Finite Group Databasebeta

← #18010608

Subgroups — #18010608

Order 4736.

342 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 66 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#14558611C211yesmaximal, characteristic, complemented
2#14558520C211yesmaximal, characteristic, complemented
3#14558505C212yesmaximal, complemented
4#14558414C212yesmaximal, complemented
5#14558041C211yesmaximal, characteristic
6#11924623—24no—
7D37⋊M16—21no—
8C2×#10596957—21no—
9C2×#10596957C2212yes—
10C2×#10596957C2212yes—
11#11924597—21no—
12#11924596—21no—
13#11924593—24no—
14C2×#10596964C2211yescharacteristic
15C22×C4×D37C2211yescharacteristic
16#11924519C411yescharacteristic
17#11924514—21no—
18#11924509—21no—
19#11924506C411yescharacteristic
20#11924504C411yescharacteristic
21#11924498—21no—
22#11924496—21no—
23#11924492C2211yescharacteristic
24#123×C37C411yescharacteristic
25C23×D37C2×C411yescharacteristic
26C2×D4×C37C2×C411yescharacteristic
27C22×C4×C37C2×C411yescharacteristic
28C2×C22⋊D37—21no—
29C2×C22⋊D37C2×C411yescharacteristic
30C2×C22⋊D37D411yescharacteristic
31C22×Dic37D411yescharacteristic
32C22×Dic37C2311yescharacteristic
33#10596964—22no—
34#10596964—22no—
35C2×D148—21no—
36C2×C4×D37—21no—
37C2×C4×D37—21no—
38C2×C4×D37—22no—
39C2×C4×D37—22no—
40C2×C4×D37D411yescharacteristic
41C2×Dic74D411yescharacteristic
42#10596957—22no—
43#10596957—22no—
44#10596957—22no—
45#10596957—22no—
46#10596957—22no—
47C2×#64438—22no—
48C2×#64438—22no—
49C2×#64438D414yescomplemented
50#10596953—22no—
51D37⋊C8—22no—
52C4⋊C4×C37—21no—
53C22⋊C4×C37—21no—
54C22⋊C4×C37C2×C411yescharacteristic
55C22⋊Dic37C2×C411yescharacteristic
56#10596938—21no—
57#10596938—21no—
58#10596938—21no—
59#10596936—21no—
60#10596936—21no—
61C4×Dic37—21no—
62C23×C37C22⋊C411yescharacteristic
63C23×C37C22×C411yescharacteristic
64C22×D37—21no—
65C22×D37—22no—
66C22×D37—42no—
67C22×D37C22⋊C411yescharacteristic
68D4×C37—22no—
69C2×C4×C37—21no—
70C2×C4×C37—21no—
71C2×C4×C37—22no—
72C2×C4×C37C22⋊C411yescharacteristic
73C22⋊D37—22no—
74C22⋊D37—22no—
75C22⋊D37—42no—
76C2×Dic37—21no—
77C2×Dic37—21no—
78C2×Dic37—21no—
79C2×Dic37C22⋊C411yescharacteristic
80C2×Dic37C2×D412yes—
81C2×Dic37C2×D411yescharacteristic
82C2×Dic37C2×D411yescharacteristic
83C2×Dic37#4112yes—
84D148—42no—
85C4×D37—21no—
86C4×D37—21no—
87C4×D37—41no—
88C4×D37—42no—
89C4×D37—41no—
90Dic74—22no—
91#64438—24no—
92#64438—42no—
93C22×C37—21no—
94C22×C37—41no—
95C22×C37—41no—
96C22×C37C2×C22⋊C411yescharacteristic
97C22×C37C4×D412yes—
98C2×D37—22no—
99C2×D37—24no—
100C2×D37—21no—
101C2×D37—41no—
102C2×D37—42no—
103C2×D37—41no—
104C2×D37—41no—
105C4×C37—21no—
106C4×C37—41no—
107C4×C37—41no—
108Dic37—21no—
109Dic37—41no—
110Dic37#12011yescharacteristic
111Dic37#12112yes—
