Finite Group Databasebeta

← C2×#34039309 #49183500

Subgroups — C2×#34039309 #49183500

Order 37952.

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×#23748732C211yesmaximal, characteristic, complemented
2C2×D4×D593C211yesmaximal, characteristic, complemented
3#34039309C218yesmaximal, direct product factor
4C2×#23748722C211yesmaximal, characteristic, complemented
5C2×#23748721C211yesmaximal, characteristic, complemented
6C2×#23748718C211yesmaximal, characteristic, complemented
7C2×#23748716C211yesmaximal, characteristic, complemented
8C2×D8×C593C211yesmaximal, characteristic, complemented
9C23×D593—21no—
10#23748732—22no—
11#23748732C2214yescomplemented
12C2×Dic1186C2211yescharacteristic, complemented
13C2×D2372C2211yescharacteristic
14C2×C22⋊D593—21no—
15C2×C22⋊D593—21no—
16D4×D593—22no—
17D4×D593C2214yescomplemented
18C22×Dic593—21no—
19C2×C4×D593C2211yescharacteristic
20#23748722C2214yescomplemented
21#23748721C2214yescomplemented
22#23748718C2214yescomplemented
23#23748716C2214yescomplemented
24C2×#18011654C2211yescharacteristic, complemented
25C2×D4×C593C2211yescharacteristic
26C2×D4×C593C2211yescharacteristic, complemented
27D8×C593C2214yescomplemented
28C2×C8×C593C2211yescharacteristic, complemented
29C22×D593—21no—
30C22×D593—24no—
31C22×D593—44no—
32C22×D593D411yescharacteristic
33Dic1186—21no—
34Dic1186C2312yescomplemented
35D2372—21no—
36D2372C2312yes—
37C22⋊D593—24no—
38C22⋊D593—24no—
39C2×Dic593—21no—
40C2×Dic593—24no—
41C2×Dic593D411yescharacteristic
42C4×D593D412yes—
43C4×D593C2312yes—
44#18011654C2312yescomplemented
45C23×C593—21no—
46C23×C593—21no—
47D4×C593—21no—
48D4×C593—21no—
49D4×C593C2312yes—
50D4×C593C2312yescomplemented
51C2×C4×C593C2311yescharacteristic
52C8×C593C2312yescomplemented
53C22×C593—22no—
54C22×C593—22no—
55C22×C593—42no—
56C22×C593—42no—
57C22×C593C2×D411yescharacteristic
58C2×D593—22no—
59C2×D593—22no—
60C2×D593—48no—
61C2×D593—42no—
62C2×D593C2×D412yes—
63C4×C593C2×D411yescharacteristic
64C4×C593C2411yescharacteristic
65Dic593—22no—
66Dic593C2×D412yes—
67C2×C593—42no—
68C2×C593—42no—
69C2×C593AGL(1,ℤ/8)12yescomplemented
70C2×C593C22×D411yescharacteristic
71D593—22no—
72D593—42no—
73C593C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
74C2×AGL(1,ℤ/8)—5931nomaximal, Sylow
75C2×#41—5931no—
76C22×D4—5931no—
77AGL(1,ℤ/8)—5938no—
78C2×SD16—5931no—
79C2×SD16—5931no—
80C2×D8—5931no—
81C2×D8D59311yescharacteristic, complemented
82C2×M16—5931no—
83C24—11861no—
84#41—5934no—
85#41—11862no—
86C2×Q8—5931no—
87C2×D4—5934no—
88C2×D4—5931no—
89C2×D4—11862no—
90C2×D4—11861no—
91C2×D4—11861no—
92C2×D4C2×D59311yescharacteristic
93C2×D4C2×D59311yescharacteristic, complemented
94C22×C4—5931no—
95C22×C4—11861no—
96SD16—5934no—
97SD16—5934no—
98D8—5934no—
99D8C2×D59314yescomplemented
100M16—5934no—
101C2×C8—5931no—
102C2×C8C2×D59311yescharacteristic, complemented
103C23—21no—
104C23—21no—
105C23—23724no—
106C23—5931no—
107C23—11864no—
108C23—11861no—
109Q8—5932no—
110Q8—11861no—
111D4—21no—
112D4—21no—
113D4—5932no—
114D4—11864no—
115D4—11864no—
116D4—11861no—
117D4C22×D59312yes—
118D4C22×D59312yescomplemented
119C2×C4—5931no—
120C2×C4—5932no—
121C2×C4—5932no—
122C2×C4—11864no—
123C2×C4—11861no—
124C2×C4C22×D59311yescharacteristic
125C8—5932no—
126C8C22×D59312yescomplemented
127C22—22no—
128C22—22no—
129C22—42no—
130C22—42no—
131C22—23728no—
132C22—23722no—
133C22—5932no—
134C22—11862no—
135C22—11862no—
136C22D4×D59311yescharacteristic
137C4—5932no—
138C4—11862no—
139C4D4×D59311yescharacteristic
140C4C23×D59311yescharacteristic
141C2—42no—
142C2—42no—
143C2—23722no—
144C2—11862no—
145C2#3403930912yesdirect product factor
146C2C2×D4×D59311yescharacteristic
subgroupG/H
centerC22D4×D593
commutator, cosocleC4×C593C24
FrattiniC4C23×D593
FittingC2×D8×C593C2
socleC22×C593C2×D4
hypercenterC2×D8D593
hypocenterC593C2×AGL(1,ℤ/8)
LCSG ▷ C4×C593 ▷ C2×C593 ▷ C593
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×#23748732C2semidirect
2. C2×D4×D593C2semidirect
3. #34039309C2direct (N × H)
4. C2×#23748722C2semidirect
5. C2×#23748721C2semidirect
6. C2×#23748718C2semidirect
7. C2×#23748716C2semidirect
8. C2×D8×C593C2semidirect
11. #23748732C22semidirect
12. C2×Dic1186C22semidirect
17. D4×D593C22semidirect
20. #23748722C22semidirect
21. #23748721C22semidirect
22. #23748718C22semidirect
23. #23748716C22semidirect
24. C2×#18011654C22semidirect
26. C2×D4×C593C22semidirect
27. D8×C593C22semidirect
28. C2×C8×C593C22semidirect
34. Dic1186C23semidirect
44. #18011654C23semidirect
50. D4×C593C23semidirect
52. C8×C593C23semidirect
69. C2×C593AGL(1,ℤ/8)semidirect
73. C593C2×AGL(1,ℤ/8)semidirect
81. C2×D8D593semidirect
93. C2×D4C2×D593semidirect
99. D8C2×D593semidirect
102. C2×C8C2×D593semidirect
118. D4C22×D593semidirect
126. C8C22×D593semidirect
145. C2#34039309direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#237487322
C2×D4×D5932
#340393092
C2×#237487222
C2×#237487212
C2×#237487182
C2×#237487162
C2×D8×C5932
C2×AGL(1,ℤ/8)593