Finite Group Databasebeta

← #17993697

Subgroups — #17993697

Order 4736.

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

normal subgroups only

This group has 250 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
1Q8×D148C211yesmaximal, characteristic, complemented
2#14557879C211yesmaximal, characteristic, complemented
3#14557725C211yesmaximal, characteristic
4#14557280C211yesmaximal, characteristic, complemented
5Q8⋊#64436C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic, complemented
7C37×#460C211yesmaximal, characteristic, complemented
8C2×Q8×D37—21no—
9C2×#10596939—21no—
10#11924536—21no—
11#11924536C2211yescharacteristic
12#11924516—21no—
13#11924516—22no—
14C4×D148—21no—
15C4×D148C2211yescharacteristic
16C4⋊#64436C2211yescharacteristic
17#11924457—21no—
18#11924457—22no—
19C4×#64436C2211yescharacteristic
20C2×SD16×C37—21no—
21#127×C37C2211yescharacteristic
22C4×Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24#102×C37—21no—
25C2×Q8×C37D411yescharacteristic
26C2×D4×C37—21no—
27C2×D4×C37—21no—
28C2×D4×C37—21no—
29Q8×D37—42no—
30Q8×D37—42no—
31C2×D148D411yescharacteristic
32C2×C4×D37—22no—
33C2×C4×D37—21no—
34C2×Dic74—22no—
35C2×Dic74—21no—
36SD16×C37—42no—
37C2×C8×C37—21no—
38C4⋊C4×C37—21no—
39C4⋊C4×C37D411yescharacteristic
40C42×C37—21no—
41C42×C37C2311yescharacteristic
42#10596939—42no—
43#10596938—22no—
44#10596938—21no—
45C4⋊Dic37—22no—
46C4⋊Dic37—21no—
47C4⋊Dic37D411yescharacteristic
48C4⋊Dic37D412yes—
49C2×#64436—21no—
50C2×#64436—21no—
51C23×C37—41no—
52C22×D37—21no—
53Q8×C37—21no—
54Q8×C37D812yescomplemented
55D4×C37—42no—
56D4×C37—41no—
57D4×C37—41no—
58D4×C37—41no—
59D4×C37—41no—
60C2×C4×C37—21no—
61C2×C4×C37—21no—
62C2×C4×C37C2×D411yescharacteristic
63C2×C4×C37C2×D411yescharacteristic
64C2×C4×C37C2×D411yescharacteristic
65C2×Dic37—21no—
66C2×Dic37—22no—
67D148—21no—
68D148SD1612yescomplemented
69C4×D37—44no—
70C4×D37—41no—
71C4×D37—41no—
72Dic74—44no—
73Dic74—41no—
74Dic74—41no—
75C8×C37—41no—
76#64436—41no—
77#64436—41no—
78C22×C37—81no—
79C22×C37—81no—
80C22×C37—81no—
81C22×C37#12011yescharacteristic
82C2×D37—22no—
83C2×D37—41no—
84C2×D37—41no—
85C4×C37—22no—
86C4×C37—21no—
87C4×C37—41no—
88C4×C37C2×D811yescharacteristic
89C4×C37C2×SD1611yescharacteristic
90C4×C37AGL(1,ℤ/8)11yescharacteristic
91C4×C37#13711yescharacteristic
92Dic37—41no—
93Dic37—42no—
94#1627—371nomaximal, Sylow
95C2×C37—161no—
96C2×C37#44711yescharacteristic
97C2×C37#44811yescharacteristic
98C2×C37#45411yescharacteristic
99D37—42no—
100D4×Q8—371no—
101#486—371no—
102#460D3711yescharacteristic, complemented
103#459—371no—
104#332—371no—
105Q8⋊C8—371no—
106D4⋊C8—371no—
107C37#162711yescharacteristic, complemented, Sylow
108C22×Q8—741no—
109C2×SD16—21no—
110C2×D8—741no—
111C4⋊Q8—371no—
112C4⋊Q8—741no—
113#127C2×D3711yescharacteristic
114C22⋊Q8—742no—
115C22⋊Q8—741no—
116C4×Q8C2×D3711yescharacteristic
117C4×D4—371no—
118C4×D4—741no—
119C4⋊C8—371no—
120C4⋊C8C2×D3711yescharacteristic
121#102—21no—
122#102—741no—
123#102—742no—
124C4×C8—371no—
125C2×Q8—742no—
126C2×Q8—741no—
127C2×Q8—1482no—
128C2×Q8—1482no—
129C2×Q8C22⋊D3711yescharacteristic
130C2×D4—21no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4—371no—
134C22×C4—742no—
135C22×C4—741no—
136SD16—42no—
137D8—1482no—
138C2×C8—21no—
139C2×C8—741no—
140C2×C8—741no—
141C4⋊C4—21no—
142C4⋊C4—371no—
143C4⋊C4—372no—
144C4⋊C4—742no—
145C4⋊C4—741no—
146C4⋊C4C22⋊D3711yescharacteristic
147C22⋊C4—742no—
148C22⋊C4—741no—
149C42—21no—
150C42C22×D3711yescharacteristic
151C23—41no—
152C23—741no—
153Q8—21no—
154Q8—1484no—
155Q8—1481no—
156Q8—1481no—
157Q8#1059693912yescomplemented
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—372no—
164D4—741no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—742no—
168C2×C4—741no—
169C2×C4—1484no—
170C2×C4—1481no—
171C2×C4—1481no—
172C2×C4D4×D3711yescharacteristic
173C2×C4D4×D3711yescharacteristic
174C2×C4C2×C22⋊D3711yescharacteristic
175C8—41no—
176C8—1481no—
177C8—1481no—
178C22—81no—
179C22—81no—
180C22—81no—
181C22—742no—
182C22—1481no—
183C22—1481no—
184C22#1192450411yescharacteristic
185C4—21no—
186C4—22no—
187C4—41no—
188C4—1482no—
189C4—1481no—
190C4C2×#1059693911yescharacteristic
191C4SD16×D3711yescharacteristic
192C4#1192456111yescharacteristic
193C4#1192456511yescharacteristic
194C2—161no—
195C2—1482no—
196C2#1455766611yescharacteristic
197C2#1455767011yescharacteristic
198C2#1455770411yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#460C2
socleC22×C37#120
prime radical#14557725C2
hypercenter#460D37
hypocenterC37#1627
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. Q8×D148C2semidirect
2. #14557879C2semidirect
4. #14557280C2semidirect
5. Q8⋊#64436C2semidirect
6. #14557260C2semidirect
7. C37×#460C2semidirect
54. Q8×C37D8semidirect
68. D148SD16semidirect
102. #460D37semidirect
107. C37#1627semidirect
157. Q8#10596939semidirect

Maximal subgroups

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

subgroupindex
Q8×D1482
#145578792
#145577252
#145572802
Q8⋊#644362
#145572602
C37×#4602
#162737