Finite Group Databasebeta

← #17995013

Subgroups — #17995013

Order 4736.

342 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 79 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#14558299C211yesmaximal, characteristic, complemented
2#14558045C211yesmaximal, characteristic
3#14557515C211yesmaximal, characteristic, complemented
4#14557496C211yesmaximal, characteristic, complemented
5#14557496C211yesmaximal, characteristic, complemented
6#14557303C211yesmaximal, characteristic, complemented
7C37×#344C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C22×C4×D37C2211yescharacteristic
10#11924544—22no—
11#11924542—22no—
12C2×#10596934C2211yescharacteristic
13C2×#10596934C2211yescharacteristic
14M16×D37—22no—
15#11924520C412yes—
16#11924516—21no—
17#11924511—21no—
18#11924506C412yes—
19C4×D148—22no—
20#11924454—21no—
21#11924452—21no—
22#11924448—22no—
23#11924448—22no—
24C2×M16×C37C2211yescharacteristic
25C2×M16×C37C2211yescharacteristic
26#117×C37C2211yescharacteristic
27C23×D37C2×C411yescharacteristic
28C22×C4×C37C2311yescharacteristic
29C2×C22⋊D37C2×C412yes—
30C22×Dic37C2×C411yescharacteristic
31#10596962—21no—
32#10596962—21no—
33#10596962—21no—
34#10596962—21no—
35C2×D148—22no—
36C2×D148D411yescharacteristic
37C2×C4×D37—21no—
38C2×C4×D37—21no—
39C2×C4×D37—21no—
40C2×C4×D37—21no—
41C2×C4×D37—21no—
42C2×C4×D37—21no—
43C2×C4×D37D412yes—
44C2×Dic74D411yescharacteristic
45M16×C37—21no—
46M16×C37—21no—
47M16×C37—21no—
48M16×C37—21no—
49C2×C8×C37—21no—
50C2×C8×C37D412yescomplemented
51C4⋊C4×C37—21no—
52C22⋊C4×C37C2×C412yes—
53C42×C37—21no—
54#10596938—22no—
55#10596938—22no—
56C4⋊Dic37—22no—
57#10596934—21no—
58#10596934—21no—
59#10596934—21no—
60#10596934—21no—
61C2×#64436—21no—
62C2×#64436D412yescomplemented
63#10596929—24no—
64C8×D37—24no—
65C23×C37C22×C411yescharacteristic
66C22×D37—21no—
67C22×D37—21no—
68C22×D37—21no—
69C22×D37—42no—
70C22×D37C22⋊C412yes—
71C2×C4×C37—22no—
72C2×C4×C37C2×D411yescharacteristic
73C2×C4×C37C2×D411yescharacteristic
74C2×C4×C37C2×D411yescharacteristic
75C2×C4×C37C2×D411yescharacteristic
76C2×C4×C37#4111yescharacteristic
77C2×C4×C37#4111yescharacteristic
78C22⋊D37—22no—
79C22⋊D37—22no—
80C2×Dic37—21no—
81C2×Dic37—21no—
82C2×Dic37—21no—
83C2×Dic37C22⋊C412yes—
84D148—21no—
85D148—21no—
86D148—44no—
87C4×D37—22no—
88C4×D37—22no—
89C4×D37—41no—
90C4×D37—41no—
91C4×D37—41no—
92C4×D37—41no—
93Dic74—21no—
94Dic74—21no—
95C8×C37—22no—
96C8×C37—41no—
97#64436—22no—
98#64436—41no—
99C22×C37—41no—
100C22×C37C2×C22⋊C411yescharacteristic
101C22×C37C4×D411yescharacteristic
102C22×C37C4×D411yescharacteristic
103C2×D37—22no—
104C2×D37—22no—
105C2×D37—22no—
106C2×D37—22no—
107C2×D37—41no—
108C2×D37—41no—
109C2×D37—41no—
110C2×D37—41no—
111C2×D37—42no—
112C4×C37—42no—
113C4×C37#12011yescharacteristic
114C4×C37#12111yescharacteristic
115C4×C37#12111yescharacteristic
116C4×C37#12311yescharacteristic
117Dic37—22no—
118Dic37—41no—
119#1891—371nomaximal, Sylow
120C2×C37—21no—
121C2×C37—21no—
122C2×C37—21no—
123C2×C37#38611yescharacteristic
124D37—42no—