112Dic37#12311yescharacteristic
113#1891—371nomaximal, Sylow
114C2×C37—21no—
115C2×C37—22no—
116C2×C37—41no—
117C2×C37#38611yescharacteristic
118D37—42no—
119D37—41no—
120#568—371no—
121#525—371no—
122#413—371no—
123#407—372no—
124#344—372no—
125C37#189111yescharacteristic, complemented, Sylow
126C2×#41—371no—
127C23×C4—371no—
128#131—744no—
129C2×M16—372no—
130C2×M16—372no—
131C2×M16—741no—
132C2×M16—741no—
133#123—371no—
134#123#386611yescharacteristic
135C22⋊Q8—741no—
136#121—741no—
137#120—371no—
138#120—371no—
139C4×D4—741no—
140C4×D4—741no—
141#117—371no—
142#101—741no—
143#100—741no—
144C22⋊C8—744no—
145C24—371no—
146#41—742no—
147#41—742no—
148C2×Q8—371no—
149C2×D4—371no—
150C2×D4—371no—
151C2×D4—741no—
152C2×D4—741no—
153C2×D4C2×#386611yescharacteristic
154C22×C4—371no—
155C22×C4—371no—
156C22×C4—371no—
157C22×C4—742no—
158C22×C4—741no—
159C22×C4—741no—
160C22×C4—742no—
161C22×C4C2×#386611yescharacteristic
162M16—742no—
163M16—742no—
164M16—742no—
165M16—742no—
166M16—742no—
167M16—742no—
168C2×C8—374no—
169C2×C8—742no—
170C2×C8—742no—
171C2×C8—742no—
172C4⋊C4—21no—
173C4⋊C4—741no—
174C4⋊C4—741no—
175C22⋊C4—21no—
176C22⋊C4—371no—
177C22⋊C4—741no—
178C22⋊C4—741no—
179C22⋊C4—741no—
180C22⋊C4C2×#386611yescharacteristic
181C42—741no—
182C23—371no—
183C23—741no—
184C23—742no—
185C23—1482no—
186C23C22⋊#386611yescharacteristic
187C23C22×#386611yescharacteristic
188Q8—742no—
189D4—22no—
190D4—742no—
191D4—742no—
192D4—1482no—
193D4—1482no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—371no—
198C2×C4—371no—
199C2×C4—372no—
200C2×C4—372no—
201C2×C4—371no—
202C2×C4—741no—
203C2×C4—741no—
204C2×C4—741no—
205C2×C4—741no—
206C2×C4—741no—
207C2×C4—1481no—
208C2×C4—1482no—
209C2×C4—1481no—
210C2×C4C22⋊#386611yescharacteristic
211C8—744no—
212C8—1482no—
213C22—21no—
214C22—41no—
215C22—41no—
216C22—742no—
217C22—744no—
218C22—741no—
219C22—1481no—
220C22—1481no—
221C22—1482no—
222C22—1481no—
223C22C2×C22⋊#386611yescharacteristic
224C22D4×#386612yes—
225C4—21no—
226C4—41no—
227C4—41no—
228C4—371no—
229C4—372no—
230C4—371no—
231C4—741no—
232C4—1481no—
233C2—21no—
234C2—22no—
235C2—41no—
236C2—1482no—
237C2—1481no—
238C2#1455848111yescharacteristic
subgroupG/H
centerC2#14558481
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
Fitting#123×C37C4
socleC2×C37#386
prime radical#14558041C2
cosocleC22×Dic37C23
hypercenter#123#3866
hypocenterC37#1891
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #14558611C2semidirect
2. #14558520C2semidirect
3. #14558505C2semidirect
4. #14558414C2semidirect
49. C2×#64438D4semidirect
125. C37#1891semidirect

Maximal subgroups

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

subgroupindex
#145586112
#145585202
#145585052
#145584142
#145580412
#189137