Finite Group Databasebeta

← #46830979

Subgroups — #46830979

Order 34624.

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#31772674C211yesmaximal, characteristic, complemented
2#31772673C211yesmaximal, characteristic, complemented
3#31772656C211yesmaximal, characteristic, complemented
4#31772655C212yesmaximal, complemented
5#31772652C212yesmaximal, complemented
6#31772649C212yesmaximal, complemented
7#31772648C211yesmaximal, characteristic, complemented
8C2×#22575821C211yesmaximal, characteristic, complemented
9D8×D541C212yesmaximal, complemented
10#31772636C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C541C211yesmaximal, characteristic, complemented
12#22575837C2212yescomplemented
13#22575836—21no—
14#22575836C2211yescharacteristic
15#22575836C2211yescharacteristic, complemented
16#22575835—21no—
17#22575835C2212yescomplemented
18C2×D2164—21no—
19C2×D2164C2211yescharacteristic, complemented
20C2×C22⋊D541—22no—
21D4×D541—21no—
22D4×D541—22no—
23D4×D541C2212yescomplemented
24D4×D541C2212yescomplemented
25#22575826C2211yescharacteristic, complemented
26#22575825C2212yescomplemented
27#22575824C2211yescharacteristic, complemented
28#22575823C2211yescharacteristic, complemented
29D4328C2212yescomplemented
30#22575821C2211yescharacteristic, complemented
31#22575821C2212yescomplemented
32#22575821C2212yescomplemented
33#22575819C2212yescomplemented
34C2×#16864513C2211yescharacteristic, complemented
35C8×D541C2212yescomplemented
36#41×C541C2211yescharacteristic, complemented
37C2×D4×C541C2211yescharacteristic, complemented
38SD16×C541C2212yescomplemented
39D8×C541C2212yescomplemented
40M16×C541C2211yescharacteristic, complemented
41C22×D541—21no—
42C22×D541—22no—
43C22×D541—22no—
44Dic1082D411yescharacteristic
45Dic1082C2311yescharacteristic
46D2164—22no—
47D2164—21no—
48D2164D411yescharacteristic
49D2164C2312yes—
50D2164C2311yescharacteristic
51C22⋊D541—21no—
52C22⋊D541—22no—
53C22⋊D541—22no—
54C22⋊D541—22no—
55C22⋊D541D412yes—
56C2×Dic541—22no—
57C4×D541—21no—
58C4×D541—22no—
59C4×D541C2312yes—
60#16864513C2311yescharacteristic
61#16864513C2311yescharacteristic
62C23×C541—21no—
63Q8×C541C2311yescharacteristic
64D4×C541—21no—
65D4×C541—21no—
66D4×C541C2311yescharacteristic
67D4×C541C2312yes—
68C2×C4×C541—21no—
69C2×C4×C541C2311yescharacteristic
70C8×C541C2312yes—
71C22×C541—22no—
72C22×C541—21no—
73C22×C541—81no—
74C22×C541C2×D411yescharacteristic
75C2×D541—21no—
76C2×D541—22no—
77C2×D541—82no—
78C2×D541—82no—
79C2×D541—81no—
80C2×D541C2×D412yes—
81C4×C541—21no—
82C4×C541C2×D411yescharacteristic
83C4×C541C2411yescharacteristic
84Dic541—21no—
85Dic541C2×D412yes—
86C2×C541—21no—
87C2×C541—41no—
88C2×C541—42no—
89C2×C541C22×D411yescharacteristic
90D541—22no—
91D541—41no—
92D541—42no—
93C541#57611yescharacteristic, complemented, Sylow
94#576—5411nomaximal, Sylow
95H(5,𝔽2)—5411no—
96H(5,𝔽2)—5411no—
97AGL(1,ℤ/8)—5412no—
98AGL(1,ℤ/8)—5412no—
99AGL(1,ℤ/8)—5411no—
100AGL(1,ℤ/8)D54111yescharacteristic, complemented
101#135—5411no—
102#135—5412no—
103C2×D8—5411no—
104C2×D8—5412no—
