Finite Group Databasebeta

← #11771521

Subgroups — #11771521

Order 1152.

209 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 209 conjugacy classes of subgroups — too many to draw. Only its 62 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×#5119C211yesmaximal, characteristic
2#10589419C211yesmaximal, characteristic
3C3×#4553C211yesmaximal, characteristic
4#67719—31nomaximal
5#67533—31nomaximal
6C2×C32×M16C2211yescharacteristic
7C3×#926C411yescharacteristic
8C22×C3×C3⋊C8C411yescharacteristic
9#63639—21no—
10C3×Dic3⋊C8—21no—
11C3×Dic3⋊C8—21no—
12C3×#812—21no—
13C3×#424—31no—
14#5119D311yescharacteristic
15C3×#349—31no—
16#4553—31no—
17#4553—31no—
18#4553—61no—
19#4553D311yescharacteristic
20C22×C32×C4C2×C411yescharacteristic
21C32×M16—41no—
22C2×C32×C8D411yescharacteristic
23C2×C32×C8D411yescharacteristic
24C3×#217C812yes—
25C3×C4⋊Dic3—21no—
26C3×C4×Dic3—21no—
27C2×C3×C3⋊C8—21no—
28C2×C3×C3⋊C8—41no—
29C3⋊(C3⋊C16)—41no—
30C3×C3⋊C16—41no—
31#1328—91noSylow
32C2×C3×M16—21no—
33C2×C3×M16C2×D311yescharacteristic
34C2×C3×M16C2×D311yescharacteristic
35C22×C3×C8—31no—
36C3×#117—31no—
37#926Dic311yescharacteristic
38C22×C3⋊C8Dic311yescharacteristic
39C3×M32—61no—
40C3×C4⋊C8—61no—
41C3×C4⋊C8—61no—
42Dic3⋊C8—21no—
43Dic3⋊C8—21no—
44#812—21no—
45#812—62no—
46#812—61no—
47#812—61no—
48C23×C32C2×C811yescharacteristic
49C2×C32×C4—21no—
50C2×C32×C4—21no—
51C2×C32×C4C22⋊C411yescharacteristic
52C2×C32×C4M1611yescharacteristic
53C2×C3×Dic3—22no—
54C32×C8—21no—
55C32×C8—21no—
56C3×C3⋊C8—41no—
57#424—31no—
58#349—31no—
59#349—91no—
60C22×C3×C4—21no—
61C22×C3×C4C4×D311yescharacteristic
62C22×C3×C4C2×Dic311yescharacteristic
63C3×M16—41no—
64C3×M16—41no—
65C3×M16—42no—
66C2×C3×C8—21no—
67C2×C3×C8—21no—
68C2×C3×C8—61no—
69C2×C3×C8—121no—
70C2×C3×C8D1211yescharacteristic
71C2×C3×C8#6711yescharacteristic
72C2×C3×C8#6711yescharacteristic
73C2×C3×C8#6711yescharacteristic
74C3×C4⋊C4—61no—
75C3×C22⋊C4—32no—
76C3×C42—61no—
77#217C3⋊C812yes—
78C4⋊Dic3—21no—
79C4×Dic3—21no—
80C2×C3⋊C8—21no—
81C2×C3⋊C8—41no—
82C3×C16—121no—
83C3⋊C16—41no—
84C3⋊C16—122no—
85C3⋊C16—121no—
86C3⋊C16—121no—
87C22×C32—21no—
88C22×C32—41no—
89C22×C32C22⋊C811yescharacteristic
90C32×C4—21no—
91C32×C4#9911yescharacteristic
92C32×C4#10111yescharacteristic
93C3×Dic3—42no—
94C2×M16D3211yescharacteristic
95C22×C8—31no—
96#117—31no—
97M32—61no—
98M32—181no—
99C4⋊C8—61no—
100C4⋊C8—61no—
101C23×C3—21no—
102C23×C3D3×C811yescharacteristic
103C23×C3C2×C3⋊C811yescharacteristic
104C2×C3×C4—21no—
105C2×C3×C4—21no—
106C2×C3×C4—21no—
107C2×C3×C4—21no—
108C2×C3×C4—21no—
109C2×C3×C4—21no—
110C2×C3×C4—41no—
111C2×C3×C4—41no—
112C2×C3×C4—62no—
113C2×C3×C4ΓL(1,𝔽25)11yescharacteristic
114C2×C3×C4#20811yescharacteristic
115C2×C3×C4(C2×D3)⋊C411yescharacteristic
116C2×C3×C4#21711yescharacteristic
117C2×Dic3—22no—
118C3×C8—22no—
119C3×C8—21no—
120C3×C8—21no—
121C3×C8—21no—
122C3×C8—21no—
123C3×C8—41no—
124C3×C8—121no—
125C3⋊C8—41no—
126C2×C32—21no—
127C2×C32—41no—
128C2×C32#32411yescharacteristic
129C22×C4D3×Dic311yescharacteristic
130M16—41no—
131C2×C8—61no—
132C2×C8—121no—
133C2×C8#62511yescharacteristic
134C2×C8#62611yescharacteristic
135C4⋊C4—61no—
136C22⋊C4—32no—
137C42—61no—
138C16—121no—
139C16—361no—
140C22×C3—21no—
141C22×C3—21no—
142C22×C3—21no—
143C22×C3—41no—
144C22×C3—41no—
145C22×C3—41no—
146C22×C3—81no—
147C22×C3(C2×D3)⋊C811yescharacteristic
148C22×C3#83011yescharacteristic
149C3×C4—21no—
150C3×C4—21no—
151C3×C4—21no—
152C3×C4—21no—
153C3×C4—41no—
154C3×C4—122no—
155C3×C4#80611yescharacteristic
156C3×C4#82411yescharacteristic
157C3×C4#83411yescharacteristic
158C3×C4#83611yescharacteristic
159Dic3—42no—
160C32#132811yescharacteristic, complemented, Sylow
161C23D3×C3⋊C811yescharacteristic
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—62no—
165C2×C4#371111yescharacteristic
166C2×C4(C2×D3)⋊Dic311yescharacteristic
167C8—21no—
168C8—21no—
169C8—121no—
170C2×C3—21no—
171C2×C3—21no—
172C2×C3—21no—
173C2×C3—41no—
174C2×C3—41no—
175C2×C3—41no—
176C2×C3—81no—
177C2×C3#446911yescharacteristic
178C2×C3#452811yescharacteristic
179C22—21no—
180C22—41no—
181C22(C2×D3)⋊(C3⋊C8)11yescharacteristic
182C4—21no—
183C4—122no—
184C4#6356011yescharacteristic
185C4#6358011yescharacteristic
186C3—21no—
187C3#6753311yescharacteristic, complemented
188C3#6771911yescharacteristic, complemented
189C2—21no—
190C2—41no—
191C2#1058914711yescharacteristic
subgroupG/H
centerC4#63580
commutator, prime radicalC23×C32C2×C8
Frattini, hypercenterC2×M16D32
Fitting, cosocleC2×C32×M16C22
socleC2×C32#324
hypocenterC32#1328
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
160. C32#1328semidirect
187. C3#67533semidirect
188. C3#67719semidirect

Maximal subgroups

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

subgroupindex
C3×#51192
#105894192
C3×#45532
#677193
#675333