Finite Group Databasebeta

← C2×D4⋊#11924753 #34059976

Subgroups — C2×D4⋊#11924753 #34059976

Order 19072.

344 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 114 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×C4⋊#11924753C211yesmaximal, characteristic, complemented
2C2×C4×#11924753C211yesmaximal, characteristic, complemented
3D4⋊#11924753C214yesmaximal, direct product factor
4C2×D4×Dic149C211yesmaximal, characteristic
5C22×#11924753—21no—
6C22×#11924753—21no—
7C4⋊#11924753—21no—
8C4⋊#11924753C2212yescomplemented
9C4×#11924753—21no—
10C4×#11924753C2212yescomplemented
11C23×Dic149—21no—
12D4×Dic149—21no—
13D4×Dic149—21no—
14D4×Dic149C412yes—
15D4×Dic149C2212yes—
16C2×C4⋊Dic149C411yescharacteristic
17C2×C22⋊Dic149—21no—
18C2×C4×Dic149C2211yescharacteristic
19C22×D4×C149C411yescharacteristic
20C2×#11924753—24no—
21C2×#11924753—22no—
22C2×#11924753—22no—
23C2×#11924753—42no—
24C22×Dic149—22no—
25C22×Dic149—22no—
26C22×Dic149—21no—
27C22×Dic149—42no—
28C22×Dic149—42no—
29C22×Dic149D411yescharacteristic
30C22×Dic149D411yescharacteristic
31C4⋊Dic149—21no—
32C4⋊Dic149C2×C412yes—
33C22⋊Dic149—22no—
34C22⋊Dic149—22no—
35C4×Dic149C2×C411yescharacteristic
36C4×Dic149D411yescharacteristic
37C4×Dic149D411yescharacteristic
38C4×Dic149C2311yescharacteristic
39C24×C149—21no—
40C2×D4×C149—21no—
41C2×D4×C149—22no—
42C2×D4×C149C814yescomplemented
43C2×D4×C149C2×C412yes—
44C22×C4×C149C2×C411yescharacteristic
45#11924753—24no—
46#11924753—42no—
47C2×Dic149—22no—
48C2×Dic149—22no—
49C2×Dic149—42no—
50C2×Dic149—44no—
51C2×Dic149—42no—
52C2×Dic149—42no—
53C2×Dic149C22⋊C411yescharacteristic
54C2×Dic149C22⋊C411yescharacteristic
55C2×Dic149D812yes—
56C2×Dic149SD1612yes—
57C2×Dic149C2×D411yescharacteristic
58C2×Dic149C2×D411yescharacteristic
59C23×C149—24no—
60C23×C149—22no—
61C23×C149—42no—
62C23×C149—42no—
63C23×C149C22⋊C411yescharacteristic
64D4×C149—24no—
65D4×C149—22no—
66D4×C149C2×C814yescomplemented
67C2×C4×C149C22⋊C411yescharacteristic
68C2×C4×C149C2×C812yes—
69C2×C4×C149M1612yes—
70C2×C4×C149C22×C411yescharacteristic
71C22×C149—24no—
72C22×C149—48no—
73C22×C149—42no—
74C22×C149—42no—
75C22×C149C22⋊C812yes—
76C22×C149#10212yes—
77C22×C149#10412yes—
78C22×C149C2×C22⋊C411yescharacteristic
79C4×C149C22⋊C812yes—
80C4×C149C22×C811yescharacteristic
81C4×C149C2×M1611yescharacteristic
82Dic149—21no—
83Dic149—21no—
84Dic149—42no—
85Dic149#10212yes—
86Dic149C2×D811yescharacteristic
87Dic149C2×SD1611yescharacteristic
88C2×C149—44no—
89C2×C149D4⋊C814yescomplemented
90C2×C149C2×C22⋊C811yescharacteristic
91C2×C149C2×#10211yescharacteristic
92C2×C149C2×#10411yescharacteristic
93C149C2×D4⋊C811yescharacteristic, complemented, Sylow
