Finite Group Databasebeta

← #17993218

Subgroups — #17993218

Order 4736.

248 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 59 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#124×D37C211yesmaximal, characteristic
2#14557588C212yesmaximal, complemented
3#14557273C211yesmaximal, characteristic, complemented
4#14557272C212yesmaximal, complemented
5C37×#329C211yesmaximal, characteristic, complemented
6C2×Q8×D37C411yescharacteristic
7C2×D4×D37C411yescharacteristic
8#11924525C411yescharacteristic
9#11924524C2211yescharacteristic
10#11924523C411yescharacteristic
11#11924522—22no—
12C22⋊C4×D37—22no—
13C42×D37C2211yescharacteristic
14#11924465—22no—
15#11924448—22no—
16#11924447C2212yescomplemented
17#124×C37C2211yescharacteristic
18#97×C37C2212yescomplemented
19C23×D37—21no—
20C2×Q8×C37C2×C411yescharacteristic
21C2×D4×C37C2×C411yescharacteristic
22C2×C22⋊D37—21no—
23Q8×D37—42no—
24D4×D37—42no—
25C2×D148C2×C411yescharacteristic
26C2×C4×D37—21no—
27C2×C4×D37C2×C411yescharacteristic
28C2×C4×D37D412yes—
29C2×Dic74—21no—
30C2×Dic74C2×C411yescharacteristic
31C2×C8×C37—22no—
32C22⋊C4×C37—22no—
33C42×C37C2311yescharacteristic
34C22⋊Dic37—22no—
35#10596938—22no—
36#10596938—22no—
37C4×Dic37C2×C411yescharacteristic
38C4×Dic37D412yes—
39C2×#64436—22no—
40C23×C37—21no—
41C22×D37—21no—
42C22×D37—44no—
43C22×D37—42no—
44C22×D37C22⋊C411yescharacteristic
45Q8×C37—41no—
46D4×C37—41no—
47C2×C4×C37—21no—
48C2×C4×C37C22×C411yescharacteristic
49C2×C4×C37C2×D412yes—
50C22⋊D37—42no—
51C2×Dic37—21no—
52C2×Dic37C22⋊C412yes—
53C2×Dic37C22⋊C411yescharacteristic
54D148—41no—
55C4×D37—22no—
56C4×D37—42no—
57C4×D37—42no—
58Dic74—42no—
59Dic74—41no—
60C8×C37—42no—
61#64436—42no—
62C22×C37—41no—
63C22×C37—42no—
64C22×C37C2×C22⋊C411yescharacteristic
65C2×D37—22no—
66C2×D37—41no—
67C2×D37—42no—
68C2×D37—84no—
69C2×D37#10012yes—
70C4×C37—21no—
71C4×C37—22no—
72C4×C37—41no—
73Dic37—21no—
74Dic37—22no—
75Dic37—41no—
76#1533—371nomaximal, Sylow
77C2×C37—81no—
78C2×C37C2×#10011yescharacteristic
79C2×C37#42112yes—
80D37—22no—
81D37—81no—
82C2×#124—371no—
83#432—372no—
84#329—371no—
85#329—372no—
86#329D3711yescharacteristic, complemented
87C37#153311yescharacteristic, complemented, Sylow
88C22×Q8—371no—
89C22×D4—371no—
90#124—371no—
91#124—371no—
92#124—371no—
93#124—742no—
94#124C2×D3711yescharacteristic
95C2×C22⋊C4—742no—
96C2×C42—371no—
97C4⋊C8—742no—
98C22⋊C8—742no—
99#97—372no—
100#97C2×D3712yescomplemented
101C24—741no—
102C2×Q8—371no—
103C2×Q8—741no—
104C2×Q8—1482no—
105C2×Q8C4×D3711yescharacteristic
106C2×D4—371no—
107C2×D4—741no—
108C2×D4—1482no—
109C2×D4C4×D3711yescharacteristic
110C22×C4—371no—
111C22×C4—372no—
112C22×C4—741no—
113C2×C8—22no—
114C2×C8—742no—
115C22⋊C4—22no—
116C22⋊C4—742no—
117C22⋊C4—742no—
118C22⋊C4—742no—
119C42—371no—
120C42—372no—
121C42C22×D3711yescharacteristic
122C23—21no—
123C23—371no—
124C23—741no—
125C23—1482no—
126C23—1484no—
127Q8—41no—
128Q8—1481no—
129Q8—1482no—
130D4—41no—
131D4—1481no—
132D4—1482no—
133C2×C4—21no—
134C2×C4—372no—
135C2×C4—371no—
136C2×C4—742no—
137C2×C4—741no—
138C2×C4—1482no—
139C2×C4—1482no—
140C2×C4C2×C4×D3711yescharacteristic
141C2×C4D4×D3712yes—
142C8—42no—
143C8—1482no—
144C22—41no—
145C22—42no—
146C22—372no—
147C22—2964no—
148C22—742no—
149C22—1481no—
150C22—1482no—
151C22C22⋊C4×D3711yescharacteristic
152C4—21no—
153C4—22no—
154C4—41no—
155C4—741no—
156C4—742no—
157C4—1481no—
158C2—81no—
159C2—2961no—
160C2—742no—
161C2#100×D3711yescharacteristic
162C2#1455754812yes—
subgroupG/H
centerC22C22⋊C4×D37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×#329C2
socleC22×C37C2×C22⋊C4
prime radicalC2×D4×D37C4
cosocleC42×C37C23
hypercenter#329D37
hypocenterC37#1533
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #14557588C2semidirect
3. #14557273C2semidirect
4. #14557272C2semidirect
5. C37×#329C2semidirect
16. #11924447C22semidirect
18. #97×C37C22semidirect
86. #329D37semidirect
87. C37#1533semidirect
100. #97C2×D37semidirect

Maximal subgroups

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

subgroupindex
#124×D372
#145575882
#145572732
#145572722
C37×#3292
#153337