Finite Group Databasebeta

← C2×#31772655 #46830963

Subgroups — C2×#31772655 #46830963

Order 34624.

298 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C2×#22575837C211yesmaximal, characteristic, complemented
2C2×D4×D541C211yesmaximal, characteristic, complemented
3#31772655C218yesmaximal, direct product factor
4C2×#22575823C211yesmaximal, characteristic, complemented
5C2×D4328C211yesmaximal, characteristic, complemented
6C2×#22575821C211yesmaximal, characteristic, complemented
7C2×#22575819C211yesmaximal, characteristic, complemented
8C2×SD16×C541C211yesmaximal, characteristic, complemented
9C23×D541—21no—
10#22575837—22no—
11#22575837C2214yescomplemented
12C2×D2164—21no—
13C2×D2164C2211yescharacteristic
14C2×D2164C2211yescharacteristic, complemented
15C2×C22⋊D541—21no—
16D4×D541—22no—
17D4×D541C2214yescomplemented
18C2×C4×D541—21no—
19C2×C4×D541C2211yescharacteristic
20#22575823C2214yescomplemented
21D4328C2214yescomplemented
22#22575821C2214yescomplemented
23#22575819C2214yescomplemented
24C2×#16864513C2211yescharacteristic, complemented
25C2×Q8×C541C2211yescharacteristic, complemented
26C2×D4×C541C2211yescharacteristic
27SD16×C541C2214yescomplemented
28C2×C8×C541C2211yescharacteristic, complemented
29C22×D541—21no—
30C22×D541—21no—
31C22×D541—24no—
32C22×D541—44no—
33C22×D541D411yescharacteristic
34D2164—24no—
35D2164—21no—
36D2164—21no—
37D2164C2312yes—
38D2164C2312yescomplemented
39C22⋊D541—24no—
40C2×Dic541D411yescharacteristic
41C4×D541—24no—
42C4×D541D412yes—
43C4×D541C2312yes—
44#16864513C2312yescomplemented
45C23×C541—21no—
46Q8×C541—21no—
47Q8×C541C2312yescomplemented
48D4×C541—21no—
49D4×C541C2312yes—
50C2×C4×C541—21no—
51C2×C4×C541C2311yescharacteristic
52C8×C541C2312yescomplemented
53C22×C541—22no—
54C22×C541—42no—
55C22×C541C2×D411yescharacteristic
56C2×D541—22no—
57C2×D541—22no—
58C2×D541—22no—
59C2×D541—48no—
60C2×D541—42no—
61C2×D541—42no—
62C2×D541C2×D412yes—
63C4×C541—22no—
64C4×C541C2×D411yescharacteristic
65C4×C541C2411yescharacteristic
66Dic541C2×D412yes—
67C2×C541—42no—
68C2×C541AGL(1,ℤ/8)12yescomplemented
69C2×C541C22×D411yescharacteristic
70D541—22no—
71D541—42no—
72D541—42no—
73C541C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
74C2×AGL(1,ℤ/8)—5411nomaximal, Sylow
75C2×#41—5411no—
76C22×D4—5411no—
77AGL(1,ℤ/8)—5418no—
78C2×SD16—5411no—
79C2×SD16D54111yescharacteristic, complemented
80C2×D8—5411no—
81C2×D8—5411no—
82C2×M16—5411no—
83C24—10821no—
84#41—5414no—
85#41—10822no—
86C2×Q8C2×D54111yescharacteristic, complemented
87C2×D4—5414no—
88C2×D4—5411no—
89C2×D4—5411no—
90C2×D4—10821no—
91C2×D4—10822no—
92C2×D4—10821no—
93C2×D4C2×D54111yescharacteristic
94C22×C4—5411no—
95C22×C4—10821no—
96SD16—5414no—
97SD16C2×D54114yescomplemented
98D8—5414no—
99D8—5414no—
100M16—5414no—
101C2×C8—5411no—
102C2×C8C2×D54111yescharacteristic, complemented
103C23—21no—
104C23—5411no—
105C23—10824no—
106C23—10821no—
107C23—10821no—
108C23—21644no—
109Q8—21no—
110Q8C22×D54112yescomplemented
111D4—21no—
112D4—5412no—
113D4—5412no—
114D4—10824no—
115D4—10824no—
116D4—10821no—
117D4—10821no—
118D4C22×D54112yes—
119C2×C4—21no—
120C2×C4—5411no—
121C2×C4—5412no—
122C2×C4—5412no—
123C2×C4—10824no—
124C2×C4C22×D54111yescharacteristic
125C8—5412no—
126C8C22×D54112yescomplemented
127C22—22no—
128C22—42no—
129C22—5412no—
130C22—10822no—
131C22—10822no—
132C22—10822no—
133C22—21648no—
134C22—21642no—
135C22—21642no—
136C22D4×D54111yescharacteristic
137C4—22no—
138C4—5412no—
139C4D4×D54111yescharacteristic
140C4C23×D54111yescharacteristic
141C2—42no—
142C2—10822no—
143C2—21642no—
144C2—21642no—
145C2#3177265512yesdirect product factor
146C2C2×D4×D54111yescharacteristic
subgroupG/H
centerC22D4×D541
commutator, cosocleC4×C541C24
FrattiniC4C23×D541
FittingC2×SD16×C541C2
socleC22×C541C2×D4
hypercenterC2×SD16D541
hypocenterC541C2×AGL(1,ℤ/8)
LCSG ▷ C4×C541 ▷ C2×C541 ▷ C541
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#22575837C2semidirect
2. C2×D4×D541C2semidirect
3. #31772655C2direct (N × H)
4. C2×#22575823C2semidirect
5. C2×D4328C2semidirect
6. C2×#22575821C2semidirect
7. C2×#22575819C2semidirect
8. C2×SD16×C541C2semidirect
11. #22575837C22semidirect
14. C2×D2164C22semidirect
17. D4×D541C22semidirect
20. #22575823C22semidirect
21. D4328C22semidirect
22. #22575821C22semidirect
23. #22575819C22semidirect
24. C2×#16864513C22semidirect
25. C2×Q8×C541C22semidirect
27. SD16×C541C22semidirect
28. C2×C8×C541C22semidirect
38. D2164C23semidirect
44. #16864513C23semidirect
47. Q8×C541C23semidirect
52. C8×C541C23semidirect
68. C2×C541AGL(1,ℤ/8)semidirect
73. C541C2×AGL(1,ℤ/8)semidirect
79. C2×SD16D541semidirect
86. C2×Q8C2×D541semidirect
97. SD16C2×D541semidirect
102. C2×C8C2×D541semidirect
110. Q8C22×D541semidirect
126. C8C22×D541semidirect
145. C2#31772655direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#225758372
C2×D4×D5412
#317726552
C2×#225758232
C2×D43282
C2×#225758212
C2×#225758192
C2×SD16×C5412
C2×AGL(1,ℤ/8)541