Finite Group Databasebeta

← #11771632

Subgroups — #11771632

Order 1152.

178 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 35 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
1C4×#3718C211yesmaximal, characteristic
2#10590148C211yesmaximal, characteristic
3#10589098C211yesmaximal, characteristic
4C3×C4×Dic6—21no—
5C2×#3718C411yescharacteristic
6C2×#3708—21no—
7C4×C3⋊(C3⋊C8)C2211yescharacteristic
8C3×C4⋊(C3⋊C8)—21no—
9#63576C411yescharacteristic
10#63565—21no—
11C4×#216—61no—
12#4480—61no—
13C2×C3×Dic6—21no—
14C32×C42D411yescharacteristic
15C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
16C2×C3⋊(C3⋊C8)D411yescharacteristic
17C3×C4⋊Dic3—21no—
18C3×Dic3⋊C4—41no—
19C3×C4×Dic3—41no—
20C2×C3×C3⋊C8—41no—
21#3718—21no—
22#3718C812yescomplemented
23#3708—22no—
24#1334—91nomaximal, Sylow
25C3×C4×Q8—61no—
26C2×#216—61no—
27C4×Dic6—21no—
28C3×C4⋊C8—61no—
29#835—61no—
30#810—61no—
31#807—61no—
32C4⋊(C3⋊C8)—21no—
33C4×C3⋊C8—61no—
34C4×C3⋊C8—61no—
35C2×C32×C4C22⋊C411yescharacteristic
36C2×C32×C4D811yescharacteristic
37C2×C32×C4SD1611yescharacteristic
38C2×C3×Dic3—41no—
39C2×C3×Dic3—41no—
40C3×Dic6—22no—
41C3×Dic6—41no—
42C3⋊(C3⋊C8)—21no—
43C3⋊(C3⋊C8)C2×C811yescharacteristic
44C3⋊(C3⋊C8)M1611yescharacteristic
45C3×C3⋊C8—81no—
46C4×Q16—91no—
47#346—91no—
48#334—91no—
49C2×C3×Q8—61no—
50C2×Dic6—21no—
51C2×C3×C8—121no—
52C3×C4⋊C4—61no—
53C3×C4⋊C4—121no—
54C3×C42—21no—
55C3×C42—21no—
56C3×C42—121no—
57#216—62no—
58#216—62no—
59C4⋊Dic3—21no—
60Dic3⋊C4—41no—
61C4×Dic3—41no—
62C2×C3⋊C8—41no—
63C2×C3⋊C8—61no—
64C2×C3⋊C8—61no—
65C2×C3⋊C8—61no—
66C2×C3⋊C8—61no—
67C22×C32#10211yescharacteristic
68C32×C4—21no—
69C32×C4—21no—
70C32×C4C22⋊C811yescharacteristic
71C32×C4#10411yescharacteristic
72C3×Dic3—42no—
73C3×Dic3—81no—
74C2×Q16—91no—
75C4×Q8—61no—
76C2×C16—181no—
77#107—91no—
78C4⋊C8—61no—
79#103—181no—
80C4×C8—91no—
81C3×Q8—62no—
82C3×Q8—121no—
83C2×C3×C4—21no—
84C2×C3×C4—21no—
85C2×C3×C4—21no—
86C2×C3×C4—21no—
87C2×C3×C4—21no—
88C2×C3×C4—21no—
89C2×C3×C4—121no—
90C2×C3×C4—121no—
91C2×Dic3—41no—
92C2×Dic3—41no—
93Dic6—22no—
94Dic6—41no—
95C3×C8—241no—
96C3⋊C8—61no—
97C3⋊C8—61no—
98C3⋊C8—61no—
99C3⋊C8—61no—
100C3⋊C8—81no—
101C3⋊C8—121no—
102C3⋊C8—121no—
103C2×C32D4⋊C811yescharacteristic
104C2×C32#36011yescharacteristic
105C2×C32#36211yescharacteristic
106C2×Q8—61no—
107Q16—92no—
108Q16—181no—
109C2×C8—91no—
110C2×C8—91no—
111C2×C8—121no—
112C4⋊C4—61no—
113C4⋊C4—121no—
114C42—121no—
115C42GO+(4,𝔽2)11yescharacteristic
116C16—182no—
117C22×C3—21no—
118C22×C3—21no—
119C3×C4—21no—
120C3×C4—21no—
121C3×C4—22no—
122C3×C4—21no—
123C3×C4—21no—
124C3×C4—21no—
125C3×C4—21no—
126C3×C4—41no—
127C3×C4—41no—
128C3×C4—122no—
129C3×C4—241no—
130Dic3—42no—
131Dic3—81no—
132C32#133411yescharacteristic, complemented, Sylow
133Q8—62no—
134Q8—121no—
135C2×C4—121no—
136C2×C4—121no—
137C2×C4D32⋊C411yescharacteristic
138C2×C4#377411yescharacteristic
139C2×C4#377511yescharacteristic
140C8—91no—
141C8—91no—
142C8—181no—
143C8—241no—
144C2×C3—21no—
145C2×C3—21no—
146C2×C3—21no—
147C2×C3—21no—
148C2×C3—21no—
149C2×C3—21no—
150C22#6373911yescharacteristic
151C4—21no—
152C4—21no—
153C4—122no—
154C4—241no—
155C4D32⋊C811yescharacteristic
156C4#6373111yescharacteristic
157C3—21no—
158C3—21no—
159C2#1059002911yescharacteristic
160C2#1059006411yescharacteristic
161C2#1059006611yescharacteristic
subgroupG/H
centerC22#63739
commutatorC3⋊(C3⋊C8)C2×C8
Frattini, hypercenterC42GO+(4,𝔽2)
FittingC32×C42D4
socle, prime radicalC22×C32#102
cosocleC4×C3⋊(C3⋊C8)C22
hypocenterC32#1334
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
22. #3718C8semidirect
132. C32#1334semidirect

Maximal subgroups

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

subgroupindex
C4×#37182
#105901482
#105890982
#13349