Finite Group Databasebeta

← #17993154

Subgroups — #17993154

Order 4736.

264 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 69 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#14558078C211yesmaximal, characteristic
2#14557583C211yesmaximal, characteristic, complemented
3#14557397C211yesmaximal, characteristic, complemented
4#14557268C211yesmaximal, characteristic, complemented
5#14557267C211yesmaximal, characteristic, complemented
6#14557266C211yesmaximal, characteristic, complemented
7C37×#327C211yesmaximal, characteristic, complemented
8C2×#10596964—21no—
9#11924535C411yescharacteristic, complemented
10#11924532C411yescharacteristic, complemented
11#11924522—21no—
12#11924510C2211yescharacteristic
13#11924508—21no—
14D4×Dic37C411yescharacteristic, complemented
15#11924498C411yescharacteristic, complemented
16#11924496—21no—
17C2×#10596936—21no—
18C2×C4×Dic37C2211yescharacteristic
19#11924465—21no—
20C22⋊#64436C2211yescharacteristic
21C8×Dic37—21no—
22#11924443—21no—
23#11924443C2211yescharacteristic
24#121×C37C2211yescharacteristic
25C22⋊C8×C37C2211yescharacteristic
26#95×C37C2211yescharacteristic
27C2×D4×C37—21no—
28C2×D4×C37C2×C411yescharacteristic
29C22×C4×C37—21no—
30C22×C4×C37C2311yescharacteristic
31C2×C22⋊D37—21no—
32C2×C22⋊D37—21no—
33C2×C22⋊D37—21no—
34C22×Dic37—21no—
35C22×Dic37—21no—
36C22×Dic37D411yescharacteristic
37C22×Dic37D411yescharacteristic
38#10596964—42no—
39#10596964—42no—
40C2×D148C2×C411yescharacteristic
41C2×C4×D37—21no—
42C2×Dic74—21no—
43C2×C8×C37—21no—
44C4⋊C4×C37C2×C411yescharacteristic
45C22⋊C4×C37—21no—
46C22⋊Dic37—21no—
47#10596938—21no—
48#10596938—21no—
49C4⋊Dic37C2×C411yescharacteristic
50#10596936—21no—
51#10596936—42no—
52C4×Dic37C2×C411yescharacteristic
53C4×Dic37C2×C411yescharacteristic
54C4×Dic37D411yescharacteristic
55C4×Dic37D411yescharacteristic
56C2×#64436—21no—
57C23×C37—21no—
58C23×C37C2×D411yescharacteristic
59C22×D37—21no—
60D4×C37—41no—
61D4×C37—41no—
62D4×C37—41no—
63C2×C4×C37—21no—
64C2×C4×C37—41no—
65C2×C4×C37—41no—
66C2×C4×C37—41no—
67C2×C4×C37—41no—
68C2×C4×C37C22×C411yescharacteristic
69C2×C4×C37C2×D411yescharacteristic
70C22⋊D37—42no—
71C22⋊D37—41no—
72C22⋊D37—41no—
73C22⋊D37—42no—
74C2×Dic37—21no—
75C2×Dic37—41no—
76C2×Dic37—42no—
77C2×Dic37—41no—
78C2×Dic37—41no—
79C2×Dic37—41no—
80C2×Dic37C22⋊C411yescharacteristic
81C2×Dic37C22⋊C411yescharacteristic
82C2×Dic37C22⋊C411yescharacteristic
83C2×Dic37C22⋊C411yescharacteristic
84C2×Dic37D812yes—
85C2×Dic37SD1612yes—
86D148—41no—
87C4×D37—42no—
88Dic74—42no—
89C8×C37—41no—
90#64436—41no—
91C22×C37—21no—
92C22×C37—21no—
93C22×C37—41no—
94C22×C37—41no—
95C22×C37—41no—
96C22×C37C2×C22⋊C411yescharacteristic
97C22×C37C2×D811yescharacteristic
98C22×C37C2×SD1611yescharacteristic
99C2×D37—41no—
100C2×D37—41no—
101C2×D37—41no—
102C4×C37—21no—
103C4×C37—21no—
104C4×C37—41no—
105C4×C37—81no—
106Dic37—21no—
107Dic37—21no—
108Dic37—41no—
109Dic37—81no—
110Dic37#10212yes—
111Dic37#10212yes—
