Finite Group Databasebeta

← #46830984

Subgroups — #46830984

Order 34624.

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

normal subgroups only

This group has 258 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#31772676C211yesmaximal, characteristic, complemented
2#31772674C211yesmaximal, characteristic, complemented
3#31772660C212yesmaximal, complemented
4#31772656C211yesmaximal, characteristic, complemented
5#31772655C212yesmaximal, complemented
6#31772651C212yesmaximal, complemented
7#31772648C211yesmaximal, characteristic, complemented
8C2×#22575823C211yesmaximal, characteristic, complemented
9SD16×D541C212yesmaximal, complemented
10#31772636C211yesmaximal, characteristic, complemented
11#137×C541C211yesmaximal, characteristic, complemented
12#22575837—21no—
13#22575837C2212yes—
14#22575837C2212yescomplemented
15#22575836—21no—
16#22575836—22no—
17#22575836C2211yescharacteristic
18#22575836C2211yescharacteristic, complemented
19Q8×D541—21no—
20Q8×D541C2212yescomplemented
21C2×D2164—21no—
22C2×D2164C2211yescharacteristic
23D4×D541—22no—
24D4×D541C2212yes—
25#22575826C2211yescharacteristic, complemented
26#22575825C2212yescomplemented
27#22575824C2211yescharacteristic, complemented
28#22575823C2212yescomplemented
29#22575823C2212yescomplemented
30#22575823C2211yescharacteristic, complemented
31D4328C2212yescomplemented
32#22575821C2211yescharacteristic, complemented
33#22575819C2212yescomplemented
34C2×#16864513C2211yescharacteristic, complemented
35C8×D541C2212yescomplemented
36#41×C541C2211yescharacteristic
37C2×Q8×C541C2211yescharacteristic, complemented
38Q16×C541C2212yescomplemented
39SD16×C541C2212yescomplemented
40M16×C541C2211yescharacteristic, complemented
41C22×D541—21no—
42C22×D541—22no—
43Dic1082—22no—
44Dic1082D411yescharacteristic
45Dic1082C2311yescharacteristic
46D2164—22no—
47D2164—22no—
48D2164—21no—
49D2164D411yescharacteristic
50D2164C2311yescharacteristic
51D2164C2312yes—
52C22⋊D541—21no—
53C22⋊D541—22no—
54C22⋊D541D412yes—
55C4×D541—22no—
56C4×D541—21no—
57C4×D541—22no—
58C4×D541—22no—
59C4×D541C2312yes—
60#16864513C2311yescharacteristic
61#16864513C2311yescharacteristic
62Q8×C541—21no—
63Q8×C541C2312yes—
64Q8×C541C2311yescharacteristic
65D4×C541—21no—
66D4×C541C2311yescharacteristic
67C2×C4×C541—21no—
68C2×C4×C541—21no—
69C2×C4×C541C2311yescharacteristic
70C8×C541C2312yes—
71C22×C541—21no—
72C22×C541C2×D411yescharacteristic
73C2×D541—21no—
74C2×D541—22no—
75C2×D541—82no—
76C2×D541—81no—
77C2×D541C2×D412yes—
78C4×C541—21no—
79C4×C541—22no—
80C4×C541C2×D411yescharacteristic
81C4×C541C2411yescharacteristic
82Dic541—21no—
83Dic541C2×D412yes—
84C2×C541—21no—
85C2×C541—41no—
86C2×C541C22×D411yescharacteristic
87D541—22no—
88D541—41no—
89D541—42no—
90C541#57711yescharacteristic, complemented, Sylow
91#577—5411nomaximal, Sylow
922−1+4—5411no—
93H(5,𝔽2)—5411no—
94#137—5412no—
95#137D54111yescharacteristic, complemented
96AGL(1,ℤ/8)—5412no—
