Finite Group Databasebeta

← #17996235

Subgroups — #17996235

Order 4736.

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

normal subgroups only

This group has 264 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#14558040C211yesmaximal, characteristic
2#14557517C211yesmaximal, characteristic, complemented
3#14557322C212yesmaximal, complemented
4#14557319C212yesmaximal, complemented
5C37×#410C211yesmaximal, characteristic, complemented
6C22×C4×D37C411yescharacteristic, complemented
7C2×#10596934—21no—
8#11924517C411yescharacteristic, complemented
9#11924517C2211yescharacteristic
10#11924512—21no—
11#11924507—21no—
12#11924504C411yescharacteristic, complemented
13#11924504C2211yescharacteristic
14C4×C22⋊D37—21no—
15C4×C22⋊D37—21no—
16#11924495C411yescharacteristic, complemented
17#11924455—21no—
18#11924453C2212yes—
19C2×#41×C37C2211yescharacteristic
20#117×C37—21no—
21#99×C37—21no—
22#99×C37C2212yes—
23C23×D37C2×C411yescharacteristic
24#41×C37—41no—
25#41×C37—41no—
26C2×Q8×C37D411yescharacteristic
27C2×D4×C37C2×C411yescharacteristic
28C2×D4×C37D411yescharacteristic
29C2×D4×C37C2311yescharacteristic
30C22×C4×C37C2×C411yescharacteristic
31C22×C4×C37D411yescharacteristic
32C22×C4×C37D411yescharacteristic
33C2×C22⋊D37—21no—
34C2×C22⋊D37—21no—
35C22×Dic37C2×C411yescharacteristic
36C2×C4×D37—21no—
37C2×C4×D37—21no—
38C2×C4×D37—41no—
39C2×C4×D37—41no—
40C4⋊C4×C37—41no—
41C22⋊C4×C37—22no—
42C42×C37—41no—
43C22⋊Dic37—21no—
44C22⋊Dic37—21no—
45C22⋊Dic37C2×C411yescharacteristic
46C22⋊Dic37C2×C411yescharacteristic
47#10596938—21no—
48#10596938—21no—
49C4⋊Dic37—21no—
50#10596936—21no—
51#10596936—21no—
52C4×Dic37—21no—
53#10596934—22no—
54#10596934—41no—
55C2×#64436—41no—
56C23×C37C22⋊C411yescharacteristic
57C23×C37C22×C411yescharacteristic
58C23×C37C2×D411yescharacteristic
59C22×D37—21no—
60C22×D37—42no—
61C22×D37—41no—
62Q8×C37—41no—
63D4×C37—41no—
64D4×C37—41no—
65D4×C37—41no—
66C2×C4×C37—21no—
67C2×C4×C37—21no—
68C2×C4×C37—21no—
69C2×C4×C37—21no—
70C2×C4×C37—21no—
71C2×C4×C37—21no—
72C2×C4×C37—42no—
73C2×C4×C37C22⋊C411yescharacteristic
74C2×C4×C37C22⋊C411yescharacteristic
75C2×C4×C37C22⋊C411yescharacteristic
76C2×C4×C37C2×D411yescharacteristic
77C22⋊D37—42no—
78C22⋊D37—42no—
79C2×Dic37—21no—
80C2×Dic37—21no—
81C2×Dic37—21no—
82C2×Dic37—41no—
83C4×D37—42no—
84C4×D37—41no—
85C4×D37—41no—
86#64436—42no—
87C22×C37—21no—
88C22×C37—21no—
89C22×C37—21no—
90C22×C37—41no—
91C22×C37—41no—
92C22×C37—41no—
93C22×C37C2×C22⋊C411yescharacteristic
94C2×D37—22no—
95C2×D37—41no—
96C2×D37—42no—
97C2×D37—41no—
98C2×D37—42no—
99C4×C37—21no—
100C4×C37—21no—
101C4×C37—21no—
102C4×C37—82no—
103C4×C37#9911yescharacteristic
104C4×C37#9911yescharacteristic
105Dic37—41no—
106Dic37—41no—
107Dic37—41no—
108#2120—371nomaximal, Sylow
109C2×C37—21no—
110C2×C37—41no—
111C2×C37—41no—
