Finite Group Databasebeta

← C2×#14558084 #18007880

Subgroups — C2×#14558084 #18007880

Order 4736.

1728 conjugacy classes of subgroups; only the 557 normal subgroups are shown.

normal subgroups only

This group has 1728 conjugacy classes of subgroups — too many to draw. Only its 557 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×#10596966C212yesmaximal, complemented
2#14558084C2116yesmaximal, direct product factor
3C2×#11924533C211yesmaximal, characteristic, complemented
4C2×#11924525C212yesmaximal, complemented
5C2×#11924511C214yesmaximal, complemented
6C2×#11924498C214yesmaximal, complemented
7C2×C42×D37C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C37C211yesmaximal, characteristic, complemented
9C2×#10596966—216no—
10C2×#10596966C22116yescomplemented
11C22×D148C2214yes—
12C22×D148C2214yes—
13C22×D148C2212yes—
14C22×C4×D37C2212yes—
15C22×C4×D37C2214yes—
16C22×C4×D37C2211yescharacteristic
17#11924533C2218yescomplemented
18#11924525C22116yescomplemented
19#11924511C22132yescomplemented
20#11924498C22132yescomplemented
21C2×#10596938C2218yes—
22C2×C4×Dic37C2212yes—
23C2×C4×Dic37C2211yescharacteristic
24C42×D37C2218yescomplemented
25C22×Q8×C37C2212yes—
26C4⋊Q8×C37C2218yescomplemented
27C2×C4⋊C4×C37C2214yes—
28C2×C42×C37C2211yescharacteristic
29C23×D37C2314yes—
30C23×D37C2311yescharacteristic
31C2×Q8×C37—28no—
32C2×Q8×C37C2318yes—
33C22×C4×C37C2314yes—
34C22×C4×C37C2311yescharacteristic
35C22×C4×C37C2312yes—
36C22×Dic37C2312yes—
37C22×Dic37C2311yescharacteristic
38#10596966—264no—
39C2×D148—216no—
40C2×D148—28no—
41C2×D148—216no—
42C2×D148C23116yes—
43C2×D148C23116yes—
44C2×D148C2318yes—
45C2×C4×D37—28no—
46C2×C4×D37—216no—
47C2×C4×D37D418yescomplemented
48C2×C4×D37C2318yes—
49C2×C4×D37C23116yes—
50C2×C4×D37C2314yes—
51C4⋊C4×C37C23116yes—
52C42×C37C2314yes—
53#10596938C23132yes—
54C4×Dic37C2318yes—
55C4×Dic37C2314yes—
56C23×C37C2411yescharacteristic
57C22×D37—24no—
58C22×D37—28no—
59C22×D37—216no—
60C22×D37C2×D414yes—
61C22×D37C2418yes—
62C22×D37C2412yes—
63Q8×C37—216no—
64C2×C4×C37—28no—
65C2×C4×C37C2×D414yes—
66C2×C4×C37#4118yescomplemented
67C2×C4×C37C2418yes—
68C2×C4×C37C2412yes—
69C2×C4×C37C2414yes—
70C2×Dic37—24no—
71C2×Dic37C2×D414yes—
72C2×Dic37C2414yes—
73C2×Dic37C2412yes—
74D148—232no—
75D148—216no—
76D148—232no—
77C4×D37—216no—
78C4×D37—232no—
79C4×D37C2×D4116yescomplemented
80C22×C37C22×D412yes—
81C22×C37C2×#4114yes—
82C22×C37C2511yescharacteristic
83C2×D37—28no—
84C2×D37—24no—
85C2×D37—28no—
86C2×D37—216no—
87C2×D37—416no—
88C2×D37C22×D414yes—
89C4×C37—28no—
90C4×C37C22×D414yes—
91C4×C37C2×#4118yescomplemented
92Dic37—24no—
93Dic37C22×D414yes—
94C2×#532—371nomaximal, Sylow
95C2×C37#53214yescomplemented
96C2×C37C23×D411yescharacteristic
97C2×C37C22×#4112yes—
98D37—24no—
99D37—48no—
100C22×#41—372no—
101#532—3716no—
102C2×C4⋊Q8D3711yescharacteristic, complemented
103C2×#127—371no—
104C2×#124—372no—
