Finite Group Databasebeta

← #17993049

Subgroups — #17993049

Order 4736.

232 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 75 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#14558087C211yesmaximal, characteristic
2#14557555C211yesmaximal, characteristic
3C4×C8×D37C211yesmaximal, characteristic
4#14557265C211yesmaximal, characteristic, complemented
5Q8⋊#64436C211yesmaximal, characteristic, complemented
6#14557263C211yesmaximal, characteristic, complemented
7C37×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#10596929—21no—
9C2×C8×D37—21no—
10#11924535C411yescharacteristic
11#11924534C411yescharacteristic
12#11924526—21no—
13#11924516C411yescharacteristic
14#11924514—21no—
15#11924512C411yescharacteristic
16C4×Dic74—21no—
17C4×Dic74C2211yescharacteristic
18#11924493—21no—
19C42×D37C2211yescharacteristic
20C4⋊#64436C2211yescharacteristic
21#11924465—21no—
22C4×#64436C2211yescharacteristic
23C8×Dic37—21no—
24C4×Q8×C37C2211yescharacteristic
25C4⋊C8×C37C2211yescharacteristic
26C4×C8×C37C2211yescharacteristic
27C2×Q8×C37C2×C411yescharacteristic
28C2×C4×D37C2×C411yescharacteristic
29C2×C4×D37D411yescharacteristic
30C2×C4×D37D411yescharacteristic
31C2×Dic74—21no—
32C2×Dic74C2×C411yescharacteristic
33C2×C8×C37—21no—
34C2×C8×C37—21no—
35C4⋊C4×C37—21no—
36C4⋊C4×C37C2×C411yescharacteristic
37C42×C37—21no—
38C42×C37C2311yescharacteristic
39#10596938—21no—
40#10596938—21no—
41C4⋊Dic37—21no—
42C4⋊Dic37C2×C411yescharacteristic
43#10596936—21no—
44#10596936—21no—
45#10596936—21no—
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—
55C8×D37—24no—
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×Dic37—21no—
66C2×Dic37C22⋊C411yescharacteristic
67C2×Dic37C22⋊C411yescharacteristic
68C2×Dic37C22⋊C411yescharacteristic
69C4×D37—21no—
70C4×D37—21no—
71C4×D37—22no—
72C4×D37SD1612yes—
73C4×D37Q1612yes—
74Dic74—21no—
75Dic74—21no—
76Dic74—42no—
77C8×C37—22no—
78C8×C37—41no—
79#64436—22no—
80#64436—41no—
81C22×C37C2×C22⋊C411yescharacteristic
82C2×D37—21no—
83C2×D37—21no—
84C2×D37#10312yes—
85C4×C37—21no—
86C4×C37—41no—
87C4×C37—41no—
88C4×C37#13111yescharacteristic
89C4×C37#13111yescharacteristic
90C4×C37C2×SD1611yescharacteristic
91C4×C37C2×Q1611yescharacteristic
92Dic37—21no—
93Dic37—41no—
94Dic37—41no—
95Dic37#10312yes—
96Dic37#10412yes—
97#1493—371nomaximal, Sylow
98C2×C37#40811yescharacteristic
99C2×C37C2×#10311yescharacteristic
100C2×C37C2×#10411yescharacteristic
101D37—22no—
102#533—371no—
103#423—371no—
104C2×C4×C8—371no—
105Q8⋊C8—371no—
106Q8⋊C8—371no—
107Q8⋊C8—371no—
108Q8⋊C8D3711yescharacteristic, complemented
109C37#149311yescharacteristic, complemented, Sylow
110C2×M16—741no—
111C22×C8—741no—
112C4⋊Q8—371no—
113C4⋊Q8—371no—
114#125—741no—
115C22⋊Q8—371no—
116C22⋊Q8—371no—
117C22⋊Q8—741no—
118C4×Q8—371no—
119C4×Q8—741no—
120C4×Q8C2×D3711yescharacteristic
121#117—741no—
122C2×C42—371no—
123C4⋊C8—371no—
124C4⋊C8—741no—
125C4⋊C8C2×D3711yescharacteristic
126C4×C8—371no—
127C4×C8—741no—
128C4×C8C2×D3711yescharacteristic
129C2×Q8—371no—
130C2×Q8—741no—
131C2×Q8C4×D3711yescharacteristic
132C22×C4—371no—
133C22×C4—371no—
134C22×C4—371no—
135M16—1482no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—744no—
139C2×C8—741no—
140C2×C8—741no—
141C4⋊C4—21no—
142C4⋊C4—371no—
143C4⋊C4—741no—
144C4⋊C4—741no—
145C4⋊C4—741no—
146C4⋊C4—741no—
147C4⋊C4—741no—
148C4⋊C4—741no—
149C4⋊C4C4×D3711yescharacteristic
150C22⋊C4—741no—
151C22⋊C4—741no—
152C42—21no—
153C42—371no—
154C42—371no—
155C42—371no—
156C42—741no—
157C42C22×D3711yescharacteristic
158C23—371no—
159Q8—21no—
160Q8—21no—
161Q8—741no—
162Q8—741no—
163Q8—1482no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—371no—
167C2×C4—371no—
168C2×C4—372no—
169C2×C4—372no—
170C2×C4—371no—
171C2×C4—742no—
172C2×C4—741no—
173C2×C4—741no—
174C2×C4—741no—
175C2×C4—741no—
176C2×C4C2×C4×D3711yescharacteristic
177C2×C4D4×D3711yescharacteristic
178C2×C4D4×D3711yescharacteristic
179C8—22no—
180C8—41no—
181C8—742no—
182C8—1481no—
183C22—372no—
184C22—741no—
185C22—741no—
186C22C22⋊C4×D3711yescharacteristic
187C4—21no—
188C4—41no—
189C4—41no—
190C4—372no—
191C4—372no—
192C4—741no—
193C4—1481no—
194C4—1481no—
195C4#1192454211yescharacteristic
196C4#1192454411yescharacteristic
197C4SD16×D3711yescharacteristic
198C4Q16×D3711yescharacteristic
199C2—742no—
200C2#1455749811yescharacteristic
201C2#103×D3711yescharacteristic
202C2#104×D3711yescharacteristic
subgroupG/H
centerC2×C4D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×Q8⋊C8C2
socleC22×C37C2×C22⋊C4
prime radicalC22×D37C22⋊C4
cosocleC42×C37C23
hypercenterQ8⋊C8D37
hypocenterC37#1493
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
4. #14557265C2semidirect
5. Q8⋊#64436C2semidirect
6. #14557263C2semidirect
7. C37×Q8⋊C8C2semidirect
108. Q8⋊C8D37semidirect
109. C37#1493semidirect

Maximal subgroups

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

subgroupindex
#145580872
#145575552
C4×C8×D372
#145572652
Q8⋊#644362
#145572632
C37×Q8⋊C82
#149337