Finite Group Databasebeta

← C2×#14557784 #18004190

Subgroups — C2×#14557784 #18004190

Order 4736.

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

normal subgroups only

This group has 596 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×#10596939C211yesmaximal, characteristic, complemented
2C22×#10596934C211yesmaximal, characteristic, complemented
3C2×#11924510C211yesmaximal, characteristic, complemented
4#14557784C218yesmaximal, direct product factor
5C2×#11924467C211yesmaximal, characteristic, complemented
6C2×#11924457C211yesmaximal, characteristic, complemented
7C2×#11924456C211yesmaximal, characteristic, complemented
8C2×#121×C37C211yesmaximal, characteristic, complemented
9C22×D148C2211yescharacteristic
10C22×C22⋊D37—21no—
11C2×#10596939—24no—
12C2×#10596939C2214yescomplemented
13C2×#10596934—24no—
14C2×#10596934C2214yescomplemented
15C22×#64436C2211yescharacteristic
16C22×#64436C2211yescharacteristic
17#11924510—22no—
18#11924510C2214yescomplemented
19C2×C4⋊Dic37C2211yescharacteristic
20C2×#10596938—21no—
21#11924467C2214yescomplemented
22#11924457C2214yescomplemented
23#11924456C2214yescomplemented
24C22×D4×C37—21no—
25C22×D4×C37C2211yescharacteristic
26C23×C4×C37C2211yescharacteristic
27#121×C37—22no—
28#121×C37C2214yescomplemented
29C2×C4⋊C4×C37C2211yescharacteristic
30C2×C22⋊C4×C37—21no—
31C24×C37—21no—
32C24×C37D411yescharacteristic
33C23×D37—21no—
34C2×D4×C37—24no—
35C2×D4×C37—22no—
36C2×D4×C37—21no—
37C2×D4×C37—22no—
38C2×D4×C37—44no—
39C2×D4×C37C2312yes—
40C22×C4×C37—22no—
41C22×C4×C37—22no—
42C22×C4×C37—21no—
43C22×C4×C37D411yescharacteristic
44C22×C4×C37D412yes—
45C22×C4×C37C2312yes—
46C22×C4×C37C2311yescharacteristic
47C2×C22⋊D37—24no—
48C2×C22⋊D37—44no—
49C22×Dic37—21no—
50C2×D148—22no—
51C2×D148—22no—
52C2×D148—21no—
53C2×D148C2312yes—
54C4⋊C4×C37—21no—
55C4⋊C4×C37C2312yes—
56C22⋊C4×C37—24no—
57#10596939—28no—
58#10596938—24no—
59C4⋊Dic37—21no—
60C4⋊Dic37C2312yes—
61#10596934—28no—
62C2×#64436—22no—
63C2×#64436D414yescomplemented
64C2×#64436C2312yes—
65C2×#64436C2312yes—
66C23×C37—22no—
67C23×C37—22no—
68C23×C37—22no—
69C23×C37—22no—
70C23×C37—42no—
71C23×C37—42no—
72C23×C37—42no—
73C23×C37C2×D412yes—
74C23×C37C2×D411yescharacteristic
75C22×D37—22no—
76C22×D37—42no—
77C22×D37—42no—
78C22×D37—42no—
79D4×C37—22no—
80D4×C37—22no—
81D4×C37—48no—
82D4×C37—42no—
83C2×C4×C37—22no—
84C2×C4×C37—24no—
85C2×C4×C37—22no—
86C2×C4×C37—22no—
87C2×C4×C37—22no—
88C2×C4×C37—42no—
89C2×C4×C37C2×D412yes—
90C2×C4×C37C2×D412yes—
91C2×C4×C37C2×D411yescharacteristic
92C2×C4×C37#4112yes—
93C2×C4×C37C2411yescharacteristic
94C22⋊D37—48no—
95C2×Dic37—22no—
96C2×Dic37—42no—
97D148—22no—
98D148—22no—
99D148—42no—
100#64436—22no—
101#64436C2×D414yescomplemented
102C22×C37—22no—
103C22×C37—22no—
104C22×C37—22no—
105C22×C37—44no—
106C22×C37—42no—
107C22×C37—42no—
108C22×C37—42no—
109C22×C37—84no—
110C22×C37#12112yes—
111C22×C37AGL(1,ℤ/8)12yes—
112C22×C37AGL(1,ℤ/8)12yes—
113C22×C37C22×D411yescharacteristic
114C2×D37—42no—
115C2×D37—42no—
116C2×D37—42no—
117C2×D37—84no—
118C4×C37—22no—
119C4×C37—42no—
120C4×C37#12112yes—
121C4×C37C22×D411yescharacteristic
122C4×C37C2×#4111yescharacteristic
123Dic37—42no—
124C2×#469—371nomaximal, Sylow
125C2×C37—42no—
126C2×C37—82no—
127C2×C37#46914yescomplemented
128C2×C37C2×#12111yescharacteristic
129C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
130C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
131D37—82no—
