Finite Group Databasebeta

← C2×#14558433 #18010841

Subgroups — C2×#14558433 #18010841

Order 4736.

438 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 58 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
1C2×#11924596C211yesmaximal, characteristic, complemented
2C2×#11924594C211yesmaximal, characteristic, complemented
3#14558433C214yesmaximal, direct product factor
4C2×#11924505C211yesmaximal, characteristic
5C2×#10596957—21no—
6C2×C22⋊#3866—21no—
7#11924596—21no—
8#11924596C2212yescomplemented
9#11924594—21no—
10#11924594C2212yescomplemented
11C22×C22⋊D37—21no—
12C22×C22⋊D37C2211yescharacteristic
13#11924505—21no—
14#11924505—21no—
15#11924505C412yescomplemented
16#11924505C2212yes—
17C2×C22⋊Dic37—21no—
18C2×C22⋊Dic37C411yescharacteristic, complemented
19C25×C37C411yescharacteristic, complemented
20C24×C37—21no—
21C24×C37—21no—
22C24×C37—44no—
23C24×C37—41no—
24C24×C37—41no—
25C24×C37C2×C411yescharacteristic
26C24×C37C2×C412yescomplemented
27C23×D37D411yescharacteristic
28C22×#3866—41no—
29C2×C22⋊D37—22no—
30C2×C22⋊D37—22no—
31C2×C22⋊D37—41no—
32C2×C22⋊D37—41no—
33C2×C22⋊D37—44no—
34C2×C22⋊D37C2×C411yescharacteristic
35C2×C22⋊D37D411yescharacteristic
36C2×C22⋊D37D411yescharacteristic
37C2×C22⋊D37C2311yescharacteristic
38C22×Dic37—21no—
39C22×Dic37D411yescharacteristic
40C22⋊#3866—22no—
41C22⋊#3866—41no—
42#10596957—22no—
43#10596957—41no—
44C2×#64438—41no—
45C22⋊Dic37—21no—
46C22⋊Dic37—22no—
47C22⋊Dic37—22no—
48C22⋊Dic37C2×C412yescomplemented
49C23×C37—24no—
50C23×C37—21no—
51C23×C37—21no—
52C23×C37—22no—
53C23×C37—42no—
54C23×C37—44no—
55C23×C37—42no—
56C23×C37—42no—
57C23×C37—44no—
58C23×C37—42no—
59C23×C37—44no—
60C23×C37—48no—
61C23×C37—44no—
62C23×C37—41no—
63C23×C37—41no—
64C23×C37C22⋊C411yescharacteristic
65C23×C37C22⋊C411yescharacteristic
66C23×C37C22×C411yescharacteristic
67C22×D37—21no—
68C22×D37—21no—
69C22×D37—42no—
70C22×D37C22⋊C411yescharacteristic
71C22×D37C2×D411yescharacteristic
72C2×#3866—42no—
73C2×#3866—82no—
74C22⋊D37—41no—
75C22⋊D37—41no—
76C22⋊D37—41no—
77C22⋊D37—41no—
78C22⋊D37—44no—
79C22⋊D37—44no—
80C2×Dic37—21no—
81C2×Dic37—21no—
82C2×Dic37—22no—
83C2×Dic37—42no—
84C2×Dic37C22⋊C411yescharacteristic
85C2×Dic37C2×D411yescharacteristic
86#64438—42no—
87C22×C37—22no—
88C22×C37—24no—
89C22×C37—21no—
90C22×C37—21no—
91C22×C37—41no—
92C22×C37—41no—
93C22×C37—42no—
94C22×C37—44no—
95C22×C37—42no—
96C22×C37—44no—
97C22×C37—44no—
98C22×C37—48no—
99C22×C37—44no—
100C22×C37—42no—
101C22×C37—42no—
102C22×C37#9911yescharacteristic
103C22×C37#9911yescharacteristic
104C22×C37C2×C22⋊C411yescharacteristic
105C2×D37—21no—
106C2×D37—21no—
107C2×D37—42no—
108C2×D37—41no—
109C2×D37—41no—
110C2×D37—81no—
111#3866—82no—
112Dic37—21no—
113Dic37—21no—
114Dic37—42no—
115C2×AΣL(1,𝔽16)—371nomaximal, Sylow
116C2×C37—21no—
117C2×C37—21no—
118C2×C37—44no—
119C2×C37—41no—
120C2×C37—41no—
121C2×C37AΣL(1,𝔽16)12yescomplemented
122C2×C37C2×#9911yescharacteristic
123D37—41no—
124D37—41no—
125C2×#120—371no—
126C2×#100—371no—
