Finite Group Databasebeta

← #37589150

Subgroups — #37589150

Order 24512.

262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C2×#20259458C211yesmaximal, characteristic, complemented
2#41×D383C211yesmaximal, characteristic, complemented
3#27133873C212yesmaximal, complemented
4#27133872C211yesmaximal, characteristic, complemented
5#27133869C211yesmaximal, characteristic, complemented
6#27133868C212yesmaximal, complemented
7#27133866C211yesmaximal, characteristic, complemented
8#27133864C212yesmaximal, complemented
9#27133862C212yesmaximal, complemented
10M16×D383C211yesmaximal, characteristic, complemented
11#137×C383C211yesmaximal, characteristic, complemented
12#20259458—21no—
13#20259458—21no—
14#20259458C2212yes—
15#20259458C2212yescomplemented
16#20259458C2211yescharacteristic, complemented
17#20259457—21no—
18#20259457C2211yescharacteristic
19#20259456—21no—
20#20259456C2211yescharacteristic, complemented
21Q8×D383C2211yescharacteristic, complemented
22C2×D1532—21no—
23C2×D1532C2211yescharacteristic, complemented
24D4×D383—21no—
25D4×D383C2211yescharacteristic, complemented
26C2×C4×D383—21no—
27C2×C4×D383—21no—
28C2×C4×D383C2211yescharacteristic
29#20259447C2212yescomplemented
30#20259446C2212yescomplemented
31#20259444C2212yescomplemented
32#20259444C2212yescomplemented
33D3064C2212yescomplemented
34#20259442C2212yescomplemented
35#20259441C2211yescharacteristic, complemented
36#20259440C2212yescomplemented
37C8×D383C2212yescomplemented
38#41×C383C2211yescharacteristic
39C2×Q8×C383C2211yescharacteristic, complemented
40Q16×C383C2212yescomplemented
41SD16×C383C2212yescomplemented
42M16×C383C2211yescharacteristic, complemented
43C22×D383—21no—
44C22×D383—21no—
45C22×D383D411yescharacteristic
46Dic766—21no—
47Dic766C2311yescharacteristic
48D1532—21no—
49D1532—22no—
50D1532—22no—
51D1532—21no—
52D1532C2312yes—
53D1532C2311yescharacteristic
54C22⋊D383—21no—
55C22⋊D383—21no—
56C22⋊D383—21no—
57C2×Dic383—21no—
58C2×Dic383D411yescharacteristic
59C4×D383—21no—
60C4×D383—21no—
61C4×D383—21no—
62C4×D383—22no—
63C4×D383—22no—
64C4×D383D411yescharacteristic
65C4×D383D411yescharacteristic
66C4×D383C2311yescharacteristic
67C4×D383C2311yescharacteristic
68C383⋊C8C2312yes—
69Q8×C383—21no—
70Q8×C383C2312yes—
71Q8×C383C2311yescharacteristic
72D4×C383—21no—
73D4×C383C2311yescharacteristic
74C2×C4×C383—21no—
75C2×C4×C383—21no—
76C2×C4×C383C2311yescharacteristic
77C8×C383C2312yes—
78C22×C383—21no—
79C22×C383C2×D411yescharacteristic
80C2×D383—21no—
81C2×D383—22no—
82C2×D383—41no—
83C2×D383—42no—
84C2×D383—42no—
85C2×D383C2×D411yescharacteristic
86C2×D383C2×D411yescharacteristic
87C4×C383—21no—
88C4×C383—22no—
89C4×C383C2×D411yescharacteristic
90C4×C383C2411yescharacteristic
91Dic383—21no—
92Dic383C2×D411yescharacteristic
93Dic383C2×D411yescharacteristic
94C2×C383—21no—
95C2×C383—41no—
96C2×C383C22×D411yescharacteristic
97D383—21no—
98D383—21no—
99D383—41no—
100D383—42no—
101C383#57511yescharacteristic, complemented, Sylow
102#575—3831nomaximal, Sylow
103C2×#41—3831no—
104C2×#41—3831no—
105#137—3831no—
106#137—3832no—
107#137D38311yescharacteristic, complemented
