Finite Group Databasebeta

← #11780515

Subgroups — #11780515

Order 1152.

618 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 125 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×#563C211yesmaximal, characteristic, complemented
2#10592766C212yesmaximal, complemented
3#10592757C211yesmaximal, characteristic
4#10589409C212yesmaximal, complemented
5#10589406C211yesmaximal, characteristic, complemented
6#71955—34nomaximal
7C32×C4⋊Q8—21no—
8C32×#126—22no—
9C32×#125C2212yes—
10C32×#124C2211yescharacteristic
11C32×#123—21no—
12C32×C22⋊Q8—22no—
13C2×#3755—21no—
14C2×#3753—21no—
15#64083C2211yescharacteristic
16#63636—22no—
17#63636—22no—
18#63630C2212yes—
19#63630C2211yescharacteristic
20C3×#563D314yescomplemented
21#5067—38no—
22#5058—34no—
23#4543—38no—
24#4540—34no—
25C2×C32×Q8—21no—
26C2×C32×Q8D411yescharacteristic
27C2×C32×D4D411yescharacteristic
28C22×C32×C4—21no—
29C2×C4⋊(C3⋊D3)—21no—
30C2×C4⋊(C3⋊D3)—22no—
31C32×C4⋊C4—22no—
32C32×C4⋊C4—22no—
33C32×C4⋊C4—22no—
34C32×C4⋊C4D412yes—
35C32×C4⋊C4D412yes—
36C32×C22⋊C4—22no—
37C32×C22⋊C4—21no—
38C32×C22⋊C4—22no—
39C32×C42—21no—
40C32×C42C2311yescharacteristic
41#3755—42no—
42#3753—42no—
43C2×C3⋊(C3⋊C8)—21no—
44C2×C3⋊(C3⋊C8)—22no—
45#1657—91noSylow
46C3×C4⋊Q8—24no—
47C3×#126—28no—
48C3×#125C2×D318yes—
49C3×#124C2×D314yes—
50C3×#123—24no—
51C3×C22⋊Q8—28no—
52C2×#215—64no—
53C2×#213—64no—
54#874—34no—
55#809—68no—
56#809—68no—
57#803—38no—
58#803—34no—
59C23×C32—21no—
60C22×C3⋊D3—41no—
61C32×Q8—41no—
62C32×Q8—81no—
63C32×D4—41no—
64C2×C32×C4—22no—
65C2×C32×C4—21no—
66C2×C32×C4—22no—
67C2×C32×C4—81no—
68C2×C32×C4C2×D412yes—
69C2×C32×C4C2×D411yescharacteristic
70C4⋊(C3⋊D3)—41no—
71C4⋊(C3⋊D3)—41no—
72C4⋊(C3⋊D3)—44no—
73C3⋊(C3⋊C8)—22no—
74C3⋊(C3⋊C8)—42no—
75#563C3⋊D311yescharacteristic, complemented
76#496—91no—
77#490—92no—
78#330—92no—
79#329—91no—
80C2×C3×Q8—24no—
81C2×C3×Q8#6714yes—
82C2×C3×D4#6714yes—
83C22×C3×C4—24no—
84C2×D12—68no—
85C2×D12—64no—
86C3×C4⋊C4—28no—
87C3×C4⋊C4—28no—
88C3×C4⋊C4—28no—
89C3×C4⋊C4#6718yes—
90C3×C4⋊C4#6718yes—
91C3×C22⋊C4—28no—
92C3×C22⋊C4—24no—
93C3×C22⋊C4—28no—
94C3×C42—24no—
95C3×C42C22×D314yes—
96#215—128no—
97#213—128no—
98C2×C3⋊C8—64no—
99C2×C3⋊C8—68no—
100C22×C32—41no—
101C22×C32—42no—
102C22×C32#12011yescharacteristic
103C2×C3⋊D3—81no—
104C2×C3⋊D3—82no—
105C32×C4—21no—
106C32×C4—22no—
107C32×C4—42no—
108C32×C4—41no—
109C32×C4—42no—
110C2×SD16—181no—
111C2×D8—181no—
112C4⋊Q8—21no—
113#127—91no—
114#126—22no—
115#125C2×C3⋊D312yes—
116#124C2×C3⋊D311yescharacteristic
117#123—21no—
118C22⋊Q8—22no—
119#102—182no—
120#102—182no—
121#97—92no—
122#97—91no—
123C23×C3—24no—
124C22×D3—124no—
125C3×Q8—44no—
126C3×Q8—84no—
127C3×D4—44no—
128C2×C3×C4—28no—
129C2×C3×C4—24no—
130C2×C3×C4—28no—
131C2×C3×C4—84no—
132C2×C3×C4C2×#6718yes—
133C2×C3×C4C2×#6714yes—
134D12—124no—
135D12—124no—
136D12—1216no—
137C3⋊C8—68no—
138C3⋊C8—128no—
139C2×C32—81no—
140C2×C32#45311yescharacteristic
141C2×C32#45412yes—
142C3⋊D3—161no—
143C2×Q8—21no—
144C2×Q8#63811yescharacteristic
145C2×D4—182no—
146C2×D4—181no—
147C2×D4#63811yescharacteristic
148C22×C4—21no—
149SD16—362no—
150D8—362no—
151C2×C8—181no—
152C2×C8—182no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4#63812yes—
157C4⋊C4#63812yes—
158C22⋊C4—22no—
159C22⋊C4—21no—
160C22⋊C4—22no—
161C42—21no—
162C42C22×C3⋊D311yescharacteristic
163C22×C3—44no—
164C22×C3—48no—
165C22×C3#95314yes—
166C2×D3—244no—
167C2×D3—248no—
168C3×C4—24no—
169C3×C4—28no—
170C3×C4—48no—
171C3×C4—44no—
172C3×C4—48no—
173C32#165711yescharacteristic, complemented, Sylow
174C23—21no—
175C23—361no—
176Q8—41no—
177Q8—81no—
178D4—41no—
179D4—361no—
180D4—361no—
181D4—364no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—81no—
186C2×C4C2×#63812yes—
187C2×C4C2×#63811yescharacteristic
188C8—182no—
189C8—362no—
190C2×C3—84no—
191C2×C3#524114yes—
192C2×C3#524518yes—
193D3—484no—
194C22—41no—
195C22—42no—
196C22—721no—
197C22—722no—
198C22#6416211yescharacteristic
199C4—21no—
200C4—22no—
201C4—42no—
202C4—41no—
203C4—42no—
204C3#7195514yescomplemented
205C2—81no—
206C2—1441no—
207C2#1059294011yescharacteristic
208C2#1059294412yes—
subgroupG/H
centerC22#64162
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#563C2
socleC22×C32#120
prime radical#10592757C2
hypercenter#563C3⋊D3
hypocenterC32#1657
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
1. C32×#563C2semidirect
2. #10592766C2semidirect
4. #10589409C2semidirect
5. #10589406C2semidirect
20. C3×#563D3semidirect
75. #563C3⋊D3semidirect
173. C32#1657semidirect
204. C3#71955semidirect

Maximal subgroups

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

subgroupindex
C32×#5632
#105927662
#105927572
#105894092
#105894062
#719553