127C2×#99—371no—
128AΣL(1,𝔽16)—374no—
129C37C2×AΣL(1,𝔽16)11yescharacteristic, complemented, Sylow
130C25#386611yescharacteristic, complemented
131C22×D4—371no—
132C22×D4—741no—
133C2×M16—741no—
134#120—372no—
135#120—372no—
136#120—741no—
137#120—741no—
138C2×C22⋊C4—371no—
139C2×C22⋊C4—741no—
140C2×C22⋊C4—741no—
141#100—372no—
142#100—741no—
143#99—372no—
144#99—741no—
145C24—21no—
146C24—21no—
147C24—44no—
148C24—41no—
149C24—41no—
150C24—371no—
151C24C2×#386611yescharacteristic
152C24C2×#386612yescomplemented
153C2×D4—371no—
154C2×D4—371no—
155C2×D4—371no—
156C2×D4—371no—
157C2×D4—742no—
158C2×D4—742no—
159C2×D4—1481no—
160C2×D4—1481no—
161C2×D4—1484no—
162C22×C4—371no—
163C22×C4—741no—
164C22×C4—1481no—
165M16—742no—
166M16—1481no—
167C2×C8—1481no—
168C22⋊C4—372no—
169C22⋊C4—742no—
170C22⋊C4—742no—
171C22⋊C4—741no—
172C22⋊C4—742no—
173C22⋊C4—1481no—
174C23—24no—
175C23—21no—
176C23—21no—
177C23—22no—
178C23—42no—
179C23—44no—
180C23—42no—
181C23—42no—
182C23—44no—
183C23—42no—
184C23—44no—
185C23—48no—
186C23—44no—
187C23—41no—
188C23—41no—
189C23—371no—
190C23—371no—
191C23—741no—
192C23—741no—
193C23—1482no—
194C23C22⋊#386611yescharacteristic
195C23C22⋊#386611yescharacteristic
196C23C22×#386611yescharacteristic
197D4—1481no—
198D4—1481no—
199D4—1481no—
200D4—1481no—
201D4—1484no—
202D4—1484no—
203C2×C4—371no—
204C2×C4—371no—
205C2×C4—2962no—
206C2×C4—741no—
207C2×C4—741no—
208C2×C4—742no—
209C2×C4—1482no—
210C2×C4—1482no—
211C8—1482no—
212C22—22no—
213C22—24no—
214C22—21no—
215C22—21no—
216C22—41no—
217C22—41no—
218C22—42no—
219C22—44no—
220C22—42no—
221C22—44no—
222C22—44no—
223C22—48no—
224C22—42no—
225C22—44no—
226C22—42no—
227C22—2961no—
228C22—741no—
229C22—741no—
230C22—1481no—
231C22—1481no—
232C22—1482no—
233C22#1192459411yescharacteristic
234C22#1192459411yescharacteristic
235C22C2×C22⋊#386611yescharacteristic
236C4—2962no—
237C4—741no—
238C4—741no—
239C4—1482no—
240C2—21no—
241C2—21no—
242C2—44no—
243C2—41no—
244C2—41no—
245C2—1481no—
246C2—1481no—
247C2#1455843312yesdirect product factor
248C2C2×#1192459411yescharacteristic
subgroupG/H
centerC22#11924594
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC25×C37C4
socleC22×C37#99
prime radicalC2×#11924505C2
cosocleC2×C22⋊D37C23
hypercenterC25#3866
hypocenterC37C2×AΣL(1,𝔽16)
LCSG ▷ C23×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23 ◁ C24 ◁ C25

Complements

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

NH ≅ G/Ntype
1. C2×#11924596C2semidirect
2. C2×#11924594C2semidirect
3. #14558433C2direct (N × H)
8. #11924596C22semidirect
10. #11924594C22semidirect
15. #11924505C4semidirect
18. C2×C22⋊Dic37C4semidirect
19. C25×C37C4semidirect
26. C24×C37C2×C4semidirect
48. C22⋊Dic37C2×C4semidirect
121. C2×C37AΣL(1,𝔽16)semidirect
129. C37C2×AΣL(1,𝔽16)semidirect
130. C25#3866semidirect
152. C24C2×#3866semidirect
247. C2#14558433direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#119245962
C2×#119245942
#145584332
C2×#119245052
C2×AΣL(1,𝔽16)37