Finite Group Databasebeta

← #11771760

Subgroups — #11771760

Order 1152.

204 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 25 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#10590840C211yesmaximal, characteristic
2#10590186C211yesmaximal, characteristic, complemented
3#10589110C211yesmaximal, characteristic, complemented
4#64283—21no—
5C2×#3743C2211yescharacteristic
6#63916—21no—
7C2×#3713C411yescharacteristic
8C3×#821—21no—
9C3×#812—21no—
10#63574C411yescharacteristic
11#4782—61no—
12#4514—61no—
13C2×C4×C3⋊D3D411yescharacteristic
14C2×C3×D12—21no—
15C2×#626—41no—
16#3792—41no—
17#3788—41no—
18#3787—22no—
19C2×C32×C8D411yescharacteristic
20C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
21#3743—41no—
22C3×C4⋊Dic3—21no—
23(C2×D3)⋊Dic3—41no—
24#3713—41no—
25C3×C3⋊C16—41no—
26#1341—91nomaximal, Sylow
27#938—61no—
28C2×#213—61no—
29C2×ΓL(1,𝔽25)—61no—
30C2×ΓL(1,𝔽25)—61no—
31#895—61no—
32C3×M32—61no—
33C3×#102—61no—
34#821—21no—
35#812—21no—
36#808—61no—
37C22×C3⋊D3SD1611yescharacteristic
38C22×C3×D3—41no—
39C2×C32×C4C22⋊C411yescharacteristic
40C2×C3⋊Dic3D811yescharacteristic
41C4×C3⋊D3—21no—
42C4×C3⋊D3—21no—
43C2×C3×Dic3—41no—
44C3×D12—41no—
45C3×D12—41no—
46#626—82no—
47#622—42no—
48C32×C8—21no—
49C3⋊(C3⋊C8)—21no—
50#469—91no—
51#349—91no—
52#338—91no—
53C2×C3×D4—61no—
54C2×#67—121no—
55C2×D12—21no—
56C2×D12—121no—
57C2×C4×D3—61no—
58C2×C4×D3—61no—
59C2×C3×C8—21no—
60C2×C3×C8—21no—
61C3×C4⋊C4—61no—
62#217—121no—
63#213—122no—
64(C2×D3)⋊C4—121no—
65C4⋊Dic3—21no—
66C2×C3⋊C8—61no—
67C2×C3⋊C8—61no—
68ΓL(1,𝔽25)—122no—
69ΓL(1,𝔽25)—121no—
70ΓL(1,𝔽25)—121no—
71C3×C16—121no—
72C3⋊C16—41no—
73C22×C32#10211yescharacteristic
74C2×C3⋊D3—21no—
75C2×C3⋊D3—41no—
76C2×C3×D3—81no—
77C2×C3×D3—81no—
78C2×C3×D3—81no—
79C32×C4#9911yescharacteristic
80C32×C4#10411yescharacteristic
81C3⋊Dic3—21no—
82C3×Dic3—81no—
83C2×D8—91no—
84C2×M16—91no—
85C2×M16—181no—
86#121—181no—
87M32—61no—
88#106—91no—
89#102—61no—
90C23×C3—121no—
91C22×D3—41no—
92C22×D3—61no—
93C22×D3—61no—
94C3×D4—121no—
95C3×D4—121no—
96C2×C3×C4—21no—
97C2×C3×C4—21no—
98C2×C3×C4—121no—
99#67—242no—
100C2×Dic3—41no—
101C2×Dic3—61no—
102C2×Dic3—61no—
103D12—41no—
104D12—41no—
105D12—242no—
106C4×D3—121no—
107C4×D3—121no—
108C4×D3—121no—
109C4×D3—121no—
110C3×C8—21no—
111C3×C8—21no—
112C3×C8—41no—
113C3⋊C8—62no—
114C3⋊C8—121no—
115C2×C32—21no—
116C2×C32#32711yescharacteristic
117C3⋊D3—41no—
118C3×D3—161no—
119C2×D4—61no—
120C2×D4—361no—
121C22×C4—91no—
122D8—361no—
123M16—361no—
124M16—361no—
125M16—361no—
126C2×C8—91no—
127C2×C8—182no—
128C2×C8GO+(4,𝔽2)11yescharacteristic
129C4⋊C4—61no—
130C22⋊C4—361no—
131C16—121no—
132C22×C3—21no—
133C22×C3—21no—
134C22×C3—241no—
135C22×C3—241no—
136C22×C3—241no—
137C2×D3—81no—
138C2×D3—81no—
139C2×D3—81no—
140C2×D3—121no—
141C2×D3—121no—
142C2×D3—121no—
143C2×D3—121no—
144C2×D3—241no—
145C3×C4—21no—
146C3×C4—21no—
147C3×C4—21no—
148C3×C4—21no—
149C3×C4—241no—
150Dic3—81no—
151Dic3—121no—
152Dic3—121no—
153C32#134111yescharacteristic, complemented, Sylow
154C23—91no—
155C23—121no—
156D4—121no—
157D4—121no—
158D4—722no—
159C2×C4—91no—
160C2×C4—121no—
161C2×C4—181no—
162C2×C4—181no—
163C2×C4D32⋊C411yescharacteristic
164C8—21no—
165C8—181no—
166C8—362no—
167C2×C3—21no—
168C2×C3—21no—
169C2×C3—21no—
170C2×C3—21no—
171C2×C3—41no—
172C2×C3—481no—
173D3—161no—
174D3—241no—
175D3—241no—
176C22—181no—
177C22—241no—
178C22—241no—
179C22—241no—
180C22—361no—
181C22#6372911yescharacteristic
182C4—181no—
183C4—241no—
184C4#6373111yescharacteristic
185C4#6373811yescharacteristic
186C3—21no—
187C3—21no—
188C2—21no—
189C2—361no—
190C2—481no—
191C2#1059003311yescharacteristic
subgroupG/H
centerC2#10590033
commutatorC2×C3⋊(C3⋊C8)C2×C4
Frattini, hypercenterC2×C8GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#327
prime radical#10590840C2
cosocleC2×#3743C22
hypocenterC32#1341
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #10590186C2semidirect
3. #10589110C2semidirect
153. C32#1341semidirect

Maximal subgroups

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

subgroupindex
#105908402
#105901862
#105891102
#13419