Finite Group Databasebeta

← #44537529

Subgroups — #44537529

Order 31424.

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#30628383C211yesmaximal, characteristic, complemented
2#30628382C211yesmaximal, characteristic, complemented
3#30628365C211yesmaximal, characteristic, complemented
4#30628364C212yesmaximal, complemented
5#30628361C212yesmaximal, complemented
6#30628358C212yesmaximal, complemented
7#30628357C211yesmaximal, characteristic, complemented
8C2×#21463313C211yesmaximal, characteristic, complemented
9D8×D491C212yesmaximal, complemented
10#30628345C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C491C211yesmaximal, characteristic, complemented
12#21463329C2212yescomplemented
13#21463328—21no—
14#21463328C2211yescharacteristic
15#21463328C2211yescharacteristic, complemented
16#21463327—21no—
17#21463327C2212yescomplemented
18C2×D1964—21no—
19C2×D1964C2211yescharacteristic, complemented
20C2×C22⋊D491—22no—
21D4×D491—21no—
22D4×D491—22no—
23D4×D491C2212yescomplemented
24D4×D491C2212yescomplemented
25#21463318C2211yescharacteristic, complemented
26#21463317C2212yescomplemented
27#21463316C2211yescharacteristic, complemented
28#21463315C2211yescharacteristic, complemented
29D3928C2212yescomplemented
30#21463313C2211yescharacteristic, complemented
31#21463313C2212yescomplemented
32#21463313C2212yescomplemented
33#21463311C2212yescomplemented
34C2×C491⋊C8C2211yescharacteristic, complemented
35C8×D491C2212yescomplemented
36#41×C491C2211yescharacteristic, complemented
37C2×D4×C491C2211yescharacteristic, complemented
38SD16×C491C2212yescomplemented
39D8×C491C2212yescomplemented
40M16×C491C2211yescharacteristic, complemented
41C22×D491—21no—
42C22×D491—22no—
43C22×D491—22no—
44Dic982D411yescharacteristic
45Dic982C2311yescharacteristic
46D1964—22no—
47D1964—21no—
48D1964D411yescharacteristic
49D1964C2312yes—
50D1964C2311yescharacteristic
51C22⋊D491—21no—
52C22⋊D491—22no—
53C22⋊D491—22no—
54C22⋊D491—22no—
55C22⋊D491D412yes—
56C2×Dic491—22no—
57C4×D491—21no—
58C4×D491—22no—
59C4×D491C2312yes—
60C491⋊C8C2311yescharacteristic
61C491⋊C8C2311yescharacteristic
62C23×C491—21no—
63Q8×C491C2311yescharacteristic
64D4×C491—21no—
65D4×C491—21no—
66D4×C491C2312yes—
67D4×C491C2311yescharacteristic
68C2×C4×C491—21no—
69C2×C4×C491C2311yescharacteristic
70C8×C491C2312yes—
71C22×C491—21no—
72C22×C491—22no—
73C22×C491—81no—
74C22×C491C2×D411yescharacteristic
75C2×D491—21no—
76C2×D491—22no—
77C2×D491—82no—
78C2×D491—82no—
79C2×D491—81no—
80C2×D491C2×D412yes—
81C4×C491—21no—
82C4×C491C2×D411yescharacteristic
83C4×C491C2411yescharacteristic
84Dic491—21no—
85Dic491C2×D412yes—
86C2×C491—21no—
87C2×C491—41no—
88C2×C491—42no—
89C2×C491C22×D411yescharacteristic
90D491—22no—
91D491—41no—
92D491—42no—
93C491#57611yescharacteristic, complemented, Sylow
94#576—4911nomaximal, Sylow
95H(5,𝔽2)—4911no—
96H(5,𝔽2)—4911no—
97AGL(1,ℤ/8)—4912no—
98AGL(1,ℤ/8)—4912no—
99AGL(1,ℤ/8)—4911no—
100AGL(1,ℤ/8)D49111yescharacteristic, complemented
101#135—4911no—
102#135—4912no—
103C2×D8—4911no—
104C2×D8—4912no—
