Finite Group Databasebeta

← C3×#73011 #11920793

Subgroups — C3×#73011 #11920793

Order 1152.

203 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 203 conjugacy classes of subgroups — too many to draw. Only its 40 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
1C3×C4⋊#226C211yesmaximal, characteristic
2C3×#5386C211yesmaximal, characteristic
3C3×C8×SL(2,𝔽3)C211yesmaximal, characteristic
4#73011C311yesmaximal, characteristic, direct product factor
5C3×#1680—31nomaximal
6C2×C3×#226—21no—
7C3×C4×SL(2,𝔽3)C2211yescharacteristic
8C3×#859—21no—
9C3×#816—41nomaximal
10C4⋊#226C2×C311yescharacteristic
11#5386C2×C311yescharacteristic
12C3×#487—31no—
13C3×#475—31no—
14C3×#462—31no—
15C3×C8×Q8D311yescharacteristic
16C8×SL(2,𝔽3)—21no—
17C8×SL(2,𝔽3)C2×C311yescharacteristic
18C3×#334—31no—
19C3×#332—31no—
20C3×#332—31no—
21C2×C3×Dic6—41no—
22C2×C3×SL(2,𝔽3)D411yescharacteristic
23C3×#226—41no—
24C2×C32×C8—41no—
25C3×C4⋊Dic3—41no—
26#1680—31noSylow
27C2×#226—21no—
28C2×C3×Q16—61no—
29C3×C4⋊Q8—31no—
30C3×C4⋊Q8—31no—
31C3×C4×Q8C2×D311yescharacteristic
32C4×SL(2,𝔽3)—21no—
33C4×SL(2,𝔽3)C22×C311yescharacteristic
34#859—21no—
35C3×#106—61no—
36C3×C4⋊C8—31no—
37C3×C4⋊C8—31no—
38C3×C4⋊C8—31no—
39C3×#103—61no—
40C3×#103—61no—
41C3×#103—61no—
42C3×#103—61no—
43C3×C4×C8—31no—
44#816—41no—
45C2×C32×C4—41no—
46C2×C3×Dic3—81no—
47C2×C3×Dic3—81no—
48C3×Dic6—42no—
49C3×Dic6—81no—
50C3×SL(2,𝔽3)SD1611yescharacteristic
51C32×C8—81no—
52#487—31no—
53#475—31no—
54#462—31no—
55C8×Q8C3×D311yescharacteristic
56#334—31no—
57#332—31no—
58#332—31no—
59C2×C3×Q8—61no—
60C2×C3×Q8—61no—
61C2×C3×Q8D1211yescharacteristic
62C2×Dic6—41no—
63C2×SL(2,𝔽3)—21no—
64C2×SL(2,𝔽3)C3×D411yescharacteristic
65#226—41no—
66C3×Q16—121no—
67C3×Q16—121no—
68C2×C3×C8—31no—
69C2×C3×C8—41no—
70C2×C3×C8—61no—
71C2×C3×C8—61no—
72C2×C3×C8—81no—
73C2×C3×C8S411yescharacteristic
74C3×C4⋊C4—31no—
75C3×C4⋊C4—61no—
76C3×C4⋊C4—61no—
77C3×C4⋊C4—61no—
78C3×C4⋊C4—61no—
79C3×C42—31no—
80C4⋊Dic3—41no—
81C22×C32—41no—
82C32×C4—41no—
83C32×C4—41no—
84C3×Dic3—82no—
85C3×Dic3—161no—
86C2×Q16—61no—
87C4⋊Q8—31no—
88C4⋊Q8—31no—
89C4×Q8C2×C3×D311yescharacteristic
90#106—61no—
91C4⋊C8—31no—
92C4⋊C8—31no—
93C4⋊C8—31no—
94#103—61no—
95#103—61no—
96#103—61no—
97#103—61no—
98C4×C8—31no—
99C3×Q8—31no—
100C3×Q8—121no—
101C3×Q8—121no—
102C3×Q8—121no—
103C3×Q8—121no—
104C3×Q8#20411yescharacteristic
105C2×C3×C4—31no—
106C2×C3×C4—31no—
107C2×C3×C4—41no—
108C2×C3×C4—81no—
109C2×C3×C4—121no—
110C2×C3×C4—121no—
111C2×C3×C4C2×S411yescharacteristic
112C2×Dic3—81no—
113C2×Dic3—81no—
114Dic6—42no—
115Dic6—81no—
116SL(2,𝔽3)—21no—
117SL(2,𝔽3)C3×SD1611yescharacteristic
118C3×C8—21no—
119C3×C8—61no—
120C3×C8—81no—
121C3×C8—82no—
122C3×C8—121no—
123C3×C8—121no—
124C2×C32—41no—
125C2×C32—41no—
126C2×C32—41no—
127C2×Q8—61no—
128C2×Q8—61no—
129C2×Q8C3×D1211yescharacteristic
130Q16—121no—
131Q16—121no—
132C2×C8—31no—
133C2×C8—61no—
134C2×C8—61no—
135C2×C8C3×S411yescharacteristic
136C4⋊C4—31no—
137C4⋊C4—61no—
138C4⋊C4—61no—
139C4⋊C4—61no—
140C4⋊C4—61no—
141C42—31no—
142C22×C3—41no—
143C22×C3—81no—
144C22×C3C4⋊S411yescharacteristic
145C3×C4—31no—
146C3×C4—31no—
147C3×C4—41no—
148C3×C4—41no—
149C3×C4—61no—
150C3×C4—81no—
151C3×C4—81no—
152C3×C4—241no—
153C3×C4—241no—
154C3×C4#98311yescharacteristic
155C3×C4#98511yescharacteristic
156Dic3—82no—
157Dic3—161no—
158C32—41noSylow
159Q8—31no—
160Q8—121no—
161Q8—121no—
162Q8—121no—
163Q8—121no—
164Q8C3×#20411yescharacteristic
165C2×C4—31no—
166C2×C4—31no—
167C2×C4—121no—
168C2×C4—121no—
169C2×C4C2×C3×S411yescharacteristic
170C8—21no—
171C8—61no—
172C8—121no—
173C8—121no—
174C2×C3—41no—
175C2×C3—41no—
176C2×C3—41no—
177C2×C3—81no—
178C2×C3—81no—
179C2×C3—81no—
180C2×C3#539511yescharacteristic
181C2×C3#540111yescharacteristic
182C2×C3#540311yescharacteristic
183C22C3×C4⋊S411yescharacteristic
184C4—31no—
185C4—31no—
186C4—61no—
187C4—241no—
188C4—241no—
189C4C3×#98311yescharacteristic
190C4C3×#98511yescharacteristic
191C3—41no—
192C3—81no—
193C3#7301111yescharacteristic, direct product factor
194C2C3×#539511yescharacteristic
195C2C3×#540111yescharacteristic
196C2C3×#540311yescharacteristic
subgroupG/H
center, socleC22×C3C4⋊S4
commutator, cosocleC4×SL(2,𝔽3)C22×C3
FrattiniC2×C4C2×C3×S4
FittingC3×C8×Q8D3
prime radicalC2×C3×SL(2,𝔽3)D4
hypercenterC2×C3×C8S4
hypocenterSL(2,𝔽3)C3×SD16
LCSG ▷ C4×SL(2,𝔽3) ▷ C2×SL(2,𝔽3) ▷ SL(2,𝔽3)
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×C8

Complements

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

NH ≅ G/Ntype
4. #73011C3direct (N × H)
193. C3#73011direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C4⋊#2262
C3×#53862
C3×C8×SL(2,𝔽3)2
#730113
C3×#16803
C3×#8164