Finite Group Databasebeta

← #17995805

Subgroups — #17995805

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#14558097C211yesmaximal, characteristic
2#14557575C211yesmaximal, characteristic, complemented
3#14557534C211yesmaximal, characteristic, complemented
4C2×#11924452C211yesmaximal, characteristic, complemented
5#14557435C211yesmaximal, characteristic, complemented
6#14557293C211yesmaximal, characteristic, complemented
7C2×#104×C37C211yesmaximal, characteristic, complemented
8C22×D148C2211yescharacteristic
9C2×#10596934C2211yescharacteristic
10#11924532—21no—
11#11924525—21no—
12#11924510—21no—
13#11924510—21no—
14#11924504—22no—
15#11924495C2211yescharacteristic
16C2×C4⋊Dic37C2211yescharacteristic
17C2×#10596938—22no—
18#11924470—21no—
19#11924468—21no—
20#11924460—21no—
21#11924457—21no—
22#11924452—22no—
23C2×#41×C37C2211yescharacteristic
24C2×M16×C37C2211yescharacteristic
25C2×C42×C37C2211yescharacteristic
26#104×C37—22no—
27C23×D37D412yes—
28#41×C37—21no—
29#41×C37—21no—
30#41×C37—21no—
31#41×C37—21no—
32C2×Q8×C37D411yescharacteristic
33C2×D4×C37—21no—
34C2×D4×C37D411yescharacteristic
35C22×C4×C37—21no—
36C22×C4×C37—21no—
37C22×C4×C37C2311yescharacteristic
38C2×C22⋊D37—22no—
39C2×C22⋊D37—22no—
40C22×Dic37—21no—
41C2×D148—21no—
42C2×D148—21no—
43C2×D148—21no—
44C2×D148—21no—
45C2×D148—21no—
46C2×D148—21no—
47M16×C37—21no—
48M16×C37D412yescomplemented
49C2×C8×C37—21no—
50C42×C37—21no—
51C42×C37—21no—
52C22⋊Dic37—21no—
53#10596938—22no—
54#10596938—22no—
55#10596938—44no—
56C4⋊Dic37—21no—
57C4⋊Dic37—21no—
58C4⋊Dic37D411yescharacteristic
59C4⋊Dic37D411yescharacteristic
60C4×Dic37—21no—
61#10596934—21no—
62#10596934—21no—
63C2×#64436—21no—
64C23×C37—21no—
65C23×C37C2×D411yescharacteristic
66C22×D37—22no—
67C22×D37—22no—
68C22×D37—22no—
69C22×D37—42no—
70C22×D37—42no—
71Q8×C37—21no—
72Q8×C37—21no—
73D4×C37—21no—
74D4×C37—21no—
75D4×C37—41no—
76D4×C37—41no—
77C2×C4×C37—22no—
78C2×C4×C37—21no—
79C2×C4×C37—41no—
80C2×C4×C37—41no—
81C2×C4×C37—41no—
82C2×C4×C37—41no—
83C2×C4×C37C2×D411yescharacteristic
84C2×C4×C37C2×D411yescharacteristic
85C2×C4×C37C2×D411yescharacteristic
86C2×C4×C37#4111yescharacteristic
87C2×C4×C37#4111yescharacteristic
88C2×C4×C37#4111yescharacteristic
89C22⋊D37—82no—
90C22⋊D37—82no—
91C2×Dic37—21no—
92C2×Dic37—21no—
93C2×Dic37—42no—
94C2×Dic37—41no—
95D148—41no—
96D148—41no—
97D148—41no—
98D148—41no—
99C8×C37—22no—
100#64436—41no—
101C22×C37—21no—
102C22×C37—21no—
103C22×C37—41no—
104C22×C37—41no—
105C22×C37—41no—
106C22×C37#12011yescharacteristic
107C22×C37#12111yescharacteristic
108C22×C37#12311yescharacteristic
109C2×D37—44no—
110C2×D37—42no—
111C2×D37—42no—
112C2×D37—42no—
113C2×D37—82no—
114C4×C37—42no—
115C4×C37—41no—
116C4×C37#12111yescharacteristic
117C4×C37#12111yescharacteristic
118C4×C37#12311yescharacteristic
119C4×C37#12411yescharacteristic
120Dic37—41no—
121Dic37—41no—
122Dic37—81no—
123#2037—371nomaximal, Sylow
124C2×C37—21no—
125C2×C37—21no—
