Finite Group Databasebeta

← #49183519

Subgroups — #49183519

Order 37952.

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#34039331C211yesmaximal, characteristic, complemented
2#34039330C211yesmaximal, characteristic, complemented
3#34039313C211yesmaximal, characteristic, complemented
4#34039312C212yesmaximal, complemented
5#34039309C212yesmaximal, complemented
6#34039306C212yesmaximal, complemented
7#34039305C211yesmaximal, characteristic, complemented
8C2×#23748718C211yesmaximal, characteristic, complemented
9D8×D593C212yesmaximal, complemented
10#34039293C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C593C211yesmaximal, characteristic, complemented
12#23748734C2212yescomplemented
13#23748733—21no—
14#23748733C2211yescharacteristic
15#23748733C2211yescharacteristic, complemented
16#23748732—21no—
17#23748732C2212yescomplemented
18C2×D2372—21no—
19C2×D2372C2211yescharacteristic, complemented
20C2×C22⋊D593—22no—
21D4×D593—21no—
22D4×D593—22no—
23D4×D593C2212yescomplemented
24D4×D593C2212yescomplemented
25#23748723C2211yescharacteristic, complemented
26#23748722C2212yescomplemented
27#23748721C2211yescharacteristic, complemented
28#23748720C2211yescharacteristic, complemented
29D4744C2212yescomplemented
30#23748718C2211yescharacteristic, complemented
31#23748718C2212yescomplemented
32#23748718C2212yescomplemented
33#23748716C2212yescomplemented
34C2×#18011654C2211yescharacteristic, complemented
35C8×D593C2212yescomplemented
36#41×C593C2211yescharacteristic, complemented
37C2×D4×C593C2211yescharacteristic, complemented
38SD16×C593C2212yescomplemented
39D8×C593C2212yescomplemented
40M16×C593C2211yescharacteristic, complemented
41C22×D593—21no—
42C22×D593—22no—
43C22×D593—22no—
44Dic1186D411yescharacteristic
45Dic1186C2311yescharacteristic
46D2372—22no—
47D2372—21no—
48D2372D411yescharacteristic
49D2372C2312yes—
50D2372C2311yescharacteristic
51C22⋊D593—21no—
52C22⋊D593—22no—
53C22⋊D593—22no—
54C22⋊D593—22no—
55C22⋊D593D412yes—
56C2×Dic593—22no—
57C4×D593—21no—
58C4×D593—22no—
59C4×D593C2312yes—
60#18011654C2311yescharacteristic
61#18011654C2311yescharacteristic
62C23×C593—21no—
63Q8×C593C2311yescharacteristic
64D4×C593—21no—
65D4×C593—21no—
66D4×C593C2311yescharacteristic
67D4×C593C2312yes—
68C2×C4×C593—21no—
69C2×C4×C593C2311yescharacteristic
70C8×C593C2312yes—
71C22×C593—21no—
72C22×C593—22no—
73C22×C593—81no—
74C22×C593C2×D411yescharacteristic
75C2×D593—21no—
76C2×D593—22no—
77C2×D593—82no—
78C2×D593—82no—
79C2×D593—81no—
80C2×D593C2×D412yes—
81C4×C593—21no—
82C4×C593C2×D411yescharacteristic
83C4×C593C2411yescharacteristic
84Dic593—21no—
85Dic593C2×D412yes—
86C2×C593—21no—
87C2×C593—41no—
88C2×C593—42no—
89C2×C593C22×D411yescharacteristic
90D593—22no—
91D593—41no—
92D593—42no—
93C593#57611yescharacteristic, complemented, Sylow
94#576—5931nomaximal, Sylow
95H(5,𝔽2)—5931no—
96H(5,𝔽2)—5931no—
97AGL(1,ℤ/8)—5932no—
98AGL(1,ℤ/8)—5932no—
99AGL(1,ℤ/8)—5931no—
100AGL(1,ℤ/8)D59311yescharacteristic, complemented
101#135—5931no—
102#135—5932no—
103C2×D8—5931no—
104C2×D8—5932no—
