Finite Group Databasebeta

← C2×D4×#10596842 #22627170

Subgroups — C2×D4×#10596842 #22627170

Order 9344.

616 conjugacy classes of subgroups; only the 215 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 215 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
1C23×#10596842C212yesmaximal, complemented
2D4×#10596842C218yesmaximal, direct product factor
3C2×C4⋊#10596842C211yesmaximal, characteristic, complemented
4C2×C22⋊#10596842C212yesmaximal, complemented
5C2×C4×#10596842C211yesmaximal, characteristic, complemented
6C2×D4×#64408C211yesmaximal, characteristic
7C22×#10596842—28no—
8C22×#10596842C2211yescharacteristic
9C22×#10596842C2212yes—
10C22×#10596842C2211yescharacteristic
11C22×#10596842C2218yescomplemented
12C4⋊#10596842C2214yescomplemented
13C22⋊#10596842C2218yescomplemented
14C4×#10596842C2214yescomplemented
15C23×#64408C2212yes—
16D4×#64408C414yes—
17D4×#64408C2214yes—
18C2×C4⋊#64408C411yescharacteristic
19C2×C22⋊#64408C412yes—
20C2×C4×#64408C2211yescharacteristic
21C2×D4×D73C411yescharacteristic
22C2×#10596842—24no—
23C2×#10596842—22no—
24C2×#10596842—216no—
25C2×#10596842D414yesdirect product factor
26C2×#10596842C2312yes—
27C2×#10596842C2314yes—
28C2×#10596842C2312yes—
29C22×#64408—24no—
30C22×#64408—24no—
31C22×#64408C2×C412yes—
32C22×#64408C2×C414yes—
33C22×#64408C2×C411yescharacteristic
34C22×#64408C2314yes—
35C22×#64408C2311yescharacteristic
36C4⋊#64408C2×C414yes—
37C22⋊#64408C2×C418yes—
38C4×#64408C2×C412yes—
39C4×#64408C2312yes—
40C23×D73C2×C412yes—
41C2×D292C811yescharacteristic, complemented
42C2×C22⋊D73C812yescomplemented
43D4×D73C814yescomplemented
44D4×D73C2×C414yes—
45C2×C4×D73C2×C411yescharacteristic
46C2×D4×C73C811yescharacteristic, complemented
47C23×C73C2×C812yescomplemented
48C22×D73—24no—
49C22×D73—24no—
50C22×D73C2×C814yescomplemented
51C22×D73C2×C812yescomplemented
52C22×D73C22×C414yes—
53C22×D73C22×C411yescharacteristic
54C2×#64408—24no—
55C2×#64408—22no—
56C2×#64408—28no—
57C2×#64408—24no—
58C2×#64408—24no—
59C2×#64408C22×C412yes—
60C2×#64408C22×C414yes—
61C2×#64408C22×C411yescharacteristic
62C2×#64408C2×D412yes—
63C2×#64408#4112yes—
64C2×#64408C2411yescharacteristic
65#10596842—24no—
66#10596842—22no—
67#10596842C2×D414yesdirect product factor
68D4×C73C2×C814yescomplemented
69C2×C4×C73C2×C811yescharacteristic, complemented
70C22⋊D73C2×C818yescomplemented
71C2×Dic73C2×C811yescharacteristic, complemented
72D292C2×C814yescomplemented
73C4×D73C2×C812yescomplemented
74C4×D73C22×C412yes—
75C22×C73—24no—
76C22×C73C22×C811yescharacteristic
77C22×C73C22×C814yescomplemented
78C2×D73—24no—
79C2×D73—24no—
80C2×D73—24no—
81C2×D73—28no—
82C2×D73C4×D412yes—
83C2×D73C22×C811yescharacteristic
84C2×D73C22×C814yescomplemented
85C2×D73#13112yes—
86C2×D73C23×C411yescharacteristic
87#64408—24no—
88#64408—22no—
89#64408C4×D412yes—
90#64408C22×D411yescharacteristic
91#64408C2×#4111yescharacteristic
92C4×C73C22×C812yescomplemented
93Dic73C22×C812yescomplemented
94C2×C73—24no—
95C2×C73C8×D412yescomplemented
96C2×C73C23×C811yescharacteristic
97D73—24no—
98D73C8×D412yescomplemented
99D73C2×C4×D411yescharacteristic
100D73C2×#13111yescharacteristic
101C2×C8×D4—731nomaximal, Sylow
