Finite Group Databasebeta

← C2×#14557718 #18003940

Subgroups — C2×#14557718 #18003940

Order 4736.

708 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11924584C211yesmaximal, characteristic
2C2×#11924569C212yesmaximal, complemented
3C2×#11924534C211yesmaximal, characteristic, complemented
4#14557718C218yesmaximal, direct product factor
5C2×#11924462C212yesmaximal, complemented
6C2×#101×C37C211yesmaximal, characteristic, complemented
7#11924584—22no—
8#11924584—24no—
9#11924584C2214yes—
10C2×#10596966—22no—
11C2×#10596962—22no—
12C2×#10596962C2212yes—
13C22×Dic74C2211yescharacteristic
14C2×Q8×D37—22no—
15#11924569—24no—
16#11924569C2218yescomplemented
17C2×Dic148—22no—
18C2×#10596930—22no—
19#11924534—22no—
20#11924534C2214yescomplemented
21C2×#10596936—22no—
22C2×C4×Dic37C2211yescharacteristic
23#11924462C2218yescomplemented
24C22×Q8×C37C2211yescharacteristic
25C2×M16×C37C2212yes—
26#101×C37C2214yescomplemented
27C2×Q8×C37—22no—
28C2×Q8×C37—22no—
29C2×Q8×C37D412yes—
30C2×Q8×C37C2312yes—
31C22×C4×C37D412yes—
32C22×C4×C37C2311yescharacteristic
33C2×C22⋊D37—22no—
34C22×Dic37—21no—
35C22×Dic37—21no—
36#10596966—28no—
37#10596966—28no—
38Q8×D37—28no—
39Q8×D37—28no—
40#10596962—28no—
41#10596962—28no—
42#10596962—22no—
43#10596962—22no—
44#10596962D414yes—
45#10596962C2314yes—
46C2×D148—22no—
47C2×D148D412yes—
48C2×C4×D37—24no—
49C2×C4×D37—22no—
50C2×Dic74—22no—
51C2×Dic74—22no—
52C2×Dic74—22no—
53C2×Dic74—21no—
54C2×Dic74D412yes—
55C2×Dic74C2312yes—
56M16×C37—22no—
57M16×C37C2314yes—
58C2×C8×C37—22no—
59#10596936—28no—
60C4×Dic37—21no—
61C4×Dic37C2312yes—
62Dic148—28no—
63#10596930—28no—
64C23×C37C2×D411yescharacteristic
65C22×D37—22no—
66Q8×C37—24no—
67Q8×C37—24no—
68C2×C4×C37—22no—
69C2×C4×C37—22no—
70C2×C4×C37C2×D414yes—
71C2×C4×C37C2×D411yescharacteristic
72C2×C4×C37C2×D412yes—
73C2×C4×C37C2×D412yes—
74C2×C4×C37C2411yescharacteristic
75C22⋊D37—24no—
76C22⋊D37—24no—
77C2×Dic37—24no—
78C2×Dic37—22no—
79C2×Dic37—22no—
80C2×Dic37—22no—
81C2×Dic37—41no—
82C2×Dic37—41no—
83D148—28no—
84D148—22no—
85D148C2×D414yes—
86C4×D37—216no—
87C4×D37—24no—
88C4×D37—24no—
89Dic74—28no—
90Dic74—22no—
91Dic74—24no—
92Dic74—42no—
93Dic74C2×D414yes—
94C8×C37—24no—
95C22×C37—22no—
96C22×C37#12011yescharacteristic
97C22×C37#12011yescharacteristic
98C22×C37C22×D411yescharacteristic
99C2×D37—24no—
100C2×D37—44no—
101C4×C37—24no—
102C4×C37#12012yes—
103C4×C37C22×D412yes—
104Dic37—24no—
105Dic37—24no—
106Dic37—42no—
107C2×#456—371nomaximal, Sylow
108C2×C37—21no—
109C2×C37—21no—
110C2×C37#45612yescomplemented
111C2×C37C2×#12011yescharacteristic
112D37—44no—
113C2×2−1+4—371no—
114C2×#137—372no—
115C2×C4⋊Q8—371no—
116#456—378no—
117C2×#104—372no—
