Finite Group Databasebeta

← #46830982

Subgroups — #46830982

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#31772675C211yesmaximal, characteristic, complemented
2#31772674C211yesmaximal, characteristic, complemented
3#31772660C212yesmaximal, complemented
4#31772658C211yesmaximal, characteristic, complemented
5#31772653C211yesmaximal, characteristic, complemented
6#31772652C212yesmaximal, complemented
7#31772649C212yesmaximal, complemented
8C2×#22575825C211yesmaximal, characteristic, complemented
9SD16×D541C212yesmaximal, complemented
10#31772634C211yesmaximal, characteristic, complemented
11#135×C541C211yesmaximal, characteristic, complemented
12#22575837C2212yes—
13#22575836—21no—
14#22575836—21no—
15#22575836C2211yescharacteristic
16#22575835—22no—
17#22575835C2212yescomplemented
18C2×Dic1082—21no—
19C2×Dic1082C2211yescharacteristic, complemented
20Q8×D541C2212yescomplemented
21C2×D2164—21no—
22C2×D2164C2211yescharacteristic
23D4×D541—22no—
24D4×D541C2212yes—
25#22575826C2212yescomplemented
26#22575825C2212yescomplemented
27#22575825C2212yescomplemented
28#22575824C2212yescomplemented
29#22575823C2212yescomplemented
30#22575821C2212yescomplemented
31#22575820C2211yescharacteristic, complemented
32#22575819C2212yescomplemented
33C8×D541C2212yescomplemented
34#41×C541C2211yescharacteristic
35#41×C541C2211yescharacteristic, complemented
36Q16×C541C2211yescharacteristic, complemented
37SD16×C541C2211yescharacteristic, complemented
38SD16×C541C2211yescharacteristic, complemented
39D8×C541C2211yescharacteristic, complemented
40C2×C8×C541C2211yescharacteristic, complemented
41C22×D541—21no—
42C22×D541—22no—
43Dic1082—21no—
44Dic1082—22no—
45Dic1082D411yescharacteristic
46Dic1082C2312yes—
47D2164—22no—
48D2164—21no—
49D2164D411yescharacteristic
50D2164C2312yes—
51C22⋊D541—22no—
52C22⋊D541—22no—
53C22⋊D541D412yes—
54C2×Dic541—21no—
55C2×Dic541—22no—
56C4×D541—22no—
57C4×D541—22no—
58C4×D541C2312yes—
59#16864513C2312yes—
60Q8×C541C2311yescharacteristic
61Q8×C541C2311yescharacteristic
62D4×C541—21no—
63D4×C541—21no—
64D4×C541C2311yescharacteristic
65D4×C541C2311yescharacteristic
66C2×C4×C541—21no—
67C2×C4×C541—21no—
68C2×C4×C541C2311yescharacteristic
69C8×C541C2311yescharacteristic
70C8×C541C2311yescharacteristic
71C22×C541—21no—
72C22×C541—21no—
73C22×C541C2×D411yescharacteristic
74C2×D541—22no—
75C2×D541—82no—
76C2×D541—81no—
77C2×D541C2×D412yes—
78C4×C541—21no—
79C4×C541—21no—
80C4×C541C2×D411yescharacteristic
81C4×C541C2411yescharacteristic
82Dic541—22no—
83Dic541C2×D412yes—
84C2×C541—21no—
85C2×C541—41no—
86C2×C541—41no—
87C2×C541C22×D411yescharacteristic
88D541—22no—
89D541—42no—
90C541#57711yescharacteristic, complemented, Sylow
91#577—5411nomaximal, Sylow
922−1+4—5411no—
93H(5,𝔽2)—5411no—
94#137—5411no—
95#137—5412no—
96AGL(1,ℤ/8)—5411no—
97AGL(1,ℤ/8)—5412no—
98#135—5412no—
99#135D54111yescharacteristic, complemented
100C2×SD16—5412no—
101C2×SD16—5411no—