105#131—5411no—
106#41—5411no—
107#41—5412no—
108#41—5412no—
109#41—5411no—
110#41—10821no—
111#41—10821no—
112#41C2×D54111yescharacteristic, complemented
113C2×D4—5412no—
114C2×D4—5412no—
115C2×D4—5411no—
116C2×D4—10821no—
117C2×D4—10822no—
118C2×D4—10821no—
119C2×D4—10822no—
120C2×D4C2×D54111yescharacteristic, complemented
121Q16—5411no—
122SD16—5411no—
123SD16—5411no—
124SD16—5412no—
125SD16C2×D54112yescomplemented
126D8—5412no—
127D8—5411no—
128D8—5412no—
129D8—5412no—
130D8C2×D54112yescomplemented
131M16—5412no—
132M16C2×D54111yescharacteristic, complemented
133C2×C8—5411no—
134C2×C8—5412no—
135C23—21no—
136C23—10822no—
137C23—10822no—
138C23—10821no—
139Q8—5411no—
140Q8—5411no—
141Q8C22×D54111yescharacteristic
142D4—21no—
143D4—21no—
144D4—5412no—
145D4—5411no—
146D4—5412no—
147D4—5411no—
148D4—10822no—
149D4—10822no—
150D4—10822no—
151D4—10822no—
152D4—10821no—
153D4—10821no—
154D4C22×D54112yes—
155D4C22×D54111yescharacteristic
156C2×C4—21no—
157C2×C4—5412no—
158C2×C4—10822no—
159C2×C4—10822no—
160C2×C4—10821no—
161C2×C4C22×D54111yescharacteristic
162C8—5411no—
163C8—5411no—
164C8C22×D54112yes—
165C22—21no—
166C22—22no—
167C22—81no—
168C22—5412no—
169C22—10822no—
170C22—10821no—
171C22—43281no—
172C22—43282no—
173C22—43282no—
174C22D4×D54111yescharacteristic
175C4—21no—
176C4—5412no—
177C4—10821no—
178C4D4×D54111yescharacteristic
179C4C23×D54111yescharacteristic
180C2—21no—
181C2—42no—
182C2—41no—
183C2—10822no—
184C2—21642no—
185C2—21641no—
186C2C2×D4×D54111yescharacteristic
subgroupG/H
centerC2C2×D4×D541
commutator, cosocleC4×C541C24
FrattiniC4C23×D541
FittingAGL(1,ℤ/8)×C541C2
socleC2×C541C22×D4
hypercenterAGL(1,ℤ/8)D541
hypocenterC541#576
LCSG ▷ C4×C541 ▷ C2×C541 ▷ C541
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #31772674C2semidirect
2. #31772673C2semidirect
3. #31772656C2semidirect
4. #31772655C2semidirect
5. #31772652C2semidirect
6. #31772649C2semidirect
7. #31772648C2semidirect
8. C2×#22575821C2semidirect
9. D8×D541C2semidirect
10. #31772636C2semidirect
11. AGL(1,ℤ/8)×C541C2semidirect
12. #22575837C22semidirect
15. #22575836C22semidirect
17. #22575835C22semidirect
19. C2×D2164C22semidirect
23. D4×D541C22semidirect
24. D4×D541C22semidirect
25. #22575826C22semidirect
26. #22575825C22semidirect
27. #22575824C22semidirect
28. #22575823C22semidirect
29. D4328C22semidirect
30. #22575821C22semidirect
31. #22575821C22semidirect
32. #22575821C22semidirect
33. #22575819C22semidirect
34. C2×#16864513C22semidirect
35. C8×D541C22semidirect
36. #41×C541C22semidirect
37. C2×D4×C541C22semidirect
38. SD16×C541C22semidirect
39. D8×C541C22semidirect
40. M16×C541C22semidirect
93. C541#576semidirect
100. AGL(1,ℤ/8)D541semidirect
112. #41C2×D541semidirect
120. C2×D4C2×D541semidirect
125. SD16C2×D541semidirect
130. D8C2×D541semidirect
132. M16C2×D541semidirect

Maximal subgroups

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

subgroupindex
#317726742
#317726732
#317726562
#317726552
#317726522
#317726492
#317726482
C2×#225758212
D8×D5412
#317726362
AGL(1,ℤ/8)×C5412
#576541