Finite Group Databasebeta

← #17993058

Subgroups — #17993058

Order 4736.

216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 65 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#14558065C211yesmaximal, characteristic
2#14557584C211yesmaximal, characteristic, complemented
3#14557555C211yesmaximal, characteristic, complemented
4#14557265C211yesmaximal, characteristic, complemented
5#14557263C211yesmaximal, characteristic, complemented
6D4⋊#64436C211yesmaximal, characteristic, complemented
7C37×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#10596929—21no—
9#11924529—21no—
10#11924527C411yescharacteristic
11#11924523C411yescharacteristic
12#11924518—21no—
13#11924516C411yescharacteristic
14#11924507C411yescharacteristic
15C4×Dic74C2211yescharacteristic
16C4×C22⋊D37—21no—
17#11924495—21no—
18C42×D37C2211yescharacteristic
19C4⋊#64436C2211yescharacteristic
20#11924465—21no—
21#11924465—21no—
22#11924448—21no—
23C4×#64436C2211yescharacteristic
24C4×D4×C37C2211yescharacteristic
25C4⋊C8×C37C2211yescharacteristic
26C4×C8×C37C2211yescharacteristic
27C2×D4×C37C2×C411yescharacteristic
28C22×C4×C37—21no—
29C2×C22⋊D37—21no—
30C2×C4×D37C2×C411yescharacteristic
31C2×C4×D37D411yescharacteristic
32C2×C4×D37D411yescharacteristic
33C2×Dic74C2×C411yescharacteristic
34C2×C8×C37—21no—
35C2×C8×C37—21no—
36C4⋊C4×C37C2×C411yescharacteristic
37C22⋊C4×C37—21no—
38C42×C37C2311yescharacteristic
39C22⋊Dic37—21no—
40C22⋊Dic37—21no—
41C22⋊Dic37—21no—
42#10596938—21no—
43C4⋊Dic37—21no—
44C4⋊Dic37—21no—
45C4⋊Dic37C2×C411yescharacteristic
46#10596936—21no—
47#10596936—21no—
48C4×Dic37—21no—
49C4×Dic37C2×C411yescharacteristic
50C4×Dic37D411yescharacteristic
51C4×Dic37D411yescharacteristic
52C2×#64436—21no—
53C2×#64436—21no—
54#10596929—42no—
55C23×C37—21no—
56C22×D37C22⋊C411yescharacteristic
57D4×C37—21no—
58D4×C37—21no—
59C2×C4×C37—21no—
60C2×C4×C37—41no—
61C2×C4×C37—41no—
62C2×C4×C37C22×C411yescharacteristic
63C2×C4×C37C2×D411yescharacteristic
64C2×C4×C37C2×D411yescharacteristic
65C22⋊D37—42no—
66C2×Dic37—21no—
67C2×Dic37—21no—
68C2×Dic37C22⋊C411yescharacteristic
69C2×Dic37C22⋊C411yescharacteristic
70C2×Dic37C22⋊C411yescharacteristic
71C4×D37—21no—
72C4×D37—21no—
73C4×D37—21no—
74C4×D37—21no—
75C4×D37—41no—
76Dic74—21no—
77Dic74—21no—
78C8×C37—41no—
79C8×C37—41no—
80#64436—41no—
81#64436—41no—
82C22×C37—41no—
83C22×C37—41no—
84C22×C37—41no—
85C22×C37C2×C22⋊C411yescharacteristic
86C2×D37—21no—
87C2×D37—21no—
88C2×D37—21no—
89C4×C37—21no—
90C4×C37—41no—
91C4×C37#13111yescharacteristic
92C4×C37#13111yescharacteristic
93C4×C37AGL(1,ℤ/8)11yescharacteristic
94C4×C37#13711yescharacteristic
95Dic37—21no—
96Dic37—21no—
97Dic37—21no—
98Dic37—41no—
99Dic37—41no—
100#1495—371nomaximal, Sylow
101C2×C37—81no—
102C2×C37#40811yescharacteristic
103C2×C37#41711yescharacteristic
104C2×C37#42111yescharacteristic
105D37—41no—
106#529—371no—
107#431—371no—
108#423—371no—
109Q8⋊C8—371no—
110Q8⋊C8—371no—
111D4⋊C8—371no—
112D4⋊C8D3711yescharacteristic, complemented
113C37#149511yescharacteristic, complemented, Sylow
114C2×M16—741no—
115#126—741no—
116#125—371no—
117#124—371no—
118#123—741no—
119C22⋊Q8—371no—
120#121—371no—
121C4×Q8—371no—
122C4×D4—741no—
123C4×D4C2×D3711yescharacteristic
124#117—741no—
125C2×C42—371no—
126C4⋊C8—371no—
127C4⋊C8—741no—
128C4⋊C8—741no—
129C4⋊C8C2×D3711yescharacteristic
130C22⋊C8—741no—
131C4×C8—371no—
132C4×C8C2×D3711yescharacteristic
133C2×Q8—371no—
134C2×D4—741no—
135C2×D4C4×D3711yescharacteristic
136C22×C4—21no—
137C22×C4—371no—
138C22×C4—371no—
139C22×C4—371no—
140M16—1482no—
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—741no—
144C2×C8—741no—
145C4⋊C4—371no—
146C4⋊C4—741no—
147C4⋊C4—741no—
148C4⋊C4—741no—
149C4⋊C4—741no—
150C4⋊C4C4×D3711yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—741no—
153C22⋊C4—741no—
154C22⋊C4—741no—
155C22⋊C4—741no—
156C42—371no—
157C42—371no—
158C42—371no—
159C42—741no—
160C42C22×D3711yescharacteristic
161C23—21no—
162C23—371no—
163Q8—741no—
164Q8—741no—
165D4—21no—
166D4—21no—
167D4—1482no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—371no—
172C2×C4—371no—
173C2×C4—371no—
174C2×C4—741no—
175C2×C4—741no—
176C2×C4—741no—
177C2×C4—741no—
178C2×C4—741no—
179C2×C4—741no—
180C2×C4—1481no—
181C2×C4C2×C4×D3711yescharacteristic
182C2×C4D4×D3711yescharacteristic
183C2×C4D4×D3711yescharacteristic
184C8—41no—
185C8—41no—
186C8—1481no—
187C8—1481no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22—741no—
192C22—741no—
193C22—741no—
194C22C22⋊C4×D3711yescharacteristic
195C4—21no—
196C4—41no—
197C4—741no—
198C4—741no—
199C4—741no—
200C4—1481no—
201C4—1481no—
202C4#1192454211yescharacteristic
203C4#1192454411yescharacteristic
204C4#1192456011yescharacteristic
205C4#1192456511yescharacteristic
206C2—81no—
207C2—1481no—
208C2#1455749811yescharacteristic
209C2#1455753111yescharacteristic
210C2#1455754811yescharacteristic
subgroupG/H
centerC2×C4D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×D4⋊C8C2
socleC22×C37C2×C22⋊C4
prime radical#11924507C4
cosocleC42×C37C23
hypercenterD4⋊C8D37
hypocenterC37#1495
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #14557584C2semidirect
3. #14557555C2semidirect
4. #14557265C2semidirect
5. #14557263C2semidirect
6. D4⋊#64436C2semidirect
7. C37×D4⋊C8C2semidirect
112. D4⋊C8D37semidirect
113. C37#1495semidirect

Maximal subgroups

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

subgroupindex
#145580652
#145575842
#145575552
#145572652
#145572632
D4⋊#644362
C37×D4⋊C82
#149537