112C2×C37—41no—
113C2×C37C2×#9911yescharacteristic
114D37—42no—
115#525—371no—
116#413—371no—
117#410D3711yescharacteristic, complemented
118#352—372no—
119AΣL(1,𝔽16)—372no—
120C37#212011yescharacteristic, complemented, Sylow
121C2×#41C2×D3711yescharacteristic
122C23×C4—371no—
123C2×M16—741no—
124#123—371no—
125#123—371no—
126C22⋊Q8—741no—
127#121—741no—
128#120—371no—
129#120—371no—
130C4×D4—741no—
131C4×D4—741no—
132#117—21no—
133#117—371no—
134#101—741no—
135#100—372no—
136#99—21no—
137#99C2×D3712yes—
138C24—371no—
139#41—41no—
140#41—41no—
141C2×Q8D14811yescharacteristic
142C2×D4—741no—
143C2×D4—741no—
144C2×D4C4×D3711yescharacteristic
145C2×D4C22⋊D3711yescharacteristic
146C2×D4C22×D3711yescharacteristic
147C22×C4—371no—
148C22×C4—741no—
149C22×C4—741no—
150C22×C4—1481no—
151C22×C4—1481no—
152C22×C4C4×D3711yescharacteristic
153C22×C4D14811yescharacteristic
154C22×C4C22⋊D3711yescharacteristic
155M16—742no—
156M16—1481no—
157C2×C8—1481no—
158C4⋊C4—41no—
159C4⋊C4—741no—
160C4⋊C4—741no—
161C4⋊C4—741no—
162C22⋊C4—22no—
163C22⋊C4—371no—
164C22⋊C4—371no—
165C22⋊C4—741no—
166C22⋊C4—741no—
167C22⋊C4—741no—
168C22⋊C4—741no—
169C42—41no—
170C42—741no—
171C23—741no—
172C23—1481no—
173C23—1482no—
174C23#1059693811yescharacteristic
175C23C2×C4×D3711yescharacteristic
176C23C2×C22⋊D3711yescharacteristic
177Q8—41no—
178D4—41no—
179D4—41no—
180D4—41no—
181D4—1482no—
182D4—1482no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—42no—
190C2×C4—741no—
191C2×C4—741no—
192C2×C4—741no—
193C2×C4—1482no—
194C2×C4—1481no—
195C2×C4—1481no—
196C2×C4—1481no—
197C2×C4#1059693811yescharacteristic
198C2×C4#1059693811yescharacteristic
199C2×C4#1059693811yescharacteristic
200C2×C4C2×D14811yescharacteristic
201C8—1482no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—742no—
209C22—1481no—
210C22—1482no—
211C22—1482no—
212C22—1481no—
213C22C2×#1059693811yescharacteristic
214C4—21no—
215C4—21no—
216C4—21no—
217C4—82no—
218C4—1481no—
219C4—1481no—
220C4—1481no—
221C4#1192445011yescharacteristic
222C4#1192445011yescharacteristic
223C2—21no—
224C2—41no—
225C2—41no—
226C2—41no—
227C2—1482no—
228C2C2×#1192445011yescharacteristic
subgroupG/H
centerC4#11924450
commutatorC23×C37C22×C4
FrattiniC2×D4C22×D37
FittingC37×#410C2
socleC2×C37C2×#99
prime radical#14558040C2
cosocleC2×D4×C37C23
hypercenter#410D37
hypocenterC37#2120
LCSG ▷ C23×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #14557517C2semidirect
3. #14557322C2semidirect
4. #14557319C2semidirect
5. C37×#410C2semidirect
6. C22×C4×D37C4semidirect
8. #11924517C4semidirect
12. #11924504C4semidirect
16. #11924495C4semidirect
117. #410D37semidirect
120. C37#2120semidirect

Maximal subgroups

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

subgroupindex
#145580402
#145575172
#145573222
#145573192
C37×#4102
#212037