Finite Group Databasebeta

← #11874965

Subgroups — #11874965

Order 1152.

1068 conjugacy classes of subgroups; only the 277 normal subgroups are shown.

normal subgroups only

This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 277 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#10596199C212yesmaximal
2C32×#498C211yesmaximal, characteristic, complemented
3#10592777C212yesmaximal, complemented
4#10592559C214yesmaximal
5#10592557C214yesmaximal, complemented
6C4×C8×C3⋊D3C211yesmaximal, characteristic
7#10592379C211yesmaximal, characteristic, complemented
8#81891—34nomaximal
9C32×C4⋊Q8C2212yes—
10#64155—22no—
11Q8×C3⋊Dic3—22no—
12C2×C8×C3⋊D3C2212yes—
13#64106—22no—
14#64101C2214yes—
15#64099C2214yes—
16#64096—22no—
17C42×C3⋊D3C2211yescharacteristic
18#64078C2212yes—
19C32×#106C2214yes—
20C32×C4×C8C2211yescharacteristic
21#63644C2214yes—
22C8×C3⋊Dic3C2212yes—
23#63634C2218yes—
24C4×C3⋊(C3⋊C8)C2211yescharacteristic
25#5728—38no—
26C3×#498D314yescomplemented
27#5078—38no—
28#4860—316no—
29#4858—316no—
30C4×D3×C8—34no—
31#4680—34no—
32C2×C32×Q8—22no—
33C2×C4×C3⋊D3D412yes—
34C2×C4×C3⋊D3C2311yescharacteristic
35C2×#634—22no—
36C2×C32×C8C2312yes—
37C32×C4⋊C4—22no—
38C32×C4⋊C4C2314yes—
39C32×C42C2311yescharacteristic
40#3752—24no—
41C4⋊(C3⋊Dic3)—22no—
42C4⋊(C3⋊Dic3)—24no—
43C4⋊(C3⋊Dic3)C2314yes—
44#3750—24no—
45C4×C3⋊Dic3—24no—
46C4×C3⋊Dic3D412yes—
47C4×C3⋊Dic3C2311yescharacteristic
48C2×C3⋊(C3⋊C8)C2312yes—
49C8×C3⋊D3Q818yescomplemented
50#3160—91noSylow
51C3×C4⋊Q8C2×D318yes—
52#946—68no—
53Q8×Dic3—68no—
54C2×D3×C8—38no—
55#897—68no—
56#892—316no—
57#890—316no—
58#887—68no—
59C42×D3—34no—
60#869—38no—
61C3×#106C2×D3116yes—
62C3×C4×C8C2×D314yes—
63#817—316no—
64C8×Dic3—38no—
65#807—332no—
66C4×C3⋊C8—34no—
67C22×C3⋊D3C2×D411yescharacteristic
68C32×Q8—44no—
69C2×C32×C4—24no—
70C2×C32×C4C2×D412yes—
71C2×C32×C4C2411yescharacteristic
72C2×C3⋊Dic3—24no—
73C2×C3⋊Dic3C2×D412yes—
74C2×C3⋊Dic3C2×D411yescharacteristic
75C4×C3⋊D3—24no—
76C4×C3⋊D3C2×Q814yes—
77#634—44no—
78C32×C8C2×Q814yes—
79C3⋊(C3⋊C8)C2×Q814yes—
80#533—92no—
81#500—92no—
82#499—94no—
83#498—91no—
84#498C3⋊D311yescharacteristic, complemented
85#427—94no—
86C2×C4×C8—91no—
87C2×C3×Q8—28no—
88C2×C4×D3—34no—
89C2×C4×D3—38no—
90C2×Dic6—68no—
91C2×C3×C8C22×D318yes—
92C3×C4⋊C4—28no—
93C3×C4⋊C4C22×D3116yes—
94C3×C42C22×D314yes—
95(C2×D3)⋊C4—616no—
96C4⋊Dic3—316no—
97C4⋊Dic3—616no—
98C4⋊Dic3—68no—
99Dic3⋊C4—616no—
100C4×Dic3—38no—
101C4×Dic3—34no—
102C4×Dic3—616no—