94C2×D4⋊C8—1491nomaximal, Sylow
95C2×C4×D4—1491no—
96C2×C4⋊C8—1491no—
97C2×C4×C8—1491no—
98D4⋊C8—1494no—
99C22×D4#1059701011yescharacteristic
100C23×C4—2981no—
101C22×C8—2981no—
102C22×C8—2981no—
103C4×D4—2981no—
104C4×D4—2981no—
105C4×D4—1492no—
106C4×D4—1492no—
107C2×C4⋊C4—1491no—
108C2×C22⋊C4—2981no—
109C2×C42—1491no—
110C4⋊C8—2981no—
111C4⋊C8—1492no—
112C4×C8—2981no—
113C4×C8—1492no—
114C24—21no—
115C2×D4—21no—
116C2×D4—22no—
117C2×D4#1192475314yescomplemented
118C2×D4C2×#1059701012yes—
119C22×C4—2981no—
120C22×C4—2982no—
121C22×C4—2982no—
122C22×C4—5962no—
123C22×C4—5962no—
124C22×C4—1491no—
125C22×C4—1491no—
126C22×C4C2×#1059701011yescharacteristic
127C2×C8—2984no—
128C2×C8—2982no—
129C2×C8—2982no—
130C2×C8—5962no—
131C4⋊C4—2981no—
132C4⋊C4—1492no—
133C22⋊C4—2982no—
134C22⋊C4—2982no—
135C42—1491no—
136C42—1491no—
137C42—1491no—
138C42—1491no—
139C23—24no—
140C23—22no—
141C23—42no—
142C23—42no—
143C23C22⋊#1059701011yescharacteristic
144D4—24no—
145D4—22no—
146D4C2×#1192475314yescomplemented
147C2×C4—2982no—
148C2×C4—2982no—
149C2×C4—5962no—
150C2×C4—5962no—
151C2×C4—5964no—
152C2×C4—5962no—
153C2×C4—1491no—
154C2×C4—1491no—
155C2×C4—1492no—
156C2×C4—1492no—
157C2×C4—1491no—
158C2×C4—1491no—
159C2×C4C22⋊#1059701011yescharacteristic
160C2×C4C2×#1192475312yes—
161C2×C4#1455874512yes—
162C2×C4C22×#1059701011yescharacteristic
163C8—2984no—
164C8—5962no—
165C22—24no—
166C22—48no—
167C22—42no—
168C22—42no—
169C22C22⋊#1192475312yes—
170C22#1801197312yes—
171C22#1801197512yes—
172C22C2×C22⋊#1059701011yescharacteristic
173C4—2981no—
174C4—2981no—
175C4—5962no—
176C4—1491no—
177C4—1492no—
178C4—1491no—
179C4C22⋊#1192475312yes—
180C4C22×#1192475311yescharacteristic
181C4C2×#1455874511yescharacteristic
182C2—44no—
183C2D4⋊#1192475314yesdirect product factor
184C2C2×C22⋊#1192475311yescharacteristic
185C2C2×#1801197311yescharacteristic
186C2C2×#1801197511yescharacteristic
subgroupG/H
centerC23C22⋊#10597010
commutatorC4×C149C22×C8
FrattiniC2×C4C22×#10597010
Fitting, prime radicalC22×D4×C149C4
socleC23×C149C22⋊C4
cosocleC4×Dic149C23
hypercenterC22×D4#10597010
hypocenterC149C2×D4⋊C8
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊#11924753C2semidirect
2. C2×C4×#11924753C2semidirect
3. D4⋊#11924753C2direct (N × H)
8. C4⋊#11924753C22semidirect
10. C4×#11924753C22semidirect
42. C2×D4×C149C8semidirect
66. D4×C149C2×C8semidirect
89. C2×C149D4⋊C8semidirect
93. C149C2×D4⋊C8semidirect
117. C2×D4#11924753semidirect
146. D4C2×#11924753semidirect
183. C2D4⋊#11924753direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4⋊#119247532
C2×C4×#119247532
D4⋊#119247532
C2×D4×Dic1492
C2×D4⋊C8149