97AGL(1,ℤ/8)—5411no—
98#135—5411no—
99#135—5412no—
100C2×SD16—5411no—
101C2×SD16—5412no—
102#131—5411no—
103#41—5411no—
104#41—5412no—
105#41—5412no—
106#41—5411no—
107#41—10822no—
108#41—10821no—
109#41—10821no—
110#41C2×D54111yescharacteristic
111C2×Q8—5412no—
112C2×Q8—10821no—
113C2×Q8C2×D54111yescharacteristic, complemented
114C2×D4—5412no—
115C2×D4—5411no—
116C2×D4—10821no—
117C2×D4—10822no—
118Q16—5411no—
119Q16C2×D54112yescomplemented
120SD16—5412no—
121SD16—5412no—
122SD16—5411no—
123SD16—5411no—
124SD16—5412no—
125SD16C2×D54112yescomplemented
126D8—5411no—
127D8—5412no—
128M16—5412no—
129M16C2×D54111yescharacteristic, complemented
130C2×C8—5411no—
131C2×C8—5412no—
132C23—10822no—
133C23—10821no—
134Q8—21no—
135Q8—5411no—
136Q8—5411no—
137Q8—10822no—
138Q8C22×D54112yes—
139Q8C22×D54111yescharacteristic
140D4—21no—
141D4—5412no—
142D4—5411no—
143D4—5411no—
144D4—5412no—
145D4—10822no—
146D4—10822no—
147D4—10822no—
148D4—10821no—
149D4—10821no—
150D4C22×D54111yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—5412no—
154C2×C4—10822no—
155C2×C4—10822no—
156C2×C4—10822no—
157C2×C4—10821no—
158C2×C4C22×D54111yescharacteristic
159C8—5411no—
160C8—5411no—
161C8C22×D54112yes—
162C22—21no—
163C22—5412no—
164C22—10821no—
165C22—10822no—
166C22—43281no—
167C22—43282no—
168C22D4×D54111yescharacteristic
169C4—21no—
170C4—22no—
171C4—5412no—
172C4—10821no—
173C4D4×D54111yescharacteristic
174C4C23×D54111yescharacteristic
175C2—21no—
176C2—41no—
177C2—10822no—
178C2—21642no—
179C2—21641no—
180C2C2×D4×D54111yescharacteristic
subgroupG/H
centerC2C2×D4×D541
commutator, cosocleC4×C541C24
FrattiniC4C23×D541
Fitting#137×C541C2
socleC2×C541C22×D4
hypercenter#137D541
hypocenterC541#577
LCSG ▷ C4×C541 ▷ C2×C541 ▷ C541
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. #31772676C2semidirect
2. #31772674C2semidirect
3. #31772660C2semidirect
4. #31772656C2semidirect
5. #31772655C2semidirect
6. #31772651C2semidirect
7. #31772648C2semidirect
8. C2×#22575823C2semidirect
9. SD16×D541C2semidirect
10. #31772636C2semidirect
11. #137×C541C2semidirect
14. #22575837C22semidirect
18. #22575836C22semidirect
20. Q8×D541C22semidirect
25. #22575826C22semidirect
26. #22575825C22semidirect
27. #22575824C22semidirect
28. #22575823C22semidirect
29. #22575823C22semidirect
30. #22575823C22semidirect
31. D4328C22semidirect
32. #22575821C22semidirect
33. #22575819C22semidirect
34. C2×#16864513C22semidirect
35. C8×D541C22semidirect
37. C2×Q8×C541C22semidirect
38. Q16×C541C22semidirect
39. SD16×C541C22semidirect
40. M16×C541C22semidirect
90. C541#577semidirect
95. #137D541semidirect
113. C2×Q8C2×D541semidirect
119. Q16C2×D541semidirect
125. SD16C2×D541semidirect
129. M16C2×D541semidirect

Maximal subgroups

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

subgroupindex
#317726762
#317726742
#317726602
#317726562
#317726552
#317726512
#317726482
C2×#225758232
SD16×D5412
#317726362
#137×C5412
#577541