Finite Group Databasebeta

← C2×#5935 #87514

Subgroups — C2×#5935 #87514

Order 384.

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

normal subgroups only

This group has 333 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, complemented
2#5935C212yesmaximal, direct product factor
3C2×#453—31nomaximal, Sylow
4C22×S4—41nomaximal
5#997C2211yescharacteristic, complemented
6C2×GL(2,𝔽3)—42nomaximal
7C2×H(5,𝔽2)D311yescharacteristic, complemented
8C2×AGL(1,ℤ/8)—32no—
9C2×#127—31no—
10#453—32no—
11#453—34no—
12#453—32no—
13C2×#104—32no—
14C2×#100—31no—
15C22×A4—41no—
16C22×A4—81no—
17C2×S4—42no—
18C2×S4—44no—
19C2×SL(2,𝔽3)—42no—
20GL(2,𝔽3)—44no—
21H(5,𝔽2)—31no—
22H(5,𝔽2)—32no—
23H(5,𝔽2)—61no—
24H(5,𝔽2)C2×D311yescharacteristic, complemented
25C2×#41—32no—
26C22×D4—31no—
27C22×D4—31no—
28C22×D4—61no—
29C22×D4—61no—
30C22×D4—61no—
31AGL(1,ℤ/8)—34no—
32AGL(1,ℤ/8)—34no—
33AGL(1,ℤ/8)—62no—
34AGL(1,ℤ/8)—62no—
35C2×SD16—62no—
36C2×D8—62no—
37C2×M16—32no—
38#127—32no—
39#127—32no—
40#127—61no—
41#127—61no—
42C2×C42—31no—
43#104—34no—
44#104—34no—
45#100—32no—
46#100—32no—
47C22×D3—161no—
48C2×A4—42no—
49C2×A4—41no—
50C2×A4—81no—
51C2×A4—82no—
52S4—44no—
53SL(2,𝔽3)—42no—
54C24—21no—
55C24—31no—
56C24—61no—
57C24S411yescharacteristic
58#41—32no—
59#41—32no—
60#41—32no—
61#41—32no—
62#41—62no—
63#41—62no—
64C2×Q8S412yescomplemented
65C2×D4—32no—
66C2×D4—31no—
67C2×D4—31no—
68C2×D4—31no—
69C2×D4—31no—
70C2×D4—32no—
71C2×D4—62no—
72C2×D4—62no—
73C2×D4—62no—
74C2×D4—62no—
75C2×D4—61no—
76C2×D4—61no—
77C2×D4—61no—
78C2×D4—62no—
79C2×D4—62no—
80C2×D4—61no—
81C2×D4—61no—
82C2×D4—62no—
83C2×D4—62no—
84C2×D4—62no—
85C2×D4—62no—
86C2×D4—124no—
87C2×D4—124no—
88C22×C4—31no—
89C22×C4—61no—
90C22×C4—61no—
91SD16—64no—
92SD16—64no—
93D8—64no—
94D8—64no—
95M16—34no—
96M16—62no—
97C2×C8—62no—
98C42—32no—
99C42—61no—
100C22×C3—161no—
101C2×D3—162no—
102C2×D3—164no—
103A4—41no—
104A4—81no—
105C23—21no—
106C23—31no—
107C23—31no—
108C23—31no—
109C23—31no—
110C23—42no—
111C23—61no—
112C23—62no—
113C23—61no—
114C23—61no—
115C23—82no—
116C23—121no—
117C23—122no—
118C23—122no—
119C23—122no—
120C23—121no—
121C23C2×S411yescharacteristic
122Q8—32no—
123Q8C2×S412yescomplemented
124D4—32no—
125D4—32no—
126D4—62no—
127D4—62no—
128D4—62no—
129D4—62no—
130D4—62no—
131D4—64no—
132D4—122no—
133D4—124no—
134D4—124no—
135D4—124no—
136D4—124no—
137C2×C4—31no—
138C2×C4—31no—
139C2×C4—32no—
140C2×C4—32no—
141C2×C4—61no—
142C2×C4—62no—
143C2×C4—61no—
144C2×C4—62no—
145C2×C4—64no—
146C8—64no—
147C2×C3—162no—
148C2×C3—161no—
149D3—164no—
150C22—31no—
151C22—31no—
152C22—41no—
153C22—62no—
154C22—61no—
155C22—61no—
156C22—81no—
157C22—121no—
158C22—121no—
159C22—121no—
160C22—122no—
161C22—122no—
162C22—122no—
163C22—122no—
164C22—241no—
165C22—242no—
166C22—241no—
167C22—242no—
168C22#102011yescharacteristic
169C4—32no—
170C4—32no—
171C4—64no—
172C3—161noSylow
173C2—61no—
174C2—61no—
175C2—121no—
176C2—121no—
177C2—242no—
178C2#593512yesdirect product factor
179C2C2×#102011yescharacteristic
subgroupG/H
center, socle, hypercenterC22#1020
commutator, cosocle, hypocenter#997C22
FrattiniC2C2×#1020
FittingC2×H(5,𝔽2)D3
LCSG ▷ #997
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C2×#997C2semidirect
2. #5935C2direct (N × H)
5. #997C22semidirect
7. C2×H(5,𝔽2)D3semidirect
24. H(5,𝔽2)C2×D3semidirect
64. C2×Q8S4semidirect
123. Q8C2×S4semidirect
178. C2#5935direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#9972
#59352
C2×#4533
C22×S44
C2×GL(2,𝔽3)4