Finite Group Databasebeta

← #17995808

Subgroups — #17995808

Order 4736.

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

normal subgroups only

This group has 326 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#14558102C211yesmaximal, characteristic
2C2×#11924462C211yesmaximal, characteristic, complemented
3#14557532C211yesmaximal, characteristic, complemented
4C2×#11924452C211yesmaximal, characteristic, complemented
5#14557434C211yesmaximal, characteristic, complemented
6#14557292C211yesmaximal, characteristic, complemented
7C37×#428C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C22×D148C2211yescharacteristic
10C2×#10596934C2211yescharacteristic
11#11924533—21no—
12#11924524—21no—
13#11924511—21no—
14#11924511—21no—
15#11924506—22no—
16C2×#10596938—22no—
17C2×C4×Dic37C2211yescharacteristic
18#11924462—22no—
19#11924459—21no—
20#11924456—21no—
21#11924452—22no—
22C2×M16×C37C2211yescharacteristic
23#117×C37C2211yescharacteristic
24C2×C4⋊C4×C37C2211yescharacteristic
25#107×C37—21no—
26#106×C37—21no—
27C23×D37D412yes—
28C22×C4×C37—21no—
29C22×C4×C37C2311yescharacteristic
30C2×C22⋊D37—21no—
31C22×Dic37—21no—
32#10596962—21no—
33#10596962—21no—
34#10596962—21no—
35#10596962—21no—
36C2×D148—21no—
37C2×D148—21no—
38C2×D148—21no—
39C2×D148—21no—
40C2×D148—21no—
41C2×D148—21no—
42C2×D148—22no—
43C2×D148—22no—
44C2×D148D411yescharacteristic
45C2×C4×D37—21no—
46C2×Dic74D411yescharacteristic
47M16×C37—21no—
48M16×C37D412yescomplemented
49C2×C8×C37—21no—
50C4⋊C4×C37—21no—
51C4⋊C4×C37—21no—
52C4⋊C4×C37D411yescharacteristic
53C4⋊C4×C37D411yescharacteristic
54C22⋊C4×C37—21no—
55C42×C37—21no—
56#10596938—22no—
57#10596938—22no—
58#10596938—44no—
59C4×Dic37—21no—
60C4×Dic37—21no—
61#10596934—21no—
62#10596934—21no—
63C2×#64436—21no—
64C23×C37C2×D411yescharacteristic
65C22×D37—22no—
66C22×D37—21no—
67C22×D37—22no—
68C22×D37—22no—
69C22×D37—42no—
70C22×D37—42no—
71C2×C4×C37—21no—
72C2×C4×C37—21no—
73C2×C4×C37—42no—
74C2×C4×C37—41no—
75C2×C4×C37C2×D411yescharacteristic
76C2×C4×C37C2×D411yescharacteristic
77C2×C4×C37C2×D411yescharacteristic
78C2×C4×C37#4111yescharacteristic
79C2×C4×C37#4111yescharacteristic
80C2×C4×C37#4111yescharacteristic
81C22⋊D37—41no—
82C22⋊D37—41no—
83C2×Dic37—22no—
84C2×Dic37—21no—
85C2×Dic37—41no—
86C2×Dic37—41no—
87D148—21no—
88D148—21no—
89D148—41no—
90D148—41no—
91D148—41no—
92D148—41no—
93D148—82no—
94D148—82no—
95C4×D37—41no—
96C4×D37—41no—
97Dic74—21no—
98Dic74—21no—
99C8×C37—22no—
100#64436—41no—
101C22×C37—21no—
102C22×C37—21no—
103C22×C37#12011yescharacteristic
104C22×C37#12111yescharacteristic
105C22×C37#12311yescharacteristic
106C2×D37—44no—
107C2×D37—41no—
108C2×D37—42no—
109C2×D37—41no—
110C2×D37—42no—
111C2×D37—41no—
112C2×D37—42no—
113C2×D37—82no—
114C4×C37—41no—
115C4×C37—41no—
116C4×C37—81no—
117C4×C37#12111yescharacteristic
118C4×C37#12111yescharacteristic
119C4×C37#12311yescharacteristic
120C4×C37#12411yescharacteristic
121Dic37—42no—
122Dic37—41no—
123#2037—371nomaximal, Sylow
124C2×C37—21no—
125C2×C37—21no—
126C2×C37#39411yescharacteristic
127C2×C37#45311yescharacteristic
128C2×C37#45511yescharacteristic
129D37—81no—