118C2×#101D3711yescharacteristic, complemented
119C37C2×#45611yescharacteristic, complemented, Sylow
1202−1+4—374no—
1212−1+4—744no—
1222−1+4—742no—
123C2×#41—372no—
124C2×#41—742no—
125C2×#41—742no—
126C22×Q8—371no—
127C22×Q8—742no—
128C22×Q8C2×D3711yescharacteristic
129#137—378no—
130#137—744no—
131C2×Q16—742no—
132C2×SD16—742no—
133C2×M16C2×D3712yes—
134C4⋊Q8—374no—
135C4⋊Q8—742no—
136C2×C4⋊C4—742no—
137C2×C42—371no—
138#104—378no—
139#101C2×D3714yescomplemented
140#41—374no—
141#41—374no—
142#41—748no—
143#41—748no—
144#41—748no—
145#41—742no—
146#41—748no—
147#41—742no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—372no—
151C2×Q8—372no—
152C2×Q8—742no—
153C2×Q8—748no—
154C2×Q8—748no—
155C2×Q8—741no—
156C2×Q8—742no—
157C2×Q8—742no—
158C2×Q8D14812yes—
159C2×Q8C22×D3712yes—
160C2×D4—372no—
161C2×D4—742no—
162C2×D4—742no—
163C22×C4—744no—
164C22×C4—741no—
165C22×C4—742no—
166C22×C4—741no—
167C22×C4D14812yes—
168C22×C4C22×D3711yescharacteristic
169Q16—748no—
170SD16—748no—
171M16—22no—
172M16C22×D3714yes—
173C2×C8—22no—
174C4⋊C4—748no—
175C42—372no—
176C42—741no—
177C23—742no—
178C23C2×D14811yescharacteristic
179Q8—24no—
180Q8—24no—
181Q8—374no—
182Q8—748no—
183Q8—742no—
184Q8—744no—
185Q8—1482no—
186D4—374no—
187D4—748no—
188D4—744no—
189D4—744no—
190D4—742no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—7416no—
194C2×C4—744no—
195C2×C4—742no—
196C2×C4—742no—
197C2×C4—744no—
198C2×C4—744no—
199C2×C4—742no—
200C2×C4—1481no—
201C2×C4—1481no—
202C2×C4C2×D14814yes—
203C2×C4C2×D14811yescharacteristic
204C2×C4D4×D3712yes—
205C2×C4D4×D3712yes—
206C2×C4C23×D3711yescharacteristic
207C8—24no—
208C22—22no—
209C22—744no—
210C22—1484no—
211C22#1192450611yescharacteristic
212C22#1192450611yescharacteristic
213C22C22×D14811yescharacteristic
214C4—24no—
215C4—744no—
216C4—744no—
217C4—1482no—
218C4#1192450612yes—
219C4C2×D4×D3712yes—
220C2—21no—
221C2—21no—
222C2—1484no—
223C2#1455771812yesdirect product factor
224C2C2×#1192450611yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC2×#101×C37C2
socleC22×C37#120
prime radicalC2×#11924584C2
hypercenterC2×#101D37
hypocenterC37C2×#456
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#11924569C2semidirect
3. C2×#11924534C2semidirect
4. #14557718C2direct (N × H)
5. C2×#11924462C2semidirect
6. C2×#101×C37C2semidirect
16. #11924569C22semidirect
20. #11924534C22semidirect
23. #11924462C22semidirect
26. #101×C37C22semidirect
110. C2×C37#456semidirect
118. C2×#101D37semidirect
119. C37C2×#456semidirect
139. #101C2×D37semidirect
223. C2#14557718direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#119245842
C2×#119245692
C2×#119245342
#145577182
C2×#119244622
C2×#101×C372
C2×#45637