Finite Group Databasebeta

← C2×#14557777 #18004182

Subgroups — C2×#14557777 #18004182

Order 4736.

544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C22×#10596940C211yesmaximal, characteristic, complemented
2C22×#10596934C211yesmaximal, characteristic, complemented
3C2×#11924515C211yesmaximal, characteristic, complemented
4#14557777C218yesmaximal, direct product factor
5C2×#11924469C211yesmaximal, characteristic, complemented
6C2×#11924459C211yesmaximal, characteristic, complemented
7C2×#11924457C211yesmaximal, characteristic, complemented
8C2×#121×C37C211yesmaximal, characteristic
9C22×Dic74C2211yescharacteristic
10C2×#10596940—24no—
11C2×#10596940C2214yescomplemented
12C2×#10596934—24no—
13C2×#10596934C2214yescomplemented
14C22×#64436C2211yescharacteristic
15C22×#64436C2211yescharacteristic
16#11924515—22no—
17#11924515C2214yescomplemented
18C2×C4⋊Dic37C2211yescharacteristic
19C2×#10596936—21no—
20C2×C22⋊Dic37—21no—
21#11924469C2214yescomplemented
22#11924459C2214yescomplemented
23#11924457C2214yescomplemented
24C22×D4×C37—21no—
25C22×D4×C37C2211yescharacteristic
26C23×C4×C37C2211yescharacteristic
27#121×C37—22no—
28#121×C37C2214yes—
29C2×C4⋊C4×C37C2211yescharacteristic
30C2×C22⋊C4×C37—21no—
31C24×C37—21no—
32C24×C37D411yescharacteristic
33C2×D4×C37—24no—
34C2×D4×C37—22no—
35C2×D4×C37—21no—
36C2×D4×C37—22no—
37C2×D4×C37—44no—
38C2×D4×C37C2312yes—
39C22×C4×C37—22no—
40C22×C4×C37—22no—
41C22×C4×C37—21no—
42C22×C4×C37D411yescharacteristic
43C22×C4×C37D412yes—
44C22×C4×C37C2312yes—
45C22×C4×C37C2311yescharacteristic
46C22×Dic37—21no—
47C22×Dic37—21no—
48C2×Dic74—22no—
49C2×Dic74—22no—
50C2×Dic74—21no—
51C2×Dic74C2312yes—
52C4⋊C4×C37—21no—
53C4⋊C4×C37C2312yes—
54C22⋊C4×C37—24no—
55C22⋊Dic37—24no—
56#10596940—28no—
57C4⋊Dic37—21no—
58C4⋊Dic37C2312yes—
59#10596936—24no—
60#10596934—28no—
61C2×#64436—22no—
62C2×#64436D414yescomplemented
63C2×#64436C2312yes—
64C2×#64436C2312yes—
65C23×C37—22no—
66C23×C37—22no—
67C23×C37—22no—
68C23×C37—22no—
69C23×C37—42no—
70C23×C37—42no—
71C23×C37—42no—
72C23×C37C2×D412yes—
73C23×C37C2×D411yescharacteristic
74D4×C37—22no—
75D4×C37—22no—
76D4×C37—48no—
77D4×C37—42no—
78C2×C4×C37—22no—
79C2×C4×C37—24no—
80C2×C4×C37—22no—
81C2×C4×C37—22no—
82C2×C4×C37—22no—
83C2×C4×C37—42no—
84C2×C4×C37C2×D412yes—
85C2×C4×C37C2×D412yes—
86C2×C4×C37C2×D411yescharacteristic
87C2×C4×C37#4112yes—
88C2×C4×C37C2411yescharacteristic
89C2×Dic37—22no—
90C2×Dic37—22no—
91C2×Dic37—42no—
92C2×Dic37—42no—
93Dic74—22no—
94Dic74—22no—
95Dic74—42no—
96#64436—22no—
97#64436C2×D414yescomplemented
98C22×C37—22no—
99C22×C37—22no—
100C22×C37—22no—
101C22×C37—44no—
102C22×C37—42no—
103C22×C37—42no—
104C22×C37—42no—
105C22×C37—84no—
106C22×C37#12112yes—
107C22×C37AGL(1,ℤ/8)12yes—
108C22×C37#13712yes—
109C22×C37C22×D411yescharacteristic
110C4×C37—22no—
111C4×C37—42no—
112C4×C37#12112yes—
113C4×C37C22×D411yescharacteristic
114C4×C37C2×#4111yescharacteristic
115Dic37—42no—
116Dic37—42no—
117C2×#468—371nomaximal, Sylow
118C2×C37—42no—
119C2×C37—82no—
120C2×C37#46814yescomplemented
121C2×C37C2×#12111yescharacteristic
122C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
123C2×C37C2×#13711yescharacteristic
124C22×SD16—371no—
125C22×M16—371no—
