Finite Group Databasebeta

← C2×#11927095 #14576919

Subgroups — C2×#11927095 #14576919

Order 2432.

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×#64545C212yesmaximal, complemented
2#11927095C2116yesmaximal, direct product factor
3C2×#10597320C211yesmaximal, characteristic, complemented
4C2×#10597393C212yesmaximal, complemented
5C2×#10597341C214yesmaximal, complemented
6C2×#10597339C214yesmaximal, complemented
7C2×C42×D19C211yesmaximal, characteristic, complemented
8C2×C19×C4⋊Q8C211yesmaximal, characteristic, complemented
9C22×Q8×C19C2212yes—
10C2×#64545—216no—
11C2×#64545C22116yescomplemented
12C22×D76C2212yes—
13C22×D76C2214yes—
14C22×D76C2214yes—
15C22×C4×D19C2214yes—
16C22×C4×D19C2212yes—
17C22×C4×D19C2211yescharacteristic
18C19×C4⋊Q8C2218yescomplemented
19C2×C4⋊C4×C19C2214yes—
20C2×C42×C19C2211yescharacteristic
21#10597393C22116yescomplemented
22C2×(C2×D19)⋊C4C2218yes—
23C2×C4×Dic19C2211yescharacteristic
24C2×C4×Dic19C2212yes—
25#10597341C22132yescomplemented
26#10597339C22132yescomplemented
27#10597320C2218yescomplemented
28C42×D19C2218yescomplemented
29C23×D19C2314yes—
30C23×D19C2311yescharacteristic
31C2×Q8×C19—28no—
32C2×Q8×C19C2318yes—
33C22×C4×C19C2314yes—
34C22×C4×C19C2311yescharacteristic
35C22×C4×C19C2312yes—
36C22×Dic19C2312yes—
37C22×Dic19C2311yescharacteristic
38#64545—264no—
39C2×D76—216no—
40C2×D76—28no—
41C2×D76—216no—
42C2×D76C2318yes—
43C2×D76C23116yes—
44C2×D76C23116yes—
45C2×C4×D19—28no—
46C2×C4×D19—216no—
47C2×C4×D19D418yescomplemented
48C2×C4×D19C23116yes—
49C2×C4×D19C2318yes—
50C2×C4×D19C2314yes—
51C4⋊C4×C19C23116yes—
52C42×C19C2314yes—
53(C2×D19)⋊C4C23132yes—
54C4×Dic19C2314yes—
55C4×Dic19C2318yes—
56C23×C19C2411yescharacteristic
57C22×D19—24no—
58C22×D19—28no—
59C22×D19—216no—
60C22×D19C2×D414yes—
61C22×D19C2418yes—
62C22×D19C2412yes—
63Q8×C19—216no—
64C2×C4×C19—28no—
65C2×C4×C19C2×D414yes—
66C2×C4×C19#4118yescomplemented
67C2×C4×C19C2418yes—
68C2×C4×C19C2412yes—
69C2×C4×C19C2414yes—
70C2×Dic19—24no—
71C2×Dic19C2×D414yes—
72C2×Dic19C2414yes—
73C2×Dic19C2412yes—
74D76—232no—
75D76—216no—
76D76—232no—
77C4×D19—216no—
78C4×D19—232no—
79C4×D19C2×D4116yescomplemented
80C2×#532—191nomaximal, Sylow
81C22×C19C22×D412yes—
82C22×C19C2×#4114yes—
83C22×C19C2511yescharacteristic
84C2×D19—28no—
85C2×D19—24no—
86C2×D19—28no—
87C2×D19—216no—
88C2×D19—416no—
89C2×D19C22×D414yes—
90C4×C19—28no—
91C4×C19C22×D414yes—
92C4×C19C2×#4118yescomplemented
93Dic19—24no—
94Dic19C22×D414yes—
95C22×#41—192no—
96#532—1916no—
97C2×C4⋊Q8D1911yescharacteristic, complemented
98C2×#127—191no—
99C2×#124—192no—
100C2×#121—194no—
101C2×C4×D4—194no—
102C22×C42—191no—
103C2×C19#53214yescomplemented
104C2×C19C23×D411yescharacteristic
105C2×C19C22×#4112yes—
106D19—24no—
107D19—48no—
108C2×#41—1916no—
109C2×#41—3816no—
