Finite Group Databasebeta

← #17993921

Subgroups — #17993921

Order 4736.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#14558277C211yesmaximal, characteristic
2#14557902C211yesmaximal, characteristic, complemented
3#14557893C211yesmaximal, characteristic, complemented
4#14557892C211yesmaximal, characteristic, complemented
5#14557274C211yesmaximal, characteristic, complemented
6#14557272C211yesmaximal, characteristic, complemented
7C37×#329C211yesmaximal, characteristic, complemented
8#11924536C2211yescharacteristic
9#11924528C2211yescharacteristic
10#11924524C2211yescharacteristic
11#11924520—21no—
12#11924518—21no—
13#11924513—21no—
14#11924512—21no—
15#11924509—21no—
16#11924508—21no—
17#11924461—21no—
18#11924461—21no—
19#11924461—21no—
20#11924460—21no—
21#11924458—21no—
22#11924457—21no—
23#11924447C2211yescharacteristic
24#124×C37C2211yescharacteristic
25#97×C37C2211yescharacteristic
26#97×C37C2211yescharacteristic
27C2×Q8×C37D411yescharacteristic
28C2×D4×C37D411yescharacteristic
29C2×C22⋊D37—21no—
30C2×C22⋊D37—21no—
31C22×Dic37—21no—
32C2×D148D411yescharacteristic
33C2×C4×D37—21no—
34C2×Dic74—21no—
35C2×Dic74D411yescharacteristic
36C2×C8×C37—21no—
37C2×C8×C37—21no—
38C22⋊C4×C37—21no—
39C22⋊C4×C37—21no—
40C42×C37C2311yescharacteristic
41C22⋊Dic37—21no—
42#10596938—21no—
43#10596938—21no—
44#10596938—21no—
45C4⋊Dic37—21no—
46C4⋊Dic37—21no—
47C4⋊Dic37—21no—
48C4⋊Dic37D411yescharacteristic
49C4⋊Dic37D411yescharacteristic
50#10596936—21no—
51#10596936—21no—
52#10596936—21no—
53C2×#64436—21no—
54C23×C37—21no—
55C22×D37—21no—
56Q8×C37—41no—
57D4×C37—41no—
58C2×C4×C37—21no—
59C2×C4×C37C2×D411yescharacteristic
60C2×C4×C37C2×D411yescharacteristic
61C2×C4×C37C2×D411yescharacteristic
62C22⋊D37—81no—
63C22⋊D37—81no—
64C2×Dic37—21no—
65C2×Dic37—21no—
66C2×Dic37—21no—
67C2×Dic37—41no—
68C2×Dic37—81no—
69D148—41no—
70C4×D37—81no—
71Dic74—41no—
72Dic74—42no—
73C8×C37—41no—
74C8×C37—41no—
75#64436—41no—
76C22×C37—41no—
77C22×C37—41no—
78C22×C37—41no—
79C22×C37#12011yescharacteristic
80C2×D37—41no—
81C2×D37—41no—
82C2×D37—41no—
83C4×C37—21no—
84C4×C37—21no—
85C4×C37—21no—
86C4×C37—41no—
87Dic37—41no—
88Dic37—41no—
89Dic37—41no—
90Dic37—81no—
91#1662—371nomaximal, Sylow
92C2×C37—81no—
93C2×C37#45411yescharacteristic
94C2×C37#45511yescharacteristic
95C2×C37#45511yescharacteristic
96D37—81no—
97#562—371no—
98#491—371no—
99#489—371no—
100#489—371no—
101#330—371no—
102#329—371no—
103#329D3711yescharacteristic, complemented
104C37#166211yescharacteristic, complemented, Sylow
105C4⋊Q8—371no—
106#125—371no—
107#124—371no—
108#124C2×D3711yescharacteristic
109#123—741no—
110#123—741no—
111C22⋊Q8—741no—
112C22⋊Q8—741no—
113#121—741no—
114#121—741no—
115#103—741no—
116#103—741no—
117#103—741no—
118#103—741no—
119#102—741no—
120#102—741no—
121#97—371no—
122#97C2×D3711yescharacteristic
123#97C2×D3711yescharacteristic
124C2×Q8—371no—
125C2×Q8—741no—
126C2×Q8D14811yescharacteristic
127C2×D4—371no—
128C2×D4—741no—
129C2×D4—741no—
130C2×D4D14811yescharacteristic
131C22×C4—741no—
132C22×C4—741no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—741no—
136C4⋊C4—371no—
137C4⋊C4—371no—
138C4⋊C4—741no—
139C4⋊C4—741no—
140C4⋊C4—741no—
141C4⋊C4—741no—
142C4⋊C4—741no—
143C4⋊C4—741no—
144C22⋊C4—21no—
145C22⋊C4—21no—
146C22⋊C4—741no—
147C22⋊C4—741no—
148C22⋊C4—741no—
149C22⋊C4—741no—
150C42C22×D3711yescharacteristic
151C23—21no—
152C23—741no—
153Q8—41no—
154Q8—1482no—
155Q8—1481no—
156D4—41no—
157D4—2961no—
158D4—2961no—
159D4—1481no—
160C2×C4—21no—
161C2×C4—2961no—
162C2×C4—2961no—
163C2×C4—741no—
164C2×C4—741no—
165C2×C4—741no—
166C2×C4—1481no—
167C2×C4C2×D14811yescharacteristic
168C2×C4D4×D3711yescharacteristic
169C2×C4D4×D3711yescharacteristic
170C8—41no—
171C8—41no—
172C8—1481no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22—1481no—
177C22—1481no—
178C22—1481no—
179C22#1192450611yescharacteristic
180C4—21no—
181C4—21no—
182C4—21no—
183C4—41no—
184C4—2961no—
185C4—1481no—
186C4—1481no—
187C4—1481no—
188C2—81no—
189C2—2961no—
190C2#1455770711yescharacteristic
191C2#1455771211yescharacteristic
192C2#1455771311yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#329C2
socleC22×C37#120
prime radical#14558277C2
hypercenter#329D37
hypocenterC37#1662
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #14557902C2semidirect
3. #14557893C2semidirect
4. #14557892C2semidirect
5. #14557274C2semidirect
6. #14557272C2semidirect
7. C37×#329C2semidirect
103. #329D37semidirect
104. C37#1662semidirect

Maximal subgroups

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

subgroupindex
#145582772
#145579022
#145578932
#145578922
#145572742
#145572722
C37×#3292
#166237