Finite Group Databasebeta

← C2×#14558434 #18010843

Subgroups — C2×#14558434 #18010843

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#14558434C214yesmaximal, direct product factor
4C2×#11924506C211yesmaximal, characteristic
5C2×#10596957—21no—
6C2×C22⋊#3866—21no—
7#11924596—21no—
8#11924596C2212yescomplemented
9#11924594—21no—
10#11924594C2212yescomplemented
11C24×D37C411yescharacteristic, complemented
12C22×D148—21no—
13C22×C22⋊D37C2211yescharacteristic
14#11924506—21no—
15#11924506—21no—
16#11924506C412yescomplemented
17#11924506C2212yes—
18C2×#10596938—21no—
19C2×C22⋊C4×C37C411yescharacteristic, complemented
20C24×C37C2×C411yescharacteristic
21C23×D37—21no—
22C23×D37—21no—
23C23×D37—44no—
24C23×D37—41no—
25C23×D37—41no—
26C23×D37C2×C412yescomplemented
27C23×D37D411yescharacteristic
28C22×#3866—41no—
29C22×C4×C37—21no—
30C2×C22⋊D37—41no—
31C2×C22⋊D37—41no—
32C2×C22⋊D37C2×C411yescharacteristic
33C2×C22⋊D37D411yescharacteristic
34C2×C22⋊D37D411yescharacteristic
35C2×C22⋊D37C2311yescharacteristic
36C22×Dic37D411yescharacteristic
37C2×D148—22no—
38C2×D148—22no—
39C2×D148—44no—
40C22⋊#3866—22no—
41C22⋊#3866—41no—
42#10596957—22no—
43#10596957—41no—
44C2×#64438—41no—
45C22⋊C4×C37—21no—
46C22⋊C4×C37C2×C412yescomplemented
47#10596938—22no—
48#10596938—22no—
49C23×C37—21no—
50C23×C37—21no—
51C23×C37—42no—
52C23×C37C22⋊C411yescharacteristic
53C23×C37C22⋊C411yescharacteristic
54C23×C37C22×C411yescharacteristic
55C22×D37—24no—
56C22×D37—21no—
57C22×D37—22no—
58C22×D37—21no—
59C22×D37—44no—
60C22×D37—44no—
61C22×D37—42no—
62C22×D37—42no—
63C22×D37—48no—
64C22×D37—44no—
65C22×D37—41no—
66C22×D37—41no—
67C22×D37—42no—
68C22×D37—44no—
69C22×D37—42no—
70C22×D37C22⋊C411yescharacteristic
71C22×D37C2×D411yescharacteristic
72C2×#3866—42no—
73C2×#3866—82no—
74C2×C4×C37—22no—
75C2×C4×C37—42no—
76C22⋊D37—41no—
77C22⋊D37—41no—
78C22⋊D37—41no—
79C22⋊D37—41no—
80C2×Dic37—21no—
81C2×Dic37—21no—
82C2×Dic37C22⋊C411yescharacteristic
83C2×Dic37C2×D411yescharacteristic
84D148—44no—
85D148—44no—
86#64438—42no—
87C22×C37—22no—
88C22×C37—21no—
89C22×C37—21no—
90C22×C37—41no—
91C22×C37—41no—
92C22×C37—42no—
93C22×C37—42no—
94C22×C37#9911yescharacteristic
95C22×C37#9911yescharacteristic
96C22×C37C2×C22⋊C411yescharacteristic
97C2×D37—24no—
98C2×D37—21no—
99C2×D37—21no—
100C2×D37—42no—
101C2×D37—44no—
102C2×D37—48no—
103C2×D37—44no—
104C2×D37—42no—
105C2×D37—44no—
106C2×D37—42no—
107C2×D37—41no—
108C2×D37—41no—
109C2×D37—44no—
110C2×D37—81no—
111#3866—82no—
112C4×C37—42no—
113Dic37—21no—
114Dic37—21no—
115C2×AΣL(1,𝔽16)—371nomaximal, Sylow
116C2×C37—21no—
117C2×C37—21no—
118C2×C37—41no—
119C2×C37—41no—
120C2×C37AΣL(1,𝔽16)12yescomplemented
121C2×C37C2×#9911yescharacteristic
122D37—41no—
123D37—44no—
124D37—41no—
125C2×#120—371no—
126C2×#100—371no—
127C2×#99—371no—
128AΣL(1,𝔽16)—374no—
129C37C2×AΣL(1,𝔽16)11yescharacteristic, complemented, Sylow
