Finite Group Databasebeta

← #50306686

Subgroups — #50306686

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×#23751077C211yesmaximal, characteristic, complemented
2#41×D599C211yesmaximal, characteristic, complemented
3#34062748C211yesmaximal, characteristic, complemented
4#34062745C211yesmaximal, characteristic, complemented
5#34062744C212yesmaximal, complemented
6#34062741C211yesmaximal, characteristic, complemented
7#34062739C212yesmaximal, complemented
8#34062736C212yesmaximal, complemented
9#34062734C212yesmaximal, complemented
10M16×D599C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C599C211yesmaximal, characteristic, complemented
12#23751079C2211yescharacteristic, complemented
13#23751078—21no—
14#23751078C2211yescharacteristic
15#23751077—21no—
16#23751077—21no—
17#23751077—21no—
18#23751077C2212yes—
19#23751077C2211yescharacteristic, complemented
20#23751077C2212yescomplemented
21C2×Dic1198C2211yescharacteristic, complemented
22Q8×D599C2211yescharacteristic, complemented
23C2×C22⋊D599—21no—
24D4×D599—21no—
25D4×D599C2211yescharacteristic, complemented
26C22×Dic599—21no—
27C2×C4×D599—21no—
28C2×C4×D599C2211yescharacteristic
29Dic2396C2212yescomplemented
30#23751068C2212yescomplemented
31#23751067C2212yescomplemented
32#23751066C2212yescomplemented
33#23751066C2212yescomplemented
34#23751063C2212yescomplemented
35#23751062C2211yescharacteristic, complemented
36#23751061C2212yescomplemented
37C8×D599C2212yescomplemented
38#41×C599C2211yescharacteristic
39C2×D4×C599C2211yescharacteristic, complemented
40SD16×C599C2212yescomplemented
41D8×C599C2212yescomplemented
42M16×C599C2211yescharacteristic, complemented
43C22×D599—21no—
44C22×D599D411yescharacteristic
45Dic1198—21no—
46Dic1198—21no—
47Dic1198C2311yescharacteristic
48Dic1198C2312yes—
49D2396—21no—
50D2396C2311yescharacteristic
51C22⋊D599—21no—
52C22⋊D599—21no—
53C22⋊D599—22no—
54C22⋊D599—22no—
55C22⋊D599—21no—
56C2×Dic599—21no—
57C2×Dic599—21no—
58C2×Dic599—22no—
59C2×Dic599—22no—
60C2×Dic599D411yescharacteristic
61C4×D599—21no—
62C4×D599—21no—
63C4×D599—21no—
64C4×D599D411yescharacteristic
65C4×D599D411yescharacteristic
66C4×D599C2311yescharacteristic
67C4×D599C2311yescharacteristic
68C599⋊C8C2312yes—
69C23×C599—21no—
70Q8×C599C2311yescharacteristic
71D4×C599—21no—
72D4×C599—21no—
73D4×C599C2311yescharacteristic
74D4×C599C2312yes—
75C2×C4×C599—21no—
76C2×C4×C599C2311yescharacteristic
77C8×C599C2312yes—
78C22×C599—21no—
79C22×C599—22no—
80C22×C599—42no—
81C22×C599C2×D411yescharacteristic
82C2×D599—21no—
83C2×D599—41no—
84C2×D599—42no—
85C2×D599C2×D411yescharacteristic
86C2×D599C2×D411yescharacteristic
87C4×C599—21no—
88C4×C599C2×D411yescharacteristic
89C4×C599C2411yescharacteristic
90Dic599—21no—
91Dic599—22no—
92Dic599C2×D411yescharacteristic
93Dic599C2×D411yescharacteristic
94C2×C599—21no—
95C2×C599—41no—
96C2×C599—42no—
97C2×C599C22×D411yescharacteristic
98D599—21no—
99D599—21no—
100D599—41no—
101C599#57511yescharacteristic, complemented, Sylow
102#575—5991nomaximal, Sylow
103C2×#41—5991no—
104C2×#41—5991no—
105#137—5991no—
106#137—5992no—
107#137—5991no—
108AGL(1,ℤ/8)—5991no—
