Finite Group Databasebeta

← #17995660

Subgroups — #17995660

Order 4736.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#14558040C212yesmaximal, complemented
2#14557550C212yesmaximal, complemented
3#14557496C211yesmaximal, characteristic, complemented
4#14557290C211yesmaximal, characteristic, complemented
5C37×#575C211yesmaximal, characteristic, complemented
6C22×C4×D37C2211yescharacteristic
7C2×#10596934C2211yescharacteristic
8#11924517—22no—
9#11924512—22no—
10#11924507—22no—
11#11924504—22no—
12C4×C22⋊D37—24no—
13#11924495C2212yes—
14#11924463—24no—
15#11924448—22no—
16C2×#41×C37C2212yes—
17#137×C37—22no—
18AGL(1,ℤ/8)×C37—22no—
19#135×C37—22no—
20C2×M16×C37C2211yescharacteristic
21C23×D37D411yescharacteristic
22#41×C37—22no—
23#41×C37—22no—
24#41×C37—22no—
25#41×C37—22no—
26C2×Q8×C37D412yescomplemented
27C2×D4×C37—22no—
28C2×D4×C37D412yescomplemented
29C22×C4×C37—22no—
30C22×C4×C37C2311yescharacteristic
31C2×C22⋊D37—24no—
32C22×Dic37D411yescharacteristic
33C2×C4×D37—22no—
34C2×C4×D37—22no—
35C2×C4×D37—21no—
36C2×C4×D37—21no—
37Q16×C37—22no—
38SD16×C37—24no—
39D8×C37—22no—
40M16×C37—22no—
41C2×C8×C37D412yescomplemented
42C22⋊Dic37—24no—
43C22⋊Dic37—22no—
44#10596938—24no—
45C4⋊Dic37—22no—
46#10596936—24no—
47C4×Dic37D414yescomplemented
48#10596934—22no—
49C2×#64436—21no—
50C23×C37—22no—
51C23×C37C2×D411yescharacteristic
52C22×D37—22no—
53C22×D37—21no—
54C22×D37—42no—
55Q8×C37—22no—
56Q8×C37—22no—
57D4×C37—22no—
58D4×C37—22no—
59D4×C37—42no—
60D4×C37—42no—
61C2×C4×C37—22no—
62C2×C4×C37—42no—
63C2×C4×C37—42no—
64C2×C4×C37C2×D412yes—
65C2×C4×C37C2×D412yes—
66C2×C4×C37C2×D411yescharacteristic
67C2×C4×C37#4111yescharacteristic
68C22⋊D37—48no—
69C2×Dic37—24no—
70C2×Dic37—22no—
71C2×Dic37—21no—
72C4×D37—41no—
73C4×D37—42no—
74C4×D37—41no—
75C8×C37—22no—
76#64436—41no—
77C22×C37—41no—
78C22×C37—44no—
79C22×C37—42no—
80C22×C37#12012yes—
81C22×C37#12111yescharacteristic
82C2×D37—24no—
83C2×D37—22no—
84C2×D37—42no—
85C2×D37—41no—
86C2×D37—41no—
87C4×C37—42no—
88C4×C37#12011yescharacteristic
89C4×C37#12112yes—
90C4×C37#12711yescharacteristic
91Dic37—44no—
92Dic37—41no—
93#2010—371nomaximal, Sylow
94C2×C37—22no—
95C2×C37—21no—
96C2×C37—82no—
97C2×C37#39211yescharacteristic
98D37—42no—
99#575D3711yescharacteristic, complemented
100#525—372no—
101#421—372no—
102#407—371no—
103H(3,ℤ/4)—371no—
104C37#201011yescharacteristic, complemented, Sylow
105C2×#41C2×D3712yes—
106C23×C4—371no—
107#137—22no—
108AGL(1,ℤ/8)—22no—
109#135—22no—
110C2×M16—371no—
111C2×M16C2×D3711yescharacteristic
112#123—742no—
113C22⋊Q8—742no—
114#121—742no—
115#120—742no—
116C4×D4—744no—
117#117—372no—
118#104—744no—
119C22⋊C8—742no—
120C24—371no—
121#41—22no—
122#41—22no—
123#41—22no—
124#41—22no—
125C2×Q8C22⋊D3712yescomplemented
126C2×D4—22no—
127C2×D4—744no—
128C2×D4C22⋊D3712yescomplemented
129C22×C4—22no—
130C22×C4—371no—
131C22×C4—742no—
132C22×C4—741no—
133C22×C4—741no—
134C22×C4—742no—
135C22×C4C22×D3711yescharacteristic
136Q16—22no—
137SD16—24no—
138D8—22no—
139M16—22no—
140M16—742no—
141C2×C8—741no—
142C2×C8C22⋊D3712yescomplemented
143C4⋊C4—744no—
144C4⋊C4—742no—
145C22⋊C4—744no—
146C22⋊C4—744no—
147C22⋊C4—742no—
148C42—374no—
149C23—22no—
150C23—742no—
151C23—741no—
152C23—1482no—
153C23D4×D3711yescharacteristic
154Q8—22no—
155Q8—22no—
156D4—22no—
157D4—22no—
158D4—42no—
159D4—42no—
160D4—1488no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—744no—
165C2×C4—742no—
166C2×C4—741no—
167C2×C4—1481no—
168C2×C4—1482no—
169C2×C4—1481no—
170C2×C4D4×D3712yes—
171C2×C4#1059696411yescharacteristic
172C2×C4C2×C22⋊D3712yes—
173C2×C4C2×C22⋊D3711yescharacteristic
174C8—22no—
175C8—1481no—
176C22—41no—
177C22—44no—
178C22—42no—
179C22—744no—
180C22—742no—
181C22—1482no—
182C22—1481no—
183C22—1481no—
184C22#1192450412yes—
185C22#1192450711yescharacteristic
186C4—42no—
187C4—1484no—
188C4—1481no—
189C4#1192450511yescharacteristic
190C4#1192450812yes—
191C4#1192453211yescharacteristic
192C2—22no—
193C2—21no—
194C2—82no—
195C2—1482no—
196C2#1455744111yescharacteristic
subgroupG/H
centerC4#11924532
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#575C2
socleC2×C37#392
hypercenter#575D37
hypocenterC37#2010
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #14558040C2semidirect
2. #14557550C2semidirect
3. #14557496C2semidirect
4. #14557290C2semidirect
5. C37×#575C2semidirect
26. C2×Q8×C37D4semidirect
28. C2×D4×C37D4semidirect
41. C2×C8×C37D4semidirect
47. C4×Dic37D4semidirect
99. #575D37semidirect
104. C37#2010semidirect
125. C2×Q8C22⋊D37semidirect
128. C2×D4C22⋊D37semidirect
142. C2×C8C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145580402
#145575502
#145574962
#145572902
C37×#5752
#201037