Finite Group Databasebeta

← #17993590

Subgroups — #17993590

Order 4736.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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#14558128C211yesmaximal, characteristic
2#14557863C211yesmaximal, characteristic, complemented
3#14557464C211yesmaximal, characteristic, complemented
4#14557271C211yesmaximal, characteristic, complemented
5#14557267C211yesmaximal, characteristic
6#14557258C211yesmaximal, characteristic, complemented
7C37×#480C211yesmaximal, characteristic
8#11924529—21no—
9#11924526—21no—
10#11924517—21no—
11#11924517—21no—
12#11924515C2211yescharacteristic
13#11924513—21no—
14D4×Dic37—21no—
15C2×#10596936—21no—
16C2×#10596936C2211yescharacteristic
17#11924467—21no—
18#11924459—21no—
19C22⋊#64436C2211yescharacteristic
20#11924443—21no—
21#11924443C2211yescharacteristic
22#121×C37C2211yescharacteristic
23C2×C4⋊C4×C37C2211yescharacteristic
24#107×C37—21no—
25#102×C37—21no—
26C22⋊C8×C37C2211yescharacteristic
27C2×D4×C37—21no—
28C2×D4×C37D411yescharacteristic
29C22×C4×C37—21no—
30C22×C4×C37C2311yescharacteristic
31C22×Dic37—21no—
32C22×Dic37—21no—
33C22×Dic37D411yescharacteristic
34C22×Dic37D411yescharacteristic
35C2×Dic74D411yescharacteristic
36C2×C8×C37—21no—
37C4⋊C4×C37—21no—
38C4⋊C4×C37—21no—
39C4⋊C4×C37D411yescharacteristic
40C22⋊C4×C37—21no—
41C22⋊Dic37—21no—
42C22⋊Dic37—21no—
43C22⋊Dic37—21no—
44C22⋊Dic37—21no—
45C4⋊Dic37—21no—
46C4⋊Dic37D411yescharacteristic
47#10596936—21no—
48#10596936—21no—
49#10596936—21no—
50#10596936—21no—
51#10596936—21no—
52#10596936—42no—
53C4×Dic37—21no—
54C2×#64436—21no—
55C23×C37—21no—
56C23×C37C2×D411yescharacteristic
57D4×C37—41no—
58D4×C37—41no—
59D4×C37—41no—
60C2×C4×C37—21no—
61C2×C4×C37—41no—
62C2×C4×C37—41no—
63C2×C4×C37—41no—
64C2×C4×C37—41no—
65C2×C4×C37C2×D411yescharacteristic
66C2×C4×C37C2×D411yescharacteristic
67C2×Dic37—22no—
68C2×Dic37—21no—
69C2×Dic37—21no—
70C2×Dic37—21no—
71C2×Dic37—21no—
72C2×Dic37—21no—
73C2×Dic37—21no—
74C2×Dic37—41no—
75C2×Dic37—41no—
76C2×Dic37—41no—
77C2×Dic37—81no—
78Dic74—41no—
79C8×C37—41no—
80#64436—41no—
81C22×C37—21no—
82C22×C37—21no—
83C22×C37—41no—
84C22×C37—41no—
85C22×C37—41no—
86C22×C37#12011yescharacteristic
87C22×C37#13511yescharacteristic
88C22×C37AGL(1,ℤ/8)11yescharacteristic
89C4×C37—21no—
90C4×C37—21no—
91C4×C37—41no—
92C4×C37—81no—
93Dic37—42no—
94Dic37—41no—
95Dic37—41no—
96Dic37—41no—
97Dic37—41no—
98#1609—371nomaximal, Sylow
99C2×C37—21no—
100C2×C37—21no—
101C2×C37—81no—
102C2×C37#44911yescharacteristic
103C2×C37#45611yescharacteristic
104C2×C37#45811yescharacteristic
105#539—371no—
106#483—371no—
107#480D3711yescharacteristic
108#398—371no—
109#328—371no—
110#327—371no—
111#324—371no—
112C37#160911yescharacteristic, complemented, Sylow
113#126—741no—
114#125—741no—
115#123—741no—
116#123—741no—
117C22⋊Q8—371no—
118C22⋊Q8—741no—
119#121C2×D3711yescharacteristic
120C4×D4—741no—
121C2×C4⋊C4—371no—
122C2×C4⋊C4—741no—
123C2×C4⋊C4C2×D3711yescharacteristic
124#107—21no—
125#106—741no—
126#103—741no—
127#102—21no—
128C22⋊C8—371no—
129C22⋊C8C2×D3711yescharacteristic
130#95—371no—
131#95—741no—
132C2×Q8—371no—
133C2×D4—21no—
134C2×D4C22⋊D3711yescharacteristic
135C22×C4—21no—
136C22×C4—371no—
137C22×C4—371no—
138C22×C4—741no—
139C22×C4—741no—
140C22×C4C22×D3711yescharacteristic
141C2×C8—21no—
142C2×C8—741no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—371no—
146C4⋊C4—741no—
147C4⋊C4—741no—
148C4⋊C4—741no—
149C4⋊C4—741no—
150C4⋊C4—741no—
151C4⋊C4—741no—
152C4⋊C4—1482no—
153C4⋊C4C22⋊D3711yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—741no—
156C22⋊C4—741no—
157C22⋊C4—741no—
158C22⋊C4—741no—
159C42—741no—
160C23—21no—
161C23D4×D3711yescharacteristic
162Q8—1481no—
163D4—41no—
164D4—41no—
165D4—41no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—2961no—
172C2×C4—742no—
173C2×C4—741no—
174C2×C4—741no—
175C2×C4—741no—
176C2×C4—741no—
177C2×C4—741no—
178C2×C4—741no—
179C2×C4—1481no—
180C2×C4—1481no—
181C2×C4—1481no—
182C2×C4D4×D3711yescharacteristic
183C2×C4C2×C22⋊D3711yescharacteristic
184C8—41no—
185C8—1481no—
186C22—21no—
187C22—21no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22#1192450411yescharacteristic
192C22#1192455511yescharacteristic
193C22#1192456011yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—81no—
198C4—1482no—
199C4—1481no—
200C4—1481no—
201C4—1481no—
202C4—1481no—
203C2—21no—
204C2—21no—
205C2—81no—
206C2#1455767511yescharacteristic
207C2#1455771411yescharacteristic
208C2#1455772211yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#480C2
socleC22×C37#120
prime radical#121×C37C22
hypercenter#480D37
hypocenterC37#1609
LCSG ▷ C22×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #14557863C2semidirect
3. #14557464C2semidirect
4. #14557271C2semidirect
6. #14557258C2semidirect
112. C37#1609semidirect

Maximal subgroups

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

subgroupindex
#145581282
#145578632
#145574642
#145572712
#145572672
#145572582
C37×#4802
#160937