130D37—82no—
131#535—371no—
132#428D3711yescharacteristic, complemented
133C2×#104—371no—
134#417—371no—
135C2×#100—371no—
136#390—371no—
137#339—371no—
138C37#203711yescharacteristic, complemented, Sylow
139C2×#41—371no—
140C22×D4—371no—
141C2×M16—371no—
142C2×M16C2×D3711yescharacteristic
143#127—741no—
144#124—741no—
145#121—741no—
146#121—741no—
147#120—742no—
148#117C2×D3711yescharacteristic
149C2×C4⋊C4C2×D3711yescharacteristic
150C2×C22⋊C4—742no—
151C2×C42—371no—
152#107—21no—
153#106—21no—
154#104—742no—
155#103—741no—
156#102—741no—
157#100—742no—
158C24—372no—
159#41—741no—
160#41—741no—
161#41—741no—
162#41—741no—
163C2×Q8—371no—
164C2×D4—371no—
165C2×D4—742no—
166C2×D4—742no—
167C2×D4—741no—
168C2×D4—741no—
169C2×D4—741no—
170C2×D4—741no—
171C2×D4—741no—
172C2×D4—741no—
173C2×D4—741no—
174C22×C4—21no—
175C22×C4—741no—
176C22×C4—741no—
177C22×C4C22×D3711yescharacteristic
178M16—21no—
179M16—741no—
180M16—741no—
181M16D14812yescomplemented
182C2×C8—21no—
183C2×C8—741no—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4C22⋊D3711yescharacteristic
187C4⋊C4C22⋊D3711yescharacteristic
188C22⋊C4—21no—
189C22⋊C4—742no—
190C22⋊C4—742no—
191C22⋊C4—1484no—
192C42—21no—
193C42—741no—
194C42—741no—
195C23—742no—
196C23—742no—
197C23—741no—
198C23—742no—
199C23—1482no—
200C23—1482no—
201C23D4×D3711yescharacteristic
202Q8—741no—
203Q8—741no—
204D4—2962no—
205D4—2962no—
206D4—741no—
207D4—741no—
208D4—1481no—
209D4—1481no—
210D4—1481no—
211D4—1481no—
212D4—1481no—
213D4—1481no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—42no—
217C2×C4—41no—
218C2×C4—742no—
219C2×C4—741no—
220C2×C4—1481no—
221C2×C4—1481no—
222C2×C4—1481no—
223C2×C4—1481no—
224C2×C4C2×D14811yescharacteristic
225C2×C4#1059696211yescharacteristic
226C2×C4D4×D3711yescharacteristic
227C2×C4#1059696611yescharacteristic
228C2×C4#1059696611yescharacteristic
229C2×C4C2×C22⋊D3711yescharacteristic
230C8—22no—
231C8—1481no—
232C22—21no—
233C22—21no—
234C22—2962no—
235C22—1484no—
236C22—1481no—
237C22—1482no—
238C22—1481no—
239C22—1482no—
240C22—1481no—
241C22—1482no—
242C22#1192450411yescharacteristic
243C22#1192451111yescharacteristic
244C22#1192452111yescharacteristic
245C4—41no—
246C4—41no—
247C4—81no—
248C4—1482no—
249C4—1481no—
250C4#1192451011yescharacteristic
251C4#1192451111yescharacteristic
252C4#1192452111yescharacteristic
253C4#1192452511yescharacteristic
254C2—21no—
255C2—21no—
256C2—2962no—
257C2—2961no—
258C2#1455745011yescharacteristic
259C2#1455769911yescharacteristic
260C2#1455770911yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#428C2
socleC22×C37#120
prime radical#14558102C2
hypercenter#428D37
hypocenterC37#2037
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. C2×#11924462C2semidirect
3. #14557532C2semidirect
4. C2×#11924452C2semidirect
5. #14557434C2semidirect
6. #14557292C2semidirect
7. C37×#428C2semidirect
48. M16×C37D4semidirect
132. #428D37semidirect
138. C37#2037semidirect
181. M16D148semidirect

Maximal subgroups

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

subgroupindex
#145581022
C2×#119244622
#145575322
C2×#119244522
#145574342
#145572922
C37×#4282
#203737