126C2×C22⋊Q8—371no—
127C2×#121D3711yescharacteristic
128#468—378no—
129C2×#107—371no—
130C2×#103—371no—
131C2×#102—371no—
132C37C2×#46811yescharacteristic, complemented, Sylow
133C22×Q8—371no—
134C22×D4—21no—
135C22×D4C2×D3711yescharacteristic
136C23×C4C2×D3711yescharacteristic
137C2×SD16—374no—
138C2×SD16—744no—
139C2×M16—374no—
140C2×M16—744no—
141C22×C8—371no—
142C22×C8—371no—
143C22⋊Q8—374no—
144C22⋊Q8—742no—
145#121—22no—
146#121C2×D3714yes—
147C2×C4⋊C4—371no—
148C2×C4⋊C4—741no—
149C2×C4⋊C4C2×D3711yescharacteristic
150C2×C22⋊C4—21no—
151C2×C22⋊C4—741no—
152#107—374no—
153#103—374no—
154#102—374no—
155C24—21no—
156C24C22⋊D3711yescharacteristic
157C2×Q8—372no—
158C2×Q8—741no—
159C2×Q8—742no—
160C2×Q8—742no—
161C2×D4—24no—
162C2×D4—22no—
163C2×D4—22no—
164C2×D4—21no—
165C2×D4—44no—
166C2×D4C22×D3712yes—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—21no—
170C22×C4—741no—
171C22×C4—741no—
172C22×C4C22⋊D3712yes—
173C22×C4C22⋊D3711yescharacteristic
174C22×C4C22×D3712yes—
175C22×C4C22×D3711yescharacteristic
176SD16—748no—
177M16—748no—
178C2×C8—374no—
179C2×C8—372no—
180C2×C8—372no—
181C2×C8—742no—
182C4⋊C4—21no—
183C4⋊C4—372no—
184C4⋊C4—744no—
185C4⋊C4—741no—
186C4⋊C4C22×D3712yes—
187C22⋊C4—24no—
188C22⋊C4—744no—
189C23—22no—
190C23—22no—
191C23—22no—
192C23—22no—
193C23—42no—
194C23—42no—
195C23—42no—
196C23C2×C22⋊D3712yes—
197C23C2×C22⋊D3711yescharacteristic
198Q8—742no—
199Q8—742no—
200Q8—1482no—
201D4—22no—
202D4—22no—
203D4—48no—
204D4—42no—
205C2×C4—22no—
206C2×C4—24no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—42no—
211C2×C4—742no—
212C2×C4—742no—
213C2×C4—1482no—
214C2×C4—1482no—
215C2×C4D4×D3712yes—
216C2×C4#1059696412yes—
217C2×C4C2×C22⋊D3712yes—
218C2×C4C2×C22⋊D3711yescharacteristic
219C2×C4C23×D3711yescharacteristic
220C8—374no—
221C8—742no—
222C22—22no—
223C22—22no—
224C22—22no—
225C22—44no—
226C22—42no—
227C22—42no—
228C22—42no—
229C22—84no—
230C22#1192450812yes—
231C22#1192456212yes—
232C22#1192456612yes—
233C22C22×C22⋊D3711yescharacteristic
234C4—22no—
235C4—42no—
236C4—1482no—
237C4—1482no—
238C4#1192450812yes—
239C4C2×D4×D3711yescharacteristic
240C4C2×#1059696411yescharacteristic
241C2—42no—
242C2—82no—
243C2#1455777714yesdirect product factor
244C2C2×#1192450811yescharacteristic
245C2C2×#1192456211yescharacteristic
246C2C2×#1192456611yescharacteristic
subgroupG/H
centerC23C2×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
Fitting, prime radicalC2×#121×C37C2
socleC23×C37C2×D4
hypercenterC2×#121D37
hypocenterC37C2×#468
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×#10596940C2semidirect
2. C22×#10596934C2semidirect
3. C2×#11924515C2semidirect
4. #14557777C2direct (N × H)
5. C2×#11924469C2semidirect
6. C2×#11924459C2semidirect
7. C2×#11924457C2semidirect
11. C2×#10596940C22semidirect
13. C2×#10596934C22semidirect
17. #11924515C22semidirect
21. #11924469C22semidirect
22. #11924459C22semidirect
23. #11924457C22semidirect
62. C2×#64436D4semidirect
97. #64436C2×D4semidirect
120. C2×C37#468semidirect
132. C37C2×#468semidirect
243. C2#14557777direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105969402
C22×#105969342
C2×#119245152
#145577772
C2×#119244692
C2×#119244592
C2×#119244572
C2×#121×C372
C2×#46837