Finite Group Databasebeta

← #11779486

Subgroups — #11779486

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×#555C211yesmaximal, characteristic
2#10592791C211yesmaximal, characteristic, complemented
3#10592707C212yesmaximal, complemented
4#10589412C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊(C3⋊C8))C212yesmaximal, complemented
6#71928—34nomaximal
7C32×C4⋊Q8C2211yescharacteristic
8C32×#124—22no—
9C32×#121—22no—
10C32×C4×D4C2212yes—
11C32×#117—22no—
12C2×#3756—22no—
13#64078C2211yescharacteristic
14#63659—22no—
15#63635—22no—
16C4⋊(C3⋊(C3⋊C8))C2212yes—
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#555D314yes—
19#5092—34no—
20#5008—38no—
21#4546—34no—
22D4⋊(C3⋊C8)—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#3756—44no—
35C4⋊(C3⋊Dic3)—22no—
36C2×C3⋊(C3⋊C8)—21no—
37C2×C3⋊(C3⋊C8)—22no—
38#1634—91noSylow
39C3×C4⋊Q8C2×D314yes—
40C3×#124—28no—
41C3×#121—28no—
42C3×C4×D4C2×D318yes—
43C3×#117—28no—
44C2×#216—68no—
45#869—34no—
46#832—68no—
47#808—68no—
48C4⋊(C3⋊C8)—38no—
49C4×C3⋊C8—34no—
50C23×C32—22no—
51C32×Q8—42no—
52C32×D4—22no—
53C32×D4—22no—
54C32×D4—82no—
55C2×C32×C4—22no—
56C2×C32×C4—22no—
57C2×C32×C4—42no—
58C2×C32×C4—42no—
59C2×C32×C4C2×D411yescharacteristic
60C2×C32×C4C2×D412yes—
61C2×C3⋊Dic3—41no—
62#634—42no—
63C3⋊(C3⋊C8)—22no—
64C3⋊(C3⋊C8)—42no—
65#555C3⋊D311yescharacteristic
66#494—91no—
67#476—92no—
68#333—91no—
69D4⋊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#216—1216no—
82C4⋊Dic3—68no—
83C2×C3⋊C8—64no—
84C2×C3⋊C8—68no—
85C22×C32—42no—
86C22×C32—42no—
87C22×C32—42no—
88C22×C32#12011yescharacteristic
89C32×C4—21no—
90C32×C4—42no—
91C32×C4—42no—
92C32×C4#13512yes—
93C32×C4#13712yes—
94C3⋊Dic3—81no—
95C2×Q16—182no—
96C4⋊Q8—91no—
97C4⋊Q8C2×C3⋊D311yescharacteristic
98#124—22no—
99#121—22no—
100C4×D4C2×C3⋊D312yes—
101#117—22no—
102#106—182no—
103C4⋊C8—92no—
104#102—182no—
105C4×C8—91no—
106C23×C3—28no—
107C3×Q8—48no—
108C3×D4—28no—
109C3×D4—28no—
110C3×D4—88no—
111C2×C3×C4—28no—
112C2×C3×C4—28no—
113C2×C3×C4—48no—
114C2×C3×C4—48no—
115C2×C3×C4C2×#6714yes—
116C2×C3×C4C2×#6718yes—
117C2×Dic3—124no—
118Dic6—128no—
119C3⋊C8—68no—
120C3⋊C8—128no—
121C2×C32—82no—
122C2×C32#45212yes—
123C2×C32#45311yescharacteristic
124C2×Q8—181no—
125C2×Q8#63812yes—
126C2×D4—22no—
127C2×D4#63812yes—
128C22×C4—22no—
129Q16—364no—
130C2×C8—181no—
131C2×C8—182no—
132C4⋊C4—22no—
133C4⋊C4—182no—
134C4⋊C4#63812yes—
135C22⋊C4—24no—
136C22⋊C4—22no—
137C42—22no—
138C42C22×C3⋊D311yescharacteristic
139C22×C3—48no—
140C22×C3—48no—
141C22×C3—48no—
142C22×C3#95314yes—
143C3×C4—24no—
144C3×C4—48no—
145C3×C4—48no—
146C3×C4#95018yes—
147C3×C4#95118yes—
148Dic3—244no—
149C32#163411yescharacteristic, complemented, Sylow
150C23—22no—
151Q8—42no—
152Q8—362no—
153D4—22no—
154D4—22no—
155D4—82no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—361no—
161C2×C4C2×#63811yescharacteristic
162C2×C4C2×#63812yes—
163C8—182no—
164C8—362no—
165C2×C3—88no—
166C2×C3#523918yes—
167C2×C3#524114yes—
168C22—42no—
169C22—42no—
170C22—42no—
171C22#6416211yescharacteristic
172C4—21no—
173C4—42no—
174C4—42no—
175C4—721no—
176C4#6415912yes—
177C4#6416012yes—
178C3#7192814yescomplemented
179C2—82no—
180C2#1059293812yes—
181C2#1059294011yescharacteristic
subgroupG/H
centerC22#64162
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
Fitting, prime radicalC32×#555C2
socleC22×C32#120
hypercenter#555C3⋊D3
hypocenterC32#1634
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #555

Complements

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

NH ≅ G/Ntype
2. #10592791C2semidirect
3. #10592707C2semidirect
4. #10589412C2semidirect
5. D4⋊(C3⋊(C3⋊C8))C2semidirect
149. C32#1634semidirect
178. C3#71928semidirect

Maximal subgroups

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

subgroupindex
C32×#5552
#105927912
#105927072
#105894122
D4⋊(C3⋊(C3⋊C8))2
#719283