110C22×Q8C2×D1912yes—
111C22×D4—194no—
112C22×D4—194no—
113C22×D4—192no—
114C23×C4—191no—
115C23×C4—194no—
116C23×C4—192no—
117C4⋊Q8C2×D1918yescomplemented
118#127—198no—
119#124—1916no—
120#121—1932no—
121C4×D4—1932no—
122C2×C4⋊C4C2×D1914yes—
123C2×C22⋊C4—198no—
124C2×C42—192no—
125C2×C42—191no—
126C2×C42—198no—
127C2×C42C2×D1911yescharacteristic
128C19C2×#53211yescharacteristic, complemented, Sylow
129C24—191no—
130C24—194no—
131#41—3864no—
132C2×Q8—28no—
133C2×Q8C22×D1918yes—
134C2×D4—1916no—
135C2×D4—1916no—
136C2×D4—198no—
137C2×D4—3816no—
138C2×D4—388no—
139C2×D4—3816no—
140C22×C4—191no—
141C22×C4—198no—
142C22×C4—194no—
143C22×C4—192no—
144C22×C4—198no—
145C22×C4—1916no—
146C22×C4—3816no—
147C22×C4—388no—
148C22×C4C22×D1914yes—
149C22×C4C22×D1911yescharacteristic
150C22×C4C22×D1912yes—
151C4⋊C4C22×D19116yes—
152C22⋊C4—1932no—
153C42—198no—
154C42—194no—
155C42C22×D1914yes—
156C23—194no—
157C23—192no—
158C23—198no—
159C23—384no—
160C23—388no—
161C23—3816no—
162C23C23×D1911yescharacteristic
163Q8—216no—
164D4—3832no—
165D4—3816no—
166D4—3832no—
167C2×C4—28no—
168C2×C4—194no—
169C2×C4—192no—
170C2×C4—1916no—
171C2×C4—194no—
172C2×C4—3832no—
173C2×C4—384no—
174C2×C4—3816no—
175C2×C4D4×D1914yes—
176C2×C4#6454518yescomplemented
177C2×C4C23×D1918yes—
178C2×C4C23×D1912yes—
179C2×C4C23×D1914yes—
180C22—194no—
181C22—388no—
182C22—384no—
183C22—388no—
184C22—3816no—
185C22—7616no—
186C22C2×D4×D1912yes—
187C22C2×#6454514yes—
188C22C24×D1911yescharacteristic
189C4—28no—
190C4—194no—
191C4—384no—
192C4C2×D4×D1914yes—
193C4C2×#6454518yescomplemented
194C2—384no—
195C2—768no—
196C2#1192709514yesdirect product factor
197C2C22×D4×D1911yescharacteristic
198C2C22×#6454512yes—
subgroupG/H
centerC23C23×D19
commutator, cosocleC22×C19C25
FrattiniC22C24×D19
FittingC2×C19×C4⋊Q8C2
socleC23×C19C24
hypercenterC2×C4⋊Q8D19
hypocenterC19C2×#532
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#64545C2semidirect
2. #11927095C2direct (N × H)
3. C2×#10597320C2semidirect
4. C2×#10597393C2semidirect
5. C2×#10597341C2semidirect
6. C2×#10597339C2semidirect
7. C2×C42×D19C2semidirect
8. C2×C19×C4⋊Q8C2semidirect
11. C2×#64545C22semidirect
18. C19×C4⋊Q8C22semidirect
21. #10597393C22semidirect
25. #10597341C22semidirect
26. #10597339C22semidirect
27. #10597320C22semidirect
28. C42×D19C22semidirect
47. C2×C4×D19D4semidirect
66. C2×C4×C19#41semidirect
79. C4×D19C2×D4semidirect
92. C4×C19C2×#41semidirect
97. C2×C4⋊Q8D19semidirect
103. C2×C19#532semidirect
117. C4⋊Q8C2×D19semidirect
128. C19C2×#532semidirect
176. C2×C4#64545semidirect
193. C4C2×#64545semidirect
196. C2#11927095direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#645452
#119270952
C2×#105973202
C2×#105973932
C2×#105973412
C2×#105973392
C2×C42×D192
C2×C19×C4⋊Q82
C2×#53219