Finite Group Databasebeta

← C8×C3⋊#226 #11920963

Subgroups — C8×C3⋊#226 #11920963

Order 1152.

272 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 53 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
1C4×C3⋊#226C211yesmaximal, characteristic
2C3×C8×SL(2,𝔽3)C211yesmaximal, characteristic
3C3⋊(SL(2,𝔽3)⋊C8)C211yesmaximal, characteristic
4C8×#226—33nomaximal
5C8×#216—31nomaximal
6C2×C3⋊#226C411yescharacteristic
7C3×C4×SL(2,𝔽3)C2211yescharacteristic
8C3⋊#859C411yescharacteristic
9C8×C3⋊Dic3—41nomaximal
10C4×#226—33no—
11C3×C8×Q8D311yescharacteristic
12C4×#216—31no—
13C8×Dic6—31no—
14C8×SL(2,𝔽3)D313yes—
15SL(2,𝔽3)⋊C8—33no—
16#4535—31no—
17#4484—31no—
18#4479—31no—
19C8×C3⋊C8—31no—
20C2×C3×SL(2,𝔽3)C2×C411yescharacteristic
21C3⋊#226C812yesdirect product factor
22C2×C32×C8—41no—
23C4×C3⋊Dic3—41no—
24C2×C3⋊(C3⋊C8)—41no—
25C8×Q16—91noSylow
26C2×#226—33no—
27C3×C4×Q8C2×D311yescharacteristic
28C2×#216—31no—
29C4×Dic6—31no—
30C4×SL(2,𝔽3)C2×D313yes—
31#859—33no—
32C3×C4⋊C8—31no—
33C3×C4×C8—31no—
34#835—31no—
35Dic3⋊C8—61no—
36C8×Dic3—61no—
37C8×Dic3—123no—
38#810—31no—
39#807—31no—
40C4⋊(C3⋊C8)—31no—
41C4×C3⋊C8—31no—
42C4×C3⋊C8—31no—
43C2×C32×C4—41no—
44C2×C3⋊Dic3—41no—
45C2×C3⋊Dic3—41no—
46C3×SL(2,𝔽3)C2×C811yescharacteristic
47C32×C8—42no—
48C3⋊(C3⋊C8)—42no—
49C8×Q8—91no—
50C8×Q8C3⋊D311yescharacteristic
51C4×Q16—91no—
52#335—91no—
53Q8⋊C8—91no—
54Q8⋊C8—91no—
55C82—91no—
56C2×C3×Q8C4×D311yescharacteristic
57C2×Dic6—31no—
58C2×SL(2,𝔽3)C4×D313yes—
59#226—36no—
60C2×C3×C8—31no—
61C2×C3×C8—43no—
62C2×C3×C8S411yescharacteristic
63C3×C4⋊C4—31no—
64C3×C42—31no—
65#216—32no—
66#216—32no—
67C4⋊Dic3—31no—
68Dic3⋊C4—61no—
69C4×Dic3—61no—
70C4×Dic3—123no—
71C2×C3⋊C8—31no—
72C2×C3⋊C8—31no—
73C2×C3⋊C8—61no—
74C2×C3⋊C8—61no—
75C2×C3⋊C8—123no—
76C22×C32—41no—
77C32×C4—41no—
78C32×C4—41no—
79C3⋊Dic3—42no—
80C3⋊Dic3—42no—
81C2×Q16—91no—
82C4×Q8—91no—
83C4×Q8C2×C3⋊D311yescharacteristic
84#107—91no—
85C4⋊C8—31no—
86C4⋊C8—91no—
87C4⋊C8—181no—
88#103—91no—
89#103—91no—
90C4×C8—31no—
91C4×C8—91no—
92C4×C8—91no—
93C4×C8—181no—
94C3×Q8—31no—
95C3×Q8D3×C811yescharacteristic
96C2×C3×C4—31no—
97C2×C3×C4—31no—
98C2×C3×C4—43no—
99C2×C3×C4C2×S411yescharacteristic
100C2×Dic3—61no—
101C2×Dic3—61no—
102C2×Dic3—123no—
103C2×Dic3—123no—
104Dic6—32no—
105Dic6—61no—
106SL(2,𝔽3)D3×C813yes—
107C3×C8—46no—
108C3×C8—61no—
109C3×C8#22612yescomplemented
110C3⋊C8—32no—
111C3⋊C8—61no—
112C3⋊C8—62no—
113C3⋊C8—126no—
114C3⋊C8—121no—
115C2×C32—41no—
116C2×C32—41no—
117C2×C32—41no—
118C2×Q8—91no—
119C2×Q8C4×C3⋊D311yescharacteristic
120Q16—92no—
121Q16—92no—
122C2×C8—31no—
123C2×C8—91no—
124C2×C8—91no—
125C2×C8—181no—
126C2×C8—181no—
127C2×C8C3⋊S411yescharacteristic
128C4⋊C4—31no—
129C4⋊C4—91no—
130C4⋊C4—181no—
131C42—31no—
132C42—181no—
133C22×C3—43no—
134C22×C3C4×S411yescharacteristic
135C3×C4—31no—
136C3×C4—31no—
137C3×C4—43no—
138C3×C4—43no—
139C3×C4—61no—
140C3×C4C2×#22611yescharacteristic
141C3×C4#98511yescharacteristic
142Dic3—62no—
143Dic3—126no—
144Dic3—126no—
145Dic3—121no—
146C32—41noSylow
147Q8—31no—
148Q8—92no—
149Q8—181no—
150Q8C8×C3⋊D311yescharacteristic
151C2×C4—31no—
152C2×C4—31no—
153C2×C4—181no—
154C2×C4—181no—
155C2×C4C2×C3⋊S411yescharacteristic
156C8—61no—
157C8—92no—
158C8—181no—
159C8—182no—
160C8—361no—
161C8C3⋊#22612yesdirect product factor
162C2×C3—43no—
163C2×C3—43no—
164C2×C3—43no—
165C2×C3C4×#22611yescharacteristic
166C2×C3C8×S411yescharacteristic
167C2×C3#540411yescharacteristic
168C22C4×C3⋊S411yescharacteristic
169C4—31no—
170C4—31no—
171C4—61no—
172C4—182no—
173C4—361no—
174C4C2×C3⋊#22611yescharacteristic
175C4#6426611yescharacteristic
176C3—43no—
177C3C8×#22611yescharacteristic, complemented
178C2C4×C3⋊#22611yescharacteristic
179C2C8×C3⋊S411yescharacteristic
180C2#1059363811yescharacteristic
subgroupG/H
center, hypercenterC2×C8C3⋊S4
commutator, hypocenterC3×SL(2,𝔽3)C2×C8
FrattiniC2×C4C2×C3⋊S4
FittingC3×C8×Q8D3
socleC22×C3C4×S4
prime radicalC2×C3×SL(2,𝔽3)C2×C4
cosocleC3×C4×SL(2,𝔽3)C22
LCSG ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
21. C3⋊#226C8direct (N × H)
109. C3×C8#226semidirect
161. C8C3⋊#226direct (N × H)
177. C3C8×#226semidirect

Maximal subgroups

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

subgroupindex
C4×C3⋊#2262
C3×C8×SL(2,𝔽3)2
C3⋊(SL(2,𝔽3)⋊C8)2
C8×#2263
C8×#2163
C8×C3⋊Dic34