105#131—4911no—
106#41—9821no—
107#41—9821no—
108#41—4912no—
109#41—4912no—
110#41—4911no—
111#41—4911no—
112#41C2×D49111yescharacteristic, complemented
113C2×D4—9821no—
114C2×D4—9822no—
115C2×D4—9821no—
116C2×D4—9822no—
117C2×D4—4912no—
118C2×D4—4912no—
119C2×D4—4911no—
120C2×D4C2×D49111yescharacteristic, complemented
121Q16—4911no—
122SD16—4911no—
123SD16—4911no—
124SD16—4912no—
125SD16C2×D49112yescomplemented
126D8—4912no—
127D8—4911no—
128D8—4912no—
129D8—4912no—
130D8C2×D49112yescomplemented
131M16—4912no—
132M16C2×D49111yescharacteristic, complemented
133C2×C8—4911no—
134C2×C8—4912no—
135C23—21no—
136C23—9822no—
137C23—9822no—
138C23—9821no—
139Q8—4911no—
140Q8—4911no—
141Q8C22×D49111yescharacteristic
142D4—21no—
143D4—21no—
144D4—9822no—
145D4—9822no—
146D4—9821no—
147D4—9822no—
148D4—9822no—
149D4—9821no—
150D4—4912no—
151D4—4911no—
152D4—4912no—
153D4—4911no—
154D4C22×D49112yes—
155D4C22×D49111yescharacteristic
156C2×C4—21no—
157C2×C4—9822no—
158C2×C4—9822no—
159C2×C4—9821no—
160C2×C4—4912no—
161C2×C4C22×D49111yescharacteristic
162C8—4911no—
163C8—4911no—
164C8C22×D49112yes—
165C22—21no—
166C22—22no—
167C22—81no—
168C22—39281no—
169C22—39282no—
170C22—39282no—
171C22—9821no—
172C22—9822no—
173C22—4912no—
174C22D4×D49111yescharacteristic
175C4—21no—
176C4—9821no—
177C4—4912no—
178C4D4×D49111yescharacteristic
179C4C23×D49111yescharacteristic
180C2—21no—
181C2—42no—
182C2—41no—
183C2—19642no—
184C2—19641no—
185C2—9822no—
186C2C2×D4×D49111yescharacteristic
subgroupG/H
centerC2C2×D4×D491
commutator, cosocleC4×C491C24
FrattiniC4C23×D491
FittingAGL(1,ℤ/8)×C491C2
socleC2×C491C22×D4
hypercenterAGL(1,ℤ/8)D491
hypocenterC491#576
LCSG ▷ C4×C491 ▷ C2×C491 ▷ C491
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #30628383C2semidirect
2. #30628382C2semidirect
3. #30628365C2semidirect
4. #30628364C2semidirect
5. #30628361C2semidirect
6. #30628358C2semidirect
7. #30628357C2semidirect
8. C2×#21463313C2semidirect
9. D8×D491C2semidirect
10. #30628345C2semidirect
11. AGL(1,ℤ/8)×C491C2semidirect
12. #21463329C22semidirect
15. #21463328C22semidirect
17. #21463327C22semidirect
19. C2×D1964C22semidirect
23. D4×D491C22semidirect
24. D4×D491C22semidirect
25. #21463318C22semidirect
26. #21463317C22semidirect
27. #21463316C22semidirect
28. #21463315C22semidirect
29. D3928C22semidirect
30. #21463313C22semidirect
31. #21463313C22semidirect
32. #21463313C22semidirect
33. #21463311C22semidirect
34. C2×C491⋊C8C22semidirect
35. C8×D491C22semidirect
36. #41×C491C22semidirect
37. C2×D4×C491C22semidirect
38. SD16×C491C22semidirect
39. D8×C491C22semidirect
40. M16×C491C22semidirect
93. C491#576semidirect
100. AGL(1,ℤ/8)D491semidirect
112. #41C2×D491semidirect
120. C2×D4C2×D491semidirect
125. SD16C2×D491semidirect
130. D8C2×D491semidirect
132. M16C2×D491semidirect

Maximal subgroups

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

subgroupindex
#306283832
#306283822
#306283652
#306283642
#306283612
#306283582
#306283572
C2×#214633132
D8×D4912
#306283452
AGL(1,ℤ/8)×C4912
#576491