Finite Group Databasebeta

← #11771856

Subgroups — #11771856

Order 1152.

260 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 32 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#10592856C211yesmaximal, characteristic
2#10590182C211yesmaximal, characteristic, complemented
3#10590176C211yesmaximal, characteristic, complemented
4C2×C4⋊#157—21no—
5C2×C32×D8C411yescharacteristic, complemented
6#64147—21no—
7C2×C8×C3⋊D3C2211yescharacteristic
8C2×#3708—21no—
9#63659—21no—
10#63645C411yescharacteristic, complemented
11#5157—62no—
12C22×#157—41no—
13C2×C32×D4—21no—
14C2×#638—41no—
15C2×C4×C3⋊D3D411yescharacteristic
16C4⋊#157—22no—
17C4⋊#157—41no—
18C32×D8—41no—
19C2×C32×C8C2×C411yescharacteristic
20#3757—41no—
21C4⋊(C3⋊Dic3)—21no—
22C2×C3⋊(C3⋊C8)D411yescharacteristic
23C8×C3⋊D3—41no—
24#3708—41no—
25#1347—91nomaximal, Sylow
26C2×C3×D8—22no—
27#938—64no—
28C2×D3×C8—62no—
29#832—64no—
30#818—62no—
31C23×C32—41no—
32C22×C3⋊D3D811yescharacteristic
33C2×#157—42no—
34C2×#157—81no—
35C2×#157—81no—
36C32×D4—41no—
37C32×D4—41no—
38C2×C32×C4C22⋊C411yescharacteristic
39#638—81no—
40#638—81no—
41C2×C3⋊Dic3—41no—
42C2×C3⋊Dic3SD1611yescharacteristic
43C4×C3⋊D3—21no—
44C4×C3⋊D3—21no—
45C32×C8—21no—
46C3⋊(C3⋊C8)—21no—
47#466—91no—
48C22⋊C16—91no—
49#340—91no—
50C2×C3×D4—24no—
51C2×#67—124no—
52C2×C4×D3—62no—
53C3×D8—44no—
54C2×C3×C8—22no—
55#217—124no—
56C4⋊Dic3—64no—
57C2×C3⋊C8—62no—
58D3×C8—124no—
59C22×C32—81no—
60C22×C32—81no—
61C22×C32—81no—
62C22×C32#10211yescharacteristic
63C2×C3⋊D3—21no—
64C2×C3⋊D3—21no—
65C2×C3⋊D3D1611yescharacteristic
66C2×C3⋊D3SD3211yescharacteristic
67#157—82no—
68C32×C4#9911yescharacteristic
69C32×C4#10411yescharacteristic
70C3⋊Dic3—21no—
71C3⋊Dic3—81no—
72C2×D8#15711yescharacteristic, complemented
73C22×C8—91no—
74#121—181no—
75C2×C4⋊C4—181no—
76C2×C16—181no—
77#107—91no—
78#102—181no—
79C23×C3—44no—
80C22×D3—62no—
81C3×D4—44no—
82C3×D4—44no—
83C2×C3×C4—22no—
84#67—244no—
85#67—244no—
86C2×Dic3—62no—
87C2×Dic3—124no—
88C4×D3—122no—
89C4×D3—122no—
90C3×C8—24no—
91C3⋊C8—122no—
92C2×C32—161no—
93C2×C32#32711yescharacteristic
94C2×C32#35711yescharacteristic
95C2×C32#36011yescharacteristic
96C3⋊D3—21no—
97C3⋊D3—21no—
98C2×D4—21no—
99C2×D4—361no—
100C22×C4—91no—
101C22×C4—361no—
102D8—41no—
103C2×C8—91no—
104C2×C8—361no—
105C2×C8C2×#15711yescharacteristic
106C4⋊C4—182no—
107C4⋊C4—181no—
108C4⋊C4—361no—
109C22⋊C4—361no—
110C16—361no—
111C22×C3—22no—
112C22×C3—84no—
113C22×C3—84no—
114C22×C3—84no—
115C2×D3—62no—
116C2×D3—62no—
117C2×D3—122no—
118C2×D3—122no—
119C3×C4—22no—
120C3×C4—22no—
121Dic3—122no—
122Dic3—244no—
123C32#134711yescharacteristic, complemented, Sylow
124C23—41no—
125C23—91no—
126D4—41no—
127D4—41no—
128D4—721no—
129D4—721no—
130C2×C4—91no—
131C2×C4—181no—
132C2×C4—181no—
133C2×C4—362no—
134C2×C4—361no—
135C2×C4—721no—
136C2×C4—721no—
137C2×C4C22⋊#15711yescharacteristic
138C8—21no—
139C8—181no—
140C2×C3—22no—
141C2×C3—22no—
142C2×C3—22no—
143C2×C3—164no—
144D3—122no—
145D3—122no—
146C22—81no—
147C22—81no—
148C22—81no—
149C22—91no—
150C22—91no—
151C22—181no—
152C22—181no—
153C22#6378211yescharacteristic
154C4—181no—
155C4—722no—
156C4—721no—
157C4#6378311yescharacteristic
158C4#6378611yescharacteristic
159C3—22no—
160C2—161no—
161C2—181no—
162C2—181no—
163C2#1059019211yescharacteristic
164C2#1059019311yescharacteristic
165C2#1059020911yescharacteristic
subgroupG/H
centerC22#63782
commutatorC2×C32×C8C2×C4
FrattiniC2×C8C2×#157
FittingC2×C32×D8C4
socleC22×C32#102
prime radical#10592856C2
cosocleC2×C8×C3⋊D3C22
hypercenterC2×D8#157
hypocenterC32#1347
LCSG ▷ C2×C32×C8 ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. #10590182C2semidirect
3. #10590176C2semidirect
5. C2×C32×D8C4semidirect
10. #63645C4semidirect
72. C2×D8#157semidirect
123. C32#1347semidirect

Maximal subgroups

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

subgroupindex
#105928562
#105901822
#105901762
#13479