Finite Group Databasebeta

← #17993641

Subgroups — #17993641

Order 4736.

240 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 49 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#14558120C211yesmaximal, characteristic
2#14557868C211yesmaximal, characteristic, complemented
3#14557468C211yesmaximal, characteristic, complemented
4#14557271C211yesmaximal, characteristic, complemented
5#14557267C211yesmaximal, characteristic, complemented
6#14557256C211yesmaximal, characteristic, complemented
7C37×#481C211yesmaximal, characteristic, complemented
8#11924531—21no—
9#11924522—21no—
10#11924520—21no—
11#11924515C2211yescharacteristic
12#11924508—21no—
13#11924504—21no—
14D4×Dic37—21no—
15C2×#10596936—21no—
16C2×#10596938—21no—
17C2×#10596938C2211yescharacteristic
18#11924469—21no—
19#11924459—21no—
20C22⋊#64436C2211yescharacteristic
21#11924443C2211yescharacteristic
22#121×C37C2211yescharacteristic
23C2×C4⋊C4×C37C2211yescharacteristic
24#106×C37—21no—
25#102×C37—21no—
26C22⋊C8×C37C2211yescharacteristic
27C23×D37D411yescharacteristic
28C2×D4×C37—21no—
29C2×D4×C37D411yescharacteristic
30C22×C4×C37—21no—
31C22×C4×C37C2311yescharacteristic
32C2×C22⋊D37—21no—
33C2×C22⋊D37—21no—
34C22×Dic37—21no—
35C22×Dic37—21no—
36C22×Dic37D411yescharacteristic
37C2×Dic74D411yescharacteristic
38C2×C8×C37—21no—
39C4⋊C4×C37—21no—
40C4⋊C4×C37—21no—
41C4⋊C4×C37D411yescharacteristic
42C22⋊C4×C37—21no—
43C22⋊Dic37—21no—
44C22⋊Dic37—21no—
45#10596938—21no—
46#10596938—21no—
47#10596938—21no—
48#10596938—21no—
49#10596938—42no—
50C4⋊Dic37—21no—
51C4⋊Dic37D411yescharacteristic
52#10596936—21no—
53#10596936—42no—
54C4×Dic37—21no—
55C2×#64436—21no—
56C23×C37—21no—
57C23×C37C2×D411yescharacteristic
58C22×D37—21no—
59C22×D37—21no—
60C22×D37—21no—
61C22×D37—41no—
62C22×D37—41no—
63D4×C37—41no—
64D4×C37—41no—
65D4×C37—41no—
66C2×C4×C37—21no—
67C2×C4×C37—41no—
68C2×C4×C37—41no—
69C2×C4×C37—41no—
70C2×C4×C37—41no—
71C2×C4×C37C2×D411yescharacteristic
72C2×C4×C37C2×D411yescharacteristic
73C22⋊D37—81no—
74C22⋊D37—81no—
75C2×Dic37—22no—
76C2×Dic37—21no—
77C2×Dic37—21no—
78C2×Dic37—21no—
79C2×Dic37—41no—
80C2×Dic37—41no—
81C2×Dic37—41no—
82C2×Dic37—81no—
83Dic74—41no—
84C8×C37—41no—
85#64436—41no—
86C22×C37—21no—
87C22×C37—21no—
88C22×C37—41no—
89C22×C37—41no—
90C22×C37—41no—
91C22×C37#12011yescharacteristic
92C22×C37#13511yescharacteristic
93C22×C37#13711yescharacteristic
94C2×D37—42no—
95C2×D37—41no—
96C2×D37—41no—
97C2×D37—41no—
98C2×D37—81no—
99C4×C37—21no—
100C4×C37—21no—
101C4×C37—41no—
102C4×C37—81no—
103Dic37—42no—
104Dic37—41no—
105Dic37—41no—
106Dic37—41no—
107#1618—371nomaximal, Sylow
108C2×C37—21no—
109C2×C37—21no—
110C2×C37—81no—
111C2×C37#45211yescharacteristic
112C2×C37#45311yescharacteristic
113C2×C37#45811yescharacteristic
114D37—81no—
115#538—371no—
116#484—371no—
117#481D3711yescharacteristic, complemented
118#399—371no—
119#328—371no—
120#327—371no—
121#323—371no—
122C37#161811yescharacteristic, complemented, Sylow
123#126—741no—
124#124—741no—
125#123—741no—
126C22⋊Q8—371no—
127#121—741no—
128#121C2×D3711yescharacteristic
129#120—741no—
130C4×D4—741no—
131C2×C4⋊C4—741no—
132C2×C4⋊C4C2×D3711yescharacteristic
133C2×C22⋊C4—371no—
134C2×C22⋊C4—741no—
135#107—741no—
136#106—21no—
137#103—741no—
138#102—21no—
139C22⋊C8—371no—
140C22⋊C8C2×D3711yescharacteristic
141#95—371no—
142C24—371no—
143C2×Q8—371no—
144C2×D4—21no—
145C2×D4—741no—
146C2×D4—741no—
147C2×D4C22⋊D3711yescharacteristic
148C22×C4—21no—
149C22×C4—371no—
150C22×C4—741no—
151C22×C4—741no—
152C22×C4C22×D3711yescharacteristic
153C2×C8—21no—
154C2×C8—741no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—371no—
158C4⋊C4—741no—
159C4⋊C4—741no—
160C4⋊C4—1482no—
161C4⋊C4C22⋊D3711yescharacteristic
162C22⋊C4—21no—
163C22⋊C4—741no—
164C22⋊C4—741no—
165C22⋊C4—741no—
166C22⋊C4—741no—
167C22⋊C4—741no—
168C22⋊C4—741no—
169C22⋊C4—1482no—
170C42—741no—
171C23—21no—
172C23—741no—
173C23—741no—
174C23—741no—
175C23—1481no—
176C23—1481no—
177C23D4×D3711yescharacteristic
178Q8—1481no—
179D4—41no—
180D4—41no—
181D4—41no—
182D4—2961no—
183D4—2961no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—2961no—
190C2×C4—742no—
191C2×C4—741no—
192C2×C4—741no—
193C2×C4—741no—
194C2×C4—1481no—
195C2×C4—1481no—
196C2×C4—1481no—
197C2×C4D4×D3711yescharacteristic
198C2×C4C2×C22⋊D3711yescharacteristic
199C8—41no—
200C8—1481no—
201C22—21no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—2961no—
207C22—1482no—
208C22—1481no—
209C22—1481no—
210C22—1481no—
211C22#1192450411yescharacteristic
212C22#1192455711yescharacteristic
213C22#1192456511yescharacteristic
214C4—21no—
215C4—21no—
216C4—41no—
217C4—81no—
218C4—1482no—
219C4—1481no—
220C4—1481no—
221C4—1481no—
222C2—21no—
223C2—21no—
224C2—81no—
225C2—2961no—
226C2#1455769211yescharacteristic
227C2#1455769911yescharacteristic
228C2#1455772211yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#481C2
socleC22×C37#120
prime radical#14558120C2
hypercenter#481D37
hypocenterC37#1618
LCSG ▷ C22×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. #14557868C2semidirect
3. #14557468C2semidirect
4. #14557271C2semidirect
5. #14557267C2semidirect
6. #14557256C2semidirect
7. C37×#481C2semidirect
117. #481D37semidirect
122. C37#1618semidirect

Maximal subgroups

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

subgroupindex
#145581202
#145578682
#145574682
#145572712
#145572672
#145572562
C37×#4812
#161837