Finite Group Databasebeta

← C2×#5389 #85317

Subgroups — C2×#5389 #85317

Order 384.

219 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 219 conjugacy classes of subgroups — too many to draw. Only its 46 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×C4×SL(2,𝔽3)C211yesmaximal, characteristic
2C2×#859C211yesmaximal, characteristic
3C2×#859C211yesmaximal, characteristic
4#5389C214yesmaximal, direct product factor
5C2×#479—31nomaximal, Sylow
6C22×SL(2,𝔽3)C2211yescharacteristic
7C2×Dic3⋊C4—41nomaximal
8C4×SL(2,𝔽3)C2212yes—
9#859C2212yes—
10#859C2212yes—
11C2×#125—31no—
12C2×C4×Q8D311yescharacteristic
13#479—34no—
14#479—34no—
15C2×#107—31no—
16C2×#106—31no—
17C2×C4⋊C8—31no—
18C2×#103—31no—
19C2×#103—31no—
20C22×C3×C4—41no—
21C22×Dic3—41no—
22C22×Dic3—41no—
23C2×SL(2,𝔽3)Q812yes—
24C2×SL(2,𝔽3)C2311yescharacteristic
25Dic3⋊C4—44no—
26C22×Q8C2×D311yescharacteristic
27C22×C8—31no—
28C22×C8—31no—
29#125—34no—
30#125—62no—
31C4×Q8—32no—
32C4×Q8C2×D312yes—
33C2×C4⋊C4—31no—
34C2×C4⋊C4—31no—
35C2×C4⋊C4—31no—
36C2×C4⋊C4—61no—
37C2×C4⋊C4—61no—
38C2×C42—31no—
39#107—34no—
40#106—34no—
41C4⋊C8—34no—
42#103—32no—
43#103—32no—
44#103—32no—
45#103—32no—
46C23×C3—41no—
47C2×C3×C4—42no—
48C2×C3×C4—82no—
49C2×Dic3—42no—
50C2×Dic3—42no—
51C2×Dic3—44no—
52C2×Dic3—82no—
53SL(2,𝔽3)C2×Q811yescharacteristic
54C2×Q8—31no—
55C2×Q8—32no—
56C2×Q8Dic612yes—
57C2×Q8C22×D311yescharacteristic
58C22×C4—31no—
59C22×C4—31no—
60C22×C4—61no—
61C22×C4—61no—
62C22×C4S411yescharacteristic
63C2×C8—32no—
64C2×C8—32no—
65C2×C8—62no—
66C2×C8—62no—
67C4⋊C4—32no—
68C4⋊C4—32no—
69C4⋊C4—32no—
70C4⋊C4—61no—
71C4⋊C4—61no—
72C4⋊C4—61no—
73C4⋊C4—64no—
74C4⋊C4—64no—
75C42—32no—
76C42—32no—
77C22×C3—42no—
78C22×C3—42no—
79C22×C3—42no—
80C22×C3—41no—
81C3×C4—82no—
82Dic3—44no—
83Dic3—82no—
84C23C2×S411yescharacteristic
85Q8—32no—
86Q8—31no—
87Q8—61no—
88Q8C2×Dic611yescharacteristic
89C2×C4—22no—
90C2×C4—32no—
91C2×C4—32no—
92C2×C4—31no—
93C2×C4—31no—
94C2×C4—32no—
95C2×C4—62no—
96C2×C4—62no—
97C2×C4—62no—
98C2×C4—122no—
99C2×C4—122no—
100C2×C4C2×S412yes—
101C8—62no—
102C8—62no—
103C2×C3—44no—
104C2×C3—41no—
105C2×C3—41no—
106C2×C3—41no—
107C22A4⋊Q812yes—
108C22#98312yes—
109C22#98512yes—
110C22C22×S411yescharacteristic
111C4—22no—
112C4—31no—
113C4—31no—
114C4—32no—
115C4—62no—
116C4—122no—
117C4—122no—
118C3—41noSylow
119C2#538914yesdirect product factor
120C2C2×A4⋊Q811yescharacteristic
121C2C2×#98311yescharacteristic
122C2C2×#98511yescharacteristic
subgroupG/H
center, socleC23C2×S4
commutator, cosocleC2×SL(2,𝔽3)C23
FrattiniC22C22×S4
FittingC2×C4×Q8D3
prime radicalC22×SL(2,𝔽3)C22
hypercenterC22×C4S4
hypocenterSL(2,𝔽3)C2×Q8
LCSG ▷ C2×SL(2,𝔽3) ▷ SL(2,𝔽3)
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #5389C2direct (N × H)
119. C2#5389direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×SL(2,𝔽3)2
C2×#8592
#53892
C2×#4793
C2×Dic3⋊C44