112#1517—371nomaximal, Sylow
113C2×C37—21no—
114C2×C37—21no—
115C2×C37—81no—
116C2×C37#41011yescharacteristic
117C2×C37C2×#10211yescharacteristic
118C2×C37#42111yescharacteristic
119D37—81no—
120#532—371no—
121#431—371no—
122#382—371no—
123#327—371no—
124#327—371no—
125#327—371no—
126#327D3711yescharacteristic, complemented
127C37#151711yescharacteristic, complemented, Sylow
128C2×#41—741no—
129C4⋊Q8—371no—
130#127—371no—
131#124—741no—
132#121—371no—
133#121—741no—
134#121C2×D3711yescharacteristic
135C4×D4—371no—
136C4×D4—371no—
137C4×D4—741no—
138C2×C4⋊C4—741no—
139C2×C42—371no—
140C4⋊C8—741no—
141C22⋊C8—371no—
142C22⋊C8C2×D3711yescharacteristic
143C4×C8—741no—
144#95—371no—
145#95—741no—
146#95C2×D3711yescharacteristic
147#41—1482no—
148#41—1482no—
149C2×Q8—741no—
150C2×D4—21no—
151C2×D4—371no—
152C2×D4—741no—
153C2×D4—741no—
154C2×D4—741no—
155C2×D4C4×D3711yescharacteristic
156C22×C4—21no—
157C22×C4—371no—
158C22×C4—371no—
159C22×C4—741no—
160C22×C4—741no—
161C22×C4—741no—
162C22×C4C22×D3711yescharacteristic
163C2×C8—21no—
164C2×C8—741no—
165C4⋊C4—371no—
166C4⋊C4—741no—
167C4⋊C4—1482no—
168C4⋊C4C4×D3711yescharacteristic
169C22⋊C4—21no—
170C22⋊C4—741no—
171C22⋊C4—741no—
172C22⋊C4—741no—
173C42—371no—
174C42—371no—
175C42—371no—
176C42—371no—
177C23—21no—
178C23—741no—
179C23D4×D3711yescharacteristic
180Q8—1482no—
181D4—41no—
182D4—41no—
183D4—41no—
184D4—1481no—
185D4—1482no—
186D4—1482no—
187D4—1481no—
188D4—1481no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—371no—
195C2×C4—371no—
196C2×C4—372no—
197C2×C4—372no—
198C2×C4—371no—
199C2×C4—371no—
200C2×C4—741no—
201C2×C4—1482no—
202C2×C4—1482no—
203C2×C4—1481no—
204C2×C4—1481no—
205C2×C4—1481no—
206C2×C4—1481no—
207C2×C4C2×C4×D3711yescharacteristic
208C2×C4D4×D3711yescharacteristic
209C8—41no—
210C8—1481no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—1481no—
217C22—1481no—
218C22—1481no—
219C22C22⋊C4×D3711yescharacteristic
220C22D8×D3711yescharacteristic
221C22SD16×D3711yescharacteristic
222C4—21no—
223C4—21no—
224C4—41no—
225C4—81no—
226C4—372no—
227C4—372no—
228C4—2961no—
229C4—741no—
230C4—741no—
231C4—1481no—
232C2—21no—
233C2—21no—
234C2—81no—
235C2—2961no—
236C2#1455750511yescharacteristic
237C2#102×D3711yescharacteristic
238C2#1455754811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#327C2
socleC22×C37C2×C22⋊C4
prime radical#14558078C2
cosocleC22×C4×C37C23
hypercenter#327D37
hypocenterC37#1517
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #14557583C2semidirect
3. #14557397C2semidirect
4. #14557268C2semidirect
5. #14557267C2semidirect
6. #14557266C2semidirect
7. C37×#327C2semidirect
9. #11924535C4semidirect
10. #11924532C4semidirect
14. D4×Dic37C4semidirect
15. #11924498C4semidirect
126. #327D37semidirect
127. C37#1517semidirect

Maximal subgroups

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

subgroupindex
#145580782
#145575832
#145573972
#145572682
#145572672
#145572662
C37×#3272
#151737