Finite Group Databasebeta

← #11781376

Subgroups — #11781376

Order 1152.

450 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 119 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#10592793C211yesmaximal, characteristic
2#10592778C211yesmaximal, characteristic
3#10592548C211yesmaximal, characteristic
4#10592529C211yesmaximal, characteristic
5C32×#332C211yesmaximal, characteristic
6#10589352C211yesmaximal, characteristic
7#10589346C211yesmaximal, characteristic
8#68468—34nomaximal
9C32×C4⋊Q8C2211yescharacteristic
10C2×#3746—21no—
11#64078C2211yescharacteristic
12C4×#634C2211yescharacteristic
13C32×C4⋊C8C2211yescharacteristic
14C32×C4⋊C8C2211yescharacteristic
15#63662—21no—
16#63662—21no—
17#63643—21no—
18#63641—21no—
19C8×C3⋊Dic3—21no—
20#63637—21no—
21#63635—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C4×C3⋊(C3⋊C8)C2211yescharacteristic
24#5094—34no—
25#5079—34no—
26#4849—34no—
27#4830—34no—
28C3×#332D314yes—
29#4486—34no—
30#4480—34no—
31C2×C32×Q8—21no—
32C2×#634—21no—
33C2×#634D411yescharacteristic
34C2×C32×C8—21no—
35C2×C32×C8—21no—
36C32×C4⋊C4—21no—
37C32×C4⋊C4—21no—
38C32×C42C2311yescharacteristic
39C4⋊(C3⋊Dic3)—21no—
40C4⋊(C3⋊Dic3)—21no—
41C4⋊(C3⋊Dic3)D411yescharacteristic
42#3750—21no—
43C4×C3⋊Dic3—21no—
44C2×C3⋊(C3⋊C8)—21no—
45C2×C3⋊(C3⋊C8)D411yescharacteristic
46C2×C3⋊(C3⋊C8)D411yescharacteristic
47#3746—42no—
48#1680—91noSylow
49C3×C4⋊Q8C2×D314yes—
50C2×Dic12—64no—
51#869—34no—
52C4×Dic6—34no—
53C3×C4⋊C8C2×D314yes—
54C3×C4⋊C8C2×D314yes—
55#835—64no—
56#835—64no—
57#816—64no—
58Dic3⋊C8—64no—
59C8×Dic3—64no—
60#810—64no—
61#808—64no—
62C4⋊(C3⋊C8)—34no—
63C4×C3⋊C8—34no—
64C32×Q8—41no—
65C32×Q8—41no—
66C2×C32×C4—41no—
67C2×C32×C4C2×D411yescharacteristic
68C2×C32×C4C2×D411yescharacteristic
69C2×C32×C4#4111yescharacteristic
70C2×C3⋊Dic3—21no—
71C2×C3⋊Dic3—21no—
72C2×C3⋊Dic3—41no—
73#634—21no—
74#634—41no—
75#634—41no—
76#634SD1612yes—
77C32×C8—41no—
78C32×C8—41no—
79C3⋊(C3⋊C8)—21no—
80C3⋊(C3⋊C8)—21no—
81C3⋊(C3⋊C8)—41no—
82#487—91no—
83#475—91no—
84#462—91no—
85C8×Q8—91no—
86#334—91no—
87#332—91no—
88#332C3⋊D311yescharacteristic
89C2×C3×Q8—24no—
90C2×Dic6—34no—
91C2×Dic6—64no—
92C2×C3×C8—24no—
93C2×C3×C8—24no—
94C3×C4⋊C4—24no—
95C3×C4⋊C4—24no—
96C3×C42C22×D314yes—
97C4⋊Dic3—34no—
98C4⋊Dic3—64no—
99C4⋊Dic3—64no—
100Dic3⋊C4—64no—
101C4×Dic3—64no—
102C2×C3⋊C8—34no—
103C2×C3⋊C8—34no—
104C2×C3⋊C8—64no—
105Dic12—128no—
106C22×C32#12111yescharacteristic
107C32×C4—21no—
108C32×C4—81no—
109C32×C4C2×SD1611yescharacteristic
110C32×C4#13511yescharacteristic
