Finite Group Databasebeta

← #17993045

Subgroups — #17993045

Order 4736.

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

normal subgroups only

This group has 276 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#14558080C211yesmaximal, characteristic
2#14557555C211yesmaximal, characteristic, complemented
3C4×C8×D37C211yesmaximal, characteristic, complemented
4#14557262C211yesmaximal, characteristic, complemented
5D4⋊#64436C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic, complemented
7C37×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#10596962—21no—
9C2×#10596929—21no—
10C2×C8×D37—21no—
11#11924535C411yescharacteristic
12#11924532C411yescharacteristic
13#11924522—21no—
14#11924511C411yescharacteristic
15#11924509—21no—
16#11924507C411yescharacteristic
17C4×D148C2211yescharacteristic
18C4×C22⋊D37—21no—
19C42×D37C2211yescharacteristic
20C4⋊#64436C2211yescharacteristic
21#11924465—21no—
22C4×#64436C2211yescharacteristic
23C8×Dic37—21no—
24C4×D4×C37C2211yescharacteristic
25C4⋊C8×C37C2211yescharacteristic
26C4×C8×C37C2211yescharacteristic
27C2×D4×C37C2×C411yescharacteristic
28C22×C4×C37—21no—
29C2×C22⋊D37—21no—
30C2×C22⋊D37—21no—
31C2×C22⋊D37—21no—
32#10596962—42no—
33#10596962—42no—
34C2×D148—21no—
35C2×D148C2×C411yescharacteristic
36C2×C4×D37—21no—
37C2×C4×D37C2×C411yescharacteristic
38C2×C4×D37D411yescharacteristic
39C2×C4×D37D411yescharacteristic
40C2×Dic74—21no—
41C2×C8×C37—21no—
42C2×C8×C37—21no—
43C4⋊C4×C37C2×C411yescharacteristic
44C22⋊C4×C37—21no—
45C42×C37C2311yescharacteristic
46C22⋊Dic37—21no—
47#10596938—21no—
48#10596938—21no—
49C4⋊Dic37C2×C411yescharacteristic
50#10596936—21no—
51C4×Dic37C2×C411yescharacteristic
52C4×Dic37D411yescharacteristic
53C4×Dic37D411yescharacteristic
54C2×#64436—21no—
55C2×#64436—21no—
56#10596929—42no—
57C8×D37—24no—
58C23×C37—21no—
59C22×D37—21no—
60C22×D37C22⋊C411yescharacteristic
61D4×C37—21no—
62D4×C37—21no—
63C2×C4×C37—21no—
64C2×C4×C37—41no—
65C2×C4×C37—41no—
66C2×C4×C37C22×C411yescharacteristic
67C2×C4×C37C2×D411yescharacteristic
68C2×C4×C37C2×D411yescharacteristic
69C22⋊D37—42no—
70C22⋊D37—42no—
71C22⋊D37—42no—
72C2×Dic37—21no—
73C2×Dic37C22⋊C411yescharacteristic
74C2×Dic37C22⋊C411yescharacteristic
75C2×Dic37C22⋊C411yescharacteristic
76D148—21no—
77D148—21no—
78D148—42no—
79C4×D37—21no—
80C4×D37—21no—
81C4×D37—22no—
82C4×D37—41no—
83C4×D37—41no—
84C4×D37D812yes—
85C4×D37SD1612yes—
86Dic74—42no—
87C8×C37—22no—
88C8×C37—41no—
89#64436—22no—
90#64436—41no—
91C22×C37—41no—
92C22×C37—41no—
93C22×C37—41no—
94C22×C37C2×C22⋊C411yescharacteristic
95C2×D37—21no—
96C2×D37—21no—
97C2×D37—41no—
98C2×D37—41no—
99C2×D37—41no—
100C2×D37#10212yes—
101C4×C37—21no—
102C4×C37—41no—
103C4×C37#13111yescharacteristic
104C4×C37#13111yescharacteristic
105C4×C37C2×D811yescharacteristic
106C4×C37C2×SD1611yescharacteristic
107Dic37—21no—
108Dic37—41no—
109Dic37#10212yes—
110Dic37#10412yes—
111#1492—371nomaximal, Sylow
