Finite Group Databasebeta

← #34094951

Subgroups — #34094951

Order 20032.

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

normal subgroups only

This group has 262 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
1C2×#19097562C211yesmaximal, characteristic, complemented
2#41×D313C211yesmaximal, characteristic, complemented
3#23756529C212yesmaximal, complemented
4#23756528C211yesmaximal, characteristic, complemented
5#23756525C211yesmaximal, characteristic, complemented
6#23756524C212yesmaximal, complemented
7#23756522C211yesmaximal, characteristic, complemented
8#23756520C212yesmaximal, complemented
9#23756518C212yesmaximal, complemented
10M16×D313C211yesmaximal, characteristic, complemented
11#137×C313C211yesmaximal, characteristic, complemented
12#19097562—21no—
13#19097562—21no—
14#19097562C2212yes—
15#19097562C2212yescomplemented
16#19097562C2211yescharacteristic, complemented
17#19097561—21no—
18#19097561C2211yescharacteristic
19#19097560—21no—
20#19097560C2211yescharacteristic, complemented
21Q8×D313C2211yescharacteristic, complemented
22C2×D1252—21no—
23C2×D1252C2211yescharacteristic, complemented
24D4×D313—21no—
25D4×D313C2211yescharacteristic, complemented
26C2×C4×D313—21no—
27C2×C4×D313—21no—
28C2×C4×D313C2211yescharacteristic
29#19097551C2212yescomplemented
30#19097550C2212yescomplemented
31#19097548C2212yescomplemented
32#19097548C2212yescomplemented
33D2504C2212yescomplemented
34#19097546C2212yescomplemented
35#19097545C2211yescharacteristic, complemented
36#19097544C2212yescomplemented
37C8×D313C2212yescomplemented
38#41×C313C2211yescharacteristic
39C2×Q8×C313C2211yescharacteristic, complemented
40Q16×C313C2212yescomplemented
41SD16×C313C2212yescomplemented
42M16×C313C2211yescharacteristic, complemented
43C22×D313—21no—
44C22×D313—21no—
45C22×D313D411yescharacteristic
46Dic626—21no—
47Dic626C2311yescharacteristic
48D1252—21no—
49D1252—22no—
50D1252—22no—
51D1252—21no—
52D1252C2312yes—
53D1252C2311yescharacteristic
54C22⋊D313—21no—
55C22⋊D313—21no—
56C22⋊D313—21no—
57C2×Dic313—21no—
58C2×Dic313D411yescharacteristic
59C4×D313—21no—
60C4×D313—21no—
61C4×D313—21no—
62C4×D313—22no—
63C4×D313—22no—
64C4×D313D411yescharacteristic
65C4×D313D411yescharacteristic
66C4×D313C2311yescharacteristic
67C4×D313C2311yescharacteristic
68#14578809C2312yes—
69Q8×C313—21no—
70Q8×C313C2312yes—
71Q8×C313C2311yescharacteristic
72D4×C313—21no—
73D4×C313C2311yescharacteristic
74C2×C4×C313—21no—
75C2×C4×C313—21no—
76C2×C4×C313C2311yescharacteristic
77C8×C313C2312yes—
78C22×C313—21no—
79C22×C313C2×D411yescharacteristic
80C2×D313—21no—
81C2×D313—22no—
82C2×D313—41no—
83C2×D313—42no—
84C2×D313—42no—
85C2×D313C2×D411yescharacteristic
86C2×D313C2×D411yescharacteristic
87C4×C313—21no—
88C4×C313—22no—
89C4×C313C2×D411yescharacteristic
90C4×C313C2411yescharacteristic
91Dic313—21no—
92Dic313C2×D411yescharacteristic
93Dic313C2×D411yescharacteristic
94C2×C313—21no—
95C2×C313—41no—
96C2×C313C22×D411yescharacteristic
97D313—21no—
98D313—21no—
99D313—41no—
100D313—42no—
101C313#57511yescharacteristic, complemented, Sylow
102#575—3131nomaximal, Sylow
103C2×#41—3131no—
104C2×#41—3131no—
105#137—3131no—
106#137—3132no—
