2×C22⋊D3711yescharacteristic
158C2×C4C2×C22⋊D3711yescharacteristic
159C2×C4C2×C22⋊D3711yescharacteristic
160C8—1481no—
161C8—1481no—
162C8—1481no—
163C22—42no—
164C22—42no—
165C22—42no—
166C22#1192450511yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—41no—
171C4—41no—
172C4—2961no—
173C4#1192455611yescharacteristic
174C4#1192455611yescharacteristic
175C4#1192456111yescharacteristic
176C4#1192456611yescharacteristic
177C2—82no—
178C2#1455767811yescharacteristic
179C2#1455769511yescharacteristic
180C2#1455771111yescharacteristic
subgroupG/H
centerC22#11924505
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#559C2
socleC22×C37#120
prime radical#127×C37C22
hypercenter#559D37
hypocenterC37#1640
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #559

Complements

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

NH ≅ G/Ntype
2. #14557818C2semidirect
3. #14557743C2semidirect
5. Q8⋊#64436C2semidirect
6. Q8⋊#64436C2semidirect
98. C37#1640semidirect

Maximal subgroups

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

subgroupindex
#145578792
#145578182
#145577432
#145572772
Q8⋊#644362
C37×#5592
#164037