102C73C2×C8×D411yescharacteristic, complemented, Sylow
103C23×C8—732no—
104C2×C4×D4—731no—
105C8×D4—738no—
106C2×C4⋊C8—731no—
107C2×C22⋊C8—732no—
108C2×C4×C8—731no—
109C22×D4—731no—
110C23×C4—732no—
111C22×C8—731no—
112C22×C8—732no—
113C22×C8—731no—
114C22×C8—738no—
115C22×C8—1468no—
116C4×D4—734no—
117C4×D4—734no—
118C2×C4⋊C4—731no—
119C2×C22⋊C4—732no—
120C2×C42—731no—
121C4⋊C8—734no—
122C22⋊C8—738no—
123C4×C8—734no—
124C24—732no—
125C2×D4—732no—
126C2×D4—734no—
127C2×D4—734no—
128C2×D4—731no—
129C2×D4#1059684211yescharacteristic, direct product factor
130C22×C4—731no—
131C22×C4—731no—
132C22×C4—731no—
133C22×C4—732no—
134C22×C4—734no—
135C22×C4—734no—
136C22×C4—1464no—
137C22×C4—1464no—
138C2×C8—734no—
139C2×C8—732no—
140C2×C8—732no—
141C2×C8—734no—
142C2×C8—14616no—
143C2×C8—1462no—
144C2×C8—1464no—
145C4⋊C4—734no—
146C22⋊C4—738no—
147C42—732no—
148C42—732no—
149C23—731no—
150C23—732no—
151C23—734no—
152C23—734no—
153C23—1464no—
154C23—1464no—
155C23C2×#1059684212yescomplemented
156D4—738no—
157D4—734no—
158D4C2×#1059684214yesdirect product factor
159C2×C4—731no—
160C2×C4—731no—
161C2×C4—732no—
162C2×C4—732no—
163C2×C4—731no—
164C2×C4—732no—
165C2×C4—732no—
166C2×C4—732no—
167C2×C4—734no—
168C2×C4—1464no—
169C2×C4—1464no—
170C2×C4—1468no—
171C2×C4—1464no—
172C2×C4—1462no—
173C2×C4C2×#1059684211yescharacteristic, complemented
174C8—734no—
175C8—1464no—
176C8—1462no—
177C22—24no—
178C22—732no—
179C22—732no—
180C22—731no—
181C22—731no—
182C22—734no—
183C22—1464no—
184C22—1464no—
185C22—1468no—
186C22—1464no—
187C22C22×#1059684211yescharacteristic
188C22C22×#1059684214yescomplemented
189C4—731no—
190C4—731no—
191C4—732no—
192C4—732no—
193C4—1464no—
194C4—1462no—
195C4C22×#1059684212yescomplemented
196C2—24no—
197C2—731no—
198C2—731no—
199C2—732no—
200C2—1464no—
201C2D4×#1059684212yesdirect product factor
202C2C23×#1059684211yescharacteristic
subgroupG/H
centerC22C22×#10596842
commutatorC2×C73C23×C8
FrattiniC2C23×#10596842
FittingC2×D4×C73C8
socleC22×C73C22×C8
hypercenterC2×D4#10596842
hypocenterC73C2×C8×D4
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C23×#10596842C2semidirect
2. D4×#10596842C2direct (N × H)
3. C2×C4⋊#10596842C2semidirect
4. C2×C22⋊#10596842C2semidirect
5. C2×C4×#10596842C2semidirect
11. C22×#10596842C22semidirect
12. C4⋊#10596842C22semidirect
13. C22⋊#10596842C22semidirect
14. C4×#10596842C22semidirect
25. C2×#10596842D4direct (N × H)
41. C2×D292C8semidirect
42. C2×C22⋊D73C8semidirect
43. D4×D73C8semidirect
46. C2×D4×C73C8semidirect
47. C23×C73C2×C8semidirect
50. C22×D73C2×C8semidirect
51. C22×D73C2×C8semidirect
67. #10596842C2×D4direct (N × H)
68. D4×C73C2×C8semidirect
69. C2×C4×C73C2×C8semidirect
70. C22⋊D73C2×C8semidirect
71. C2×Dic73C2×C8semidirect
72. D292C2×C8semidirect
73. C4×D73C2×C8semidirect
77. C22×C73C22×C8semidirect
84. C2×D73C22×C8semidirect
92. C4×C73C22×C8semidirect
93. Dic73C22×C8semidirect
95. C2×C73C8×D4semidirect
98. D73C8×D4semidirect
102. C73C2×C8×D4semidirect
129. C2×D4#10596842direct (N × H)
155. C23C2×#10596842semidirect
158. D4C2×#10596842direct (N × H)
173. C2×C4C2×#10596842semidirect
188. C22C22×#10596842semidirect
195. C4C22×#10596842semidirect
201. C2D4×#10596842direct (N × H)