Finite Group Databasebeta

← #11779332

Subgroups — #11779332

Order 1152.

654 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 129 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#10596184C211yesmaximal, characteristic
2#10592775C211yesmaximal, characteristic
3#10592549C212yesmaximal, complemented
4C32×#331C211yesmaximal, characteristic
5#10589350C212yesmaximal, complemented
6#68404—34nomaximal
7C32×#127C2211yescharacteristic
8#64145—22no—
9#64144—22no—
10D4×C3⋊Dic3—22no—
11C2×#3754—22no—
12#64078C2211yescharacteristic
13C4×#634C2212yes—
14C32×C4⋊C8C2212yes—
15#63645—22no—
16#63643—22no—
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18#5713—34no—
19#5076—34no—
20#4850—38no—
21C3×#331D314yes—
22#4484—38no—
23C2×C32×D4—22no—
24C2×C32×D4D412yes—
25C22×C3⋊Dic3—22no—
26C2×#634—21no—
27C2×#634D412yes—
28C2×C32×C8—22no—
29C32×C42C2311yescharacteristic
30#3757—24no—
31#3757—22no—
32#3754—44no—
33C4⋊(C3⋊Dic3)—22no—
34C4⋊(C3⋊Dic3)D412yes—
35#3750—22no—
36C4×C3⋊Dic3—22no—
37C2×C3⋊(C3⋊C8)—21no—
38#1630—91noSylow
39C3×#127C2×D314yes—
40#936—68no—
41#935—68no—
42D4×Dic3—68no—
43C2×#214—68no—
44#869—34no—
45C4×Dic6—38no—
46C3×C4⋊C8C2×D318yes—
47#818—68no—
48#816—68no—
49C4×C3⋊C8—34no—
50C23×C32—22no—
51C32×D4—42no—
52C32×D4—42no—
53C32×D4—42no—
54C2×C32×C4C2×D411yescharacteristic
55C2×C32×C4C2×D412yes—
56C2×C3⋊Dic3—22no—
57C2×C3⋊Dic3—22no—
58C2×C3⋊Dic3—41no—
59C2×C3⋊Dic3—82no—
60#634—22no—
61#634—22no—
62#634—42no—
63C32×C8—42no—
64C3⋊(C3⋊C8)—22no—
65#559—91no—
66#492—91no—
67#477—92no—
68#331C3⋊D311yescharacteristic
69Q8⋊C8—92no—
70C2×C3×D4—28no—
71C2×C3×D4D1218yes—
72C22×Dic3—68no—
73C2×Dic6—38no—
74C2×Dic6—64no—
75C2×C3×C8—28no—
76C3×C42C22×D314yes—
77#217—616no—
78#217—68no—
79#214—1216no—
80C4⋊Dic3—38no—
81C4⋊Dic3—68no—
82Dic3⋊C4—68no—
83C4×Dic3—68no—
84C2×C3⋊C8—64no—
85C22×C32—44no—
86C22×C32—42no—
87C22×C32#12011yescharacteristic
88C32×C4—21no—
89C32×C4#13512yes—
90C32×C4#13712yes—
91C3⋊Dic3—42no—
92C3⋊Dic3—42no—
93C3⋊Dic3—81no—
94C2×SD16—182no—
95C4⋊Q8—91no—
96#127C2×C3⋊D311yescharacteristic
97#124—182no—
98#123—182no—
99C4×Q8—92no—
100C4×D4—182no—
101#107—182no—
102C4⋊C8C2×C3⋊D312yes—
103#103—182no—
104C4×C8—91no—
105C23×C3—28no—
106C3×D4—48no—
107C3×D4—48no—
108C3×D4—48no—
109C2×C3×C4C2×D1214yes—
110C2×C3×C4D3×D418yes—
111C2×Dic3—68no—
112C2×Dic3—68no—
113C2×Dic3—124no—
114C2×Dic3—248no—
115Dic6—68no—
116Dic6—68no—
117Dic6—128no—
118C3×C8—48no—
119C3⋊C8—68no—
120C2×C32—82no—
121C2×C32#45212yes—
122C2×C32#45311yescharacteristic
123C2×Q8—92no—
124C2×Q8—181no—
125C2×D4—22no—
126C2×D4C4⋊(C3⋊D3)12yes—
127C22×C4—182no—
128SD16—364no—
129C2×C8—22no—
130C2×C8—181no—
131C4⋊C4—92no—
132C4⋊C4—182no—
133C4⋊C4—182no—
134C22⋊C4—184no—
135C22⋊C4—182no—
136C42—182no—
137C42C22×C3⋊D311yescharacteristic
138C22×C3—48no—
139C22×C3—416no—
140C22×C3#88214yes—
141C3×C4—24no—
142C3×C4#91218yes—
143C3×C4#91518yes—
144Dic3—128no—
145Dic3—128no—
146Dic3—244no—
147C32#163011yescharacteristic, complemented, Sylow
148C23—22no—
149Q8—182no—
150Q8—182no—
151Q8—362no—
152D4—42no—
153D4—42no—
154D4—42no—
155C2×C4—182no—
156C2×C4—182no—
157C2×C4—361no—
158C2×C4—722no—
159C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
160C2×C4D4×C3⋊D312yes—
161C8—42no—
162C8—182no—
163C2×C3—88no—
164C2×C3#474714yes—
165C2×C3#478318yes—
166C22—42no—
167C22—44no—
168C22#6409111yescharacteristic
169C4—21no—
170C4—362no—
171C4—362no—
172C4—721no—
173C4#6412112yes—
174C4#6412412yes—
175C3#6840414yescomplemented
176C2—82no—
177C2#1059244611yescharacteristic
178C2#1059248212yes—
subgroupG/H
centerC22#64091
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#331C2
socleC22×C32#120
prime radicalC32×#127C22
hypercenter#331C3⋊D3
hypocenterC32#1630
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
3. #10592549C2semidirect
5. #10589350C2semidirect
147. C32#1630semidirect
175. C3#68404semidirect

Maximal subgroups

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

subgroupindex
#105961842
#105927752
#105925492
C32×#3312
#105893502
#684043