Finite Group Databasebeta

← C3×#3363⋊C3 #11919602

Subgroups — C3×#3363⋊C3 #11919602

Order 1152.

272 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 70 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×Q8×SL(2,𝔽3)C211yesmaximal, characteristic
2C3×#557⋊C3C211yesmaximal, characteristic
3C3×C8×SL(2,𝔽3)C211yesmaximal, characteristic
4C3×#3363C311yesmaximal, characteristic, complemented
5#3363⋊C3C313yesmaximal, direct product factor
6C3×C4×SL(2,𝔽3)—21no—
7C3×C4×SL(2,𝔽3)—21no—
8C3×C4×SL(2,𝔽3)C2211yescharacteristic
9C32×#103—41nomaximal
10C3×Q82C2×C311yescharacteristic
11C3×#557C2×C311yescharacteristic
12Q8×SL(2,𝔽3)C2×C313yes—
13#557⋊C3C2×C313yes—
14C3×#487—31no—
15C3×#477—31no—
16C3×#462—31no—
17C3×C8×Q8C2×C311yescharacteristic
18C3×C4×Q16—31no—
19C8×SL(2,𝔽3)C2×C313yes—
20C2×C32×Q8—41no—
21C2×C3×SL(2,𝔽3)D411yescharacteristic
22C2×C32×C8—41no—
23C32×C4⋊C4—41no—
24#3363C3211yescharacteristic, complemented, Sylow
25C2×C3×Q16—31no—
26C3×C4⋊Q8—31no—
27C3×C4⋊Q8—31no—
28C3×C4⋊Q8—61no—
29C3×#125—61no—
30C3×C4×Q8—21no—
31C3×C4×Q8—21no—
32C3×C4×Q8—31no—
33C3×C4×Q8—31no—
34C3×C4×Q8C22×C311yescharacteristic
35C4×SL(2,𝔽3)—23no—
36C4×SL(2,𝔽3)—23no—
37C4×SL(2,𝔽3)C22×C313yes—
38C3×#107—31no—
39C3×C4⋊C8—31no—
40C3×#103—32no—
41C3×#103—31no—
42C3×#103—43no—
43C3×#103A411yescharacteristic
44C3×C4×C8—31no—
45C32×Q8—42no—
46C32×Q8—81no—
47C2×C32×C4—41no—
48C2×C32×C4—81no—
49C2×C32×C4—81no—
50C3×SL(2,𝔽3)Q1611yescharacteristic, complemented
51C32×C8—81no—
52Q82C2×C3211yescharacteristic
53#557C2×C3211yescharacteristic
54#487—31no—
55#477—31no—
56#462—31no—
57C8×Q8C2×C3211yescharacteristic
58C4×Q16—31no—
59C2×C3×Q8—31no—
60C2×C3×Q8—43no—
61C2×C3×Q8—61no—
62C2×C3×Q8C3×D411yescharacteristic
63C2×C3×Q8C2×A411yescharacteristic
64C2×SL(2,𝔽3)C3×D413yes—
65C3×Q16—62no—
66C2×C3×C8—31no—
67C2×C3×C8—43no—
68C2×C3×C8C2×A411yescharacteristic
69C3×C4⋊C4—31no—
70C3×C4⋊C4—31no—
71C3×C4⋊C4—43no—
72C3×C4⋊C4—61no—
73C3×C4⋊C4—61no—
74C3×C4⋊C4—61no—
75C3×C4⋊C4—61no—
76C3×C4⋊C4—61no—
77C3×C4⋊C4C2×A411yescharacteristic
78C3×C42—31no—
79C3×C42—61no—
80C3×C42—61no—
81C22×C32—41no—
82C32×C4—41no—
83C32×C4—41no—
84C32×C4—82no—
85C32×C4—161no—
86C2×Q16—31no—
87C4⋊Q8—31no—
88C4⋊Q8—31no—
89C4⋊Q8—61no—
90#125—61no—
91C4×Q8—21no—
92C4×Q8—21no—
93C4×Q8—31no—
94C4×Q8—31no—
95C4×Q8C22×C3211yescharacteristic
96#107—31no—
97C4⋊C8—31no—
98#103—32no—
99#103—31no—
100#103C3×A411yescharacteristic
101C4×C8—31no—
102C3×Q8—21no—
103C3×Q8—31no—
104C3×Q8—46no—
105C3×Q8—61no—
106C3×Q8—61no—