109AGL(1,ℤ/8)—5992no—
110AGL(1,ℤ/8)D59911yescharacteristic, complemented
111#135—5992no—
112#135—5992no—
113C2×M16—5991no—
114#41—5991no—
115#41—5992no—
116#41—5991no—
117#41—5992no—
118#41—5991no—
119#41—11981no—
120#41—11981no—
121#41—11981no—
122#41—11981no—
123#41C2×D59911yescharacteristic
124C2×Q8—5991no—
125C2×Q8—5991no—
126C2×D4—5991no—
127C2×D4—11981no—
128C2×D4—11981no—
129C2×D4C2×D59911yescharacteristic, complemented
130C22×C4—5991no—
131C22×C4—11981no—
132C22×C4—11981no—
133Q16—5992no—
134Q16—5992no—
135SD16—5992no—
136SD16—5992no—
137SD16—5992no—
138SD16C2×D59912yescomplemented
139D8—5992no—
140D8C2×D59912yescomplemented
141M16—5991no—
142M16—5992no—
143M16C2×D59911yescharacteristic, complemented
144C2×C8—5992no—
145C23—21no—
146C23—5991no—
147C23—11981no—
148Q8—5991no—
149Q8—5992no—
150Q8—11981no—
151Q8—11981no—
152Q8C22×D59911yescharacteristic
153D4—21no—
154D4—21no—
155D4—5991no—
156D4—11981no—
157D4—11981no—
158D4—11981no—
159D4—11982no—
160D4—11982no—
161D4—11981no—
162D4C22×D59912yes—
163D4C22×D59911yescharacteristic
164C2×C4—21no—
165C2×C4—5991no—
166C2×C4—5991no—
167C2×C4—5991no—
168C2×C4—5991no—
169C2×C4—5991no—
170C2×C4—11981no—
171C2×C4—11981no—
172C2×C4—11981no—
173C2×C4—11982no—
174C2×C4—11982no—
175C2×C4—11981no—
176C2×C4—11981no—
177C2×C4C22×D59911yescharacteristic
178C8—5992no—
179C8C22×D59912yes—
180C22—21no—
181C22—22no—
182C22—42no—
183C22—5991no—
184C22—5991no—
185C22—23961no—
186C22—23962no—
187C22—11981no—
188C22D4×D59911yescharacteristic
189C4—21no—
190C4—5991no—
191C4—5991no—
192C4—11981no—
193C4—11982no—
194C4D4×D59911yescharacteristic
195C4C23×D59911yescharacteristic
196C2—21no—
197C2—42no—
198C2—41no—
199C2—23961no—
200C2—11981no—
201C2—11981no—
202C2C2×D4×D59911yescharacteristic
subgroupG/H
centerC2C2×D4×D599
commutator, cosocleC4×C599C24
FrattiniC4C23×D599
FittingAGL(1,ℤ/8)×C599C2
socleC2×C599C22×D4
hypercenterAGL(1,ℤ/8)D599
hypocenterC599#575
LCSG ▷ C4×C599 ▷ C2×C599 ▷ C599
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#23751077C2semidirect
2. #41×D599C2semidirect
3. #34062748C2semidirect
4. #34062745C2semidirect
5. #34062744C2semidirect
6. #34062741C2semidirect
7. #34062739C2semidirect
8. #34062736C2semidirect
9. #34062734C2semidirect
10. M16×D599C2semidirect
11. AGL(1,ℤ/8)×C599C2semidirect
12. #23751079C22semidirect
19. #23751077C22semidirect
20. #23751077C22semidirect
21. C2×Dic1198C22semidirect
22. Q8×D599C22semidirect
25. D4×D599C22semidirect
29. Dic2396C22semidirect
30. #23751068C22semidirect
31. #23751067C22semidirect
32. #23751066C22semidirect
33. #23751066C22semidirect
34. #23751063C22semidirect
35. #23751062C22semidirect
36. #23751061C22semidirect
37. C8×D599C22semidirect
39. C2×D4×C599C22semidirect
40. SD16×C599C22semidirect
41. D8×C599C22semidirect
42. M16×C599C22semidirect
101. C599#575semidirect
110. AGL(1,ℤ/8)D599semidirect
129. C2×D4C2×D599semidirect
138. SD16C2×D599semidirect
140. D8C2×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×#237510772
#41×D5992
#340627482
#340627452
#340627442
#340627412
#340627392
#340627362
#340627342
M16×D5992
AGL(1,ℤ/8)×C5992
#575599