126C2×C37—81no—
127C2×C37#39411yescharacteristic
128C2×C37#45311yescharacteristic
129C2×C37#45511yescharacteristic
130D37—82no—
131#535—371no—
132#428—371no—
133C2×#104D3711yescharacteristic, complemented
134#417—371no—
135C2×#100—371no—
136#390—371no—
137#339—371no—
138C37#203711yescharacteristic, complemented, Sylow
139C2×#41C2×D3711yescharacteristic
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#117—371no—
149C2×C4⋊C4—371no—
150C2×C22⋊C4—742no—
151C2×C42C2×D3711yescharacteristic
152#107—741no—
153#106—741no—
154#104—22no—
155#103—741no—
156#102—741no—
157#100—742no—
158C24—372no—
159#41—21no—
160#41—21no—
161#41—21no—
162#41—21no—
163C2×Q8D14811yescharacteristic
164C2×D4—21no—
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×D4D14811yescharacteristic
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—741no—
177C22×C4C22×D3711yescharacteristic
178M16—21no—
179M16—741no—
180M16—741no—
181M16C22⋊D3712yescomplemented
182C2×C8—21no—
183C2×C8—741no—
184C4⋊C4—371no—
185C4⋊C4—371no—
186C4⋊C4—741no—
187C4⋊C4—741no—
188C22⋊C4—742no—
189C22⋊C4—742no—
190C22⋊C4—741no—
191C22⋊C4—1484no—
192C42—21no—
193C42—21no—
194C42—741no—
195C23—21no—
196C23—742no—
197C23—742no—
198C23—742no—
199C23—1482no—
200C23—1482no—
201C23D4×D3711yescharacteristic
202Q8—21no—
203Q8—21no—
204D4—21no—
205D4—21no—
206D4—41no—
207D4—41no—
208D4—2962no—
209D4—2962no—
210D4—1481no—
211D4—1481no—
212D4—1481no—
213D4—1481no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—741no—
221C2×C4—741no—
222C2×C4—1482no—
223C2×C4—1481no—
224C2×C4C2×D14811yescharacteristic
225C2×C4#1059696211yescharacteristic
226C2×C4D4×D3711yescharacteristic
227C2×C4#1059696411yescharacteristic
228C2×C4#1059696411yescharacteristic
229C2×C4C2×C22⋊D3711yescharacteristic
230C8—22no—
231C8—1481no—
232C22—21no—
233C22—21no—
234C22—41no—
235C22—41no—
236C22—41no—
237C22—2962no—
238C22—1484no—
239C22—1482no—
240C22—1482no—
241C22—1482no—
242C22#1192450611yescharacteristic
243C22#1192450711yescharacteristic
244C22#1192451811yescharacteristic
245C4—42no—
246C4—41no—
247C4—2961no—
248C4—1481no—
249C4—1481no—
250C4#1192450811yescharacteristic
251C4#1192451011yescharacteristic
252C4#1192452011yescharacteristic
253C4#1192452211yescharacteristic
254C2—21no—
255C2—21no—
256C2—81no—
257C2—2962no—
258C2#1455744911yescharacteristic
259C2#1455770211yescharacteristic
260C2#1455771211yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC2×#104×C37C2
socleC22×C37#120
prime radical#14558097C2
hypercenterC2×#104D37
hypocenterC37#2037
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. #14557575C2semidirect
3. #14557534C2semidirect
4. C2×#11924452C2semidirect
5. #14557435C2semidirect
6. #14557293C2semidirect
7. C2×#104×C37C2semidirect
48. M16×C37D4semidirect
133. C2×#104D37semidirect
138. C37#2037semidirect
181. M16C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145580972
#145575752
#145575342
C2×#119244522
#145574352
#145572932
C2×#104×C372
#203737