Finite Group Databasebeta

← #11790543

Subgroups — #11790543

Order 1152.

286 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 61 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#10593775C211yesmaximal, characteristic
2#10593331C211yesmaximal, characteristic
3C2×#63733C211yesmaximal, characteristic
4#10590974C212yesmaximal
5#10590055C212yesmaximal
6#64286C2211yescharacteristic
7C2×#3787C2211yescharacteristic
8M16×C3⋊D3C2211yescharacteristic
9C2×#3712C2212yes—
10#63818C2212yes—
11#63767—21no—
12C8×#157—21no—
13#63733—21no—
14#63733—21no—
15#63733C414yescomplemented
16C3×#822—22no—
17#63577—22no—
18#4893—62no—
19C2×C4×C3⋊D3C2311yescharacteristic
20C22⋊#157Q812yes—
21C2×#622Q812yes—
22C4⋊#157—21no—
23C4×#157—21no—
24#3787C2×C412yes—
25#3787D411yescharacteristic
26#3787D411yescharacteristic
27C32×M16D411yescharacteristic
28#3748D411yescharacteristic
29#3743—21no—
30C8×C3⋊D3—21no—
31C3×#208—22no—
32C2×C3×C3⋊C8—22no—
33#3712—22no—
34#3712—22no—
35#3712C2×C414yes—
36#3710—22no—
37#1953—91nomaximal, Sylow
38D3×M16—62no—
39D3×M16—62no—
40C2×ΓL(1,𝔽25)—62no—
41C3×#108—62no—
42#822—22no—
43#822—62no—
44#819—62no—
45C22×C3⋊D3C2×Q811yescharacteristic
46C2×#157—22no—
47C2×C32×C4C2×D411yescharacteristic
48C2×C3⋊Dic3C2×Q811yescharacteristic
49C4×C3⋊D3C22×C411yescharacteristic
50C4×C3⋊D3C2×D411yescharacteristic
51C4×C3⋊D3#4111yescharacteristic
52C4×C3⋊D3#4111yescharacteristic
53#622C4⋊C412yes—
54#622C4⋊C412yes—
55C32×C8—21no—
56C3⋊(C3⋊C8)—21no—
57C3×C3⋊C8—24no—
58C3×C3⋊C8—42no—
59#430—92no—
60C2×#108—91no—
61C2×#108—91no—
62#405—91no—
63#344—92no—
64C2×C4×D3—62no—
65C3×M16—22no—
66C3×M16—62no—
67C2×C3×C8—62no—
68#208—22no—
69#208—62no—
70C2×C3⋊C8—22no—
71ΓL(1,𝔽25)—64no—
72ΓL(1,𝔽25)—64no—
73ΓL(1,𝔽25)—122no—
74ΓL(1,𝔽25)—122no—
75D3×C8—122no—
76D3×C8—122no—
77C22×C32C4⋊Q811yescharacteristic
78C2×C3⋊D3—41no—
79C2×C3⋊D3C4×Q811yescharacteristic
80C2×C3⋊D3C22⋊Q811yescharacteristic
81#157—42no—
82C32×C4C4×D411yescharacteristic
83C32×C4#12111yescharacteristic
84C3⋊Dic3C2×C4⋊C411yescharacteristic
85C3⋊Dic3#12511yescharacteristic
86C2×M16—92no—
87C2×M16—92no—
88C2×M16—91no—
89C22×C8—91no—
90#117—91no—
91#108—62no—
92#108—94no—
93#108—182no—
94#108—181no—
95#108—181no—
96#97—181no—
97C4×C8—181no—
98C22×D3—62no—
99C2×C3×C4—22no—
100C2×Dic3—62no—
101C4×D3—62no—
102C4×D3—62no—
103C4×D3—62no—
104C4×D3—62no—
105C3×C8—42no—
106C3×C8—64no—
107C3×C8—122no—
108C3⋊C8—24no—
109C3⋊C8—42no—
110C3⋊C8—122no—
111C2×C32—21no—
112C2×C32#38911yescharacteristic
113C3⋊D3—21no—
114C3⋊D3—21no—
115C22×C4—91no—
116M16—62no—
117M16—94no—
118M16—91no—
119M16—181no—
120M16—182no—
121M16—182no—
122M16GO+(4,𝔽2)11yescharacteristic
123C2×C8—62no—
124C2×C8—91no—
125C2×C8—91no—
126C2×C8—92no—
127C2×C8—92no—
128C2×C8—181no—
129C2×C8—182no—
130C4⋊C4—181no—
131C22⋊C4—92no—
132C42—181no—
133C22×C3—22no—
134C2×D3—62no—
135C2×D3—62no—
136C2×D3—242no—
137C3×C4—22no—
138C3×C4—22no—
139Dic3—62no—
140Dic3—62no—
141C32#195311yescharacteristic, complemented, Sylow
142C23—91no—
143C2×C4—91no—
144C2×C4—91no—
145C2×C4—91no—
146C2×C4—91no—
147C2×C4—91no—
148C2×C4—182no—
149C2×C4C2×GO+(4,𝔽2)11yescharacteristic
150C8—21no—
151C8—64no—
152C8—92no—
153C8—92no—
154C8—122no—
155C8—181no—
156C2×C3—22no—
157C2×C3—42no—
158D3—122no—
159D3—122no—
160C22—91no—
161C22—91no—
162C22—361no—
163C22#6422211yescharacteristic
164C4—91no—
165C4—91no—
166C4—362no—
167C4C4×GO+(4,𝔽2)11yescharacteristic
168C4#6424211yescharacteristic
169C3—22no—
170C2—21no—
171C2—181no—
172C2—181no—
173C2#1059341011yescharacteristic
subgroupG/H
centerC4#64242
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×M16D4
socleC2×C32#389
prime radicalC22×C3⋊D3C2×Q8
cosocleC2×C4×C3⋊D3C23
hypercenterM16GO+(4,𝔽2)
hypocenterC32#1953
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ M16

Complements

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

NH ≅ G/Ntype
15. #63733C4semidirect
141. C32#1953semidirect

Maximal subgroups

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

subgroupindex
#105937752
#105933312
C2×#637332
#105909742
#105900552
#19539