Finite Group Databasebeta

← #11886901

Subgroups — #11886901

Order 1152.

1428 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 1428 conjugacy classes of subgroups — too many to draw. Only its 217 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#10596228C214yesmaximal, complemented
2C32×#493C211yesmaximal, characteristic, complemented
3#10592859C214yesmaximal, complemented
4#10592776C214yesmaximal, complemented
5#10592399C212yesmaximal, complemented
6#81791—34nomaximal
7#64361C2214yescomplemented
8C2×C32×D8C2214yescomplemented
9C32×#127C2212yescomplemented
10#64141C2218yescomplemented
11#64121—24no—
12#64120—28no—
13D8×C3⋊D3—24no—
14#64113C2212yes—
15#64110C2214yescomplemented
16C32×C4×C8C2211yescharacteristic, complemented
17#63660C2214yescomplemented
18#63646C2212yescomplemented
19#63632C2214yescomplemented
20#5757—316no—
21C3×#493D314yescomplemented
22#5160—316no—
23#5077—316no—
24#4700—38no—
25C2×C32×D4—42no—
26C2×C32×D4C2314yes—
27C2×#638—44no—
28#3830—28no—
29D4×C3⋊D3—28no—
30#3828C2314yes—
31C32×D8—24no—
32C32×D8—24no—
33C2×C32×C8C2312yes—
34C32×C42C2311yescharacteristic
35#3754—28no—
36#3753—28no—
37#3748C2314yes—
38#3746D412yescomplemented
39#3745D412yescomplemented
40#3744D414yescomplemented
41#3743—24no—
42C8×C3⋊D3—24no—
43#3292—91noSylow
44#1004—316no—
45C2×C3×D8C2×D3116yescomplemented
46C3×#127C2×D318yescomplemented
47#932—332no—
48#912—616no—
49#911—632no—
50D3×D8—616no—
51#904—38no—
52#901—316no—
53C3×C4×C8C2×D314yescomplemented
54#833—316no—
55#819—38no—
56#805—316no—
57C23×C32—24no—
58C22×C3⋊D3—44no—
59C32×D4—28no—
60C32×D4—84no—
61C2×C32×C4—21no—
62C2×C32×C4C2411yescharacteristic
63#638—24no—
64#638—48no—
65C2×C3⋊Dic3—44no—
66C4⋊(C3⋊D3)C2×D414yes—
67C4×C3⋊D3—24no—
68#634C2×D414yes—
69C32×C8C2×D412yes—
70C32×C8C2×D412yes—
71C3⋊(C3⋊C8)—24no—
72#576—94no—
73#493C3⋊D311yescharacteristic, complemented
74#472—94no—
75#453—94no—
76#443—92no—
77C2×C3×D4—48no—
78C2×C3×D4C22×D3116yes—
79C2×#67—1216no—
80#237—632no—
81D3×D4—632no—
82#235—316no—
83C3×D8—216no—
84C3×D8—216no—
85C2×C3×C8C22×D318yes—
86C3×C42C22×D314yes—
87#214—632no—
88#213—632no—
89#208—316no—
90Dic12—38no—
91D24—38no—
92#204—316no—
93ΓL(1,𝔽25)—616no—
94D3×C8—616no—
95C22×C32—44no—
96C22×C32—84no—
97C22×C32H(5,𝔽2)11yescharacteristic
98C2×C3⋊D3—24no—
99C2×C3⋊D3—164no—
100C32×C4—22no—
101C32×C4C22×D412yes—
102C3⋊Dic3—24no—
103H(5,𝔽2)—94no—
104AGL(1,ℤ/8)—98no—
105AGL(1,ℤ/8)—188no—
106#135—92no—
107#135—184no—
108C2×D8—184no—
109C2×D8C2×C3⋊D314yescomplemented
110#131—94no—
111#127C2×C3⋊D312yescomplemented
112#108—92no—
113#104—94no—
114#100—94no—
115C4×C8C2×C3⋊D311yescharacteristic, complemented
116C23×C3—216no—
117C22×D3—1216no—
118C3×D4—232no—
119C3×D4—816no—
120C2×C3×C4—24no—
121C2×C3×C4C23×D314yes—
122#67—616no—
123#67—1232no—
124C2×Dic3—1216no—
125D12—316no—
126C4×D3—616no—
127Dic6—316no—
128C3×C8D3×D418yes—
129C3×C8D3×D418yes—
130C3⋊C8—616no—
131C2×C32—21no—
132C2×C32—84no—
133C2×C32D4211yescharacteristic
134C3⋊D3—44no—
135#41—94no—
136#41—188no—
137C2×D4—42no—
138C2×D4—188no—
139C2×D4—364no—
140C2×D4C22×C3⋊D314yes—
141Q16—92no—
142SD16—94no—
143SD16—188no—
144D8—24no—
145D8—24no—
146D8—92no—
147D8—188no—
148M16—94no—
149M16—184no—
150C2×C8—184no—
151C2×C8C22×C3⋊D312yes—
152C42C22×C3⋊D311yescharacteristic
153C22×C3—416no—
154C22×C3—816no—
155C22×C3#100414yes—
156C2×D3—616no—
157C2×D3—4816no—
158C3×C4—28no—
159C3×C4C2×D3×D418yes—
160Dic3—616no—
161C32#329211yescharacteristic, complemented, Sylow
162C23—24no—
163C23—364no—
164Q8—94no—
165D4—28no—
166D4—84no—
167D4—94no—
168D4—184no—
169D4—368no—
170C2×C4—21no—
171C2×C4—184no—
172C2×C4—364no—
173C2×C4C23×C3⋊D311yescharacteristic
174C8—184no—
175C8D4×C3⋊D312yes—
176C8D4×C3⋊D312yes—
177C2×C3—24no—
178C2×C3—816no—
179C2×C3#571714yes—
180D3—1216no—
181C22—44no—
182C22—84no—
183C22—184no—
184C22—1444no—
185C22#6436111yescharacteristic
186C4—22no—
187C4—184no—
188C4C2×D4×C3⋊D312yes—
189C3#8179114yescomplemented
190C2—21no—
191C2—84no—
192C2—364no—
193C2#1059618811yescharacteristic
subgroupG/H
centerC2#10596188
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#493C2
socleC2×C32D42
hypercenter#493C3⋊D3
hypocenterC32#3292
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #10596228C2semidirect
2. C32×#493C2semidirect
3. #10592859C2semidirect
4. #10592776C2semidirect
5. #10592399C2semidirect
7. #64361C22semidirect
8. C2×C32×D8C22semidirect
9. C32×#127C22semidirect
10. #64141C22semidirect
15. #64110C22semidirect
16. C32×C4×C8C22semidirect
17. #63660C22semidirect
18. #63646C22semidirect
19. #63632C22semidirect
21. C3×#493D3semidirect
38. #3746D4semidirect
39. #3745D4semidirect
40. #3744D4semidirect
45. C2×C3×D8C2×D3semidirect
46. C3×#127C2×D3semidirect
53. C3×C4×C8C2×D3semidirect
73. #493C3⋊D3semidirect
109. C2×D8C2×C3⋊D3semidirect
111. #127C2×C3⋊D3semidirect
115. C4×C8C2×C3⋊D3semidirect
161. C32#3292semidirect
189. C3#81791semidirect

Maximal subgroups

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

subgroupindex
#105962282
C32×#4932
#105928592
#105927762
#105923992
#817913