Finite Group Databasebeta

← #11874962

Subgroups — #11874962

Order 1152.

714 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 714 conjugacy classes of subgroups — too many to draw. Only its 147 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#10593909C212yesmaximal
2C4×#3787C211yesmaximal, characteristic
3#10593396C214yesmaximal
4#10593395C214yesmaximal, complemented
5#10593388C214yesmaximal, complemented
6C2×#3797—22no—
7C2×#3787C2212yes—
8C42×C3⋊D3C2211yescharacteristic
9C3×#869—22no—
10#63919—22no—
11#63919C2214yes—
12#63900—22no—
13#63900C2214yes—
14#63873C2214yes—
15C4×#622C2212yes—
16C4×#622C2212yes—
17#63743C22116yes—
18D3×C4⋊Q8—62no—
19C2×C4×C3⋊D3D411yescharacteristic
20C2×C4×C3⋊D3D411yescharacteristic
21C2×C4×C3⋊D3C2311yescharacteristic
22C2×C3×Dic6—24no—
23C2×#627—24no—
24C2×#624—24no—
25#3797—48no—
26C2×#622C2314yes—
27#3787Q818yescomplemented
28C32×C42D411yescharacteristic
29C4×C3⋊Dic3D411yescharacteristic
30C4×C3⋊Dic3C2311yescharacteristic
31C4×C3⋊Dic3C2311yescharacteristic
32C3×C4⋊Dic3—24no—
33C3×C4⋊Dic3—24no—
34#3724—24no—
35#3724C2318yes—
36C2×#500—91nomaximal, Sylow
37C2×D3×Q8—64no—
38C3×C4⋊Q8—62no—
39#944—64no—
40D3×C4⋊C4—64no—
41D3×C4⋊C4—64no—
42#888—64no—
43#888—64no—
44C42×D3—62no—
45#869—22no—
46C22×C3⋊D3C2×D411yescharacteristic
47C2×C32×C4C2×D411yescharacteristic
48C2×C32×C4C2×D411yescharacteristic
49C2×C32×C4C2×D411yescharacteristic
50C2×C3⋊Dic3C2×D411yescharacteristic
51C2×C3⋊Dic3C2×D411yescharacteristic
52C2×C3⋊Dic3C2411yescharacteristic
53C4×C3⋊D3D814yes—
54C4×C3⋊D3Q1614yes—
55C4×C3⋊D3C2×Q814yes—
56C2×C3×Dic3—28no—
57C3×Dic6—48no—
58#627—48no—
59#624—48no—
60#622C2×Q818yescomplemented
61C2×C4⋊Q8—92no—
62#500—94no—
63#500—94no—
64C2×#107—94no—
65C2×C4×C8—91no—
66C2×C3×Q8—64no—
67D3×Q8—1216no—
68C2×C4×D3—62no—
69C2×C4×D3—62no—
70C2×C4×D3—62no—
71C2×C4×D3—68no—
72C2×Dic6—24no—
73C2×Dic6—68no—
74C3×C4⋊C4—64no—
75C3×C4⋊C4—64no—
76C3×C42—22no—
77C4⋊Dic3—24no—
78C4⋊Dic3—24no—
79Dic3⋊C4—68no—
80Dic3⋊C4—68no—
81C4×Dic3—62no—
82C4×Dic3—62no—
83C4×Dic3—62no—
84C22×C32C22×D411yescharacteristic
85C2×C3⋊D3C4⋊Q812yes—
86C2×C3⋊D3C2×D812yes—
87C2×C3⋊D3C2×Q1612yes—
88C32×C4C4⋊Q812yes—
89C32×C4C2×D812yes—
90C32×C4C2×Q1612yes—
91C3⋊Dic3C2×D812yes—
92C3⋊Dic3C2×Q1612yes—
93C3⋊Dic3C22×Q812yes—
94C3×Dic3—48no—
95C22×Q8—182no—
96C22×C8—92no—
97C4⋊Q8—62no—
98C4⋊Q8—94no—
99C4⋊Q8—94no—
100C4⋊Q8—182no—
101C2×C4⋊C4—94no—
102C2×C4⋊C4—182no—
103C2×C42—91no—
104#107—916no—
105C4×C8—92no—
106C4×C8—92no—
107C22×D3—62no—
108C3×Q8—128no—
109C2×C3×C4—22no—
110C2×C3×C4—22no—
111C2×C3×C4—22no—
112C2×C3×C4—68no—
113C2×Dic3—28no—
114C2×Dic3—62no—
115C2×Dic3—62no—
116C2×Dic3—62no—
117C4×D3—68no—
118C4×D3—68no—
119C4×D3—68no—
120C4×D3—1216no—
121Dic6—48no—
122Dic6—1216no—
123C2×C32C2×C4⋊Q811yescharacteristic
124C2×C32C22×D811yescharacteristic
125C2×C32C22×Q1611yescharacteristic
126C3⋊D3#50014yescomplemented
127C2×Q8—64no—
128C2×Q8—184no—
129C2×Q8—368no—
130C22×C4—91no—
131C22×C4—91no—
132C22×C4—91no—
133C22×C4—184no—
134C2×C8—94no—
135C2×C8—98no—
136C4⋊C4—64no—
137C4⋊C4—64no—
138C4⋊C4—98no—
139C4⋊C4—184no—
140C42—91no—
141C42—91no—
142C42—91no—
143C42GO+(4,𝔽2)11yescharacteristic
144C22×C3—22no—
145C2×D3—64no—
146C2×D3—64no—
147C2×D3—64no—
148C3×C4—24no—
149C3×C4—24no—
150C3×C4—24no—
151C3×C4—128no—
152Dic3—48no—
153Dic3—64no—
154Dic3—64no—
155Dic3—64no—
156C32C2×#50011yescharacteristic, complemented, Sylow
157C23—91no—
158Q8—128no—
159Q8—368no—
160C2×C4—68no—
161C2×C4—91no—
162C2×C4—91no—
163C2×C4—91no—
164C2×C4—94no—
165C2×C4—94no—
166C2×C4—94no—
167C2×C4—368no—
168C2×C4C2×GO+(4,𝔽2)11yescharacteristic
169C2×C4C2×GO+(4,𝔽2)11yescharacteristic
170C2×C4C2×GO+(4,𝔽2)11yescharacteristic
171C8—98no—
172C2×C3—22no—
173C2×C3—22no—
174C2×C3—22no—
175D3—68no—
176C22—92no—
177C22—92no—
178C22—92no—
179C22C22×GO+(4,𝔽2)11yescharacteristic
180C4—92no—
181C4—92no—
182C4—92no—
183C4—128no—
184C4#6422212yes—
185C4#6422512yes—
186C4#6422812yes—
187C3—22no—
188C2—94no—
189C2C2×#6422211yescharacteristic
190C2C2×#6422511yescharacteristic
191C2C2×#6422811yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC32×C42D4
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC42GO+(4,𝔽2)
hypocenterC32C2×#500
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #10593395C2semidirect
5. #10593388C2semidirect
27. #3787Q8semidirect
60. #622C2×Q8semidirect
126. C3⋊D3#500semidirect
156. C32C2×#500semidirect

Maximal subgroups

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

subgroupindex
#105939092
C4×#37872
#105933962
#105933952
#105933882
C2×#5009