Finite Group Databasebeta

← C2×#1407 #13576

Subgroups — C2×#1407 #13576

Order 256.

208 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 47 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×#497C211yesmaximal, characteristic
2C2×#355C211yesmaximal, characteristic
3C2×#354C211yesmaximal, characteristic
4#1407C214yesmaximal, direct product factor
5C22×Q16—21no—
6C22×SD16—21no—
7C2×C4⋊Q8C411yescharacteristic, complemented
8C2×#124C2211yescharacteristic
9#497—21no—
10#497—21no—
11#497C412yescomplemented
12#497C2212yes—
13C2×#101—21no—
14C2×#99—21no—
15C2×#97C411yescharacteristic, complemented
16#355—21no—
17#355C2212yes—
18#354—21no—
19#354C2212yes—
20C22×Q8—21no—
21C22×Q8D411yescharacteristic
22C22×D4D411yescharacteristic
23C2×Q16—22no—
24C2×Q16—22no—
25C2×Q16—42no—
26C2×Q16—42no—
27C2×SD16—22no—
28C2×SD16—22no—
29C2×SD16—42no—
30C2×SD16—42no—
31C2×M16—41no—
32C22×C8—21no—
33C4⋊Q8—21no—
34C4⋊Q8—41no—
35C4⋊Q8C2×C412yescomplemented
36#124—41no—
37#124C2×C411yescharacteristic
38#124D411yescharacteristic
39#124D411yescharacteristic
40#124C2311yescharacteristic
41C2×C4⋊C4—41no—
42C2×C22⋊C4—41no—
43C2×C22⋊C4—41no—
44C2×C42C2×C411yescharacteristic
45#101—22no—
46#101—41no—
47#99—22no—
48#99—41no—
49#97—21no—
50#97C2×C412yescomplemented
51C24—21no—
52C2×Q8—21no—
53C2×Q8—22no—
54C2×Q8—41no—
55C2×Q8—41no—
56C2×Q8—41no—
57C2×Q8—41no—
58C2×Q8—41no—
59C2×Q8—41no—
60C2×Q8—41no—
61C2×Q8C22⋊C411yescharacteristic
62C2×Q8C2×D411yescharacteristic
63C2×D4—21no—
64C2×D4—41no—
65C2×D4—41no—
66C2×D4C22⋊C411yescharacteristic
67C2×D4C2×D411yescharacteristic
68C22×C4—21no—
69C22×C4—21no—
70C22×C4—41no—
71C22×C4—81no—
72C22×C4C22⋊C411yescharacteristic
73Q16—44no—
74Q16—44no—
75SD16—44no—
76SD16—44no—
77M16—42no—
78M16—81no—
79C2×C8—22no—
80C2×C8—22no—
81C2×C8—22no—
82C2×C8—81no—
83C4⋊C4—42no—
84C4⋊C4—42no—
85C22⋊C4—41no—
86C22⋊C4—41no—
87C22⋊C4—41no—
88C22⋊C4—41no—
89C22⋊C4—42no—
90C22⋊C4—81no—
91C42—21no—
92C42C22⋊C411yescharacteristic
93C42C22×C411yescharacteristic
94C23—21no—
95C23—21no—
96C23—41no—
97C23—41no—
98C23—82no—
99C23#9911yescharacteristic
100Q8—41no—
101Q8—41no—
102Q8—42no—
103Q8—42no—
104Q8—81no—
105Q8—81no—
106Q8—81no—
107D4—41no—
108D4—41no—
109D4—81no—
110C2×C4—21no—
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—42no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—42no—
120C2×C4—81no—
121C2×C4—81no—
122C2×C4—82no—
123C2×C4—162no—
124C2×C4#9911yescharacteristic
125C2×C4C2×C22⋊C411yescharacteristic
126C8—24no—
127C8—82no—
128C22—22no—
129C22—41no—
130C22—41no—
131C22—81no—
132C22—81no—
133C22—82no—
134C22—161no—
135C22#35311yescharacteristic
136C22#35311yescharacteristic
137C22C2×#9911yescharacteristic
138C4—21no—
139C4—21no—
140C4—41no—
141C4—41no—
142C4—41no—
143C4—41no—
144C4—82no—
145C4—162no—
146C2—21no—
147C2—21no—
148C2—81no—
149C2—81no—
150C2#140712yesdirect product factor
151C2C2×#35311yescharacteristic
subgroupG/H
center, socleC22#353
commutatorC42C22×C4
Frattini, cosocle#124C23
prime radicalC22×D4D4
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×#124 ◁ G
LECSG ▷ #124 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #1407C2direct (N × H)
7. C2×C4⋊Q8C4semidirect
11. #497C4semidirect
15. C2×#97C4semidirect
35. C4⋊Q8C2×C4semidirect
50. #97C2×C4semidirect
150. C2#1407direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#4972
C2×#3552
C2×#3542
#14072