105#131—5931no—
106#41—5931no—
107#41—5932no—
108#41—5932no—
109#41—5931no—
110#41—11861no—
111#41—11861no—
112#41C2×D59311yescharacteristic, complemented
113C2×D4—5932no—
114C2×D4—5932no—
115C2×D4—5931no—
116C2×D4—11861no—
117C2×D4—11862no—
118C2×D4—11861no—
119C2×D4—11862no—
120C2×D4C2×D59311yescharacteristic, complemented
121Q16—5931no—
122SD16—5931no—
123SD16—5931no—
124SD16—5932no—
125SD16C2×D59312yescomplemented
126D8—5932no—
127D8—5931no—
128D8—5932no—
129D8—5932no—
130D8C2×D59312yescomplemented
131M16—5932no—
132M16C2×D59311yescharacteristic, complemented
133C2×C8—5931no—
134C2×C8—5932no—
135C23—21no—
136C23—11862no—
137C23—11862no—
138C23—11861no—
139Q8—5931no—
140Q8—5931no—
141Q8C22×D59311yescharacteristic
142D4—21no—
143D4—21no—
144D4—5932no—
145D4—5931no—
146D4—5932no—
147D4—5931no—
148D4—11862no—
149D4—11862no—
150D4—11862no—
151D4—11862no—
152D4—11861no—
153D4—11861no—
154D4C22×D59312yes—
155D4C22×D59311yescharacteristic
156C2×C4—21no—
157C2×C4—5932no—
158C2×C4—11862no—
159C2×C4—11862no—
160C2×C4—11861no—
161C2×C4C22×D59311yescharacteristic
162C8—5931no—
163C8—5931no—
164C8C22×D59312yes—
165C22—21no—
166C22—22no—
167C22—81no—
168C22—5932no—
169C22—47441no—
170C22—47442no—
171C22—47442no—
172C22—11862no—
173C22—11861no—
174C22D4×D59311yescharacteristic
175C4—21no—
176C4—5932no—
177C4—11861no—
178C4D4×D59311yescharacteristic
179C4C23×D59311yescharacteristic
180C2—21no—
181C2—42no—
182C2—41no—
183C2—23722no—
184C2—23721no—
185C2—11862no—
186C2C2×D4×D59311yescharacteristic
subgroupG/H
centerC2C2×D4×D593
commutator, cosocleC4×C593C24
FrattiniC4C23×D593
FittingAGL(1,ℤ/8)×C593C2
socleC2×C593C22×D4
hypercenterAGL(1,ℤ/8)D593
hypocenterC593#576
LCSG ▷ C4×C593 ▷ C2×C593 ▷ C593
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #34039331C2semidirect
2. #34039330C2semidirect
3. #34039313C2semidirect
4. #34039312C2semidirect
5. #34039309C2semidirect
6. #34039306C2semidirect
7. #34039305C2semidirect
8. C2×#23748718C2semidirect
9. D8×D593C2semidirect
10. #34039293C2semidirect
11. AGL(1,ℤ/8)×C593C2semidirect
12. #23748734C22semidirect
15. #23748733C22semidirect
17. #23748732C22semidirect
19. C2×D2372C22semidirect
23. D4×D593C22semidirect
24. D4×D593C22semidirect
25. #23748723C22semidirect
26. #23748722C22semidirect
27. #23748721C22semidirect
28. #23748720C22semidirect
29. D4744C22semidirect
30. #23748718C22semidirect
31. #23748718C22semidirect
32. #23748718C22semidirect
33. #23748716C22semidirect
34. C2×#18011654C22semidirect
35. C8×D593C22semidirect
36. #41×C593C22semidirect
37. C2×D4×C593C22semidirect
38. SD16×C593C22semidirect
39. D8×C593C22semidirect
40. M16×C593C22semidirect
93. C593#576semidirect
100. AGL(1,ℤ/8)D593semidirect
112. #41C2×D593semidirect
120. C2×D4C2×D593semidirect
125. SD16C2×D593semidirect
130. D8C2×D593semidirect
132. M16C2×D593semidirect

Maximal subgroups

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

subgroupindex
#340393312
#340393302
#340393132
#340393122
#340393092
#340393062
#340393052
C2×#237487182
D8×D5932
#340392932
AGL(1,ℤ/8)×C5932
#576593