105C2×#121—374no—
106C2×C4×D4—374no—
107C22×C42—371no—
108C37C2×#53211yescharacteristic, complemented, Sylow
109C2×#41—3716no—
110C2×#41—7416no—
111C22×Q8C2×D3712yes—
112C22×D4—374no—
113C22×D4—374no—
114C22×D4—372no—
115C23×C4—371no—
116C23×C4—374no—
117C23×C4—372no—
118C4⋊Q8C2×D3718yescomplemented
119#127—378no—
120#124—3716no—
121#121—3732no—
122C4×D4—3732no—
123C2×C4⋊C4C2×D3714yes—
124C2×C22⋊C4—378no—
125C2×C42—372no—
126C2×C42—371no—
127C2×C42—378no—
128C2×C42C2×D3711yescharacteristic
129C24—371no—
130C24—374no—
131#41—7464no—
132C2×Q8—28no—
133C2×Q8C22×D3718yes—
134C2×D4—3716no—
135C2×D4—3716no—
136C2×D4—378no—
137C2×D4—7416no—
138C2×D4—748no—
139C2×D4—7416no—
140C22×C4—371no—
141C22×C4—378no—
142C22×C4—374no—
143C22×C4—372no—
144C22×C4—378no—
145C22×C4—3716no—
146C22×C4—7416no—
147C22×C4—748no—
148C22×C4C22×D3714yes—
149C22×C4C22×D3711yescharacteristic
150C22×C4C22×D3712yes—
151C4⋊C4C22×D37116yes—
152C22⋊C4—3732no—
153C42—378no—
154C42—374no—
155C42C22×D3714yes—
156C23—374no—
157C23—372no—
158C23—378no—
159C23—744no—
160C23—748no—
161C23—7416no—
162C23C23×D3711yescharacteristic
163Q8—216no—
164D4—7432no—
165D4—7416no—
166D4—7432no—
167C2×C4—28no—
168C2×C4—374no—
169C2×C4—372no—
170C2×C4—3716no—
171C2×C4—374no—
172C2×C4—7432no—
173C2×C4—744no—
174C2×C4—7416no—
175C2×C4D4×D3714yes—
176C2×C4#1059696618yescomplemented
177C2×C4C23×D3718yes—
178C2×C4C23×D3712yes—
179C2×C4C23×D3714yes—
180C22—374no—
181C22—748no—
182C22—744no—
183C22—748no—
184C22—7416no—
185C22—14816no—
186C22C2×D4×D3712yes—
187C22C2×#1059696614yes—
188C22C24×D3711yescharacteristic
189C4—28no—
190C4—374no—
191C4—744no—
192C4C2×D4×D3714yes—
193C4C2×#1059696618yescomplemented
194C2—744no—
195C2—1488no—
196C2#1455808414yesdirect product factor
197C2C22×D4×D3711yescharacteristic
198C2C22×#1059696612yes—
subgroupG/H
centerC23C23×D37
commutator, cosocleC22×C37C25
FrattiniC22C24×D37
FittingC2×C4⋊Q8×C37C2
socleC23×C37C24
hypercenterC2×C4⋊Q8D37
hypocenterC37C2×#532
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#10596966C2semidirect
2. #14558084C2direct (N × H)
3. C2×#11924533C2semidirect
4. C2×#11924525C2semidirect
5. C2×#11924511C2semidirect
6. C2×#11924498C2semidirect
7. C2×C42×D37C2semidirect
8. C2×C4⋊Q8×C37C2semidirect
10. C2×#10596966C22semidirect
17. #11924533C22semidirect
18. #11924525C22semidirect
19. #11924511C22semidirect
20. #11924498C22semidirect
24. C42×D37C22semidirect
26. C4⋊Q8×C37C22semidirect
47. C2×C4×D37D4semidirect
66. C2×C4×C37#41semidirect
79. C4×D37C2×D4semidirect
91. C4×C37C2×#41semidirect
95. C2×C37#532semidirect
102. C2×C4⋊Q8D37semidirect
108. C37C2×#532semidirect
118. C4⋊Q8C2×D37semidirect
176. C2×C4#10596966semidirect
193. C4C2×#10596966semidirect
196. C2#14558084direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105969662
#145580842
C2×#119245332
C2×#119245252
C2×#119245112
C2×#119244982
C2×C42×D372
C2×C4⋊Q8×C372
C2×#53237