Finite Group Databasebeta

← #17993700

Subgroups — #17993700

Order 4736.

250 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 57 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#14558198C211yesmaximal, characteristic, complemented
2#14557881C211yesmaximal, characteristic, complemented
3#14557734C211yesmaximal, characteristic, complemented
4#14557729C211yesmaximal, characteristic
5#14557263C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic, complemented
7C37×#332C211yesmaximal, characteristic, complemented
8C2×Q8×D37—21no—
9C2×#10596930—21no—
10C2×D296—21no—
11#11924535—21no—
12#11924533C2211yescharacteristic
13#11924514—22no—
14#11924512—21no—
15C4×Dic74C2211yescharacteristic
16C4×D148C2211yescharacteristic
17#11924498—21no—
18#11924458—21no—
19#11924458—21no—
20#11924456—22no—
21C4×#64436C2211yescharacteristic
22C4⋊Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4⋊C8×C37C2211yescharacteristic
25C2×Q8×C37—21no—
26Q8×D37—42no—
27Q8×D37—42no—
28C2×D148—21no—
29C2×D148—21no—
30C2×D148—21no—
31C2×D148D411yescharacteristic
32C2×C4×D37—22no—
33C2×C4×D37—21no—
34C2×Dic74—22no—
35C2×Dic74D411yescharacteristic
36C2×C8×C37—21no—
37C2×C8×C37—21no—
38C4⋊C4×C37—21no—
39C4⋊C4×C37D412yes—
40C42×C37C2311yescharacteristic
41#10596938—22no—
42#10596938—21no—
43C4⋊Dic37D411yescharacteristic
44C4⋊Dic37D411yescharacteristic
45#10596936—22no—
46#10596936—21no—
47C4×Dic37—21no—
48C2×#64436—21no—
49D296—42no—
50#10596930—42no—
51C22×D37—21no—
52C22×D37—41no—
53Q8×C37—41no—
54Q8×C37—41no—
55C2×C4×C37—22no—
56C2×C4×C37C2×D411yescharacteristic
57C2×C4×C37C2×D411yescharacteristic
58C2×C4×C37C2×D411yescharacteristic
59C2×Dic37—21no—
60C2×Dic37—21no—
61C2×Dic37—21no—
62D148—21no—
63D148—42no—
64D148—41no—
65D148—41no—
66D148—41no—
67D148—41no—
68D148SD1612yescomplemented
69C4×D37—44no—
70C4×D37—41no—
71C4×D37—41no—
72Dic74—21no—
73Dic74—44no—
74Dic74D812yescomplemented
75C8×C37—41no—
76C8×C37—41no—
77#64436—41no—
78C22×C37#12011yescharacteristic
79C2×D37—22no—
80C2×D37—41no—
81C2×D37—41no—
82C2×D37—81no—
83C2×D37—81no—
84C2×D37—81no—
85C4×C37—21no—
86C4×C37—42no—
87C4×C37C2×D811yescharacteristic
88C4×C37C2×SD1611yescharacteristic
89C4×C37AGL(1,ℤ/8)11yescharacteristic
90C4×C37#13711yescharacteristic
91Dic37—22no—
92Dic37—41no—
93Dic37—41no—
94#1627—371nomaximal, Sylow
95C2×C37#44711yescharacteristic
96C2×C37#44811yescharacteristic
97C2×C37#45411yescharacteristic
98D37—42no—
99D37—161no—
100D4×Q8—371no—
101#486—371no—
102#460—371no—
103#459—371no—
104#332D3711yescharacteristic, complemented
105Q8⋊C8—371no—
106D4⋊C8—371no—
107C37#162711yescharacteristic, complemented, Sylow
108C22×Q8—741no—
109C2×SD16—741no—
110C2×D8—741no—
111C4⋊Q8—741no—
112C4⋊Q8C2×D3711yescharacteristic
113#127—371no—
114C22⋊Q8—741no—
115C22⋊Q8—742no—
116C4×Q8—371no—
117C4×D4—371no—
118C4×D4—741no—
119C4⋊C8C2×D3711yescharacteristic
120C4⋊C8C2×D3711yescharacteristic
121#102—741no—
122#102—741no—
123#102—742no—
124C4×C8—371no—
125C2×Q8—21no—
126C2×Q8—371no—
127C2×Q8—742no—
128C2×Q8—1482no—
129C2×Q8—1482no—
130C2×D4—371no—
131C2×D4—741no—
132C2×D4—741no—
133C2×D4—741no—
134C22×C4—742no—
135C22×C4—741no—
136SD16—1482no—
137D8—1482no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—741no—
141C4⋊C4—21no—
142C4⋊C4—371no—
143C4⋊C4—371no—
144C4⋊C4—742no—
145C4⋊C4—741no—
146C4⋊C4D14812yes—
147C22⋊C4—742no—
148C22⋊C4—741no—
149C42—741no—
150C42C22×D3711yescharacteristic
151C23—741no—
152C23—1481no—
153Q8—41no—
154Q8—41no—
155Q8—372no—
156Q8—741no—
157Q8—1484no—
158D4—372no—
159D4—741no—
160D4—1482no—
161D4—1481no—
162D4—1481no—
163D4—1481no—
164D4—1481no—
165C2×C4—22no—
166C2×C4—741no—
167C2×C4—741no—
168C2×C4—741no—
169C2×C4—1484no—
170C2×C4—1481no—
171C2×C4—1481no—
172C2×C4C2×D14811yescharacteristic
173C2×C4D4×D3711yescharacteristic
174C2×C4D4×D3711yescharacteristic
175C8—41no—
176C8—41no—
177C8—1481no—
178C22—2961no—
179C22—2961no—
180C22—2961no—
181C22—742no—
182C22—1481no—
183C22—1481no—
184C22#1192450611yescharacteristic
185C4—21no—
186C4—42no—
187C4—742no—
188C4—1481no—
189C4—1481no—
190C4D8×D3711yescharacteristic
191C4SD16×D3711yescharacteristic
192C4#1192456311yescharacteristic
193C4#1192456811yescharacteristic
194C2—5921no—
195C2—1482no—
196C2#1455766811yescharacteristic
197C2#1455767311yescharacteristic
198C2#1455770811yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#332C2
socleC22×C37#120
prime radical#14557729C2
hypercenter#332D37
hypocenterC37#1627
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #14558198C2semidirect
2. #14557881C2semidirect
3. #14557734C2semidirect
5. #14557263C2semidirect
6. #14557260C2semidirect
7. C37×#332C2semidirect
68. D148SD16semidirect
74. Dic74D8semidirect
104. #332D37semidirect
107. C37#1627semidirect

Maximal subgroups

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

subgroupindex
#145581982
#145578812
#145577342
#145577292
#145572632
#145572602
C37×#3322
#162737