Finite Group Databasebeta

← #17993055

Subgroups — #17993055

Order 4736.

230 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 67 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#14558070C211yesmaximal, characteristic
2#14557589C211yesmaximal, characteristic, complemented
3C4×C8×D37C211yesmaximal, characteristic, complemented
4Q8⋊#64436C211yesmaximal, characteristic, complemented
5#14557262C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic, complemented
7C37×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×C8×D37—21no—
9#11924531—21no—
10#11924527C411yescharacteristic
11#11924525C411yescharacteristic
12#11924521—21no—
13#11924512C411yescharacteristic
14#11924511C411yescharacteristic
15C4×D148—21no—
16C4×D148C2211yescharacteristic
17#11924493—21no—
18C42×D37C2211yescharacteristic
19C4⋊#64436C2211yescharacteristic
20#11924448—21no—
21#11924446—21no—
22C4×#64436C2211yescharacteristic
23C8×Dic37—21no—
24C4×Q8×C37C2211yescharacteristic
25C4⋊C8×C37C2211yescharacteristic
26C4×C8×C37C2211yescharacteristic
27C2×Q8×C37C2×C411yescharacteristic
28C2×D148—21no—
29C2×D148C2×C411yescharacteristic
30C2×C4×D37—21no—
31C2×C4×D37C2×C411yescharacteristic
32C2×C4×D37D411yescharacteristic
33C2×C4×D37D411yescharacteristic
34C2×C8×C37—21no—
35C2×C8×C37—21no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37C2×C411yescharacteristic
38C42×C37—21no—
39C42×C37C2311yescharacteristic
40#10596938—21no—
41#10596938—21no—
42#10596938—21no—
43#10596938—21no—
44#10596938—21no—
45C4⋊Dic37—21no—
46C4⋊Dic37C2×C411yescharacteristic
47#10596936—21no—
48#10596936—21no—
49C4×Dic37C2×C411yescharacteristic
50C4×Dic37D411yescharacteristic
51C4×Dic37D411yescharacteristic
52C2×#64436—21no—
53C2×#64436—21no—
54C8×D37—24no—
55C22×D37—21no—
56C22×D37C22⋊C411yescharacteristic
57Q8×C37—21no—
58Q8×C37—21no—
59C2×C4×C37—21no—
60C2×C4×C37—21no—
61C2×C4×C37C22×C411yescharacteristic
62C2×C4×C37C2×D411yescharacteristic
63C2×C4×C37C2×D411yescharacteristic
64C2×Dic37—21no—
65C2×Dic37C22⋊C411yescharacteristic
66C2×Dic37C22⋊C411yescharacteristic
67C2×Dic37C22⋊C411yescharacteristic
68D148—21no—
69D148—21no—
70D148—42no—
71C4×D37—22no—
72C4×D37—21no—
73C4×D37—21no—
74C4×D37—21no—
75C4×D37—21no—
76C4×D37—41no—
77C4×D37—41no—
78C8×C37—22no—
79C8×C37—41no—
80#64436—22no—
81#64436—41no—
82C22×C37C2×C22⋊C411yescharacteristic
83C2×D37—21no—
84C2×D37—21no—
85C2×D37—41no—
86C2×D37—41no—
87C2×D37—41no—
88C2×D37#10412yes—
89C4×C37—21no—
90C4×C37—41no—
91C4×C37—41no—
92C4×C37#13111yescharacteristic
93C4×C37#13111yescharacteristic
94C4×C37#13511yescharacteristic
95C4×C37#13511yescharacteristic
96Dic37—21no—
97Dic37—21no—
98Dic37—21no—
99Dic37—41no—
100#1494—371nomaximal, Sylow
101C2×C37#40811yescharacteristic
102C2×C37#41611yescharacteristic
103C2×C37C2×#10411yescharacteristic
104D37—22no—
105D37—81no—
106#529—371no—
107#432—371no—
108C2×C4×C8—371no—
109Q8⋊C8—371no—
110Q8⋊C8D3711yescharacteristic, complemented
111D4⋊C8—371no—
112D4⋊C8—371no—
113C37#149411yescharacteristic, complemented, Sylow
114C22×C8—741no—
115#126—741no—
116#125—371no—
117#124—371no—
118#123—741no—
119C22⋊Q8—371no—
120#121—371no—
121C4×Q8C2×D3711yescharacteristic
122C4×D4—371no—
123C4×D4—741no—
124#117—741no—
125C2×C42—371no—
126C4⋊C8—371no—
127C4⋊C8C2×D3711yescharacteristic
128C22⋊C8—741no—
129#97—741no—
130C4×C8—371no—
131C4×C8—741no—
132C4×C8C2×D3711yescharacteristic
133C2×Q8C4×D3711yescharacteristic
134C2×D4—371no—
135C2×D4—741no—
136C22×C4—371no—
137C22×C4—371no—
138C22×C4—371no—
139C22×C4—741no—
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—744no—
143C2×C8—741no—
144C2×C8—741no—
145C4⋊C4—21no—
146C4⋊C4—371no—
147C4⋊C4—741no—
148C4⋊C4—741no—
149C4⋊C4—741no—
150C4⋊C4C4×D3711yescharacteristic
151C22⋊C4—741no—
152C22⋊C4—741no—
153C22⋊C4—741no—
154C22⋊C4—741no—
155C22⋊C4—741no—
156C42—21no—
157C42—371no—
158C42—371no—
159C42—371no—
160C42C22×D3711yescharacteristic
161C23—371no—
162C23—741no—
163Q8—21no—
164Q8—21no—
165D4—741no—
166D4—741no—
167D4—1482no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—371no—
171C2×C4—371no—
172C2×C4—371no—
173C2×C4—742no—
174C2×C4—741no—
175C2×C4—741no—
176C2×C4—741no—
177C2×C4—741no—
178C2×C4—741no—
179C2×C4—1481no—
180C2×C4—1481no—
181C2×C4C2×C4×D3711yescharacteristic
182C2×C4D4×D3711yescharacteristic
183C2×C4D4×D3711yescharacteristic
184C8—22no—
185C8—41no—
186C8—742no—
187C8—1481no—
188C22—372no—
189C22—741no—
190C22—741no—
191C22—1481no—
192C22—1481no—
193C22—1481no—
194C22C22⋊C4×D3711yescharacteristic
195C4—21no—
196C4—41no—
197C4—41no—
198C4—741no—
199C4—741no—
200C4—741no—
201C4—1481no—
202C4#1192454211yescharacteristic
203C4#1192454411yescharacteristic
204C4#1192455711yescharacteristic
205C4#1192455911yescharacteristic
206C2—2961no—
207C2—742no—
208C2#1455749811yescharacteristic
209C2#1455752811yescharacteristic
210C2#104×D3711yescharacteristic
subgroupG/H
centerC2×C4D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×Q8⋊C8C2
socleC22×C37C2×C22⋊C4
prime radical#11924511C4
cosocleC42×C37C23
hypercenterQ8⋊C8D37
hypocenterC37#1494
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #14557589C2semidirect
3. C4×C8×D37C2semidirect
4. Q8⋊#64436C2semidirect
5. #14557262C2semidirect
6. #14557260C2semidirect
7. C37×Q8⋊C8C2semidirect
110. Q8⋊C8D37semidirect
113. C37#1494semidirect

Maximal subgroups

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

subgroupindex
#145580702
#145575892
C4×C8×D372
Q8⋊#644362
#145572622
#145572602
C37×Q8⋊C82
#149437