Finite Group Databasebeta

← #11920604

Subgroups — #11920604

Order 1152.

209 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 209 conjugacy classes of subgroups — too many to draw. Only its 27 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
1#5753⋊C3C211yesmaximal, characteristic, complemented
2#10593641C211yesmaximal, characteristic, complemented
3C3×#4628C211yesmaximal, characteristic, complemented
4#73139—31nomaximal
5#69127—31nomaximal
6#1010⋊C3—21no—
7#64267—21no—
8C3×#131⋊C3C2211yescharacteristic
9#63546—41nomaximal
10#5753D311yescharacteristic, complemented
11#578⋊C3—31no—
12#5407—31no—
13#5407—61no—
14#5142—31no—
15#4908—31no—
16C2×#800—31no—
17#4628D311yescharacteristic, complemented
18C3×#350—31no—
19#4517—31no—
20#4510—31no—
21C3×#41⋊C3D411yescharacteristic
22D3×SL(2,𝔽3)—41no—
23C3⋊GL(2,𝔽3)—41no—
24#3745—41no—
25C3×D24—41no—
26C3×C3⋊C16—41no—
27#2193—91noSylow
28#1010—21no—
292−1+4⋊C3—61no—
30#986—62no—
31#986—61no—
32C3×#131C2×D311yescharacteristic
33#949—61no—
34#909—61no—
35C2×Dic12—31no—
36#904—31no—
37C2×D24—31no—
38#131⋊C3—21no—
39#131⋊C3C2×D311yescharacteristic
40C3×M32—31no—
41C2×C3×C16—31no—
42#826—121no—
43#823—61no—
44#819—31no—
45#800—62no—
46#800—61no—
47D48—61no—
48C4⋊(C3⋊D3)—81no—
49C3×D12—81no—
50C3×SL(2,𝔽3)D811yescharacteristic
51C32×C8—41no—
52#578—31no—
53#509—91no—
54C2×SD32—91no—
55#472—91no—
56#362—91no—
57#359—91no—
58#350—31no—
59C3×#41#6711yescharacteristic
60D3×Q8—41no—
61#237—121no—
62#235—61no—
63C2×D12—61no—
64C2×Dic6—61no—
65#41⋊C3—21no—
66#41⋊C3D1211yescharacteristic
67C2×SL(2,𝔽3)—121no—
68GL(2,𝔽3)—122no—
69GL(2,𝔽3)—121no—
70C3×D8—121no—
71C3×M16—31no—
72C2×C3×C8—31no—
73#215—121no—
74#213—121no—
75#208—61no—
76Dic12—32no—
77Dic12—31no—
78D24—61no—
79D24—61no—
80D24—121no—
81D24—241no—
82D24S411yescharacteristic
83#204—61no—
84C3×C16—61no—
85C3×C16—61no—
86C3⋊C16—41no—
87C2×C3⋊D3—161no—
88C2×C3×D3—161no—
89C32×C4—41no—
902−1+4—61no—
91#137—181no—
92AGL(1,ℤ/8)—181no—
93#135—91no—
94C2×Q16—91no—
95C2×D8—91no—
96#131D3211yescharacteristic
97SD32—182no—
98SD32—181no—
99D16—181no—
100M32—31no—
101C2×C16—31no—
102#108—91no—
103#100—181no—
104C22×D3—121no—
105C3×Q8#21311yescharacteristic
106C3×D4—31no—
107C3×D4—241no—
108C2×C3×C4—31no—
109#67—121no—
110C2×Dic3—121no—
111D12—21no—
112D12—121no—
113D12—121no—
114D12—241no—
115D12—242no—
116C4×D3—121no—
117Dic6—61no—
118Dic6—121no—
119SL(2,𝔽3)—21no—
120SL(2,𝔽3)D2411yescharacteristic
121C3×C8—31no—
122C3×C8—41no—
123C3×C8—81no—
124C3×C8C2×S411yescharacteristic
125C3⋊C8—121no—
126C2×C32—41no—
127C3⋊D3—321no—
128C3×D3—321no—
129#41—181no—
130#41—361no—
131#41#62611yescharacteristic
132C2×Q8—121no—
133C2×Q8—181no—
134C2×D4—181no—
135Q16—92no—
136Q16—91no—
137SD16—181no—
138SD16—361no—
139D8—31no—
140D8—181no—
141D8—181no—
142D8—361no—
143M16—31no—
144M16—181no—
145C2×C8—31no—
146C16—61no—
147C16—61no—
148C22×C3—31no—
149C22×C3—481no—
150C2×D3—41no—
151C2×D3—241no—
152C2×D3—481no—
153C2×D3—482no—
154C2×D3—481no—
155C3×C4—31no—
156C3×C4—41no—
157C3×C4—81no—
158C3×C4GL(2,ℤ/4)11yescharacteristic
159Dic3—121no—
160C32—41noSylow
161C23—361no—
162Q8—181no—
163Q8—361no—
164Q8#371411yescharacteristic
165D4—31no—
166D4—61no—
167D4—361no—
168D4—361no—
169D4—361no—
170C2×C4—31no—
171C2×C4—361no—
172C2×C4—361no—
173C8—31no—
174C8—361no—
175C8D3×S411yescharacteristic
176C2×C3—41no—
177C2×C3—61no—
178C2×C3—81no—
179C2×C3—961no—
180C2×C3#541511yescharacteristic
181D3—81no—
182D3—481no—
183D3—961no—
184D3—962no—
185C22—31no—
186C22—121no—
187C22—721no—
188C22—1441no—
189C4—31no—
190C4—361no—
191C4#6421011yescharacteristic
192C3—41no—
193C3—81no—
194C3#7313911yescharacteristic, complemented
195C2—61no—
196C2—241no—
197C2—1441no—
198C2#1059318411yescharacteristic
subgroupG/H
centerC2#10593184
commutator, cosocleC3×#131⋊C3C22
Frattini, hypercenterC8D3×S4
FittingC3×#131C2×D3
socleC2×C3#5415
hypocenterC3×SL(2,𝔽3)D8
LCSG ▷ C3×#131⋊C3 ▷ C3×#41⋊C3 ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C2 ◁ C4 ◁ C8

Complements

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

NH ≅ G/Ntype
1. #5753⋊C3C2semidirect
2. #10593641C2semidirect
3. C3×#4628C2semidirect
10. #5753D3semidirect
17. #4628D3semidirect
194. C3#73139semidirect

Maximal subgroups

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

subgroupindex
#5753⋊C32
#105936412
C3×#46282
#731393
#691273
#635464