Finite Group Databasebeta

← #17995131

Subgroups — #17995131

Order 4736.

314 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 85 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#14558107C211yesmaximal, characteristic
2#14558011C211yesmaximal, characteristic, complemented
3#14557549C212yesmaximal
4#14557290C212yesmaximal, complemented
5C2×#101×C37C211yesmaximal, characteristic, complemented
6C2×#10596962C2211yescharacteristic
7#11924534C412yescomplemented
8#11924525C412yescomplemented
9#11924519—22no—
10#11924512—22no—
11Q8×Dic37—24no—
12#11924495—22no—
13#11924495C2211yescharacteristic
14#11924495C2212yes—
15#11924462—24no—
16C22×Q8×C37C2211yescharacteristic
17C2×M16×C37C2212yes—
18#101×C37—22no—
19C2×Q8×C37—22no—
20C2×Q8×C37—22no—
21C2×Q8×C37C2×C412yes—
22C2×Q8×C37D412yes—
23C22×C4×C37D412yes—
24C22×C4×C37C2311yescharacteristic
25C2×C22⋊D37—21no—
26#10596962—22no—
27#10596962—22no—
28C2×D148C2×C411yescharacteristic
29C2×C4×D37—21no—
30C2×Dic74C2×C411yescharacteristic
31M16×C37—22no—
32M16×C37—22no—
33C2×C8×C37—22no—
34C22⋊Dic37—22no—
35C22⋊Dic37—21no—
36#10596938—24no—
37C4⋊Dic37—24no—
38C4⋊Dic37—22no—
39C4⋊Dic37—21no—
40#10596936—24no—
41C4×Dic37—24no—
42C4×Dic37C2×C412yes—
43C4×Dic37D414yes—
44C23×C37C2×D411yescharacteristic
45C22×D37—21no—
46Q8×C37—24no—
47Q8×C37—24no—
48C2×C4×C37—22no—
49C2×C4×C37—22no—
50C2×C4×C37C22⋊C414yes—
51C2×C4×C37C22×C411yescharacteristic
52C2×C4×C37C2×D412yes—
53C2×C4×C37C2×D411yescharacteristic
54C2×C4×C37#4112yes—
55C22⋊D37—41no—
56C22⋊D37—41no—
57C2×Dic37—22no—
58C2×Dic37—21no—
59C2×Dic37—24no—
60D148—22no—
61C4×D37—42no—
62Dic74—22no—
63C8×C37—42no—
64C22×C37—41no—
65C22×C37C2×C22⋊C411yescharacteristic
66C22×C37#12011yescharacteristic
67C22×C37#12311yescharacteristic
68C2×D37—42no—
69C2×D37—41no—
70C4×C37—24no—
71C4×C37C4×D412yes—
72C4×C37#12112yes—
73Dic37—44no—
74Dic37—42no—
75Dic37—41no—
76#1912—371nomaximal, Sylow
77C2×C37—21no—
78C2×C37—21no—
79C2×C37—21no—
80C2×C37#38611yescharacteristic
81D37—81no—
82#536—371no—
83#519—371no—
84#421—372no—
85C2×#101D3711yescharacteristic, complemented
86H(3,ℤ/4)—372no—
87C37#191211yescharacteristic, complemented, Sylow
88C2×#41—371no—
89C22×Q8C2×D3711yescharacteristic
90C2×M16C2×D3712yes—
91C4⋊Q8—372no—
92#124—372no—
93#123—742no—
94C22⋊Q8—742no—
95C4×Q8—744no—
96#117—372no—
97#117—371no—
98#117—742no—
99#104—744no—
100#101—22no—
101#41—742no—
102#41—742no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8—371no—
106C2×Q8C4×D3712yes—
107C2×Q8C22⋊D3712yes—
108C2×D4—371no—
109C2×D4—741no—
110C22×C4—741no—
111C22×C4D14812yes—
112C22×C4C22×D3711yescharacteristic
113M16—22no—
114M16—22no—
115C2×C8—22no—
116C4⋊C4—744no—
117C4⋊C4—744no—
118C4⋊C4—742no—
119C4⋊C4—741no—
120C22⋊C4—742no—
121C22⋊C4—741no—
122C22⋊C4—744no—
123C42—372no—
124C42—374no—
125C42—744no—
126C23—741no—
127C23C2×D14811yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—742no—
131D4—742no—
132D4—1481no—
133D4—1481no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—742no—
137C2×C4—741no—
138C2×C4—744no—
139C2×C4—1482no—
140C2×C4#1059693814yes—
141C2×C4C2×C4×D3711yescharacteristic
142C2×C4D4×D3712yes—
143C2×C4#1059696412yes—
144C2×C4C2×C22⋊D3711yescharacteristic
145C8—42no—
146C22—41no—
147C22—1482no—
148C22—1481no—
149C22C2×#1059693811yescharacteristic
150C22#1192450611yescharacteristic
151C22#1192452011yescharacteristic
152C4—24no—
153C4—1484no—
154C4—1482no—
155C4—1481no—
156C4#1192449612yes—
157C4#1192450812yes—
158C2—21no—
159C2—21no—
160C2—21no—
161C2—2961no—
162C2#1455741011yescharacteristic
subgroupG/H
centerC2#14557410
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC2×#101×C37C2
socleC2×C37#386
prime radicalC2×#10596962C22
cosocleC22×C4×C37C23
hypercenterC2×#101D37
hypocenterC37#1912
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #14558011C2semidirect
4. #14557290C2semidirect
5. C2×#101×C37C2semidirect
7. #11924534C4semidirect
8. #11924525C4semidirect
85. C2×#101D37semidirect
87. C37#1912semidirect

Maximal subgroups

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

subgroupindex
#145581072
#145580112
#145575492
#145572902
C2×#101×C372
#191237