Finite Group Databasebeta

← C2×#16840037 #21455532

Subgroups — C2×#16840037 #21455532

Order 7808.

448 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14519807C212yesmaximal
2C22×Dic244C211yesmaximal, characteristic, complemented
3#16840037C218yesmaximal, direct product factor
4C2×#14519713C211yesmaximal, characteristic, complemented
5C2×#14519695C212yesmaximal, complemented
6C2×#131×C61C211yesmaximal, characteristic
7C22×Dic122C2212yes—
8#14519807—24no—
9#14519807C2218yes—
10C2×Dic244—21no—
11C2×Dic244—21no—
12C2×Dic244—22no—
13C2×Dic244C2214yescomplemented
14C2×#11758202—22no—
15C2×#11758200—22no—
16C2×#11758194C2212yes—
17#14519713C2214yescomplemented
18#14519695C2218yescomplemented
19C2×#41×C61C2211yescharacteristic
20#131×C61—22no—
21#131×C61C2214yes—
22C2×M16×C61—21no—
23C2×M16×C61C2211yescharacteristic
24C22×C8×C61—21no—
25C22×C8×C61C2211yescharacteristic
26#41×C61—21no—
27#41×C61—21no—
28#41×C61D412yes—
29#41×C61C2312yes—
30C2×Q8×C61D411yescharacteristic
31C2×D4×C61—21no—
32C2×D4×C61D411yescharacteristic
33C22×C4×C61—21no—
34C22×C4×C61C2311yescharacteristic
35C22×Dic61—22no—
36C2×Dic122—22no—
37C2×Dic122—22no—
38C2×Dic122—22no—
39C2×Dic122—22no—
40C2×Dic122—22no—
41C2×Dic122C2314yes—
42M16×C61—21no—
43M16×C61—24no—
44M16×C61C2312yes—
45C2×C8×C61—21no—
46C2×C8×C61—24no—
47C2×C8×C61D411yescharacteristic
48C2×C8×C61D411yescharacteristic
49C2×C8×C61D412yes—
50C2×C8×C61C2312yes—
51#11758202—28no—
52#11758200—28no—
53#11758194—22no—
54#11758194C2314yes—
55C2×#92418—22no—
56Dic244—24no—
57Dic244—24no—
58C23×C61—21no—
59C23×C61#4111yescharacteristic
60Q8×C61—21no—
61Q8×C61C2×D412yes—
62D4×C61—22no—
63D4×C61—22no—
64D4×C61—21no—
65D4×C61C2×D412yes—
66C2×C4×C61—21no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61#4111yescharacteristic
74C2×C4×C61C2411yescharacteristic
75C2×Dic61—24no—
76C2×Dic61—42no—
77C2×Dic61—42no—
78Dic122—24no—
79Dic122—24no—
80Dic122—42no—
81Dic122—42no—
82C8×C61—22no—
83C8×C61C2×D412yes—
84C8×C61C2×D412yes—
85#92418—24no—
86C22×C61—22no—
87C22×C61—22no—
88C22×C61—42no—
89C22×C61#12111yescharacteristic
90C22×C61#12111yescharacteristic
91C22×C61C2×#4111yescharacteristic
92C4×C61—22no—
93C4×C61#12111yescharacteristic
94C4×C61#12111yescharacteristic
95C4×C61C22×D411yescharacteristic
96C4×C61C22×D411yescharacteristic
97Dic61—44no—
98C2×#473—611nomaximal, Sylow
99C2×C61—21no—
100C2×C61—21no—
101C2×C61—42no—
102C2×C61#47312yescomplemented
103C2×C61C2×#12111yescharacteristic
104C2×#137—612no—
105C22×Q16—611no—
106C2×#131D6111yescharacteristic
107#473—618no—
108C2×#108—611no—
109C2×#101—612no—
110C61C2×#47311yescharacteristic, complemented, Sylow
111C2×#41C2×D6111yescharacteristic
112C22×Q8—612no—
113#137—618no—
114#137—1224no—
115C2×Q16—614no—
116C2×Q16—1222no—
117C2×Q16—1221no—
118C2×Q16—1221no—
119C2×Q16—1222no—
120C2×SD16—1222no—
121#131—22no—
122#131C2×D6114yes—
123C2×M16—21no—
124C2×M16—612no—
125C2×M16C2×D6111yescharacteristic
126C22×C8—21no—
127C22×C8C2×D6111yescharacteristic
128#108—614no—
129#101—618no—
130#41—21no—
131#41—21no—
132#41D24412yes—
133#41C22×D6112yes—
134C2×Q8—614no—
135C2×Q8—1222no—
136C2×Q8—1222no—
137C2×Q8—1222no—
138C2×Q8—1222no—
139C2×Q8—1222no—
140C2×Q8D24411yescharacteristic
141C2×D4—21no—
142C2×D4D24411yescharacteristic
143C22×C4—21no—
144C22×C4—1222no—
145C22×C4C22×D6111yescharacteristic
146Q16—1228no—
147Q16—1224no—
148Q16—1224no—
149SD16—1228no—
150M16—21no—
151M16—24no—
152M16—614no—
153M16—1222no—
154M16C22×D6112yes—
155C2×C8—21no—
156C2×C8—24no—
157C2×C8—1222no—
158C2×C8C22⋊D6111yescharacteristic
159C2×C8C22⋊D6111yescharacteristic
160C2×C8C22⋊D6112yes—
161C2×C8C22×D6112yes—
162C23—21no—
163C23#1175822211yescharacteristic
164Q8—21no—
165Q8—1224no—
166Q8—1224no—
167Q8—2442no—
168Q8—2442no—
169Q8C2×D24412yes—
170D4—22no—
171D4—22no—
172D4—21no—
173D4C2×D24412yes—
174C2×C4—21no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—1224no—
178C2×C4—2442no—
179C2×C4—2442no—
180C2×C4C2×D24411yescharacteristic
181C2×C4C2×D24411yescharacteristic
182C2×C4#1175822211yescharacteristic
183C2×C4C2×C22⋊D6111yescharacteristic
184C2×C4C2×C22⋊D6111yescharacteristic
185C2×C4C23×D6111yescharacteristic
186C8—22no—
187C8—1224no—
188C8C2×C22⋊D6112yes—
189C8C2×C22⋊D6112yes—
190C22—22no—
191C22—22no—
192C22—42no—
193C22#1451975111yescharacteristic
194C22#1451975111yescharacteristic
195C22C2×#1175822211yescharacteristic
196C4—22no—
197C4—2444no—
198C4#1451975111yescharacteristic
199C4#1451975111yescharacteristic
200C4C22×C22⋊D6111yescharacteristic
201C4C22×D24411yescharacteristic
202C2—21no—
203C2—21no—
204C2—42no—
205C2#1684003712yesdirect product factor
206C2C2×#1451975111yescharacteristic
subgroupG/H
centerC22#14519751
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#131×C61C2
socleC22×C61#121
hypercenterC2×#131D61
hypocenterC61C2×#473
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
2. C22×Dic244C2semidirect
3. #16840037C2direct (N × H)
4. C2×#14519713C2semidirect
5. C2×#14519695C2semidirect
13. C2×Dic244C22semidirect
17. #14519713C22semidirect
18. #14519695C22semidirect
102. C2×C61#473semidirect
110. C61C2×#473semidirect
205. C2#16840037direct (N × H)