132C22×D8—371no—
133C22×M16—371no—
134C2×#121—371no—
135C2×#121D3711yescharacteristic, complemented
136#469—378no—
137C2×#106—371no—
138C2×#102—371no—
139C2×#102—371no—
140C37C2×#46911yescharacteristic, complemented, Sylow
141C22×D4—21no—
142C22×D4—371no—
143C22×D4—741no—
144C22×D4C2×D3711yescharacteristic
145C23×C4C2×D3711yescharacteristic
146C2×D8—374no—
147C2×D8—744no—
148C2×M16—374no—
149C2×M16—744no—
150C22×C8—371no—
151C22×C8—371no—
152#121—22no—
153#121—374no—
154#121—742no—
155#121C2×D3714yescomplemented
156C2×C4⋊C4—371no—
157C2×C4⋊C4C2×D3711yescharacteristic
158C2×C22⋊C4—21no—
159C2×C22⋊C4—741no—
160#106—374no—
161#102—374no—
162#102—374no—
163C24—21no—
164C24—741no—
165C24C22⋊D3711yescharacteristic
166C2×D4—24no—
167C2×D4—22no—
168C2×D4—22no—
169C2×D4—21no—
170C2×D4—44no—
171C2×D4—372no—
172C2×D4—744no—
173C2×D4—742no—
174C2×D4—742no—
175C2×D4—741no—
176C2×D4—1484no—
177C2×D4C22×D3712yes—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—21no—
181C22×C4—741no—
182C22×C4C22⋊D3712yes—
183C22×C4C22⋊D3711yescharacteristic
184C22×C4C22×D3712yes—
185C22×C4C22×D3711yescharacteristic
186D8—748no—
187M16—748no—
188C2×C8—374no—
189C2×C8—372no—
190C2×C8—372no—
191C2×C8—742no—
192C4⋊C4—21no—
193C4⋊C4—372no—
194C4⋊C4—741no—
195C4⋊C4C22×D3712yes—
196C22⋊C4—24no—
197C22⋊C4—744no—
198C23—22no—
199C23—22no—
200C23—22no—
201C23—22no—
202C23—42no—
203C23—42no—
204C23—42no—
205C23—742no—
206C23—1482no—
207C23—1482no—
208C23—1482no—
209C23C2×C22⋊D3712yes—
210C23C2×C22⋊D3711yescharacteristic
211D4—22no—
212D4—22no—
213D4—48no—
214D4—42no—
215D4—742no—
216D4—742no—
217D4—1488no—
218D4—1482no—
219C2×C4—22no—
220C2×C4—24no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—742no—
226C2×C4—1482no—
227C2×C4D4×D3712yes—
228C2×C4#1059696412yes—
229C2×C4C2×C22⋊D3712yes—
230C2×C4C2×C22⋊D3711yescharacteristic
231C2×C4C23×D3711yescharacteristic
232C8—374no—
233C8—742no—
234C22—22no—
235C22—22no—
236C22—22no—
237C22—44no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—84no—
242C22—2964no—
243C22—1482no—
244C22—1482no—
245C22—1482no—
246C22#1192450812yes—
247C22#1192456112yes—
248C22#1192456212yes—
249C22C22×C22⋊D3711yescharacteristic
250C4—22no—
251C4—42no—
252C4—1482no—
253C4#1192450812yes—
254C4C2×D4×D3711yescharacteristic
255C4C2×#1059696411yescharacteristic
256C2—42no—
257C2—82no—
258C2—2962no—
259C2#1455778414yesdirect product factor
260C2C2×#1192450811yescharacteristic
261C2C2×#1192456111yescharacteristic
262C2C2×#1192456211yescharacteristic
subgroupG/H
centerC23C2×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#121×C37C2
socleC23×C37C2×D4
hypercenterC2×#121D37
hypocenterC37C2×#469
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×#10596939C2semidirect
2. C22×#10596934C2semidirect
3. C2×#11924510C2semidirect
4. #14557784C2direct (N × H)
5. C2×#11924467C2semidirect
6. C2×#11924457C2semidirect
7. C2×#11924456C2semidirect
8. C2×#121×C37C2semidirect
12. C2×#10596939C22semidirect
14. C2×#10596934C22semidirect
18. #11924510C22semidirect
21. #11924467C22semidirect
22. #11924457C22semidirect
23. #11924456C22semidirect
28. #121×C37C22semidirect
63. C2×#64436D4semidirect
101. #64436C2×D4semidirect
127. C2×C37#469semidirect
135. C2×#121D37semidirect
140. C37C2×#469semidirect
155. #121C2×D37semidirect
259. C2#14557784direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105969392
C22×#105969342
C2×#119245102
#145577842
C2×#119244672
C2×#119244572
C2×#119244562
C2×#121×C372
C2×#46937