Finite Group Databasebeta

← C4⋊#5932 #11715727

Subgroups — C4⋊#5932 #11715727

Order 768.

541 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 541 conjugacy classes of subgroups — too many to draw. Only its 26 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×#5932C212yesmaximal
2C4×#997C211yesmaximal, characteristic
3#32927—31nomaximal, Sylow
4C2×#997C2211yescharacteristic
5#5932—22no—
6C4⋊SL(2,ℤ/4)—43nomaximal
7C4×H(5,𝔽2)D311yescharacteristic
8C2×#458—32no—
9#2486—33no—
10#1890—36no—
11#1799—33no—
12#997D411yescharacteristic
13C2×C4×A4—43no—
14C2×SL(2,ℤ/4)—46no—
15C4×SL(2,𝔽3)—81no—
16C2×H(5,𝔽2)C2×D311yescharacteristic
17C2×#123—36no—
18#520—61no—
19#518—33no—
20C4×#41—61no—
21C2×C4×D4—33no—
22C22×C4⋊C4—31no—
23#458—66no—
24#458—62no—
25C2×#99—36no—
26#398—63no—
27#397—63no—
28#389—63no—
29#381—36no—
30#380—33no—
31#380—63no—
32#342—36no—
33C22×A4—43no—
34C2×SL(2,𝔽3)—81no—
35C4×A4—46no—
36SL(2,ℤ/4)—86no—
37C4⋊Dic3—161no—
38H(5,𝔽2)—33no—
39H(5,𝔽2)—61no—
40H(5,𝔽2)D1211yescharacteristic
41C2×#41—61no—
42C22×D4—33no—
43C23×C4—31no—
44C23×C4—32no—
45C23×C4S413yes—
46#123—66no—
47#123—66no—
48#123—66no—
49#123—66no—
50C4×Q8—21no—
51C4×Q8—61no—
52C4×D4—63no—
53C4×D4—66no—
54C4×D4—63no—
55#117—63no—
56C2×C4⋊C4—33no—
57C2×C4⋊C4—63no—
58C2×C4⋊C4—63no—
59C2×C4⋊C4—66no—
60C2×C4⋊C4—63no—
61C2×C22⋊C4—33no—
62C2×C22⋊C4—33no—
63C2×C22⋊C4—36no—
64C2×C22⋊C4—66no—
65C2×C42—33no—
66#99—66no—
67#99—66no—
68#95—63no—
69#95—66no—
70#95—66no—
71C2×A4—43no—
72C2×A4—43no—
73C2×A4—43no—
74C2×C3×C4—161no—
75C2×Dic3—162no—
76SL(2,𝔽3)—81no—
77C24—31no—
78C24C2×S413yes—
79#41—61no—
80#41—63no—
81#41—63no—
82#41—61no—
83C2×Q8—21no—
84C2×D4—33no—
85C2×D4—33no—
86C2×D4—33no—
87C2×D4—33no—
88C2×D4—63no—
89C2×D4—66no—
90C22×C4—33no—
91C22×C4—33no—
92C22×C4—33no—
93C22×C4—33no—
94C22×C4—33no—
95C22×C4—46no—
96C22×C4—66no—
97C22×C4—66no—
98C22×C4—62no—
99C22×C4—66no—
100C22×C4—122no—
101C4⋊C4—63no—
102C4⋊C4—61no—
103C4⋊C4—123no—
104C4⋊C4—126no—
105C4⋊C4—126no—
106C4⋊C4—126no—
107C4⋊C4—121no—
108C22⋊C4—66no—
109C22⋊C4—66no—
110C22⋊C4—66no—
111C22⋊C4—126no—
112C22⋊C4—126no—
113C42—63no—
114C42—61no—
115C22×C3—161no—
116A4—43no—
117C3×C4—162no—
118Dic3—322no—
119C23—31no—
120C23—33no—
121C23—33no—
122C23—33no—
123C23—43no—
124C23—43no—
125C23—121no—
126C23—121no—
127C23C4⋊S413yes—
128Q8—21no—
129Q8—61no—
130D4—63no—
131D4—63no—
132D4—66no—
133C2×C4—33no—
134C2×C4—33no—
135C2×C4—33no—
136C2×C4—63no—
137C2×C4—61no—
138C2×C4—66no—
139C2×C4—61no—
140C2×C4—123no—
141C2×C4—123no—
142C2×C4—123no—
143C2×C4—126no—
144C2×C4—126no—
145C2×C4—126no—
146C2×C4—126no—
147C2×C4—126no—
148C2×C4—122no—
149C2×C4#102011yescharacteristic
150C2×C3—161no—
151C2×C3—161no—
152C2×C3—161no—
153C22—33no—
154C22—33no—
155C22—43no—
156C22—63no—
157C22—63no—
158C22—123no—
159C22—121no—
160C22—123no—
161C22C2×#102011yescharacteristic
162C4—61no—
163C4—61no—
164C4—63no—
165C4—121no—
166C4—246no—
167C4—242no—
168C4#593212yescomplemented
169C3—161noSylow
170C2—63no—
171C2—63no—
172C2C4⋊#102011yescharacteristic
173C2C2×#593211yescharacteristic
174C2#8751711yescharacteristic
subgroupG/H
center, Frattini, socleC22C2×#1020
commutator, prime radical, cosocleC2×#997C22
FittingC4×H(5,𝔽2)D3
hypercenterC2×C4#1020
hypocenter#997D4
LCSG ▷ C2×#997 ▷ #997
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
168. C4#5932semidirect

Maximal subgroups

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

subgroupindex
C2×#59322
C4×#9972
#329273
C4⋊SL(2,ℤ/4)4