103C2×C3⋊C8—38no—
104D3×C8—332no—
105C22×C32C22×D411yescharacteristic
106C2×C3⋊D3—22no—
107C2×C3⋊D3C4⋊Q812yes—
108C32×C4—44no—
109C32×C4#13514yes—
110C32×C4C22×Q812yes—
111C3⋊Dic3—22no—
112C3⋊Dic3—44no—
113C3⋊Dic3C4⋊Q812yes—
114C22×C8—92no—
115C4⋊Q8—92no—
116C4⋊Q8C2×C3⋊D312yes—
117#125—94no—
118C22⋊Q8—182no—
119C22⋊Q8—182no—
120C4×Q8—182no—
121C4×Q8—182no—
122#117—94no—
123C2×C42—91no—
124#107—98no—
125#106—94no—
126#106C2×C3⋊D314yes—
127C4×C8—92no—
128C4×C8—91no—
129C4×C8C2×C3⋊D311yescharacteristic
130C22×D3—34no—
131C3×Q8—416no—
132C2×C3×C4—216no—
133C2×C3×C4D3×D418yes—
134C2×C3×C4C23×D314yes—
135C2×Dic3—34no—
136C2×Dic3—38no—
137C2×Dic3—616no—
138C4×D3—316no—
139C4×D3—616no—
140Dic6—1216no—
141C3×C8D3×Q8116yes—
142C3⋊C8—316no—
143C2×C32C2×C4⋊Q811yescharacteristic
144C2×C32C2×#13512yes—
145C3⋊D3—22no—
146C2×Q8—22no—
147C2×Q8—182no—
148C22×C4—91no—
149C22×C4—92no—
150C2×C8—92no—
151C2×C8—98no—
152C2×C8C22×C3⋊D312yes—
153C4⋊C4—22no—
154C4⋊C4—94no—
155C4⋊C4—184no—
156C4⋊C4—184no—
157C4⋊C4—182no—
158C4⋊C4C22×C3⋊D314yes—
159C22⋊C4—184no—
160C42—91no—
161C42—92no—
162C42—184no—
163C42C22×C3⋊D311yescharacteristic
164C22×C3C2×D3×D414yes—
165C2×D3—38no—
166C2×D3—68no—
167C3×C4—416no—
168C3×C4#916116yes—
169C3×C4C2×D3×Q818yes—
170Dic3—38no—
171Dic3—68no—
172Dic3—1216no—
173C32#316011yescharacteristic, complemented, Sylow
174C23—91no—
175Q8—44no—
176Q8—364no—
177C2×C4—24no—
178C2×C4—91no—
179C2×C4—94no—
180C2×C4—92no—
181C2×C4—184no—
182C2×C4—184no—
183C2×C4D4×C3⋊D312yes—
184C2×C4C23×C3⋊D311yescharacteristic
185C8—94no—
186C8Q8×C3⋊D314yes—
187C2×C3D3×C4⋊Q814yes—
188C2×C3C2×#91618yes—
189D3—68no—
190C22—92no—
191C22—182no—
192C22C2×D4×C3⋊D311yescharacteristic
193C4—44no—
194C4—92no—
195C4—182no—
196C4—364no—
197C4#6412514yes—
198C4C2×Q8×C3⋊D312yes—
199C3#8189114yescomplemented
200C2—182no—
201C2C3⋊D3×C4⋊Q811yescharacteristic
202C2C2×#6412512yes—
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#498C2
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#498C3⋊D3
hypocenterC32#3160
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
2. C32×#498C2semidirect
3. #10592777C2semidirect
5. #10592557C2semidirect
7. #10592379C2semidirect
26. C3×#498D3semidirect
49. C8×C3⋊D3Q8semidirect
84. #498C3⋊D3semidirect
173. C32#3160semidirect
199. C3#81891semidirect

Maximal subgroups

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

subgroupindex
#105961992
C32×#4982
#105927772
#105925592
#105925572
C4×C8×C3⋊D32
#105923792
#818913