Finite Group Databasebeta

← #17993229

Subgroups — #17993229

Order 4736.

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

normal subgroups only

This group has 238 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#14558082C211yesmaximal, characteristic
2#14557588C212yesmaximal, complemented
3#14557273C211yesmaximal, characteristic, complemented
4#14557272C212yesmaximal, complemented
5C37×#329C211yesmaximal, characteristic, complemented
6C2×#10596966C411yescharacteristic
7C2×#10596964C411yescharacteristic
8#11924534C411yescharacteristic
9#11924532C411yescharacteristic
10#11924524C2211yescharacteristic
11#11924509—22no—
12#11924496—22no—
13C42×D37C2211yescharacteristic
14#11924465—22no—
15#11924448—22no—
16#11924447C2212yes—
17#124×C37C2211yescharacteristic
18#97×C37C2212yes—
19C2×Q8×C37C2×C411yescharacteristic
20C2×D4×C37C2×C411yescharacteristic
21C2×C22⋊D37—21no—
22C2×C22⋊D37—22no—
23C22×Dic37—21no—
24#10596966—42no—
25#10596964—42no—
26C2×D148—21no—
27C2×D148C2×C411yescharacteristic
28C2×C4×D37—21no—
29C2×C4×D37C2×C411yescharacteristic
30C2×C4×D37D412yes—
31C2×Dic74C2×C411yescharacteristic
32C2×C8×C37—22no—
33C22⋊C4×C37—22no—
34C42×C37C2311yescharacteristic
35#10596938—22no—
36#10596936—22no—
37C4×Dic37C2×C411yescharacteristic
38C4×Dic37D412yes—
39C2×#64436—22no—
40C23×C37—21no—
41C22×D37—21no—
42C22×D37C22⋊C411yescharacteristic
43Q8×C37—41no—
44D4×C37—41no—
45C2×C4×C37—21no—
46C2×C4×C37C22×C411yescharacteristic
47C2×C4×C37C2×D412yes—
48C22⋊D37—44no—
49C22⋊D37—42no—
50C2×Dic37—21no—
51C2×Dic37—42no—
52C2×Dic37C22⋊C412yes—
53C2×Dic37C22⋊C411yescharacteristic
54D148—41no—
55D148—42no—
56C4×D37—22no—
57C4×D37—42no—
58C4×D37—42no—
59Dic74—41no—
60C8×C37—42no—
61#64436—42no—
62C22×C37—41no—
63C22×C37—42no—
64C22×C37C2×C22⋊C411yescharacteristic
65C2×D37—21no—
66C2×D37—22no—
67C2×D37—41no—
68C2×D37—42no—
69C4×C37—21no—
70C4×C37—22no—
71C4×C37—41no—
72Dic37—22no—
73Dic37—41no—
74Dic37#10012yes—
75#1536—371nomaximal, Sylow
76C2×C37—81no—
77C2×C37C2×#10011yescharacteristic
78C2×C37#42112yes—
79D37—41no—
80D37—81no—
81#532—371no—
82#432—372no—
83#329—371no—
84#329—372no—
85#329D3711yescharacteristic, complemented
86C37#153611yescharacteristic, complemented, Sylow
87C2×#41—371no—
88C2×#41—371no—
89C4⋊Q8—371no—
90#127—371no—
91#124—371no—
92#124C2×D3711yescharacteristic
93#121—742no—
94C4×D4—742no—
95C2×C42—371no—
96C4⋊C8—742no—
97C22⋊C8—742no—
98#97—372no—
99#97C2×D3712yes—
100#41—1482no—
101#41—1482no—
102C2×Q8—371no—
103C2×Q8C4×D3711yescharacteristic
104C2×D4—371no—
105C2×D4—741no—
106C2×D4—742no—
107C2×D4—741no—
108C2×D4C4×D3711yescharacteristic
109C22×C4—371no—
110C22×C4—372no—
111C22×C4—741no—
112C22×C4—741no—
113C2×C8—22no—
114C2×C8—742no—
115C4⋊C4—742no—
116C22⋊C4—22no—
117C22⋊C4—742no—
118C42—371no—
119C42—372no—
120C42C22×D3711yescharacteristic
121C23—21no—
122C23—371no—
123C23—741no—
124Q8—41no—
125Q8—1481no—
126D4—41no—
127D4—1481no—
128D4—1482no—
129D4—1484no—
130D4—1482no—
131C2×C4—21no—
132C2×C4—371no—
133C2×C4—372no—
134C2×C4—742no—
135C2×C4—741no—
136C2×C4—1482no—
137C2×C4—1482no—
138C2×C4—1482no—
139C2×C4C2×C4×D3711yescharacteristic
140C2×C4D4×D3712yes—
141C8—42no—
142C8—1482no—
143C22—41no—
144C22—42no—
145C22—741no—
146C22—742no—
147C22—1481no—
148C22—1482no—
149C22C22⋊C4×D3711yescharacteristic
150C4—21no—
151C4—22no—
152C4—41no—
153C4—372no—
154C4—742no—
155C4—1481no—
156C2—81no—
157C2—2961no—
158C2—1481no—
159C2#100×D3711yescharacteristic
160C2#1455754812yes—
subgroupG/H
centerC22C22⋊C4×D37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×#329C2
socleC22×C37C2×C22⋊C4
prime radical#14558082C2
cosocleC42×C37C23
hypercenter#329D37
hypocenterC37#1536
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
85. #329D37semidirect
86. C37#1536semidirect

Maximal subgroups

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

subgroupindex
#145580822
#145575882
#145572732
#145572722
C37×#3292
#153637