125D37—42no—
126#568—371no—
127#525—371no—
128#413—371no—
129#407—371no—
130#407—371no—
131#344—371no—
132#344D3711yescharacteristic, complemented
133C37#189111yescharacteristic, complemented, Sylow
134C2×#41—371no—
135C23×C4—371no—
136#131—742no—
137#131—742no—
138C2×M16—371no—
139C2×M16—371no—
140C2×M16—742no—
141C2×M16C2×D3711yescharacteristic
142C2×M16C2×D3711yescharacteristic
143#123—372no—
144C22⋊Q8—741no—
145#121—741no—
146#120—372no—
147C4×D4—742no—
148#117C2×D3711yescharacteristic
149#101—741no—
150#100—741no—
151C22⋊C8—742no—
152C22⋊C8—742no—
153C24—371no—
154#41—741no—
155#41—741no—
156#41—741no—
157#41—741no—
158C2×Q8—371no—
159C2×D4—372no—
160C2×D4—371no—
161C2×D4—742no—
162C22×C4—372no—
163C22×C4—371no—
164C22×C4—741no—
165C22×C4—741no—
166C22×C4—741no—
167C22×C4—741no—
168C22×C4—741no—
169C22×C4—741no—
170C22×C4C22×D3711yescharacteristic
171M16—21no—
172M16—21no—
173M16—21no—
174M16—21no—
175M16—744no—
176M16—741no—
177M16—741no—
178M16—741no—
179M16—741no—
180C2×C8—21no—
181C2×C8—372no—
182C2×C8—744no—
183C2×C8—741no—
184C2×C8D14812yescomplemented
185C4⋊C4—21no—
186C4⋊C4—742no—
187C22⋊C4—742no—
188C22⋊C4—742no—
189C22⋊C4C4×D3712yes—
190C42—21no—
191C23—372no—
192C23—741no—
193C23—741no—
194C23—741no—
195C23—1482no—
196C23C2×C4×D3711yescharacteristic
197Q8—741no—
198Q8—741no—
199D4—742no—
200D4—742no—
201D4—741no—
202D4—741no—
203D4—1484no—
204C2×C4—22no—
205C2×C4—372no—
206C2×C4—742no—
207C2×C4—742no—
208C2×C4—741no—
209C2×C4—741no—
210C2×C4—741no—
211C2×C4—1481no—
212C2×C4—1481no—
213C2×C4—1481no—
214C2×C4—1481no—
215C2×C4C2×D14811yescharacteristic
216C2×C4#1059696211yescharacteristic
217C2×C4D4×D3711yescharacteristic
218C2×C4D4×D3711yescharacteristic
219C2×C4D4×D3711yescharacteristic
220C2×C4#1059696611yescharacteristic
221C8—22no—
222C8—41no—
223C8—742no—
224C8—1481no—
225C22—41no—
226C22—742no—
227C22—742no—
228C22—742no—
229C22—742no—
230C22—1482no—
231C22—1481no—
232C22—1481no—
233C22—1481no—
234C22—1481no—
235C22C22⋊C4×D3711yescharacteristic
236C22#1192449811yescharacteristic
237C22C4×D14811yescharacteristic
238C4—42no—
239C4—742no—
240C4—1481no—
241C4#1192450611yescharacteristic
242C4#1192450911yescharacteristic
243C4#1192451111yescharacteristic
244C4#1192452111yescharacteristic
245C2—21no—
246C2—21no—
247C2—21no—
248C2—1482no—
249C2—1482no—
250C2#1455741111yescharacteristic
subgroupG/H
centerC4#11924506
commutatorC23×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#344C2
socleC2×C37#386
prime radical#14558045C2
cosocleC22×C4×C37C23
hypercenter#344D37
hypocenterC37#1891
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
1. #14558299C2semidirect
3. #14557515C2semidirect
4. #14557496C2semidirect
5. #14557496C2semidirect
6. #14557303C2semidirect
7. C37×#344C2semidirect
50. C2×C8×C37D4semidirect
62. C2×#64436D4semidirect
132. #344D37semidirect
133. C37#1891semidirect
184. C2×C8D148semidirect

Maximal subgroups

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

subgroupindex
#145582992
#145580452
#145575152
#145574962
#145573032
C37×#3442
#189137