Finite Group Databasebeta

← #37566048

Subgroups — #37566048

Order 24256.

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

normal subgroups only

This group has 268 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
1#27131377C211yesmaximal, characteristic, complemented
2#27131376C211yesmaximal, characteristic, complemented
3#27131359C211yesmaximal, characteristic, complemented
4#27131358C212yesmaximal, complemented
5#27131355C212yesmaximal, complemented
6#27131352C212yesmaximal, complemented
7#27131351C211yesmaximal, characteristic, complemented
8C2×#20258591C211yesmaximal, characteristic, complemented
9D8×D379C212yesmaximal, complemented
10#27131339C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C379C211yesmaximal, characteristic, complemented
12#20258607C2212yescomplemented
13#20258606—21no—
14#20258606C2211yescharacteristic
15#20258606C2211yescharacteristic, complemented
16#20258605—21no—
17#20258605C2212yescomplemented
18C2×D1516—21no—
19C2×D1516C2211yescharacteristic, complemented
20C2×C22⋊D379—22no—
21D4×D379—21no—
22D4×D379—22no—
23D4×D379C2212yescomplemented
24D4×D379C2212yescomplemented
25#20258596C2211yescharacteristic, complemented
26#20258595C2212yescomplemented
27#20258594C2211yescharacteristic, complemented
28#20258593C2211yescharacteristic, complemented
29D3032C2212yescomplemented
30#20258591C2211yescharacteristic, complemented
31#20258591C2212yescomplemented
32#20258591C2212yescomplemented
33#20258589C2212yescomplemented
34C2×C379⋊C8C2211yescharacteristic, complemented
35C8×D379C2212yescomplemented
36#41×C379C2211yescharacteristic, complemented
37C2×D4×C379C2211yescharacteristic, complemented
38SD16×C379C2212yescomplemented
39D8×C379C2212yescomplemented
40M16×C379C2211yescharacteristic, complemented
41C22×D379—21no—
42C22×D379—22no—
43C22×D379—22no—
44Dic758D411yescharacteristic
45Dic758C2311yescharacteristic
46D1516—22no—
47D1516—21no—
48D1516D411yescharacteristic
49D1516C2312yes—
50D1516C2311yescharacteristic
51C22⋊D379—21no—
52C22⋊D379—22no—
53C22⋊D379—22no—
54C22⋊D379—22no—
55C22⋊D379D412yes—
56C2×Dic379—22no—
57C4×D379—21no—
58C4×D379—22no—
59C4×D379C2312yes—
60C379⋊C8C2311yescharacteristic
61C379⋊C8C2311yescharacteristic
62C23×C379—21no—
63Q8×C379C2311yescharacteristic
64D4×C379—21no—
65D4×C379—21no—
66D4×C379C2311yescharacteristic
67D4×C379C2312yes—
68C2×C4×C379—21no—
69C2×C4×C379C2311yescharacteristic
70C8×C379C2312yes—
71C22×C379—21no—
72C22×C379—22no—
73C22×C379—81no—
74C22×C379C2×D411yescharacteristic
75C2×D379—21no—
76C2×D379—22no—
77C2×D379—82no—
78C2×D379—82no—
79C2×D379—81no—
80C2×D379C2×D412yes—
81C4×C379—21no—
82C4×C379C2×D411yescharacteristic
83C4×C379C2411yescharacteristic
84Dic379—21no—
85Dic379C2×D412yes—
86C2×C379—21no—
87C2×C379—41no—
88C2×C379—42no—
89C2×C379C22×D411yescharacteristic
90D379—22no—
91D379—41no—
92D379—42no—
93C379#57611yescharacteristic, complemented, Sylow
94#576—3791nomaximal, Sylow
95H(5,𝔽2)—3791no—
96H(5,𝔽2)—3791no—
97AGL(1,ℤ/8)—3792no—
98AGL(1,ℤ/8)—3792no—
99AGL(1,ℤ/8)—3791no—
100AGL(1,ℤ/8)D37911yescharacteristic, complemented
101#135—3791no—
