Finite Group Databasebeta

← C2×#1410 #13587

Subgroups — C2×#1410 #13587

Order 256.

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

normal subgroups only

This group has 225 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×#492C211yesmaximal, characteristic
2C2×#356C212yesmaximal, complemented
3#1410C214yesmaximal, direct product factor
4C22×SD16—22no—
5C2×C4⋊Q8C2211yescharacteristic
6C2×#127C411yescharacteristic
7#492—22no—
8#492C412yes—
9#492C2212yes—
10C2×#101—22no—
11C2×C4×C8C411yescharacteristic
12#356—22no—
13#356C2214yescomplemented
14C22×Q8D412yes—
15C22×D4—21no—
16C22×D4—41no—
17C2×SD16—24no—
18C2×SD16—24no—
19C2×SD16—44no—
20C2×SD16—44no—
21C2×M16—42no—
22C22×C8—21no—
23C4⋊Q8—41no—
24C4⋊Q8C2×C411yescharacteristic
25C4⋊Q8D412yes—
26C4⋊Q8C2311yescharacteristic
27#127—21no—
28#127—41no—
29#127C2×C412yes—
30C2×C4⋊C4—41no—
31C2×C42C2×C411yescharacteristic
32#101—24no—
33#101—42no—
34C4×C8—21no—
35C4×C8C2×C412yes—
36C24—41no—
37C2×Q8—22no—
38C2×Q8—42no—
39C2×Q8—42no—
40C2×Q8C22⋊C412yes—
41C2×Q8C2×D412yes—
42C2×D4—22no—
43C2×D4—42no—
44C2×D4—42no—
45C2×D4—42no—
46C2×D4—42no—
47C2×D4—41no—
48C2×D4—84no—
49C22×C4—21no—
50C22×C4—22no—
51C22×C4C22⋊C411yescharacteristic
52SD16—48no—
53SD16—48no—
54M16—44no—
55M16—82no—
56C2×C8—22no—
57C2×C8—22no—
58C2×C8—22no—
59C2×C8—82no—
60C4⋊C4—41no—
61C4⋊C4—42no—
62C4⋊C4—41no—
63C42—21no—
64C42C22⋊C411yescharacteristic
65C42C22×C411yescharacteristic
66C23—42no—
67C23—84no—
68C23—81no—
69C23—81no—
70C23#9911yescharacteristic
71Q8—42no—
72Q8—42no—
73Q8—82no—
74D4—44no—
75D4—82no—
76D4—84no—
77D4—84no—
78C2×C4—24no—
79C2×C4—21no—
80C2×C4—21no—
81C2×C4—21no—
82C2×C4—21no—
83C2×C4—22no—
84C2×C4—22no—
85C2×C4—42no—
86C2×C4—42no—
87C2×C4#9911yescharacteristic
88C2×C4C2×C22⋊C411yescharacteristic
89C8—24no—
90C8—84no—
91C22—22no—
92C22—84no—
93C22—82no—
94C22—162no—
95C22—162no—
96C22#35311yescharacteristic
97C22#35311yescharacteristic
98C22C2×#9911yescharacteristic
99C4—22no—
100C4—22no—
101C4—21no—
102C4—21no—
103C4—42no—
104C4—42no—
105C2—21no—
106C2—21no—
107C2—162no—
108C2#141012yesdirect product factor
109C2C2×#35311yescharacteristic
subgroupG/H
center, socleC22#353
commutatorC42C22×C4
Frattini, cosocleC4⋊Q8C23
prime radicalC2×#127C4
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊Q8 ◁ G
LECSG ▷ C4⋊Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#356C2semidirect
3. #1410C2direct (N × H)
13. #356C22semidirect
108. C2#1410direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#4922
C2×#3562
#14102