Finite Group Databasebeta

← C2×#23749960 #34054596

Subgroups — C2×#23749960 #34054596

Order 19072.

460 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 165 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×#18011890C211yesmaximal, characteristic
2#23749960C218yesmaximal, direct product factor
3C2×#18011844C212yesmaximal, complemented
4C2×#18011834C212yesmaximal, complemented
5C2×C22⋊#11924746C211yesmaximal, characteristic
6C22×C4⋊C4×C149C211yesmaximal, characteristic
7C22×Dic298C2211yescharacteristic
8C22×#11924746C2212yes—
9#18011890—22no—
10#18011890C2214yes—
11C2×C4⋊Dic149C2211yescharacteristic
12C2×#14558715—21no—
13C2×C22⋊Dic149—21no—
14#18011844C2218yescomplemented
15#18011834C2218yescomplemented
16C22⋊#11924746C2214yes—
17C23×C4×C149—21no—
18C23×C4×C149C2211yescharacteristic
19C2×C4⋊C4×C149—21no—
20C2×C4⋊C4×C149—22no—
21C2×C4⋊C4×C149C2212yes—
22C2×C4⋊C4×C149C2214yes—
23C2×Dic298—21no—
24C2×Dic298—24no—
25C2×Dic298C2312yes—
26C22×Dic149—21no—
27C22×Dic149—21no—
28C2×#11924746—24no—
29C2×#11924746C2314yes—
30C4⋊Dic149—21no—
31C4⋊Dic149C2312yes—
32#14558715—24no—
33C22⋊Dic149—24no—
34C24×C149D411yescharacteristic
35C22×C4×C149—24no—
36C22×C4×C149—24no—
37C22×C4×C149—22no—
38C22×C4×C149—44no—
39C22×C4×C149D411yescharacteristic
40C22×C4×C149D412yes—
41C22×C4×C149C2312yes—
42C22×C4×C149C2311yescharacteristic
43C4⋊C4×C149—24no—
44C4⋊C4×C149—22no—
45C4⋊C4×C149C2314yes—
46Dic298—24no—
47Dic298—42no—
48C2×Dic149—22no—
49C2×Dic149—22no—
50C2×Dic149—42no—
51C2×Dic149—42no—
52#11924746—24no—
53C23×C149—22no—
54C23×C149—22no—
55C23×C149Q1614yes—
56C23×C149C2×D412yes—
57C23×C149C2×D411yescharacteristic
58C2×C4×C149—22no—
59C2×C4×C149—24no—
60C2×C4×C149—24no—
61C2×C4×C149—24no—
62C2×C4×C149—48no—
63C2×C4×C149—44no—
64C2×C4×C149C2×D412yes—
65C2×C4×C149C2×D411yescharacteristic
66C2×C4×C149#4114yes—
67C2×C4×C149C2411yescharacteristic
68C22×C149—22no—
69C22×C149—22no—
70C22×C149—28no—
71C22×C149#12312yes—
72C22×C149C2×Q1614yes—
73C22×C149C2×Q1612yes—
74C22×C149AGL(1,ℤ/8)12yes—
75C22×C149C22×D411yescharacteristic
76C4×C149—22no—
77C4×C149—44no—
78C4×C149#12312yes—
79C4×C149C2×#4112yes—
80Dic149—42no—
81Dic149—42no—
82C2×C149—24no—
83C2×C149#48414yescomplemented
84C2×C149C2×#12311yescharacteristic
85C2×C149C22×Q1611yescharacteristic
86C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
87C149C2×#48411yescharacteristic, complemented, Sylow
88C2×#484—1491nomaximal, Sylow
89C2×C22⋊Q8—1491no—
90C22×C4⋊C4D14911yescharacteristic
91#484—1498no—
92C2×#107—1492no—
93C2×#103—1492no—
94C2×C22⋊C8—1491no—
95C22×Q8—1491no—
96C23×C4—21no—
97C23×C4C2×D14911yescharacteristic
98C22×C8—1492no—
99C22⋊Q8—2982no—
100C22⋊Q8—1494no—
101C2×C4⋊C4—22no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—2981no—
104C2×C4⋊C4—1491no—
105C2×C4⋊C4C2×D14912yes—
106C2×C4⋊C4C2×D14914yes—
107C2×C22⋊C4—2981no—
108#107—1498no—
109#103—1498no—
110C22⋊C8—1494no—
111C24C22⋊D14911yescharacteristic
112C2×Q8—2981no—
113C2×Q8—2984no—
114C2×Q8—1492no—
115C22×C4—24no—
116C22×C4—24no—
117C22×C4—22no—
118C22×C4—44no—
119C22×C4—2981no—
120C22×C4—2981no—
121C22×C4C22⋊D14912yes—
122C22×C4C22⋊D14911yescharacteristic
123C22×C4C22×D14912yes—
124C22×C4C22×D14911yescharacteristic
125C2×C8—2984no—
126C2×C8—1494no—
127C4⋊C4—24no—
128C4⋊C4—22no—
129C4⋊C4—2984no—
130C4⋊C4—2981no—
131C4⋊C4—1492no—
132C4⋊C4C22×D14914yes—
133C22⋊C4—2984no—
134C23—22no—
135C23—22no—
136C23#1455872614yes—
137C23C2×C22⋊D14912yes—
138C23C2×C22⋊D14911yescharacteristic
139Q8—2984no—
140Q8—5962no—
141C2×C4—22no—
142C2×C4—24no—
143C2×C4—24no—
144C2×C4—24no—
145C2×C4—48no—
146C2×C4—44no—
147C2×C4—2982no—
148C2×C4—2982no—
149C2×C4—5962no—
150C2×C4—5962no—
151C2×C4C2×C22⋊D14912yes—
152C2×C4C2×C22⋊D14911yescharacteristic
153C2×C4#1455873614yes—
154C2×C4C23×D14911yescharacteristic
155C8—2984no—
156C22—22no—
157C22—28no—
158C22—22no—
159C22#1801189412yes—
160C22C2×#1455872614yes—
161C22C2×#1455872612yes—
162C22#1801193712yes—
163C22C22×C22⋊D14911yescharacteristic
164C4—22no—
165C4—44no—
166C4—5962no—
167C4—5962no—
168C4#1801189412yes—
169C4C2×#1455873612yes—
170C2—24no—
171C2#2374996014yesdirect product factor
172C2C2×#1801189411yescharacteristic
173C2C22×#1455872611yescharacteristic
174C2C2×#1801193711yescharacteristic
subgroupG/H
centerC23C2×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC22×C4⋊C4×C149C2
socleC23×C149C2×D4
prime radicalC24×C149D4
hypercenterC22×C4⋊C4D149
hypocenterC149C2×#484
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #23749960C2direct (N × H)
3. C2×#18011844C2semidirect
4. C2×#18011834C2semidirect
14. #18011844C22semidirect
15. #18011834C22semidirect
83. C2×C149#484semidirect
87. C149C2×#484semidirect
171. C2#23749960direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#180118902
#237499602
C2×#180118442
C2×#180118342
C2×C22⋊#119247462
C22×C4⋊C4×C1492
C2×#484149