Finite Group Databasebeta

← C2×#5933 #87512

Subgroups — C2×#5933 #87512

Order 384.

275 conjugacy classes of subgroups; only the 18 normal subgroups are shown.

normal subgroups only

This group has 275 conjugacy classes of subgroups — too many to draw. Only its 18 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×#997C211yesmaximal, characteristic
2#5933C212yesmaximal, direct product factor
3C2×#455—31nomaximal, Sylow
4#997C2211yescharacteristic
5C2×SL(2,ℤ/4)—41nomaximal
6C2×#226—42nomaximal
7C2×H(5,𝔽2)D311yescharacteristic
8C2×#137—32no—
9C2×#124—31no—
10#455—32no—
11#455—34no—
12#455—32no—
13C2×#104—32no—
14C2×#100—31no—
15C22×A4—41no—
16C22×A4—81no—
17C2×SL(2,𝔽3)—42no—
18SL(2,ℤ/4)—42no—
19#226—44no—
20H(5,𝔽2)—31no—
21H(5,𝔽2)—32no—
22H(5,𝔽2)—61no—
23H(5,𝔽2)C2×D311yescharacteristic
24C2×#41—32no—
25C22×Q8—31no—
26C22×D4—31no—
27C22×D4—61no—
28#137—34no—
29#137—34no—
30#137—62no—
31#137—62no—
32C2×Q16—62no—
33C2×SD16—62no—
34C2×M16—32no—
35#124—32no—
36#124—32no—
37#124—61no—
38#124—61no—
39C2×C22⋊C4—61no—
40C2×C22⋊C4—61no—
41C2×C42—31no—
42#104—34no—
43#104—34no—
44#100—32no—
45#100—32no—
46C2×A4—42no—
47C2×A4—41no—
48C2×A4—81no—
49C2×A4—82no—
50C2×Dic3—161no—
51SL(2,𝔽3)—42no—
52C24—21no—
53C24—31no—
54C24S411yescharacteristic
55#41—32no—
56#41—32no—
57#41—32no—
58#41—32no—
59#41—62no—
60#41—62no—
61C2×Q8—32no—
62C2×Q8—61no—
63C2×Q8—62no—
64C2×Q8—62no—
65C2×Q8S412yes—
66C2×D4—32no—
67C2×D4—31no—
68C2×D4—31no—
69C2×D4—31no—
70C2×D4—31no—
71C2×D4—62no—
72C2×D4—62no—
73C2×D4—61no—
74C2×D4—61no—
75C2×D4—62no—
76C2×D4—62no—
77C2×D4—61no—
78C2×D4—61no—
79C22×C4—31no—
80C22×C4—61no—
81C22×C4—61no—
82C22×C4—61no—
83Q16—64no—
84Q16—64no—
85SD16—64no—
86SD16—64no—
87M16—34no—
88M16—62no—
89C2×C8—62no—
90C22⋊C4—62no—
91C22⋊C4—62no—
92C22⋊C4—62no—
93C22⋊C4—62no—
94C42—32no—
95C42—61no—
96C22×C3—161no—
97A4—41no—
98A4—81no—
99Dic3—162no—
100C23—21no—
101C23—31no—
102C23—31no—
103C23—31no—
104C23—31no—
105C23—42no—
106C23—61no—
107C23—61no—
108C23—61no—
109C23—82no—
110C23—122no—
111C23C2×S411yescharacteristic
112Q8—32no—
113Q8—64no—
114Q8—122no—
115Q8C2×S412yes—
116D4—32no—
117D4—32no—
118D4—62no—
119D4—62no—
120D4—62no—
121D4—62no—
122D4—62no—
123C2×C4—31no—
124C2×C4—31no—
125C2×C4—32no—
126C2×C4—32no—
127C2×C4—61no—
128C2×C4—62no—
129C2×C4—61no—
130C2×C4—62no—
131C2×C4—62no—
132C2×C4—121no—
133C2×C4—122no—
134C2×C4—121no—
135C8—64no—
136C2×C3—162no—
137C2×C3—161no—
138C22—31no—
139C22—31no—
140C22—41no—
141C22—62no—
142C22—61no—
143C22—61no—
144C22—81no—
145C22—121no—
146C22—121no—
147C22—121no—
148C22—122no—
149C22—241no—
150C22—241no—
151C22#102011yescharacteristic
152C4—32no—
153C4—32no—
154C4—122no—
155C4—122no—
156C3—161noSylow
157C2—61no—
158C2—61no—
159C2—121no—
160C2—121no—
161C2#593312yesdirect product factor
162C2C2×#102011yescharacteristic
subgroupG/H
center, socle, hypercenterC22#1020
commutator, cosocle, hypocenter#997C22
FrattiniC2C2×#1020
FittingC2×H(5,𝔽2)D3
prime radicalC2×#997C2
LCSG ▷ #997
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. #5933C2direct (N × H)
161. C2#5933direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#9972
#59332
C2×#4553
C2×SL(2,ℤ/4)4
C2×#2264