130C25—371no—
131C22×D4—371no—
132C22×D4—741no—
133C2×M16—741no—
134#120—372no—
135#120—372no—
136#120—741no—
137#120—741no—
138C2×C22⋊C4—741no—
139C2×C22⋊C4—741no—
140C2×C22⋊C4#386611yescharacteristic, complemented
141#100—372no—
142#100—741no—
143#99—372no—
144#99—741no—
145C24—371no—
146C24—372no—
147C24—741no—
148C24—741no—
149C24—1481no—
150C24—1481no—
151C24—1484no—
152C24C2×#386611yescharacteristic
153C2×D4—371no—
154C2×D4—371no—
155C2×D4—371no—
156C2×D4—371no—
157C2×D4—742no—
158C2×D4—742no—
159C2×D4—1484no—
160C2×D4—1481no—
161C2×D4—1481no—
162C22×C4—21no—
163C22×C4—371no—
164C22×C4—1481no—
165M16—742no—
166M16—1481no—
167C2×C8—1481no—
168C22⋊C4—21no—
169C22⋊C4—742no—
170C22⋊C4—742no—
171C22⋊C4—742no—
172C22⋊C4—1481no—
173C22⋊C4C2×#386612yescomplemented
174C23—21no—
175C23—21no—
176C23—42no—
177C23—371no—
178C23—371no—
179C23—744no—
180C23—741no—
181C23—741no—
182C23—742no—
183C23—1482no—
184C23—1482no—
185C23—1482no—
186C23—1482no—
187C23—1484no—
188C23—1484no—
189C23—1484no—
190C23—1488no—
191C23—1484no—
192C23—1481no—
193C23—1481no—
194C23C22⋊#386611yescharacteristic
195C23C22⋊#386611yescharacteristic
196C23C22×#386611yescharacteristic
197D4—1484no—
198D4—1484no—
199D4—1481no—
200D4—1481no—
201D4—1481no—
202D4—1481no—
203C2×C4—22no—
204C2×C4—42no—
205C2×C4—371no—
206C2×C4—371no—
207C2×C4—2962no—
208C2×C4—741no—
209C2×C4—741no—
210C2×C4—1482no—
211C8—1482no—
212C22—22no—
213C22—21no—
214C22—21no—
215C22—41no—
216C22—41no—
217C22—42no—
218C22—42no—
219C22—2961no—
220C22—744no—
221C22—741no—
222C22—741no—
223C22—1481no—
224C22—1481no—
225C22—1482no—
226C22—1484no—
227C22—1484no—
228C22—1484no—
229C22—1488no—
230C22—1482no—
231C22—1482no—
232C22—1484no—
233C22#1192459511yescharacteristic
234C22#1192459511yescharacteristic
235C22C2×C22⋊#386611yescharacteristic
236C4—42no—
237C4—2962no—
238C4—741no—
239C4—741no—
240C2—21no—
241C2—21no—
242C2—41no—
243C2—41no—
244C2—1481no—
245C2—1481no—
246C2—1484no—
247C2#1455843412yesdirect product factor
248C2C2×#1192459511yescharacteristic
subgroupG/H
centerC22#11924595
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC2×C22⋊C4×C37C4
socleC22×C37#99
prime radicalC2×#11924506C2
cosocleC2×C22⋊D37C23
hypercenterC2×C22⋊C4#3866
hypocenterC37C2×AΣL(1,𝔽16)
LCSG ▷ C23×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11924596C2semidirect
2. C2×#11924594C2semidirect
3. #14558434C2direct (N × H)
8. #11924596C22semidirect
10. #11924594C22semidirect
11. C24×D37C4semidirect
16. #11924506C4semidirect
19. C2×C22⋊C4×C37C4semidirect
26. C23×D37C2×C4semidirect
46. C22⋊C4×C37C2×C4semidirect
120. C2×C37AΣL(1,𝔽16)semidirect
129. C37C2×AΣL(1,𝔽16)semidirect
140. C2×C22⋊C4#3866semidirect
173. C22⋊C4C2×#3866semidirect
247. C2#14558434direct (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
#145584342
C2×#119245062
C2×AΣL(1,𝔽16)37