107#137D31311yescharacteristic, complemented
108AGL(1,ℤ/8)—3131no—
109AGL(1,ℤ/8)—3132no—
110AGL(1,ℤ/8)—3131no—
111#135—3132no—
112#135—3132no—
113C2×M16—3131no—
114#41—3131no—
115#41—3132no—
116#41—3132no—
117#41—3131no—
118#41—3131no—
119#41—6261no—
120#41—6261no—
121#41—6261no—
122#41—6261no—
123#41C2×D31311yescharacteristic
124C2×Q8—3131no—
125C2×Q8C2×D31311yescharacteristic, complemented
126C2×D4—3131no—
127C2×D4—3131no—
128C2×D4—6261no—
129C2×D4—6261no—
130C22×C4—3131no—
131C22×C4—6261no—
132C22×C4—6261no—
133Q16—3132no—
134Q16C2×D31312yescomplemented
135SD16—3132no—
136SD16—3132no—
137SD16—3132no—
138SD16C2×D31312yescomplemented
139D8—3132no—
140D8—3132no—
141M16—3131no—
142M16—3132no—
143M16C2×D31311yescharacteristic, complemented
144C2×C8—3132no—
145C23—3131no—
146C23—6261no—
147C23—6261no—
148Q8—21no—
149Q8—3131no—
150Q8—6261no—
151Q8C22×D31311yescharacteristic
152Q8C22×D31312yes—
153D4—21no—
154D4—3132no—
155D4—3131no—
156D4—6261no—
157D4—6262no—
158D4—6262no—
159D4—6261no—
160D4—6261no—
161D4—6261no—
162D4—6261no—
163D4C22×D31311yescharacteristic
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—3131no—
167C2×C4—3131no—
168C2×C4—3131no—
169C2×C4—3131no—
170C2×C4—3131no—
171C2×C4—6261no—
172C2×C4—6262no—
173C2×C4—6262no—
174C2×C4—6261no—
175C2×C4—6261no—
176C2×C4—6261no—
177C2×C4C22×D31311yescharacteristic
178C8—3132no—
179C8C22×D31312yes—
180C22—21no—
181C22—3131no—
182C22—3131no—
183C22—6262no—
184C22—6261no—
185C22—12521no—
186C22—12522no—
187C22—12522no—
188C22D4×D31311yescharacteristic
189C4—21no—
190C4—22no—
191C4—3131no—
192C4—3131no—
193C4—6261no—
194C4D4×D31311yescharacteristic
195C4C23×D31311yescharacteristic
196C2—21no—
197C2—41no—
198C2—6261no—
199C2—6261no—
200C2—12522no—
201C2—12521no—
202C2C2×D4×D31311yescharacteristic
subgroupG/H
centerC2C2×D4×D313
commutator, cosocleC4×C313C24
FrattiniC4C23×D313
Fitting#137×C313C2
socleC2×C313C22×D4
hypercenter#137D313
hypocenterC313#575
LCSG ▷ C4×C313 ▷ C2×C313 ▷ C313
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. C2×#19097562C2semidirect
2. #41×D313C2semidirect
3. #23756529C2semidirect
4. #23756528C2semidirect
5. #23756525C2semidirect
6. #23756524C2semidirect
7. #23756522C2semidirect
8. #23756520C2semidirect
9. #23756518C2semidirect
10. M16×D313C2semidirect
11. #137×C313C2semidirect
15. #19097562C22semidirect
16. #19097562C22semidirect
20. #19097560C22semidirect
21. Q8×D313C22semidirect
23. C2×D1252C22semidirect
25. D4×D313C22semidirect
29. #19097551C22semidirect
30. #19097550C22semidirect
31. #19097548C22semidirect
32. #19097548C22semidirect
33. D2504C22semidirect
34. #19097546C22semidirect
35. #19097545C22semidirect
36. #19097544C22semidirect
37. C8×D313C22semidirect
39. C2×Q8×C313C22semidirect
40. Q16×C313C22semidirect
41. SD16×C313C22semidirect
42. M16×C313C22semidirect
101. C313#575semidirect
107. #137D313semidirect
125. C2×Q8C2×D313semidirect
134. Q16C2×D313semidirect
138. SD16C2×D313semidirect
143. M16C2×D313semidirect

Maximal subgroups

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

subgroupindex
C2×#190975622
#41×D3132
#237565292
#237565282
#237565252
#237565242
#237565222
#237565202
#237565182
M16×D3132
#137×C3132
#575313