Finite Group Databasebeta

← #17995134

Subgroups — #17995134

Order 4736.

314 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 93 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#14558011C211yesmaximal, characteristic, complemented
2#14557550C212yesmaximal
3C2×#11924455C211yesmaximal, characteristic, complemented
4#14557289C212yesmaximal, complemented
5C37×#536C211yesmaximal, characteristic
6C2×#10596934C2212yes—
7Q8×Dic37—24no—
8#11924495—22no—
9#11924495C2212yes—
10#11924463—24no—
11#11924455—22no—
12C2×#41×C37C2211yescharacteristic
13C22×Q8×C37C2211yescharacteristic
14C4⋊Q8×C37C412yescomplemented
15#124×C37C412yescomplemented
16#123×C37—22no—
17C22⋊Q8×C37—22no—
18#117×C37C2211yescharacteristic
19#41×C37—22no—
20#41×C37—22no—
21C2×Q8×C37—22no—
22C2×Q8×C37—22no—
23C2×Q8×C37C2×C411yescharacteristic
24C2×Q8×C37C2×C412yes—
25C2×Q8×C37D412yes—
26C2×D4×C37—21no—
27C2×D4×C37C2×C411yescharacteristic
28C22×C4×C37—21no—
29C22×C4×C37D412yes—
30C22×C4×C37C2311yescharacteristic
31C4⋊C4×C37—24no—
32C4⋊C4×C37—21no—
33C22⋊C4×C37—21no—
34C22⋊C4×C37—24no—
35C42×C37C2×C412yes—
36C22⋊Dic37—22no—
37C4⋊Dic37—24no—
38C4⋊Dic37—22no—
39C4×Dic37—24no—
40C4×Dic37D414yes—
41#10596934—22no—
42#10596934—22no—
43C2×#64436—22no—
44C23×C37—21no—
45C23×C37C2×D411yescharacteristic
46Q8×C37—24no—
47Q8×C37—24no—
48Q8×C37—22no—
49D4×C37—22no—
50D4×C37—41no—
51D4×C37—41no—
52C2×C4×C37—22no—
53C2×C4×C37—22no—
54C2×C4×C37—22no—
55C2×C4×C37—21no—
56C2×C4×C37—42no—
57C2×C4×C37C22⋊C414yes—
58C2×C4×C37C22×C411yescharacteristic
59C2×C4×C37C2×D412yes—
60C2×C4×C37C2×D411yescharacteristic
61C2×C4×C37#4112yes—
62C2×Dic37—24no—
63#64436—42no—
64C22×C37—41no—
65C22×C37—42no—
66C22×C37—41no—
67C22×C37C2×C22⋊C411yescharacteristic
68C22×C37#12011yescharacteristic
69C22×C37#12311yescharacteristic
70C4×C37—24no—
71C4×C37—42no—
72C4×C37—41no—
73C4×C37C4×D412yes—
74C4×C37#12112yes—
75Dic37—44no—
76#1912—371nomaximal, Sylow
77C2×C37—21no—
78C2×C37—21no—
79C2×C37—21no—
80C2×C37—81no—
81C2×C37#38611yescharacteristic
82#536D3711yescharacteristic
83#519—371no—
84#421—372no—
85C2×#101—371no—
86H(3,ℤ/4)—372no—
87C37#191211yescharacteristic, complemented, Sylow
88C2×#41C2×D3711yescharacteristic
89C22×Q8C2×D3711yescharacteristic
90C2×M16—372no—
91C4⋊Q8Dic3712yescomplemented
92#124Dic3712yescomplemented
93#123—22no—
94C22⋊Q8—22no—
95C4×Q8—744no—
96#117—372no—
97#117—742no—
98#117C2×D3711yescharacteristic
99#104—744no—
100#101—742no—
101#41—22no—
102#41—22no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8C2×Dic3711yescharacteristic
106C2×Q8C2×Dic3712yes—
107C2×Q8C22⋊D3712yes—
108C2×D4—21no—
109C2×D4C2×Dic3711yescharacteristic
110C22×C4—21no—
111C22×C4C22⋊D3712yes—
112C22×C4C22×D3711yescharacteristic
113M16—742no—
114M16—742no—
115C2×C8—742no—
116C4⋊C4—24no—
117C4⋊C4—21no—
118C4⋊C4—744no—
119C4⋊C4—742no—
120C22⋊C4—21no—
121C22⋊C4—24no—
122C22⋊C4—742no—
123C42—374no—
124C42—744no—
125C42C2×Dic3712yes—
126C23—21no—
127C23C2×C22⋊D3711yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—22no—
131D4—22no—
132D4—41no—
133D4—41no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—21no—
138C2×C4—42no—
139C2×C4—744no—
140C2×C4C22⋊Dic3714yes—
141C2×C4D4×D3712yes—
142C2×C4#1059696412yes—
143C2×C4C22×Dic3711yescharacteristic
144C2×C4C2×C22⋊D3711yescharacteristic
145C8—1482no—
146C22—41no—
147C22—42no—
148C22—41no—
149C22C2×C22⋊Dic3711yescharacteristic
150C22#1192450411yescharacteristic
151C22#1192451711yescharacteristic
152C4—24no—
153C4—42no—
154C4—41no—
155C4—1484no—
156C4D4×Dic3712yes—
157C4#1192450812yes—
158C2—21no—
159C2—21no—
160C2—21no—
161C2—81no—
162C2#1455741311yescharacteristic
subgroupG/H
centerC2#14557413
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#536C2
socleC2×C37#386
prime radicalC2×#41×C37C22
cosocleC22×C4×C37C23
hypercenter#536D37
hypocenterC37#1912
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
1. #14558011C2semidirect
3. C2×#11924455C2semidirect
4. #14557289C2semidirect
14. C4⋊Q8×C37C4semidirect
15. #124×C37C4semidirect
87. C37#1912semidirect
91. C4⋊Q8Dic37semidirect
92. #124Dic37semidirect

Maximal subgroups

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

subgroupindex
#145580112
#145575502
C2×#119244552
#145572892
C37×#5362
#191237