107C3×Q8—83no—
108C3×Q8—241no—
109C3×Q8C3×Q1611yescharacteristic
110C3×Q8#41⋊C312yes—
111C2×C3×C4—21no—
112C2×C3×C4—21no—
113C2×C3×C4—31no—
114C2×C3×C4—31no—
115C2×C3×C4—43no—
116C2×C3×C4—61no—
117C2×C3×C4—61no—
118C2×C3×C4—83no—
119C2×C3×C4—83no—
120C2×C3×C4C22×A411yescharacteristic
121SL(2,𝔽3)C3×Q1613yescomplemented
122C3×C8—21no—
123C3×C8—61no—
124C3×C8—83no—
125C2×C32—41no—
126C2×C32—41no—
127C2×C32—41no—
128C2×Q8—31no—
129C2×Q8—61no—
130C2×Q8C32×D411yescharacteristic
131C2×Q8C2×C3×A411yescharacteristic
132Q16—62no—
133C2×C8—31no—
134C2×C8C2×C3×A411yescharacteristic
135C4⋊C4—31no—
136C4⋊C4—31no—
137C4⋊C4—61no—
138C4⋊C4—61no—
139C4⋊C4—61no—
140C4⋊C4—61no—
141C4⋊C4—61no—
142C4⋊C4C2×C3×A411yescharacteristic
143C42—31no—
144C42—61no—
145C42—61no—
146C22×C3—43no—
147C22×C3D4×A411yescharacteristic
148C3×C4—22no—
149C3×C4—31no—
150C3×C4—31no—
151C3×C4—41no—
152C3×C4—43no—
153C3×C4—43no—
154C3×C4—61no—
155C3×C4—86no—
156C3×C4—121no—
157C3×C4—121no—
158C3×C4—163no—
159C3×C4C2×#41⋊C311yescharacteristic
160C3×C42−1+4⋊C311yescharacteristic
161C32—41noSylow
162Q8—21no—
163Q8—31no—
164Q8—61no—
165Q8—61no—
166Q8—241no—
167Q8C32×Q1611yescharacteristic
168Q8C3×#41⋊C312yes—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—31no—
172C2×C4—31no—
173C2×C4—61no—
174C2×C4—61no—
175C2×C4C22×C3×A411yescharacteristic
176C8—21no—
177C8—61no—
178C2×C3—43no—
179C2×C3—43no—
180C2×C3—43no—
181C2×C3#548⋊C311yescharacteristic
182C2×C3A4×Q1611yescharacteristic
183C2×C3#577⋊C311yescharacteristic
184C22C3×D4×A411yescharacteristic
185C4—22no—
186C4—31no—
187C4—31no—
188C4—41no—
189C4—61no—
190C4—121no—
191C4—121no—
192C4C2×C3×#41⋊C311yescharacteristic
193C4C3×2−1+4⋊C311yescharacteristic
194C3—43no—
195C3#3363⋊C311yescharacteristic, direct product factor
196C2C3×#548⋊C311yescharacteristic
197C2C3×A4×Q1611yescharacteristic
198C2C3×#577⋊C311yescharacteristic
subgroupG/H
center, socleC22×C3D4×A4
commutator, cosocleC4×Q8C22×C32
FrattiniC2×C4C22×C3×A4
FittingC3×#3363C3
prime radicalC2×C3×SL(2,𝔽3)D4
hypercenterC3×#103A4
hypocenterQ8C32×Q16
LCSG ▷ C4×Q8 ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#103

Complements

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

NH ≅ G/Ntype
4. C3×#3363C3semidirect
5. #3363⋊C3C3direct (N × H)
24. #3363C32semidirect
50. C3×SL(2,𝔽3)Q16semidirect
121. SL(2,𝔽3)C3×Q16semidirect
195. C3#3363⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C3×Q8×SL(2,𝔽3)2
C3×#557⋊C32
C3×C8×SL(2,𝔽3)2
C3×#33633
#3363⋊C33
C32×#1034