102#135—3792no—
103C2×D8—3791no—
104C2×D8—3792no—
105#131—3791no—
106#41—3791no—
107#41—3792no—
108#41—3792no—
109#41—3791no—
110#41—7581no—
111#41—7581no—
112#41C2×D37911yescharacteristic, complemented
113C2×D4—3792no—
114C2×D4—3792no—
115C2×D4—3791no—
116C2×D4—7581no—
117C2×D4—7582no—
118C2×D4—7581no—
119C2×D4—7582no—
120C2×D4C2×D37911yescharacteristic, complemented
121Q16—3791no—
122SD16—3791no—
123SD16—3791no—
124SD16—3792no—
125SD16C2×D37912yescomplemented
126D8—3792no—
127D8—3791no—
128D8—3792no—
129D8—3792no—
130D8C2×D37912yescomplemented
131M16—3792no—
132M16C2×D37911yescharacteristic, complemented
133C2×C8—3791no—
134C2×C8—3792no—
135C23—21no—
136C23—7582no—
137C23—7582no—
138C23—7581no—
139Q8—3791no—
140Q8—3791no—
141Q8C22×D37911yescharacteristic
142D4—21no—
143D4—21no—
144D4—3792no—
145D4—3791no—
146D4—3792no—
147D4—3791no—
148D4—7582no—
149D4—7582no—
150D4—7582no—
151D4—7582no—
152D4—7581no—
153D4—7581no—
154D4C22×D37912yes—
155D4C22×D37911yescharacteristic
156C2×C4—21no—
157C2×C4—3792no—
158C2×C4—7582no—
159C2×C4—7582no—
160C2×C4—7581no—
161C2×C4C22×D37911yescharacteristic
162C8—3791no—
163C8—3791no—
164C8C22×D37912yes—
165C22—21no—
166C22—22no—
167C22—81no—
168C22—3792no—
169C22—30321no—
170C22—30322no—
171C22—30322no—
172C22—7582no—
173C22—7581no—
174C22D4×D37911yescharacteristic
175C4—21no—
176C4—3792no—
177C4—7581no—
178C4D4×D37911yescharacteristic
179C4C23×D37911yescharacteristic
180C2—21no—
181C2—42no—
182C2—41no—
183C2—15162no—
184C2—15161no—
185C2—7582no—
186C2C2×D4×D37911yescharacteristic
subgroupG/H
centerC2C2×D4×D379
commutator, cosocleC4×C379C24
FrattiniC4C23×D379
FittingAGL(1,ℤ/8)×C379C2
socleC2×C379C22×D4
hypercenterAGL(1,ℤ/8)D379
hypocenterC379#576
LCSG ▷ C4×C379 ▷ C2×C379 ▷ C379
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #27131377C2semidirect
2. #27131376C2semidirect
3. #27131359C2semidirect
4. #27131358C2semidirect
5. #27131355C2semidirect
6. #27131352C2semidirect
7. #27131351C2semidirect
8. C2×#20258591C2semidirect
9. D8×D379C2semidirect
10. #27131339C2semidirect
11. AGL(1,ℤ/8)×C379C2semidirect
12. #20258607C22semidirect
15. #20258606C22semidirect
17. #20258605C22semidirect
19. C2×D1516C22semidirect
23. D4×D379C22semidirect
24. D4×D379C22semidirect
25. #20258596C22semidirect
26. #20258595C22semidirect
27. #20258594C22semidirect
28. #20258593C22semidirect
29. D3032C22semidirect
30. #20258591C22semidirect
31. #20258591C22semidirect
32. #20258591C22semidirect
33. #20258589C22semidirect
34. C2×C379⋊C8C22semidirect
35. C8×D379C22semidirect
36. #41×C379C22semidirect
37. C2×D4×C379C22semidirect
38. SD16×C379C22semidirect
39. D8×C379C22semidirect
40. M16×C379C22semidirect
93. C379#576semidirect
100. AGL(1,ℤ/8)D379semidirect
112. #41C2×D379semidirect
120. C2×D4C2×D379semidirect
125. SD16C2×D379semidirect
130. D8C2×D379semidirect
132. M16C2×D379semidirect

Maximal subgroups

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

subgroupindex
#271313772
#271313762
#271313592
#271313582
#271313552
#271313522
#271313512
C2×#202585912
D8×D3792
#271313392
AGL(1,ℤ/8)×C3792
#576379