111C32×C4#13511yescharacteristic
112C32×C4#13711yescharacteristic
113C3⋊Dic3—22no—
114C3⋊Dic3—41no—
115C3⋊Dic3—81no—
116C2×Q16—181no—
117C4⋊Q8—91no—
118C4⋊Q8C2×C3⋊D311yescharacteristic
119C4×Q8—91no—
120#106—181no—
121C4⋊C8—91no—
122C4⋊C8—181no—
123C4⋊C8C2×C3⋊D311yescharacteristic
124C4⋊C8C2×C3⋊D311yescharacteristic
125#103—181no—
126#103—181no—
127#103—181no—
128#103—181no—
129C4×C8—91no—
130C4×C8—181no—
131C3×Q8—44no—
132C3×Q8—44no—
133C2×C3×C4—44no—
134C2×C3×C4#23514yes—
135C2×C3×C4D3×D414yes—
136C2×C3×C4D3×D414yes—
137C2×Dic3—64no—
138C2×Dic3—64no—
139C2×Dic3—124no—
140Dic6—38no—
141Dic6—64no—
142Dic6—124no—
143Dic6—124no—
144C3×C8—44no—
145C3×C8—44no—
146C3⋊C8—64no—
147C3⋊C8—64no—
148C3⋊C8—124no—
149C2×C32#46411yescharacteristic
150C2×C32#46511yescharacteristic
151C2×C32#47311yescharacteristic
152C2×Q8—21no—
153C2×Q8—91no—
154C2×Q8—181no—
155Q16—362no—
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—91no—
159C2×C8—91no—
160C2×C8—181no—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—91no—
164C4⋊C4—181no—
165C4⋊C4—181no—
166C4⋊C4—181no—
167C42—181no—
168C42C22×C3⋊D311yescharacteristic
169C22×C3#88414yes—
170C3×C4—24no—
171C3×C4—84no—
172C3×C4#91214yes—
173C3×C4D3×SD1614yes—
174C3×C4#91514yes—
175C3×C4#91914yes—
176Dic3—68no—
177Dic3—124no—
178Dic3—244no—
179C32#168011yescharacteristic, complemented, Sylow
180Q8—41no—
181Q8—41no—
182Q8—92no—
183Q8—181no—
184Q8—361no—
185Q8—361no—
186C2×C4—41no—
187C2×C4—181no—
188C2×C4—181no—
189C2×C4—361no—
190C2×C4#382811yescharacteristic
191C2×C4D4×C3⋊D311yescharacteristic
192C2×C4D4×C3⋊D311yescharacteristic
193C8—41no—
194C8—41no—
195C8—181no—
196C8—181no—
197C8—361no—
198C2×C3#475514yes—
199C2×C3#476714yes—
200C2×C3#480714yes—
201C22#6409311yescharacteristic
202C4—21no—
203C4—81no—
204C4—182no—
205C4—361no—
206C4—721no—
207C4#6412111yescharacteristic
208C4SD16×C3⋊D311yescharacteristic
209C4#6412411yescharacteristic
210C4#6412811yescharacteristic
211C3#6846814yescomplemented
212C2#1059245411yescharacteristic
213C2#1059246611yescharacteristic
214C2#1059250611yescharacteristic
subgroupG/H
centerC22#64093
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#332C2
socle, prime radicalC22×C32#121
hypercenter#332C3⋊D3
hypocenterC32#1680
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
179. C32#1680semidirect
211. C3#68468semidirect

Maximal subgroups

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

subgroupindex
#105927932
#105927782
#105925482
#105925292
C32×#3322
#105893522
#105893462
#684683