Finite Group Databasebeta

← #17993687

Subgroups — #17993687

Order 4736.

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

normal subgroups only

This group has 256 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#14558187C211yesmaximal, characteristic, complemented
2#14557880C211yesmaximal, characteristic, complemented
3#14557729C211yesmaximal, characteristic, complemented
4#14557728C211yesmaximal, characteristic, complemented
5#14557278C211yesmaximal, characteristic, complemented
6#14557262C211yesmaximal, characteristic, complemented
7C37×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#10596964—21no—
9C2×D296—21no—
10C2×#10596939—21no—
11#11924536C2211yescharacteristic
12#11924533C2211yescharacteristic
13#11924520—22no—
14#11924516—21no—
15#11924510—21no—
16C4×D148C2211yescharacteristic
17C2×C4⋊Dic37—21no—
18C4⋊#64436C2211yescharacteristic
19#11924458—21no—
20#11924458—22no—
21#11924456—21no—
22C4×D4×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4×C8×C37C2211yescharacteristic
25C2×D4×C37D411yescharacteristic
26C22×C4×C37—21no—
27C2×C22⋊D37—22no—
28C22×Dic37—22no—
29#10596964—42no—
30#10596964—42no—
31C2×D148—21no—
32C2×D148—21no—
33C2×D148—21no—
34C2×D148D411yescharacteristic
35C2×C4×D37—21no—
36C2×Dic74—21no—
37C2×C8×C37—21no—
38C2×C8×C37—21no—
39C4⋊C4×C37D411yescharacteristic
40C22⋊C4×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—
50D296—42no—
51C23×C37—21no—
52C22×D37—21no—
53C22×D37—41no—
54D4×C37—21no—
55D4×C37D812yescomplemented
56C2×C4×C37—21no—
57C2×C4×C37—41no—
58C2×C4×C37—41no—
59C2×C4×C37C2×D411yescharacteristic
60C2×C4×C37C2×D411yescharacteristic
61C2×C4×C37C2×D411yescharacteristic
62C22⋊D37—44no—
63C2×Dic37—22no—
64C2×Dic37—21no—
65C2×Dic37—44no—
66D148—21no—
67D148—21no—
68D148—42no—
69D148—41no—
70D148—41no—
71D148—41no—
72D148—41no—
73C4×D37—41no—
74C4×D37—41no—
75Dic74—41no—
76Dic74—41no—
77C8×C37—41no—
78C8×C37—41no—
79#64436—41no—
80C22×C37—22no—
81C22×C37—41no—
82C22×C37—41no—
83C22×C37#12011yescharacteristic
84C2×D37—41no—
85C2×D37—41no—
86C2×D37—41no—
87C2×D37—81no—
88C2×D37—81no—
89C2×D37—81no—
90C4×C37—21no—
91C4×C37—41no—
92C4×C37C2×D811yescharacteristic
93C4×C37#13511yescharacteristic
94C4×C37AGL(1,ℤ/8)11yescharacteristic
95C4×C37AGL(1,ℤ/8)11yescharacteristic
96Dic37—42no—
97Dic37—41no—
98#1625—371nomaximal, Sylow
99C2×C37—42no—
100C2×C37#44711yescharacteristic
101C2×C37#44911yescharacteristic
102C2×C37#45411yescharacteristic
103D37—81no—
104D37—161no—
105#547—371no—
106#486—371no—
107#459—371no—
108#459—371no—
109#332—371no—
110D4⋊C8—371no—
111D4⋊C8D3711yescharacteristic, complemented
112C37#162511yescharacteristic, complemented, Sylow
113C2×#41—741no—
114C2×D8—741no—
115C2×D8—741no—
116C4⋊Q8—371no—
117#127—371no—
118#123—742no—
119C22⋊Q8—741no—
120#121—741no—
121C4×D4—371no—
122C4×D4C2×D3711yescharacteristic
123C2×C4⋊C4—741no—
124C4⋊C8—371no—
125C4⋊C8C2×D3711yescharacteristic
126#102—741no—
127#102—742no—
128#102—741no—
129C4×C8C2×D3711yescharacteristic
130#41—1482no—
131#41—1482no—
132C2×Q8—741no—
133C2×D4—371no—
134C2×D4—742no—
135C2×D4—741no—
136C2×D4—741no—
137C2×D4—741no—
138C2×D4D14811yescharacteristic
139C22×C4—21no—
140C22×C4—742no—
141C22×C4—741no—
142D8—1482no—
143D8—1482no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—741no—
147C4⋊C4—371no—
148C4⋊C4—372no—
149C4⋊C4—742no—
150C4⋊C4—741no—
151C4⋊C4D14811yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—742no—
154C22⋊C4—741no—
155C42C22×D3711yescharacteristic
156C23—21no—
157C23—741no—
158C23—1481no—
159Q8—1481no—
160Q8—1481no—
161D4—21no—
162D4—741no—
163D4—741no—
164D4—1482no—
165D4—1484no—
166D4—1481no—
167D4—1481no—
168D4—1481no—
169D4—1481no—
170D4D29612yescomplemented
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—741no—
175C2×C4—742no—
176C2×C4—1484no—
177C2×C4—1481no—
178C2×C4—1481no—
179C2×C4C2×D14811yescharacteristic
180C2×C4D4×D3711yescharacteristic
181C2×C4D4×D3711yescharacteristic
182C8—41no—
183C8—41no—
184C8—1481no—
185C22—22no—
186C22—41no—
187C22—41no—
188C22—2961no—
189C22—2961no—
190C22—2961no—
191C22—1481no—
192C22—1481no—
193C22—1481no—
194C22#1192450611yescharacteristic
195C4—21no—
196C4—41no—
197C4—1481no—
198C4—1482no—
199C4C2×D29611yescharacteristic
200C4#1192455711yescharacteristic
201C4#1192456011yescharacteristic
202C4#1192456411yescharacteristic
203C2—42no—
204C2—2961no—
205C2—5921no—
206C2#1455766911yescharacteristic
207C2#1455767911yescharacteristic
208C2#1455770711yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×D4⋊C8C2
socleC22×C37#120
hypercenterD4⋊C8D37
hypocenterC37#1625
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #14558187C2semidirect
2. #14557880C2semidirect
3. #14557729C2semidirect
4. #14557728C2semidirect
5. #14557278C2semidirect
6. #14557262C2semidirect
7. C37×D4⋊C8C2semidirect
55. D4×C37D8semidirect
111. D4⋊C8D37semidirect
112. C37#1625semidirect
170. D4D296semidirect

Maximal subgroups

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

subgroupindex
#145581872
#145578802
#145577292
#145577282
#145572782
#145572622
C37×D4⋊C82
#162537