Finite Group Databasebeta

← #11771651

Subgroups — #11771651

Order 1152.

176 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 31 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#10590921C211yesmaximal, characteristic
2C8×#622C211yesmaximal, characteristic, complemented
3#10589135C211yesmaximal, characteristic, complemented
4C3×#901—21no—
5#63822C411yescharacteristic
6C4×#622—21no—
7C8×C3⋊Dic3C2211yescharacteristic
8C3×#812—21no—
9#63578C411yescharacteristic
10#63568—21no—
11#5144—61no—
12#4511—61no—
13C3×#235—21no—
14C2×#622—22no—
15C2×C32×C8D411yescharacteristic
16C4×C3⋊Dic3D411yescharacteristic
17C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
18C3×#208—21no—
19C3×ΓL(1,𝔽25)—41no—
20C3×D3×C8—41no—
21#3718C811yescharacteristic, complemented
22#3715—21no—
23#3713C811yescharacteristic, complemented
24C3×C3⋊C16—41no—
25#1335—91nomaximal, Sylow
26C3×#131—61no—
27#950—61no—
28#901—21no—
29C3×M32—61no—
30#837—61no—
31#825—61no—
32#822—61no—
33C8×Dic3—61no—
34C8×Dic3—61no—
35#812—21no—
36C2×C32×C4C22⋊C411yescharacteristic
37C2×C3⋊Dic3—21no—
38C3×#67—41no—
39C3×D12—21no—
40C3×C4×D3—41no—
41C3×Dic6—21no—
42#622—24no—
43C32×C8D811yescharacteristic
44C32×C8SD1611yescharacteristic
45C3⋊(C3⋊C8)C2×C811yescharacteristic
46C3⋊(C3⋊C8)M1611yescharacteristic
47C3×C3⋊C8—41no—
48#443—91no—
49#364—91no—
50C82—91no—
51C3×#41—61no—
52#235—21no—
53C3×M16—61no—
54C3×M16—121no—
55C2×C3×C8—21no—
56C2×C3×C8—21no—
57C2×C3×C8—121no—
58#216—61no—
59#215—61no—
60#214—61no—
61#213—61no—
62C4×Dic3—61no—
63C4×Dic3—61no—
64#208—21no—
65C2×C3⋊C8—61no—
66C2×C3⋊C8—61no—
67ΓL(1,𝔽25)—41no—
68D3×C8—41no—
69C3×C16—121no—
70C3⋊C16—41no—
71C22×C32#10411yescharacteristic
72C2×C3×D3—41no—
73C32×C4C22⋊C811yescharacteristic
74C32×C4#10211yescharacteristic
75C3⋊Dic3—22no—
76C3×Dic3—41no—
77#135—91no—
78#131—61no—
79M32—61no—
80#108—91no—
81#104—181no—
82C4×C8—91no—
83C4×C8—181no—
84C3×Q8—61no—
85C3×D4—61no—
86C3×D4—121no—
87C2×C3×C4—21no—
88C2×C3×C4—21no—
89C2×C3×C4—121no—
90#67—41no—
91C2×Dic3—121no—
92C2×Dic3—121no—
93D12—21no—
94C4×D3—41no—
95Dic6—21no—
96C3×C8—21no—
97C3×C8—21no—
98C3×C8—21no—
99C3×C8—21no—
100C3×C8—121no—
101C3⋊C8—41no—
102C3⋊C8—61no—
103C3⋊C8—61no—
104C3⋊C8—61no—
105C3⋊C8—61no—
106C2×C32—21no—
107C2×C32D4⋊C811yescharacteristic
108C3×D3—81no—
109#41—61no—
110Q16—91no—
111SD16—181no—
112D8—91no—
113M16—61no—
114M16—121no—
115C2×C8—91no—
116C2×C8—121no—
117C2×C8—182no—
118C2×C8GO+(4,𝔽2)11yescharacteristic
119C42—91no—
120C16—121no—
121C22×C3—21no—
122C22×C3—21no—
123C22×C3—121no—
124C2×D3—41no—
125C3×C4—21no—
126C3×C4—21no—
127C3×C4—21no—
128C3×C4—21no—
129C3×C4—121no—
130Dic3—41no—
131Dic3—122no—
132Dic3—122no—
133C32#133511yescharacteristic, complemented, Sylow
134Q8—61no—
135D4—61no—
136D4—121no—
137C2×C4—121no—
138C2×C4—181no—
139C2×C4D32⋊C411yescharacteristic
140C8—91no—
141C8—91no—
142C8—121no—
143C8—184no—
144C8#377411yescharacteristic
145C8#377511yescharacteristic
146C2×C3—21no—
147C2×C3—21no—
148C2×C3—41no—
149C2×C3—41no—
150C2×C3—241no—
151D3—81no—
152C22—121no—
153C22#6373111yescharacteristic
154C4—121no—
155C4—182no—
156C4D32⋊C811yescharacteristic
157C4#6373911yescharacteristic
158C3—21no—
159C3—21no—
160C2—21no—
161C2—241no—
162C2#1059002911yescharacteristic
subgroupG/H
centerC8#3774
commutatorC3⋊(C3⋊C8)C2×C8
Frattini, hypercenterC2×C8GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32D4⋊C8
prime radical#63822C4
cosocleC8×C3⋊Dic3C22
hypocenterC32#1335
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C8 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C8×#622C2semidirect
3. #10589135C2semidirect
21. #3718C8semidirect
23. #3713C8semidirect
133. C32#1335semidirect

Maximal subgroups

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

subgroupindex
#105909212
C8×#6222
#105891352
#13359