108AGL(1,ℤ/8)—3831no—
109AGL(1,ℤ/8)—3832no—
110AGL(1,ℤ/8)—3831no—
111#135—3832no—
112#135—3832no—
113C2×M16—3831no—
114#41—3832no—
115#41—3831no—
116#41—3832no—
117#41—3831no—
118#41—3831no—
119#41—7661no—
120#41—7661no—
121#41—7661no—
122#41—7661no—
123#41C2×D38311yescharacteristic
124C2×Q8—3831no—
125C2×Q8C2×D38311yescharacteristic, complemented
126C2×D4—3831no—
127C2×D4—3831no—
128C2×D4—7661no—
129C2×D4—7661no—
130C22×C4—3831no—
131C22×C4—7661no—
132C22×C4—7661no—
133Q16—3832no—
134Q16C2×D38312yescomplemented
135SD16—3832no—
136SD16—3832no—
137SD16—3832no—
138SD16C2×D38312yescomplemented
139D8—3832no—
140D8—3832no—
141M16—3831no—
142M16—3832no—
143M16C2×D38311yescharacteristic, complemented
144C2×C8—3832no—
145C23—3831no—
146C23—7661no—
147C23—7661no—
148Q8—21no—
149Q8—3831no—
150Q8—7661no—
151Q8C22×D38311yescharacteristic
152Q8C22×D38312yes—
153D4—21no—
154D4—3832no—
155D4—3831no—
156D4—7661no—
157D4—7662no—
158D4—7662no—
159D4—7661no—
160D4—7661no—
161D4—7661no—
162D4—7661no—
163D4C22×D38311yescharacteristic
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—3831no—
167C2×C4—3831no—
168C2×C4—3831no—
169C2×C4—3831no—
170C2×C4—3831no—
171C2×C4—7661no—
172C2×C4—7662no—
173C2×C4—7662no—
174C2×C4—7661no—
175C2×C4—7661no—
176C2×C4—7661no—
177C2×C4C22×D38311yescharacteristic
178C8—3832no—
179C8C22×D38312yes—
180C22—21no—
181C22—3831no—
182C22—3831no—
183C22—15322no—
184C22—15321no—
185C22—15322no—
186C22—7662no—
187C22—7661no—
188C22D4×D38311yescharacteristic
189C4—21no—
190C4—22no—
191C4—3831no—
192C4—3831no—
193C4—7661no—
194C4D4×D38311yescharacteristic
195C4C23×D38311yescharacteristic
196C2—21no—
197C2—41no—
198C2—15322no—
199C2—15321no—
200C2—7661no—
201C2—7661no—
202C2C2×D4×D38311yescharacteristic
subgroupG/H
centerC2C2×D4×D383
commutator, cosocleC4×C383C24
FrattiniC4C23×D383
Fitting#137×C383C2
socleC2×C383C22×D4
hypercenter#137D383
hypocenterC383#575
LCSG ▷ C4×C383 ▷ C2×C383 ▷ C383
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. C2×#20259458C2semidirect
2. #41×D383C2semidirect
3. #27133873C2semidirect
4. #27133872C2semidirect
5. #27133869C2semidirect
6. #27133868C2semidirect
7. #27133866C2semidirect
8. #27133864C2semidirect
9. #27133862C2semidirect
10. M16×D383C2semidirect
11. #137×C383C2semidirect
15. #20259458C22semidirect
16. #20259458C22semidirect
20. #20259456C22semidirect
21. Q8×D383C22semidirect
23. C2×D1532C22semidirect
25. D4×D383C22semidirect
29. #20259447C22semidirect
30. #20259446C22semidirect
31. #20259444C22semidirect
32. #20259444C22semidirect
33. D3064C22semidirect
34. #20259442C22semidirect
35. #20259441C22semidirect
36. #20259440C22semidirect
37. C8×D383C22semidirect
39. C2×Q8×C383C22semidirect
40. Q16×C383C22semidirect
41. SD16×C383C22semidirect
42. M16×C383C22semidirect
101. C383#575semidirect
107. #137D383semidirect
125. C2×Q8C2×D383semidirect
134. Q16C2×D383semidirect
138. SD16C2×D383semidirect
143. M16C2×D383semidirect

Maximal subgroups

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

subgroupindex
C2×#202594582
#41×D3832
#271338732
#271338722
#271338692
#271338682
#271338662
#271338642
#271338622
M16×D3832
#137×C3832
#575383