112C2×C37—81no—
113C2×C37#40811yescharacteristic
114C2×C37C2×#10211yescharacteristic
115C2×C37C2×#10411yescharacteristic
116D37—22no—
117D37—81no—
118#532—371no—
119#423—371no—
120C2×C4×C8—371no—
121D4⋊C8—371no—
122D4⋊C8—371no—
123D4⋊C8—371no—
124D4⋊C8D3711yescharacteristic, complemented
125C37#149211yescharacteristic, complemented, Sylow
126C2×#41—741no—
127C2×M16—741no—
128C22×C8—741no—
129C4⋊Q8—371no—
130#127—371no—
131#124—741no—
132#121—371no—
133#121—371no—
134#121—741no—
135C4×D4—371no—
136C4×D4—741no—
137C4×D4C2×D3711yescharacteristic
138C2×C42—371no—
139C4⋊C8—371no—
140C4⋊C8—741no—
141C4⋊C8C2×D3711yescharacteristic
142C4×C8—371no—
143C4×C8—741no—
144C4×C8C2×D3711yescharacteristic
145#41—1482no—
146#41—1482no—
147C2×Q8—741no—
148C2×D4—371no—
149C2×D4—741no—
150C2×D4—741no—
151C2×D4—741no—
152C2×D4—741no—
153C2×D4C4×D3711yescharacteristic
154C22×C4—21no—
155C22×C4—371no—
156C22×C4—371no—
157C22×C4—371no—
158C22×C4—741no—
159M16—1482no—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—744no—
163C2×C8—741no—
164C2×C8—741no—
165C4⋊C4—371no—
166C4⋊C4—741no—
167C4⋊C4C4×D3711yescharacteristic
168C22⋊C4—21no—
169C22⋊C4—741no—
170C22⋊C4—741no—
171C22⋊C4—741no—
172C42—371no—
173C42—371no—
174C42—371no—
175C42C22×D3711yescharacteristic
176C23—21no—
177C23—371no—
178C23—741no—
179Q8—1482no—
180D4—21no—
181D4—21no—
182D4—741no—
183D4—741no—
184D4—1482no—
185D4—1482no—
186D4—1482no—
187D4—1482no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—371no—
192C2×C4—371no—
193C2×C4—372no—
194C2×C4—372no—
195C2×C4—371no—
196C2×C4—742no—
197C2×C4—741no—
198C2×C4—741no—
199C2×C4—741no—
200C2×C4—1481no—
201C2×C4—1481no—
202C2×C4C2×C4×D3711yescharacteristic
203C2×C4D4×D3711yescharacteristic
204C2×C4D4×D3711yescharacteristic
205C8—22no—
206C8—41no—
207C8—742no—
208C8—1481no—
209C22—41no—
210C22—41no—
211C22—41no—
212C22—372no—
213C22—741no—
214C22—741no—
215C22—1481no—
216C22—1481no—
217C22—1481no—
218C22C22⋊C4×D3711yescharacteristic
219C4—21no—
220C4—41no—
221C4—372no—
222C4—372no—
223C4—741no—
224C4—1481no—
225C4#1192454211yescharacteristic
226C4#1192454411yescharacteristic
227C4D8×D3711yescharacteristic
228C4SD16×D3711yescharacteristic
229C2—81no—
230C2—2961no—
231C2—742no—
232C2#1455749811yescharacteristic
233C2#102×D3711yescharacteristic
234C2#104×D3711yescharacteristic
subgroupG/H
centerC2×C4D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×D4⋊C8C2
socleC22×C37C2×C22⋊C4
prime radical#14558080C2
cosocleC42×C37C23
hypercenterD4⋊C8D37
hypocenterC37#1492
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. #14557555C2semidirect
3. C4×C8×D37C2semidirect
4. #14557262C2semidirect
5. D4⋊#64436C2semidirect
6. #14557260C2semidirect
7. C37×D4⋊C8C2semidirect
124. D4⋊C8D37semidirect
125. C37#1492semidirect

Maximal subgroups

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

subgroupindex
#145580802
#145575552
C4×C8×D372
#145572622
D4⋊#644362
#145572602
C37×D4⋊C82
#149237