Finite Group Databasebeta

← #11779290

Subgroups — #11779290

Order 1152.

471 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 471 conjugacy classes of subgroups — too many to draw. Only its 76 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#10589819C211yesmaximal, characteristic
2C9×#492C211yesmaximal, characteristic, complemented
3#10588769C212yesmaximal, complemented
4#10588221C211yesmaximal, characteristic, complemented
5#10588136C212yesmaximal, complemented
6#71266—31nomaximal
7C2×D4×D9—22no—
8C2×C9×SD16—22no—
9C9×C4⋊Q8C2211yescharacteristic, complemented
10C9×#127C2211yescharacteristic
11#63500—22no—
12#63499—22no—
13C4×D36C2212yes—
14C4×C8×C9C2211yescharacteristic, complemented
15#63369—22no—
16#63367—22no—
17C4⋊(C9⋊C8)C2212yescomplemented
18#5717—31no—
19C3×#492D311yescharacteristic
20#5084—32no—
21#4544—31no—
22#4459—32no—
23C23×D9—22no—
24C2×Q8×C9—21no—
25C2×D4×C9—22no—
26C2×D4×C9D412yes—
27C2×#611—24no—
28D4×D9—44no—
29D4×D9—44no—
30C2×D36D412yes—
31C2×C4×D9—22no—
32C9×SD16—44no—
33C2×C8×C9—21no—
34C9×C4⋊C4—22no—
35C42×C9C2311yescharacteristic
36#3676—22no—
37(C2×D9)⋊C4—22no—
38C4⋊Dic9D412yes—
39C2×C9⋊C8—22no—
40#1629—91noSylow
41C2×D3×D4—62no—
42C2×C3×SD16—22no—
43C3×C4⋊Q8C2×D311yescharacteristic
44C3×#127C2×D311yescharacteristic
45#938—62no—
46#937—62no—
47C4×D12—32no—
48C3×C4×C8C2×D311yescharacteristic
49#809—62no—
50#808—62no—
51C4⋊(C3⋊C8)—32no—
52C23×C9—22no—
53C22×D9—22no—
54C22×D9—48no—
55C22×D9—82no—
56Q8×C9—42no—
57D4×C9—42no—
58D4×C9—42no—
59D4×C9—42no—
60C2×C4×C9—41no—
61C2×C4×C9C2×D412yes—
62C2×C4×C9C2×D411yescharacteristic
63#611—48no—
64C2×Dic9—22no—
65D36—22no—
66D36SD1614yescomplemented
67C4×D9—42no—
68C4×D9—42no—
69C8×C9—22no—
70C9⋊C8—42no—
71D42—91no—
72#492D911yescharacteristic, complemented
73#476—92no—
74#331—91no—
75D4⋊C8—92no—
76C23×D3—62no—
77C2×C3×Q8—21no—
78C2×C3×D4—22no—
79C2×C3×D4#6712yes—
80C2×#67—64no—
81D3×D4—124no—
82D3×D4—124no—
83C2×D12—32no—
84C2×C4×D3—62no—
85C3×SD16—44no—
86C2×C3×C8—21no—
87C3×C4⋊C4—22no—
88C3×C42C22×D311yescharacteristic
89#217—62no—
90(C2×D3)⋊C4—62no—
91C4⋊Dic3—32no—
92C2×C3⋊C8—62no—
93C22×C9—44no—
94C22×C9—42no—
95C22×C9#12011yescharacteristic
96C2×D9—24no—
97C2×D9—42no—
98C2×D9—42no—
99C2×D9—88no—
100C4×C9—21no—
101C4×C9—81no—
102C4×C9C2×SD1612yes—
103C4×C9AGL(1,ℤ/8)12yes—
104Dic9—42no—
105C22×D4—182no—
106C2×SD16—22no—
107C4⋊Q8C2×D911yescharacteristic, complemented
108#127C2×D911yescharacteristic
109#121—182no—
110#120—182no—
111C4×D4—92no—
112#106—182no—
113C4⋊C8—92no—
114#102—182no—
115C4×C8C2×D911yescharacteristic, complemented
116C23×C3—22no—
117C22×D3—62no—
118C22×D3—128no—
119C22×D3—242no—
120C3×Q8—42no—
121C3×D4—42no—
122C3×D4—42no—
123C3×D4—42no—
124C2×C3×C4—41no—
125C2×C3×C4D3×D412yes—
126C2×C3×C4C2×#6711yescharacteristic
127#67—128no—
128C2×Dic3—62no—
129D12—34no—
130D12—62no—
131C4×D3—122no—
132C4×D3—122no—
133C3×C8—22no—
134C3⋊C8—122no—
135C2×C9—82no—
136C2×C9#45012yes—
137C2×C9#45311yescharacteristic
138D9—44no—
139C24—182no—
140C2×Q8—21no—
141C2×D4—22no—
142C2×D4—92no—
143C2×D4—184no—
144C2×D4—364no—
145C2×D4—364no—
146C2×D4#61112yes—
147C22×C4—182no—
148SD16—44no—
149C2×C8—21no—
150C2×C8—182no—
151C4⋊C4—22no—
152C4⋊C4—92no—
153C22⋊C4—182no—
154C22⋊C4—182no—
155C42C22×D911yescharacteristic
156C22×C3—44no—
157C22×C3—42no—
158C22×C3#93711yescharacteristic
159C2×D3—64no—
160C2×D3—122no—
161C2×D3—122no—
162C2×D3—248no—
163C3×C4—21no—
164C3×C4—81no—
165C3×C4D3×SD1612yes—
166C3×C4#91412yes—
167Dic3—122no—
168C9#162911yescharacteristic, complemented, Sylow
169C23—22no—
170C23—182no—
171C23—368no—
172C23—722no—
173Q8—42no—
174D4—42no—
175D4—42no—
176D4—42no—
177D4—94no—
178D4—182no—
179D4—368no—
180C2×C4—41no—
181C2×C4—182no—
182C2×C4—362no—
183C2×C4—362no—
184C2×C4D4×D912yes—
185C2×C4C2×#61111yescharacteristic
186C8—22no—
187C8—362no—
188C2×C3—82no—
189C2×C3#507711yescharacteristic
190C2×C3#516912yes—
191D3—124no—
192C22—42no—
193C22—44no—
194C22—184no—
195C22—362no—
196C22—362no—
197C22—728no—
198C22#6349911yescharacteristic
199C4—21no—
200C4—81no—
201C4—362no—
202C4SD16×D912yes—
203C4#6347612yes—
204C3#7126611yescharacteristic
205C2—82no—
206C2—364no—
207C2#1058875711yescharacteristic
208C2#1058884912yes—
subgroupG/H
centerC22#63499
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#492C2
socleC22×C3#937
prime radical#10589819C2
hypercenter#492D9
hypocenterC9#1629
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
2. C9×#492C2semidirect
3. #10588769C2semidirect
4. #10588221C2semidirect
5. #10588136C2semidirect
9. C9×C4⋊Q8C22semidirect
14. C4×C8×C9C22semidirect
17. C4⋊(C9⋊C8)C22semidirect
66. D36SD16semidirect
72. #492D9semidirect
107. C4⋊Q8C2×D9semidirect
115. C4×C8C2×D9semidirect
168. C9#1629semidirect

Maximal subgroups

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

subgroupindex
#105898192
C9×#4922
#105887692
#105882212
#105881362
#712663