Finite Group Databasebeta

← #11779329

Subgroups — #11779329

Order 1152.

654 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C32×#559C211yesmaximal, characteristic
2#10592775C211yesmaximal, characteristic
3#10592720C212yesmaximal, complemented
4#10589410C211yesmaximal, characteristic
5#10589401C212yesmaximal, complemented
6#71944—34nomaximal
7C32×#127C2211yescharacteristic
8C32×#124—22no—
9C32×#123—22no—
10C32×C4×Q8C2212yes—
11C32×C4×D4—22no—
12C2×#3754—22no—
13#64078C2211yescharacteristic
14#63662—22no—
15#63634—22no—
16C4⋊(C3⋊(C3⋊C8))C2212yes—
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#559D314yes—
19#5076—34no—
20#5021—38no—
21#4544—34no—
22#4535—38no—
23C2×C32×Q8D412yes—
24C2×C32×D4—22no—
25C2×C32×D4D412yes—
26C22×C32×C4—22no—
27C2×#634—21no—
28C32×C4⋊C4—22no—
29C32×C4⋊C4D412yes—
30C32×C22⋊C4—24no—
31C32×C22⋊C4—22no—
32C32×C42—22no—
33C32×C42C2311yescharacteristic
34#3754—44no—
35C4⋊(C3⋊Dic3)—22no—
36C2×C3⋊(C3⋊C8)—21no—
37C2×C3⋊(C3⋊C8)—22no—
38#1630—91noSylow
39C3×#127C2×D314yes—
40C3×#124—28no—
41C3×#123—28no—
42C3×C4×Q8C2×D318yes—
43C3×C4×D4—28no—
44C2×#214—68no—
45#869—34no—
46#835—68no—
47#807—68no—
48C4⋊(C3⋊C8)—38no—
49C4×C3⋊C8—34no—
50C23×C32—22no—
51C32×Q8—22no—
52C32×Q8—22no—
53C32×D4—42no—
54C32×D4—42no—
55C32×D4—42no—
56C2×C32×C4—22no—
57C2×C32×C4—22no—
58C2×C32×C4—82no—
59C2×C32×C4C2×D411yescharacteristic
60C2×C32×C4C2×D412yes—
61C2×C3⋊Dic3—41no—
62#634—42no—
63C3⋊(C3⋊C8)—22no—
64C3⋊(C3⋊C8)—42no—
65#559C3⋊D311yescharacteristic
66#492—91no—
67#477—92no—
68#331—91no—
69Q8⋊C8—92no—
70C2×C3×Q8#6718yes—
71C2×C3×D4—28no—
72C2×C3×D4#6718yes—
73C22×C3×C4—28no—
74C2×Dic6—64no—
75C3×C4⋊C4—28no—
76C3×C4⋊C4#6718yes—
77C3×C22⋊C4—216no—
78C3×C22⋊C4—28no—
79C3×C42—28no—
80C3×C42C22×D314yes—
81#214—1216no—
82C4⋊Dic3—68no—
83C2×C3⋊C8—64no—
84C2×C3⋊C8—68no—
85C22×C32—44no—
86C22×C32—42no—
87C22×C32#12011yescharacteristic
88C32×C4—21no—
89C32×C4—42no—
90C32×C4—42no—
91C32×C4#13512yes—
92C32×C4#13712yes—
93C3⋊Dic3—81no—
94C2×SD16—182no—
95C4⋊Q8—91no—
96#127C2×C3⋊D311yescharacteristic
97#124—22no—
98#123—22no—
99C4×Q8C2×C3⋊D312yes—
100C4×D4—22no—
101#107—182no—
102C4⋊C8—92no—
103#103—182no—
104C4×C8—91no—
105C23×C3—28no—
106C3×Q8—28no—
107C3×Q8—28no—
108C3×D4—48no—
109C3×D4—48no—
110C3×D4—48no—
111C2×C3×C4—28no—
112C2×C3×C4—28no—
113C2×C3×C4—88no—
114C2×C3×C4C2×#6714yes—
115C2×C3×C4C2×#6718yes—
116C2×Dic3—124no—
117Dic6—128no—
118C3⋊C8—68no—
119C3⋊C8—128no—
120C2×C32—82no—
121C2×C32#45212yes—
122C2×C32#45311yescharacteristic
123C2×Q8—181no—
124C2×Q8#63812yes—
125C2×D4—22no—
126C2×D4#63812yes—
127C22×C4—22no—
128SD16—364no—
129C2×C8—181no—
130C2×C8—182no—
131C4⋊C4—22no—
132C4⋊C4—182no—
133C4⋊C4#63812yes—
134C22⋊C4—24no—
135C22⋊C4—22no—
136C42—22no—
137C42C22×C3⋊D311yescharacteristic
138C22×C3—416no—
139C22×C3—48no—
140C22×C3#95314yes—
141C3×C4—24no—
142C3×C4—48no—
143C3×C4—48no—
144C3×C4#95018yes—
145C3×C4#95118yes—
146Dic3—244no—
147C32#163011yescharacteristic, complemented, Sylow
148C23—22no—
149Q8—22no—
150Q8—22no—
151Q8—362no—
152D4—42no—
153D4—42no—
154D4—42no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—82no—
158C2×C4—361no—
159C2×C4C2×#63811yescharacteristic
160C2×C4C2×#63812yes—
161C8—182no—
162C8—362no—
163C2×C3—88no—
164C2×C3#523918yes—
165C2×C3#524114yes—
166C22—44no—
167C22—42no—
168C22#6416211yescharacteristic
169C4—21no—
170C4—42no—
171C4—42no—
172C4—721no—
173C4#6415912yes—
174C4#6416012yes—
175C3#7194414yescomplemented
176C2—82no—
177C2#1059293812yes—
178C2#1059294011yescharacteristic
subgroupG/H
centerC22#64162
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#559C2
socleC22×C32#120
prime radicalC32×#127C22
hypercenter#559C3⋊D3
hypocenterC32#1630
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #559

Complements

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

NH ≅ G/Ntype
3. #10592720C2semidirect
5. #10589401C2semidirect
147. C32#1630semidirect
175. C3#71944semidirect

Maximal subgroups

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

subgroupindex
C32×#5592
#105927752
#105927202
#105894102
#105894012
#719443