Finite Group Databasebeta

← #11920522

Subgroups — #11920522

Order 1152.

201 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 201 conjugacy classes of subgroups — too many to draw. Only its 39 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⋊C8×SL(2,𝔽3)C211yesmaximal, characteristic
3C3⋊(SL(2,𝔽3)⋊C8)C211yesmaximal, characteristic
4#73009—31nomaximal
5#70904—31nomaximal
6C2×C3×#226C411yescharacteristic
7C3×C4×SL(2,𝔽3)C2211yescharacteristic
8C3×#859C411yescharacteristic
9Dic3⋊(C3⋊C8)—41nomaximal
10C4×#226D311yescharacteristic
11C3×C4×Q16—31no—
12#5024—31no—
13Q8×C3⋊C8D311yescharacteristic
14C8×SL(2,𝔽3)—31no—
15SL(2,𝔽3)⋊C8—31no—
16SL(2,𝔽3)⋊C8—61no—
17#4535—31no—
18#4535—31no—
19#4457—31no—
20#4454—31no—
21C2×C3×SL(2,𝔽3)C2×C411yescharacteristic
22C3×#226—21no—
23C2×C3⋊(C3⋊C8)—41no—
24C3×C4×Dic3—41no—
25C2×C3×C3⋊C8—41no—
26#1587—91noSylow
27C2×#226Dic311yescharacteristic
28C2×C3×Q16—31no—
29C3×C4×Q8—31no—
30C3×C4×Q8C2×D311yescharacteristic
31C4×SL(2,𝔽3)—21no—
32C4×SL(2,𝔽3)C2×D311yescharacteristic
33#859Dic311yescharacteristic
34C3×#107—31no—
35C3×#103—31no—
36C3×#103—31no—
37C3×C4×C8—31no—
38Dic3⋊C8—121no—
39C4⋊(C3⋊C8)—31no—
40C4⋊(C3⋊C8)—31no—
41C4⋊(C3⋊C8)—61no—
42#803—61no—
43C4×C3⋊C8—31no—
44C4×C3⋊C8—31no—
45C2×C32×C4—41no—
46C2×C3×Dic3—41no—
47C2×C3×Dic3—41no—
48C3×SL(2,𝔽3)M1611yescharacteristic
49C3⋊(C3⋊C8)—81no—
50C3×C3⋊C8—81no—
51#446—91no—
52C8×Q8—31no—
53C4×Q16—31no—
54#334—91no—
55Q8⋊C8—91no—
56Q8⋊C8—91no—
57#322—91no—
58C2×C3×Q8—31no—
59C2×C3×Q8C4×D311yescharacteristic
60C2×SL(2,𝔽3)—21no—
61C2×SL(2,𝔽3)C2×Dic311yescharacteristic
62#226—21no—
63C3×Q16—61no—
64C3×Q16—61no—
65C2×C3×C8—31no—
66C2×C3×C8—31no—
67C2×C3×C8—121no—
68C3×C4⋊C4—31no—
69C3×C4⋊C4—31no—
70C3×C4⋊C4—61no—
71C3×C42—31no—
72C3×C42—61no—
73C4×Dic3—41no—
74C2×C3⋊C8—31no—
75C2×C3⋊C8—61no—
76C2×C3⋊C8—61no—
77C2×C3⋊C8—121no—
78C2×C3⋊C8—241no—
79C2×C3⋊C8S411yescharacteristic
80C22×C32—41no—
81C32×C4—41no—
82C32×C4—41no—
83C3×Dic3—42no—
84C3×Dic3—81no—
85C2×Q16—31no—
86C4×Q8—31no—
87C4×Q8D3211yescharacteristic
88#107—31no—
89C4⋊C8—91no—
90C4⋊C8—91no—
91C4⋊C8—181no—
92#103—31no—
93#103—31no—
94#97—181no—
95C4×C8—31no—
96C4×C8—91no—
97C4×C8—91no—
98C3×Q8—31no—
99C3×Q8—61no—
100C3×Q8—61no—
101C3×Q8ΓL(1,𝔽25)11yescharacteristic
102C2×C3×C4—31no—
103C2×C3×C4—31no—
104C2×C3×C4—41no—
105C2×C3×C4—61no—
106C2×C3×C4—61no—
107C2×C3×C4—81no—
108C2×C3×C4C2×S411yescharacteristic
109C2×Dic3—41no—
110C2×Dic3—41no—
111SL(2,𝔽3)—21no—
112SL(2,𝔽3)#20811yescharacteristic
113C3×C8—61no—
114C3×C8—61no—
115C3×C8—241no—
116C3⋊C8—21no—
117C3⋊C8—62no—
118C3⋊C8—61no—
119C3⋊C8—121no—
120C3⋊C8—241no—
121C3⋊C8—242no—
122C2×C32—41no—
123C2×C32—41no—
124C2×C32—41no—
125C2×Q8—31no—
126C2×Q8D3×Dic311yescharacteristic
127Q16—61no—
128Q16—61no—
129C2×C8—31no—
130C2×C8—31no—
131C2×C8—31no—
132C2×C8—91no—
133C2×C8—181no—
134C2×C8—181no—
135C4⋊C4—31no—
136C4⋊C4—31no—
137C4⋊C4—61no—
138C42—31no—
139C42—61no—
140C22×C3—41no—
141C22×C3—81no—
142C22×C3C4×S411yescharacteristic
143C3×C4—31no—
144C3×C4—31no—
145C3×C4—41no—
146C3×C4—41no—
147C3×C4—61no—
148C3×C4—81no—
149C3×C4—81no—
150C3×C4—121no—
151C3×C4—121no—
152C3×C4#98311yescharacteristic
153C3×C4#98411yescharacteristic
154Dic3—42no—
155Dic3—81no—
156C32—41noSylow
157Q8—31no—
158Q8—61no—
159Q8—61no—
160Q8#371111yescharacteristic
161C2×C4—31no—
162C2×C4—31no—
163C2×C4—61no—
164C2×C4—61no—
165C2×C4D3×S411yescharacteristic
166C8—61no—
167C8—61no—
168C8—61no—
169C8—182no—
170C8—181no—
171C8—361no—
172C2×C3—41no—
173C2×C3—41no—
174C2×C3—41no—
175C2×C3—81no—
176C2×C3—81no—
177C2×C3—81no—
178C2×C3#538811yescharacteristic
179C2×C3#540011yescharacteristic
180C2×C3#540411yescharacteristic
181C22Dic3×S411yescharacteristic
182C4—31no—
183C4—31no—
184C4—61no—
185C4—121no—
186C4—121no—
187C4#6419611yescharacteristic
188C4#6420211yescharacteristic
189C3—41no—
190C3—81no—
191C3#7300911yescharacteristic, complemented
192C2#1059317511yescharacteristic
193C2#1059319811yescharacteristic
194C2#1059321911yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2×C4D3×S4
commutator, prime radicalC2×C3×SL(2,𝔽3)C2×C4
FittingC3×C4×Q8C2×D3
socleC22×C3C4×S4
cosocleC3×C4×SL(2,𝔽3)C22
hypocenterC3×SL(2,𝔽3)M16
LCSG ▷ C2×C3×SL(2,𝔽3) ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
191. C3#73009semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2262
C3⋊C8×SL(2,𝔽3)2
C3⋊(SL(2,𝔽3)⋊C8)2
#730093
#709043
Dic3⋊(C3⋊C8)4