Finite Group Databasebeta

← #50306689

Subgroups — #50306689

Order 38336.

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×#23751079C211yesmaximal, characteristic, complemented
2#41×D599C211yesmaximal, characteristic, complemented
3#34062747C212yesmaximal, complemented
4#34062746C211yesmaximal, characteristic, complemented
5#34062743C211yesmaximal, characteristic, complemented
6#34062742C212yesmaximal, complemented
7#34062740C211yesmaximal, characteristic, complemented
8#34062738C212yesmaximal, complemented
9#34062736C212yesmaximal, complemented
10M16×D599C211yesmaximal, characteristic, complemented
11#137×C599C211yesmaximal, characteristic, complemented
12#23751079—21no—
13#23751079—21no—
14#23751079C2212yes—
15#23751079C2212yescomplemented
16#23751079C2211yescharacteristic, complemented
17#23751078—21no—
18#23751078C2211yescharacteristic
19#23751077—21no—
20#23751077C2211yescharacteristic, complemented
21Q8×D599C2211yescharacteristic, complemented
22C2×D2396—21no—
23C2×D2396C2211yescharacteristic, complemented
24D4×D599—21no—
25D4×D599C2211yescharacteristic, complemented
26C2×C4×D599—21no—
27C2×C4×D599—21no—
28C2×C4×D599C2211yescharacteristic
29#23751068C2212yescomplemented
30#23751067C2212yescomplemented
31#23751065C2212yescomplemented
32#23751065C2212yescomplemented
33D4792C2212yescomplemented
34#23751063C2212yescomplemented
35#23751062C2211yescharacteristic, complemented
36#23751061C2212yescomplemented
37C8×D599C2212yescomplemented
38#41×C599C2211yescharacteristic
39C2×Q8×C599C2211yescharacteristic, complemented
40Q16×C599C2212yescomplemented
41SD16×C599C2212yescomplemented
42M16×C599C2211yescharacteristic, complemented
43C22×D599—21no—
44C22×D599—21no—
45C22×D599D411yescharacteristic
46Dic1198—21no—
47Dic1198C2311yescharacteristic
48D2396—21no—
49D2396—22no—
50D2396—22no—
51D2396—21no—
52D2396C2312yes—
53D2396C2311yescharacteristic
54C22⋊D599—21no—
55C22⋊D599—21no—
56C22⋊D599—21no—
57C2×Dic599—21no—
58C2×Dic599D411yescharacteristic
59C4×D599—21no—
60C4×D599—21no—
61C4×D599—21no—
62C4×D599—22no—
63C4×D599—22no—
64C4×D599D411yescharacteristic
65C4×D599D411yescharacteristic
66C4×D599C2311yescharacteristic
67C4×D599C2311yescharacteristic
68C599⋊C8C2312yes—
69Q8×C599—21no—
70Q8×C599C2312yes—
71Q8×C599C2311yescharacteristic
72D4×C599—21no—
73D4×C599C2311yescharacteristic
74C2×C4×C599—21no—
75C2×C4×C599—21no—
76C2×C4×C599C2311yescharacteristic
77C8×C599C2312yes—
78C22×C599—21no—
79C22×C599C2×D411yescharacteristic
80C2×D599—21no—
81C2×D599—22no—
82C2×D599—41no—
83C2×D599—42no—
84C2×D599—42no—
85C2×D599C2×D411yescharacteristic
86C2×D599C2×D411yescharacteristic
87C4×C599—21no—
88C4×C599—22no—
89C4×C599C2×D411yescharacteristic
90C4×C599C2411yescharacteristic
91Dic599—21no—
92Dic599C2×D411yescharacteristic
93Dic599C2×D411yescharacteristic
94C2×C599—21no—
95C2×C599—41no—
96C2×C599C22×D411yescharacteristic
97D599—21no—
98D599—21no—
99D599—41no—
100D599—42no—
101C599#57511yescharacteristic, complemented, Sylow
102#575—5991nomaximal, Sylow
103C2×#41—5991no—
104C2×#41—5991no—
105#137—5991no—
106#137—5992no—
107#137D59911yescharacteristic, complemented
108AGL(1,ℤ/8)—5991no—