102#131—5411no—
103#41—5411no—
104#41—5412no—
105#41—5412no—
106#41—10821no—
107#41—10821no—
108#41—10822no—
109#41C2×D54111yescharacteristic
110#41C2×D54111yescharacteristic, complemented
111C2×Q8—5412no—
112C2×Q8—5411no—
113C2×Q8—10821no—
114C2×D4—5412no—
115C2×D4—5411no—
116C2×D4—10821no—
117C2×D4—10822no—
118Q16—5412no—
119Q16C2×D54111yescharacteristic, complemented
120SD16—5412no—
121SD16—5412no—
122SD16—5412no—
123SD16—5412no—
124SD16C2×D54111yescharacteristic, complemented
125SD16C2×D54111yescharacteristic, complemented
126D8—5412no—
127D8C2×D54111yescharacteristic, complemented
128M16—5411no—
129M16—5412no—
130C2×C8—5412no—
131C2×C8C2×D54111yescharacteristic, complemented
132C23—10822no—
133C23—10821no—
134Q8—5411no—
135Q8—5412no—
136Q8—10822no—
137Q8—10821no—
138Q8C22×D54111yescharacteristic
139Q8C22×D54111yescharacteristic
140D4—21no—
141D4—21no—
142D4—5412no—
143D4—5411no—
144D4—5412no—
145D4—10822no—
146D4—10822no—
147D4—10822no—
148D4—10821no—
149D4C22×D54111yescharacteristic
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—5412no—
160C8C22×D54111yescharacteristic
161C8C22×D54111yescharacteristic
162C22—21no—
163C22—21no—
164C22—5412no—
165C22—10822no—
166C22—43281no—
167C22—43282no—
168C22D4×D54111yescharacteristic
169C4—21no—
170C4—21no—
171C4—5412no—
172C4—10822no—
173C4D4×D54111yescharacteristic
174C4C23×D54111yescharacteristic
175C2—21no—
176C2—41no—
177C2—41no—
178C2—10822no—
179C2—21642no—
180C2C2×D4×D54111yescharacteristic
subgroupG/H
centerC2C2×D4×D541
commutator, cosocleC4×C541C24
FrattiniC4C23×D541
Fitting#135×C541C2
socleC2×C541C22×D4
hypercenter#135D541
hypocenterC541#577
LCSG ▷ C4×C541 ▷ C2×C541 ▷ C541
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #31772675C2semidirect
2. #31772674C2semidirect
3. #31772660C2semidirect
4. #31772658C2semidirect
5. #31772653C2semidirect
6. #31772652C2semidirect
7. #31772649C2semidirect
8. C2×#22575825C2semidirect
9. SD16×D541C2semidirect
10. #31772634C2semidirect
11. #135×C541C2semidirect
17. #22575835C22semidirect
19. C2×Dic1082C22semidirect
20. Q8×D541C22semidirect
25. #22575826C22semidirect
26. #22575825C22semidirect
27. #22575825C22semidirect
28. #22575824C22semidirect
29. #22575823C22semidirect
30. #22575821C22semidirect
31. #22575820C22semidirect
32. #22575819C22semidirect
33. C8×D541C22semidirect
35. #41×C541C22semidirect
36. Q16×C541C22semidirect
37. SD16×C541C22semidirect
38. SD16×C541C22semidirect
39. D8×C541C22semidirect
40. C2×C8×C541C22semidirect
90. C541#577semidirect
99. #135D541semidirect
110. #41C2×D541semidirect
119. Q16C2×D541semidirect
124. SD16C2×D541semidirect
125. SD16C2×D541semidirect
127. D8C2×D541semidirect
131. C2×C8C2×D541semidirect

Maximal subgroups

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

subgroupindex
#317726752
#317726742
#317726602
#317726582
#317726532
#317726522
#317726492
C2×#225758252
SD16×D5412
#317726342
#135×C5412
#577541