Finite Group Databasebeta

← #11781956

Subgroups — #11781956

Order 1152.

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

normal subgroups only

This group has 456 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#10592789C211yesmaximal, characteristic
2#10592777C211yesmaximal, characteristic
3#10592548C211yesmaximal, characteristic
4#10592530C211yesmaximal, characteristic
5C32×#332C211yesmaximal, characteristic
6#10589352C211yesmaximal, characteristic
7#10589346C211yesmaximal, characteristic
8#68475—34nomaximal
9C32×C4⋊Q8C2211yescharacteristic
10C2×#3756—21no—
11C2×#3746—21no—
12#64078C2211yescharacteristic
13C4×#634C2211yescharacteristic
14C32×C4⋊C8C2211yescharacteristic
15C32×C4⋊C8C2211yescharacteristic
16#63662—21no—
17#63643—21no—
18#63642—21no—
19#63641—21no—
20#63634—21no—
21#63634—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C4×C3⋊(C3⋊C8)C2211yescharacteristic
24#5090—34no—
25#5078—34no—
26#4849—34no—
27#4831—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
39#3756—42no—
40C4⋊(C3⋊Dic3)—21no—
41C4⋊(C3⋊Dic3)—21no—
42C4⋊(C3⋊Dic3)D411yescharacteristic
43#3750—21no—
44C4×C3⋊Dic3—21no—
45C2×C3⋊(C3⋊C8)—21no—
46C2×C3⋊(C3⋊C8)D411yescharacteristic
47C2×C3⋊(C3⋊C8)D411yescharacteristic
48#3746—42no—
49#1694—91noSylow
50C3×C4⋊Q8C2×D314yes—
51C2×#216—64no—
52C2×Dic12—64no—
53#869—34no—
54C4×Dic6—34no—
55C3×C4⋊C8C2×D314yes—
56C3×C4⋊C8C2×D314yes—
57#835—64no—
58#816—64no—
59#815—64no—
60Dic3⋊C8—64no—
61#807—64no—
62#807—64no—
63C4⋊(C3⋊C8)—34no—
64C4×C3⋊C8—34no—
65C32×Q8—41no—
66C32×Q8—41no—
67C2×C32×C4—41no—
68C2×C32×C4C2×D411yescharacteristic
69C2×C32×C4C2×D411yescharacteristic
70C2×C32×C4#4111yescharacteristic
71C2×C3⋊Dic3—21no—
72C2×C3⋊Dic3—21no—
73C2×C3⋊Dic3—41no—
74#634—21no—
75#634—21no—
76#634—41no—
77#634—41no—
78C32×C8—41no—
79C32×C8—41no—
80C3⋊(C3⋊C8)—21no—
81C3⋊(C3⋊C8)—41no—
82C3⋊(C3⋊C8)Q1612yescomplemented
83#500—91no—
84#462—91no—
85#462—91no—
86#446—91no—
87#334—91no—
88#332—91no—
89#332C3⋊D311yescharacteristic
90C2×C3×Q8—24no—
91C2×Dic6—34no—
92C2×Dic6—64no—
93C2×C3×C8—24no—
94C2×C3×C8—24no—
95C3×C4⋊C4—24no—
96C3×C4⋊C4—24no—
97C3×C42C22×D314yes—
98#216—128no—
99C4⋊Dic3—34no—
100C4⋊Dic3—64no—
101C4⋊Dic3—64no—
102Dic3⋊C4—64no—
103C4×Dic3—64no—
104C2×C3⋊C8—34no—
105C2×C3⋊C8—34no—
106C2×C3⋊C8—64no—
107Dic12—128no—
108C22×C32#12111yescharacteristic
109C32×C4—21no—
110C32×C4—81no—
111C32×C4C2×Q1611yescharacteristic
112C32×C4AGL(1,ℤ/8)11yescharacteristic
113C32×C4AGL(1,ℤ/8)11yescharacteristic
114C32×C4#13711yescharacteristic
115C3⋊Dic3—41no—
116C3⋊Dic3—41no—
117C3⋊Dic3—81no—
118C2×Q16—181no—
119C2×Q16—181no—
120C4⋊Q8—91no—
121C4⋊Q8C2×C3⋊D311yescharacteristic
122C4×Q8—91no—
123#107—181no—
124#107—181no—
125C4⋊C8—91no—
126C4⋊C8—181no—
127C4⋊C8C2×C3⋊D311yescharacteristic
128C4⋊C8C2×C3⋊D311yescharacteristic
129#103—181no—
130#103—181no—
131#97—181no—
132C4×C8—91no—
133C3×Q8—44no—
134C3×Q8—44no—
135C2×C3×C4—44no—
136C2×C3×C4#23514yes—
137C2×C3×C4D3×D414yes—
138C2×C3×C4D3×D414yes—
139C2×Dic3—64no—
140C2×Dic3—64no—
141C2×Dic3—124no—
142Dic6—64no—
143Dic6—64no—
144Dic6—124no—
145Dic6—124no—
146C3×C8—44no—
147C3×C8—44no—
148C3⋊C8—38no—
149C3⋊C8—64no—
150C3⋊C8—124no—
151C2×C32#46211yescharacteristic
152C2×C32#46911yescharacteristic
153C2×C32#47311yescharacteristic
154C2×Q8—21no—
155C2×Q8—91no—
156C2×Q8—181no—
157Q16—362no—
158Q16—362no—
159C2×C8—21no—
160C2×C8—21no—
161C2×C8—91no—
162C2×C8—91no—
163C2×C8—181no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—91no—
167C4⋊C4—181no—
168C4⋊C4—181no—
169C4⋊C4—181no—
170C42—181no—
171C42C22×C3⋊D311yescharacteristic
172C22×C3#88414yes—
173C3×C4—24no—
174C3×C4—84no—
175C3×C4#91114yes—
176C3×C4#91414yes—
177C3×C4#91514yes—
178C3×C4D3×Q1614yes—
179Dic3—124no—
180Dic3—124no—
181Dic3—244no—
182C32#169411yescharacteristic, complemented, Sylow
183Q8—41no—
184Q8—41no—
185Q8—181no—
186Q8—181no—
187Q8—361no—
188Q8—361no—
189C2×C4—41no—
190C2×C4—181no—
191C2×C4—181no—
192C2×C4—361no—
193C2×C4#382811yescharacteristic
194C2×C4D4×C3⋊D311yescharacteristic
195C2×C4D4×C3⋊D311yescharacteristic
196C8—41no—
197C8—41no—
198C8—92no—
199C8—181no—
200C8—361no—
201C2×C3#475514yes—
202C2×C3#478214yes—
203C2×C3#479514yes—
204C22#6409311yescharacteristic
205C4—21no—
206C4—81no—
207C4—361no—
208C4—361no—
209C4—721no—
210C4#6412011yescharacteristic
211C4#6412311yescharacteristic
212C4#6412411yescharacteristic
213C4Q16×C3⋊D311yescharacteristic
214C3#6847514yescomplemented
215C2#1059245411yescharacteristic
216C2#1059248111yescharacteristic
217C2#1059249411yescharacteristic
subgroupG/H
centerC22#64093
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#332C2
socle, prime radicalC22×C32#121
hypercenter#332C3⋊D3
hypocenterC32#1694
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
82. C3⋊(C3⋊C8)Q16semidirect
182. C32#1694semidirect
214. C3#68475semidirect

Maximal subgroups

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

subgroupindex
#105927892
#105927772
#105925482
#105925302
C32×#3322
#105893522
#105893462
#684753