109AGL(1,ℤ/8)—5992no—
110AGL(1,ℤ/8)—5991no—
111#135—5992no—
112#135—5992no—
113C2×M16—5991no—
114#41—5991no—
115#41—5992no—
116#41—5992no—
117#41—5991no—
118#41—5991no—
119#41—11981no—
120#41—11981no—
121#41—11981no—
122#41—11981no—
123#41C2×D59911yescharacteristic
124C2×Q8—5991no—
125C2×Q8C2×D59911yescharacteristic, complemented
126C2×D4—5991no—
127C2×D4—5991no—
128C2×D4—11981no—
129C2×D4—11981no—
130C22×C4—5991no—
131C22×C4—11981no—
132C22×C4—11981no—
133Q16—5992no—
134Q16C2×D59912yescomplemented
135SD16—5992no—
136SD16—5992no—
137SD16—5992no—
138SD16C2×D59912yescomplemented
139D8—5992no—
140D8—5992no—
141M16—5991no—
142M16—5992no—
143M16C2×D59911yescharacteristic, complemented
144C2×C8—5992no—
145C23—5991no—
146C23—11981no—
147C23—11981no—
148Q8—21no—
149Q8—5991no—
150Q8—11981no—
151Q8C22×D59911yescharacteristic
152Q8C22×D59912yes—
153D4—21no—
154D4—5992no—
155D4—5991no—
156D4—11981no—
157D4—11982no—
158D4—11982no—
159D4—11981no—
160D4—11981no—
161D4—11981no—
162D4—11981no—
163D4C22×D59911yescharacteristic
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—5991no—
167C2×C4—5991no—
168C2×C4—5991no—
169C2×C4—5991no—
170C2×C4—5991no—
171C2×C4—11981no—
172C2×C4—11982no—
173C2×C4—11982no—
174C2×C4—11981no—
175C2×C4—11981no—
176C2×C4—11981no—
177C2×C4C22×D59911yescharacteristic
178C8—5992no—
179C8C22×D59912yes—
180C22—21no—
181C22—5991no—
182C22—5991no—
183C22—23962no—
184C22—23961no—
185C22—23962no—
186C22—11982no—
187C22—11981no—
188C22D4×D59911yescharacteristic
189C4—21no—
190C4—22no—
191C4—5991no—
192C4—5991no—
193C4—11981no—
194C4D4×D59911yescharacteristic
195C4C23×D59911yescharacteristic
196C2—21no—
197C2—41no—
198C2—23962no—
199C2—23961no—
200C2—11981no—
201C2—11981no—
202C2C2×D4×D59911yescharacteristic
subgroupG/H
centerC2C2×D4×D599
commutator, cosocleC4×C599C24
FrattiniC4C23×D599
Fitting#137×C599C2
socleC2×C599C22×D4
hypercenter#137D599
hypocenterC599#575
LCSG ▷ C4×C599 ▷ C2×C599 ▷ C599
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. C2×#23751079C2semidirect
2. #41×D599C2semidirect
3. #34062747C2semidirect
4. #34062746C2semidirect
5. #34062743C2semidirect
6. #34062742C2semidirect
7. #34062740C2semidirect
8. #34062738C2semidirect
9. #34062736C2semidirect
10. M16×D599C2semidirect
11. #137×C599C2semidirect
15. #23751079C22semidirect
16. #23751079C22semidirect
20. #23751077C22semidirect
21. Q8×D599C22semidirect
23. C2×D2396C22semidirect
25. D4×D599C22semidirect
29. #23751068C22semidirect
30. #23751067C22semidirect
31. #23751065C22semidirect
32. #23751065C22semidirect
33. D4792C22semidirect
34. #23751063C22semidirect
35. #23751062C22semidirect
36. #23751061C22semidirect
37. C8×D599C22semidirect
39. C2×Q8×C599C22semidirect
40. Q16×C599C22semidirect
41. SD16×C599C22semidirect
42. M16×C599C22semidirect
101. C599#575semidirect
107. #137D599semidirect
125. C2×Q8C2×D599semidirect
134. Q16C2×D599semidirect
138. SD16C2×D599semidirect
143. M16C2×D599semidirect

Maximal subgroups

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

subgroupindex
C2×#237510792
#41×D5992
#340627472
#340627462
#340627432
#340627422
#340627402
#340627382
#340627362
M16×D5992
#137×C5992
#575599