Finite Group Databasebeta

← #11780595

Subgroups — #11780595

Order 1152.

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

normal subgroups only

This group has 588 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
2#10592763C212yesmaximal, complemented
3#10592759C211yesmaximal, characteristic
4#10589409C212yesmaximal, complemented
5#10589406C211yesmaximal, characteristic
6#71956—34nomaximal
7C32×C4⋊Q8—21no—
8C32×#126—22no—
9C32×#125C2212yes—
10C32×#124C2211yescharacteristic
11C32×#123—21no—
12C32×C22⋊Q8—22no—
13C2×#3756—21no—
14C2×#3754—21no—
15#64078C2211yescharacteristic
16#63635—22no—
17#63634—22no—
18#63630C2212yes—
19#63630C2211yescharacteristic
20C3×#563D314yes—
21#5064—38no—
22#5060—34no—
23#4543—38no—
24#4540—34no—
25C2×C32×Q8—21no—
26C2×C32×Q8D411yescharacteristic
27C2×C32×D4D411yescharacteristic
28C22×C32×C4—21no—
29C2×#634—21no—
30C32×C4⋊C4—22no—
31C32×C4⋊C4—22no—
32C32×C4⋊C4—22no—
33C32×C4⋊C4D412yes—
34C32×C4⋊C4D412yes—
35C32×C22⋊C4—22no—
36C32×C22⋊C4—21no—
37C32×C22⋊C4—22no—
38C32×C42—21no—
39C32×C42C2311yescharacteristic
40#3756—42no—
41#3754—42no—
42C4⋊(C3⋊Dic3)—22no—
43C2×C3⋊(C3⋊C8)—21no—
44C2×C3⋊(C3⋊C8)—22no—
45#1660—91noSylow
46C3×C4⋊Q8—24no—
47C3×#126—28no—
48C3×#125C2×D318yes—
49C3×#124C2×D314yes—
50C3×#123—24no—
51C3×C22⋊Q8—28no—
52C2×#216—64no—
53C2×#214—64no—
54#869—34no—
55#808—68no—
56#807—68no—
57#803—38no—
58#803—34no—
59C23×C32—21no—
60C32×Q8—41no—
61C32×Q8—81no—
62C32×D4—41no—
63C2×C32×C4—22no—
64C2×C32×C4—21no—
65C2×C32×C4—22no—
66C2×C32×C4—81no—
67C2×C32×C4C2×D412yes—
68C2×C32×C4C2×D411yescharacteristic
69C2×C3⋊Dic3—41no—
70#634—41no—
71#634—41no—
72C3⋊(C3⋊C8)—24no—
73C3⋊(C3⋊C8)—22no—
74#563C3⋊D311yescharacteristic
75#501—92no—
76#497—91no—
77#330—92no—
78#329—91no—
79C2×C3×Q8—24no—
80C2×C3×Q8#6714yes—
81C2×C3×D4#6714yes—
82C22×C3×C4—24no—
83C2×Dic6—64no—
84C3×C4⋊C4—28no—
85C3×C4⋊C4—28no—
86C3×C4⋊C4—28no—
87C3×C4⋊C4#6718yes—
88C3×C4⋊C4#6718yes—
89C3×C22⋊C4—28no—
90C3×C22⋊C4—24no—
91C3×C22⋊C4—28no—
92C3×C42—24no—
93C3×C42C22×D314yes—
94#216—128no—
95#214—128no—
96C4⋊Dic3—68no—
97C2×C3⋊C8—68no—
98C2×C3⋊C8—64no—
99C22×C32—41no—
100C22×C32—42no—
101C22×C32#12011yescharacteristic
102C32×C4—21no—
103C32×C4—22no—
104C32×C4—42no—
105C32×C4—41no—
106C32×C4—42no—
107C3⋊Dic3—81no—
108C2×Q16—181no—
109C2×SD16—181no—
110C4⋊Q8—21no—
111C4⋊Q8—91no—
112#126—22no—
113#125C2×C3⋊D312yes—
114#124C2×C3⋊D311yescharacteristic
115#123—21no—
116C22⋊Q8—22no—
117#107—182no—
118#106—182no—
119#97—92no—
120#97—91no—
121C23×C3—24no—
122C3×Q8—44no—
123C3×Q8—84no—
124C3×D4—44no—
125C2×C3×C4—28no—
126C2×C3×C4—24no—
127C2×C3×C4—28no—
128C2×C3×C4—84no—
129C2×C3×C4C2×#6718yes—
130C2×C3×C4C2×#6714yes—
131C2×Dic3—124no—
132Dic6—124no—
133Dic6—124no—
134C3⋊C8—616no—
135C3⋊C8—68no—
136C2×C32—81no—
137C2×C32#45311yescharacteristic
138C2×C32#45612yes—
139C2×Q8—21no—
140C2×Q8—181no—
141C2×Q8#63811yescharacteristic
142C2×D4#63811yescharacteristic
143C22×C4—21no—
144Q16—362no—
145SD16—362no—
146C2×C8—182no—
147C2×C8—181no—
148C4⋊C4—22no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—182no—
152C4⋊C4#63812yes—
153C4⋊C4#63812yes—
154C22⋊C4—22no—
155C22⋊C4—21no—
156C22⋊C4—22no—
157C42—21no—
158C42C22×C3⋊D311yescharacteristic
159C22×C3—44no—
160C22×C3—48no—
161C22×C3#95314yes—
162C3×C4—24no—
163C3×C4—28no—
164C3×C4—48no—
165C3×C4—44no—
166C3×C4—48no—
167Dic3—244no—
168C32#166011yescharacteristic, complemented, Sylow
169C23—21no—
170Q8—41no—
171Q8—81no—
172Q8—361no—
173Q8—361no—
174D4—41no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—81no—
179C2×C4—361no—
180C2×C4C2×#63812yes—
181C2×C4C2×#63811yescharacteristic
182C8—182no—
183C8—184no—
184C2×C3—84no—
185C2×C3#524114yes—
186C2×C3#524618yes—
187C22—41no—
188C22—42no—
189C22#6416211yescharacteristic
190C4—21no—
191C4—22no—
192C4—42no—
193C4—41no—
194C4—42no—
195C4—721no—
196C3#7195614yescomplemented
197C2—81no—
198C2#1059294011yescharacteristic
199C2#1059294512yes—
subgroupG/H
centerC22#64162
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#563C2
socleC22×C32#120
prime radicalC2×C32×D4D4
hypercenter#563C3⋊D3
hypocenterC32#1660
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
2. #10592763C2semidirect
4. #10589409C2semidirect
168. C32#1660semidirect
196. C3#71956semidirect

Maximal subgroups

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

subgroupindex
C32×#5632
#105927632
#105927592
#105894092
#105894062
#719563