Finite Group Databasebeta

← C2×#15689399 #20253102

Subgroups — C2×#15689399 #20253102

Order 6016.

448 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13094057C212yesmaximal
2C22×Dic188C211yesmaximal, characteristic, complemented
3C2×#13094030C211yesmaximal, characteristic
4#15689399C218yesmaximal, direct product factor
5C2×#13093942C212yesmaximal, complemented
6C2×#108×C47C211yesmaximal, characteristic, complemented
7C2×#10625350C2211yescharacteristic
8C22×Dic94C2212yes—
9#13094057—24no—
10#13094057C2218yes—
11C2×Dic188—22no—
12C2×Dic188—21no—
13C2×Dic188—21no—
14C2×Dic188—22no—
15C2×Dic188C2214yescomplemented
16C2×#10625325—22no—
17#13094030—22no—
18#13094030C2214yes—
19C2×#10625329C2211yescharacteristic
20C2×#10625324—21no—
21C2×C8×D47—21no—
22#13093942C2218yescomplemented
23C2×M16×C47C2212yes—
24C22×C8×C47C2211yescharacteristic
25#108×C47C2214yescomplemented
26C22×C4×C47C2311yescharacteristic
27C2×C22⋊D47—21no—
28C22×Dic47—22no—
29#10625350—21no—
30#10625350—21no—
31#10625350D412yes—
32#10625350C2312yes—
33C2×D188D411yescharacteristic
34C2×C4×D47—21no—
35C2×Dic94—22no—
36C2×Dic94—22no—
37C2×Dic94—22no—
38C2×Dic94—22no—
39C2×Dic94—22no—
40C2×Dic94D411yescharacteristic
41C2×Dic94C2314yes—
42M16×C47—22no—
43M16×C47C2314yes—
44C2×C8×C47—22no—
45C2×C8×C47D411yescharacteristic
46C2×C8×C47D411yescharacteristic
47C2×C8×C47D412yes—
48C2×C8×C47C2312yes—
49#10625329—21no—
50#10625329C2312yes—
51C2×C47⋊C8—21no—
52Dic188—28no—
53Dic188—24no—
54Dic188—24no—
55#10625325—28no—
56#10625324—24no—
57C8×D47—24no—
58C23×C47#4111yescharacteristic
59C22×D47—21no—
60C2×C4×C47C2×D411yescharacteristic
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47C2×D411yescharacteristic
64C2×C4×C47#4111yescharacteristic
65C2×C4×C47C2411yescharacteristic
66C22⋊D47—22no—
67C22⋊D47—22no—
68C2×Dic47—21no—
69C2×Dic47—24no—
70C2×Dic47—42no—
71C2×Dic47—42no—
72D188—21no—
73D188C2×D412yes—
74C4×D47—22no—
75C4×D47—22no—
76Dic94—21no—
77Dic94—24no—
78Dic94—24no—
79Dic94—42no—
80Dic94—42no—
81Dic94C2×D412yes—
82C8×C47—24no—
83C8×C47C2×D412yes—
84C8×C47C2×D412yes—
85C47⋊C8—22no—
86C22×C47—22no—
87C22×C47#12111yescharacteristic
88C22×C47#12111yescharacteristic
89C22×C47C2×#4111yescharacteristic
90C2×D47—22no—
91C2×D47—42no—
92C4×C47#12111yescharacteristic
93C4×C47#12111yescharacteristic
94C4×C47C22×D411yescharacteristic
95C4×C47C22×D411yescharacteristic
96Dic47—22no—
97Dic47—44no—
98C2×#473—471nomaximal, Sylow
99C2×C47—21no—
100C2×C47—21no—
101C2×C47#47312yescomplemented
102C2×C47C2×#12111yescharacteristic
103D47—42no—
104C2×#137—472no—
105C22×Q16—471no—
106C2×#131—471no—
107#473—478no—
108C2×#108D4711yescharacteristic, complemented
109C2×#101—472no—
110C47C2×#47311yescharacteristic, complemented, Sylow
111C2×#41—471no—
112C22×Q8—472no—
113#137—478no—
114#137—944no—
115C2×Q16—474no—
116C2×Q16—942no—
117C2×Q16—941no—
118C2×Q16—941no—
119C2×Q16—942no—
120C2×SD16—942no—
121#131—474no—
122#131—942no—
123C2×M16—471no—
124C2×M16—941no—
125C2×M16C2×D4712yes—
126C22×C8—941no—
127C22×C8C2×D4711yescharacteristic
128#108C2×D4714yescomplemented
129#101—478no—
130#41—472no—
131#41—472no—
132#41—941no—
133#41—941no—
134C2×Q8—471no—
135C2×Q8—474no—
136C2×Q8—942no—
137C2×Q8—942no—
138C2×Q8—942no—
139C2×Q8—942no—
140C2×Q8—942no—
141C2×D4—471no—
142C2×D4—941no—
143C22×C4—941no—
144C22×C4—942no—
145C22×C4C22×D4711yescharacteristic
146Q16—948no—
147Q16—944no—
148Q16—944no—
149SD16—948no—
150M16—22no—
151M16—472no—
152M16—941no—
153M16—944no—
154M16C22×D4714yes—
155C2×C8—22no—
156C2×C8—941no—
157C2×C8—944no—
158C2×C8D18811yescharacteristic
159C2×C8D18811yescharacteristic
160C2×C8D18812yes—
161C2×C8C22×D4712yes—
162C23—941no—
163C23#1062535411yescharacteristic
164Q8—472no—
165Q8—941no—
166Q8—944no—
167Q8—944no—
168Q8—1882no—
169Q8—1882no—
170D4—472no—
171D4—942no—
172D4—942no—
173D4—941no—
174C2×C4—941no—
175C2×C4—942no—
176C2×C4—942no—
177C2×C4—944no—
178C2×C4—1882no—
179C2×C4—1882no—
180C2×C4C2×D18811yescharacteristic
181C2×C4C2×D18811yescharacteristic
182C2×C4D4×D4711yescharacteristic
183C2×C4D4×D4711yescharacteristic
184C2×C4#1062535411yescharacteristic
185C2×C4C23×D4711yescharacteristic
186C8—24no—
187C8—942no—
188C8C2×D18812yes—
189C8C2×D18812yes—
190C22—22no—
191C22—942no—
192C22—1882no—
193C22#1309399911yescharacteristic
194C22#1309399911yescharacteristic
195C22C2×#1062535411yescharacteristic
196C4—942no—
197C4—1884no—
198C4#1309399911yescharacteristic
199C4#1309399911yescharacteristic
200C4C2×D4×D4711yescharacteristic
201C4C22×D18811yescharacteristic
202C2—21no—
203C2—21no—
204C2—1882no—
205C2#1568939912yesdirect product factor
206C2C2×#1309399911yescharacteristic
subgroupG/H
centerC22#13093999
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#108×C47C2
socleC22×C47#121
hypercenterC2×#108D47
hypocenterC47C2×#473
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#108

Complements

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

NH ≅ G/Ntype
2. C22×Dic188C2semidirect
4. #15689399C2direct (N × H)
5. C2×#13093942C2semidirect
6. C2×#108×C47C2semidirect
15. C2×Dic188C22semidirect
22. #13093942C22semidirect
25. #108×C47C22semidirect
101. C2×C47#473semidirect
108. C2×#108D47semidirect
110. C47C2×#473semidirect
128. #108C2×D47semidirect
205. C2#15689399direct (N × H)